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Phase-Field Modeling of Biomineralization in Mollusks and Corals: Microstructure vs Formation Mechanism
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Phase-Field Modeling of Biomineralization in Mollusks and Corals: Microstructure vs Formation Mechanism
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  • László Gránásy*
    László Gránásy
    Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary
    Brunel Centre of Advanced Solidification Technology, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K.
    *Tel: +36 1 392 2222, Ext. 3371. Fax: +36 1 392 2219. Email: [email protected]
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    Orcidhttps://orcid.org/0000-0001-5825-7632
  • László Rátkai
    László Rátkai
    Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary
    More by László Rátkai
    Orcidhttps://orcid.org/0000-0002-7644-253X
  • Gyula I. Tóth
    Gyula I. Tóth
    Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, U.K.
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    Orcidhttps://orcid.org/0000-0002-8446-9572
  • Pupa U. P. A. Gilbert
    Pupa U. P. A. Gilbert
    Departments of Physics, Chemistry, Geoscience, Materials Science, University of Wisconsin−Madison, Madison, Wisconsin 53706, United States
    Lawrence Berkeley National Laboratory, Chemical Sciences Division, Berkeley, California 94720, United States
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    Orcidhttps://orcid.org/0000-0002-0139-2099
  • Igor Zlotnikov
    Igor Zlotnikov
    B CUBE−Center for Molecular Bioengineering, Technische Universität Dresden, 01307 Dresden, Germany
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    Orcidhttps://orcid.org/0000-0003-2388-9028
  • Tamás Pusztai
    Tamás Pusztai
    Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary
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    Orcidhttps://orcid.org/0000-0002-1281-2933
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JACS Au

Cite this: JACS Au 2021, 1, 7, 1014–1033
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https://doi.org/10.1021/jacsau.1c00026
Published June 4, 2021

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Abstract

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While biological crystallization processes have been studied on the microscale extensively, there is a general lack of models addressing the mesoscale aspects of such phenomena. In this work, we investigate whether the phase-field theory developed in materials’ science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route, via ion-by-ion addition from a fluid state, and a nonclassical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with an appropriate choice of the model parameters, microstructures similar to those found in biomineralized systems can be obtained along both routes, though the time-scale of the nonclassical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math and simulated by phase-field theory.

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1. Introduction

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Crystalline materials formed by solidification from the liquid state play an essential role in our civilization. (1,2) This class of matter incorporates most of the technical alloys, polymers, minerals, drugs, food products, and so on. Owing to their importance, mathematical models describing the process of crystallization under the respective conditions were and are being developed. Relying on the statistical physical description of phase transitions, the evolving numerical methods, and the ever-increasing computational power, computational materials science reached the level where knowledge-based design of crystalline matter is possible for certain classes of materials (see, e.g., refs (2−4)). The models that address the behavior of matter during crystalline solidification range from the molecular time and length scales to the engineering scales. They include ab initio computations; particle-based methods like molecular dynamics (MD), Monte Carlo, or population dynamics simulations and different types of continuum models ranging from the density functional theory of classical particles, via coarse-grained models (such as the time-dependent Ginzburg–Landau, Cahn–Hilliard, and phase-field type order parameter theories that belong to the family of classical field theoretical models widely used in modeling phase transitions of various complexity), to the macroscopic continuum models applicable on engineering time- and length-scales. While this inventory allows the modeling of a substantial range of crystallization phenomena, there are complex cases, for which its use is not straightforward. Such examples are the biomorphic (inorganic) materials (5−10) that form worm-shape or arboresque morphologies by aggregation of crystalline particles, and the process of biomineralization; (11−19) that is, the formation of hierarchically structured organic–inorganic composites in biological systems. Examples of biomineralization include the formation of mollusk shells, (13,14) skeletons of corals (15) and cell walls of diatoms, (16) kidney stones, (17) bones and teeth, (18) and magnetite crystals in the magnetosomes of magnetotactic bacteria, (19) to name a few. The materials formed by biomineralization often have surprisingly good mechanical properties owing to their hierarchical microstructure (see e.g., refs (13,14)). Recent imaging and analytic methods provide detailed information on the respective microstructures, which in turn may give clues to the formation mechanism: many of these microstructures are well-known from materials science (such as dendrites, spherulites, cellular, columnar shapes, etc.). (11−15,17−19) This raises the possibility that with some adjustment/further development, the models developed in materials science can be used to reverse engineer the biomineralization process and learn the pathways used by nature to create these complex structures, which may inspire new technologies for creating novel composite materials. (20−25)
Recently, we explored the possibility of developing predictive mathematical models for biomorphic crystallization and for relatively simple biomineralization processes by adopting well-established methods of computational materials science and adjusting them to the circumstances as necessary. (26−28) The research done so far is confined yet to relatively simple cases of extracellular biomineralization such as mollusk shell formation (26,27) or microstructure evolution of spherulitic structures in coral skeletons (28) but is expected to deepen the general understanding in the field, and the tools developed in the course of this research might open the way for modeling more complex cases of crystallization in biological systems such as formation of bones, kidney stones, and so on.
In the present paper, we concentrate on the modeling aspects of such an approach, outlining possible minimum requirements for phase-field modeling of biological crystallization processes, and demonstrate that with appropriate choice of the model parameters and boundary conditions phase-field models can approximate the polycrystalline microstructure formed in simple cases of biomineralization (shell formation in mollusks such as bivalves, gastropods and cephalopods, and sprinkle formation in coral skeletons).

1.1. Microstructures Formed during Biomineralization

Before outlining the phase-field models we used in the present research, we give a short account of the experimental results on the observed microstructures. Polycrystalline microstructures formed in biomineralization processes have been investigated by a variety of experimental methods, including optical microscopy (OM), scanning electron microscopy (SEM), electron back scattering diffraction (EBSD), X-ray tomography, and polarization-dependent imaging contrast (PIC, (29,30)), among others. Here we concentrate on experimental results obtained on the microstructure of molluscan shells and coral skeletons.

1.1.2. Mollusk Shells

Mollusk shells are complex organo-mineral biocomposites with a broad range of species-dependent microstructures. (13,14,30−39) A schematic view of bivalve anatomy having a nacre-prismatic shell is shown in Figure 1. Moving inward, the sequence of the individual layers is as follows: the organic periostracum, a leathery “skin”, that encloses the domain where biominerlization takes place, a dominantly mineral (calcium carbonate, CC) prismatic layer, and the nacre composed of CC tablets and organic interlamellar membranes, the submicron thick extrapallial liquid, (31,34−36) and then the outer calcifying epithelum layer of the mantle. Images showing typical microstructures of mollusk shells of similar type are displayed in Figure 2. (13,26,37,38)

Figure 1

Figure 1. Schematic view of bivalve molluscan anatomy with successive magnification of the mantle–nacre interface. (39) A thin liquid-filled extrapallial space is indicated (its thickness and content is open to debate). The interlamellar membrane is made of a viscoelastic chitin-based organic substance, whereas the mineral constituent is crystalline CC (aragonite). (Reproduced with permission from ref (39). Copyright 2009 United States National Academy of Sciences). Here “growth direction” indicates the lateral growth of the shell. However, this is based on layerwise growth perpendicular to the surface via formation of new layers that also grow laterally, a process which is responsible for both the thickening and the sidewise spreading of the shell. In the present work, we model the local thickening of the shell.

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Figure 2

Figure 2. Some typical mircrostructures observed in mollusk shells: (a) cross-sectional EBSD orientation map for the shell of Katelysia rhytiphora, (37) the outer side is on the left (note the transitions between layers of different crystallite morphologies); (b) outer randomly oriented granular domain in the shell of Unio pictorum (SEM); (26) (c) columnar prismatic domain of Pinna nobilis (X-ray tomography reconstruction), (13) and (d) plate-like structure of the nacre of Unio pictorum (SEM); (26) (e) spherulitic layer, section perpendicular to growth in the shell of Haliotis rufescens (SEM). (38) [(a) Reproduced from ref (37) under Creative Commons Attribution 4.0 License. Copyright Authors 2019. (b), (d) Reproduced with permission from ref (26) . Copyright 2018 Wiley. (c) Reproduced with permission from ref (13) . Copyright 2014 Springer Nature. (e) Reproduced from ref (38) . Copyright 2002 American Chemical Society.].

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A recent study shows that in members of three classes of mollusks Unio pictorum (bivalve), Nautilus pompilius (cephalopod), and Haliotis asinine (gastropod), the shell displays a common sequence of ultrastructures: a granular domain composed of randomly oriented crystallites, a prismatic domain of columnar crystallites, and the nacre (26,27) (Figure 3). It has been shown that the layered structure of nacre may contain screw dislocation-like defects (see Figure 4). (14,39−44)

Figure 3

Figure 3. Hierarchy of ultrastructures in the shell of some of the mollusks. Left: for bivalve Unio pictorum (growth direction: upward); (A) The shell, (B) schematic drawing of microstructure, (C–F) scanning electronmicroscopy (SEM) images. Right top: for cephalopod Nautilus pompilius (growth direction: to the right). Right bottom: for gastropod Haliotis asinina (growth direction: to the right); (A–C) SEM image, (C,D) magnified views of the granular domain and the prismatic → nacre transition. Note the similar sequence of ultrastructures during growth: granular → prismatic (columnar) → nacre (alternating mineral/organic layers). (Left: Reproduced with permission from ref (26). Copyright 2018 Wiley. Right: Reproduced with permission from ref (27). Copyright 2019 United States National Academy of Sciences).

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Figure 4

Figure 4. (a–h) Screw dislocation-like defects at the growth front of the nacreous layer of various species. (14,39) (a) Aragonitic nacre structure in the shell of the bivalve Pteria avicula. Reproduced with permission from ref (40). Copyright 2007 The Royal Society (U.K.). (b) Calcitic seminacre structure in the shell of brachiopod Novocrania anomala. Reproduced with permission from ref (41). Copyright 2010 The Paleontological Association. (c) Calcitic foliated structure in the shell of Ostrea edulis. Reproduced with permission from ref (42). Copyright 2007 Elsevier. (d) Aragonitic foliated structure in the shell of monoplacophoran Rokopella euglypta. Reproduced with permission from ref (43). Copyright 2009 American Chemical Society. Scale bars indicate 5 μm. SEM images showing the growth front of the nacreous layer for bivalves: (e–g) Pteria avicula and (h) Pteria hirundo. Reproduced with permission ref (40). Copyright 2007 The Royal Society (U.K.). (i,j) Target and spiral patterns formed in Belousov–Zhabotinsky reaction. Reproduced with permission from ref (44). Copyright 1996 Royal Society of Chemistry.

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Of these structures, the prismatic layers show mechanical flexibility, whereas the nacre (also called “mother of pearl”) is fairly rigid but hard; the combination of the two yields a surprisingly strong yet flexible biocomposite (see e.g., ref (22)).

1.1.3. Microstructure of Coral Skeletons

The multiply branched shapes of coral skeletons are covered by a large number of coral polyps (45) and the connecting living tissue, which secretes calcium carbonate to create a hard shelter (the corallite, a tubular hollow structure on which the polyp sits), (46) into which the polyp can retreat if danger is detected (see Figure 5a,b). The polyps are transparent, their color originates from photosynthesizing algae (zooxanthallea) that live in symbiosis with the polyp and feed the polyp sugars and oxygen. The surface of the skeleton is intricately structured, (46) depressions, ridges, cavities are arranged into complex patterns reflecting the radial symmetry of the polyp (Figure 5b). The CC crystal (aragonite) building the porous skeleton (Figure 5c) has a spherulitic microstructure, that is, a radial arrangement of crystals radiating from a common center. The center does not have to be a point; it can be a line or a plane in plumose spherulites. In the case of coral skeletons, the centers are curved planes, termed centers of calcification (CoCs) (Figure 5d). (15,47) From these CoCs, acicular fibers grow radially and then arrange into fan-like bundles that finally group into a feather-duster-like shape termed “trabecula”. (15) Besides the plumose spherulitic structure, randomly oriented nanoscale crystallites “sprinkles” are also present (28,48,49) (Figure 5e). Recent PIC mapping experiments performed at synchrotron indicate that the amount of the submicron-sized sprinkle crystallites varies considerably among different coral species: in some of them, the sprinkles are missing (Figure 5f), whereas in others, submicron size crystallites appear at the perimeter of the skeleton, along grain boundaries, at the growth front of spherulitic trabeculae, or in bands formed in the interior of the skeleton. (28) The discovery of sprinkles inspired a refined model for spherulitic growth in corals, described in detail in ref (28). Randomly oriented sprinkles are the first nucleated crystals at the growth front. With further growth, those oriented radially have space and thus continue to grow, and those oriented tangentially run into each other and stop growing. This is why they stay small. A coarsening process then makes the larger crystal grow larger at the expense of the smaller ones, which disappear. In most mature spherulites, therefore, no sprinkles remain. In the skeleton of some coral species, however, some sprinkles do not disappear, presumably because they are kinetically trapped.

Figure 5

Figure 5. From coral polyps to the CC (aragonite) skeleton they form, highly structured from the cm to the nm scale. (a) Schematic drawing of the coral polyp (colored) sitting on the porous skeleton (white). (45) Reproduced with permission from Britannica eReader.com, a service of Encyclopædia Britannica, Inc. (b) SEM image of the surface formed below coral polyps (corallites) in the case of Porites sp. Reproduced with permission from ref (46). Copyright 2011 Elsevier. (c) Cross-section of corallite, Pollicipora damicornis (linear size of image is ∼3 mm, “d” stands for mineral bridges termed distally convex dissepiments). Reproduced with permission from ref (47). Copyright 2006 Springer Nature. (d) Schematic drawing of a “plumose” spherulite. Reproduced with permission from ref (15). Copyright 2017 American Chemical Society. (e) PIC map of Acropora pharaonis coral skeleton showing spherulitic microstructure of crystals radiating from a band of randomly oriented sprinkles (linear center of calcification, the bar indicates 10 μm). Reproduced with permission from ref (28) under Creative Commons CC-BY-NC-ND 4.0 license. Copyright 2020 Elsevier. (f) PIC map of Phyllangia coral skeleton showing spherulitic microstructure of crystals radiating from centers of calcification, however, with no sprinkles.

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In our previous work, we modeled this process by phase-field simulations (28) and raised the possibility that other spherulites may grow this way, including aspirin, chocolate, and geologic crystals. However, the formation mechanism of sprinkle bands and the origin of different amount of sprinkles in the skeleton of different coral species is not yet fully understood. Mathematical modeling is expected to help to identify the governing factors. Molecular/ionic mobility in the calcifying fluid is expected to be orders of magnitude higher than in the solid. As a result, in the case of growth via ion-by-ion addition, either a slow supply of the ions or a kinetic barrier of ion deposition can keep the growth rate sufficiently low. This offers limitations to the possible mechanisms, as will be discussed later.

1.1.4. Biomineralization on the Nano- and Macroscale

The complexity of biomineralization stems mainly from the fact that the fluid and solids incorporate organic molecules, the role of which is largely unknown. (35,36,50,51)
For example, nanoscale amorphous calcium carbonate (ACC) globules are essential for the formation of mollusk shells and coral skeletons. (13,14,52−54) Possible pathways from free ions to crystalline CC are reviewed in ref (55). Evidently, all the possible processes cannot be explicitly incorporated into an orientation field based phase-field (OF-PF) approach designed to model polycrystalline microstructures on the mesoscale. In this work, we investigate two specific cases: (i) formation of crystalline CC via the classical route of ion-by-ion addition of Ca2+ and CO32–, and (ii) the nonclassical route via an amorphous precursor (ACC) deposited at the solidification front. In the latter case, we hypothesize that the crystallization rate is determined by the velocity of crystal growth into the ACC layer and not by the rate of supplementing ACC; that is, growth is controlled by the self-diffusion in ACC. This hypothesis can account for the typically months’ time scale of shell/skeleton formation, which would be difficult to interpret, for example, on the basis of ion-by-ion deposition directly from the extrapallial fluid or other aqueous solutions. A specific realization of mechanism (ii) is presented in ref (56). The extrapallial fluid contains various ions and organic molecules as shown by in vivo studies. (35,36)

1.1.5. Growth Rate of Mollusk Shells and Coral Skeletons

The shell of bivalves grows typically by 100–300 μm lunar-day increments, (57,58) corresponding to a growth rate of about v ≈ 4.2 × 10–11–1.3 × 10–10 m/s, which decreases with age. (57) The thickening rate of the shell of Tridacna deresa was estimated to be v ≈ 1.6 × 10–10–4.9 × 10–10 m/s in its early life, which decreases to v ≈ 3.2 × 10–11–2.3 × 10–10 m/s in the later life. (59) Comparable growth rates were reported for freshwater gastropods v ≈ 9.5 × 10–11 m/s. (60) In contrast, the coral skeleton growth rates range between about 1 and 37 cm/year, corresponding to 3.2 × 10–10 to 1.2 × 10–8 m/s. (61−63)

2. Modeling Section

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There are two main categories of the phase-field (PF) models developed to address polycrystalline freezing: (a) the multiphase-field (MPF) models that assign a separate phase field for every crystal grain (64−70) and (b) the orientation-field based phase-field (OF-PF) approaches, in which the local crystallographic orientation is monitored by a scalar field (2D) (71−78) or quaternion/rotation matrix fields (3D). (78−85) Recent developments in these areas were reviewed in refs (70) and (78), respectively.
Both the MPF and OF-PF approaches have their advantages, yet complex polycrystalline growth forms (such as disordered dendrites, crystal sheaves, various types of spherulites, and fractal-like polycrystalline aggregates, etc.) were so far modeled exclusively using the OF-PF approach. A further advantage of these models is that they allow a continuous variation of the orientation, a feature particularly useful in modeling biomineralization.
In the OF-PF models, the local phase state of the matter is characterized by a coarse grained structural order parameter, the “phase field”, that is time- and space-dependent and monitors the transition between the liquid and solid states. This field is usually coupled to other slowly changing fields, such as the concentration field of the constituents, and the orientation field. The free energy contains bulk free energy and gradient terms for these fields. The equations of motion can be obtained via a variational route. The thermal fluctuations are represented by adding noise (nonconserved fields) or flux noise (conserved fields) to the equations of motion that satisfy the fluctuation–dissipation theorem, allowing for homogeneous nucleation (72)
The inclusion of foreign surfaces/particles, represented by appropriate boundary conditions that set the wetting properties, allows the modeling of heterogeneous nucleation (83−85) and solidification in confined space. (77,86) The addition of phase-field noise makes the modeling of Brownian motion of solid particles possible. (87) The OF-PF models may also be coupled to hydrodynamic flow, which can be represented by either the Navier–Stokes equation (88,89) or the lattice Boltzmann technique. With an appropriate overlapping grid technique, flow coupled motion of growing solid particles can also be treated. (90)
The main virtue of PF modeling is that the growth morphology can be computed on the basis of the freezing conditions and the thermophysical properties. Images obtained by OF-PF modeling in two- and three dimensions (2D and 3D) (74,78,84,86) are compared with experiments (74,86,91−101) in Figure 6.

Figure 6

Figure 6. Complex crystallization structures in the experiments (1st and 3rd rows) and in the corresponding simulations performed using OF-PF models at the Wigner Research Centre for Physics (2nd and 4th rows). Upper block: From left to right: Rhombic dodecahedron crystals (upper panel reproduced from ref (91), lower panel reproduced with permission from ref (84). Copyright 2008 IOP Publishing Ltd.). Columnar dendrites (upper panel reproduced with permission from ref (92). Copyright 2016 Elsevier). Equiaxed dendrites (upper panel reproduced with permission from ref (93). Copyright 2016 Elsevier, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). “Dizzy” dendrites (reproduced with permission from ref (74). Copyright 2003 Springer Nature). Crystal sheaves (upper panel reproduced with permission from ref (94). Copyright 1993 American Chemical Society, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). Orientation field in spherulites (upper panel reproduced with permission from ref (95). Copyright 2007 American Chemical Society). Arboresque spherulites (upper panel reproduced with permission from ref (96). Copyright 2003 American Chemical Society, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). Lower block: From left to right: Scratch induced dendritic crystallization in polymer film (reproduced with permission from ref (86). Copyright 2003 Springer Nature). Dumbbell-shape spherulites (upper panel reproduced with permission from ref (97). Copyright 2006 Wiley, lower panel reproduced with permission from ref (84). Copyright 2008 IOP Publishing Ltd.). Spherulites in temperature gradient (upper panel reproduced with permission from ref (98). Copyright 2003 Springer Nature, lower panel reproduced with permission from and ref (86). Copyright 2013 Springer Nature). Freezing soap bubble vs dendrite growing in spherical shell (upper panel reproduced with permission from ref (99)). Effect of oscillating temperature (reproduced with permission from ref (78). Copyright 2013 Springer Nature). “Quadrites” formed by nearly 90° branching (upper panel by courtesy of B. Okerberg, (100) lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). “One eyed” spherulites (upper panel reproduced with permission from ref (101). Copyright 2002 Elsevier).

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Recently, PF modeling has been extended for microstructure formation in mollusk shells and coral skeletons, and promising agreement was seen between experiment and the predicted microstructures. (26−28) We give below a detailed account of the modeling efforts and present new results.
Herein, we continue further the quest for a minimum phase-field model of the biomineralization process during the formation of mollusk shells and coral skeletons. Evidently, we cannot model the living organism in the framework of this approach; their functions are represented by appropriate boundary conditions. Unfortunately, usually little is known of the thermodynamics of the multicomponent fluids involved, of the interfacial free energies and their anisotropies, and the respective diffusion coefficients. Therefore, we aim at identifying the main components that a minimal theory needs to incorporate for qualitatively reproducing the microstructures seen in the experiments.
In the present study, we rely on three specific formulations of the phase-field theory. In two of them, (26,27) the local state is characterized by the phase field, ϕ(r, t) that monitors the process of crystallization, the concentration field c(r, t) specifying the local composition, and a scalar orientation field θ (r, t), which represents the local crystallographic orientation in 2D. The latter field is made to fluctuate in time and space in the liquid, a feature that represents the short-range order present in the liquid state (as done in refs (72,74−79) and (83−86)). The third model does not include an orientation field. It has been developed to handle two-phase spiraling dendrites during eutectic solidification in ternary alloys in 3D, (102) assuming a fixed relative orientation of the solid phases.
In Figure 7, we summarize the problems addressed herein, the models used, the assumed micromechanisms, and the corresponding phase transitions.

Figure 7

Figure 7. Summary of biomineralization-related problems that are addressed within this work using phase-field methods. In each case, the applied model, the respective micromechanism, and the relevant phase transition are specified. Phase-field models PF1, PF2, and PF3 are defined in the text.

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2.1. Phase-Field Model 1 (PF1)

The first model will be used to address four cases of biomineralization: (i) mollusk shell formation from aqueous solution by ion-by-ion addition (ions from the extrapallial fluid attach to the surface of the crystalline phase), (ii) mollusk shell formation via amorphous precursor (ACC → CCC transition), (iii) formation of columnar nacre via ion-by-ion attachment, and (iv) formation of coral skeletons via ion-by-ion attachment. In all these cases, the same mathematical model will be used, however, with specific input parameters and initial- and boundary conditions.
Model PF1 is defined by eqs 1−6 shown below. This model is similar to the standard binary PF theory by Warren and Boettinger; (103) however, it is supplemented with an orientation field as done in refs (72,74−78) Accordingly, the free energy of the heterogeneous system is expressed as
(1)
where T is the temperature. Parameters εϕ2 = (12/√2) γiδi /Ti and w(c) = (1 – c) wA + c wB, where wi = (12/√2) γi/(δiTi) are expressed in terms of the free energy γi, the thickness δi of the crystal–liquid interface, and the melting point Ti of the ith pure component (i = A or B that stand for the organic and mineral components, respectively). In model PF1 εc2 = 0 is chosen. s = s(ϑ, θ) = 1 + s0 cos{kϑ – 2πθ} is an anisotropy function corresponding to an interfacial free energy of k-fold symmetry and strength s0, whereas ϑ = arctan(ϕy/ϕx) is the angle of the normal of the interface in the laboratory frame, while ∇ϕ = [ϕx, ϕy]. The angular (circular) variables ϑ and θ are normalized so that they vary between 0 and 1. The bulk free energy density reads as,
(2)
and varies between the free energy densities of the crystal and mother phases (fC and fM, respectively) as prescribed by the interpolation function p(ϕ) = ϕ3 (10–15ϕ + 6ϕ2). Here fC and fM were taken from the ideal solution model. The orientation free energy density is as follows:
(3)
where the parameter H can be used to tune the magnitude of the grain boundary energy. Owing to the scalar orientation field, model PF1 is applicable exclusively in 2D.
The time evolution of the heterogeneous system is described by variational equations of motion (EOMs):
(4)
(5)
(6)
where Mϕ, Mc, and Mθ are mobilities that determine the time scale of the evolution of the individual fields, and are related to coefficients of the self-diffusion, interdiffusion, and rotational diffusion. (72,74−78) The chemical and orientation mobilities are made phase-dependent as Mi = Mi,C + [1 − p(ϕ)]{Mi,M – Mi,C}, where i = c or θ, and indices M and C denote values for the mother and crystalline phases. The corresponding dimensionless mobilities are defined as mϕ = Mϕεϕ2T/Dc,M, mc = Mc/Dc,M, where Mc,C,M= (vm/RT)c(1 – c)Dc,C,M, and mθ = MθξHT/Dc,M. Here vm is the average molar volume of the components, R the gas constant, ξ the length scale, whereas HT is the energy scale of the grain boundary energy. Gaussian white noise terms ζi are added to the EOMs to represent the thermal fluctuations (here i = ϕ, c, and θ). 3D generalizations of model PF1 can be found elsewhere, (78−82) which, however, require quaternion or rotation matrix representation of the crystallographic orientation, as opposed to the scalar field used here.

2.2. Phase-Field Model 2 (PF2)

The second model will be used to provide a refined model of mollusk shell formation including the nacreous structures in the case of (i) ion-by-ion attachment and (ii) amorphous precursor mediated process. This OF-PF model was originally developed to describe eutectic solidification, while keeping a fixed orientational relationship between the two solid phases inside the crystal grains. (104) To realize this, the square-gradient term, (1/2)εc2T (∇c)2, was retained in the free energy density (choosing εc2 = 2εϕ2), and a more complex orientational free energy term was used
(7)
that realizes a fixed orientational relationship at the solid–solid phase boundaries. Here h(c) = (1/2){1 + cos[2π (c – cα)/(cβ – cα)]}, cα and cβ are the CC concentrations in the two solid solution phases, whereas F1(|∇θ|) = |∇θ| and F2(|∇θ|) = a + b|cos(2mπd|∇θ|)|. Here a, b, m, are constants, and d is the characteristic thickness of the sold-solid phase boundary. The EOMs are derived the same way as in the case of model PF1. Accordingly, model PF2 is defined by eqs 1, 2, 4–6, and 7.

2.3. Phase-Field Model 3 (PF3)

This model will be used to address the formation of 3D topological defects in sheet nacre via crystal growth into hACC (here the third component plays the role of water that has smaller solubility in CCC than hACC). Modeling of sheet nacre by PF3 is a 3D analogue of the amorphous precursor mediated case in PF2. The free energy of the crystallizing system is given by the expression (102)
(8)
where c = [c1,c2,c3] and Σici = 1, whereas w and εc2 are constants. The bulk free energies of the solid and liquid phases are taken from the regular and ideal solution model:
(9)
and
(10)
where Ωi,j are the binary interaction coefficients in the solid.
The respective EOMs obtained variationally are as follows
(11)
and
(12)
where Mc is the 3 × 3 mobility matrix. With the choice of 1 and −0.5 for the diagonal and off-diagonal elements, the criterion Σici = 1 is automatically satisfied. The diffusion is switched off in the bulk solid. Further information on model PF3 is given in ref (102).

2.4. Numerical Solutions

The EOMs were solved numerically in a dimensionless form, on rectangular uniform grids, using finite difference discretization with forward Euler time stepping. The PF1 and PF2 codes were run on a CPU cluster of 480 CPU cores using MPI protocol. Typical runs on a 1000 × 2000 grid took between about 8 to 15 h, depending on the number of time steps that varied from 2.4 × 105 to 5 × 105, as required by the velocity of crystallization. The code for PF3 was run on high-end graphics processing units (GPUs) and was solved on a 3D rectangular grid.

2.5. Materials’ Parameters

We review here the present status of input data required for a quantitative modeling. The OF-PF models require a fairly detailed information on the systems studied. This incorporates the free energy of all the relevant phases as a function of temperature and composition; all the interface energies; and the translational, chemical, and rotational diffusion coefficients. Since in the biomineralization problems, we address here, the dominant CC polymorph is the metastable aragonite, we use the thermophysical data available for this polymorph, as much as possible. In case, where no information is available, we use values for another CC polymorph (calcite). The input data are collected in Tables 1 and 2 for Model PF1, in Tables 3 and 4 for Model PF2, a few common ones are presented in Table 5. In these Tables, “aq. sol. → CCC” indicates data relevant to the ion-by-ion mechanism, whereas “ACC → CCC” denote those for the amorphous precursor mediated case.
Table 1. Dimensionless Mobility Coefficients for Model PF1a
 mφmc,Mmc,Cmθ,Mmθ,C
aq. sol. → CCC3.751.010–20120120 × 10–20
ACC → CCC3.751.010–14120120 × 10–14
a

The subscripts M and C stand for the mother and crystalline phases. The chemical mobility of the former was used as reference, as its chemical diffusion coefficient was used in making the EOMs dimensionless.

Table 2. Dimensionless Thermodynamic Data Used in Model PF1 (Ideal Solution Thermodynamics (26))a
quantity value
Tr= T/TA0.911
Tr,B= TB/TA0.786
ΔgA= ΔGA/RT–0.1184
ΔgB= ΔGB/RT0.1554
a

Here ΔGA,B = ΔHA,B(T–TA,B)/TA,B (A stands for CC and B for the organic component).

Table 3. Dimensionless Mobility Coefficients for Model PF2a
 mφmc,Mmc,Cmθ,Mmθ,C
aq. sol. → CCC0.01441.010–201212 × 10–20
ACC → CCC0.01441.010–141212 × 10–14
a

The subscripts M and C stand for the mother and crystalline phases. The chemical mobility of the former was used as reference, as its chemical diffusion coefficient was used in making the EOMs dimensionless.

Table 4. Dimensionless Thermodynamic Data Used in Model PF2 (Regular Solution Thermodynamics (27))a
quantity value
Tr= T/TE0.720
Tr,A= TA/TE1.169
Tr,B= TB/TE1.286
ΔgA= ΔGA/RT– 0.5802
ΔgB= ΔGB/RT– 1.0477
ωM= ΩM/RT2.0510
ωC= ΩC/RT3.6335
a

Here ΩM,C = Ω0,M,C – Ω1,M,CT.

Table 5. Materials and Computational Data Used in PF1/PF2
quantityvalueunitref
γA (CCC – aq. sol.)150mJ/m2 (123,124)
γB (organic–aq. sol.)118mJ/m2this work
γA (CCC – ACC)87mJ/m2this work
γB (organic – ACC)68mJ/m2this work
vm (CCC – aq. sol.)26.7cm3/mol 
vm (CCC – ACC)32.4cm3/mol 
ξ2.1 × 10–6m 
δ4.15 × 10–8m 
Δx6.25 × 10–3dimensionless 
Δt4.75 × 10–6dimensionless 

2.5.1. Thermodynamics

Unfortunately, only limited thermophysical information is available even for the pure CC system from experiment and MD simulations, such as the phase diagrams (105,106) and the equilibrium shapes reflecting the anisotropy of the interface energy. (107,108) During biomineralization, however, a variety of ions and organic macromolecules are present that may influence/control the crystallization process. (109−115) Accordingly, it is a nontrivial task to obtain accurate input data for mesoscale modeling; for example, selective adsorption of ions or organic molecules on different crystal faces may change growth morphology (111,112) or influence the formation of polymorphs of CC. (114,115)
Owing to this lack of information, we present here generic approaches that are based on simplified hypothetical model systems of properties similar to those used in refs (26−28).

2.5.2. Diffusion Coefficients

As noted above, we address here two scenarios for the formation of crystalline CC (CCC): (i) diffusion controlled growth of crystalline CC directly from aqueous solution via ion-by-ion addition; (ii) diffusion controlled growth of crystalline CC into a hydrated ACC (hACC) layer that is assumed to be deposited on the solidification front (by vesicles or the-ion-by-ion process) with a sufficient rate so that deposition is not the rate-limiting process. These scenarios differ in the diffusion coefficient we assign to the “mother phase” (either aqueous solution or ACC) that crystallizes. Since the equations of motion were made dimensionless using the diffusion coefficient of the mother phase, and we assume that the relative magnitudes of Mϕ, Mc, and Mθ remain the same in the mother phase independently whether it is liquid or amorphous, the two scenarios differ in only the dimensionless mobilities assigned to the crystalline phase.
Aqueous Solutions
The coefficient of ion diffusion in aqueous solutions at room temperature is in the order of DL ≈10–9 m2/s. (116)
Amorphous CC
The ion diffusion in ACC at 300 K is in the order of DACC,ion ≈ 10–15m2/s. (117) However, the diffusion coefficient of the water molecules from MD simulations is typically DhACC,H2O ≈ 10–14–10–13m2/s for the slow H2O molecules, although a few percent of H2O molecules that have orders of magnitude faster diffusion (DhACC,H2O ≈ 10–11 m2/s) are also present. (117,118) However, biogenic ACC is almost anhydrous. (119) Therefore, water diffusion is expected to play a negligible role. The rate limiting factor for the structural transition is expected to be the slowest of these processes; accordingly, we use the diffusion coefficient for the ions, DACC,ion ≈ 10–15m2/s. (117)
Crystalline CC
We are unaware of self-diffusion data for aragonite. There are, however, experimental data for calcite. The Mg diffusion coefficient in calcite is about Dcalcite ≈ 10–21 m2/s at 823 K, which, extrapolates to Dcalcite ≈ 10–53 m2/s at room temperature provided that the diffusion mechanism does not change. (120) A different estimate is obtained via extrapolating the Mg–Ca interdiffusion data of ref (121) to room temperature, which yields Dcalcite ≈ 10–29 m2/s at 300 K for Mg diffusion in calcite. An even higher value emerges from the radioactive tracer method Dcalcite ≈ 10–23 m2/s. (122)
Summarizing, herein, we opt for DACC,ion ≈ 10–15m2/s and Dcalcite ≈ 10–29 m2/s for ion diffusion in ACC and calcite, respectively; assuming thus that the diffusion data for calcite can be viewed as a reasonable order-of-magnitude estimate for the other polymorphs, including aragonite. The corresponding dimensionless mobility data are presented in Tables 1 and 3. The data of magnitude 10–20 to 10–12 indicate that in the crystal, independently of the mother phase, the reduced mobilities are essentially zero for the concentration and orientation fields; that is, these fields do not show time evolution within the crystal on the time scale of the simulations.

2.5.3. Interfacial Free Energies

The experimental and theoretical results for the water-aragonite interfacial free energy are about 150 mJ/m2. (123,124) A recent ab initio theoretical treatment provides a considerably larger value (280 mJ/m2), and information on its anisotropy for small aragonite clusters. (125) Herein, we use 150 mJ/m2. We are unaware of data for the free energy of the ACC-aragonite interface. Using Turnbull’s relationship (126) for the interfacial free energy, γ = αΔH/(N0vmc2)1/3, where α is a constant, ΔH heat of transformation, N0 the Avogadro-number, and vmc is the molar volume of the crystalline phase, a crude estimate can be made on the basis of the enthalpy difference between ACC and calcite: ΔHcalcite-ACC = (14.3 ± 1.0) kJ/mol. (119) A similar value may be expected for aragonite. (119) Considering α = 0.55 from MD simulations, (127) one obtains γaragonite-ACC ≈ 87 mJ/m2, which result, however, needs independent confirmation by other experimental/theoretical methods.
Once the thermodynamic data are fixed for components A and B, and the interfacial free energy is given for one of the components, models PF1 and PF2 predict the interfacial free energy for the other component, provided that the interface thicknesses are similar. (103) For materials of comparable entropy of transformation, this realizes γ ∝ Ttrans, where Ttrans is the temperature of the phase transition, a relationship that works well for the solid–liquid interfacial free energy of metals. (128)

2.5.4. Qualitative Modeling

Despite our efforts to collect a full set of the required materials parameters, owing to uncertainties of the thermodynamic diving force of crystallization and of the interface energy estimates, the simulations we present can only be regarded as qualitative. They are aimed at demonstrating that phase-field modeling has the potential to capture various microstructural/morphological aspects of biomineralization. This summary of the present status of input data may give hints where further experiments and microscopic theory can help mesoscale modeling.

3. Results and Discussion

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3.1. Modeling of Microstructures Mimicking Mollusk Shells

Herein, we hypothesize that (1) the granular domain is produced by heterogeneous nucleation (either on the surface of periostracum or on organic particles); and (2) the physical background of the columnar → nacre morphological transition is the observation that decreasing the driving force of solidification, an initially diffusionless process (full solute trapping) is replaced by partitioning, which first appears in the form of alternating layers rich in one or the other component (see Figure 8). (129,130)

Figure 8

Figure 8. Band formation as predicted by the binary Warren-Boettinger (103) (WB) type phase-field models: (a) transition from diffusionless solidification to partitioning with decreasing driving force (supersaturation decreases from left to right) in the presence of a single solid phase (ideal solution); and (b) transition from lamellar eutectics toward bands parallel to the growth front with increasing driving force (undercooling) in a WB model supplemented with square gradient term for concentration, (130) a case in which two solids of different composition form (regular solution). Lower panel was reproduced with permission from ref (130). Copyright 2017 Springer.

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The latter mechanism is the one that causes band formation in Figures 9 and 10. Further assumptions made during the application of these models (e.g., boundary conditions specific to the studied problems) are recapitulated below. In the case of PF1, reduction of the driving force leads to a transition of a chemically homogeneous solid to alternating solid–liquid layers, whereas in the case of PF2 partitioning appears via alternating α–β bands. For even smaller driving forces, PF1 would produce seaweed/dendritic structures, whereas PF2 would yield lamellae perpendicular to the growth front.

Figure 9

Figure 9. Comparison of the microstructure of (a) the shell of mollusk Unio pictorum (26) as shown by electron microscopy images (see also Figure 3 left block; reproduced with permission from ref (26). Copyright 2018 Wiley) with simulations (b–e) obtained by model PF1 assuming (b, c) ion-by-ion attachment from extrapallial fluid (Dc,M = 10–9 m2/s) or (d, e) crystallization from an ACC layer (Dc,M = 10–15 m2/s). Growth direction is upward. Orientation (b, d) and grain boundary (c, e) maps are shown. In panels (b) and (d), colors denote different crystallographic orientations. In the experimental images of (a), the bars correspond to 3, 3, 1, and 1 μm, respectively, from top to bottom. Note the presence of the three characteristic domains in the experiment and in both types of simulations: granular, columnar prismatic, and sheet nacre structures. The qualitative phase-field simulations were performed on 1000 × 2000 grids (corresponding to 13.125 μm × 26.25 μm with the present choice of model parameters). (In the high driving force (lower) part of both these simulations lDv /Dc,M > 1; that is, diffusionless crystallization takes place, whereas in the upper domain, alternating mineral and organic layers mimicking the sheet nacre form.).

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Figure 10

Figure 10. Three stages of microstructure evolution in Model PF2 obtained assuming (a–d) ion-by-ion attachment from extrapallial fluid and (e–h) by crystallization from ACC precursor(orientation (a–c) and (e–g), and composition maps (d) and (h) are shown.): (a,e) Formation of granular structure via heterogeneous nucleation dominated equiaxed solidification; (b, f) columnar growth via directional solidification in concentration gradient yielding the prismatic structure, and (c, g) layerwise formation of alternating CCC and organic layers (sheet nacre). In panels (a–c) the mother phase is an aqueous solution (Dc,M = 10–9 m2/s) in the simulation shown; whereas an amorphous precursor (Dc,M = 10–15 m2/s) is assumed in the simulation shown in panels (d–f). The wavelength of the layered structure is roughly proportional to the free energy of the mother phase – CCC interface. The thickness of the mother phase (extrapallial domain) is assumed to be constant. In (a–c) and (e–g) different colors stand for different crystallographic orientation, while colors white and black stand for the mantle of the mollusk and the mother phase, respectively. In (d) and (h), gray, yellow, and blue indicate the mother phase, the organic phase, and CCC. The qualitative phase-field simulations were performed on 2000 × 200 grids (corresponding to an area of 26.25 μm × 2.625 μm with the present choice of model parameters). In (a–c) and (e–g) time elapses downward, whereas (c) and (d) and (g) and (h) display snapshots taken at the same time.

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3.1.1. Shell-Like Microstructure in Model PF1

In a recent OF-PF study, (26) we made the following assumptions that define the conditions under which eqs 1–6 were solved, when modeling the formation of mollusk shells within model PF1:

  • The CC crystals grow into the extrapallial fluid by the molecule/ion attachment mechanism.

  • Binary ideal solution thermodynamics (CC and organic component) is applied. Evidently, treating the extrapallial fluid as a quasi-binary solution is a gross simplification. During crystallization of the CC-rich crystal, and an organic-component-rich “fluid” forms from the original homogeneous mixture. This construction was used as a simple means to provide thermodynamic driving force for CCC precipitation.

  • CC-supersaturation of the extrapallial fluid decreases exponentially with the distance x from the periostracum, owing to a spatially dependent amount of the organic component: c(x) = cmin + (cmax – cmin){1–exp(− 9x/L)}, where L is the thickness of the extrapallial space. (This is a hypothesis. We are unaware of any experimental information pro or contra.)

  • Crystallization of CC starts via heterogeneous nucleation on the periostracum.

  • The anisotropy of the CCC-mother phase interfacial free energy is neglected.

In the present work, besides this, we explore a different scenario shown in Figure 7, in which the CCC crystal grows into an ACC precursor that forms continuously ahead of the crystallization front. The CCC front propagates into this ACC layer and has no direct contact with the extrapallial fluid. It is also assumed that the formation of the ACC layer is fast enough, so that it is not the rate-limiting process. The respective amorphous → crystal transition has in principle a reduced driving force, while orders of magnitude smaller diffusion coefficients prevail in the amorphous phase, yielding a far longer time scale for crystallization, when compared with crystallization from an aqueous solution. In this scenario, the phase field monitors the amorphous → crystal transition, rather than the crystallization of a liquid. We furthermore assume that the coefficients of the translational, chemical, and rotational diffusion decrease proportionally by orders of magnitude during this process, retaining the same relative magnitudes of the mobilities as in the liquid (see Table 1).
Since the EOMs are solved in dimensionless form, where time is dedimensionalized using the chemical diffusion coefficient of the mother phase, the dimensionless chemical mobilities of the mother phase remain unchanged. What differs between the present computation and the previous one in ref (26) is the magnitude of the individual mobilities in the crystalline and the mother phase (see Table 1). Following the general principles of phase-field modeling (see e.g. ref (131)), the phase-field mobility is assumed to be independent of the phase. In contrast, in agreement with the experimental diffusion coefficients, the chemical and orientational mobilities are assumed to be 20 orders of magnitude larger in the extrapallial fluid then in the crystal, and 14 orders of magnitude larger in ACC than in CCC.
We retain the assumptions made in ref (26), as listed above with the difference that in the nonclassical mechanism it is the CC content of the ACC layer that decreases exponentially (while the organic content increases) with the distance from the periostracum. For the sake of simplicity, we employ the same dimensionless driving force as in ref (26) for both the classical and the nonclassical cases.
The microstructures that evolved in the two cases are compared in Figure 9. The characteristic microstructural transitions are present in both simulations. Whether from the fluid or the amorphous phase, first small randomly oriented CCC grains form in the neighborhood of the periostracum, of which crystal grains grow further inward yielding elongated crystals of random orientation that compete with each other. With increasing distance from the periostracum, that is, with decreasing supersaturation, growth slows down, and the separation of the two constituents becomes possible, which leads to the formation of alternating CCC and organic-rich layers, closely resembling the nacre. The mineral layers in the “nacre” are composed of segments of different orientations (see Figure 9b,d), which can be viewed as a 2D analogue of the usual 3D mineral platelets. The predicted sequence of the morphological transitions is similar for both mechanisms (i.e., for aq. sol. → CCC and ACC → CCC); however, there are minor differences in the relative thicknesses of the granular, columnar prismatic, and layered nacre structures.
While the respective microstructures are rather similar, the typical size scales for the ACC → CCC transition is smaller than for the aq. sol. → CCC, roughly proportionally with the respective interfacial free energies. Alternating CCC and organic-rich layers akin to sheet nacre form here due to a process described in ref (129), with the difference that under the present conditions a roughly flat “banded structure” forms, and thermal diffusion is replaced by chemical diffusion. Apparently, the orientational information is only partly transferred through the organic layers. Mineral bridges (discontinuities of the organic layers) are also observed. The granular → columnar → layered morphological transitions occur here because of changes in the growth velocity.
At high supersaturations nucleation and diffusionless solidification takes place forming the granular domain. At medium supersaturations nucleation ceases, only competing growth of the existing particles takes place yielding the columnar domain, whereas at small supersaturations alternating CCC and organic layers occur, forming a layered structure that closely resembles the sheet nacre.
Diffusionless crystallization is possible, when the diffusion length lD = Dc,M /v is comparable to the thickness of liquid/crystal or amorphous/crystal interfaces (d ≈ 10–9–10–8 m (132,133)), where v is the growth rate. The transition from diffusion controlled to diffusionless growth takes place in the regimes 10–4 < dv/Dc,M < 1 or 10–2 < dv/Dc,M < 10, depending on the model. (134) Considering lD ≈ 10–9 m and a typical experimental growth rate of v ≈ 10–10 m/s, one finds that the mother phase needs to have a diffusion coefficient of Dc,M ≈ 10–15–10–20 m2/s to show transition toward diffusionless growth on the time scale required. This clearly rules out the possibility that the CC crystals form dominantly by direct ion-by-ion attachment from the extrapallial fluid as Dc,M ≈ 10–9 m2/s applies for the latter process. In turn, this range of Dc,M is consistent with crystallization from amorphous CC, as the magnitude of Dc,M falls in the range diffusion coefficient takes in the amorphous state. (135)
Summarizing, while the two mechanisms considered here lead to similar microstructures, crystallization via the ACC precursor seems preferable to direct solidification via ion-by-ion addition from the extrapallial fluid, as in the latter case the diffusion coefficients are rather high, that is, crystallization is expected to be fast, unless the “fluid” is of high viscosity (not realistic for the extrapallial fluid). Another problem of direct precipitation from the aqueous solution is that due to the high diffusion coefficient, the assumed initial exponential spatial dependence of CC supersaturation is only temporary on the time scale of shell growth, unless crystal growth is so fast that diffusional equilibration cannot take place. This is, however, at odds with the experimental growth rates.
Note that modeling of the experimentally observed orientational ordering in the columnar (prismatic) and nacre domains that yields coalignment of the c’ axis of the crystallites, requires a 3D orientation field. Work is underway in this direction.
Finally, we note that the thickness of the organic and mineral layers in the nacre are typically 10–40 nm and 300–600 nm, (136−140) respectively. Our qualitative simulations give a considerably larger relative thickness for the organic layer. This is partly because we intended to model the whole granular → columnar → nacre sequence, and because of limitations of available computational power, we cannot have sufficient spatial resolution to realize a more realistic thickness ratio. If modeling is limited to the nacre, one is expected to achieve a better agreement.

3.1.2. Shell-Like Microstructures in Model PF2

To relax some of the simplifying assumptions made in PF1, a refined model (PF2) was proposed for modeling the formation of mollusk shells in ref (27). In this model, two solid phases form simultaneously from the liquid state, a mineral-rich and an organic-rich, while a fixed relative orientational relationship is forced between the solid phases formed inside the same crystal grain. This realizes a strong orientational coupling between the solid phases. Simultaneous formation of two solids occurs, for example, in eutectic or peritectic systems. In the refined approach, we opted for the former case. The main assumptions that set the conditions, under which eqs 1, 2, 4, 6, and 7 defining model FP2 were solved, are as follows: (27)

  • Crystal growth of CC happens via molecule/ion attachment.

  • A binary eutectic model thermodynamics (regular solution) applies.

  • The mineral content of the extrapallial fluid emitted at the surface of the mantle decreases exponentially with time.

  • Formation of granular CC crystals starts by heterogeneous nucleation on organic heterogeneities, whose number density is assumed to decrease exponentially with the distance from the periostracum.

  • The thickness of the extrapallial domain (distance between the mantle and the solidification front) remains constant. (In the simulation, the position of the mantle surface varies in accord with the solidification rate.)

In this approach, the assumption that CC supersaturation decreases toward the mantle is removed and is replaced by the more natural assumption that the CC supersaturation at the mantle decreases exponentially with time that leads to an analogous result, however, in a more natural way. The simulation presented in ref (27) shows a good qualitative agreement with the experimental microstructures observed in various types of mollusk shells. It is reassuring that model PF2 recovers the experimental microstructure though in a somewhat more ordered form, which could however be made more random by varying the noise added to the equations of motion. At the present state of affairs, it is difficult to decide which of models PF1 or PF2 should be considered superior to the other, yet the two-solid model is probably closer to the reality.
Herein, we explore whether the microstructure remains similar, when assuming ACC mediated crystallization in the framework of model PF2. The results obtained by the two mechanisms of crystallization are compared Figure 10. Apparently, as in the case of model PF1, the two micromechanisms for crystalline CC formation yield similar microstructures.
Note that in model PF2, the nacre is composed of two alternating solid phases. Under the conditions used in our simulation the organic component remains in an amorphous or nanocrystalline state. Remarkably, the predicted “nacre” structure recovers such details of the experimentally observed microstructure as the “mineral bridges” and the line defects across the organic layers termed “aligned holes”. (33,34,138,140) We will show, however, in the next section that despite this close similarity, the formation mechanism of the nacre can be considerably more complex than predicted here.

3.1.3. Discussion of Results from Models PF1 and PF2

First, we compare the solidification rates obtained from the simulations performed assuming DL ≈10–9 m2/s (aqueous solution) for the mother phase, with those using DACC,ion ≈ 10–15m2/s (ionic diffusion in ACC). We wish to stress that the velocities evaluated from the simulations can only be considered qualitative, as the thermodynamic driving force we used in this study might be well away from the true ones, which in turn may differ from the value obtained for the pure aqueous solution–CCC system, or the ACC–CCC system. Work is underway to perform more quantitative phase-field simulations to determine the growth and dissolution rates in pure systems, for which reasonably accurate experimental data are available.
The growth rate results are presented in Figure 11. As one expects the average growth rate is roughly proportional to the diffusion coefficient of the mother phase. The growth velocities predicted for crystallization from ACC by models PF1 and PF2 are about two and one orders of magnitude higher (v ≈ 10–8 and 10–9 m/s, respectively) than the experimental ones (57−60) (≈10–10 m/s, see gray zone in Figure 11), whereas the rates predicted for the ion-by-ion addition are about v ≈ 10–1 and 10–2 m/s, which are about 8–9 orders of magnitude too high. On this ground, the mechanism based on the fast ion-by-ion addition can be excluded. One may perhaps argue that the production of calcium and carbonate ions in the surface layer of the mantle (outer epithelium) may be the rate-limiting process, which may be then taken so slow as to match the experimental growth rate. However, in that case, it is not the diffusion in the mother phase that controls the time scale of the process, and thus, the mechanisms models PF1 and PF2 rely on would not be present.

Figure 11

Figure 11. Growth rates predicted by models PF1 (red lines) and PF2 (blue lines) for the ion-by-ion mechanism from aqueous solution and for crystallization from ACC precursor. Note the ∼7 orders of magnitude difference in growth velocity predicted for the two mechanisms. For comparison, the range of experimental data is also shown (gray domain). Note the oscillating growth rate in the layered domain.

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The velocity vs time relationships show characteristic differences for the two models: PF1predicts a steeply increasing velocity, followed by a plateau decreasing slowly with time for the domain of alternating solid–liquid layers. In the present simulations, the early stage behavior of the two models is different due to reasons different of the growth mode: while model PF1 starts with surface induced heterogeneous nucleation on the periostracum, PF2 relies on volumetric heterogeneous nucleation on organic impurities (note that both heterogeneous nucleation mechanisms can be adopted in both models). As a result, in model PF2, fast initial crystallization is observed during the formation of the granular layer via volumetric heterogeneous nucleation. This is followed by steady-state growth (roughly constant growth velocity) in both the prismatic and the nacreous domains, due to the lack of long-range diffusion during fast eutectic solidification. In contrast, in PF1 a continuously decelerating solidification is observed, which is combined with oscillating growth rate in the nacre. The hypothesized mechanism (volumetric heterogeneous nucleation in a thick layer at the periostracum) that creates protection for the mollusk fast in the early stage of shell formation is advantageous from the viewpoint of survival.
We note that because of computational limitations the maximum linear size of the computational domain we used was about 26.4 μm both in the PF1 and PF2 simulations. However, analogous structures can be produced on a larger size scale via reducing the rate by which the driving force of crystallization decreases with position/time and with an extended initial domain filled with heterogeneous nucleation centers.
It is appropriate to mention that while our models describe the formation of the granular and prismatic layers and the sheet nacre reasonably well within the framework of directional solidification, the predicted mechanism for the formation of the nacre via alternately precipitating mineral and organic layers may be oversimplified.
This is especially true for columnar nacre: experiments indicate that the formation of a quasi-periodic network of organic membranes precedes the formation of the CCC layers, which fill the space between the organic membranes later, as illustrated in Figure 12. (136−140) Although one could imagine that the organic membranes form periodically in space via an oscillating chemical reaction of the diffusion-reaction type, while the extrapallial fluid fills the space between the membranes, apparently, the real mechanism is more complex: first a multilayer outer membrane forms, of which the individual layers are exfoliated by nucleating CC crystals. (136,137) Furthermore, recent experimental works show a thin ACC layer on the surface of the CCC tablets of the nacre, (141,142) implying that (h)ACC particles may play an essential role in the formation of nacre. This, in turn, indicates that a particle-by-particle addition is more appropriate for solidification, as in the case of coral skeletons (see discussion in section 3.3).

Figure 12

Figure 12. Electron microscopy images displaying the formation of columnar nacre in the case of (a) Haliotis rufescens (reproduced with permission from ref (136), under Creative Commons Attribution 4.0 License, Copyright 1982 Authors; the linear size is about 7.1 μm), and (b) Phorcus turbinatus (reproduced with permission from ref (137). Copyright 2015 Trans Tech). Here ss and s stand for “surface sheets” and “organic sheet”, whereas sm and ilm indicate “surface membrane” and “interlamellar membrane”, respectively.

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Summarizing, while models PF1 and PF2 cannot capture all details of the formation mechanism of nacre, remarkably similar microstructures are generated. This raises the possibility that on the basis of the mechanisms these models realize (diffusion controlled solidification at high driving forces), one may design and prepare artificial mollusk shell structures that inherit the mechanical excellence emerging from the hierarchical sequence of the granular, prismatic, and nacre-like ultrastructures. Thus, the present work opens up the way toward a novel design strategy for creating biomimetic/bioinspired composite materials.
Finally, to address the evolution of columnar nacre within the phase-field theory, one can incorporate preexisting organic membranes into the simulations “by hand”, including the mineral bridges/aligned holes seen in the experiments. (33,34,138,140) We used PF1 to model the formation of CCC stacks shown in Figure 12. The thin organic walls were assumed to have amorphous structure (local orientation varied randomly pixelwise) and we applied a boundary condition that ensured a contact angle of 100° with the solid–liquid interface. Simulations of this kind yield 2D “pyramid-like” stacks of CC layers as shown in Figure 13. Such simulations can be used to explore the effect of such parameters as growth anisotropy, contact angle, hole size/position, and so on. For example, Figure 13b implies that the growth velocity of stack height increases with increasing hole width.

Figure 13

Figure 13. Snapshots of 2D phase-field simulations (model PF1), showing the formation of columnar nacre-like CCC tile stacks (gray/yellow - different colors denote different crystallographic orientations) via solidification between preexisting organic membranes (brown horizontal lines) with mineral bridges provided by (a) aligned holes of uniform width (20 Δx), and (b) aligned holes of three different widths (from left to right, 20, 5, and 10 Δx, respectively). The simulations were performed on 2000 × 500 and 2000 × 1000 grids (a) with anisotropic interfacial free energy and with (b) kinetic and interfacial free energy anisotropy. The horizontal size of the simulations is 26.25 μm.

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3.2. Helical Structures Predicted by Model PF3

Spectacular screw dislocation-like helical structures have been observed in mollusk shells akin to patterns formed in oscillating chemical reactions (Figure 4). These 3D structures cannot be addressed in models PF1 and PF2 as the scalar orientation field used in them is valid in only 2D (as in 3D minimum the three Euler angle are needed to define the crystallographic orientation). Therefore, we use model PF3 to explore the possibility of forming such objects within the framework of the phase-field theory. Here two solid phases (α and β) precipitate from a homogeneous ternary liquid. Owing to the lack of relevant information, we retain the materials parameters used in ref (102). Under appropriate conditions, shown by the green diamonds in Figure 14, a layerwise structure composed of alternating α (mineral) and β (organic) layers form (the third component is water, the crystal grows into hACC), an analogue of the “nacre” observed in model PF2. Note that the layer-by-layer growth mechanism, by which the layered structure forms is spinodal nucleation of one phase on the other, and thus can be viewed as an extreme case of island growth. In this regime, we see the formation of helical structures that emerge in pairs of opposite chirality. As the spiraling eutectic dendrites in ref (102), these defects originate from an instability associated with diffusion of the third component.

Figure 14

Figure 14. Domain in an idealized ternary phase diagram, (102) in which screw dislocation like structures form (green diamonds). For comparison, domains of spiraling eutectic dendrites (red dots), and unordered eutectic structures (blue crosses) are also shown.

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Different views and sections of such structures are shown in Figure 15. This chiral structure closely resembles the screw dislocation-like defects reported in experiments. (14,39) The similarity could be enhanced by incorporating kinetic/interfacial energy anisotropies yielding faceted growth perimeters. It cannot, however, be excluded that the screw dislocation-like helical structures have here a different origin than in the reality. For example, our dislocation pairs do not recombine even in the long time limit, presumably because of the lack of mechanical stresses that are not incorporated into the phase-field models used in this study. Further investigations are yet needed to clarify whether phase-field models of island growth (143) or anisotropic pinning (144) could provide more realistic dynamics.

Figure 15

Figure 15. Screw dislocation pair formed in model PF3 at composition c = (0.43, 0.55, 0.02). (a) cross section through the axes of the pair. (b) Top view. (c) Front view of the central part of the section shown in panel (a). (d) Multiple screw dislocation pairs formed at c = (0.44, 0.54, 0.02). Red and yellow colors indicate solid solution phases rich in the mineral and organic components. These are generic dimensionless computations (performed on 256 × 256 × 272 grids moving with the solidification front), illustrating the ability of model PF3 to capture the formation of helical structures, but they are not optimized for modeling screw dislocations in sheet nacre.

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Simultaneous formation of alternating organic and mineral layers in the vicinity of topological defects predicted by our simulations is a working hypothesis. Previous work suggests that the formation of spiraling organic membranes precedes mineral deposition. (39,145) Biological systems often use liquid crystals based on chitin as a template. (146) It is hypothesized (39,40,145) in this case that self-organization of the liquid crystal phase leads to the formation of a helical organic scaffold, which serves as a template for the mineralized structures of the same configuration. This mechanism of scaffold formation may be analogous to the formation of helical structures in Liesegang systems, (147,148) which raises the possibility of using the phase-field inventory developed for such systems. (149)
Note that the present simulations were not optimized for the case of nacre. Further work is underway to characterize these structures and the dynamics of their formation within the phase-field theory.

3.3. Modeling of Coral Skeletons in Model PF1

Next, using model PF1, we try to find a qualitative answer to the question of why the skeleton of some corals species contain small randomly oriented crystallites, “sprinkles” (see Figure 4e), which occur at the perimeter and along grain boundaries and even form bands, whereas other species do not display this behavior, an observation discussed in some detail in ref (28). In our previous work, we demonstrated that conditions of mineralization can influence the amount of sprinkles; however, we have addressed only tangentially the formation of sprinkle bands.
In this section, we address the latter phenomenon. We hypothesize that the coral polyp sits on the corallite (top of the skeleton) and emits a supersaturated extracellular calcifying fluid (CF), which is not in direct contact with the seawater but fills in the cavities of the porous skeleton. Recent work indicates that the coral skeletons are deposited biologically and actively via attachment of hACC nanoparticles (of diameter 50 to 400 nm), while ion-by-ion addition fills the interstitial space among them. (150) This leads to the formation of a thin (<1 μm) amorphous surface layer: diffusion of solid hACC nanoparticles and ion diffusion in CF contribute to the deposition. The hACC surface layer crystallizes into aragonite plumose spherulites after dehydration.
As the hACC/ACC surface layer remains thin, crystallization is apparently fast enough to keep pace with hACC deposition. Thus, diffusion of the hACC nanoparticles is expected to be the rate-limiting phenomenon. Thus, although particle diffusion does not influence the thermodynamic driving force of the ACC → CCC transition, it does influence the effective crystal growth rate. The effective rate is small on the sides of the fingers due to the low concentration of nanoparticles and allows a longer time the consolidation of the crystal layer yielding larger grain sizes. At the tips, the effective crystal growth rate is larger because of a higher concentration of the nanoparticles; thus, a shorter time is available for consolidation, and the crystal grains remain smaller. This is observed in the experimental images (Figure 16a–c).

Figure 16

Figure 16. Comparison of the cross sectional microstructure of top part (corallite) of the skeleton of coral species Balanophyllia europea (a–c) to a simulation performed using by model PF1. The 2D simulation was performed on a 1000 × 2000 grid. Orientation maps obtained by PIC mapping are shown in (a–c). Reproduced with permission from ref (28) under Creative Commons license CC-BY-NC-ND 4.0. Copyright 2020 Elsevier. At high magnification, an abundance of small crystallites, sprinkles, can be seen around the centerline of the finger shown in panel (c). For comparison, the computed orientation maps are displayed in (d) and (e), whereas the computed composition map is presented in panel (f). In panels (b–e) different colors correspond to different crystallographic orientation. The white rectangles in (a) and (b) denote areas magnified in (b) and (c), respectively, whereas the white rectangles in panels (e) and (f) indicate the area shown magnified in panel (d). Panels (d–f) show results of a generic dimensionless computations that incorporate several dimensionless combinations of the relevant physical properties; accordingly, the corresponding physical size scale depends on the choice of these parameters. With appropriate choice of these parameters, the length scale of the experiments can be recovered.

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The diffusion coefficient for hACC particles of radius Rp = 150 nm can be estimated by the Stokes–Einstein relationship Dp = kBT/(6πRpη), which leads to Dp ≈ 2 × 10–12 m2/s, for T = 300 K and a viscosity of η = 1 mPa·s. Taking a medium growth rate (61−63) of v = 5 cm/yr ≈ 1.6 × 10–10 m/s for the coral skeleton, one obtains a diffusion length of lD ≈ 0.92 mm, whereas for fast-growing corals (37 cm/yr) (63)lD ≈ 0.12 mm, which do not rule out diffusion-controlled solidification.
Accordingly, model PF1 is applied here as follows: the phase-field and the coupled (particle-) concentration field control solidification on the time scale of particle diffusion and lead to a Mullins–Sekerka-type diffusional instability (151) of the interface. The magnitude of the orientational mobility, in turn, determines whether the forming solid becomes orientationally homogeneous (single crystal), partly ordered (polycrystalline), or fully disordered (amorphous).
Since in the case of coral skeletons we do not need to produce nacre-like alternating organic–inorganic layers via a transition from diffusionless to diffusive growth, in model PF1 we can use conditions, where dv/Dc,M ≪ 1; that is, the system is far from the diffusionless growth regime. The dimensionless model parameters and boundary conditions are the same as those we used in ref (28) for coral skeletons.
The polycrystalline structure emerging under these conditions due to the diffusional instability is shown in Figure 16d–f. Note the rough surface and the liquid channels, with small crystallites at the tips and along the spine of the branches, and larger crystallites at the lateral surfaces. This distribution of grain size is the result of the fact that the growth velocity at the tips is larger because of the larger supersaturation (the tip meets fresh, nondepleted liquid, see Figure 16f), whereas in the interarm channels, the fluid is depleted, so growth is slow, yielding larger crystallites. This phenomenon is the result of growth front nucleation (GFN) that leads to more frequent GFN events with increasing growth velocity as discussed in refs (75−78,152). Whether the combination of diffusional instability with GFN or some other biology directed mechanisms is responsible for the appearance of the rough surface of the skeleton is unclear at present. It is thus desirable to investigate further consequences of the hypothesized control of the grain size distribution via diffusional instabilities and GFN.
Along these lines, we make predictions using model PF1 that may be tested experimentally and validate or disprove our assumptions. For this reason, we investigate the effect of model parameters that influence the amount of sprinkles forming in the model and thus may offer explanation why it varies from one species to the other.
Previous work indicated that the orientational mobility (related to the rotational diffusion coefficient), the thermodynamic driving force (influenced by supersaturation or temperature) may influence the intensity of GFN (formation of new grains at the growth front). (75−78,153) In the framework of this study, we varied individually these parameters, and in all cases, we obtained a transition from microstructures dominated by sprinkles to microstructures with few or no sprinkles. Of these parameters, only the temperature can be controlled with relative ease. Variation of particle concentration in the calcifying fluid below the coral polyp, or controlling the rotational diffusion coefficient of the particles in the fluid are probably beyond the reach of the experimenter. Therefore, we present only the microstructural/morphological changes predicted as a function of temperature (see Figure 17). Apparently, according to our model, the coral skeletons grown at low temperatures should have larger amount of sprinkles than those grown at higher temperatures. This finding raises the question whether the amount of sprinkles is indeed a characteristic feature of the individual coral species (i.e., determined biologically) or some differences in the circumstances of mineralization (temperature and/or supersaturation) are responsible for the deviations. In any event, these simulations may offer a natural explanation for the differences seen in the amount of sprinkles in the skeleton of different coral species.

Figure 17

Figure 17. Morphology and microstructure evolution as a function of temperature as predicted by model PF1. The reference computation is shown in panel (d). The relative temperatures from left to right are ΔT = −3, – 2, – 1, 0, 1, and 2 K. The simulations were performed on 1000 × 2000 grids. Note the decreasing amount of sprinkles with increasing temperature (from left to right). These are generic dimensionless computations that incorporate several dimensionless combinations of the relevant physical properties; accordingly, the corresponding physical size scale depends on the choice of these parameters. With an appropriate choice of them, the length scale of the experiments can be recovered.

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4. Conclusions

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We have demonstrated that qualitative coarse-grained phase-field modeling offers a methodology to address specific mesoscale aspects of nonclassical crystallization phenomena taking place during biomineralization. In particular, we investigated to what extent qualitative phase-field modeling can contribute to the understanding of microstructure evolution during the formation of mollusk shells and coral skeletons for various species. We applied three different phase-field models: PF1, PF2, and PF3.
Our present findings can be summarized as follows:
(1)

Ultrastructure specific to the shells of mollusks Unio pictorum, Nautilus pompilius, and Haliotis asinina: Driving the solidification process from solute trapping toward partitioning via decreasing the thermodynamic driving force, binary phase-field models PF1 and PF2 recover the common sequence of granular → prismatic → nacre ultrastructures on a reasonable time scale, if CC crystallization takes place via an amorphous precursor. In contrast, within this scenario, CC crystallization via ion-by-ion deposition from aqueous solution appears to be orders of magnitude too fast when compared to experiments.

(2)

Nacre formation in mollusk shells: Models PF1 and PF2 describe reasonably well the formation of not only the granular and prismatic domains, but the appearance of sheet nacre as well, in which case the models indicate alternating precipitation of the organic and mineral components. The models seem to reproduce even such details as mineral bridges and aligned holes. Yet, for obvious reasons, they cannot predict the formation mechanism of columnar nacre, in which the formation of organic membranes precedes CC precipitation. However, representing the preexisting organic membranes via appropriate boundary conditions, a reasonable description can be obtained even in this case.

(3)

Screw dislocations in mollusk shells: Ternary phase field model PF3 predicts the formation of screw dislocations pairs in 3D, a phenomenon analogous to the experimental findings. Inclusion of elasticity into the model is needed to capture the proper dynamic behavior during growth.

(4)

Sprinkle formation in coral skeletons: model PF1 was used to explore the possible mechanism for the formation of nanoscale crystallites “sprinkles”, whose presence was reported recently in the skeletons of certain coral species. Assuming a diffusion controlled mechanism in confined space, we observe the formation of sprinkle bands at the spine of the arms of the corallite as a trace of fast solidification at the arm tips, whereas larger crystallites form at the sides of the arms. The simulations show that varying the orientation mobility (proportional to the rotational diffusion coefficient of the molecules/ions) or the driving force of crystallization (via changing either the supersaturation or the temperature), one can control the amount of sprinkles between essentially no sprinkle and dominantly sprinkled microstructures.

Unquestionably, the applied models should be viewed as only minimum models of the processes taking place during biomineralization. Yet, we believe that phase-field modeling complemented with biochemical/biological information has the potential to contribute to a better qualitative or even quantitative understanding of morphogenesis in simple cases. Introduction of more complex models can certainly improve the mathematical representation of the associated phenomena. Ultimate limitations of such approaches stem from the fact that living organisms cannot be modeled within this framework: they can only be represented by boundary conditions of different complexity. Despite these, in specific cases, we recovered structures closely resembling their biogenic counterpart. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be so simple that they can be understood with simple math and simulated by phase-field theory.
Finally, we note that our simulations outline conditions, under which standard materials science processes can be used to create inorganic substances that mimic the microstructures observed to form in living organisms, a knowledge that may open up ways for creating new biomimetic/bioinspired composite materials.

Author Information

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  • Corresponding Author
    • László Gránásy - Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary;  Brunel Centre of Advanced Solidification Technology, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K.;  Orcidhttps://orcid.org/0000-0001-5825-7632;  Email: [email protected]
  • Authors
    • László Rátkai - Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary;  Orcidhttps://orcid.org/0000-0002-7644-253X
    • Gyula I. Tóth - Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, U.K.;  Orcidhttps://orcid.org/0000-0002-8446-9572
    • Pupa U. P. A. Gilbert - Departments of Physics, Chemistry, Geoscience, Materials Science, University of Wisconsin−Madison, Madison, Wisconsin 53706, United States;  Lawrence Berkeley National Laboratory, Chemical Sciences Division, Berkeley, California 94720, United States;  Orcidhttps://orcid.org/0000-0002-0139-2099
    • Igor Zlotnikov - B CUBE−Center for Molecular Bioengineering, Technische Universität Dresden, 01307 Dresden, Germany;  Orcidhttps://orcid.org/0000-0003-2388-9028
    • Tamás Pusztai - Laboratory of Advanced Structural Studies, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H−1525 Budapest, Hungary;  Orcidhttps://orcid.org/0000-0002-1281-2933
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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L.G., R.L., and T.P. acknowledges support by the National Agency for Research, Development, and Innovation (NKFIH), Hungary under contract No. KKP-126749. Eutectic codes used in this work were partly developed under the NKFIH contract No. NN-125832. Research infrastructure in Hungary was provided by the Hungarian Academy of Sciences (MTA). P.U.P.A.G. received 40% support from DOE–BES–Chemical Sciences, Geosciences, Biosciences–Geosciences Grant DE-FG02-07ER15899, 40% support from the Laboratory Directed Research and Development (LDRD) program at Berkeley Lab, through DOE-BES, under Award Number DE-AC02-05CH11231, and 20% support from NSF Biomaterials Grant DMR-1603192. I.Z. acknowledges the financial support provided by Bundesministerium für Bildung und Forschung through Grant 03Z22EN11.

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    Imai, H. Self-Organized Formation of Hierarchical Structures. Top. Curr. Chem. 2007, 270, 43– 72,  DOI: 10.1007/128_054
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    Self-organized formation of hierarchical structures
    Imai, Hiroaki
    Topics in Current Chemistry (2007), 270 (Biomineralization I), 43-72CODEN: TPCCAQ; ISSN:0340-1022. (Springer GmbH)
    A review. Hierarchical architectures consisting of small building blocks of inorg. crystals are widely found in biominerals. Crystal growth mimicking biomineralization has been studied using various kinds of org. mols. and mol. assembly. The emergence of complex organization of inorg. crystals was obsd. through biomimetic approaches in aq. soln. A wide variety of hierarchical architectures including fractals, dendrites, self-similar and helical structures were achieved in the artificial systems. Self-organized formation, with exquisite control of mass transport and the variation of surface energy with org. mols., is essential for versatile morphogenesis of inorg. crystals similar to biominerals.
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  13. 13
    Bayerlein, B.; Zaslansky, P.; Dauphin, Y.; Rack, A.; Fratzl, P.; Zlotnikov, I. Self-Similar Mesostructure Evolution of the Growing Mollusc Shell Reminiscent of Thermodynamically Driven Grain Growth. Nat. Mater. 2014, 13 (12), 1102– 1107,  DOI: 10.1038/nmat4110
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    13
    Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth
    Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor
    Nature Materials (2014), 13 (12), 1102-1107CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    Significant progress has been made in understanding the interaction between mineral precursors and org. components leading to material formation and structuring in biomineralizing systems. The mesostructure of biol. materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biol. Here, we analyze the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resoln. synchrotron-based microtomog. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphol. and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biol. organisms make use of thermodn. to generate complex morphologies.
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  14. 14
    Zlotnikov, I.; Schoeppler, V. Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis. Adv. Funct. Mater. 2017, 27 (28), 1700506,  DOI: 10.1002/adfm.201700506
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  15. 15
    Sun, C. Y.; Marcus, M. A.; Frazier, M. J.; Giuffre, A. J.; Mass, T.; Gilbert, P. U. P. A. Spherulitic Growth of Coral Skeletons and Synthetic Aragonite: Nature’s Three-Dimensional Printing. ACS Nano 2017, 11 (7), 6612– 6622,  DOI: 10.1021/acsnano.7b00127
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    15
    Spherulitic Growth of Coral Skeletons and Synthetic Aragonite: Nature's Three-Dimensional Printing
    Sun, Chang-Yu; Marcus, Matthew A.; Frazier, Matthew J.; Giuffre, Anthony J.; Mass, Tali; Gilbert, Pupa U. P. A.
    ACS Nano (2017), 11 (7), 6612-6622CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Coral skeletons were long assumed to have a spherulitic structure, i.e., a radial distribution of acicular aragonite (CaCO3) crystals with their c-axes radiating from series of points, termed centers of calcification (CoCs). This assumption was based on morphol. alone, not on crystallog. Here we measure the orientation of crystals and nanocrystals and confirm that corals grow their skeletons in bundles of aragonite crystals, with their c-axes and long axes oriented radially and at an angle from the CoCs, thus precisely as expected for feather-like or "plumose" spherulites. Furthermore, we find that in both synthetic and coral aragonite spherulites at the nanoscale adjacent crystals have similar but not identical orientations, thus demonstrating by direct observation that even at nanoscale the mechanism of spherulite formation is non-crystallog. branching (NCB), as predicted by theory. Finally, synthetic aragonite spherulites and coral skeletons have similar angle spreads, and angular distances of adjacent crystals, further confirming that coral skeletons are spherulites. This is important because aragonite grows anisotropically, 10 times faster along the c-axis than along the a-axis direction, and spherulites fill space with crystals growing almost exclusively along the c-axis, thus they can fill space faster than any other aragonite growth geometry, and create isotropic materials from anisotropic crystals. Greater space filling rate and isotropic mech. behavior are key to the skeleton's supporting function and therefore to its evolutionary success. In this sense, spherulitic growth is Nature's 3D printing.
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  16. 16
    De Tommasi, E.; Gielis, J.; Rogato, A. Diatom Frustule Morphogenesis and Function: A Multidisciplinary Survey. Marine Genomics 2017, 35, 1– 18,  DOI: 10.1016/j.margen.2017.07.001
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    16
    Diatom Frustule Morphogenesis and Function: a Multidisciplinary Survey
    De Tommasi Edoardo; Gielis Johan; Rogato Alessandra
    Marine genomics (2017), 35 (), 1-18 ISSN:.
    Diatoms represent the major component of phytoplankton and are responsible for about 20-25% of global primary production. Hundreds of millions of years of evolution led to tens of thousands of species differing in dimensions and morphologies. In particular, diatom porous silica cell walls, the frustules, are characterized by an extraordinary, species-specific diversity. It is of great interest, among the marine biologists and geneticists community, to shed light on the origin and evolutionary advantage of this variability of dimensions, geometries and pore distributions. In the present article the main reported data related to frustule morphogenesis and functionalities with contributions from fundamental biology, genetics, mathematics, geometry and physics are reviewed.
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  17. 17
    Cloutier, J.; Villa, L.; Traxer, O.; Daudon, M. Kidney Stone Analysis: “Give Me Your Stone, I Will Tell You Who You Are!. World J. Urol. 2015, 33 (2), 157– 169,  DOI: 10.1007/s00345-014-1444-9
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    17
    Kidney stone analysis: "Give me your stone, I will tell you who you are!"
    Cloutier Jonathan; Villa Luca; Traxer Olivier; Daudon Michel
    World journal of urology (2015), 33 (2), 157-69 ISSN:.
    INTRODUCTION: Stone analysis is an important part in the evaluation of patients having stone disease. This could orientate the physician toward particular etiologies. MATERIAL AND METHODS: Chemical and physical methods are both used for analysis. Unfortunately, chemical methods often are inadequate to analyze accurately urinary calculi and could fail to detect some elements into the stone. Physical methods, in counterpart, are becoming more and more used in high-volume laboratories. The present manuscript will provide a review on analytic methods, and review all the information that should be included into an appropriate morpho-constitutional analysis. CONCLUSION: This report can supply an excellent summarization of the stone morphology and give the opportunity to find specific metabolic disorders and different lithogenic process into the same stone. Here, specific chemical types with their different crystalline phases are shown in connection with their different etiologies involved.
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    Boskey, A. L. Mineralization of Bones and Teeth. Elements 2007, 3 (6), 385– 391,  DOI: 10.2113/GSELEMENTS.3.6.385
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    Mineralization of bones and teeth
    Boskey, Adele L.
    Elements (Chantilly, VA, United States) (2007), 3 (6), 385-391CODEN: EOOCAG; ISSN:1811-5209. (Mineralogical Society of America)
    A review. Bones and teeth consist of an inorg. calcium phosphate mineral approximated by hydroxylapatite and matrix proteins. The phys. and chem. properties of these "bioapatite" crystals are different from those of geol. hydroxylapatite because of the way they are formed, and these unique properties are required for fulfilling the biol. functions of bones and teeth. Recent biochem. studies provide insight into the factors controlling the formation and growth of bioapatite crystals and how alteration in the mineralization process can lead to diseases such as osteoporosis. New spectroscopic and microscopic techniques are enabling scientists to characterize changes in crystal properties in these diseases, providing potentially fruitful areas of collaboration among geochemists, mineralogists, and biol. researchers and offering hope for the development of novel therapies.
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  19. 19
    Lin, W.; Zhang, W.; Zhao, X.; Roberts, A. P.; Paterson, G. A.; Bazylinski, D. A.; Pan, Y. Genomic Expansion of Magnetotactic Bacteria Reveals an Early Common Origin of Magnetotaxis with Lineage-Specific Evolution. ISME J. 2018, 12 (6), 1508– 1519,  DOI: 10.1038/s41396-018-0098-9
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    19
    Genomic expansion of magnetotactic bacteria reveals an early common origin of magnetotaxis with lineage-specific evolution
    Lin, Wei; Zhang, Wensi; Zhao, Xiang; Roberts, Andrew P.; Paterson, Greig A.; Bazylinski, Dennis A.; Pan, Yongxin
    ISME Journal (2018), 12 (6), 1508-1519CODEN: IJSOCF; ISSN:1751-7362. (Nature Research)
    The origin and evolution of magnetoreception, which in diverse prokaryotes and protozoa is known as magnetotaxis and enables these microorganisms to detect Earth's magnetic field for orientation and navigation, is not well understood in evolutionary biol. The only known prokaryotes capable of sensing the geomagnetic field are magnetotactic bacteria (MTB), motile microorganisms that biomineralize intracellular, membrane-bounded magnetic single-domain crystals of either magnetite (Fe3O4) or greigite (Fe3S4) called magnetosomes. Magnetosomes are responsible for magnetotaxis in MTB. Here we report the first large-scale metagenomic survey of MTB from both northern and southern hemispheres combined with 28 genomes from uncultivated MTB. These genomes expand greatly the coverage of MTB in the Proteobacteria, Nitrospirae, and Omnitrophica phyla, and provide the first genomic evidence of MTB belonging to the Zetaproteobacteria and "Candidatus Lambdaproteobacteria" classes. The gene content and organization of magnetosome gene clusters, which are phys. grouped genes that encode proteins for magnetosome biosynthesis and organization, are more conserved within phylogenetically similar groups than between different taxonomic lineages. Moreover, the phylogenies of core magnetosome proteins form monophyletic clades. Together, these results suggest a common ancient origin of iron-based (Fe3O4 and Fe3S4) magnetotaxis in the domain Bacteria that underwent lineage-specific evolution, shedding new light on the origin and evolution of biomineralization and magnetotaxis, and expanding significantly the phylogenomic representation of MTB.
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  20. 20
    Kaplan, D. L. Mollusc Shell Structures: Novel Design Strategies for Synthetic Materials. Curr. Opin. Solid State Mater. Sci. 1998, 3 (3), 232– 236,  DOI: 10.1016/S1359-0286(98)80096-X
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    Mollusk shell structures: novel design strategies for synthetic materials
    Kaplan, David L.
    Current Opinion in Solid State & Materials Science (1998), 3 (3), 232-236CODEN: COSSFX; ISSN:1359-0286. (Current Chemistry)
    A review, with 32 refs. Mollusk shells are layered org.-inorg. composites bioengineered at the nanoscale. The structural features of these composites result in toughened shells and can provide a useful paradigm to consider in the design of biomaterials. Recent studies in vitro illustrate the function of proteins in controlling the nucleation and growth of the inorg. phases in these structures. Characterization of the morphol. of the org. matrix provides new insights into the registry between layers of inorg. material. Biomimetic methods are being used to duplicate these biomineralization processes to achieve comparable structural features in ceramic composites.
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    Barthelat, F. Growing a Synthetic Mollusk Shell. Science 2016, 354 (6308), 32– 33,  DOI: 10.1126/science.aah6507
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    21
    Growing a synthetic mollusk shell
    Barthelat, Francois
    Science (Washington, DC, United States) (2016), 354 (6308), 32-33CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    There is no expanded citation for this reference.
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  22. 22
    Gao, H. L.; Chen, S. M.; Mao, L. B.; Song, Z. Q.; Yao, H. B.; Cölfen, H.; Luo, X. S.; Zhang, F.; Pan, Z.; Meng, Y. F.; Ni, Y.; Yu, S. H. Mass Production of Bulk Artificial Nacre with Excellent Mechanical Properties. Nat. Commun. 2017, 8 (1), 287,  DOI: 10.1038/s41467-017-00392-z
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    22
    Mass production of bulk artificial nacre with excellent mechanical properties
    Gao Huai-Ling; Chen Si-Ming; Mao Li-Bo; Yao Hong-Bin; Pan Zhao; Meng Yu-Feng; Yu Shu-Hong; Song Zhao-Qiang; Ni Yong; Yu Shu-Hong; Colfen Helmut; Luo Xi-Sheng; Zhang Fu
    Nature communications (2017), 8 (1), 287 ISSN:.
    Various methods have been exploited to replicate nacre features into artificial structural materials with impressive structural and mechanical similarity. However, it is still very challenging to produce nacre-mimetics in three-dimensional bulk form, especially for further scale-up. Herein, we demonstrate that large-sized, three-dimensional bulk artificial nacre with comprehensive mimicry of the hierarchical structures and the toughening mechanisms of natural nacre can be facilely fabricated via a bottom-up assembly process based on laminating pre-fabricated two-dimensional nacre-mimetic films. By optimizing the hierarchical architecture from molecular level to macroscopic level, the mechanical performance of the artificial nacre is superior to that of natural nacre and many engineering materials. This bottom-up strategy has no size restriction or fundamental barrier for further scale-up, and can be easily extended to other material systems, opening an avenue for mass production of high-performance bulk nacre-mimetic structural materials in an efficient and cost-effective way for practical applications.Artificial materials that replicate the mechanical properties of nacre represent important structural materials, but are difficult to produce in bulk. Here, the authors exploit the bottom-up assembly of 2D nacre-mimetic films to fabricate 3D bulk artificial nacre with an optimized architecture and excellent mechanical properties.
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  23. 23
    Song, P.; Xu, Z.; Wu, Y.; Cheng, Q.; Guo, Q.; Wang, H. Super-Tough Artificial Nacre Based on Graphene Oxide via Synergistic Interface Interactions of π-π Stacking and Hydrogen Bonding. Carbon 2017, 111, 807– 812,  DOI: 10.1016/j.carbon.2016.10.067
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    23
    Super-tough artificial nacre based on graphene oxide via synergistic interface interactions of π-π stacking and hydrogen bonding
    Song, Pingan; Xu, Zhiguang; Wu, Yuanpeng; Cheng, Qunfeng; Guo, Qipeng; Wang, Hao
    Carbon (2017), 111 (), 807-812CODEN: CRBNAH; ISSN:0008-6223. (Elsevier Ltd.)
    Inspired by interfacial interactions of protein matrix and the crystal platelets in nacre, herein, a super-tough artificial nacre was produced through constructing the synergistic interface interactions of π-π interaction and hydrogen bonding between graphene oxide (GO) nanosheets and sulfonated styrene-ethylene/butylene-styrene copolymer synthesized with multifunctional benzene. The resultant GO-based artificial nacre showed super-high toughness of 15.3 ± 2.5 MJ/m3, superior to natural nacre and other GO-based nanocomposites. The ultra-tough property of the novel nacre was attributed to synergistic effect of π-π stacking interactions and hydrogen bonding. This bioinspired synergistic toughening strategy opens a new avenue for constructing high performance GO-based nanocomposites in the near future.
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  24. 24
    Spiesz, E. M.; Schmieden, D. T.; Grande, A. M.; Liang, K.; Schwiedrzik, J.; Natalio, F.; Michler, J.; Garcia, S. J.; Aubin-Tam, M. E.; Meyer, A. S. Bacterially Produced, Nacre-Inspired Composite Materials. Small 2019, 15 (22), 1805312,  DOI: 10.1002/smll.201805312
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    Chen, Y.; Fu, J.; Dang, B.; Sun, Q.; Li, H.; Zhai, T. Artificial Wooden Nacre: A High Specific Strength Engineering Material. ACS Nano 2020, 14 (2), 2036– 2043,  DOI: 10.1021/acsnano.9b08647
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    25
    Artificial Wooden Nacre: A High Specific Strength Engineering Material
    Chen, Yipeng; Fu, Jinzhou; Dang, Baokang; Sun, Qingfeng; Li, Huiqiao; Zhai, Tianyou
    ACS Nano (2020), 14 (2), 2036-2043CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Nacre, an org.-inorg. composite biomaterial that forms an ordered multilayer microstructure after years of slow biomineralization, is known as the strongest and toughest material within the mollusc family. Its unique structure provides inspiration for robust artificial engineering materials. Lignocellulose is ultralightweight, abundant, and possesses a high mech. performance and has been used for ages as a significant renewable raw material in wooden engineering composites. However, the inherent lack of mech. properties of current wooden composites assocd. with the fragile microstructure has limited their applications in advanced engineering materials. Here, we develop a large-size ultralightweight artificial "wood nacre" with an ordered layer structure through a fast and scalable "mech./chem. mineralization and assembly" approach. The millimeter-thick artificial wooden nacre mimics the stratified construction of natural nacre, resulting in a bulk hybrid material that can achieve almost the same strength as natural nacre while consisting of only one-sixth of the total inorg. content of natural nacre. The specific strength and toughness of the artificial wooden nacre is even superior to engineering alloy materials (such as Cu and Fe). This approach represents an efficient strategy for the mass prodn. of lightwt. sustainable structural materials with high strength and toughness.
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  26. 26
    Schoeppler, V.; Gránásy, L.; Reich, E.; Poulsen, N.; de Kloe, R.; Cook, P.; Rack, A.; Pusztai, T.; Zlotnikov, I. Biomineralization as a Paradigm of Directional Solidification: A Physical Model for Molluscan Shell Ultrastructural Morphogenesis. Adv. Mater. 2018, 30 (45), 1803855,  DOI: 10.1002/adma.201803855
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    Schoeppler, V.; Lemanis, R.; Reich, E.; Pusztai, T.; Gránásy, L.; Zlotnikov, I. Crystal Growth Kinetics as an Architectural Constraint on the Evolution of Molluscan Shells. Proc. Natl. Acad. Sci. U. S. A. 2019, 116 (41), 20388– 20397,  DOI: 10.1073/pnas.1907229116
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    27
    Crystal growth kinetics as an architectural constraint on the evolution of molluscan shells
    Schoeppler, Vanessa; Lemanis, Robert; Reich, Elke; Pusztai, Tamas; Granasy, Lalkszlo; Zlotnikov, Igor
    Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (41), 20388-20397CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Molluscan shells are a classic model system to study formation-structure-function relationships in biol. materials and the process of biomineralized tissue morphogenesis. Typically, each shell consists of a no. of highly mineralized ultrastructures, each characterized by a specific 3D mineral-org. architecture. Surprisingly, in some cases, despite the lack of a mutual biochem. toolkit for biomineralization or evidence of homol., shells from different independently evolved species contain similar ultrastructural motifs. In the present study, using a recently developed phys. framework, which is based on an analogy to the process of directional solidification and simulated by phase-field modeling, we compare the process of ultrastructural morphogenesis of shells from 3 major molluscan classes: A bivalve Unio pictorum, a cephalopod Nautilus pompilius, and a gastropod Haliotis asinina. We demonstrate that the fabrication of these tissues is guided by the organisms by regulating the chem. and phys. boundary conditions that control the growth kinetics of the mineral phase. This biomineralization concept is postulated to act as an architectural constraint on the evolution of molluscan shells by defining a morphospace of possible shell ultrastructures that is bounded by the thermodn. and kinetics of crystal growth.
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  28. 28
    Sun, C. Y.; Gránásy, L.; Stifler, C. A.; Zaquin, T.; Chopdekar, R. V.; Tamura, N.; Weaver, J. C.; Zhang, J. A. Y.; Goffredo, S.; Falini, G.; Marcus, M. A.; Pusztai, T.; Schoeppler, V.; Mass, T.; Gilbert, P. Crystal Nucleation and Growth of Spherulites Demonstrated by Coral Skeletons and Phase-Field Simulations. Acta Biomater. 2021, 120, 277– 292,  DOI: 10.1016/j.actbio.2020.06.027
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    28
    Crystal nucleation and growth of spherulites demonstrated by coral skeletons and phase-field simulations
    Sun, Chang-Yu; Granasy, Laszlo; Stifler, Cayla A.; Zaquin, Tal; Chopdekar, Rajesh V.; Tamura, Nobumichi; Weaver, James C.; Zhang, Jun A. Y.; Goffredo, Stefano; Falini, Giuseppe; Marcus, Matthew A.; Pusztai, Tamas; Schoeppler, Vanessa; Mass, Tali; Gilbert, Pupa U. P. A.
    Acta Biomaterialia (2021), 120 (), 277-292CODEN: ABCICB; ISSN:1742-7061. (Elsevier Ltd.)
    Spherulites are radial distributions of acicular crystals, common in biogenic, geol., and synthetic systems, yet exactly how spherulitic crystals nucleate and grow is still poorly understood. To investigate these processes in more detail, we chose scleractinian corals as a model system, because they are well known to form their skeletons from aragonite (CaCO3) spherulites, and because a comparative study of crystal structures across coral species has not been performed previously. We obsd. that all 12 diverse coral species analyzed here exhibit plumose spherulites in their skeletons, with well-defined centers of calcification (CoCs), and cryst. fibers radiating from them. In 7 of the 12 species, we obsd. a skeletal structural motif not obsd. previously: randomly oriented, equant crystals, which we termed "sprinkles". In Acropora pharaonis, these sprinkles are localized at the CoCs, while in 6 other species, sprinkles are either layered at the growth front (GF) of the spherulites, or randomly distributed. At the nano- and micro-scale, coral skeletons fill space as much as single crystals of aragonite. Based on these observations, we tentatively propose a spherulite formation mechanism in which growth front nucleation (GFN) of randomly oriented sprinkles, competition for space, and coarsening produce spherulites, rather than the previously assumed slightly misoriented nucleations termed "non-crystallog. branching". Phase-field simulations support this mechanism, and, using a minimal set of thermodn. parameters, are able to reproduce all of the microstructural variation obsd. exptl. in all of the investigated coral skeletons. Beyond coral skeletons, other spherulitic systems, from aspirin to semicryst. polymers and chocolate, may also form according to the mechanism for spherulite formation proposed here. Understanding the fundamental mechanisms of spherulite nucleation and growth has broad ranging applications in the fields of metallurgy, polymers, food science, and pharmaceutical prodn. Using the skeletons of reef-building corals as a model system for investigating these processes, we propose a new spherulite growth mechanism that can not only explain the micro-structural diversity obsd. in distantly related coral species, but may point to a universal growth mechanism in a wide range of biol. and technol. relevant spherulitic materials systems.
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    Metzler, R. A.; Zhou, D.; Abrecht, M.; Chiou, J. W.; Guo, J.; Ariosa, D.; Coppersmith, S. N.; Gilbert, P. U. P. A. Polarization-Dependent Imaging Contrast in Abalone Shells. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77 (6), 064110,  DOI: 10.1103/PhysRevB.77.064110
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    Polarization-dependent imaging contrast in abalone shells
    Metzler, Rebecca A.; Zhou, Dong; Abrecht, Mike; Chiou, Jau-Wern; Guo, Jinghua; Ariosa, Daniel; Coppersmith, Susan N.; Gilbert, P. U. P. A.
    Physical Review B: Condensed Matter and Materials Physics (2008), 77 (6), 064110/1-064110/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Many biominerals contain micro- or nanocryst. mineral components, organized accurately into architectures that confer the material with improved mech. performance at the macroscopic scale. An effect is presented which enables observation of the relative orientation of individual crystals at the submicron scale. The effect is called the polarization-dependent imaging contrast (PIC), since it is an imaging development of the well-known x-ray linear dichroism. Most importantly, PIC is obtained in situ, in biominerals. PIC in the prismatic and nacreous layers of Haliotis rufescens (red abalone) confirms the presence of calcite and aragonite and corroborates the exptl. data with theor. simulated spectra. PIC reveals different and unexpected aspects of nacre architecture that have inspired theor. models for nacre formation.
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  30. 30
    Gilbert, P. U. P. A.; Young, A.; Coppersmith, S. N. Measurement of C-Axis Angular Orientation in Calcite (CaCO3) Nanocrystals Using X-Ray Absorption Spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2011, 108 (28), 11350– 11355,  DOI: 10.1073/pnas.1107917108
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    30
    Measurement of c-axis angular orientation in calcite (CaCO3) nanocrystals using X-ray absorption spectroscopy
    Gilbert, P. U. P. A.; Young, Anthony; Coppersmith, Susan N.
    Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (28), 11350-11355, S11350/1-S11350/3CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    We demonstrate that the ability to manipulate the polarization of synchrotron radiation can be exploited to enhance the capabilities of X-ray absorption near-edge structure (XANES) spectroscopy, to include linear dichroism effects. By acquiring spectra at the same photon energies but different polarizations, and using a photoelectron emission spectro-microscope (PEEM), one can quant. det. the angular orientation of micro- and nanocrystals with a spatial resoln. down to 10 nm. XANES-PEEM instruments are already present at most synchrotrons, hence these methods are readily available. The methods are demonstrated here on geol. calcite (CaCO3) and used to investigate the prismatic layer of a mollusk shell, Pinctada fucata. These XANES-PEEM data reveal multiply oriented nanocrystals within calcite prisms, previously thought to be monocryst. The subdivision into multiply oriented nanocrystals, spread by more than 50°, may explain the excellent mech. properties of the prismatic layer, known for decades but never explained.
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    Addadi, L.; Joester, D.; Nudelman, F.; Weiner, S. Mollusk Shell Formation: A Source of New Concepts for Understanding Biomineralization Processes. Chem. - Eur. J. 2006, 12 (4), 980– 987,  DOI: 10.1002/chem.200500980
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    Mollusk shell formation: a source of new concepts for understanding biomineralization processes
    Addadi, Lia; Joester, Derk; Nudelman, Fabio; Weiner, Steve
    Chemistry - A European Journal (2006), 12 (4), 980-987CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. The biol. approach to forming crystals is proving to be most surprising. Mollusks build their shells by using a hydrophobic silk gel, very acidic aspartic acid rich proteins, and apparently also an amorphous precursor phase from which the crystals form. All this takes place in a highly structured chitinous framework. The authors present ideas on how these disparate components work together to produce the highly structured pearly nacreous layer of the mollusk shell.
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    Marin, F.; Le Roy, N.; Marie, B. The Formation and Mineralization of Mollusk Shell. Front. Biosci., Scholar Ed. 2012, S4 (3), 1099– 1125,  DOI: 10.2741/s321
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    The formation and mineralization of mollusk shell
    Marin, Frederic; Le Roy, Nathalie; Marie, Benjamin
    Frontiers in Bioscience, Scholar Edition (2012), S4 (3), 1099-1125CODEN: FBSEAU; ISSN:1945-0524. (Frontiers in Bioscience)
    A review. In the last years, the field of mollusk biomineralization has known a tremendous mutation. The most recent advances deal with the nanostructure of shell biominerals, and with the identification of several shell matrix proteins: on one hand, the complex hierarchical organization of shell biominerals has been deciphered in few models, like nacre. On the other hand, although proteins represent a minor shell component, they are the major macromols. that control biocrystal synthesis. Until recently, the paradigm was to consider that this control occurs by 2 antagonist mechanisms: crystal nucleation and growth inhibition. Emerging models try to translate a more complex reality, illustrated by the huge variety of shell proteins, characterized so far. The primary structure of many of them is composed of different functional domains, some of which exhibit enzymic activity, while others may be involved in cell signaling. Many of them have unknown functions. Today, the shell matrix appears as a whole system, which regulates protein-mineral, protein-protein, and epithelium-mineral interactions. These aspects should be taken in account for the future models of shell formation.
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    Sun, J.; Bhushan, B. Hierarchical Structure and Mechanical Properties of Nacre: A Review. RSC Adv. 2012, 2 (20), 7617– 7632,  DOI: 10.1039/c2ra20218b
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    Hierarchical structure and mechanical properties of nacre: a review
    Sun, Jiyu; Bhushan, Bharat
    RSC Advances (2012), 2 (20), 7617-7632CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
    A review. Nacre (known as mother of pearl) is the iridescent inner shell layer of some mollusks. Nacre is composed of 95 wt% aragonite (a crystallog. form of CaCO3) and 5 wt% org. materials (proteins and polysaccharides). It is well known that it exhibits high fracture toughness, much greater than that of monolithic aragonite, because of its ingenious structure. It also exhibits energy absorption properties. It has a complex hierarchical microarchitecture that spans multiple length scales from the nanoscale to the macroscale. It includes columnar architectures and sheet tiles, mineral bridges, polygonal nanograins, nanoasperities, plastic microbuckling, crack deflection, and interlocking bricks, which exhibit a remarkable combination of stiffness, low wt. and strength. Nacre's special self-assembly characteristics have attracted interest from materials scientists for the development of laminated composite materials, mol. scale self-assembly and biomineralization. This paper reviews the characteristics of hierarchical structure and the mech. properties of nacre that provide the desired properties, and the latest developments and biomimetic applications.
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  34. 34
    Checa, A. G. Physical and Biological Determinants of the Fabrication of Molluscan Shell Microstructures. Front. Mar. Sci. 2018, 5, 353,  DOI: 10.3389/fmars.2018.00353
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    Crenshaw, M. A. The Inorganic Composition of Molluscan Extrapallial Fluid. Biol. Bull. 1972, 143 (3), 506– 512,  DOI: 10.2307/1540180
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    Inorganic composition of molluscan extrapallial fluid
    Crenshaw, Miles A.
    Biological Bulletin (Woods Hole, MA, United States) (1972), 143 (3), 506-12CODEN: BIBUBX; ISSN:0006-3185.
    The inorg. compn. of the extrapallial fluids of Mercenaria mercenaria, Mytilus edulis, and Crassosterea virginica was significantly different from sea water. The Donnan ratio for each ion except for Ca was calcd. to be almost identical for each extrapallial fluid sample. The pH of each sample was well below that of sea water. pH values obtained in situ for Mercenaria mercenaria and Mytilus edulis were within the range of those obtained by the sampling method. The pH of the extrapallial fluid decreased when the animal closed its valves and increased when it opened them, as did the Ca concn. The Donnan ratios of the ions, except for K in the blood plasma and Ca in the extrapallial fluid, were reduced to unity by dialysis against sea water. Anal. of the nondialyzable material for protein showed that 50% of the blood plasma impermeate was protein. The SO42-/hexosamine ratio in the acid muccopolysaccharide fraction was 0.9-1.1.
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    Allam, B.; Paillard, C. Defense Factors in Clam Extrapallial Fluids. Dis. Aquat. Org. 1998, 33, 123– 128,  DOI: 10.3354/dao033123
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    Otter, L. M.; Agbaje, O. B. A.; Kilburn, M. R.; Lenz, C.; Henry, H.; Trimby, P.; Hoppe, P.; Jacob, D. E. Architecture, Growth Dynamics and Biomineralization of Pulsed Sr-Labelled Katelysia rhytiphora (Mollusca, Bivalvia). Biogeosciences 2019, 16, 3439– 3455,  DOI: 10.5194/bg-16-3439-2019
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    Insights into architecture, growth dynamics, and biomineralization from pulsed Sr-labelled Katelysia rhytiphora shells (Mollusca, Bivalvia)
    Otter, Laura M.; Agbaje, Oluwatoosin B. A.; Kilburn, Matt R.; Lenz, Christoph; Henry, Hadrien; Trimby, Patrick; Hoppe, Peter; Jacob, Dorrit E.
    Biogeosciences (2019), 16 (17), 3439-3455CODEN: BIOGGR; ISSN:1726-4189. (Copernicus Publications)
    The intertidal bivalve Katelysia rhytiphora, endemic to south Australia and Tasmania, is used here for pulsed Sr-labeling expts. in aquaculture expts. to visualize shell growth at the micro- to nanoscale. The ventral margin area of the outer shell layer composed of (i) an outermost outer shell layer (oOSL) with compd. composite prismatic architecture with three hierarchical orders of prisms and (ii) an innermost outer shell layer (iOSL) with crossed-acicular architecture consisting of intersecting lamellae bundles. All structural orders in both layers are enveloped by an org. sheath and the smallest mineralized units are nano-granules. Electron backscatter diffraction reveals a strong preferred orientation of the aragonite c axes perpendicular to the growth layers, while the a and b axes are scattered within a plane normal to the local growth direction and >46 % twin grain boundaries are detected. The Young's modulus shows a girdle-like max. of elastically stiffer orientations for the shell following the inner shell surface. For 6 d, the bivalves were subjected twice to seawater with an increased Sr concn. of 18x mean ocean water by dissolving 144 μg g-1 Sr (159.88 Sr/Ca mmol / mol) in seawater. The pulse labeling intervals in the shell are 17x (oOSL) and 12x (iOSL) enriched in Sr relative to the Sr-spiked seawater. All architectural units in the shell are transected by the Sr label, demonstrating shell growth to progress homogeneously instead of forming one individual architectural unit after the other. Distribution coeffs., DSr / Ca, for labeled and unlabeled shells are similar to shell proportions formed in the wild (0.12 to 0.15). All DSr / Ca values are lower than values for equil. partitioning of Sr in synthetic aragonite.
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  38. 38
    Su, X.; Belcher, A. M.; Zaremba, C. M.; Morse, D. E.; Stucky, G. D.; Heuer, A. H. Structural and Microstructural Characterization of the Growth Lines and Prismatic Microarchitecture in Red Abalone Shell and the Microstructures of Abalone “Flat Pearls. Chem. Mater. 2002, 14 (7), 3106– 3117,  DOI: 10.1021/cm011739q
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    Structural and microstructural characterization of the growth lines and prismatic microarchitecture in red abalone shell and the microstructures of abalone "flat pearls"
    Su, Xiaowei; Belcher, Angela M.; Zaremba, Charlotte M.; Morse, Daniel E.; Stucky, Galen D.; Heuer, Arthur H.
    Chemistry of Materials (2002), 14 (7), 3106-3117CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    The structure of the growth lines in the shell of the red abalone, Haliotis rufescens, has been characterized by x-ray diffraction anal. and by scanning and TEM. The growth lines consist of a block-like microstructure and a spherulitic microstructure, sepd. by a green org. matrix interlayer. The minerals in both the block-like and spherulitic structures have been detd. to be aragonite, the same CaCO3 polymorph as in the nacreous microstructure in these shells. The spherulitic structure is composed of radially distributed elongated crystals, whereas the block like structure involves cryst. aggregates with irregular shape. The individual aggregates are approx. single crystal, with orientations identical to that of the adjacent stack of tablets in the nacreous structure. The interfaces defining the transition from nacreous to block like microstructures are abrupt; on the other hand, the transition from spherulitic to nacreous microstructures shows more irregularity because of the occasional intergrowth of elongated crystals into the nacreous region. The microstructures of flat pearls, produced by mineralization of an abiotic substrate (a glass cover slip) inserted between the mantle tissue and the growing edge of the shell in a live abalone, have also been studied. A thin calcitic CaCO3 layer is produced on the center of the glass substrate, which is soon covered by green org. matrix. This matrix extends beyond the calcitic region; i.e., it can be secreted directly onto the glass. Mineralization of this green matrix layer involves the deposition of spherulitic aragonite, similar to that occurring in the native shell, which is then capped by nacreous aragonite. Thus, the microstructures within the flat pearls mimic very closely certain aspects of the microstructures within the growth lines of the native shell.
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  39. 39
    Cartwright, J. H. E.; Checa, A. G.; Escribano, B.; Sainz-Díaz, C. I. Spiral and Target Patterns in Bivalve Nacre Manifest a Natural Excitable Medium from Layer Growth of a Biological Liquid Crystal. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (26), 10499– 10504,  DOI: 10.1073/pnas.0900867106
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    Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal
    Cartwright, Julyan H. E.; Checa, Antonio G.; Escribano, Bruno; Ignacio Sainz-Diaz, C.
    Proceedings of the National Academy of Sciences of the United States of America (2009), 106 (26), 10499-10504, S10499/1-S10499/5CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Nacre is an exquisitely structured biocomposite of the calcium carbonate mineral aragonite with small amts. of proteins and the polysaccharide chitin. For many years, it has been the subject of research, not just because of its beauty, but also to discover how nature can produce such a superior product with excellent mech. properties from such relatively weak raw materials. Four decades ago, Wada proposed that the spiral patterns in nacre could be explained by using the theory Frank had put forward of the growth of crystals by means of screw dislocations. Frank's mechanism of crystal growth has been amply confirmed by exptl. observations of screw dislocations in crystals, but it is a growth mechanism for a single crystal, with growth fronts of mols. However, the growth fronts composed of many tablets of cryst. aragonite visible in micrographs of nacre are not a mol.-scale but a mesoscale phenomenon, so it has not been evident how the Frank mechanism might be of relevance. Here, we demonstrate that nacre growth is organized around a liq.-crystal core of chitin crystallites, a skeleton that the other components of nacre subsequently flesh out in a process of hierarchical self-assembly. We establish that spiral and target patterns can arise in a liq. crystal formed layer by layer through the Burton-Cabrera-Frank dynamics, and furthermore that this layer growth mechanism is an instance of an important class of phys. systems termed excitable media. Artificial liq. crystals grown in this way may have many technol. applications.
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    Cartwright, J. H. E.; Checa, A. G. The Dynamics of Nacre Self-Assembly. J. R. Soc., Interface 2007, 4, 491– 504,  DOI: 10.1098/rsif.2006.0188
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    The dynamics of nacre self-assembly
    Cartwright, Julyan H. E.; Checa, Antonio G.
    Journal of the Royal Society, Interface (2007), 4 (14), 491-504CODEN: JRSICU; ISSN:1742-5689. (Royal Society)
    The authors show how nacre and pearl construction in bivalve and gastropod mollusks can be understood in terms of successive processes of controlled self-assembly from the mol.- to the macro-scale. This dynamics involves the physics of the formation of both solid and liq. crystals and of membranes and fluids to produce a nanostructured hierarchically constructed biol. composite of polysaccharides, proteins and mineral, whose mech. properties far surpass those of its component parts.
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    Taylor, P. D.; Vinn, O.; Wilson, M. A. Evolution of Biomineralization in ‘Lophophorates’;. Spec. Pap. Paleontol. 2010, 84, 317– 333
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    Checa, A. G.; Esteban-Delgado, F. J.; Rodriguez-Navarro, A. B. Crystallographic Structure of the Foliated Calcite of Bivalves. J. Struct. Biol. 2007, 157, 393– 402,  DOI: 10.1016/j.jsb.2006.09.005
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    Crystallographic structure of the foliated calcite of bivalves
    Checa, Antonio G.; Esteban-Delgado, Francisco J.; Rodriguez-Navarro, Alejandro B.
    Journal of Structural Biology (2007), 157 (2), 393-402CODEN: JSBIEM; ISSN:1047-8477. (Elsevier)
    The foliated layer of bivalves is constituted by platy calcite crystals, or laths, surrounded by an org. layer, and which are arranged into sheets (folia). Therefore, the foliated microstructure can be considered the calcitic analog to nacre. In this paper, the foliated microstructure has been studied in detail using electron and X-ray diffraction techniques, together with SEM observations on naturally decalcified shells, to investigate the crystallog. organization on different length scales and to resolve among previous contradictory results. This layer is highly organized and displays a coherent crystallog. orientation. The surface of the laths of the foliated layer is constituted by calcite crystals oriented with their c-axis tilted opposite to the growth direction of the laths and one of its {1 0 ‾1 4} rhombohedral faces looking in the growth direction. These faces are only expressed as the terminal faces of the laths, whereas the main surfaces of laths coincide with {1 0 ‾1 8} rhombohedral faces. This arrangement was consistently found in all specimens studied, which leads us to the provisional conclusion that, unlike previous studies, there is only one possible crystallog. arrangement for the foliated layer. Future studies on other species will help to ascertain this assertion.
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    Checa, A. G.; Sánchez-Navas, A.; Rodriguez-Navarro, A. Crystal Growth in the Foliated Aragonite of Monoplacophorans (Mollusca). Cryst. Growth Des. 2009, 9, 4574– 4580,  DOI: 10.1021/cg9005949
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    Crystal Growth in the Foliated Aragonite of Monoplacophorans (Mollusca)
    Checa, Antonio G.; Sanchez-Navas, Antonio; Rodriguez-Navarro, Alejandro
    Crystal Growth & Design (2009), 9 (10), 4574-4580CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    Crystal-growth features of the foliated aragonite from two species of the rare monoplacophoran molluscs have been analyzed. The crystals have unique morphologies. They are very thin along the c axis and elongated along the a axis, and their arrangement varies depending on the species. Surface energy minimization in the crystal arrangement obsd. in Micropilina leads to a discrete no. of const. angular relationships, which is explained by twin laws and epitaxy. Textural anal. shows that crystals form oriented aggregates with their c axes perpendicular to the shell surface. Close to the shell margin, crystals compete so as to orient their a axes nearly perpendicular to the growth front of the lamellae, although the scattering of the a axis soon increases toward the shell interior. In contrast to inorg. crystals, growth along the c axis is inhibited by org. mols. Their incorporation may be related to the existence of weak intermol. interactions between CO3 groups along this axis. Conversely, there is no chem. affinity to incorporate org. mols. along the a axis, where particularly short CO3-Ca ionic bonds occur. These structural factors explain the formation of crystals which are elongated and free of org. inclusions along the a axis.
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    New approaches to chemical patterns
    Johnson, Barry R.; Scott, Stephen K.
    Chemical Society Reviews (1996), 25 (4), 265-273CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review with 35 refs.; we survey the various new observations made along the route to taming of so-called Turing Structures in the lab. and attempt to set these in the context of their relevance in chem. and other areas of science.
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    Benzerara, K.; Menguy, N.; Obst, M.; Stolarski, J.; Mazur, M.; Tylisczak, T.; Brown, G. E.; Meibom, A. Study of the Crystallographic Architecture of Corals at the Nanoscale by Scanning Transmission X-Ray Microscopy and Transmission Electron Microscopy. Ultramicroscopy 2011, 111 (8), 1268– 1275,  DOI: 10.1016/j.ultramic.2011.03.023
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    Study of the crystallographic architecture of corals at the nanoscale by scanning transmission X-ray microscopy and transmission electron microscopy
    Benzerara, Karim; Menguy, Nicolas; Obst, Martin; Stolarski, JarosLaw; Mazur, Maciej; Tylisczak, Tolek; Brown, Gordon E., Jr.; Meibom, Anders
    Ultramicroscopy (2011), 111 (8), 1268-1275CODEN: ULTRD6; ISSN:0304-3991. (Elsevier B.V.)
    We have investigated the nanotexture and crystallog. orientation of aragonite in a coral skeleton using synchrotron-based scanning transmission X-ray microscopy (STXM) and transmission electron microscopy (TEM). Polarization-dependent STXM imaging at 40-nm spatial resoln. was used to obtain an orientation map of the c-axis of aragonite on a focused ion beam milled ultrathin section of a Porites coral. This imaging showed that one of the basic units of coral skeletons, referred to as the center of calcification (COC), consists of a cluster of 100-nm aragonite globules crystallog. aligned over several micrometers with a fan-like distribution and with the properties of single crystals at the mesoscale. The remainder of the skeleton consists of aragonite single-crystal fibers in crystallog. continuity with the nanoglobules comprising the COC. Our observation provides information on the nm-scale processes that led to biomineral formation in this sample. Importantly, the present study illustrates how the methodol. described here, which combines HRTEM and polarization-dependent synchrotron-based STXM imaging, offers an interesting new approach for investigating biomineralizing systems at the nm-scale.
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    Nothdurft, L. D.; Webb, G. E. Microstructure of Common Reef-Building Coral Genera Acropora, Pocillopora, Goniastrea and Porites: Constraints on Spatial Resolution in Geochemical Sampling. Facies 2007, 53 (1), 1– 26,  DOI: 10.1007/s10347-006-0090-0
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    Vielzeuf, D.; Garrabou, J.; Baronnet, A.; Grauby, O.; Marschal, C. Nano to Macroscale Biomineral Architecture of Red Coral (Corallium rubrum). Am. Mineral. 2008, 93 (11–12), 1799– 1815,  DOI: 10.2138/am.2008.2923
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    Nano to macroscale biomineral architecture of red coral (Corallium rubrum)
    Vielzeuf, Daniel; Garrabou, Joaquim; Baronnet, Alain; Grauby, Olivier; Marschal, Christian
    American Mineralogist (2008), 93 (11-12), 1799-1815CODEN: AMMIAY; ISSN:0003-004X. (Mineralogical Society of America)
    Different techniques have been used to characterize the phys. and chem. structure of the red coral calcitic skeleton. A section normal to the axis of the skeleton shows a medullar zone surrounded by a circular domain composed of concentric rings. Growth rings are revealed by the cyclic variation of org. matter (OM) and Mg/Ca ratio. These growth rings are annual; thus, both OM and Mg/Ca ratio can be used to date red coral colonies. Growth rings display wavelets. The internal structure of each wavelet results from the stacking of layers with tortuous interfaces. Tortuosity is due to the presence of microprotuberances. Interfaces between layers may display sharp discontinuities indicative of interruption of the mineralizing process. SEM and TEM studies show that each layer is made of (1) fibers, organized or not in fan-shaped structures; and (2) submicrometer (apparently mono-) cryst. units. Fibers are superstructures made of submicrometer units possibly assembled by an oriented aggregation mechanism. HRTEM studies show that in spite of displaying single-crystal scattering behavior, the submicrometer cryst. units are made of 2-5 nm nanograins again possibly aggregated by a mechanism of oriented attachment. Thus, submicrometer cryst. units and polycryst. fibers can be both defined as mesocrystals. The red coral skeleton is a hierarchically organized org.-inorg. composite that exhibits porosity and structural and compositional order on length scales from the nanoscale to the macroscale.
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    van de Locht, R.; Verch, A.; Saunders, M.; Dissard, D.; Rixen, T.; Moya, A.; Kröger, R. Microstructural Evolution and Nanoscale Crystallography in Scleractinian Coral Spherulites. J. Struct. Biol. 2013, 183 (1), 57– 65,  DOI: 10.1016/j.jsb.2013.05.005
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    Microstructural evolution and nanoscale crystallography in scleractinian coral spherulites
    van de Locht, Renee; Verch, Andreas; Saunders, Martin; Dissard, Delphine; Rixen, Tim; Moya, Aurelie; Kroger, Roland
    Journal of Structural Biology (2013), 183 (1), 57-65CODEN: JSBIEM; ISSN:1047-8477. (Elsevier Inc.)
    One of the most important aspects in the research on reef-building corals is the process by which corals accrete biogenic calcium carbonate. This process leads to the formation of a mineral/org. composite and it is believed that the development of the nano- and microstructure of the mineral phase is highly sensitive to the growth conditions. Transmission electron microscopy (TEM) anal. of large-scale (10 × 30 μm) focused ion beam (FIB) prepd. lamellae was performed on adult and juvenile scleractinian coral skeleton specimens. This allowed for the investigation of the nano- and microstructure and the crystallog. orientation of the aragonite mineral. We found the following microstructural evolution in the adult Porites lobata specimens: randomly oriented nanocrystals with high porosity, partly aligned nanocrystals with high porosity and areas of dense acicular crystals of several micrometers extension, the latter 2 areas are aligned close to the [0 0 1] direction (Pmcn space group). To the best of our knowledge, for the 1st time the obsd. microstructure could be directly correlated with the dark/bright bands characteristic of the diurnal growth cycle. We hypothesize that this mineral structure sequence and alignment in the adult specimen is linked to the photosynthetic diurnal cycle of the zooxanthellea regulating the oxygen levels and org. mol. transport to the calcifying medium. These observations reveal a strong control of crystal morphol. by the organism and the correlation of the accretion process. No indication for a self-assembly of nanocryst. units, i.e., a mesocrystal structure, on the micrometer scale could be found.
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  50. 50
    Mass, T.; Drake, J. L.; Peters, E. C.; Jiang, W.; Falkowski, P. G. Immunolocalization of Skeletal Matrix Proteins in Tissue and Mineral of the Coral Stylophora pistillata. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (35), 12728– 12733,  DOI: 10.1073/pnas.1408621111
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    Immunolocalization of skeletal matrix proteins in tissue and mineral of the coral Stylophora pistillata
    Mass, Tali; Drake, Jeana L.; Peters, Esther C.; Jiang, Wenge; Falkowski, Paul G.
    Proceedings of the National Academy of Sciences of the United States of America (2014), 111 (35), 12728-12733CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    By using immunogold labeling and immunohistochem. assays, we show the spatial arrangement of key matrix proteins in tissue and skeleton of the common zooxanthellate coral, Stylophora pistillata. Our results reveal for the 1st time that, at the nanoscale, skeletal proteins are embedded within the aragonite crystals in a highly ordered arrangement consistent with a diel calcification pattern. In the tissue, these proteins are not restricted to the calcifying epithelium, suggesting that they also play other roles in the coral's metabolic pathways.
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    Marin, F.; Luquet, G. Molluscan Shell Proteins. Comptes Rendus Palevol 2004, 3 (6–7), 469– 492,  DOI: 10.1016/j.crpv.2004.07.009
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    Weiner, S.; Addadi, L. Crystallization Pathways in Biomineralization. Annu. Rev. Mater. Res. 2011, 41 (1), 21– 40,  DOI: 10.1146/annurev-matsci-062910-095803
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    Crystallization pathways in biomineralization
    Weiner, Steve; Addadi, Lia
    Annual Review of Materials Research (2011), 41 (), 21-40CODEN: ARMRCU; ISSN:1531-7331. (Annual Reviews Inc.)
    A review. A crystn. pathway describes the movement of ions from their source to the final product. Cells are intimately involved in biol. crystn. pathways. In many pathways the cells utilize a unique strategy: They temporarily conc. ions in intracellular membrane-bound vesicles in the form of a highly disordered solid phase. This phase is then transported to the final mineralization site, where it is destabilized and crystallizes. The authors present 4 case studies, each of which demonstrates specific aspects of biol. crystn. pathways: (1) seawater uptake by foraminifera; (2) calcite spicule formation by sea urchin larvae; (3) goethite formation in the teeth of limpets; and (4) guanine crystal formation in fish skin and spider cuticles. Three representative crystn. pathways are described, and aspects of the different stages of crystn. are discussed. An in-depth understanding of these complex processes can lead to new ideas for synthetic crystn. processes of interest to materials science.
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    De Yoreo, J. J.; Gilbert, P. U. P. A.; Sommerdijk, N. A. J. M.; Penn, R. L.; Whitelam, S.; Joester, D.; Zhang, H.; Rimer, J. D.; Navrotsky, A.; Banfield, J. F.; Wallace, A. F.; Michel, F. M.; Meldrum, F. C.; Colfen, H.; Dove, P. M. Crystallization by Particle Attachment in Synthetic, Biogenic, and Geologic Environments. Science 2015, 349 (6247), aaa6760  DOI: 10.1126/science.aaa6760
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    Mass, T.; Giuffre, A. J.; Sun, C. Y.; Stifler, C. A.; Frazier, M. J.; Neder, M.; Tamura, N.; Stan, C. V.; Marcus, M. A.; Gilbert, P. U. P. A. Amorphous Calcium Carbonate Particles Form Coral Skeletons. Proc. Natl. Acad. Sci. U. S. A. 2017, 114 (37), E7670– E7678,  DOI: 10.1073/pnas.1707890114
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    Amorphous calcium carbonate particles form coral skeletons
    Mass, Tali; Giuffre, Anthony J.; Sun, Chang-Yu; Stifler, Cayla A.; Frazier, Matthew J.; Neder, Maayan; Tamura, Nobumichi; Stan, Camelia V.; Marcus, Matthew A.; Gilbert, Pupa U. P. A.
    Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (37), E7670-E7678CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Do corals form their skeletons by pptn. from soln. or by attachment of amorphous precursor particles as obsd. in other minerals and biominerals. The classical model assumes pptn. in contrast with obsd. "vital effects," i.e., deviations from elemental and isotopic compns. at thermodn. equil. Here, we show direct spectromicroscopy evidence in Stylophora pistillata corals that two amorphous precursors exist, one hydrated and one anhyd. amorphous calcium carbonate (ACC); that these are formed in the tissue as 400-nm particles; and that they attach to the surface of coral skeletons, remain amorphous for hours, and finally, crystallize into aragonite (CaCO3). We show in both coral and synthetic aragonite spherulites that crystal growth by attachment of ACC particles is more than 100 times faster than ion-by-ion growth from soln. Fast growth provides a distinct physiol. advantage to corals in the rigors of the reef, a crowded and fiercely competitive ecosystem. Corals are affected by warming-induced bleaching and postmortem dissoln., but the finding here that ACC particles are formed inside tissue may make coral skeleton formation less susceptible to ocean acidification than previously assumed. If this is how other corals form their skeletons, perhaps this is how a few corals survived past CO2 increases, such as the Paleocene-Eocene Thermal Maximum that occurred 56 Mya.
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    Dorvee, J. R.; Veis, A. Water in the Formation of Biogenic Minerals: Peeling Away the Hydration Layers. J. Struct. Biol. 2013, 183 (2), 278– 303,  DOI: 10.1016/j.jsb.2013.06.007
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    Water in the formation of biogenic minerals: Peeling away the hydration layers
    Dorvee, Jason R.; Veis, Arthur
    Journal of Structural Biology (2013), 183 (2), 278-303CODEN: JSBIEM; ISSN:1047-8477. (Elsevier Inc.)
    A review. Minerals of biogenic origin form and crystallize from aq. environments at ambient temps. and pressures. The in vivo environment either intracellular or intercellular, contains many components that modulate both the activity of the ions which assoc. to form the mineral, as well as the activity and structure of the crowded water. Most of the studies about the mechanism of mineralization, i.e., the detailed pathways by which the mineral ions proceed from soln. to crystal state, have been carried out in relatively dil. solns. and clean solns. These studies have considered both thermodn. and kinetic controls. Most have not considered the water itself. Is the water a passive bystander, or is it intimately a participant in the mineral ion densification reaction A wide range of expts. show that the mineralization pathways proceed through a series of densification stages with intermediates, such as a "dense liq." phase and the prenucleation clusters that form within it. This is in contrast to the idea of a single step phase transition, but consistent with the Gibbs concept of discontinuous phase transitions from supersatd. mother liquor to crystal. Further changes in the water structure at every surface and interface during densification guides the free energy trajectory leading to the cryst. state. In vertebrates, mineralization takes place in a hydrated collagen matrix, thus water must be considered as a direct participant. Although different in detail, the crystn. of calcium phosphates, as apatite, and calcium carbonates, as calcite, are mechanistically identical from the viewpoint of water.
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    Bots, P.; Benning, L. G.; Rodriguez-Blanco, J. D.; Roncal-Herrero, T.; Shaw, S. Mechanistic Insights into the Crystallization of Amorphous Calcium Carbonate (ACC). Cryst. Growth Des. 2012, 12 (7), 3806– 3814,  DOI: 10.1021/cg300676b
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    Mechanistic Insights into the Crystallization of Amorphous Calcium Carbonate (ACC)
    Bots, Pieter; Benning, Liane G.; Rodriguez-Blanco, Juan-Diego; Roncal-Herrero, Teresa; Shaw, Samuel
    Crystal Growth & Design (2012), 12 (7), 3806-3814CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    Many organisms use amorphous calcium carbonate (ACC) during cryst. calcium carbonate biomineralization, as a means to control particle shape/size and phase stability. An in situ small- and wide-angle X-ray scattering (SAXS/WAXS) study is presented of the mechanisms and kinetics of ACC crystn. at rapid time scales (seconds). Combined with offline solid and soln. characterization, the authors show that ACC crystallizes to vaterite via a three-stage process. First, hydrated and disordered ACC forms, then rapidly transforms to more ordered and dehydrated ACC; in conjunction with this, vaterite forms via a spherulitic growth mechanism. Second, when the supersatn. of the soln. with respect to vaterite decreases sufficiently, the mechanism changes to ACC dissoln. and vaterite crystal growth. The third stage is controlled by Ostwald ripening of the vaterite particles. Combining this information with previous studies, allowed development of a mechanistic understanding of the abiotic crystn. process from ACC to vaterite and all the way to calcite. This is the underlying abiotic mechanism for calcium carbonate biomineralization from ACC. This process is then augmented or altered by organisms (e.g., using org. compds.) to form intricate biominerals. This study also highlights the applicability of in situ time-resolved SAXS/WAXS to study rapid crystn. reactions.
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    Jones, D. S. Annual Cycle of Shell Growth Increment Formation in Two Continental Shelf Bivalves and its Paleoecologic Significance. Paleobiology 1980, 6 (3), 331– 340,  DOI: 10.1017/S0094837300006837
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    Tanabe, K.; Miyaji, T.; Murakami-Sugihara, N.; Shirai, K.; Moriya, K. Annual Shell Growth Patterns of Three Venerid Bivalve Mollusk Species in the Subtropical Northwestern Pacific as Revealed by Sclerochronological and Stable Oxygen Isotope Analyses. Mar. Biol. 2020, 167 (2), 20,  DOI: 10.1007/s00227-019-3637-7
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    Annual shell growth patterns of three venerid bivalve mollusk species in the subtropical northwestern Pacific as revealed by sclerochronological and stable oxygen isotope analyses
    Tanabe, Kazushige; Miyaji, Tsuzumi; Murakami-Sugihara, Naoko; Shirai, Kotaro; Moriya, Kazuyoshi
    Marine Biology (Heidelberg, Germany) (2020), 167 (2), 20CODEN: MBIOAJ; ISSN:0025-3162. (Springer)
    Annual shell growth patterns of the three venerid bivalve species, Gafrarium pectinatum, Pitar citrinus, and Katelysia japonica were investigated based on the results of sclerochronol. and stable oxygen isotope analyses of live-caught specimens from the intertidal zone of Iriomote Island, southern Ryukyu Archipelago. In the study area, these three species temporally stopped shell deposition, when sea surface temp. (SST) dropped to 23-26°C, during the first three years. However, the shutdown temp. for shell growth increased slightly to higher than 26°C after 6 years old for G. pectinatum combined with a shortening in the length of shell growing period. Seasonal changes in daily shell growth in these species were controlled mainly by SST and primary prodn. Shell δ18O-derived summer temps. recorded in the annual increments were higher by 3-5°C than the highest SST records of the habitat. This data mismatch might be caused by an abrupt decrease in seawater δ18O values during the summer and fall typhoon seasons because of the influx of fresh water into the study area from nearby rivers. This study suggests that in the study area the annual shell growth patterns and shell δ18O values in the three species examd. were controlled by mutually related biol. and environmental factors such as ontogenetic age and seasonal changes in SST, salinity and primary prodn.
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    Yamanashi, J.; Takayanagi, H.; Isaji, A.; Asami, R.; Iryu, Y. Carbon and Oxygen Isotope Records from Tridacna derasa Shells: Toward Establishing a Reliable Proxy for Sea Surface Environments. PLoS One 2016, 11 (6), e0157659  DOI: 10.1371/journal.pone.0157659
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    Carbon and oxygen isotope records from Tridacna derasa shells: toward establishing a reliable proxy for sea surface environments
    Yamanashi, Junpei; Takayanagi, Hideko; Isaji, Ayaka; Asami, Ryuji; Iryu, Yasufumi
    PLoS One (2016), 11 (6), e0157659/1-e0157659/19CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
    We report the carbon (δ13C) and oxygen (δ18O) isotope records of three modern Tridacna derasa shells from Ishigaki-jima, southwestern Japan. The high-resoln. δ13C profiles of samples from the inner shell layer on cross-sections fall within similar narrow ranges and display no regular variations or trends, such as an ontogenetic trend or abrupt short-term drops likely to be related to reproductive activity. This suggests that the calcification site of this species is not likely affected by photosynthetic CO2 uptake or CO2 incorporation during respiration. The δ18O profiles show distinct seasonal cycles. The intraspecific variability in the δ18O values is small in parts of the shell pptd. in the adult stage, but is not negligible in the juvenile and senescent stages. The differences in the monthly and seasonally resolved δ18O values among shells are less than 0.51‰ and 0.76‰, resp. The shell δ18O values are nearly identical or close to the δ18O values for aragonite pptd. in oxygen isotope equil. with ambient seawater (δ18OEA). The largest differences between the shell δ18O and δ18OEA values calcd. from the monthly and seasonally resolved data correspond to an overestimate of the seawater temp. by as much as 1.7°C and 2.3°C, resp. However, these differences are smaller in the adult stage (<0.25‰) than in the other stages. This small difference allows an accurate reconstruction of the seawater temp. with an error of <1.1°C. Consequently, we recommend that multiple shell records be obtained because of the non-negligible intraspecific variations in their δ18O values. Growth banding, composed of alternating narrow white bands and wide light-gray bands, is discernible on cross-sections of the inner shell layer. The δ18Oshell data indicate that they were formed in winter and the other seasons, resp.
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    Serbina, E. A. Shell as an Indicator of the Growth Rate of Freshwater Gastropods of the Family Bithyniidae. Contemporary Problems of Ecology 2010, 3 (1), 19– 27,  DOI: 10.1134/S1995425510010054
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    Edinger, E. N.; Limmon, G. V.; Jompa, J.; Widjatmoko, W.; Heikoop, J. M.; Risk, M. J. Normal Coral Growth Rates on Dying Reefs: Are Coral Growth Rates Good Indicators of Reef Health?. Mar. Pollut. Bull. 2000, 40 (5), 404– 425,  DOI: 10.1016/S0025-326X(99)00237-4
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    Normal coral growth rates on dying reefs: are coral growth rates good indicators of reef health?
    Edinger, Evan N.; Limmon, Gino V.; Jompa, Jamaluddin; Widjatmoko, Wisnu; Heikoop, Jeffrey M.; Risk, Michel J.
    Marine Pollution Bulletin (2000), 40 (5), 404-425CODEN: MPNBAZ; ISSN:0025-326X. (Elsevier Science Ltd.)
    Massive coral growth rates may be poor indicators of coral reef health where coral reefs are subject to combined eutrophication and sedimentation. Massive coral growth (vertical extension) rates on polluted reefs were not different from extension rates on unpolluted reefs, while live coral cover was low and bioerosion intensity high, leading to net reef erosion and death of the polluted reefs. These combined patterns of coral growth rates, coral cover, and bioerosion were documented on reefs affected by land-based pollution in the Java Sea, South Sulawesi and Ambon, Indonesia. Acid-insol. content in coral skeletons reflected land-based pollution stress on reefs more reliably than did coral extension rates. Coral skeletal d. was lower on polluted Java Sea reefs than on unpolluted reefs used as ref. sites, but coral calcification rates were not significantly different. The most eutrophied Java Sea reefs had net carbonate loss, indicating net reef erosion, while a fringing reef adjacent to mangroves and 2 unpolluted coral cays both had pos. net carbonate prodn. Coral growth and reef growth were decoupled, in that coral growth rates did not reliably predict rates of reef accretion. The apparently paradoxical combination of normal to rapid coral growth and net reef erosion on polluted reefs illustrates the need for a whole-reef perspective on coral reef health.
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    Anderson, K. D.; Cantin, N. E.; Heron, S. F.; Pisapia, C.; Pratchett, M. S. Variation in Growth Rates of Branching Corals along Australia’s Great Barrier Reef. Sci. Rep. 2017, 7, 2920,  DOI: 10.1038/s41598-017-03085-1
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    Variation in growth rates of branching corals along Australia's Great Barrier Reef
    Anderson Kristen D; Pisapia Chiara; Pratchett Morgan S; Anderson Kristen D; Cantin Neal E; Heron Scott F; Heron Scott F; Heron Scott F
    Scientific reports (2017), 7 (1), 2920 ISSN:.
    Coral growth is an important component of reef health and resilience. However, few studies have investigated temporal and/or spatial variation in growth of branching corals, which are important contributors to the structure and function of reef habitats. This study assessed growth (linear extension, density, and calcification) of three branching coral species (Acropora muricata, Pocillopora damicornis and Isopora palifera) at three distinct locations (Lizard Island, Davies/Trunk Reef, and Heron Island) along Australia's Great Barrier Reef (GBR). Annual growth rates of all species were highest at Lizard Island and declined with increasing latitude, corresponding with differences in temperature. Within locations, however, seasonal variation in growth did not directly correlate with temperature. Between October 2012 and October 2014, the highest growth of A. muricata was in the 2013-14 summer at Lizard Island, which was unusually cool and ~0.5 °C less than the long-term summer average temperature. At locations where temperatures reached or exceeded the long-term summer maxima, coral growth during summer periods was equal to, if not lower than, winter periods. This study shows that temperature has a significant influence on spatiotemporal patterns of branching coral growth, and high summer temperatures in the northern GBR may already be constraining coral growth and reef resilience.
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    Weil, E.; Hammerman, N. M.; Becicka, R. L.; Cruz-Motta, J. J. Growth Dynamics in Acropora cervicornis and A. prolifera in Southwest Puerto Rico. PeerJ 2020, 8, e8435  DOI: 10.7717/peerj.8435
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    Chen, L. Q.; Yang, W. Computer Simulation of the Domain Dynamics of a Quenched System with a Large Number of Nonconserved Order Parameters: The Grain-Growth Kinetics. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50 (21), 15752– 15756,  DOI: 10.1103/PhysRevB.50.15752
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    Steinbach, I.; Pezzolla, F.; Nestler, B.; Seeßelberg, M.; Prieler, R.; Schmitz, G. J.; Rezende, J. L. L. A Phase Field Concept for Multiphase Systems. Phys. D 1996, 94 (3), 135– 147,  DOI: 10.1016/0167-2789(95)00298-7
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    Folch, R.; Plapp, M. Publisher’s Note: Quantitative Phase-Field Modeling of Two-Phase Growth. Phys. Rev. E 2005, 72 (2), 011602,  DOI: 10.1103/PhysRevE.72.011602
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    Quantitative phase-field modeling of two-phase growth
    Folch, R.; Plapp, M.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2005), 72 (1-1), 011602/1-011602/27CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    A phase-field model that allows for quant. simulations of low-speed eutectic and peritectic solidification under typical exptl. conditions is developed. Its cornerstone is a smooth free-energy functional, specifically designed so that the stable solns. that connect any two phases are completely free of the third phase. For the simplest choice for this functional, the equations of motion for each of the two solid-liq. interfaces can be mapped to the std. phase-field model of single-phase solidification with its quartic double-well potential. By applying the thin-interface asymptotics and by extending the antitrapping current previously developed for this model, all spurious corrections to the dynamics of the solid-liq. interfaces linear in the interface thickness W can be eliminated. This means that, for small enough values of W, simulation results become independent of it. As a consequence, accurate results can be obtained using values of W much larger than the phys. interface thickness, which yields a tremendous gain in computational power and makes simulations for realistic exptl. parameters feasible. Convergence of the simulation outcome with decreasing W is explicitly demonstrated. Furthermore, the results are compared to a boundary-integral formulation of the corresponding free-boundary problem. Excellent agreement is found, except in the immediate vicinity of bifurcation points, a very sensitive situation where noticeable differences arise. These differences reveal that, in contrast to the std. assumptions of the free-boundary problem, out of equil. the diffuse trijunction region of the phase-field model can (i) slightly deviate from Young's law for the contact angles, and (ii) advance in a direction that forms a finite angle with the solid-solid interface at each instant. While the deviation (i) extrapolates to zero in the limit of vanishing interface thickness, the small angle in (ii) remains roughly const., which indicates that it might be a genuine phys. effect, present even for an at.-scale interface thickness.
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    Steinbach, I. Phase-Field Models in Materials Science. Modell. Simul. Mater. Sci. Eng. 2009, 17 (7), 073001,  DOI: 10.1088/0965-0393/17/7/073001
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    Phase-field models in materials science
    Steinbach, Ingo
    Modelling and Simulation in Materials Science and Engineering (2009), 17 (7), 073001/1-073001/31CODEN: MSMEEU; ISSN:1361-651X. (Institute of Physics Publishing)
    A review. The phase-field method is reviewed against its historical and theor. background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.
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    Bollada, P. C.; Jimack, P. K.; Mullis, A. M. A New Approach to Multi-Phase Formulation for the Solidification of Alloys. Phys. D 2012, 241 (8), 816– 829,  DOI: 10.1016/j.physd.2012.01.006
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    Kamachali, R. D.; Kim, S. J.; Steinbach, I. Texture Evolution in Deformed AZ31 Magnesium Sheets: Experiments and Phase-Field Study. Comput. Mater. Sci. 2015, 104, 193– 199,  DOI: 10.1016/j.commatsci.2015.04.006
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    Tóth, G. I.; Pusztai, T.; Gránásy, L. Consistent Multiphase-Field Theory for Interface Driven Multidomain Dynamics. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92 (18), 184105,  DOI: 10.1103/PhysRevB.92.184105
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    Consistent multiphase-field theory for interface driven multidomain dynamics
    Toth, Gyula I.; Pusztai, Tamas; Granasy, Laszlo
    Physical Review B: Condensed Matter and Materials Physics (2015), 92 (18), 184105/1-184105/19CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We present a multiphase-field theory for describing pattern formation in multidomain and/or multicomponent systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure math. and phys. consistency. We first analyze previous multiphase-field theories and identify their advantageous and disadvantageous features. On the basis of this anal., we introduce a way of constructing the free energy surface and derive a generalized multiphase description for arbitrary no. of phases (or domains). The presented approach retains the variational formalism, reduces (or extends) naturally to lower (or higher) no. of fields on the level of both the free energy functional and the dynamic equations, enables the use of arbitrary pairwise equil. interfacial properties, penalizes multiple junctions increasingly with the no. of phases, ensures non-neg. entropy prodn. and the convergence of the dynamic solns. to the equil. solns., and avoids the appearance of spurious phases on binary interfaces. The approach is tested for multicomponent phase sepn. and grain coarsening.
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    Kobayashi, R.; Warren, J. A.; Carter, W. C. Vector-Valued Phase Field Model for Crystallization and Grain Boundary Formation. Phys. D 1998, 119 (3–4), 415– 423,  DOI: 10.1016/S0167-2789(98)00026-8
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    Vector-valued phase field model for crystallization and grain boundary formation
    Kobayashi, R.; Warren, J. A.; Carter, W. C.
    Physica D: Nonlinear Phenomena (Amsterdam) (1998), 119 (3-4), 415-423CODEN: PDNPDT; ISSN:0167-2789. (Elsevier Science B.V.)
    The authors propose a new model for calcn. of the crystn. and impingement of many particles with differing orientations. Based on earlier phase field models, a vector order parameter is introduced, and thus orientation of crystal/disordered interfaces can be detd. relative to a cryst. frame. This model improves upon previous attempts to describe this phenomenon, as it requires far fewer equations of motion, and is energetically invariant under rotations. A 1-dimensional simulation of the model will be presented along with preliminary studies of two-dimensional simulations.
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    Gránásy, L.; Börzsönyi, T.; Pusztai, T. Nucleation and Bulk Crystallization in Binary Phase Field Theory. Phys. Rev. Lett. 2002, 88 (20), 206105,  DOI: 10.1103/PhysRevLett.88.206105
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    Nucleation and Bulk Crystallization in Binary Phase Field Theory
    Granasy, Laszlo; Borzsonyi, Tamas; Pusztai, Tamas
    Physical Review Letters (2002), 88 (20), 206105/1-206105/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We present a phase field theory for binary crystal nucleation. In the one-component limit, quant. agreement is achieved with computer simulations (Lennard-Jones system) and expts. (ice-water system) using model parameters evaluated from the free energy and thickness of the interface. The crit. undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft impingement" of particles via diffusion fields are consistent with expt.
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  73. 73
    Warren, J. A.; Kobayashi, R.; Lobkovsky, A. E.; Craig Carter, W. Extending Phase Field Models of Solidification to Polycrystalline Materials. Acta Mater. 2003, 51 (20), 6035– 6058,  DOI: 10.1016/S1359-6454(03)00388-4
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    Extending phase-field models of solidification to polycrystalline materials
    Warren, James A.; Kobayashi, Ryo; Lobkovsky, Alexander E.; Carter, W. Craig
    Acta Materialia (2003), 51 (20), 6035-6058CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
    The 2-dimensional phase field model with grain boundary features is presented. The model includes microstructure implications with: the grain boundary energy as a function of misorientation; the 3-phase junction of liq.-grain-grain type; wetting condition for a grain boundary; and stabilized widths of intercalating phases at the grain boundaries. The evolution of a polycryst. microstructure is considered by solidification and impingement, followed by both grain boundary migration and grain rotation.
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  74. 74
    Gránásy, L.; Pusztai, T.; Warren, J. A.; Douglas, J. F.; Börzsönyi, T.; Ferreiro, V. Growth of ‘Dizzy Dendrites’ in a Random Field of Foreign Particles. Nat. Mater. 2003, 2 (2), 92– 96,  DOI: 10.1038/nmat815
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    Growth of 'dizzy dendrites' in a random field of foreign particles
    Granasy, Laszlo; Pusztai, Tamas; Warren, James A.; Douglas, Jack F.; Boerzsoenyi, Tamas; Ferreiro, Vincent
    Nature Materials (2003), 2 (2), 92-96CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    Microstructure plays an essential role in detg. the properties of cryst. materials. A widely used method to influence microstructure is the addn. of nucleating agents. Observations on films formed from clay-polymer blends indicate that particulate additives, in addn. to serving as nucleating agents, may also perturb crystal growth, leading to the formation of irregular dendritic morphologies. The formation of such dendrites is described using a phase-field theory, in which randomly distributed foreign particle inclusions perturb the crystn. by deflecting the tips of the growing dendrite arms. This mechanism of crystn., which is verified exptl., leads to a polycryst. structure dependent on particle configuration and orientation. Using computer simulations, it is demonstrated that additives of controlled crystal orientation should allow for a substantial manipulation of the crystn. morphol.
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    Gránásy, L.; Pusztai, T.; Börzsönyi, T.; Warren, J. A.; Douglas, J. F. A General Mechanism of Polycrystalline Growth. Nat. Mater. 2004, 3 (9), 645– 650,  DOI: 10.1038/nmat1190
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    A general mechanism of polycrystalline growth
    Granasy, Laszlo; Pusztai, Tamas; Boerzsoenyi, Tamas; Warren, James A.; Douglas, Jack F.
    Nature Materials (2004), 3 (9), 645-650CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    Most research into microstructure formation during solidification has focused on single-crystal growth ranging from faceted crystals to sym. dendrites. However, these growth forms can be perturbed by heterogeneities, yielding a rich variety of polycryst. growth patterns. Phase-field simulations show that the presence of particulates (for example, dirt) or a small rotational-translational mobility ratio (characteristic of high supercooling) in crystg. fluids give rise to similar growth patterns, implying a duality in the growth process in these structurally heterogeneous fluids. Similar crystn. patterns are also found in thin polymer films with particulate additives and pure films with high supercooling. This duality between the static and dynamic heterogeneity explains the ubiquity of polycryst. growth patterns in polymeric and other complex fluids.
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    Gránásy, L.; Pusztai, T.; Tegze, G.; Warren, J. A.; Douglas, J. F. Growth and Form of Spherulites. Phys. Rev. E 2005, 72 (1), 011615,  DOI: 10.1103/PhysRevE.72.011605
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    Gránásy, L.; Pusztai, T.; Warren, J. A. Modelling Polycrystalline Solidification Using Phase Field Theory. J. Phys.: Condens. Matter 2004, 16 (41), R1205– R1235,  DOI: 10.1088/0953-8984/16/41/R01
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    Modeling polycrystalline solidification using phase field theory
    Granasy, Laszlo; Pusztai, Tamas; Warren, James A.
    Journal of Physics: Condensed Matter (2004), 16 (41), R1205-R1235CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    The authors review recent advances made in the phase field modeling of polycryst. solidification. Areas covered include the development of theory from early approaches that allow for only a few crystal orientations, to the latest models relying on a continuous orientation field and a free energy functional that is invariant to the rotation of the lab. frame. The authors discuss a variety of phenomena, including homogeneous nucleation and competitive growth of cryst. particles having different crystal orientations, the kinetics of crystn., grain boundary dynamics, and the formation of complex polycryst. growth morphologies including disordered ('dizzy') dendrites, spherulites, fractal-like polycryst. aggregates, etc. Finally, the authors extend the approach by incorporating walls, and explore phenomena such as heterogeneous nucleation, particle-front interaction, and solidification in confined geometries (in channels or porous media).
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    Gránásy, L.; Rátkai, L.; Szállás, A.; Korbuly, B.; Tóth, G. I.; Környei, L.; Pusztai, T. Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites—A Review. Metall. Mater. Trans. A 2014, 45 (4), 1694– 1719,  DOI: 10.1007/s11661-013-1988-0
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    Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites-A Review
    Granasy, Laszlo; Ratkai, Laszlo; Szallas, Attila; Korbuly, Balint; Toth, Gyula I.; Kornyei, Laszlo; Pusztai, Tamas
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science (2014), 45 (4), 1694-1719CODEN: MMTAEB; ISSN:1073-5623. (Springer)
    A review. Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycryst. structures are shown as impinging sym. dendrites, polycryst. growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solns. assocd. with quant. PF simulations are discussed briefly.
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    Pusztai, T.; Bortel, G.; Gránásy, L. Phase Field Theory of Polycrystalline Solidification in Three Dimensions. Europhys. Lett. 2005, 71 (1), 131– 137,  DOI: 10.1209/epl/i2005-10081-7
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    Phase field theory of polycrystalline solidification in three dimensions
    Pusztai, T.; Bortel, G.; Granasy, L.
    Europhysics Letters (2005), 71 (1), 131-137CODEN: EULEEJ; ISSN:0295-5075. (EDP Sciences)
    A phase field theory of polycryst. solidification is presented that describes the nucleation and growth of anisotropic particles with different crystallog. orientation in three dimensions. As opposed to the two-dimensional case, where a single orientation field suffices, in three dimensions, a min. no. of three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four sym. Euler parameters. The equations of motion for these fields were obtained from variational principles. Illustrative calcns. were performed for polycryst. solidification with dendritic, needle and spherulitic growth morphologies.
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    Kobayashi, R.; Warren, J. A. Modeling the Formation and Dynamics of Polycrystals in 3D. Phys. A 2005, 356 (1), 127– 132,  DOI: 10.1016/j.physa.2005.05.024
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    Kobayashi, R.; Warren, J. A. Extending phase field models of grain boundaries to three dimensions. TMS Lett. 2005, 2, 1− 2. https://www.tms.org/membercontent/pdf/LET-0501-1.pdf.
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    Admal, N. C.; Segurado, J.; Marian, J. A Three-Dimensional Misorientation Axis- and Inclination-Dependent Kobayashi-Warren-Carter Grai Boundary Model. J. Mech. Phys. Solids 2019, 128, 32– 53,  DOI: 10.1016/j.jmps.2019.03.020
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    Gránásy, L.; Pusztai, T.; Saylor, D.; Warren, J. A. Phase Field Theory of Heterogeneous Crystal Nucleation. Phys. Rev. Lett. 2007, 98 (3), 035703,  DOI: 10.1103/PhysRevLett.98.035703
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    Phase Field Theory of Heterogeneous Crystal Nucleation
    Granasy, Laszlo; Pusztai, Tamas; Saylor, David; Warren, James A.
    Physical Review Letters (2007), 98 (3), 035703/1-035703/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The phase field approach is used to model heterogeneous crystal nucleation in an undercooled pure liq. in contact with a foreign wall. We discuss various choices for the boundary condition at the wall and det. the properties of crit. nuclei, including their free energy of formation and the contact angle as a function of undercooling. For particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly nonclassical behavior, where the contact angle decreases from its value taken at the m.p. towards complete wetting at a crit. undercooling, an analog of the surface spinodal of liq.-wall interfaces.
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    Pusztai, T.; Tegze, G.; Tóth, G. I.; Környei, L.; Bansel, G.; Fan, Z.; Gránásy, L. Phase-Field Approach to Polycrystalline Solidification Including Heterogeneous and Homogeneous Nucleation. J. Phys.: Condens. Matter 2008, 20 (40), 404205,  DOI: 10.1088/0953-8984/20/40/404205
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    Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
    Pusztai, Tamas; Tegze, Gyorgy; Toth, Gyula I.; Kornyei, Laszlo; Bansel, Gurvinder; Fan, Zhungyun; Granasy, Laszlo
    Journal of Physics: Condensed Matter (2008), 20 (40), 404205/1-404205/16CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    Advanced phase-field techniques were applied to address various aspects of polycryst. solidification including different modes of crystal nucleation. The height of the nucleation barrier was detd. by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single-component hard sphere fluid. Extending previous work for pure systems, heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallog. orientation of the individual particles was applied for modeling a broad variety of polycryst. structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombo-dodecahedral and truncated octahedral growth morphologies. Finally, the authors present illustrative results for dendritic polycryst. solidification obtained using an atomistic phase-field model.
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    Warren, J. A.; Pusztai, T.; Környei, L.; Gránásy, L. Phase Field Approach to Heterogeneous Crystal Nucleation in Alloys. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79 (1), 014204,  DOI: 10.1103/PhysRevB.79.014204
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    Phase field approach to heterogeneous crystal nucleation in alloys
    Warren, James A.; Pusztai, Tamas; Kornyei, Laszlo; Granasy, Laszlo
    Physical Review B: Condensed Matter and Materials Physics (2009), 79 (1), 014204/1-014204/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    The phase field model of heterogeneous crystal nucleation developed recently was extended to binary alloys. Three approaches incorporate foreign walls of tunable wetting properties into phase field simulations as a (1) continuum realization of the classical spherical cap model (2) non-classical approach that leads to ordering of the liq. at the wall and to the appearance of a surface spinodal (3) non-classical model that allows for the appearance of local states at the wall that are accessible in the bulk phases only by thermal fluctuations. The potential of the presented phase field methods is illustrated for describing complex polycryst. solidification morphols. including the shish-kebab structure, columnar-to-equiaxed transition, and front-particle interaction in binary alloys.
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    Gránásy, L.; Pusztai, T.; Douglas, J. F. Insights into Polymer Crystallization from Phase-Field Theory. In Encyclopedia of Polymers and Composites: A Reference Series; Palsule, S., Ed., Springer: Berlin, Heidelberg, 2013; p 1– 35.
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    Pusztai, T.; Rátkai, L.; Szállás, A.; Gránásy, L. Phase-Field Modeling of Solidification in Light-Metal Matrix Nanocomposites. In Magnesium Technology 2014; Alderman, M., Manuel, M. V., Hort, N., Neelameggham, N. R., Eds.; The Minerals, Metals and Materials Society/Wiley: Hoboken, 2014; p 455– 459.
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    Tegze, G.; Pusztai, T.; Gránásy, L. Phase Field Simulation of Liquid Phase Separation with Fluid Flow. Mater. Sci. Eng., A 2005, 413–414, 418– 422,  DOI: 10.1016/j.msea.2005.09.045
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    Phase field simulation of liquid phase separation with fluid flow
    Tegze, G.; Pusztai, T.; Granasy, L.
    Materials Science & Engineering, A: Structural Materials: Properties, Microstructure and Processing (2005), A413-A414 (), 418-422CODEN: MSAPE3; ISSN:0921-5093. (Elsevier B.V.)
    A phase-field theory of binary liq. phase sepn. coupled to fluid flow is presented. The resp. Cahn-Hilliard-type and Navier-Stokes equations are solved numerically. Compn. and temp. dependent capillary forces are incorporated. The free energies of the bulk liq. phases are taken from the regular soln. model. In the simulations, Marangoni motion, and direct and indirect hydrodynamic interactions between the drops are obsd. The coagulation is dramatically accelerated by flow effects. Possible extension of the model to solidification is discussed.
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    Tegze, G.; Gránásy, L. Phase Field Theory of Liquid Phase Separation and Solidification with Melt Flow. In Modeling and Casting, Welding and Advanced Solidification Processes - XI; Gandin, C. A., Bellet, M., Eds.; The Minerals, Metals, & Materials Soc.: Warrendale, 2006; p 513– 520.
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    Rátkai, L.; Pusztai, T.; Gránásy, L. Phase-Field Lattice Boltzmann Model for Dendrites Growing and Moving in Melt Flow. npj Comput. Mater. 2019, 5 (1), 113,  DOI: 10.1038/s41524-019-0250-8
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    Cai, B.; Wang, J.; Kao, A.; Pericleous, K.; Phillion, A. B.; Atwood, R. C.; Lee, P. D. 4D Synchrotron X-ray Tomographic Quantification of the Transition from Cellular to Dendrite Growth During Directional Solidification. Acta Mater. 2016, 117, 160– 169,  DOI: 10.1016/j.actamat.2016.07.002
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    4D synchrotron X-ray tomographic quantification of the transition from cellular to dendrite growth during directional solidification
    Cai, B.; Wang, J.; Kao, A.; Pericleous, K.; Phillion, A. B.; Atwood, R. C.; Lee, P. D.
    Acta Materialia (2016), 117 (), 160-169CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
    Solidification morphol. directly impacts the mech. properties of materials; hence many models of the morphol. evolution of dendritic structures have been formulated. However, there is a paucity of validation data for directional solidification models, esp. the direct observations of metallic alloys, both for cellular and dendritic structures. In this study, we performed 4D synchrotron X-ray tomog. imaging (three spatial directions plus time), to study the transition from cellular to a columnar dendritic morphol. and the subsequent growth of columnar dendrite in a temp. gradient stage. The cellular morphol. was found to be highly complex, with frequent lateral bridging. Protrusions growing out of the cellular front with the onset of morphol. instabilities were captured, together with the subsequent development of these protrusions into established dendrites. Other mechanisms affecting the solidification microstructure, including dendrite fragmentation/pinch-off were also captured and the quant. results were compared to proposed mechanisms. The results demonstrate that 4D imaging can provide new data to both inform and validate solidification models.
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    Shuai, S.; Guo, E.; Phillion, A. B.; Callaghan, M. D.; Jing, T.; Lee, P. D. Fast Synchrotron X-ray Tomographic Quantification of Dendrite Evolution During the Solidification of Mg. Sn alloys. Acta Mater. 2016, 118, 260– 269,  DOI: 10.1016/j.actamat.2016.07.047
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    Fast synchrotron X-ray tomographic quantification of dendrite evolution during the solidification of Mg-Sn alloys
    Shuai, Sansan; Guo, Enyu; Phillion, A. B.; Callaghan, Mark D.; Jing, Tao; Lee, Peter D.
    Acta Materialia (2016), 118 (), 260-269CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
    The evolution of dendritic microstructures during the solidification of a Mg-15 wt%Sn alloy was investigated in situ via fast synchrotron X-ray microtomog. To enable these in situ observations a novel encapsulation method was developed and integrated into a fast, pink beam, imaging beam-line at Diamond Light Source. The dendritic growth was quantified with time using: solid vol. fraction, tip velocity, interface sp. surface area, and surface curvature. The influence of cooling rate upon these quantities and primary phase nucleation was investigated. The primary dendrites grew with an 18-branch, 6-fold symmetry structure, accompanied by coarsening. The coarsening process was assessed by the sp. surface area and was compared with the existing models. These results provide the first quantification of dendritic growth during the solidification of Mg alloys, confirming existing analytic models and providing exptl. data to inform and validate more complex numeric models.
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    Ojeda, J. R.; Martin, D. C. High Resolution Microscopy of PMDA-ODA Poly(imide) Single Crystals. Macromolecules 1993, 26, 6557– 6565,  DOI: 10.1021/ma00076a038
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    High-resolution microscopy of PMDA-ODA polyimide single crystals
    Ojeda, Jaime R.; Martin, David C.
    Macromolecules (1993), 26 (24), 6557-65CODEN: MAMOBX; ISSN:0024-9297.
    Single crystals of the title polyimide, pyromellitic dianhydride-4,4-oxydianiline copolymer (PMDA-ODA) were grown from a 1.4% by wt. soln. of the precursor poly(amic acid) in 1-methyl-2-pyrrolidinone solvent. The morphol. of the crystals was examd. by high-resoln. electron (HREM) and at.-force microscopies (AFM). The crystals formed spherulitic bundles of well-defined lamellae similar to that typically obsd. in semicryst. polymers. The crystallog. growth direction was found to be [010] in all cases. The nucleation and growth patterns of these crystals permitted imaging of the lateral ((100) 0.6-nm and (010) 0.4-nm) packing directions as well as that along the chain axis. High contrast 1.6-nm (002) lattice fringes seen within the polymer lamellae provided direct evidence of the cryst. perfection and for screw dislocation mediated crystal growth and lamellar branching. The lamellar crystal thickness was found to be 10.2 ± 0.5 nm, corresponding to six PMDA-ODA repeat units along the (c) chain axis. Evidence from [001] zone HREM images and electron diffraction patterns indicated that the crystallog. angle (γ) fluctuated locally from 81 to 99°. This was consistent with mol. simulations indicating that the crystal energy of PMDA-ODA was relatively insensitive to fluctuations over a similar range of angles. The theor. simulations also indicate that fluctuations in γ should be accompanied by simultaneous variations in the mol. setting angle.
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    Gatos, K. G.; Minogianni, C.; Galiotis, C. Quantifying Crystalline Fraction within Polymer Spherulites. Macromolecules 2007, 40, 786– 789,  DOI: 10.1021/ma0623284
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    Quantifying Crystalline Fraction within Polymer Spherulites
    Gatos, Konstantinos G.; Minogianni, Chrysa; Galiotis, Costas
    Macromolecules (2007), 40 (4), 786-789CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)
    The current study attempts for the first time to obtain the crystallinity profile in the interior of a single isotactic polypropylene (iPP) spherulite crystd. from the melt. As is evident, Raman microscopy appears to be an ideal technique for fast quantification of crystallinity at the microscale. The methodol. presented here can be further elaborated by Raman measurements at resolns. under the diffraction limit of classical optics to yield information on even finer scale. However, in that case, cryst. anisotropy at the submicron scale may affect the relative intensities of the two peaks, and further calibration measurements may be required. Other problems that can be studied by laser micro-Raman could be secondary crystn. during spherulite annealing. Finally, the anal. presented here can also be applied to iPP/polymer blends to assess the crystallinity of the iPP domains and to iPP composites for which important issues such as the development of crystallinity at the vicinity of filler/fiber can be quantified at the microscale.
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    Walker, M. L.; Smith, A. P.; Karim, A. Combinatorial Approach for Studying the Effects of 4-Biphenyl Carboxylic Acid on Polypropylene Films. Langmuir 2003, 19, 6582– 6585,  DOI: 10.1021/la026733+
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    Combinatorial Approach for Studying the Effects of 4-Biphenyl Carboxylic Acid on Polypropylene Films
    Walker, Marlon L.; Smith, Archie P.; Karim, Alamgir
    Langmuir (2003), 19 (17), 6582-6585CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    The crystn. mechanism of thin polypropylene films with and without 4-biphenylcarboxylic acid as nucleating agent was studied using high-throughput methodol. in conjunction with optical microscopy. The high-throughput approach involves the use of thin films cast with a thickness gradient, placed on a hot stage possessing a temp. gradient orthogonal to the thickness gradient. This system is used to study the effect of the nucleating agent on the morphol. at different temp. and film thickness combinations. The addn. of the nucleating agent, upon annealing and undercooling, results in spherulite formation at 10-15° higher than neat crystn. temps. and spherulite sizes an order of magnitude smaller than those of neat polypropylene. Thus 4-Biphenylcarboxylic acid can have a significant effect on the morphol. of thin polypropylene films.
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  97. 97
    Tlatlik, H.; Simon, P.; Kawska, A.; Zahn, D.; Kniep, R. Biomimetic Fluorapatite-Gelatine Nanocomposites: Pre-Structuring of Gelatine Matrices by Ion Impregnation and Its Effect on Form Development. Angew. Chem., Int. Ed. 2006, 45, 1905– 1910,  DOI: 10.1002/anie.200503610
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    Biomimetic fluorapatite-gelatine nanocomposites: pre-structuring of gelatine matrices by ion impregnation and its effect on form development
    Tlatlik, Harald; Simon, Paul; Kawska, Agnieszka; Zahn, Dirk; Kniep, Ruediger
    Angewandte Chemie, International Edition (2006), 45 (12), 1905-1910CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Form follows the ion: The morphogenesis of fluorapatite-gelatine nanocomposites is studied from both electron microscopy and atomistic simulation revealing ion impregnation effects on the growth mechanisms. Depending on the ionic species used for pre-treatment of the org. component dramatic changes of the mesoscopic structuring are obsd.
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    Pawlak, A.; Piorkowska, E. Crystallization of Isotactic Polypropylene in a Temperature Gradient. Colloid Polym. Sci. 2001, 279, 939– 946,  DOI: 10.1007/s003960100519
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    Crystallization of isotactic polypropylene in a temperature gradient
    Pawlak, A.; Piorkowska, E.
    Colloid and Polymer Science (2001), 279 (10), 939-946CODEN: CPMSB6; ISSN:0303-402X. (Springer-Verlag)
    The crystn. of isotactic polypropylene films was studied in const. and in time-dependent temp. gradients. The temp. gradient influences a spherulitic pattern and an internal structure of spherulites. The gradient can accelerate conversion of the melt into spherulites although it has no effect on spherulitic nucleation. The acceleration of the local conversion results from a contribution of spherulites nucleated in colder parts of a sample. The obsd. effects intensify with the increase of the temp. gradient and they are also enhanced by a higher crystn. temp.
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    Komarechka, D. Don Komarechka Photography. Private communication , 2019.
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    Okerberg, B. Virginia Polytechnic Institute and State University. Private communication , 2005.
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    Wang, C.; Chen, C.-C.; Cheng, Y.-W.; Liao, W.-P.; Wang, M.-L. Simultaneous Presence of positive and Negative Spherulites in Syndiotactic Polystyrene and its Blends with Atactic Polystyrene. Polymer 2002, 43, 5271– 5279,  DOI: 10.1016/S0032-3861(02)00351-8
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    Simultaneous presence of positive and negative spherulites in syndiotactic polystyrene and its blends with atactic polystyrene
    Wang, Chi; Chen, Chao-Chen; Cheng, Yong-Wen; Liao, Wei-Po; Wang, Min-Ling
    Polymer (2002), 43 (19), 5271-5279CODEN: POLMAG; ISSN:0032-3861. (Elsevier Science Ltd.)
    Crystal growth rates of syndiotactic polystyrene (sPS) and its blends with atactic polystyrene (aPS) at various temps. (Tc) were measured using a polarized optical microscope (POM). In addn. to the pos. birefringent spherulites and axilites (P-spherulites and P-axilites) which are predominantly obsd., small population of neg. birefringent spherulites (N-spherulites) is also detected in the neat sPS as well as in the sPS/aPS blends at a given Tc. Both P-spherulites and P-axilites possess a similar growth rate, whereas a smaller growth rate is found for N-spherulites at all Tc and samples investigated. Melting behavior of individual P- and N-spherulites was feasibly traced using hot-stage heating and a highly sensitive CCD through the decay of transmitted light intensity under cross-polars. Both P- and N-spherulites demonstrate exactly the same melting behavior under POM, which well corresponds to the differential scanning calorimetry measurements, suggesting no difference in lamellar thickness distribution or crystal perfection within P- and N-spherulites. Lamellar morphologies within spherulites were extensively investigated using transmission electron microscopy (TEM) as well as SEM. Results obtained from TEM and SEM show that the lamellar stacks within P-spherulites grow radially, whereas those within N-spherulites are packed relatively tangentially. The growth of P-spherulites is assocd. with the gradual increase of lamellae' lateral dimensions which follows the conventional theory of growth mechanism. However, the measured growth rate of N-spherulites is relevant to the gradual deposition of new lamellar nuclei adjacent to the fold surfaces of already-existing lamellar stacks. The difference in measured growth rate between P- and N-spherulites is attributed to the different energy barrier required to develop stable nuclei. Based on the exhaustive TEM and SEM observations, plausible origin of N-spherulites is provided and discussed as well.
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    Rátkai, L.; Szállás, A.; Pusztai, T.; Mohri, T.; Granasy, L. Ternary Eutectic Dendrites: Pattern Formation and Scaling Properties. J. Chem. Phys. 2015, 142 (15), 154501,  DOI: 10.1063/1.4917201
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    Ternary eutectic dendrites: Pattern formation and scaling properties
    Ratkai, Laszlo; Szallas, Attila; Pusztai, Tamas; Mohri, Tetsuo; Granasy, Laszlo
    Journal of Chemical Physics (2015), 142 (15), 154501/1-154501/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Extending previous work [Pusztai et al., Phys. Rev. E 87, 032401(2013)], the authors have studied the formation of eutectic dendrites in a model ternary system within the framework of the phase-field theory. The authors have mapped out the domain in which two-phase dendritic structures grow. With increasing pulling velocity, the following sequence of growth morphologies is obsd.: flat front lamellae → eutectic colonies → eutectic dendrites → dendrites with target pattern → partitionless dendrites → partitionless flat front. The two-phase and 1-phase dendrites have similar forms and display a similar scaling of the dendrite tip radius with the interface free energy. Also the possible eutectic patterns include the target pattern, and single- and multiarm spirals, of which the thermal fluctuations choose. The most probable no. of spiral arms increases with increasing tip radius and with decreasing kinetic anisotropy. The authors' numerical simulations confirm that in agreement with the assumptions of a recent anal. of two-phase dendrites [Akamatsu et al., Phys. Rev. Lett. 112, 105502(2014)], the Jackson-Hunt scaling of the eutectic wavelength with pulling velocity is obeyed in the parameter domain explored, and that the natural eutectic wavelength is proportional to the tip radius of the two-phase dendrites. Finally, it is very difficult/virtually impossible to form spiraling two-phase dendrites without anisotropy, an observation that seems to contradict the expectations of Akamatsu et al. Yet, it cannot be excluded that in isotropic systems, two-phase dendrites are rare events difficult to observe in simulations. (c) 2015 American Institute of Physics.
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    Warren, J. A.; Boettinger, W. J. Prediction of Dendritic Growth and Microsegregation Patterns in a Binary Alloy Using the Phase-Field Method. Acta Metall. Mater. 1995, 43 (2), 689– 703,  DOI: 10.1016/0956-7151(94)00285-P
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    Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method
    Warren, J. A.; Boettinger, W. J.
    Acta Metallurgica et Materialia (1995), 43 (2), 689-703CODEN: AMATEB; ISSN:0956-7151. (Elsevier)
    A comprehensive model is developed for solving the heat and solute diffusion equations during solidification that avoids tracking the liq.-solid interface. The bulk liq. and solid phases are treated as regular solns. and an order parameter (the phase field) is introduced to describe the interfacial region between them. Two-dimensional computations are performed for ideal solns. and for dendritic growth into an isothermal and highly supersatd. liq. phase. The dependence upon various material and computational parameters, including the approach to conventional sharp interface theories, is investigated. Realistic growth patterns are obtained that include the development, coarsening, and coalescence of secondary and tertiary dendrite arms. Microsegregation patterns are examd. and compared for different values of the solid diffusion coeff.
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    Lewis, D.; Warren, J.; Boettinger, W.; Pusztai, T.; Gránásy, L. Phase-Field Models for Eutectic Solidification. JOM 2004, 56 (4), 34– 39,  DOI: 10.1007/s11837-004-0070-1
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    Phase-field models for eutectic solidification
    Lewis, Daniel; Pusztai, Tamas; Granasy, Laszlo; Warren, James; Boettinger, William
    JOM (2004), 56 (4), 34-39CODEN: JOMMER; ISSN:1047-4838. (Minerals, Metals & Materials Society)
    This article discusses two methods for modeling eutectic solidification using the phase-field approach. First, a multi-phase-field model is used to study the three-dimensional morphol. evolution of binary eutectics. Performing the calcns. in three dimensions allows observation of both lamellar and rod-like structures as well as transient phenomena such as lamellar fault motion, rod-branching, and nucleation or elimination of phases as solidification progresses. The second approach models multiple eutectic grains where the crystg. phases have an orientation relationship. This approach is promising for modeling complex solidification microstructures.
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    Zou, Z.; Habraken, W. J. E. M.; Bertinetti, L.; Politi, Y.; Gal, A.; Weiner, S.; Addadi, L.; Fratzl, P. On the Phase Diagram of Calcium Carbonate Solutions. Adv. Mater. Interfaces 2017, 4 (1), 1600076,  DOI: 10.1002/admi.201600076
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    Wallace, A. F.; Hedges, L. O.; Fernandez-Martinez, A.; Raiteri, P.; Gale, J. D.; Waychunas, G. A.; Whitelam, S.; Banfield, J. F.; De Yoreo, J. J. Microscopic Evidence for Liquid-Liquid Separation in Supersaturated CaCO3 Solutions. Science 2013, 341 (6148), 885– 889,  DOI: 10.1126/science.1230915
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    Microscopic Evidence for Liquid-Liquid Separation in Supersaturated CaCO3 Solutions
    Wallace, Adam F.; Hedges, Lester O.; Fernandez-Martinez, Alejandro; Raiteri, Paolo; Gale, Julian D.; Waychunas, Glenn A.; Whitelam, Stephen; Banfield, Jillian F.; De Yoreo, James J.
    Science (Washington, DC, United States) (2013), 341 (6148), 885-889CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Recent exptl. observations of the onset of calcium carbonate (CaCO3) mineralization suggest the emergence of a population of clusters that are stable rather than unstable as predicted by classical nucleation theory. Mol. dynamics simulations were used to probe the structure, dynamics, and energetics of hydrated CaCO3 clusters and lattice gas simulations to explore the behavior of cluster populations before nucleation. The simulations predict the formation of a dense liq. phase through liq.-liq. sepn. within the concn. range in which clusters are obsd. Coalescence and solidification of nanoscale droplets results in formation of a solid phase, the structure of which is consistent with amorphous CaCO3. The presence of a liq.-liq. binodal enables a diverse set of exptl. observations to be reconciled within the context of established phase-sepn. mechanisms.
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    Bruno, M.; Massaro, F. R.; Pastero, L.; Costa, E.; Rubbo, M.; Prencipe, M.; Aquilano, D. New Estimates of the Free Energy of Calcite/Water Interfaces for Evaluating the Equilibrium Shape and Nucleation Mechanisms. Cryst. Growth Des. 2013, 13 (3), 1170– 1179,  DOI: 10.1021/cg3015817
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    New Estimates of the Free Energy of Calcite/Water Interfaces for Evaluating the Equilibrium Shape and Nucleation Mechanisms
    Bruno, Marco; Massaro, Francesco Roberto; Pastero, Linda; Costa, Emanuele; Rubbo, Marco; Prencipe, Mauro; Aquilano, Dino
    Crystal Growth & Design (2013), 13 (3), 1170-1179CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    The solvated surface energies at 0 K of various calcite facets have been detd. using the COSMIC simulations. The presence of water reduced the dry surface energy at 0 K by ∼7-14% in a homogeneous way. The solvated and dry equil. shapes were nearly homothetic, in both cases the {10‾14}, {10‾10}, {01‾12}, and {0001} planes were present. The free energy at 300 K of the {10‾14}/water interface was detd. as 0.412 ± 0.020 J/m2 by combining thermodn. relations and contact angle measurements. Some considerations on the free energy of other interfaces were proposed. Rough ests. of the vibrational energy, entropy, and configurational entropy of the (10‾14)/water interface was obtained as -0.066 ± 0.038 J/m2. Activation energy of the homogeneous and the heterogeneous crystal nucleation at room temp. was rather high, suggesting that the direct formation of calcite should be prevented. This supported the view that calcite formation should proceed throughout the early formation of an amorphous calcium carbonate phase.
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    Sekkal, W.; Zaoui, A. Nanoscale Analysis of the Morphology and Surface Stability of Calcium Carbonate Polymorphs. Sci. Rep. 2013, 3, 1587– 1587,  DOI: 10.1038/srep01587
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    Nanoscale analysis of the morphology and surface stability of calcium carbonate polymorphs
    Sekkal, W.; Zaoui, A.
    Scientific Reports (2013), 3 (), 1587, 10 pp.CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
    Under earth surface conditions, in ocean and natural water, calcium carbonate is ubiquitous, forming anhyd. and hydrous minerals. These hydrous phases are of considerable interest for their role as precursors to stable carbonate minerals. Atomistic simulation techniques have been employed here to perform a comprehensive and quant. study of the structural and energetic stability of dry and hydrous surfaces of calcium carbonate polymorphs using two recently developed forcefields. Results show that the dry forms are prone to ductility; while hydrous phases are found to be brittle. The (001) surface of monohydrocalcite appears to be the most stable (0.99 J/m2) whereas for the ikaite phase, the (001) surface is the most stable. The corresponding value is 0.2 J/m2, i.e. even lower than the surface energy of the (1‾014) surface of calcite. Beautiful computed morphol. pictures are obtained with Xiao's model and are very similar to the obsd. SEM images.
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    Kocot, K. M.; Aguilera, F.; McDougall, C.; Jackson, D. J.; Degnan, B. M. Sea Shell Diversity and Rapidly Evolving Secretomes: Insights into the Evolution of Biomineralization. Front. Zool. 2016, 13, 23,  DOI: 10.1186/s12983-016-0155-z
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    Sea shell diversity and rapidly evolving secretomes: insights into the evolution of biomineralization
    Kocot, Kevin M.; Aguilera, Felipe; McDougall, Carmel; Jackson, Daniel J.; Degnan, Bernard M.
    Frontiers in Zoology (2016), 13 (), 23/1-23/10CODEN: FZROAJ; ISSN:1742-9994. (BioMed Central Ltd.)
    An external skeleton is an essential part of the body plan of many animals and is thought to be one of the key factors that enabled the great expansion in animal diversity and disparity during the Cambrian explosion. Molluscs are considered ideal to study the evolution of biomineralization because of their diversity of highly complex, robust and patterned shells. The molluscan shell forms externally at the interface of animal and environment, and involves controlled deposition of calcium carbonate within a framework of macromols. that are secreted from the dorsal mantle epithelium. Despite its deep conservation within Mollusca, the mantle is capable of producing an incredible diversity of shell patterns, and macro- and micro-architectures. Here we review recent developments within the field of molluscan biomineralization, focusing on the genes expressed in the mantle that encode secreted proteins. The so-called mantle secretome appears to regulate shell deposition and patterning and in some cases becomes part of the shell matrix. Recent transcriptomic and proteomic studies have revealed marked differences in the mantle secretomes of even closely-related molluscs; these typically exceed expected differences based on characteristics of the external shell. All mantle secretomes surveyed to date include novel genes encoding lineage-restricted proteins and unique combinations of co-opted ancient genes. A surprisingly large proportion of both ancient and novel secreted proteins contg. simple repetitive motifs or domains that are often modular in construction. These repetitive low complexity domains (RLCDs) appear to further promote the evolvability of the mantle secretome, resulting in domain shuffling, expansion and loss. RLCD families further evolve via slippage and other mechanisms assocd. with repetitive sequences. As analogous types of secreted proteins are expressed in biomineralizing tissues in other animals, insights into the evolution of the genes underlying molluscan shell formation may be applied more broadly to understanding the evolution of metazoan biomineralization.
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    Metzler, R. A.; Tribello, G. A.; Parrinello, M.; Gilbert, P. U. P. A. Asprich Peptides are Occluded in Calcite and Permanently Disorder Biomineral Crystals. J. Am. Chem. Soc. 2010, 132 (33), 11585– 11591,  DOI: 10.1021/ja103089r
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    Asprich Peptides Are Occluded in Calcite and Permanently Disorder Biomineral Crystals
    Metzler, Rebecca A.; Tribello, Gareth A.; Parrinello, Michele; Gilbert, P. U. P. A.
    Journal of the American Chemical Society (2010), 132 (33), 11585-11591CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Macromols. are a minority but important component of the minerals formed by living organisms, or biominerals. The role these macromols. play at the early stages of biomineral formation, as well as their long-term and long-range effects on the mature biomineral, is poorly understood. A 42-amino acid peptide, asp2, was derived from the Asprich family of proteins. In this study we present X-ray absorption near-edge structure spectroscopy and X-ray photoelectron emission microscopy data from the asp2 peptide, the calcite (CaCO3) crystals, and the peptide + crystal composites. The results clearly show that asp2 is occluded in fully formed biomineral crystals and slightly but permanently disorders the crystal structure at short- and long-range distances.
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    Söhnel, O.; Mullin, J. W. Precipitation of Calcium Carbonate. J. Cryst. Growth 1982, 60 (2), 239– 250,  DOI: 10.1016/0022-0248(82)90095-1
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    Precipitation of calcium carbonate
    Sohnel, O.; Mullin, J. W.
    Journal of Crystal Growth (1982), 60 (2), 239-50CODEN: JCRGAE; ISSN:0022-0248.
    The pptn. of CaCO3, formed by mixing equimolar solns. of Na2CO3 and CaCl2 at different dilns. in aq. soln., was studied at 25°. Induction periods were detd. as functions of the initial supersatn. by different methods (visually, turbidimetrically and conductometrically) for the pure system and in the presence of Mg2+, Mn2+, Br-, and NO3- as trace impurities. The nos. of crystals formed in supersatd. solns. were detd. for pure and Mn-contaminated systems and the crystal-soln. interfacial tensions were calcd. Desupersatn. curves of slightly supersatd. solns. of CaCO3 were followed conductometrically and the data were used to est. growth rates of CaCO3 crystals, taking into account the change of total external crystal surface area with time. The influences of Mg2+, Mn2+, Cr3+, Ni2+, and F- on the growth kinetics and the modification of crystal habit were detd.
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    Qi, X.; Balankura, T.; Fichthorn, K. A. Theoretical Perspectives on the Influence of Solution-Phase Additives in Shape-Controlled Nanocrystal Synthesis. J. Phys. Chem. C 2018, 122 (33), 18785– 18794,  DOI: 10.1021/acs.jpcc.8b00562
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    Theoretical Perspectives on the Influence of Solution-Phase Additives in Shape-Controlled Nanocrystal Synthesis
    Qi, Xin; Balankura, Tonnam; Fichthorn, Kristen A.
    Journal of Physical Chemistry C (2018), 122 (33), 18785-18794CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Shape-selective soln.-phase nanocrystal growth is facilitated by capping agents, or structure-directing agents (SDAs), which guide shape evolution. It is often stated that these chem. additives impart shape selectivity by promoting nanocrystals with a majority of facets to which they bind most strongly. However, little is known on the mechanisms through which they impart shape selectivity. In this Feature Article, we highlight our recent studies aimed at understanding the thermodn. and kinetic influences of SDAs using theory and computational tools. We review our studies of the poly(vinylpyrrolidone) (PVP)-mediated synthesis of {100}-faceted Ag nanocubes in ethylene glycol soln., which has been studied exptl. Our studies of the interfacial free energy of Ag-PVP soln. interfaces show that while soln.-phase PVP does bind more strongly to Ag(100) than to Ag(111), this selectivity is not sufficient to thermodynamically change the Wulff shape of a PVP-covered Ag nanocrystal in soln. from that of the bare metal in vacuum. These studies indicate that a strong facet binding selectivity is needed for a SDA to thermodynamically alter the soln.-phase crystal shape from that of the bare metal. Interestingly, the binding selectivity of PVP for Ag(100) is sufficient to regulate the atom deposition fluxes to Ag(100) and Ag(111), so that cubic Ag(100) nanocrystals form kinetically. Altogether, our studies indicate that kinetic control of metal nanocrystal shapes is likely more prevalent than thermodn. control. We outline some current challenges in understanding shape-selective soln.-phase nanocrystal syntheses.
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    Albéric, M.; Bertinetti, L.; Zou, Z.; Fratzl, P.; Habraken, W.; Politi, Y. The Crystallization of Amorphous Calcium Carbonate is Kinetically Governed by Ion Impurities and Water. Adv. Sci. 2018, 5 (5), 1701000,  DOI: 10.1002/advs.201701000
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    The Crystallization of Amorphous Calcium Carbonate is Kinetically Governed by Ion Impurities and Water
    Alberic Marie; Bertinetti Luca; Zou Zhaoyong; Fratzl Peter; Habraken Wouter; Politi Yael
    Advanced science (Weinheim, Baden-Wurttemberg, Germany) (2018), 5 (5), 1701000 ISSN:2198-3844.
    Many organisms use amorphous calcium carbonate (ACC) and control its stability by various additives and water; however, the underlying mechanisms are yet unclear. Here, the effect of water and inorganic additives commonly found in biology on the dynamics of the structure of ACC during crystallization and on the energetics of this process is studied. Total X-ray scattering and pair distribution function analysis show that the short- and medium-range order of all studied ACC samples are similar; however, the use of in situ methodologies allow the observation of small structural modifications that are otherwise easily overlooked. Isothermal calorimetric coupled with microgravimetric measurements show that the presence of Mg(2+) and of PO4(3-) in ACC retards the crystallization whereas increased water content accelerates the transformation. The enthalpy of ACC with respect to calcite appears, however, independent of the additive concentration but decreases with water content. Surprisingly, the enthalpic contribution of water is compensated for by an equal and opposite entropic term leading to a net independence of ACC thermodynamic stability on its hydration level. Together, these results point toward a kinetic stabilization effect of inorganic additives and water, and may contribute to the understanding of the biological control of mineral stability.
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  114. 114
    Falini, G.; Albeck, S.; Weiner, S.; Addadi, L. Control of Aragonite or Calcite Polymorphism by Mollusk Shell Macromolecules. Science 1996, 271 (5245), 67– 69,  DOI: 10.1126/science.271.5245.67
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    Belcher, A. M.; Wu, X. H.; Christensen, R. J.; Hansma, P. K.; Stucky, G. D.; Morse, D. E. Control of Crystal Phase Switching and Orientation by Soluble Mollusc-Shell Proteins. Nature 1996, 381 (6577), 56– 58,  DOI: 10.1038/381056a0
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    115
    Control of crystal phase switching and orientation by soluble mollusk-shell proteins
    Belcher, A. M.; Wu, X. H.; Christensen, R. J.; Hansma, P. K.; Stucky, G. D.; Morse, D. E.
    Nature (London) (1996), 381 (6577), 56-58CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)
    In the initial stages of the biomineralization of abalone shells, a primer layer of oriented calcite crystals grows on a nucleating protein sheet. The deposition of this primer is followed by an abrupt transition to c-axis-oriented crystals of aragonite, another cryst. form of calcium carbonate. The formation of each of the 2 crystal types is accompanied by the synthesis of specific polyanionic proteins, suggesting that cooperative interactions between these proteins and the inorg. ions during crystal nucleation and growth control the phase of the deposited mineral and that differential expression of the proteins allows the organism to induce phase changes. It is known that sol. shell proteins can control crystal morphol., but it has been suspected that the switch in phase from calcite to aragonite-might require the deposition of a new nucleating protein sheet. Here the authors describe in vitro studies of the crystn. of calcium carbonate in the presence of sol. polyanionic proteins extd. from abalone shell. These proteins alone are sufficient to control the crystal phase, allowing us to switch abruptly and sequentially between aragonite and calcite without the need for deposition of an intervening protein sheet. These results show that sol. org. components can exert greater control over hierarchical biomineral growth than hitherto suspected, offering the prospect of similar phase control in materials chem.
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    Vanysek, P. Ionic Conductivity and Diffusion at Infinite Dilution. In Handbook of Chemistry and Physics; CRC Press: Boca Raton, 2000; pp ( 5-77)–( 5-79).
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    Malini, R. I.; Bushuev, Y. G.; Hall, S. A.; Freeman, C. L.; Rodger, P. M.; Harding, J. H. Using Simulation to Understand the Structure and Properties of Hydrated Amorphous Calcium Carbonate. CrystEngComm 2016, 18 (1), 92– 101,  DOI: 10.1039/C5CE01536G
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    Bushuev, Y. G.; Finney, A. R.; Rodger, P. M. Stability and Structure of Hydrated Amorphous Calcium Carbonate. Cryst. Growth Des. 2015, 15 (11), 5269– 5279,  DOI: 10.1021/acs.cgd.5b00771
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    118
    Stability and Structure of Hydrated Amorphous Calcium Carbonate
    Bushuev, Yuriy G.; Finney, Aaron R.; Rodger, P. Mark
    Crystal Growth & Design (2015), 15 (11), 5269-5279CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    The results of mol. dynamics simulations of hydrated amorphous Ca carbonate (CaCO3·nH2O: ACC) are presented. ACC properties were studied on atomistic, supramol., and thermodn. levels. The clustering of H2O occluded in the ionic ACC framework is well described by percolation theory, and with a percolation transition for H2O through ACC at a hydration level, n, of ∼0.8. Percolation in ACC systems is quant. similar to site percolation on a simple cubic lattice where the percolation threshold is obsd. at pc = 0.312. Predominantly 4-fold tetrahedral mol. coordination of H2O mols. in the bulk liq. state is changed to 6-fold connectivity in ACC. Kinetic stability of ACC is enhanced by dehydration and reaches maximal values when the H2O content is below the percolation threshold. The computed free energy shows a region of thermodn. stability of hydrated ACC (1 < n < 6) with respect to calcite and pure H2O. This region is bounded by two crystallohydrates, monohydrocalcite (n = 1) and ikaite (n = 6), that have lower free energies than ACC. During dehydration at n < 1 the thermodn. stability of ACC decreases, which favors the processes of nucleation and crystn. However, H2O mobility within ACC also decreases during dehydration, thus making dehydration more difficult. So, the stability of hydrated ACC is controlled by a balance of two opposing factors: kinetics and thermodn.
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  119. 119
    Radha, A. V.; Forbes, T. Z.; Killian, C. E.; Gilbert, P. U. P. A.; Navrotsky, A. Transformation and Crystallization Energetics of Synthetic and Biogenic Amorphous Calcium Carbonate. Proc. Natl. Acad. Sci. U. S. A. 2010, 107 (38), 16438– 16443,  DOI: 10.1073/pnas.1009959107
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    119
    Transformation and crystallization energetics of synthetic and biogenic amorphous calcium carbonate
    Radha, A. V.; Forbes, Tori Z.; Killian, Christopher E.; Gilbert, P. U. P. A.; Navrotsky, Alexandra
    Proceedings of the National Academy of Sciences of the United States of America (2010), 107 (38), 16438-16443, S16438/1-S16438/7CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Amorphous CaCO3 (ACC) is a metastable phase often obsd. during low temp. inorg. synthesis and biomineralization. ACC transforms with aging or heating into a less hydrated form, and with time crystallizes to calcite or aragonite. The energetics of transformation and crystn. of synthetic and biogenic (extd. from California purple sea urchin larval spicules, Strongylocentrotus purpuratus) ACC were studied using isothermal acid soln. calorimetry and differential scanning calorimetry. Transformation and crystn. of ACC can follow an energetically downhill sequence: more metastable hydrated ACC → less metastable hydrated ACC → anhyd. ACC ∼ biogenic anhyd. ACC → vaterite → aragonite → calcite. In a given reaction sequence, not all these phases need to occur. The transformations involve a series of ordering, dehydration, and crystn. processes, each lowering the enthalpy (and free energy) of the system, with crystn. of the dehydrated amorphous material lowering the enthalpy the most. ACC is much more metastable with respect to calcite than the cryst. polymorphs vaterite or aragonite..The anhyd. ACC is less metastable than the hydrated, implying that the structural reorganization during dehydration is exothermic and irreversible. Dehydrated synthetic and anhyd. biogenic ACC are similar in enthalpy. The transformation sequence obsd. in biomineralization could be mainly energetically driven; the 1st phase deposited is hydrated ACC, which then converts to anhyd. ACC, and finally crystallizes to calcite. The initial formation of ACC may be a 1st step in the pptn. of calcite under a wide variety of conditions, including geol. CO2 sequestration.
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  120. 120
    Fisler, D. K.; Cygan, R. T. Diffusion of Ca and Mg in Calcite. Am. Mineral. 1999, 84 (9), 1392– 1399,  DOI: 10.2138/am-1999-0917
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    120
    Diffusion of Ca and Mg in calcite
    Fisler, Diana K.; Cygan, Randall T.
    American Mineralogist (1999), 84 (9), 1392-1399CODEN: AMMIAY; ISSN:0003-004X. (Mineralogical Society of America)
    The self-diffusion of Ca and the tracer diffusion of Mg in calcite have been measured exptl. using isotopic tracers of 25Mg and 44Ca. Natural single crystals of calcite were coated with a thermally sputtered oxide thin film and then annealed in a CO2 gas at 1 atm total pressure and temps. from 550 to 800 °C. Diffusion coeff. values were derived from the depth profiles obtained by ion microprobe anal. The resultant activation energies for Mg tracer diffusion and Ca self-diffusion are, resp.: Ea(Mg) = 284±74 kJ/mol and Ea(Ca) = 271 ± 80 kJ/mol. For the temp. ranges in these expts., the diffusion of Mg is faster than Ca. The results are generally consistent in magnitude with divalent cation diffusion rates obtained in previous studies, and provide a means of interpreting the thermal histories of carbonate minerals, the mechanism of dolomitization, and other diffusion-controlled processes. The results indicate that cation diffusion in calcite is relatively slow and cations are the rate-limiting diffusing species for the deformation of calcite and carbonate rocks. Application of the calcite-dolomite geothermometer to metamorphic assemblages will be constrained by cation diffusion and cooling rates. The direct measurement of Mg tracer diffusion in calcite indicates that dolomitization is unlikely to be accomplished by Mg diffusion in the solid state but by a recrystn. process.
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  121. 121
    Kent, A. J. R.; Hutcheon, I. D.; Ryerson, F. J.; Phinney, D. L. The Temperature of Formation of Carbonate in Martian Meteorite ALH84001: Constraints from Cation Diffusion. Geochim. Cosmochim. Acta 2001, 65 (2), 311– 321,  DOI: 10.1016/S0016-7037(00)00528-7
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    121
    The temperature of formation of carbonate in Martian meteorite ALH84001: constraints from cation diffusion
    Kent, A. J. R.; Hutcheon, I. D.; Ryerson, F. J.; Phinney, D. L.
    Geochimica et Cosmochimica Acta (2001), 65 (2), 311-321CODEN: GCACAK; ISSN:0016-7037. (Elsevier Science Inc.)
    The authors measured the rates of chem. diffusion of Mg in calcite and Ca in magnesite and used these new data to constrain the formation temp. and thermal history of carbonates in the Martian meteorite ALH84001. The data have been collected at lower temps. than in previous studies and provide improved constraints on carbonate formation during relatively low-temp. processes (≤400°C). Measured log D0 values for chem. diffusion of Mg in calcite and Ca in magnesite are -16.0 ± 1.1 and -7.8 ± 4.3 m2/s and the activation energies (EA) are 76 ± 16 and 214 ± 60 kJ/mol, resp. Measured diffusion rates of Mg in calcite at temps. between 400 and 550°C are substantially faster than expected from extrapolation of existing higher-temp. data, suggesting that different mechanisms may govern diffusion of Mg at temps. above and below ∼550°C. These data were used to constrain thermal histories which will allow the ∼1 μm variations in Ca-Mg compn. in ALH84001 carbonates to survive homogenization by diffusion. Results are generally consistent with models for formation of carbonates in ALH84001 at low temps. For initial cooling rates of between ∼ 10-1 and 103 °/Myr results demonstrate that carbonates formed at temps. no higher than 400°C and most probably less than 200°C. This range of cooling rates is similar to those obsd. within the terrestrial crust, and suggests that formation of the carbonates by igneous, metamorphic or hydrothermal (or other) processes in the Martian crust most plausibly occurred at temps. below 200 to 400°C. Models that suggest ALH84001 carbonates formed during a Martian impact event are also constrained. The thermal histories of terrestrial impact structures suggest that cooling rates sufficiently rapid to allow preservation of the obsd. carbonate zoning at formation temps. in excess of 600°C (> ∼ 107 °/Myr) occur only within the uppermost, melt-rich portions of an impact structure. Material deeper within the impact structure (where cooling is dominated by uplifted crustal material and where much of the formation of hydrothermal minerals is concd.) cools much slower, typically at rates of ∼102 to 103 °/Myr. Carbonates formed within this region would also only preserve ∼ 1 μm compositional zoning at formation temps. of less than ∼ 200 to 400°C.
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  122. 122
    Lahav, N.; Bolt, G. H. Self-Diffusion of Ca45 into Certain Carbonates. Soil Sci. 1964, 97 (5), 293– 299,  DOI: 10.1097/00010694-196405000-00001
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    Self-diffusion of 45Ca into certain carbonates
    Lahav, N.; Bolt, G. H.
    Soil Science (1964), 97 (5), 293-9CODEN: SOSCAK; ISSN:0038-075X.
    cf. CA 60, 7822d. Self-diffusion of 45Ca, supplied as CaCl2 to aq. suspensions of calcite, dolomite, CaCO3 ppt., and a com. lime, was measured. The exptl. data of the 1st 3 carbonates were in agreement with the theoretical diffusion equation and thus enabled the calcn. of the self-diffusion const. as 10-20 cm.2 sec.-1. Grinding the 1st 2 carbonates to <5 μ did not affect the value of the const. Lack of self-diffusion in the com. lime was probably due to silicate impurities coating the particles.
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    Möller, P.; Rajagopalan, G. Changes of Excess Free Energies in the Crystal Growth Processes of Calcite and Aragonite Due to the Presence of Mg2+ Ions in Solution. Z. Phys. Chem. 1976, 99 (4–6), 187– 198,  DOI: 10.1524/zpch.1976.99.4-6.187
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    Donnet, M.; Bowen, P.; Lemaȋtre, J. A Thermodynamic Solution Model for Calcium Carbonate: Towards an Understanding of Multi-Equilibria Precipitation Pathways. J. Colloid Interface Sci. 2009, 340 (2), 218– 224,  DOI: 10.1016/j.jcis.2009.09.005
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    124
    A thermodynamic solution model for calcium carbonate Towards an understanding of multi-equilibria precipitation pathways
    Donnet, Marcel; Bowen, Paul; Lemaitre, Jacques
    Journal of Colloid and Interface Science (2009), 340 (2), 218-224CODEN: JCISA5; ISSN:0021-9797. (Elsevier B.V.)
    Thermodn. soly. calcns. are normally only related to thermodn. equil. in soln. We extend the use of such soly. calcns. to help elucidate possible pptn. reaction pathways during the entire reaction. We also est. the interfacial energy of particles using only soly. data by a modification of Mersmann's approach. We have carried this out by considering pptn. reactions as a succession of small quasi-equil. states. Thus possible equil. pptn. pathways can be evaluated by calcg. the evolution of surface charge, particle size and/or interfacial energy during the ongoing reaction. The approach includes the use of the Kelvin's law to express the influence of particle size on the soly. const. of ppts., the use of Nernst's law to calc. surface potentials from soly. calcns. and relate this to exptl. measured zeta potentials. CaCO3 pptn. and zeta potential measurements of well characterized high purity calcite were used as a model system to validate the calcd. values. The clarification of the change in zeta potential on titrn. illustrates the power of this approach as a tool for reaction pathway prediction and hence knowledge based tailoring of pptn. reactions.
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    Sun, W.; Jayaraman, S.; Chen, W.; Persson, K. A.; Ceder, G. Nucleation of Metastable Aragonite CaCO3 in Seawater. Proc. Natl. Acad. Sci. U. S. A. 2015, 112 (11), 3199– 3204,  DOI: 10.1073/pnas.1423898112
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    125
    Nucleation of metastable aragonite CaCO3 in seawater
    Sun, Wenhao; Jayaraman, Saivenkataraman; Chen, Wei; Persson, Kristin A.; Ceder, Gerbrand
    Proceedings of the National Academy of Sciences of the United States of America (2015), 112 (11), 3199-3204CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Predicting the conditions in which a compd. adopts a metastable structure when it crystallizes out of soln. is an unsolved and fundamental problem in materials synthesis, and one which, if understood and harnessed, could enable the rational design of synthesis pathways toward or away from metastable structures. Crystn. of metastable phases is particularly accessible via low-temp. soln.-based routes, such as chimie douce and hydrothermal synthesis, but although the chem. of the soln. plays a crucial role in governing which polymorph forms, how it does so is poorly understood. We demonstrate an ab initio technique to quantify thermodn. parameters of surfaces and bulks in equil. with an aq. environment, enabling the calcn. of nucleation barriers of competing polymorphs as a function of soln. chem., thereby predicting the soln. conditions governing polymorph selection. We apply this approach to resolve the long-standing calcite-aragonite problem, the observation that Ca carbonate ppts. as the metastable aragonite polymorph in marine environments, rather than the stable phase calcite, which is of tremendous relevance to biomineralization, carbon sequestration, paleogeochem., and the vulnerability of marine life to ocean acidification. We identify a direct relation between the calcite surface energy and soln. Mg-Ca ion concns., showing that the calcite nucleation barrier surpasses that of metastable aragonite in solns. with Mg:Ca ratios consistent with modern seawater, allowing aragonite to dominate the kinetics of nucleation. Our ability to quantify how soln. parameters distinguish between polymorphs marks an important step toward the ab initio prediction of materials synthesis pathways in soln.
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    Turnbull, D. Formation of Crystal Nuclei in Liquid Metals. J. Appl. Phys. 1950, 21, 1022– 1028,  DOI: 10.1063/1.1699435
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    Formation of crystal nuclei in liquid metals
    Turnbull, D.
    Journal of Applied Physics (1950), 21 (), 1022-7CODEN: JAPIAU; ISSN:0021-8979.
    The known facts about nucleation phenomena in liquid metals are interpreted satisfactorily on the basis of the crit. size and interfacial energy concepts. In large continuous masses nucleation is almost always catalyzed by extraneous interfaces. However, in very small droplets the probability that a catalytic inclusion is present is so much less that their min. nucleation frequencies are reproducible and form a consistent set of values. Interfacial energies, σ, between crystal nuclei and the corresponding liquids were calcd. from nucleation frequencies of small droplets on the basis of the theory of homogeneous nucleation. Energies of interfaces, σg, one atom thick and contg. N atoms were calcd. from the σ's. The ratio of σg to the gram at. heat of fusion, ΔHf, was approx. 0.45 for most metals but ∼0.32 for H2O, Bi, Sb, and Ge. The effect of relative complexity of crystal structure on the supercooling behavior of pure metals apparently is a reflection of its effect on ΔHf.
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    Asta, M.; Beckermann, C.; Karma, A.; Kurz, W.; Napolitano, R.; Plapp, M.; Purdy, G.; Rappaz, M.; Trivedi, R. Solidification Microstructures and Solid-State Parallels: Recent Developments, Future Directions. Acta Mater. 2009, 57 (4), 941– 971,  DOI: 10.1016/j.actamat.2008.10.020
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    Solidification microstructures and solid-state parallels: Recent developments, future directions
    Asta, M.; Beckermann, C.; Karma, A.; Kurz, W.; Napolitano, R.; Plapp, M.; Purdy, G.; Rappaz, M.; Trivedi, R.
    Acta Materialia (2009), 57 (4), 941-971CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
    A review. Rapid advances in atomistic and phase-field modeling techniques as well as new expts. have led to major progress in solidification science in metal systems during the first years of this century. The most important findings in this technol. are reviewed and impact quant. understanding of (1) key anisotropic properties of the solid-liq. interface that govern solidification pattern evolution, including the solid-liq. interface free energy and kinetic coeff. (2) dendritic solidification at low and high growth rates, with particular emphasis on orientation selection (3) regular and irregular eutectic and peritectic microstructures (4) effects of convection on microstructure formation (5) solidification at a high vol. fraction of solid and the related formation of pores and hot cracks (6) solid-state transformations as far as they relate to solidification models and techniques. In light of this progress, crit. issues that point to directions for future research in both solidification and solid-state transformations are identified.
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    Laird, B. B. The Solid-Liquid Interfacial Free Energy of Close-Packed Metals: Hard-Spheres and the Turnbull Coefficient. J. Chem. Phys. 2001, 115 (7), 2887– 2888,  DOI: 10.1063/1.1391481
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    The solid-liquid interfacial free energy of close-packed metals: Hard-spheres and the Turnbull coefficient
    Laird, Brian B.
    Journal of Chemical Physics (2001), 115 (7), 2887-2888CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Largely due to its role in nucleation and crystal-growth, the free energy of the crystal-melt interfacial free energy is an object of considerable interest across a no. of scientific disciplines, esp. in the materials-, colloid-, and atm. sciences. Over 50 yr ago, Turnbull obsd. that the interfacial free energies (scaled by the mean interfacial area per particle) of a variety of metallic elements exhibit a linear correlation with the enthalpy of fusion. This correlation provides an important empirical "rule-of-thumb" for estg. interfacial free energies, but lacks a compelling phys. explanation. In this work it is shown that the interfacial free energies for close-packed metals are linearly correlated with the melting temp. and are therefore primarily entropic in origin. The slope of this linear relationship can be detd. with quant. accuracy using a hard-sphere model, and that the correlation with the enthalpy of fusion reported by Turnbull follows as a consequence of the fact that the entropy of fusion for close-packed metals is relatively const.
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    Wang, X.-D.; Ouyang, J.; Su, J.; Zhou, W. Phase Field Modeling of the Ring-Banded Spherulites of Crystalline Polymers: The Role of Thermal Diffusion. Chin. Phys. B 2014, 23 (12), 126103,  DOI: 10.1088/1674-1056/23/12/126103
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    Rátkai, L.; Tóth, G. I.; Környei, L.; Pusztai, T.; Gránásy, L. Phase-Field Modeling of Eutectic Structures on the Nanoscale: The Effect of Anisotropy. J. Mater. Sci. 2017, 52 (10), 5544– 5558,  DOI: 10.1007/s10853-017-0853-8
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    Phase-field modeling of eutectic structures on the nanoscale: the effect of anisotropy
    Ratkai, Laszlo; Toth, Gyula I.; Kornyei, Laszlo; Pusztai, Tamas; Granasy, Laszlo
    Journal of Materials Science (2017), 52 (10), 5544-5558CODEN: JMTSAS; ISSN:0022-2461. (Springer)
    A simple phase-field model is used to address anisotropic eutectic freezing on the nanoscale in two (2D) and three dimensions (3D). Comparing parameter-free simulations with expts., the employed model can be made quant. for Ag-Cu. Next, we explore the effect of material properties and the conditions of freezing on the eutectic pattern. We find that the anisotropies of kinetic coeff. and the interfacial free energies (solid-liq. and solid-solid), the crystal misorientation relative to pulling, the lateral temp. gradient play essential roles in detg. the eutectic pattern. Finally, we explore eutectic morphologies, which form when one of the solid phases are faceted, and investigate cases, in which the kinetic anisotropy for the two solid phases is drastically different.
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    Provatas, N.; Elder, K. R. Phase-Field Methods in Materials Science and Engineering; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2010.
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    Study of the Phase Structure of Linear Polyethylene by Means of Small-Angle X-ray Scattering and Raman Spectroscopy
    Stribeck, Norbert; Alamo, Rufina G.; Mandelkern, Leo; Zachmann, Hans Gerhard
    Macromolecules (1995), 28 (14), 5029-36CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)
    A study of the phase structure of two linear polyethylene fractions has been carried out by Raman spectroscopy and from the anal. of the interface distribution function from the SAXS intensity data. Very good agreement is obtained for the core crystallite thickness, the liq.-like region, and the thickness of the interface from these two independent techniques. Moreover, the X-ray anal. distinguishes isothermally formed crystals from quenched crystals in cases where the Raman technique is not selective.
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    Savage, R. C.; Mullin, N.; Hobbs, J. K. Molecular Conformation at the Crystal-Amorphous Interface in Polyethylene. Macromolecules 2015, 48 (17), 6160– 6165,  DOI: 10.1021/ma5025736
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    Molecular Conformation at the Crystal-Amorphous Interface in Polyethylene
    Savage, R. C.; Mullin, N.; Hobbs, J. K.
    Macromolecules (Washington, DC, United States) (2015), 48 (17), 6160-6165CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)
    Torsional-tapping AFM with supersharp carbon-whisker tips is used to explore the mol. conformations at the surface of a semicryst. polymer. Images of the crystal-amorphous interface of oriented polyethylene have allowed us to measure hitherto inaccessible parameters that can be directly compared to polymer crystn. theories and mol. simulations, such as the length of stem-to-stem overhang. It has also been possible to identify both first- and second-neighbor folds and to det. the surface roughness of lamellae which we find approx. doubles the interfacial area. Finally, we calc. the interfacial d. profile from the images and find it to be sigmoidal but narrower than values reported by SAXS measurements.
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  134. 134
    Ahmad, N. A.; Wheeler, A. A.; Boettinger, W. J.; McFadden, G. B. Solute Trapping and Solute Drag in a Phase-Field Model of Rapid Solidification. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1998, 58 (3), 3436– 3450,  DOI: 10.1103/PhysRevE.58.3436
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    134
    Solute trapping and solute drag in a phase-field model of rapid solidification
    Ahmad, N. A.; Wheeler, A. A.; Boettinger, W. J.; McFadden, G. B.
    Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (1998), 58 (3-B), 3436-3450CODEN: PLEEE8; ISSN:1063-651X. (American Physical Society)
    During rapid solidification, solute may be incorporated into the solid phase at a concn. significantly different from that predicted by equil. thermodn. This process, known as solute trapping, leads to a progressive redn. in the concn. change across the interface as the solidification rate increases. Theor. treatments of rapid solidification using traditional sharp-interface descriptions require the introduction of sep. derived nonequil. models for the behavior of the interfacial temp. and solute concns. In contrast, phase-field models employ a diffuse-interface description and eliminate the need to specify interfacial conditions sep. While at low solidification rates equil. behavior is recovered, at high solidification rates nonequil. effects naturally emerge from these models. In particular, in a previous study we proposed a phase-field model of a binary alloy [A. A. Wheeler et al., Phys.Rev. E 47, 1893 (1993)] in which we demonstrated solute trapping. Here we show that solute trapping is also possible in a simpler diffuse interface model. We show that solute trapping occurs when the solute diffusion length DI/V is comparable to the diffuse interface thickness. Here V is the interface velocity and DI characterizes the solute diffusivity in the interfacial region. We characterize the dependence of the crit. speed for solute trapping on the equil. partition coeff. kE that shows good agreement with expts. by Aziz and co-workers [see M. J. Aziz, Metall. Mater. Trans. A 27, 671 (1996)]. We also show that in the phase-field model, there is a dissipation of energy in the interface region resulting in a solute drag, which we quantify by detg. the relationship between the interface temp. and velocity.
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  135. 135
    Brady, J. B. Diffusion Data for Silicate Minerals, Glasses, and Liquids. In Mineral Physics and Crystallography: A Handbook of Physical Constants; Ahrens, T. J., Ed.; American Geophysical Union: Washington, DC, 2013; p 269– 290.
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    Nakahara, H.; Bevelander, G.; Kakei, M. Electron Microscopic and Amino Acid Studies on the Outer and Inner Shell Layers of Haliotis rufescens. Venus (Japanese Journal of Malacology) 1982, 41, 33– 46
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    Macías-Sánchez, E.; Checa, A. G.; Willinger, M. G. The Transport System of Nacre Components through the Surface Membrane of Gastropods. Key Eng. Mater. 2016, 672, 103– 112,  DOI: 10.4028/www.scientific.net/KEM.672.103
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    Checa, A. G.; Cartwright, J. H. E.; Willinger, M. G. Mineral Bridges in Nacre. J. Struct. Biol. 2011, 176 (3), 330– 339,  DOI: 10.1016/j.jsb.2011.09.011
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    138
    Mineral bridges in nacre
    Checa, Antonio G.; Cartwright, Julyan H. E.; Willinger, Marc-Georg
    Journal of Structural Biology (2011), 176 (3), 330-339CODEN: JSBIEM; ISSN:1047-8477. (Elsevier B.V.)
    The authors confirm with high-resoln. techniques the existence of mineral bridges between superposed nacre tablets. In the towered nacre of both gastropods and the cephalopod Nautilus there are large bridges aligned along the tower axes, corresponding to gaps (150-200 nm) in the interlamellar membranes. Gaps were produced by the interaction of the nascent tablets with a surface membrane that covers the nacre compartment. In the terraced nacre of bivalves bridges assocd. with elongated gaps in the interlamellar membrane (>100 nm) have mainly been found at or close to the edges of superposed parental tablets. To explain this placement, the authors hypothesize that the interlamellar membrane breaks due to differences in osmotic pressure across it when the interlamellar space below becomes reduced at an advanced stage of calcification. In no cases are the minor connections between superimposed tablets (<60 nm), earlier reported to be mineral bridges, found to be such.
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  139. 139
    Gilbert, P. U. P. A.; Bergmann, K. D.; Myers, C. E.; Marcus, M. A.; DeVol, R. T.; Sun, C. Y.; Blonsky, A. Z.; Tamre, E.; Zhao, J.; Karan, E. A.; Tamura, N.; Lemer, S.; Giuffre, A. J.; Giribet, G.; Eiler, J. M.; Knoll, A. H. Nacre Tablet Thickness Records Formation Temperature in Modern and Fossil Shells. Earth Planet. Sci. Lett. 2017, 460, 281– 292,  DOI: 10.1016/j.epsl.2016.11.012
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    139
    Nacre tablet thickness records formation temperature in modern and fossil shells
    Gilbert, Pupa U. P. A.; Bergmann, Kristin D.; Myers, Corinne E.; Marcus, Matthew A.; DeVol, Ross T.; Sun, Chang-Yu; Blonsky, Adam Z.; Tamre, Erik; Zhao, Jessica; Karan, Elizabeth A.; Tamura, Nobumichi; Lemer, Sarah; Giuffre, Anthony J.; Giribet, Gonzalo; Eiler, John M.; Knoll, Andrew H.
    Earth and Planetary Science Letters (2017), 460 (), 281-292CODEN: EPSLA2; ISSN:0012-821X. (Elsevier B.V.)
    Nacre, the iridescent outer lining of pearls and inner lining of many mollusk shells, is composed of periodic, parallel, org. sheets alternating with aragonite (CaCO3) tablet layers. Nacre tablet thickness (TT) generates both nacre's iridescence and its remarkable resistance to fracture. Despite extensive studies on how nacre forms, the mechanisms controlling TT remain unknown, even though they det. the most conspicuous of nacre's characteristics, visible even to the naked eye.Thermodn. predicts that temp. (T) will affect both phys. and chem. components of biomineralized skeletons. The chem. compn. of biominerals is well-established to record environmental parameters, and has therefore been extensively used in paleoclimate studies. The phys. structure, however, has been hypothesized but never directly demonstrated to depend on the environment. Here we observe that the phys. TT in nacre from modern and fossil shallow-water shells of the bivalves Pinna and Atrina correlates with T as measured by the carbonate clumped isotope thermometer. Based on the obsd. TT vs. T correlation, we anticipate that TT will be used as a paleothermometer, useful to est. paleotemperature in shallow-water paleoenvironments. Here we successfully test the proposed new nacre TT thermometer on two Jurassic Pinna shells. The increase of TT with T is consistent with greater aragonite growth rate at higher T, and with greater metabolic rate at higher T. Thus, it reveals a complex, T-dependent biophys. mechanism for nacre formation.
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  140. 140
    Wang, R.; Gao, R.; Feng, X.; Zhang, G. Nacre Crystal Growth as a Paradigm of Island Growth Mode: Hydrophobic Substrate is One of the Keys to the Biomineralization. Mater. Express 2020, 10 (5), 762– 769,  DOI: 10.1166/mex.2020.1752
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    140
    Nacre crystal growth as a paradigm of island growth mode: hydrophobic substrate is one of the keys to the biomineralization
    Wang, Rize; Gao, Ruohe; Feng, Xin; Zhang, Gangsheng
    Materials Express (2020), 10 (5), 762-769CODEN: MEAXBS; ISSN:2158-5857. (American Scientific Publishers)
    Nacre is a multilayered film material consisting of alternating layers of aragonitic tablets and org. membranes (OMs). However, at this time, no authors have discussed the growth mode of nacre from the perspective of the science of typical film materials. Here, for the first time, we focus on measuring the contact angles of the nacre growth surface (GS) using the contact angle meter. Addnl., we also investigate the GS's structure and phases using field emission SEM and X-ray diffractometer, resp. We firstly found that: (1) The contact angles of the GS are always greater than 90°, with a max. value of 113° and min. value of 91°, indicating that the GS is hydrophobic. (2) The growth mode of GS is similar to the island growth mode (V-W) of the typical films. (3) The hydrophobicity of OMs plays an important role in the nucleation and growth of nacre. This research may provide new insights into the mechanism underlying nacre formation. In the field of thin-film, this conclusion will provide a new direction for the prepn. and research of hydrophobic substrates, and a new idea for the development of thin-film technol.
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  141. 141
    Nassif, N.; Pinna, N.; Gehrke, N.; Antonietti, M.; Jäger, C.; Cölfen, H. Amorphous Layer around Aragonite Platelets in Nacre. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 12653,  DOI: 10.1073/pnas.0502577102
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    141
    Amorphous layer around aragonite platelets in nacre
    Nassif, Nadine; Pinna, Nicola; Gehrke, Nicole; Antonietti, Markus; Jaeger, Christian; Coelfen, Helmut
    Proceedings of the National Academy of Sciences of the United States of America (2005), 102 (36), 12653-12655CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    The authors reveal that the aragonite CaCO3 platelets in nacre of Haliotis laevigata are covered with a continuous layer of disordered amorphous CaCO3 and that there is no protein interaction with this layer. This finding contradicts classical paradigms of biomineralization, e.g., an epitaxial match between the structural org. matrix and the formed mineral. This finding also highlights the role of physicochem. effects in morphogenesis, complementing the previously assumed total control by biomols. and bioprocesses, with many implications in nanotechnol. and materials science.
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  142. 142
    DeVol, R. T.; Sun, C.-Y.; Marcus, M. A.; Coppersmith, S. N.; Myneni, S. C. B.; Gilbert, P. U. P. A. Nanoscale Transforming Mineral Phases in Fresh Nacre. J. Am. Chem. Soc. 2015, 137, 13325– 13333,  DOI: 10.1021/jacs.5b07931
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    142
    Nanoscale Transforming Mineral Phases in Fresh Nacre
    DeVol, Ross T.; Sun, Chang-Yu; Marcus, Matthew A.; Coppersmith, Susan N.; Myneni, Satish C. B.; Gilbert, Pupa U. P. A.
    Journal of the American Chemical Society (2015), 137 (41), 13325-13333CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Nacre, or mother-of-pearl, the iridescent inner layer of many mollusk shells, is a biomineral lamellar composite of aragonite (CaCO3) and org. sheets. Biomineralization frequently occurs via transient amorphous precursor phases, crystg. into the final stable biomineral. In nacre, despite extensive attempts, amorphous calcium carbonate (ACC) precursors have remained elusive. They were inferred from non-nacre-forming larval shells, or from a residue of amorphous material surrounding mature gastropod nacre tablets, and have only once been obsd. in bivalve nacre. Here we present the first direct observation of ACC precursors to nacre formation, obtained from the growth front of nacre in gastropod shells from red abalone (Haliotis rufescens), using synchrotron spectromicroscopy. Surprisingly, the abalone nacre data show the same ACC phases that are precursors to calcite (CaCO3) formation in sea urchin spicules, and not proto-aragonite or poorly cryst. aragonite (pAra), as expected for aragonitic nacre. In contrast, we find pAra in coral.
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  143. 143
    Miura, H.; Kobayashi, R. Phase-Field Modeling of Step Dynamics on Growing Crystal Surface: Direct Integration of Growth Units to Step Front. Cryst. Growth Des. 2015, 15 (5), 2165– 2175,  DOI: 10.1021/cg501806d
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    143
    Phase-Field Modeling of Step Dynamics on Growing Crystal Surface: Direct Integration of Growth Units to Step Front
    Miura, Hitoshi; Kobayashi, Ryo
    Crystal Growth & Design (2015), 15 (5), 2165-2175CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    The authors propose a new formulation for numerically simulating step dynamics on growing crystal surfaces in the framework of a phase-field technique. The step advancement rate is proportional to a supersatn. at the crystal surface when the growth units in the ambient phase are integrated to the step front directly (direct integration hypothesis). The authors conduct numerical simulations of some std. step dynamics problems: the advancement of a straight step, the growth or dissoln. of a two-dimensional island, and the vertical growth of the crystal surface due to single or multiple screw dislocations. During evaluations, the authors' phase-field model accurately calcd. the rate of advancement of a straight step for various supersaturations. The calcd. time variation of the radius of the two-dimensional island showed good agreement with the exact soln. The vertical growth rate due to screw dislocations qual. agreed with the predictions of the classical theory of Burton, Cabrera, and Frank. The authors' simple formulation requires only a single parabolic partial differential equation to be solved numerically. Thus, the authors' phase-field model provides a simple numerical tool for a quant. step-by-step trajectory calcn., when the advancing velocity of each step follows the direct integration hypothesis.
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  144. 144
    Demange, G.; Zapolsky, H.; Patte, R.; Brunel, M. (2017). A Phase Field Model for Snow Crystal Growth in Three Dimensions. npj Computational Mater. 2017, 3 (1), 1– 7,  DOI: 10.1038/s41524-017-0015-1
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    144
    A phase field model for snow crystal growth in three dimensions
    Demange, Gilles; Zapolsky, Helena; Patte, Renaud; Brunel, Marc
    npj Computational Materials (2017), 3 (1), 1-7CODEN: NCMPCS; ISSN:2057-3960. (Nature Research)
    Snowflake growth provides a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equil. dynamics obsd. in various active scientific fields, ranging from pattern formation in phys. and chem. systems, to self-assembly problems in biol. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodn. quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapor phase transition, through anisotropic water mols. attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous exptl. observations.
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  145. 145
    Cartwright, J. H. E.; Checa, A. G.; Escribano, B.; Sainz-Díaz, C. I. Crystal Growth as an Excitable Medium. Philos. Trans. R. Soc., A 2012, 370, 2866– 2876,  DOI: 10.1098/rsta.2011.0600
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    145
    Crystal growth as an excitable medium
    Cartwright, Julyan H. E.; Checa, Antonio G.; Escribano, Bruno; Sainz-Diaz, C. Ignacio
    Philosophical Transactions of the Royal Society, A: Mathematical, Physical & Engineering Sciences (2012), 370 (1969), 2866-2876CODEN: PTRMAD; ISSN:1364-503X. (Royal Society)
    Crystal growth was widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface were understood as forms of tangential crystal growth mediated by defects and by 2-dimensional nucleation. Similar spirals and target patterns are ubiquitous in phys. systems describable as excitable media. Here, this is not merely a superficial resemblance, the physics of crystal growth can be set within the framework of an excitable medium, and appreciating this correspondence may prove useful to both fields. Apart from solid crystals, how model applies to the biomaterial nacre, formed by layer growth of a biol. liq. crystal are discussed.
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  146. 146
    Almagro, I.; Cartwright, J. H.E.; Checa, A. G.; Macias-Sanchez, E.; Sainz-Diaz, C. I. Evidence for a Liquid-Crystal Precursor Involved in the Formation of the Crossed-Lamellar Microstructure of the Mollusc Shell. Acta Biomater. 2021, 120, 12– 19,  DOI: 10.1016/j.actbio.2020.06.018
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    146
    Evidence for a liquid-crystal precursor involved in the formation of the crossed-lamellar microstructure of the mollusc shell
    Almagro, Io; Cartwright, Julyan H. E.; Checa, Antonio G.; Macias-Sanchez, Elena; Sainz-Diaz, C. Ignacio
    Acta Biomaterialia (2021), 120 (), 12-19CODEN: ABCICB; ISSN:1742-7061. (Elsevier Ltd.)
    A review. Many biol. structures use liq. crystals as self-organizing templates for their formation. We review and analyze evidence that the crossed-lamellar biomineral microstructure of mollusc shells may be formed from such a liq.-crystal precursor.
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    Thomas, S.; Lagzi, I.; Molnár, F., Jr.; Rácz, Z. Probability of the Emergence of Helical Precipitation Patterns in the Wake of Reaction-Diffusion Fronts. Phys. Rev. Lett. 2013, 110, 078303,  DOI: 10.1103/PhysRevLett.110.078303
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    147
    Probability of the emergence of helical precipitation patterns in the wake of reaction-diffusion fronts
    Thomas, Shibi; Lagzi, Istvan; Molnar, Ferenc, Jr.; Racz, Zoltan
    Physical Review Letters (2013), 110 (7), 078303/1-078303/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Helical and helicoidal pptn. patterns emerging in the wake of reaction-diffusion fronts are studied. In our expts., these chiral structures arise with well-defined probabilities PH controlled by conditions such as, e.g., the initial concn. of the reagents. We develop a model which describes the obsd. exptl. trends. The results suggest that PH is detd. by a delicate interplay among the time and length scales related to the front and to the unstable pptn. modes and, furthermore, that the noise amplitude also plays a quantifiable role.
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    Thomas, S.; Lagzi, I.; Molnár, F., Jr.; Rácz, Z. Helices in the Wake of Precipitation Fronts. Phys. Rev. E 2013, 88, 022141,  DOI: 10.1103/PhysRevE.88.022141
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    Helices in the wake of precipitation fronts
    Thomas, Shibi; Lagzi, Istvan; Molnar, Ferenc, Jr.; Racz, Zoltan
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2013), 88 (2-A), 022141/1-022141/6CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    A theor. study of the emergence of helixes in the wake of pptn. fronts is presented. The pptn. dynamics is described by the Cahn-Hilliard equation and the fronts are obtained by quenching the system into a linearly unstable state. Confining the process onto the surface of a cylinder and using the pulled-front formalism, our anal. calcns. show that there are front solns. that propagate into the unstable state and leave behind a helical structure. We find that helical patterns emerge only if the radius of the cylinder R is larger than a crit. value R > Rc, in agreement with recent expts.
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    Zegeling, P. A.; Lagzi, I.; Izsák, F. Transition of Liesegang Precipitation Systems: Simulations with an Adaptive Grid PDE Method. Commun. Comput. Phys. 2011, 10 (4), 867– 881,  DOI: 10.4208/cicp.050510.031210a
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    Sun, C. Y.; Stifler, C. A.; Chopdekar, R. V.; Schmidt, C. A.; Parida, G.; Schoeppler, V.; Fordyce, B. I.; Brau, J. H.; Mass, T.; Tambutté, S.; Gilbert, P. U. P. A. From Particle Attachment to Space-Filling Coral Skeletons. Proc. Natl. Acad. Sci. U. S. A. 2020, 117 (48), 30159– 30170,  DOI: 10.1073/pnas.2012025117
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    150
    From particle attachment to space-filling coral skeletons
    Sun, Chang-Yu; Stifler, Cayla A.; Chopdekar, Rajesh V.; Schmidt, Connor A.; Parida, Ganesh; Schoeppler, Vanessa; Fordyce, Benjamin I.; Brau, Jack H.; Mass, Tali; Tambutte, Sylvie; P. A. Gilbert, Pupa U.
    Proceedings of the National Academy of Sciences of the United States of America (2020), 117 (48), 30159-30170CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Reef-building corals and their aragonite (CaCO3) skeletons support entire reef ecosystems, yet their formation mechanism is poorly understood. Here we used synchrotron spectromicroscopy to observe the nanoscale mineralogy of fresh, forming skeletons from six species spanning all reef-forming coral morphologies: Branching, encrusting, massive, and table. In all species, hydrated and anhyd. amorphous calcium carbonate nanoparticles were precursors for skeletal growth, as previously obsd. in a single species. The amorphous precursors here were obsd. in tissue, between tissue and skeleton, and at growth fronts of the skeleton, within a low-d. nano- or microporous layer varying in thickness from 7 to 20 Aμm. Brunauer-Emmett-Teller measurements, however, indicated that the mature skeletons at the microscale were space-filling, comparable to single crystals of geol. aragonite. Nanoparticles alone can never fill space completely, thus ion-by-ion filling must be invoked to fill interstitial pores. Such ion-by-ion diffusion and attachment may occur from the supersatd. calcifying fluid known to exist in corals, or from a dense liq. precursor, obsd. in synthetic systems but never in biogenic ones. Concomitant particle attachment and ion-by-ion filling was previously obsd. in synthetic calcite rhombohedra, but never in aragonite pseudohexagonal prisms, synthetic or biogenic, as obsd. here. Models for biomineral growth, isotope incorporation, and coral skeletons' resilience to ocean warming and acidification must take into account the dual formation mechanism, including particle attachment and ion-by-ion space filling.
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    Mullins, W. W.; Sekerka, R. F. Stability of a Planar Interface During Solidification of a Dilute Binary Alloy. J. Appl. Phys. 1964, 35 (2), 444– 451,  DOI: 10.1063/1.1713333
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    Podmaniczky, F.; Tóth, G. I.; Tegze, G.; Gránásy, L. Hydrodynamic Theory of Freezing: Nucleation and Polycrystalline Growth. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2017, 95 (5), 052801,  DOI: 10.1103/PhysRevE.95.052801
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    Hendler, N.; Mentovich, E.; Korbuly, B.; Pusztai, T.; Gránásy, L.; Richter, S. Growth Control of Peptide-Nanotube Spherulitic Films: Experiments and Simulations. Nano Res. 2015, 8 (11), 3630– 3638,  DOI: 10.1007/s12274-015-0863-2
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    Growth control of peptide-nanotube spherulitic films: Experiments and simulations
    Hendler, Netta; Mentovich, Elad; Korbuly, Balint; Pusztai, Tamas; Granasy, Laszlo; Richter, Shachar
    Nano Research (2015), 8 (11), 3630-3638CODEN: NRAEB5; ISSN:1998-0000. (Springer GmbH)
    Multi-hierarchical self-assembly (MHSA) is a key process responsible for the spontaneous formation of many complex structures. However, because of the complexity of the process, the underlying mechanism remains largely unclear. Thus, a deeper understanding of MHSA is required, esp. for the prepn. of MHSA systems via bottom-up methodologies. We show here, exptl. and theor., that the complex-formation MHSA of peptide nanotube films can be controlled solely by manipulating the exptl. parameter of humidity. Furthermore, we identify growth-front nucleation (GFN; the formation of new grains at the perimeter) as the phys. background for the obsd. morphol. transitions by correlating exptl. observations with phase-field modeling of the morphol. evolution. Our findings indicate a simple way to control multi-hierarchical morphologies, crucial for the employment of bottom-up techniques in constructing complex structures for practical applications. [Figure not available: see fulltext.].
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  • Abstract

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    Figure 1

    Figure 1. Schematic view of bivalve molluscan anatomy with successive magnification of the mantle–nacre interface. (39) A thin liquid-filled extrapallial space is indicated (its thickness and content is open to debate). The interlamellar membrane is made of a viscoelastic chitin-based organic substance, whereas the mineral constituent is crystalline CC (aragonite). (Reproduced with permission from ref (39). Copyright 2009 United States National Academy of Sciences). Here “growth direction” indicates the lateral growth of the shell. However, this is based on layerwise growth perpendicular to the surface via formation of new layers that also grow laterally, a process which is responsible for both the thickening and the sidewise spreading of the shell. In the present work, we model the local thickening of the shell.

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    Figure 2

    Figure 2. Some typical mircrostructures observed in mollusk shells: (a) cross-sectional EBSD orientation map for the shell of Katelysia rhytiphora, (37) the outer side is on the left (note the transitions between layers of different crystallite morphologies); (b) outer randomly oriented granular domain in the shell of Unio pictorum (SEM); (26) (c) columnar prismatic domain of Pinna nobilis (X-ray tomography reconstruction), (13) and (d) plate-like structure of the nacre of Unio pictorum (SEM); (26) (e) spherulitic layer, section perpendicular to growth in the shell of Haliotis rufescens (SEM). (38) [(a) Reproduced from ref (37) under Creative Commons Attribution 4.0 License. Copyright Authors 2019. (b), (d) Reproduced with permission from ref (26) . Copyright 2018 Wiley. (c) Reproduced with permission from ref (13) . Copyright 2014 Springer Nature. (e) Reproduced from ref (38) . Copyright 2002 American Chemical Society.].

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    Figure 3

    Figure 3. Hierarchy of ultrastructures in the shell of some of the mollusks. Left: for bivalve Unio pictorum (growth direction: upward); (A) The shell, (B) schematic drawing of microstructure, (C–F) scanning electronmicroscopy (SEM) images. Right top: for cephalopod Nautilus pompilius (growth direction: to the right). Right bottom: for gastropod Haliotis asinina (growth direction: to the right); (A–C) SEM image, (C,D) magnified views of the granular domain and the prismatic → nacre transition. Note the similar sequence of ultrastructures during growth: granular → prismatic (columnar) → nacre (alternating mineral/organic layers). (Left: Reproduced with permission from ref (26). Copyright 2018 Wiley. Right: Reproduced with permission from ref (27). Copyright 2019 United States National Academy of Sciences).

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    Figure 4

    Figure 4. (a–h) Screw dislocation-like defects at the growth front of the nacreous layer of various species. (14,39) (a) Aragonitic nacre structure in the shell of the bivalve Pteria avicula. Reproduced with permission from ref (40). Copyright 2007 The Royal Society (U.K.). (b) Calcitic seminacre structure in the shell of brachiopod Novocrania anomala. Reproduced with permission from ref (41). Copyright 2010 The Paleontological Association. (c) Calcitic foliated structure in the shell of Ostrea edulis. Reproduced with permission from ref (42). Copyright 2007 Elsevier. (d) Aragonitic foliated structure in the shell of monoplacophoran Rokopella euglypta. Reproduced with permission from ref (43). Copyright 2009 American Chemical Society. Scale bars indicate 5 μm. SEM images showing the growth front of the nacreous layer for bivalves: (e–g) Pteria avicula and (h) Pteria hirundo. Reproduced with permission ref (40). Copyright 2007 The Royal Society (U.K.). (i,j) Target and spiral patterns formed in Belousov–Zhabotinsky reaction. Reproduced with permission from ref (44). Copyright 1996 Royal Society of Chemistry.

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    Figure 5

    Figure 5. From coral polyps to the CC (aragonite) skeleton they form, highly structured from the cm to the nm scale. (a) Schematic drawing of the coral polyp (colored) sitting on the porous skeleton (white). (45) Reproduced with permission from Britannica eReader.com, a service of Encyclopædia Britannica, Inc. (b) SEM image of the surface formed below coral polyps (corallites) in the case of Porites sp. Reproduced with permission from ref (46). Copyright 2011 Elsevier. (c) Cross-section of corallite, Pollicipora damicornis (linear size of image is ∼3 mm, “d” stands for mineral bridges termed distally convex dissepiments). Reproduced with permission from ref (47). Copyright 2006 Springer Nature. (d) Schematic drawing of a “plumose” spherulite. Reproduced with permission from ref (15). Copyright 2017 American Chemical Society. (e) PIC map of Acropora pharaonis coral skeleton showing spherulitic microstructure of crystals radiating from a band of randomly oriented sprinkles (linear center of calcification, the bar indicates 10 μm). Reproduced with permission from ref (28) under Creative Commons CC-BY-NC-ND 4.0 license. Copyright 2020 Elsevier. (f) PIC map of Phyllangia coral skeleton showing spherulitic microstructure of crystals radiating from centers of calcification, however, with no sprinkles.

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    Figure 6

    Figure 6. Complex crystallization structures in the experiments (1st and 3rd rows) and in the corresponding simulations performed using OF-PF models at the Wigner Research Centre for Physics (2nd and 4th rows). Upper block: From left to right: Rhombic dodecahedron crystals (upper panel reproduced from ref (91), lower panel reproduced with permission from ref (84). Copyright 2008 IOP Publishing Ltd.). Columnar dendrites (upper panel reproduced with permission from ref (92). Copyright 2016 Elsevier). Equiaxed dendrites (upper panel reproduced with permission from ref (93). Copyright 2016 Elsevier, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). “Dizzy” dendrites (reproduced with permission from ref (74). Copyright 2003 Springer Nature). Crystal sheaves (upper panel reproduced with permission from ref (94). Copyright 1993 American Chemical Society, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). Orientation field in spherulites (upper panel reproduced with permission from ref (95). Copyright 2007 American Chemical Society). Arboresque spherulites (upper panel reproduced with permission from ref (96). Copyright 2003 American Chemical Society, lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). Lower block: From left to right: Scratch induced dendritic crystallization in polymer film (reproduced with permission from ref (86). Copyright 2003 Springer Nature). Dumbbell-shape spherulites (upper panel reproduced with permission from ref (97). Copyright 2006 Wiley, lower panel reproduced with permission from ref (84). Copyright 2008 IOP Publishing Ltd.). Spherulites in temperature gradient (upper panel reproduced with permission from ref (98). Copyright 2003 Springer Nature, lower panel reproduced with permission from and ref (86). Copyright 2013 Springer Nature). Freezing soap bubble vs dendrite growing in spherical shell (upper panel reproduced with permission from ref (99)). Effect of oscillating temperature (reproduced with permission from ref (78). Copyright 2013 Springer Nature). “Quadrites” formed by nearly 90° branching (upper panel by courtesy of B. Okerberg, (100) lower panel reproduced with permission from ref (78). Copyright 2013 Springer Nature). “One eyed” spherulites (upper panel reproduced with permission from ref (101). Copyright 2002 Elsevier).

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    Figure 7

    Figure 7. Summary of biomineralization-related problems that are addressed within this work using phase-field methods. In each case, the applied model, the respective micromechanism, and the relevant phase transition are specified. Phase-field models PF1, PF2, and PF3 are defined in the text.

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    Figure 8

    Figure 8. Band formation as predicted by the binary Warren-Boettinger (103) (WB) type phase-field models: (a) transition from diffusionless solidification to partitioning with decreasing driving force (supersaturation decreases from left to right) in the presence of a single solid phase (ideal solution); and (b) transition from lamellar eutectics toward bands parallel to the growth front with increasing driving force (undercooling) in a WB model supplemented with square gradient term for concentration, (130) a case in which two solids of different composition form (regular solution). Lower panel was reproduced with permission from ref (130). Copyright 2017 Springer.

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    Figure 9

    Figure 9. Comparison of the microstructure of (a) the shell of mollusk Unio pictorum (26) as shown by electron microscopy images (see also Figure 3 left block; reproduced with permission from ref (26). Copyright 2018 Wiley) with simulations (b–e) obtained by model PF1 assuming (b, c) ion-by-ion attachment from extrapallial fluid (Dc,M = 10–9 m2/s) or (d, e) crystallization from an ACC layer (Dc,M = 10–15 m2/s). Growth direction is upward. Orientation (b, d) and grain boundary (c, e) maps are shown. In panels (b) and (d), colors denote different crystallographic orientations. In the experimental images of (a), the bars correspond to 3, 3, 1, and 1 μm, respectively, from top to bottom. Note the presence of the three characteristic domains in the experiment and in both types of simulations: granular, columnar prismatic, and sheet nacre structures. The qualitative phase-field simulations were performed on 1000 × 2000 grids (corresponding to 13.125 μm × 26.25 μm with the present choice of model parameters). (In the high driving force (lower) part of both these simulations lDv /Dc,M > 1; that is, diffusionless crystallization takes place, whereas in the upper domain, alternating mineral and organic layers mimicking the sheet nacre form.).

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    Figure 10

    Figure 10. Three stages of microstructure evolution in Model PF2 obtained assuming (a–d) ion-by-ion attachment from extrapallial fluid and (e–h) by crystallization from ACC precursor(orientation (a–c) and (e–g), and composition maps (d) and (h) are shown.): (a,e) Formation of granular structure via heterogeneous nucleation dominated equiaxed solidification; (b, f) columnar growth via directional solidification in concentration gradient yielding the prismatic structure, and (c, g) layerwise formation of alternating CCC and organic layers (sheet nacre). In panels (a–c) the mother phase is an aqueous solution (Dc,M = 10–9 m2/s) in the simulation shown; whereas an amorphous precursor (Dc,M = 10–15 m2/s) is assumed in the simulation shown in panels (d–f). The wavelength of the layered structure is roughly proportional to the free energy of the mother phase – CCC interface. The thickness of the mother phase (extrapallial domain) is assumed to be constant. In (a–c) and (e–g) different colors stand for different crystallographic orientation, while colors white and black stand for the mantle of the mollusk and the mother phase, respectively. In (d) and (h), gray, yellow, and blue indicate the mother phase, the organic phase, and CCC. The qualitative phase-field simulations were performed on 2000 × 200 grids (corresponding to an area of 26.25 μm × 2.625 μm with the present choice of model parameters). In (a–c) and (e–g) time elapses downward, whereas (c) and (d) and (g) and (h) display snapshots taken at the same time.

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    Figure 11

    Figure 11. Growth rates predicted by models PF1 (red lines) and PF2 (blue lines) for the ion-by-ion mechanism from aqueous solution and for crystallization from ACC precursor. Note the ∼7 orders of magnitude difference in growth velocity predicted for the two mechanisms. For comparison, the range of experimental data is also shown (gray domain). Note the oscillating growth rate in the layered domain.

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    Figure 12

    Figure 12. Electron microscopy images displaying the formation of columnar nacre in the case of (a) Haliotis rufescens (reproduced with permission from ref (136), under Creative Commons Attribution 4.0 License, Copyright 1982 Authors; the linear size is about 7.1 μm), and (b) Phorcus turbinatus (reproduced with permission from ref (137). Copyright 2015 Trans Tech). Here ss and s stand for “surface sheets” and “organic sheet”, whereas sm and ilm indicate “surface membrane” and “interlamellar membrane”, respectively.

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    Figure 13

    Figure 13. Snapshots of 2D phase-field simulations (model PF1), showing the formation of columnar nacre-like CCC tile stacks (gray/yellow - different colors denote different crystallographic orientations) via solidification between preexisting organic membranes (brown horizontal lines) with mineral bridges provided by (a) aligned holes of uniform width (20 Δx), and (b) aligned holes of three different widths (from left to right, 20, 5, and 10 Δx, respectively). The simulations were performed on 2000 × 500 and 2000 × 1000 grids (a) with anisotropic interfacial free energy and with (b) kinetic and interfacial free energy anisotropy. The horizontal size of the simulations is 26.25 μm.

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    Figure 14

    Figure 14. Domain in an idealized ternary phase diagram, (102) in which screw dislocation like structures form (green diamonds). For comparison, domains of spiraling eutectic dendrites (red dots), and unordered eutectic structures (blue crosses) are also shown.

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    Figure 15

    Figure 15. Screw dislocation pair formed in model PF3 at composition c = (0.43, 0.55, 0.02). (a) cross section through the axes of the pair. (b) Top view. (c) Front view of the central part of the section shown in panel (a). (d) Multiple screw dislocation pairs formed at c = (0.44, 0.54, 0.02). Red and yellow colors indicate solid solution phases rich in the mineral and organic components. These are generic dimensionless computations (performed on 256 × 256 × 272 grids moving with the solidification front), illustrating the ability of model PF3 to capture the formation of helical structures, but they are not optimized for modeling screw dislocations in sheet nacre.

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    Figure 16

    Figure 16. Comparison of the cross sectional microstructure of top part (corallite) of the skeleton of coral species Balanophyllia europea (a–c) to a simulation performed using by model PF1. The 2D simulation was performed on a 1000 × 2000 grid. Orientation maps obtained by PIC mapping are shown in (a–c). Reproduced with permission from ref (28) under Creative Commons license CC-BY-NC-ND 4.0. Copyright 2020 Elsevier. At high magnification, an abundance of small crystallites, sprinkles, can be seen around the centerline of the finger shown in panel (c). For comparison, the computed orientation maps are displayed in (d) and (e), whereas the computed composition map is presented in panel (f). In panels (b–e) different colors correspond to different crystallographic orientation. The white rectangles in (a) and (b) denote areas magnified in (b) and (c), respectively, whereas the white rectangles in panels (e) and (f) indicate the area shown magnified in panel (d). Panels (d–f) show results of a generic dimensionless computations that incorporate several dimensionless combinations of the relevant physical properties; accordingly, the corresponding physical size scale depends on the choice of these parameters. With appropriate choice of these parameters, the length scale of the experiments can be recovered.

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    Figure 17

    Figure 17. Morphology and microstructure evolution as a function of temperature as predicted by model PF1. The reference computation is shown in panel (d). The relative temperatures from left to right are ΔT = −3, – 2, – 1, 0, 1, and 2 K. The simulations were performed on 1000 × 2000 grids. Note the decreasing amount of sprinkles with increasing temperature (from left to right). These are generic dimensionless computations that incorporate several dimensionless combinations of the relevant physical properties; accordingly, the corresponding physical size scale depends on the choice of these parameters. With an appropriate choice of them, the length scale of the experiments can be recovered.

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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXnt1eitbc%253D&md5=aaa53a550aeb0954b40d7c1848e0a73c
    10. 10
      Holtus, T.; Helmbrecht, L.; Hendrikse, H. C.; Baglai, I.; Meuret, S.; Adhyaksa, G. W. P.; Garnett, E. C.; Noorduin, W. L. Shape-Preserving Transformation of Carbonate Minerals into Lead Halide Perovskite Semiconductors Based on Ion Exchange/Insertion Reactions. Nat. Chem. 2018, 10 (7), 740– 745,  DOI: 10.1038/s41557-018-0064-1
      10
      Shape-preserving transformation of carbonate minerals into lead halide perovskite semiconductors based on ion exchange/insertion reactions
      Holtus, Tim; Helmbrecht, Lukas; Hendrikse, Hans C.; Baglai, Iaroslav; Meuret, Sophie; Adhyaksa, Gede W. P.; Garnett, Erik C.; Noorduin, Willem L.
      Nature Chemistry (2018), 10 (7), 740-745CODEN: NCAHBB; ISSN:1755-4330. (Nature Research)
      Biol. and bio-inspired mineralization processes yield a variety of three-dimensional structures with relevance for fields such as photonics, electronics and photovoltaics. However, these processes are only compatible with specific material compns., often carbonate salts, thereby hampering widespread applications. Here we present a strategy to convert a wide range of metal carbonate structures into lead halide perovskite semiconductors with tunable bandgaps, while preserving the 3D shape. First, we introduce lead ions by cation exchange. Second, we use carbonate as a leaving group, facilitating anion exchange with halide, which is followed rapidly by methylammonium insertion to form the perovskite. As proof of principle, pre-programmed carbonate salt shapes such as vases, coral-like forms and helixes are transformed into perovskites while preserving the morphol. and crystallinity of the initial micro-architectures. This approach also readily converts calcium carbonate biominerals into semiconductors, furnishing biol. and programmable synthetic shapes with the performance of artificial compns. such as perovskite-based semiconductors.
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    11. 11
      Simkiss, K.; Wilbur, K. Biomineralization; Academic Press, Inc.: San Diego, 1989.
      There is no corresponding record for this reference.
    12. 12
      Imai, H. Self-Organized Formation of Hierarchical Structures. Top. Curr. Chem. 2007, 270, 43– 72,  DOI: 10.1007/128_054
      12
      Self-organized formation of hierarchical structures
      Imai, Hiroaki
      Topics in Current Chemistry (2007), 270 (Biomineralization I), 43-72CODEN: TPCCAQ; ISSN:0340-1022. (Springer GmbH)
      A review. Hierarchical architectures consisting of small building blocks of inorg. crystals are widely found in biominerals. Crystal growth mimicking biomineralization has been studied using various kinds of org. mols. and mol. assembly. The emergence of complex organization of inorg. crystals was obsd. through biomimetic approaches in aq. soln. A wide variety of hierarchical architectures including fractals, dendrites, self-similar and helical structures were achieved in the artificial systems. Self-organized formation, with exquisite control of mass transport and the variation of surface energy with org. mols., is essential for versatile morphogenesis of inorg. crystals similar to biominerals.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhs1Whs7s%253D&md5=e8cb990faec9ab30cd5e3b1ae95fc422
    13. 13
      Bayerlein, B.; Zaslansky, P.; Dauphin, Y.; Rack, A.; Fratzl, P.; Zlotnikov, I. Self-Similar Mesostructure Evolution of the Growing Mollusc Shell Reminiscent of Thermodynamically Driven Grain Growth. Nat. Mater. 2014, 13 (12), 1102– 1107,  DOI: 10.1038/nmat4110
      13
      Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth
      Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor
      Nature Materials (2014), 13 (12), 1102-1107CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Significant progress has been made in understanding the interaction between mineral precursors and org. components leading to material formation and structuring in biomineralizing systems. The mesostructure of biol. materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biol. Here, we analyze the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resoln. synchrotron-based microtomog. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphol. and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biol. organisms make use of thermodn. to generate complex morphologies.
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    14. 14
      Zlotnikov, I.; Schoeppler, V. Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis. Adv. Funct. Mater. 2017, 27 (28), 1700506,  DOI: 10.1002/adfm.201700506
      There is no corresponding record for this reference.
    15. 15
      Sun, C. Y.; Marcus, M. A.; Frazier, M. J.; Giuffre, A. J.; Mass, T.; Gilbert, P. U. P. A. Spherulitic Growth of Coral Skeletons and Synthetic Aragonite: Nature’s Three-Dimensional Printing. ACS Nano 2017, 11 (7), 6612– 6622,  DOI: 10.1021/acsnano.7b00127
      15
      Spherulitic Growth of Coral Skeletons and Synthetic Aragonite: Nature's Three-Dimensional Printing
      Sun, Chang-Yu; Marcus, Matthew A.; Frazier, Matthew J.; Giuffre, Anthony J.; Mass, Tali; Gilbert, Pupa U. P. A.
      ACS Nano (2017), 11 (7), 6612-6622CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Coral skeletons were long assumed to have a spherulitic structure, i.e., a radial distribution of acicular aragonite (CaCO3) crystals with their c-axes radiating from series of points, termed centers of calcification (CoCs). This assumption was based on morphol. alone, not on crystallog. Here we measure the orientation of crystals and nanocrystals and confirm that corals grow their skeletons in bundles of aragonite crystals, with their c-axes and long axes oriented radially and at an angle from the CoCs, thus precisely as expected for feather-like or "plumose" spherulites. Furthermore, we find that in both synthetic and coral aragonite spherulites at the nanoscale adjacent crystals have similar but not identical orientations, thus demonstrating by direct observation that even at nanoscale the mechanism of spherulite formation is non-crystallog. branching (NCB), as predicted by theory. Finally, synthetic aragonite spherulites and coral skeletons have similar angle spreads, and angular distances of adjacent crystals, further confirming that coral skeletons are spherulites. This is important because aragonite grows anisotropically, 10 times faster along the c-axis than along the a-axis direction, and spherulites fill space with crystals growing almost exclusively along the c-axis, thus they can fill space faster than any other aragonite growth geometry, and create isotropic materials from anisotropic crystals. Greater space filling rate and isotropic mech. behavior are key to the skeleton's supporting function and therefore to its evolutionary success. In this sense, spherulitic growth is Nature's 3D printing.
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    16. 16
      De Tommasi, E.; Gielis, J.; Rogato, A. Diatom Frustule Morphogenesis and Function: A Multidisciplinary Survey. Marine Genomics 2017, 35, 1– 18,  DOI: 10.1016/j.margen.2017.07.001
      16
      Diatom Frustule Morphogenesis and Function: a Multidisciplinary Survey
      De Tommasi Edoardo; Gielis Johan; Rogato Alessandra
      Marine genomics (2017), 35 (), 1-18 ISSN:.
      Diatoms represent the major component of phytoplankton and are responsible for about 20-25% of global primary production. Hundreds of millions of years of evolution led to tens of thousands of species differing in dimensions and morphologies. In particular, diatom porous silica cell walls, the frustules, are characterized by an extraordinary, species-specific diversity. It is of great interest, among the marine biologists and geneticists community, to shed light on the origin and evolutionary advantage of this variability of dimensions, geometries and pore distributions. In the present article the main reported data related to frustule morphogenesis and functionalities with contributions from fundamental biology, genetics, mathematics, geometry and physics are reviewed.
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    17. 17
      Cloutier, J.; Villa, L.; Traxer, O.; Daudon, M. Kidney Stone Analysis: “Give Me Your Stone, I Will Tell You Who You Are!. World J. Urol. 2015, 33 (2), 157– 169,  DOI: 10.1007/s00345-014-1444-9
      17
      Kidney stone analysis: "Give me your stone, I will tell you who you are!"
      Cloutier Jonathan; Villa Luca; Traxer Olivier; Daudon Michel
      World journal of urology (2015), 33 (2), 157-69 ISSN:.
      INTRODUCTION: Stone analysis is an important part in the evaluation of patients having stone disease. This could orientate the physician toward particular etiologies. MATERIAL AND METHODS: Chemical and physical methods are both used for analysis. Unfortunately, chemical methods often are inadequate to analyze accurately urinary calculi and could fail to detect some elements into the stone. Physical methods, in counterpart, are becoming more and more used in high-volume laboratories. The present manuscript will provide a review on analytic methods, and review all the information that should be included into an appropriate morpho-constitutional analysis. CONCLUSION: This report can supply an excellent summarization of the stone morphology and give the opportunity to find specific metabolic disorders and different lithogenic process into the same stone. Here, specific chemical types with their different crystalline phases are shown in connection with their different etiologies involved.
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    18. 18
      Boskey, A. L. Mineralization of Bones and Teeth. Elements 2007, 3 (6), 385– 391,  DOI: 10.2113/GSELEMENTS.3.6.385
      18
      Mineralization of bones and teeth
      Boskey, Adele L.
      Elements (Chantilly, VA, United States) (2007), 3 (6), 385-391CODEN: EOOCAG; ISSN:1811-5209. (Mineralogical Society of America)
      A review. Bones and teeth consist of an inorg. calcium phosphate mineral approximated by hydroxylapatite and matrix proteins. The phys. and chem. properties of these "bioapatite" crystals are different from those of geol. hydroxylapatite because of the way they are formed, and these unique properties are required for fulfilling the biol. functions of bones and teeth. Recent biochem. studies provide insight into the factors controlling the formation and growth of bioapatite crystals and how alteration in the mineralization process can lead to diseases such as osteoporosis. New spectroscopic and microscopic techniques are enabling scientists to characterize changes in crystal properties in these diseases, providing potentially fruitful areas of collaboration among geochemists, mineralogists, and biol. researchers and offering hope for the development of novel therapies.
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    19. 19
      Lin, W.; Zhang, W.; Zhao, X.; Roberts, A. P.; Paterson, G. A.; Bazylinski, D. A.; Pan, Y. Genomic Expansion of Magnetotactic Bacteria Reveals an Early Common Origin of Magnetotaxis with Lineage-Specific Evolution. ISME J. 2018, 12 (6), 1508– 1519,  DOI: 10.1038/s41396-018-0098-9
      19
      Genomic expansion of magnetotactic bacteria reveals an early common origin of magnetotaxis with lineage-specific evolution
      Lin, Wei; Zhang, Wensi; Zhao, Xiang; Roberts, Andrew P.; Paterson, Greig A.; Bazylinski, Dennis A.; Pan, Yongxin
      ISME Journal (2018), 12 (6), 1508-1519CODEN: IJSOCF; ISSN:1751-7362. (Nature Research)
      The origin and evolution of magnetoreception, which in diverse prokaryotes and protozoa is known as magnetotaxis and enables these microorganisms to detect Earth's magnetic field for orientation and navigation, is not well understood in evolutionary biol. The only known prokaryotes capable of sensing the geomagnetic field are magnetotactic bacteria (MTB), motile microorganisms that biomineralize intracellular, membrane-bounded magnetic single-domain crystals of either magnetite (Fe3O4) or greigite (Fe3S4) called magnetosomes. Magnetosomes are responsible for magnetotaxis in MTB. Here we report the first large-scale metagenomic survey of MTB from both northern and southern hemispheres combined with 28 genomes from uncultivated MTB. These genomes expand greatly the coverage of MTB in the Proteobacteria, Nitrospirae, and Omnitrophica phyla, and provide the first genomic evidence of MTB belonging to the Zetaproteobacteria and "Candidatus Lambdaproteobacteria" classes. The gene content and organization of magnetosome gene clusters, which are phys. grouped genes that encode proteins for magnetosome biosynthesis and organization, are more conserved within phylogenetically similar groups than between different taxonomic lineages. Moreover, the phylogenies of core magnetosome proteins form monophyletic clades. Together, these results suggest a common ancient origin of iron-based (Fe3O4 and Fe3S4) magnetotaxis in the domain Bacteria that underwent lineage-specific evolution, shedding new light on the origin and evolution of biomineralization and magnetotaxis, and expanding significantly the phylogenomic representation of MTB.
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    20. 20
      Kaplan, D. L. Mollusc Shell Structures: Novel Design Strategies for Synthetic Materials. Curr. Opin. Solid State Mater. Sci. 1998, 3 (3), 232– 236,  DOI: 10.1016/S1359-0286(98)80096-X
      20
      Mollusk shell structures: novel design strategies for synthetic materials
      Kaplan, David L.
      Current Opinion in Solid State & Materials Science (1998), 3 (3), 232-236CODEN: COSSFX; ISSN:1359-0286. (Current Chemistry)
      A review, with 32 refs. Mollusk shells are layered org.-inorg. composites bioengineered at the nanoscale. The structural features of these composites result in toughened shells and can provide a useful paradigm to consider in the design of biomaterials. Recent studies in vitro illustrate the function of proteins in controlling the nucleation and growth of the inorg. phases in these structures. Characterization of the morphol. of the org. matrix provides new insights into the registry between layers of inorg. material. Biomimetic methods are being used to duplicate these biomineralization processes to achieve comparable structural features in ceramic composites.
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    21. 21
      Barthelat, F. Growing a Synthetic Mollusk Shell. Science 2016, 354 (6308), 32– 33,  DOI: 10.1126/science.aah6507
      21
      Growing a synthetic mollusk shell
      Barthelat, Francois
      Science (Washington, DC, United States) (2016), 354 (6308), 32-33CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      There is no expanded citation for this reference.
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    22. 22
      Gao, H. L.; Chen, S. M.; Mao, L. B.; Song, Z. Q.; Yao, H. B.; Cölfen, H.; Luo, X. S.; Zhang, F.; Pan, Z.; Meng, Y. F.; Ni, Y.; Yu, S. H. Mass Production of Bulk Artificial Nacre with Excellent Mechanical Properties. Nat. Commun. 2017, 8 (1), 287,  DOI: 10.1038/s41467-017-00392-z
      22
      Mass production of bulk artificial nacre with excellent mechanical properties
      Gao Huai-Ling; Chen Si-Ming; Mao Li-Bo; Yao Hong-Bin; Pan Zhao; Meng Yu-Feng; Yu Shu-Hong; Song Zhao-Qiang; Ni Yong; Yu Shu-Hong; Colfen Helmut; Luo Xi-Sheng; Zhang Fu
      Nature communications (2017), 8 (1), 287 ISSN:.
      Various methods have been exploited to replicate nacre features into artificial structural materials with impressive structural and mechanical similarity. However, it is still very challenging to produce nacre-mimetics in three-dimensional bulk form, especially for further scale-up. Herein, we demonstrate that large-sized, three-dimensional bulk artificial nacre with comprehensive mimicry of the hierarchical structures and the toughening mechanisms of natural nacre can be facilely fabricated via a bottom-up assembly process based on laminating pre-fabricated two-dimensional nacre-mimetic films. By optimizing the hierarchical architecture from molecular level to macroscopic level, the mechanical performance of the artificial nacre is superior to that of natural nacre and many engineering materials. This bottom-up strategy has no size restriction or fundamental barrier for further scale-up, and can be easily extended to other material systems, opening an avenue for mass production of high-performance bulk nacre-mimetic structural materials in an efficient and cost-effective way for practical applications.Artificial materials that replicate the mechanical properties of nacre represent important structural materials, but are difficult to produce in bulk. Here, the authors exploit the bottom-up assembly of 2D nacre-mimetic films to fabricate 3D bulk artificial nacre with an optimized architecture and excellent mechanical properties.
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    23. 23
      Song, P.; Xu, Z.; Wu, Y.; Cheng, Q.; Guo, Q.; Wang, H. Super-Tough Artificial Nacre Based on Graphene Oxide via Synergistic Interface Interactions of π-π Stacking and Hydrogen Bonding. Carbon 2017, 111, 807– 812,  DOI: 10.1016/j.carbon.2016.10.067
      23
      Super-tough artificial nacre based on graphene oxide via synergistic interface interactions of π-π stacking and hydrogen bonding
      Song, Pingan; Xu, Zhiguang; Wu, Yuanpeng; Cheng, Qunfeng; Guo, Qipeng; Wang, Hao
      Carbon (2017), 111 (), 807-812CODEN: CRBNAH; ISSN:0008-6223. (Elsevier Ltd.)
      Inspired by interfacial interactions of protein matrix and the crystal platelets in nacre, herein, a super-tough artificial nacre was produced through constructing the synergistic interface interactions of π-π interaction and hydrogen bonding between graphene oxide (GO) nanosheets and sulfonated styrene-ethylene/butylene-styrene copolymer synthesized with multifunctional benzene. The resultant GO-based artificial nacre showed super-high toughness of 15.3 ± 2.5 MJ/m3, superior to natural nacre and other GO-based nanocomposites. The ultra-tough property of the novel nacre was attributed to synergistic effect of π-π stacking interactions and hydrogen bonding. This bioinspired synergistic toughening strategy opens a new avenue for constructing high performance GO-based nanocomposites in the near future.
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    24. 24
      Spiesz, E. M.; Schmieden, D. T.; Grande, A. M.; Liang, K.; Schwiedrzik, J.; Natalio, F.; Michler, J.; Garcia, S. J.; Aubin-Tam, M. E.; Meyer, A. S. Bacterially Produced, Nacre-Inspired Composite Materials. Small 2019, 15 (22), 1805312,  DOI: 10.1002/smll.201805312
      There is no corresponding record for this reference.
    25. 25
      Chen, Y.; Fu, J.; Dang, B.; Sun, Q.; Li, H.; Zhai, T. Artificial Wooden Nacre: A High Specific Strength Engineering Material. ACS Nano 2020, 14 (2), 2036– 2043,  DOI: 10.1021/acsnano.9b08647
      25
      Artificial Wooden Nacre: A High Specific Strength Engineering Material
      Chen, Yipeng; Fu, Jinzhou; Dang, Baokang; Sun, Qingfeng; Li, Huiqiao; Zhai, Tianyou
      ACS Nano (2020), 14 (2), 2036-2043CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Nacre, an org.-inorg. composite biomaterial that forms an ordered multilayer microstructure after years of slow biomineralization, is known as the strongest and toughest material within the mollusc family. Its unique structure provides inspiration for robust artificial engineering materials. Lignocellulose is ultralightweight, abundant, and possesses a high mech. performance and has been used for ages as a significant renewable raw material in wooden engineering composites. However, the inherent lack of mech. properties of current wooden composites assocd. with the fragile microstructure has limited their applications in advanced engineering materials. Here, we develop a large-size ultralightweight artificial "wood nacre" with an ordered layer structure through a fast and scalable "mech./chem. mineralization and assembly" approach. The millimeter-thick artificial wooden nacre mimics the stratified construction of natural nacre, resulting in a bulk hybrid material that can achieve almost the same strength as natural nacre while consisting of only one-sixth of the total inorg. content of natural nacre. The specific strength and toughness of the artificial wooden nacre is even superior to engineering alloy materials (such as Cu and Fe). This approach represents an efficient strategy for the mass prodn. of lightwt. sustainable structural materials with high strength and toughness.
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    26. 26
      Schoeppler, V.; Gránásy, L.; Reich, E.; Poulsen, N.; de Kloe, R.; Cook, P.; Rack, A.; Pusztai, T.; Zlotnikov, I. Biomineralization as a Paradigm of Directional Solidification: A Physical Model for Molluscan Shell Ultrastructural Morphogenesis. Adv. Mater. 2018, 30 (45), 1803855,  DOI: 10.1002/adma.201803855
      There is no corresponding record for this reference.
    27. 27
      Schoeppler, V.; Lemanis, R.; Reich, E.; Pusztai, T.; Gránásy, L.; Zlotnikov, I. Crystal Growth Kinetics as an Architectural Constraint on the Evolution of Molluscan Shells. Proc. Natl. Acad. Sci. U. S. A. 2019, 116 (41), 20388– 20397,  DOI: 10.1073/pnas.1907229116
      27
      Crystal growth kinetics as an architectural constraint on the evolution of molluscan shells
      Schoeppler, Vanessa; Lemanis, Robert; Reich, Elke; Pusztai, Tamas; Granasy, Lalkszlo; Zlotnikov, Igor
      Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (41), 20388-20397CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Molluscan shells are a classic model system to study formation-structure-function relationships in biol. materials and the process of biomineralized tissue morphogenesis. Typically, each shell consists of a no. of highly mineralized ultrastructures, each characterized by a specific 3D mineral-org. architecture. Surprisingly, in some cases, despite the lack of a mutual biochem. toolkit for biomineralization or evidence of homol., shells from different independently evolved species contain similar ultrastructural motifs. In the present study, using a recently developed phys. framework, which is based on an analogy to the process of directional solidification and simulated by phase-field modeling, we compare the process of ultrastructural morphogenesis of shells from 3 major molluscan classes: A bivalve Unio pictorum, a cephalopod Nautilus pompilius, and a gastropod Haliotis asinina. We demonstrate that the fabrication of these tissues is guided by the organisms by regulating the chem. and phys. boundary conditions that control the growth kinetics of the mineral phase. This biomineralization concept is postulated to act as an architectural constraint on the evolution of molluscan shells by defining a morphospace of possible shell ultrastructures that is bounded by the thermodn. and kinetics of crystal growth.
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    28. 28
      Sun, C. Y.; Gránásy, L.; Stifler, C. A.; Zaquin, T.; Chopdekar, R. V.; Tamura, N.; Weaver, J. C.; Zhang, J. A. Y.; Goffredo, S.; Falini, G.; Marcus, M. A.; Pusztai, T.; Schoeppler, V.; Mass, T.; Gilbert, P. Crystal Nucleation and Growth of Spherulites Demonstrated by Coral Skeletons and Phase-Field Simulations. Acta Biomater. 2021, 120, 277– 292,  DOI: 10.1016/j.actbio.2020.06.027
      28
      Crystal nucleation and growth of spherulites demonstrated by coral skeletons and phase-field simulations
      Sun, Chang-Yu; Granasy, Laszlo; Stifler, Cayla A.; Zaquin, Tal; Chopdekar, Rajesh V.; Tamura, Nobumichi; Weaver, James C.; Zhang, Jun A. Y.; Goffredo, Stefano; Falini, Giuseppe; Marcus, Matthew A.; Pusztai, Tamas; Schoeppler, Vanessa; Mass, Tali; Gilbert, Pupa U. P. A.
      Acta Biomaterialia (2021), 120 (), 277-292CODEN: ABCICB; ISSN:1742-7061. (Elsevier Ltd.)
      Spherulites are radial distributions of acicular crystals, common in biogenic, geol., and synthetic systems, yet exactly how spherulitic crystals nucleate and grow is still poorly understood. To investigate these processes in more detail, we chose scleractinian corals as a model system, because they are well known to form their skeletons from aragonite (CaCO3) spherulites, and because a comparative study of crystal structures across coral species has not been performed previously. We obsd. that all 12 diverse coral species analyzed here exhibit plumose spherulites in their skeletons, with well-defined centers of calcification (CoCs), and cryst. fibers radiating from them. In 7 of the 12 species, we obsd. a skeletal structural motif not obsd. previously: randomly oriented, equant crystals, which we termed "sprinkles". In Acropora pharaonis, these sprinkles are localized at the CoCs, while in 6 other species, sprinkles are either layered at the growth front (GF) of the spherulites, or randomly distributed. At the nano- and micro-scale, coral skeletons fill space as much as single crystals of aragonite. Based on these observations, we tentatively propose a spherulite formation mechanism in which growth front nucleation (GFN) of randomly oriented sprinkles, competition for space, and coarsening produce spherulites, rather than the previously assumed slightly misoriented nucleations termed "non-crystallog. branching". Phase-field simulations support this mechanism, and, using a minimal set of thermodn. parameters, are able to reproduce all of the microstructural variation obsd. exptl. in all of the investigated coral skeletons. Beyond coral skeletons, other spherulitic systems, from aspirin to semicryst. polymers and chocolate, may also form according to the mechanism for spherulite formation proposed here. Understanding the fundamental mechanisms of spherulite nucleation and growth has broad ranging applications in the fields of metallurgy, polymers, food science, and pharmaceutical prodn. Using the skeletons of reef-building corals as a model system for investigating these processes, we propose a new spherulite growth mechanism that can not only explain the micro-structural diversity obsd. in distantly related coral species, but may point to a universal growth mechanism in a wide range of biol. and technol. relevant spherulitic materials systems.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFGmsbvP&md5=fede652908f5bbd47d520cafbe3f721a
    29. 29
      Metzler, R. A.; Zhou, D.; Abrecht, M.; Chiou, J. W.; Guo, J.; Ariosa, D.; Coppersmith, S. N.; Gilbert, P. U. P. A. Polarization-Dependent Imaging Contrast in Abalone Shells. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77 (6), 064110,  DOI: 10.1103/PhysRevB.77.064110
      29
      Polarization-dependent imaging contrast in abalone shells
      Metzler, Rebecca A.; Zhou, Dong; Abrecht, Mike; Chiou, Jau-Wern; Guo, Jinghua; Ariosa, Daniel; Coppersmith, Susan N.; Gilbert, P. U. P. A.
      Physical Review B: Condensed Matter and Materials Physics (2008), 77 (6), 064110/1-064110/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Many biominerals contain micro- or nanocryst. mineral components, organized accurately into architectures that confer the material with improved mech. performance at the macroscopic scale. An effect is presented which enables observation of the relative orientation of individual crystals at the submicron scale. The effect is called the polarization-dependent imaging contrast (PIC), since it is an imaging development of the well-known x-ray linear dichroism. Most importantly, PIC is obtained in situ, in biominerals. PIC in the prismatic and nacreous layers of Haliotis rufescens (red abalone) confirms the presence of calcite and aragonite and corroborates the exptl. data with theor. simulated spectra. PIC reveals different and unexpected aspects of nacre architecture that have inspired theor. models for nacre formation.
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    30. 30
      Gilbert, P. U. P. A.; Young, A.; Coppersmith, S. N. Measurement of C-Axis Angular Orientation in Calcite (CaCO3) Nanocrystals Using X-Ray Absorption Spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2011, 108 (28), 11350– 11355,  DOI: 10.1073/pnas.1107917108
      30
      Measurement of c-axis angular orientation in calcite (CaCO3) nanocrystals using X-ray absorption spectroscopy
      Gilbert, P. U. P. A.; Young, Anthony; Coppersmith, Susan N.
      Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (28), 11350-11355, S11350/1-S11350/3CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      We demonstrate that the ability to manipulate the polarization of synchrotron radiation can be exploited to enhance the capabilities of X-ray absorption near-edge structure (XANES) spectroscopy, to include linear dichroism effects. By acquiring spectra at the same photon energies but different polarizations, and using a photoelectron emission spectro-microscope (PEEM), one can quant. det. the angular orientation of micro- and nanocrystals with a spatial resoln. down to 10 nm. XANES-PEEM instruments are already present at most synchrotrons, hence these methods are readily available. The methods are demonstrated here on geol. calcite (CaCO3) and used to investigate the prismatic layer of a mollusk shell, Pinctada fucata. These XANES-PEEM data reveal multiply oriented nanocrystals within calcite prisms, previously thought to be monocryst. The subdivision into multiply oriented nanocrystals, spread by more than 50°, may explain the excellent mech. properties of the prismatic layer, known for decades but never explained.
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    31. 31
      Addadi, L.; Joester, D.; Nudelman, F.; Weiner, S. Mollusk Shell Formation: A Source of New Concepts for Understanding Biomineralization Processes. Chem. - Eur. J. 2006, 12 (4), 980– 987,  DOI: 10.1002/chem.200500980
      31
      Mollusk shell formation: a source of new concepts for understanding biomineralization processes
      Addadi, Lia; Joester, Derk; Nudelman, Fabio; Weiner, Steve
      Chemistry - A European Journal (2006), 12 (4), 980-987CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. The biol. approach to forming crystals is proving to be most surprising. Mollusks build their shells by using a hydrophobic silk gel, very acidic aspartic acid rich proteins, and apparently also an amorphous precursor phase from which the crystals form. All this takes place in a highly structured chitinous framework. The authors present ideas on how these disparate components work together to produce the highly structured pearly nacreous layer of the mollusk shell.
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    32. 32
      Marin, F.; Le Roy, N.; Marie, B. The Formation and Mineralization of Mollusk Shell. Front. Biosci., Scholar Ed. 2012, S4 (3), 1099– 1125,  DOI: 10.2741/s321
      32
      The formation and mineralization of mollusk shell
      Marin, Frederic; Le Roy, Nathalie; Marie, Benjamin
      Frontiers in Bioscience, Scholar Edition (2012), S4 (3), 1099-1125CODEN: FBSEAU; ISSN:1945-0524. (Frontiers in Bioscience)
      A review. In the last years, the field of mollusk biomineralization has known a tremendous mutation. The most recent advances deal with the nanostructure of shell biominerals, and with the identification of several shell matrix proteins: on one hand, the complex hierarchical organization of shell biominerals has been deciphered in few models, like nacre. On the other hand, although proteins represent a minor shell component, they are the major macromols. that control biocrystal synthesis. Until recently, the paradigm was to consider that this control occurs by 2 antagonist mechanisms: crystal nucleation and growth inhibition. Emerging models try to translate a more complex reality, illustrated by the huge variety of shell proteins, characterized so far. The primary structure of many of them is composed of different functional domains, some of which exhibit enzymic activity, while others may be involved in cell signaling. Many of them have unknown functions. Today, the shell matrix appears as a whole system, which regulates protein-mineral, protein-protein, and epithelium-mineral interactions. These aspects should be taken in account for the future models of shell formation.
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    33. 33
      Sun, J.; Bhushan, B. Hierarchical Structure and Mechanical Properties of Nacre: A Review. RSC Adv. 2012, 2 (20), 7617– 7632,  DOI: 10.1039/c2ra20218b
      33
      Hierarchical structure and mechanical properties of nacre: a review
      Sun, Jiyu; Bhushan, Bharat
      RSC Advances (2012), 2 (20), 7617-7632CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
      A review. Nacre (known as mother of pearl) is the iridescent inner shell layer of some mollusks. Nacre is composed of 95 wt% aragonite (a crystallog. form of CaCO3) and 5 wt% org. materials (proteins and polysaccharides). It is well known that it exhibits high fracture toughness, much greater than that of monolithic aragonite, because of its ingenious structure. It also exhibits energy absorption properties. It has a complex hierarchical microarchitecture that spans multiple length scales from the nanoscale to the macroscale. It includes columnar architectures and sheet tiles, mineral bridges, polygonal nanograins, nanoasperities, plastic microbuckling, crack deflection, and interlocking bricks, which exhibit a remarkable combination of stiffness, low wt. and strength. Nacre's special self-assembly characteristics have attracted interest from materials scientists for the development of laminated composite materials, mol. scale self-assembly and biomineralization. This paper reviews the characteristics of hierarchical structure and the mech. properties of nacre that provide the desired properties, and the latest developments and biomimetic applications.
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    34. 34
      Checa, A. G. Physical and Biological Determinants of the Fabrication of Molluscan Shell Microstructures. Front. Mar. Sci. 2018, 5, 353,  DOI: 10.3389/fmars.2018.00353
      There is no corresponding record for this reference.
    35. 35
      Crenshaw, M. A. The Inorganic Composition of Molluscan Extrapallial Fluid. Biol. Bull. 1972, 143 (3), 506– 512,  DOI: 10.2307/1540180
      35
      Inorganic composition of molluscan extrapallial fluid
      Crenshaw, Miles A.
      Biological Bulletin (Woods Hole, MA, United States) (1972), 143 (3), 506-12CODEN: BIBUBX; ISSN:0006-3185.
      The inorg. compn. of the extrapallial fluids of Mercenaria mercenaria, Mytilus edulis, and Crassosterea virginica was significantly different from sea water. The Donnan ratio for each ion except for Ca was calcd. to be almost identical for each extrapallial fluid sample. The pH of each sample was well below that of sea water. pH values obtained in situ for Mercenaria mercenaria and Mytilus edulis were within the range of those obtained by the sampling method. The pH of the extrapallial fluid decreased when the animal closed its valves and increased when it opened them, as did the Ca concn. The Donnan ratios of the ions, except for K in the blood plasma and Ca in the extrapallial fluid, were reduced to unity by dialysis against sea water. Anal. of the nondialyzable material for protein showed that 50% of the blood plasma impermeate was protein. The SO42-/hexosamine ratio in the acid muccopolysaccharide fraction was 0.9-1.1.
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    36. 36
      Allam, B.; Paillard, C. Defense Factors in Clam Extrapallial Fluids. Dis. Aquat. Org. 1998, 33, 123– 128,  DOI: 10.3354/dao033123
      There is no corresponding record for this reference.
    37. 37
      Otter, L. M.; Agbaje, O. B. A.; Kilburn, M. R.; Lenz, C.; Henry, H.; Trimby, P.; Hoppe, P.; Jacob, D. E. Architecture, Growth Dynamics and Biomineralization of Pulsed Sr-Labelled Katelysia rhytiphora (Mollusca, Bivalvia). Biogeosciences 2019, 16, 3439– 3455,  DOI: 10.5194/bg-16-3439-2019
      37
      Insights into architecture, growth dynamics, and biomineralization from pulsed Sr-labelled Katelysia rhytiphora shells (Mollusca, Bivalvia)
      Otter, Laura M.; Agbaje, Oluwatoosin B. A.; Kilburn, Matt R.; Lenz, Christoph; Henry, Hadrien; Trimby, Patrick; Hoppe, Peter; Jacob, Dorrit E.
      Biogeosciences (2019), 16 (17), 3439-3455CODEN: BIOGGR; ISSN:1726-4189. (Copernicus Publications)
      The intertidal bivalve Katelysia rhytiphora, endemic to south Australia and Tasmania, is used here for pulsed Sr-labeling expts. in aquaculture expts. to visualize shell growth at the micro- to nanoscale. The ventral margin area of the outer shell layer composed of (i) an outermost outer shell layer (oOSL) with compd. composite prismatic architecture with three hierarchical orders of prisms and (ii) an innermost outer shell layer (iOSL) with crossed-acicular architecture consisting of intersecting lamellae bundles. All structural orders in both layers are enveloped by an org. sheath and the smallest mineralized units are nano-granules. Electron backscatter diffraction reveals a strong preferred orientation of the aragonite c axes perpendicular to the growth layers, while the a and b axes are scattered within a plane normal to the local growth direction and >46 % twin grain boundaries are detected. The Young's modulus shows a girdle-like max. of elastically stiffer orientations for the shell following the inner shell surface. For 6 d, the bivalves were subjected twice to seawater with an increased Sr concn. of 18x mean ocean water by dissolving 144 μg g-1 Sr (159.88 Sr/Ca mmol / mol) in seawater. The pulse labeling intervals in the shell are 17x (oOSL) and 12x (iOSL) enriched in Sr relative to the Sr-spiked seawater. All architectural units in the shell are transected by the Sr label, demonstrating shell growth to progress homogeneously instead of forming one individual architectural unit after the other. Distribution coeffs., DSr / Ca, for labeled and unlabeled shells are similar to shell proportions formed in the wild (0.12 to 0.15). All DSr / Ca values are lower than values for equil. partitioning of Sr in synthetic aragonite.
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    38. 38
      Su, X.; Belcher, A. M.; Zaremba, C. M.; Morse, D. E.; Stucky, G. D.; Heuer, A. H. Structural and Microstructural Characterization of the Growth Lines and Prismatic Microarchitecture in Red Abalone Shell and the Microstructures of Abalone “Flat Pearls. Chem. Mater. 2002, 14 (7), 3106– 3117,  DOI: 10.1021/cm011739q
      38
      Structural and microstructural characterization of the growth lines and prismatic microarchitecture in red abalone shell and the microstructures of abalone "flat pearls"
      Su, Xiaowei; Belcher, Angela M.; Zaremba, Charlotte M.; Morse, Daniel E.; Stucky, Galen D.; Heuer, Arthur H.
      Chemistry of Materials (2002), 14 (7), 3106-3117CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      The structure of the growth lines in the shell of the red abalone, Haliotis rufescens, has been characterized by x-ray diffraction anal. and by scanning and TEM. The growth lines consist of a block-like microstructure and a spherulitic microstructure, sepd. by a green org. matrix interlayer. The minerals in both the block-like and spherulitic structures have been detd. to be aragonite, the same CaCO3 polymorph as in the nacreous microstructure in these shells. The spherulitic structure is composed of radially distributed elongated crystals, whereas the block like structure involves cryst. aggregates with irregular shape. The individual aggregates are approx. single crystal, with orientations identical to that of the adjacent stack of tablets in the nacreous structure. The interfaces defining the transition from nacreous to block like microstructures are abrupt; on the other hand, the transition from spherulitic to nacreous microstructures shows more irregularity because of the occasional intergrowth of elongated crystals into the nacreous region. The microstructures of flat pearls, produced by mineralization of an abiotic substrate (a glass cover slip) inserted between the mantle tissue and the growing edge of the shell in a live abalone, have also been studied. A thin calcitic CaCO3 layer is produced on the center of the glass substrate, which is soon covered by green org. matrix. This matrix extends beyond the calcitic region; i.e., it can be secreted directly onto the glass. Mineralization of this green matrix layer involves the deposition of spherulitic aragonite, similar to that occurring in the native shell, which is then capped by nacreous aragonite. Thus, the microstructures within the flat pearls mimic very closely certain aspects of the microstructures within the growth lines of the native shell.
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    39. 39
      Cartwright, J. H. E.; Checa, A. G.; Escribano, B.; Sainz-Díaz, C. I. Spiral and Target Patterns in Bivalve Nacre Manifest a Natural Excitable Medium from Layer Growth of a Biological Liquid Crystal. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (26), 10499– 10504,  DOI: 10.1073/pnas.0900867106
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      Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal
      Cartwright, Julyan H. E.; Checa, Antonio G.; Escribano, Bruno; Ignacio Sainz-Diaz, C.
      Proceedings of the National Academy of Sciences of the United States of America (2009), 106 (26), 10499-10504, S10499/1-S10499/5CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Nacre is an exquisitely structured biocomposite of the calcium carbonate mineral aragonite with small amts. of proteins and the polysaccharide chitin. For many years, it has been the subject of research, not just because of its beauty, but also to discover how nature can produce such a superior product with excellent mech. properties from such relatively weak raw materials. Four decades ago, Wada proposed that the spiral patterns in nacre could be explained by using the theory Frank had put forward of the growth of crystals by means of screw dislocations. Frank's mechanism of crystal growth has been amply confirmed by exptl. observations of screw dislocations in crystals, but it is a growth mechanism for a single crystal, with growth fronts of mols. However, the growth fronts composed of many tablets of cryst. aragonite visible in micrographs of nacre are not a mol.-scale but a mesoscale phenomenon, so it has not been evident how the Frank mechanism might be of relevance. Here, we demonstrate that nacre growth is organized around a liq.-crystal core of chitin crystallites, a skeleton that the other components of nacre subsequently flesh out in a process of hierarchical self-assembly. We establish that spiral and target patterns can arise in a liq. crystal formed layer by layer through the Burton-Cabrera-Frank dynamics, and furthermore that this layer growth mechanism is an instance of an important class of phys. systems termed excitable media. Artificial liq. crystals grown in this way may have many technol. applications.
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    40. 40
      Cartwright, J. H. E.; Checa, A. G. The Dynamics of Nacre Self-Assembly. J. R. Soc., Interface 2007, 4, 491– 504,  DOI: 10.1098/rsif.2006.0188
      40
      The dynamics of nacre self-assembly
      Cartwright, Julyan H. E.; Checa, Antonio G.
      Journal of the Royal Society, Interface (2007), 4 (14), 491-504CODEN: JRSICU; ISSN:1742-5689. (Royal Society)
      The authors show how nacre and pearl construction in bivalve and gastropod mollusks can be understood in terms of successive processes of controlled self-assembly from the mol.- to the macro-scale. This dynamics involves the physics of the formation of both solid and liq. crystals and of membranes and fluids to produce a nanostructured hierarchically constructed biol. composite of polysaccharides, proteins and mineral, whose mech. properties far surpass those of its component parts.
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    41. 41
      Taylor, P. D.; Vinn, O.; Wilson, M. A. Evolution of Biomineralization in ‘Lophophorates’;. Spec. Pap. Paleontol. 2010, 84, 317– 333
      There is no corresponding record for this reference.
    42. 42
      Checa, A. G.; Esteban-Delgado, F. J.; Rodriguez-Navarro, A. B. Crystallographic Structure of the Foliated Calcite of Bivalves. J. Struct. Biol. 2007, 157, 393– 402,  DOI: 10.1016/j.jsb.2006.09.005
      42
      Crystallographic structure of the foliated calcite of bivalves
      Checa, Antonio G.; Esteban-Delgado, Francisco J.; Rodriguez-Navarro, Alejandro B.
      Journal of Structural Biology (2007), 157 (2), 393-402CODEN: JSBIEM; ISSN:1047-8477. (Elsevier)
      The foliated layer of bivalves is constituted by platy calcite crystals, or laths, surrounded by an org. layer, and which are arranged into sheets (folia). Therefore, the foliated microstructure can be considered the calcitic analog to nacre. In this paper, the foliated microstructure has been studied in detail using electron and X-ray diffraction techniques, together with SEM observations on naturally decalcified shells, to investigate the crystallog. organization on different length scales and to resolve among previous contradictory results. This layer is highly organized and displays a coherent crystallog. orientation. The surface of the laths of the foliated layer is constituted by calcite crystals oriented with their c-axis tilted opposite to the growth direction of the laths and one of its {1 0 ‾1 4} rhombohedral faces looking in the growth direction. These faces are only expressed as the terminal faces of the laths, whereas the main surfaces of laths coincide with {1 0 ‾1 8} rhombohedral faces. This arrangement was consistently found in all specimens studied, which leads us to the provisional conclusion that, unlike previous studies, there is only one possible crystallog. arrangement for the foliated layer. Future studies on other species will help to ascertain this assertion.
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    43. 43
      Checa, A. G.; Sánchez-Navas, A.; Rodriguez-Navarro, A. Crystal Growth in the Foliated Aragonite of Monoplacophorans (Mollusca). Cryst. Growth Des. 2009, 9, 4574– 4580,  DOI: 10.1021/cg9005949
      43
      Crystal Growth in the Foliated Aragonite of Monoplacophorans (Mollusca)
      Checa, Antonio G.; Sanchez-Navas, Antonio; Rodriguez-Navarro, Alejandro
      Crystal Growth & Design (2009), 9 (10), 4574-4580CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
      Crystal-growth features of the foliated aragonite from two species of the rare monoplacophoran molluscs have been analyzed. The crystals have unique morphologies. They are very thin along the c axis and elongated along the a axis, and their arrangement varies depending on the species. Surface energy minimization in the crystal arrangement obsd. in Micropilina leads to a discrete no. of const. angular relationships, which is explained by twin laws and epitaxy. Textural anal. shows that crystals form oriented aggregates with their c axes perpendicular to the shell surface. Close to the shell margin, crystals compete so as to orient their a axes nearly perpendicular to the growth front of the lamellae, although the scattering of the a axis soon increases toward the shell interior. In contrast to inorg. crystals, growth along the c axis is inhibited by org. mols. Their incorporation may be related to the existence of weak intermol. interactions between CO3 groups along this axis. Conversely, there is no chem. affinity to incorporate org. mols. along the a axis, where particularly short CO3-Ca ionic bonds occur. These structural factors explain the formation of crystals which are elongated and free of org. inclusions along the a axis.
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    44. 44
      Johnson, B. R.; Scott, S. K. New Approaches to Chemical Patterns. Chem. Soc. Rev. 1996, 25 (4), 265– 273,  DOI: 10.1039/cs9962500265
      44
      New approaches to chemical patterns
      Johnson, Barry R.; Scott, Stephen K.
      Chemical Society Reviews (1996), 25 (4), 265-273CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review with 35 refs.; we survey the various new observations made along the route to taming of so-called Turing Structures in the lab. and attempt to set these in the context of their relevance in chem. and other areas of science.
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    45. 45
      Polyp. Encyclopedia Britannica. https://www.britannica.com/science/polyp-zoology (accessed Apr. 12, 2021).
      There is no corresponding record for this reference.
    46. 46
      Benzerara, K.; Menguy, N.; Obst, M.; Stolarski, J.; Mazur, M.; Tylisczak, T.; Brown, G. E.; Meibom, A. Study of the Crystallographic Architecture of Corals at the Nanoscale by Scanning Transmission X-Ray Microscopy and Transmission Electron Microscopy. Ultramicroscopy 2011, 111 (8), 1268– 1275,  DOI: 10.1016/j.ultramic.2011.03.023
      46
      Study of the crystallographic architecture of corals at the nanoscale by scanning transmission X-ray microscopy and transmission electron microscopy
      Benzerara, Karim; Menguy, Nicolas; Obst, Martin; Stolarski, JarosLaw; Mazur, Maciej; Tylisczak, Tolek; Brown, Gordon E., Jr.; Meibom, Anders
      Ultramicroscopy (2011), 111 (8), 1268-1275CODEN: ULTRD6; ISSN:0304-3991. (Elsevier B.V.)
      We have investigated the nanotexture and crystallog. orientation of aragonite in a coral skeleton using synchrotron-based scanning transmission X-ray microscopy (STXM) and transmission electron microscopy (TEM). Polarization-dependent STXM imaging at 40-nm spatial resoln. was used to obtain an orientation map of the c-axis of aragonite on a focused ion beam milled ultrathin section of a Porites coral. This imaging showed that one of the basic units of coral skeletons, referred to as the center of calcification (COC), consists of a cluster of 100-nm aragonite globules crystallog. aligned over several micrometers with a fan-like distribution and with the properties of single crystals at the mesoscale. The remainder of the skeleton consists of aragonite single-crystal fibers in crystallog. continuity with the nanoglobules comprising the COC. Our observation provides information on the nm-scale processes that led to biomineral formation in this sample. Importantly, the present study illustrates how the methodol. described here, which combines HRTEM and polarization-dependent synchrotron-based STXM imaging, offers an interesting new approach for investigating biomineralizing systems at the nm-scale.
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    47. 47
      Nothdurft, L. D.; Webb, G. E. Microstructure of Common Reef-Building Coral Genera Acropora, Pocillopora, Goniastrea and Porites: Constraints on Spatial Resolution in Geochemical Sampling. Facies 2007, 53 (1), 1– 26,  DOI: 10.1007/s10347-006-0090-0
      There is no corresponding record for this reference.
    48. 48
      Vielzeuf, D.; Garrabou, J.; Baronnet, A.; Grauby, O.; Marschal, C. Nano to Macroscale Biomineral Architecture of Red Coral (Corallium rubrum). Am. Mineral. 2008, 93 (11–12), 1799– 1815,  DOI: 10.2138/am.2008.2923
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      Nano to macroscale biomineral architecture of red coral (Corallium rubrum)
      Vielzeuf, Daniel; Garrabou, Joaquim; Baronnet, Alain; Grauby, Olivier; Marschal, Christian
      American Mineralogist (2008), 93 (11-12), 1799-1815CODEN: AMMIAY; ISSN:0003-004X. (Mineralogical Society of America)
      Different techniques have been used to characterize the phys. and chem. structure of the red coral calcitic skeleton. A section normal to the axis of the skeleton shows a medullar zone surrounded by a circular domain composed of concentric rings. Growth rings are revealed by the cyclic variation of org. matter (OM) and Mg/Ca ratio. These growth rings are annual; thus, both OM and Mg/Ca ratio can be used to date red coral colonies. Growth rings display wavelets. The internal structure of each wavelet results from the stacking of layers with tortuous interfaces. Tortuosity is due to the presence of microprotuberances. Interfaces between layers may display sharp discontinuities indicative of interruption of the mineralizing process. SEM and TEM studies show that each layer is made of (1) fibers, organized or not in fan-shaped structures; and (2) submicrometer (apparently mono-) cryst. units. Fibers are superstructures made of submicrometer units possibly assembled by an oriented aggregation mechanism. HRTEM studies show that in spite of displaying single-crystal scattering behavior, the submicrometer cryst. units are made of 2-5 nm nanograins again possibly aggregated by a mechanism of oriented attachment. Thus, submicrometer cryst. units and polycryst. fibers can be both defined as mesocrystals. The red coral skeleton is a hierarchically organized org.-inorg. composite that exhibits porosity and structural and compositional order on length scales from the nanoscale to the macroscale.
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      van de Locht, R.; Verch, A.; Saunders, M.; Dissard, D.; Rixen, T.; Moya, A.; Kröger, R. Microstructural Evolution and Nanoscale Crystallography in Scleractinian Coral Spherulites. J. Struct. Biol. 2013, 183 (1), 57– 65,  DOI: 10.1016/j.jsb.2013.05.005
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      Microstructural evolution and nanoscale crystallography in scleractinian coral spherulites
      van de Locht, Renee; Verch, Andreas; Saunders, Martin; Dissard, Delphine; Rixen, Tim; Moya, Aurelie; Kroger, Roland
      Journal of Structural Biology (2013), 183 (1), 57-65CODEN: JSBIEM; ISSN:1047-8477. (Elsevier Inc.)
      One of the most important aspects in the research on reef-building corals is the process by which corals accrete biogenic calcium carbonate. This process leads to the formation of a mineral/org. composite and it is believed that the development of the nano- and microstructure of the mineral phase is highly sensitive to the growth conditions. Transmission electron microscopy (TEM) anal. of large-scale (10 × 30 μm) focused ion beam (FIB) prepd. lamellae was performed on adult and juvenile scleractinian coral skeleton specimens. This allowed for the investigation of the nano- and microstructure and the crystallog. orientation of the aragonite mineral. We found the following microstructural evolution in the adult Porites lobata specimens: randomly oriented nanocrystals with high porosity, partly aligned nanocrystals with high porosity and areas of dense acicular crystals of several micrometers extension, the latter 2 areas are aligned close to the [0 0 1] direction (Pmcn space group). To the best of our knowledge, for the 1st time the obsd. microstructure could be directly correlated with the dark/bright bands characteristic of the diurnal growth cycle. We hypothesize that this mineral structure sequence and alignment in the adult specimen is linked to the photosynthetic diurnal cycle of the zooxanthellea regulating the oxygen levels and org. mol. transport to the calcifying medium. These observations reveal a strong control of crystal morphol. by the organism and the correlation of the accretion process. No indication for a self-assembly of nanocryst. units, i.e., a mesocrystal structure, on the micrometer scale could be found.
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    50. 50
      Mass, T.; Drake, J. L.; Peters, E. C.; Jiang, W.; Falkowski, P. G. Immunolocalization of Skeletal Matrix Proteins in Tissue and Mineral of the Coral Stylophora pistillata. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (35), 12728– 12733,  DOI: 10.1073/pnas.1408621111
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