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Superionic Conduction in the Plastic Crystal Polymorph of Na4P2S6
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  • Tanja Scholz
    Tanja Scholz
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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    Orcidhttps://orcid.org/0000-0003-3474-1272
  • Christian Schneider
    Christian Schneider
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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  • Maxwell W. Terban
    Maxwell W. Terban
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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    Orcidhttps://orcid.org/0000-0002-7094-1266
  • Zeyu Deng
    Zeyu Deng
    Department of Materials Science and Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore
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    Orcidhttps://orcid.org/0000-0003-0109-9367
  • Roland Eger
    Roland Eger
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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  • Martin Etter
    Martin Etter
    Deutsches Elektronensynchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany
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  • Robert E. Dinnebier
    Robert E. Dinnebier
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
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  • Pieremanuele Canepa*
    Pieremanuele Canepa
    Department of Materials Science and Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore
    Department of Chemical and Biomolecular Engineering, National University of Singapore, Engineering Drive 4, 117585 Singapore
    *(P.C.) Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-5168-9253
  • Bettina V. Lotsch*
    Bettina V. Lotsch
    LMU Munich, Butenandtstraße 5-13, 81377 Munich, Germany
    Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
    *(B.V.L.) Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-3094-303X
Open PDFSupporting Information (4)

ACS Energy Letters

Cite this: ACS Energy Lett. 2022, 7, 4, 1403–1411
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https://doi.org/10.1021/acsenergylett.1c02815
Published March 22, 2022

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Abstract

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Sodium thiophosphates are promising materials for large-scale energy storage applications benefiting from high ionic conductivities and the geopolitical abundance of the elements. A representative of this class is Na4P2S6, which currently shows two known polymorphs−α and β. This work describes a third polymorph of Na4P2S6, γ, that forms above 580 °C, exhibits fast-ion conduction with low activation energy, and is mechanically soft. Based on high-temperature diffraction, pair distribution function analysis, thermal analysis, impedance spectroscopy, and ab initio molecular dynamics calculations, the γ-Na4P2S6 phase is identified to be a plastic crystal characterized by dynamic orientational disorder of the P2S64– anions translationally fixed on a body-centered cubic lattice. The prospect of stabilizing plastic crystals at operating temperatures of solid-state batteries, with benefits from their high ionic conductivities and mechanical properties, could have a strong impact in the field of solid-state battery research.

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The rich chemistry of thiophosphates is an excellent platform for exploring compounds with interesting and functional properties. The plethora of possible thiophosphate anions ranges from the tetrahedral ortho-thiophospate PS43– to larger units, such as corner-sharing P2S74– or P2S64– having a P–P central bond. The ability of sulfur to form disulfur -S–S- bridges and the broad range of oxidation states of phosphorus allow for even larger, ring-like or square-shaped anions. (1,2)
Many thiophosphate compounds containing alkaline metals are ion conductors. However, the number of highly conducting phases is still limited to a few well-known representatives (e.g., Na3PS4). The as-prepared tetragonal (low-temperature) structure of Na3PS4 shows a low ionic conductivity of around 4.2 × 10–6 S cm–1 (50 °C), but it can be improved up to ∼4.6 × 10–4 S cm–1 (room temperature) by stabilizing the high-temperature cubic phase as a glass–ceramic. (3−5) This was achieved by ball-milling the starting materials and subsequently annealing the glass at a low temperature of 270 °C to precipitate the cubic phase. Recently, Krauskopf et al. have suggested that the room-temperature stabilized cubic phase comprises tetragonal-like local-structure motifs. (6)
Another example of the phase-space flexibility of thiophosphates is Na4P2S6. (7,8) This material can be synthesized via a precipitation route, as well as by high-temperature solid-state synthesis. (9,10) Depending on the preparation method, Na4P2S6 crystallizes in the monoclinic polymorphs α- and β-Na4P2S6. (10,11) These polymorphs can be transformed into each other by heating or annealing the sample. In this study, we identify a new high-temperature polymorph of Na4P2S6, γ, which displays plastic crystal characteristics.
Plastic crystals are characterized by a high degree of reorientational freedom, often found for spherical molecules, or conformational freedom, often found for polymers, of a cationic, anionic, or neutral sublattice of a solid. (12−14) The disordered species are translationally fixed, therefore maintaining the lattice. This renders the material a solid with weak interactions in the partly “molten” anion sublattice. A number of inorganic ion conductors show these characteristics, including ABH4 (A = Li, Na, K, Rb, Cs), (15−17) Li2SO4, (18,19) LiAgSO4, (20) LiNaSO4, (21) Li4Zn(SO4)3 (21) Na3PO4, (22,23) Na2AC60 (A = K, Rb, Cs), (24−26) Na2B12H12, (27−29) Na2B10H10, (30) ACB11H12 (A = Li, Na), (31) Li2B12H12, (29) Rb2B10H10, (32) Na3PS4, (33) and Na4Zn(PO4)2 (34) (sorted by publication year). All of these examples contain rather globular-shaped anions with high point-group symmetries, such as Ih (e.g., B12H122– and C603–), D4d (e.g., B10H102–), or Td (e.g., SO42–). High intrinsic symmetry of the anion species lowers the sterical hindrance for fast reorientational motion. (35)
The implementation of fast sodium-ion conductors in solid-state batteries is vital for large-scale applications such as power-grid regulation and short-term wind or solar energy storage. Cost and resource analyses have shown that using cheaper current collectors and cathode materials can reduce the price and weight of Na-ion (solid-state) batteries compared to their Li analogs, especially if prices of relevant resources such as copper and cobalt continue to rise. (36) The more homogeneous distribution of Na deposits and the higher natural abundance (2.36% Na versus 0.002% Li) (37) point to a sodium-driven future in grid (solid-state) battery technology. Solid-state batteries require among other properties high intrinsic ion conductivity and a robust mechanical interface between the ion conductor and the electrodes to provide high performance and long cycle life. Plastic ion conductor materials can beneficially provide weaker cation–anion interactions and increased volumes that allow for easier ion transport. Furthermore, the ductility of the plastic phase can help to maintain better contact with the electrode and reduce physical degradation of the interface during cycling. A major caveat is that plastic phase transitions in ion conductors are often observed at high temperatures, which impedes their application in real devices. Thus, it is vital to better understand the nature and formation behavior of plastic crystals to inform strategies for rationally lowering the transition temperature toward ambient conditions.
Here, we discover the new γ polymorph of Na4P2S6, which exhibits fast Na+ conduction with a low activation energy, a cubic crystal structure, and plastic crystal characteristics. The plastic phase transition is driven by the reorientational freedom of the elongated thiophosphate anion P2S64–, rendering Na4P2S6 the first example of a salt, based on a prolate, complex anion, showing plastic crystal behavior.
Variable-temperature powder X-ray diffraction (PXRD) experiments were performed on Na4P2S6 well above the α–β phase transition at 160 °C. (11) A new set of Bragg peaks is observed to emerge at 580 °C, as shown in Figure 1. The diffraction peaks of β-Na4P2S6 and the new crystalline phase coexist up to 585 °C (measured every 5 K), at which point the β phase disappears. This suggests the existence of a third polymorph of Na4P2S6, which we refer to as γ-Na4P2S6. Upon cooling, the transition is reversible with the re-formation of β- and α-Na4P2S6.

Figure 1

Figure 1. Variable-temperature PXRD of Na4P2S6 upon heating (bottom) and cooling (top) across the β–γ phase transition: contour plot of diffractograms (the color code, red to purple/blue, indicates the ranges from low to high diffraction intensities, respectively) and exemplary diffractograms (black) at 520 °C (β), 620 °C (γ), and 520 °C (β after heating above the phase transition). The selected diffractograms are additionally depicted in Supporting Information Figure S1.

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Several remarkable features of the PXRD patterns of γ-Na4P2S6 are discussed in the following (labeled i–iv). These points lead us to conclude that γ is a newly observed member of the plastic crystal family.
(i)

The Bragg peaks of γ-Na4P2S6 can be indexed to the cubic space group Im3̅m (No. 229) with a lattice parameter of 8.4509(3) Å at 580 °C. However, this high symmetry is not compatible with the ethane-like D3d configuration of the P2S64– anions, suggesting that the anions cannot be crystallographically oriented in the structure. This observation suggests that some kind of static or dynamic disorder is present in the anion orientations.

(ii)

The β–γ phase transition is accompanied by a large increase in diffuse scattering intensities, and the observed Bragg peak intensities rapidly decrease and disappear at higher angles. The diffuse scattering can be due to significant disorder, which could result for instance from different anion orientations, and lead to the destructive interference of higher order diffraction components. These are common features observable in the plastic crystal materials mentioned above.

(iii)

The β to γ phase transition is accompanied by an unusually high increase in the volume of the unit cell, from 575.4 to 603.8 Å3/f.u. (assuming Z = 2 for γ). This gives an increase of ∼4.9% (see Figure 2a), which compares well to, e.g., ∼3.2% for the monoclinic to cubic transition in Li2SO4 and ∼10% for the cubic to orthorhombic transition in Na3PS4. (18,33,38)

(iv)

A considerable hysteresis of ∼30 K in the β–γ transformation is observed from the diffraction data between heating and cooling, comparable to 40 K in Na3PS4. (33)

It is worth noting that, after cooling γ-Na4P2S6, changes in relative peak intensities are sometimes observed for the subsequent β and α phases (see Figure 1 and ESI). Similar behavior reported for γ-Na3PS4 was attributed to the development of preferred orientation. (33) However, as no clear preferential orientations could be identified, and the effect was not observed in other experiments where the sample spent less time at elevated temperature (e.g., Figure S2), possible effects due to reaction or degradation of the sample cannot be excluded.

Figure 2

Figure 2. (a) Temperature-dependent volume expansion and contraction across the β → γ phase transition relative to the room-temperature unit cell volume, Vrt, of Na4P2S6. (b) Differential scanning calorimetry (DSC) curve.

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The phase transitions in Na4P2S6 were additionally studied with differential scanning calorimetry (DSC) as shown in Figure 2b, using a much faster heating rate (20 K min–1) than in the diffraction experiments. Overall, the DSC data confirm all three transitions α → β (160 °C), β → γ (580 °C), and γ to the melt (∼800 °C), and back. Additional PXRD patterns of α-, β-, γ- and molten-Na4P2S6 are displayed in Supporting Information Figure S2. The α → β phase transition involves very small atomic rearrangements and shows a correspondingly small latent heat of ∼8.7 J/g. (11) In contrast, the β → γ transition has a latent heat corresponding to about half that of the melting transition (∼60 versus ∼90–120 J/g). This implies that substantial structural rearrangements are now required to form the γ phase. Other known plastic phase transitions also exhibit latent heats of similar magnitude, for example, 214 J/g in Li2SO4 or 150 J/g in Na3PS4. (18,33) While the β → γ phase transition is observed at the same temperature as in the diffraction experiments (580 °C), the hysteresis on cooling appears much larger, ∼60 K. This could suggest kinetic limitations for the transformation back to the β phase.
To check if the P2S64– anion undergoes any structural change during the β → γ transition, we measured high-temperature Raman spectra. The spectra of Figure S3 display no change in the local D3h anion symmetry from β → γ-Na4P2S6, supporting the assumption of an intact P2S64– unit at high temperature.
A direct structural solution of the γ-phase from the PXRD pattern is complicated by the incompatibility between the observed space group symmetry and the lower symmetry of the P2S64– anions. Therefore, we turned to the pair distribution function (PDF) analysis (39,40) of synchrotron diffraction data to determine possible configurations to describe the local structure. Figure 3a shows the experimental PDF of γ-Na4P2S6 at ∼650 °C. Sharp peaks observed at 2.048 and 3.392 Å can be assigned to P–P/P–S and S–S (i–iii) atom-pair distances within the P2S64– anion. Another sharp peak at 2.801 Å can be assigned to the nearest-neighbor Na–S atom pairs. The peaks expected to correspond to pairs of S atoms located at opposite ends of the anion are not distinctly observed, which may suggest some flexibilty of the anion dihedral angle.

Figure 3

Figure 3. (a) Experimental synchrotron PDF with PDFs simulated from the fitted structure models and P2S64– anion only and (b) Rietveld fit of the PXRD pattern for γ-Na4P2S6 at 650 °C. The gray shaded region in (a) represents the unphysical interatomic distance range that is more highly affected by systematic errors from data processing. (c) Illustration of the PDF-refined γ-structure with a static approximation of the P2S64– anions in a 2 × 2 × 2 cell, and (d) in a single unit cell. (e) Overlay of bond valence energy landscape (red surface) and the crystal structure visualizing the three-dimensional Na+ conducting pathways.

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Above 6 Å, the features in the PDF are broad and low intensity, in contrast to the PDFs measured for the α and β phases (see SI Figure S4). In line with the body-centered cubic (bcc) space group from indexing, a pseudocubic model was constructed, with P1 space group symmetry, in which the P2S64– anion barycenters are translationally fixed on the lattice points. The rotational orientations about the lattice points were allowed to refine freely against the experimental PDF data. A single-cell model (Z′ = 2) gives good agreement to short-range distances and indicates that neighboring anions prefer not to align in the same orientation. However, the model fails when r is greater than the lattice parameter due to the fixed geometry of the second nearest neighbor anions. A 2 × 2 × 2 supercell (Z′ = 16) was further constructed to test against the data at longer distances. This model allows for a much larger distribution of relative anion orientations sampled at any given distance and also showed good agreement to the data up to approximately 16 Å. Overall, the data at higher distances prefer models with more orientational disorder. This suggests weak or no correlation between relative anion orientations at long distances (see SI Figure S5).
In order to generate a complete model that is compatible with the data, 8 Na sites were introduced to the single-cell model (64 Na sites to the supercell model) and allowed to refine with restraints set for the distances of closest approach: 2.5 Å (Na–S), 3.4 Å (Na–P), and 3.5 Å (Na–Na). A unique set of positions could not be determined, but the refinements preferred the Na atoms to distribute throughout the “interstitial” space around the structure-forming anions, optimizing to give the best agreement to the preferred Na–S neighbor distance. The good agreement between simulated and experimental PDFs and resulting structure are shown in Figures 3a,c,d.
Inspired by the real-space model, Rietveld refinements were performed using the space group Im3̅m with a single anion fixed at the origin, giving 48 anions each at the corner and body-center position (mirroring free rotation of the anions averaged over all unit cells). Crystallographic data and refinement details, as well as atomic positions and displacement parameters, are compiled in Tables S1 and S2 in the Supporting Information. The occupancy was fixed to . Then Na atom sites were sequentially added and refined until the Bragg peaks could be reproduced. This resulted in two symmetry-independent sites giving 96 positions each, with the occupancies constrained to give the expected stoichiometry (details in the Experimental Section). Similar to the model from PDF refinement, the Na atoms again distribute to fill the “interstitial” space around the structure-forming anions. The Rietveld fit is shown in Figure 3b. By comparison of the Im3̅m model to higher distances in real space (see SI Figure S5), it is found to accurately reproduce the on-average pair-density fluctuations beyond ∼8 Å. For the real-space refinements, it was necessary to set up the models with separate intra- and intermolecular atomic displacement parameters to properly describe the correlated motion. (41) To test for disorder within the anions, separate parameters were defined to describe the peak widths of different atom-pair types. (42) We found that correlations between opposing S–S pairs were broader than other atom-pair contributions by a factor of more than 2, which further supports the hypothesis of torsional distortions (along the P–P bond) of the anions.
In a complementary approach to locate and count low-energy sites and possible migration pathways for Na+, softBV (bond valence) analysis (43,44) was conducted for the PDF-derived static approximation in a 2 × 2 × 2 cell. Figure 3e illustrates the BV landscape and reveals many of the possible interstitials that exceed the number of Na+ by far. Therefore, the crystal structure offers a high number of vacancies, which are beneficial for fast-ion conduction. A large number of alternative pathways can be found in this structure with energy barriers of comparable barrier heights of ∼230 meV.
After obtaining insights into the ion transport pathways of γ-Na4P2S6 via BV modeling, an experimental characterization was attempted. High-temperature electrochemical impedance spectroscopy (EIS) measurements were performed on pellets of Na4P2S6. The malleability of γ-Na4P2S6 resulted in pellets being deformed under the slightest contact pressure, changing their thickness as a result, and even leaking out of the setup. Additionally, the chemically aggressive nature of Na4P2S6 had major implications on the corrosion of electrodes and contacts within a short amount of time. Contrary to good EIS measuring practice, the data shown here were obtained with low contact pressures on the pellets, short equilibration time, and low-temperature-step density, but, nevertheless, highlight the characteristics of the phase transition. The results of the measurement are presented in the Arrhenius plot of Figure 4a (see SI Figure S8 for exemplary spectra). For β-Na4P2S6 (520–578 °C), an activation energy of 562(48) meV was found, which is slightly higher than the previously reported value obtained in measurements at lower temperature. (11) The β → γ transition at around 580 °C causes an abrupt increase in the ionic conductivity from 92(11) to 140(12) mS cm–1. The order of magnitude in ionic conductivities for β- and γ-Na4P2S6 is comparable to Na3PS4, where the β → γ transition at 500 °C is accompanied by a jump from ∼40 to ∼400 mS cm–1. (33) γ-Na4P2S6 exhibits a lower activation energy of about 89(18) meV, much lower than the BV calculated value on a rigid model, but comparable to γ-Na3PS4 (110(10) meV). (33) The behavior of ionic conduction is reversible on cooling, with a similar hysteresis of ∼40 K as found in the diffraction experiments. The extracted ionic conductivities upon cooling the pellet are higher than for heating. This unusual behavior can be explained by accelerated decomposition of Na4P2S6 at elevated temperatures. The visual appearance of the pellet changed from initially white to dark gray after cooling. The aggressive nature of Na4P2S6 at elevated temperatures is reflected in the corrosion of the platinum electrodes after the EIS measurement (see images in Figure S7). Presumably, Na4P2S6 reacts with the Pt electrodes and forms some electronically conducting phases that increase the conductivity, leading to apparent lower activation energies compared to the heating cycle. Hence, the extraction of a true activation energy for ionic motion is vitiated for the cooling cycle. We suspect the loss of sulfur and the reaction of sodium ions with ceramic or quartz glass parts of our setups to be the origin of the accelerated decomposition of γ-Na4P2S6 that we observed in some experiments. We refer to the Supporting Informaiton for more details. Extrapolating the linear Arrhenius behavior of γ-Na4P2S6 to 25 °C results in a room-temperature ionic conductivity of 50(24) mS cm–1, similar to the findings of Famprikis et al. for Na3PS4. (33) Despite our efforts to rapidly quench Na4P2S6 from high temperature by submerging an ampoule in ice water, we were not successful in stabilizing the cubic γ phase at room temperature.

Figure 4

Figure 4. (a) Arrhenius plot of ionic conductivity and activation energies derived from impedance spectroscopy. The heating and cooling segments are indicated by orange and blue circles. The activation energy was extracted from the orange (heating) data points, since the cooling data points possibly describe a mixed ionic–electronic conducting (MIEC) phase. The error bars arise from the standard deviation of ionic conductivity measured on three distinct pellets. (b) Mean-squared displacements (MSDs) of Na, P, and S at 1000 K from AIMD simulations. (c) Arrhenius plot of the ionic conductivity and activation energy from AIMD simulations.

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So far, the experimental results strongly suggest plastic behavior of γ-Na4P2S6, but do not yet distinguish a dynamic versus static nature of the rotational disorder of the P2S64– anions. Therefore, the atomic motions of Na+ and P2S64– were tested using ab initio molecular dynamics (AIMD) simulations, with the PDF-derived 2 × 2 × 2 model as a starting point for optimization and subsequent MD calculations at different sampling temperatures (600–1200 K). The average mean-squared displacement of the atoms of Figure 4b supports the significant mobility of all Na+, while P and S atoms do not undergo long-range motion. The calculated activation energy for Na+ migration above 800 K (the MD calculation temperature) is 223 meV, though it is again much higher than the experimentally obtained activation barrier (89(18) meV). For the 600 K calculation, the Na+ diffusivity is many orders of magnitude smaller.
To determine the possibility for dynamic rotational motion of P2S64– anions, the P–P bond orientations were tracked during the AIMD simulations. A detailed discussion about the analysis of the AIMD simulation can be found in the Supporting Information. The orientation of individual P–P bonds within the cubic cell can be expressed in terms of azimuthal (ϕ) and polar (θ) angles as depicted in Figure 5a. Starting from P–P orientations marked as orange dots, the orientation of all 16 P2S64– anions were tracked throughout the AIMD simulation and shown as a 2D histogram in Figure 5b. The polar coordinate system allows for the division of the observed eight clusters into eight octants as depicted at the bottom right in Figure 5a. Because the anions rotate about their center of mass, rather than the P atom fixed at the origin, octants related by inversion (e.g., octants II and VIII) signify the same orientation of the P–P handle with respect to the crystal lattice (but with inverted P atoms). Thus, the ensuing population of these initially empty octants indicates that significant reorientation of individual anions occurs. The four orientational groupings point approximately along the body diagonals of the cell. Notably, the population density of the 2D histogram at 1000 K is not uniform after the simulation time of 300 ps. With higher simulation temperature the population density approaches a more uniform distribution of orientations, as depicted in Figure S9. Longer simulation runs would result in a similar picture, i.e., a more equal distribution of orientations.

Figure 5

Figure 5. (a) Scheme of the definition of the azimuthal angle (ϕ) and polar angle (θ) with respect to the P–P handle and scheme of the P–P orientation in Cartesian octants. (b) Orientation heat map of all P2S64– in a 2 × 2 × 2 cell at 1000 K in a 300 ps simulation. (c) ϕ and (d) θ as a function of time of an exemplary P2S64– at 1000 K.

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Panels c and d of Figure 5 illustrate the ϕ and θ angles of an exemplary anion from the AIMD simulations at 1000 K and enable the derivation of reorientation times of 20–100 ps. The time evolution of the azimuthal and polar angles of four other anions are illustrated in Figure S10. Here, a direct comparison to plastic phases of sodium closo-borane Na2B12H12 can be made: just above the first-order transition from the low-T monoclinic to the high-T cubic phase near 520 K, the reorientational jump rate, τ–1, derived from NMR experiments, is 1011 Hz (equal to 10 ps), (27) a value comparable to the time between P2S64– reorientations, although the different shape and size of the anions should be taken into account. Meanwhile, the Na+ short-ranged hopping time was calculated to be ∼0.6 ps at 1000 K (see SI Figure S13), 2 orders of magnitude faster than the anion motion.
Another degree of freedom for the anion is conformational freedom or rotation around the PS3–PS3 bond, similar to ethane and its derivatives. This is measured as the dihedral angle spanned by S–P–P–S. The AIMD simulations suggest that the P–P bond rotation happens on a time scale similar to that of the directional reorientation of the entire anion. We refer to the Supporting Information for a more detailed analysis, including figures depicting the time and population evolution of the dihedral angle.
To summarize, while showing dynamic disorder, the orientation distribution after 300 ps suggests that the anions prefer to point roughly along the four body diagonals of their respective unit cells. This is in agreement with the on-average (Im3̅m) structure obtained from Rietveld refinement, where the P–P bonds of all orientations on the lattice point overlap to form a roughly cubic distribution that is co-oriented with the crystallographic cell (see the Supporting Information). The results suggest that dynamic reorientation of the P2S64– units occurs, consisting primarily of hops between the four body diagonal orientations of the cubic lattice. The frequency of the P2S64– reorientation increases with the simulation temperature. Further analysis of this behavior suggests that reorientation of one anion does not necessarily induce a change in its neighbors’ orientations.
In this work we have identified a new high-temperature phase transition at 580 °C in the thiophosphate Na+ conductor Na4P2S6. The phase transition is accompanied by a large latent heat and a change in crystal structure (from monoclinic C2/m to cubic Im3̅m), as well as a jump in sodium ion transport properties. A structure model with P2S64– anions occupying the bcc lattice points was derived from pair distribution function analysis. The PDF structure model was used to simulate cation and anion dynamics with ab initio molecular dynamics. We demonstrate that while sodium shows a high diffusion coefficient in the AIMD simulation, the P2S64– anions form a translationally fixed sublattice characterized by orientational disorder and the ability to dynamically reorient, primarily between the four body diagonal directions. Na4P2S6 is malleable at high temperature and mechanically deforms under even slight compressive stress: a property in solid ion conductors that is unique to plastic phases. Altogether, the evidence suggests that γ-Na4P2S6 is a new member of the plastic ionic conductors.
Despite the advantageous mechanical and conduction properties of plastic ion conductors, the temperatures needed to stabilize these phases are still far too high for operation in solid-state batteries. A key goal in solid-state battery chemistry is thus to stabilize such plastic phases at close to ambient temperature. Thus, further search and a detailed understanding of the underlying structure–property relationships of such phases will be necessary to identify plastic phases with lower transition temperatures.

Experimental Methods

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Preparation of Na4P2S6

Na4P2S6 can be prepared using two different synthesis routes. A solid-state reaction as described in ref (10) yields a very crystalline powder from which also single crystals can be extracted. Further, the solution synthesis via the hydrated compound Na4P2S6·6H2O as in ref (9) gives a powder product with stacking faults. The latter anneals above 500 °C to a product very similar to the solid-state material. The structural differences are discussed in detail in ref (11). The β → γ phase transition is not affected by the Na4P2S6 synthesis.

Variable-Temperature Powder X-ray Diffraction

Variable-temperature powder X-ray diffraction (PXRD) patterns were measured using a STOE StadiP diffractometer (Mo-Kα1 radiation (λ = 0.7093 Å), curved germanium (111) monochromator, DECTRIS Mythen2R 1K detector) with a STOE capillary furnace in Debye–Scherrer geometry. Fine powdered samples were filled in quartz glass capillaries of 0.5 mm diameter by Hilgenberg and sealed under argon. Data collection was done in the range from 2° to 62° 2θ with a step size of 0.015° in the temperature range of 510, 650, and 440 °C in steps of 5 K around the immediate β → γ phase transition and 10 K for more distant temperatures. The indexing of the powder patterns was performed with Jana2006 (45) in space groups C/2m and Im3̅m for β- and γ-Na4P2S6, respectively. Errors of the results of the Rietveld refinements are specified as 3σ.

Total Scattering Measurements

Total scattering measurements were carried out using beamline P02.1 at PETRA III of the Deutsches Elektronen-Synchrotron (DESY). Data were collected in rapid acquisition mode (46) with a large-area 2D PerkinElmer detector (2048 × 2048 pixels, 200 × 200 μm2 each) and sample-to-detector distance of 311.36 mm. The incident energy of the X-rays was 59.772 keV (λ = 0.20743 Å). Samples were loaded into 0.7 mm diameter quartz glass capillaries and measured at roughly 30 and 100–650 °C in increments of 50 °C. An empty capillary was measured to account for the background, and a LaB6 standard was measured at room temperature for calibration of the setup. Sample temperature was controlled using a custom ceramic heater operated using a Eurotherm 2408 temperature controller. Calibration, polarization correction, and azimuthal integration to 1D diffraction patterns were performed using the software pyFAI. (47) Further correction, background subtraction, and normalization of the 1D diffraction intensities were carried out to obtain the total scattering structure function, F(Q), which was Fourier transformed to the PDF, and G(r), using PDFgetX3 within xPDFsuite. (48,49) The maximum value of the momentum transfer, Q, used in the Fourier transform was 19.5 Å–1. Additional total scattering measurements were performed using a Stoe Stadi-P diffractometer with Ag Kα1 radiation (λ = 0.55941 Å), a Ge(111) Johann monochromator, and an array of three DECTRIS Mythen 1K detectors measured at two different positions in Debye–Scherrer geometry. The temperature was controlled using a hot air blower from FMB Oxford. Data were directly corrected for the 2θ offset of the instrument, polarization, and background scattering.

Pair Distribution Function and Rietveld Refinements

Pair distribution function (PDF) refinements were carried out using TOPAS Academic v6. (50,51) In all refinements, the P2S64– anions were set up as rigid bodies defined by the P–P and P–S bond lengths and P–P–S bond angle. Anion positions were fixed at the lattice points but allowed to rotate freely about their center of mass. When added, Na atom positions were allowed to be refined with antibump constraints set to prevent unrealistic interatomic distances. PDF refinements were performed in P1 symmetry with either two separate anions (single-cell model) refined over 1.5–7 Å, or 16 separate anions (supercell model) refined over 1.5–16 Å. The damping of the experimental signal due to instrumental resolution and effects of data truncation were accounted for and fixed, and the lattice parameter and scale factor were refined. Biso was fixed to 2.0 Å2 for S and P atoms, and separate intramolecular pair line widths were described with five parameters corresponding to P–P, bonding P–S, adjacent S–S, nonbonding P–S, and opposing S–S, to account for intra-anion disorder. (42) Since Na atoms only show correlation at short distances, the partial pair widths were described using an empirical function (x1 + x2r + x3r2) that allows for high correlation with neighbor atoms at short distances and progression to low structural correlation at higher distances.
Rietveld refinements (52,53) were performed with the Im3̅m model refined over a range of 4–28° 2θ. The background was described using Chebychev polynomials of 19th order. The Lorentz polarization factor was set to 9.825. A zero-error correction was refined to correct for detector offset, and a simple axial model was used to describe the instrumental peak shape along with Gaussian and Lorentzian components for crystallite size and strain broadening. The lattice parameter, global scaling factor, and two separate isotropic displacement parameters for Na and S/P were additionally refined. Convergence of the reciprocal- and real-space refinements was achieved using the global optimization method of simulated annealing in real space. (54)

Differential Scanning Calorimetry

For differential scanning calorimetry (DSC) measurements, fine powdered samples of 50 mg each were sealed in quartz ampoules (6 mm diameter, 10–15 mm in height) under vacuum. For improved heat flow, ampoules with a flat bottom were used. DSC measurements were performed on a NETZSCH STA 449 F5 Jupiter in a temperature range of 30–850 °C. The heating rate for all segments was set to 20 K min–1. This rate is a good trade-off between measurement stability (rate linearity) and sensitivity. Data evaluation was performed using the NETZSCH software package Proteus.

Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) measurements were performed using a NOVOCONTROL Technologies Alpha-A analyzer. For sample preparation a fine powder of Na4P2S6 (ca. 70 mg) was pressed uniaxillly at 1 GPa into pellets of 6 mm diameter. Both sides of the pellets were sputtered with platinum to ensure electrical contact during the high-temperature impedance measurement. Pellets were placed between two lithium-ion blocking platinum electrodes and loaded onto an in-house-built cell. To prevent the deformation of the pellet due to mechanical softening in the γ phase, the pellet was placed in a hole in a ceramic spacer of 1 mm height. This has proven to give reproducible results that are only affected by sample decomposition and corrosion of the electrode by sulfur at high temperature. The equilibration time prior to each impedance measurement at the programmed temperature steps was set to 15 min. A short equilibration time translates into a shorter time the sample is exposed to high temperatures. This was necessary as the sample decomposes within a day at 600 °C or above. On the other hand, short equilibration times bear the difficulty of measuring in a non-equilibrium state that can result in visible drifts in long impedance measurements. Hence, the spectra were recorded in a frequency range of 1 MHz to 10 Hz and with an applied voltage of VRMS = 100 mV. The spectra were recorded between 500 and 640 °C. Data treatment and evaluation was performed using the rhd instruments software package RelaxIS 3. To check data reliability Kramers–Kronig relation tests were performed prior to fitting. Fitting the impedance spectra to equivalent circuits was done by weighting the data points proportionally. Given error bars stem from error propagation of uncertainties in pellet geometric area, pellet thickness, and applied temperature as well as errors in resistance obtained by equivalent circuit fitting.

Raman Spectroscopy

Temperature-dependent Raman spectra were recorded using a Jobin Yvon Type 010 labram single grating spectrometer equipped with a double super razor edge filter. Data collection was performed with a Peltier cooled CCD camera (spectral resolution: 1 cm–1).

Computational Methods

DFT simulations were performed using the Vienna ab initio Simulation Package. (55,56) The unknown exchange correlation energy in DFT was approximated by the generalized gradient approximation, (57) and van der Waals forces were captured using the Grimme scheme. (58) Valence electrons were expanded as plane-waves with a maximum kinetic energy of 520 eV, and DFT total energies integrated at the Γ-point. Core electrons were described with projected augmented wave potentials, (59,60) treating the following electrons explicitly: Na (2s1), S (3s23p4) and P (3s23p3).
Starting from the PDF-derived crystal structures of γ-Na4P2S6 (2 × 2 × 2 cell), all P2S64– units were oriented along the ⟨111⟩ directions and being perpendicular with each other in the (100) and (010) planes. Then a structure optimization was performed until the interatomic forces are less than 0.01 eV/Å while keeping the cell volume fixed to that derived from the temperature-dependent diffraction experiments.
Using the DFT-optimized γ-Na4P2S6 model, canonical (NVT) ensemble ab initio molecular dynamics (AIMD) simulations were performed at selected temperatures of 600, 800, 900, 1000, and 1200 K, respectively. The NVT ensemble was achived via a Nosé–Hoover thermostat (61,62) with a 2 fs time step. The simulations were initialized at 100 K, and temperatures were ramped to target values within 2 ps. MD runs were performed with a production time of 600 ps (for 600 and 800 K) and 300 ps (for 1000 and 1200 K). Trajectories were collected for the data analysis excluding the initial period of 20 ps for equilibration.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsenergylett.1c02815.

  • Additional details on diffraction experiments, Raman spectroscopy, pair distribution function analysis, impedance spectroscopy, photographs of impedance samples, and AIMD simulation results (PDF)

  • Single-cell γ-Na4P2S6 structure obtained from PDF refinement (CIF)

  • 2 × 2 × 2 supercell γ-Na4P2S6 structure obtained from PDF refinement (CIF)

  • γ-Na4P2S6 structure obtained from Rietveld refinement (CIF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Authors
    • Pieremanuele Canepa - Department of Materials Science and Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore;  Department of Chemical and Biomolecular Engineering, National University of Singapore, Engineering Drive 4, 117585 Singapore;  Orcidhttps://orcid.org/0000-0002-5168-9253;  Email: [email protected]
    • Bettina V. Lotsch - LMU Munich, Butenandtstraße 5-13, 81377 Munich, Germany;  Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany;  Orcidhttps://orcid.org/0000-0002-3094-303X;  Email: [email protected]
  • Authors
    • Tanja Scholz - Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany;  Orcidhttps://orcid.org/0000-0003-3474-1272
    • Christian Schneider - Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
    • Maxwell W. Terban - Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany;  Orcidhttps://orcid.org/0000-0002-7094-1266
    • Zeyu Deng - Department of Materials Science and Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore;  Orcidhttps://orcid.org/0000-0003-0109-9367
    • Roland Eger - Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
    • Martin Etter - Deutsches Elektronensynchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany
    • Robert E. Dinnebier - Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
  • Author Contributions

    T.S. and C.S. contributed equally to this work.

  • Funding

    Open access funded by Max Planck Society.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We acknowledge Armin Schulz and Christine Stefani for measuring Raman and PXRD, respectively. We acknowledge financial support by the Max Planck Society, the German Federal Ministry of Research and Education (BMBF), Project 03XP0177B (FestBatt), the Center for Nanoscience (CeNS) and the Cluster of Excellence e-conversion (EXC2089). P.C. and Z.D. are grateful for funding from the National Research Foundation (Singapore) under P.C. NRF Fellowship NRFF12-2020-0012. P.C. was also supproted by the ANR-NRF NRF2019-NRF-ANR073 Na-MASTER. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at beamline P02.1. We thank Vera Hiendl (e-conversion) for graphical support.

References

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    Advanced Materials (Weinheim, Germany) (2001), 13 (12-13), 957-966CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH)
    Plastic crystal materials have long been known but have only relatively recently become of interest as solid-state ion conductors. Their properties are often assocd. with dynamic orientational disorder or rotator motions in the cryst. lattice. This paper describes recent work in the field including the range of org. ionic compds. that exhibit ion conduction at room temp. Cond. in some cases is high enough to render the compds. of interest as electrolyte materials in all solid state electrochem. devices. Doping of the plastic crystal phase with a small ion such as Li+ in some cases produces an even higher cond. In this case, the plastic crystal acts as a solid state "solvent" for the doped ion and supports the conductive motion of the dopant via motions of the matrix ions. These doped materials are also described in detail.
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  15. 15
    Tsang, T.; Farrar, T. C. Nuclear Magnetic Relaxation Studies of Internal Rotations and Phase Transitions in Borohydrides of Lithium, Sodium, and Potassium. J. Chem. Phys. 1969, 50, 3498– 3502,  DOI: 10.1063/1.1671574
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    Nuclear magnetic relaxation studies of internal rotations and phase transitions in borohydrides of lithium, sodium, and potassium
    Tsang, Tung; Farrar, Thomas C.
    Journal of Chemical Physics (1969), 50 (8), 3498-502CODEN: JCPSA6; ISSN:0021-9606.
    Proton spin-lattice relaxation times, T1, have been measured as a function of temp. for KBH4, NaBH4, and LiBH4. For NaBH4 and KBH4, 23Na and 11B relaxation measurements were also made. In all cases, the magnetization recovery is approx. exponential. Correlation times, τc, derived from the T1 data were used to calc. activation energies, V, for BH4- ion reorientations. For the cubic phase of KBH4, V = 14.8 ± 0.4 kj./mole (3.55 ± 0.1 kcal./mole) (± always refers to root mean sq. error) from measurements on proton and 11B. For NaBH4, V was 11.2 ± 0.5 and 14.8 ± 0.7 kj./mole (2.7 ± 0.1 and 3.5 ± 0.2 kcal./mole) for the high-(cubic) and low-temp. (tetragonal) phases; and anomaly in τc was observed at temps. slightly below the phase transition, and may be interpreted as a relatively sudden change in V assocd. with the phase transition. In LiBH4, a rather broad min. was observed for the proton T1 vs. temp.; this has been interpreted as due to 2 inequiv. BH4- tetrahedra with activation energies of 20 ± 1 and 16 ± 1 kj./mole (4.7 ± 0.3 and 3.8 ± 0.3 kcal./ mole). The proton and 11B nuclei are relaxed by magnetic dipolar interactions, but quadrupolar fluctuations are the dominating relaxation mechanism for 23Na in the cubic phase of NaBH4.
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    Matsuo, M.; Nakamori, Y.; Orimo, S.-I.; Maekawa, H.; Takamura, H. Lithium superionic conduction in lithium borohydride accompanied by structural transition. Appl. Phys. Lett. 2007, 91, 224103,  DOI: 10.1063/1.2817934
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    Lithium superionic conduction in lithium borohydride accompanied by structural transition
    Matsuo, Motoaki; Nakamori, Yuko; Orimo, Shin-ichi; Maekawa, Hideki; Takamura, Hitoshi
    Applied Physics Letters (2007), 91 (22), 224103/1-224103/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    The elec. cond. of LiBH4 measured by a.c. complex impedance increased by 3 orders of magnitude due to structural transition from orthorhombic to hexagonal at ∼390 K. The hexagonal phase exhibited a high elec. cond. of about 10-3 S/cm. The cond. calcd. from the Nernst-Einstein equation using the correlation time obtained from 7Li NMR agreed with the measured elec. cond. The elec. cond. in the hexagonal phase is due to Li superionic conduction.
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    Hagemann, H.; Gomes, S.; Renaudin, G.; Yvon, K. Raman studies of reorientation motions of [BH4]− anions in alkali borohydrides. J. Alloys Compd. 2004, 363, 129– 132,  DOI: 10.1016/S0925-8388(03)00468-7
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    Nilsson, L.; Thomas, J. O.; Tofield, B. C. The structure of the high-temperature solid electrolyte lithium sulphate at 908 K. J. phys., C, Solid state phys. 1980, 13, 6441– 6451,  DOI: 10.1088/0022-3719/13/35/004
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    The structure of the high-temperature solid electrolyte lithium sulfate at 908 K
    Nilsson, Leif; Thomas, John O.; Tofield, Bruce C.
    Journal of Physics C: Solid State Physics (1980), 13 (35), 6441-51CODEN: JPSOAW; ISSN:0022-3719.
    The structure of the high-temp., plastic phase of Li2SO4 was detd. from neutron powder diffraction at 908 K. The structure is fcc., a = 7.07 Å, with the SO42- ion situated at the origin and the O atoms rotationally disordered about the S atom. The Li+ ions occupy the ± (1/4, 1/4, 1/4) positions. The large isotropic temp. factors [B(SO4) = 17.5 Å2 and B(Li) = 33 Å2] suggest that the Li+ ions occupy a statistical distribution of sites instantaneously displaced from ± (1/4, 1/4, 1/4), in short-range correlation with the instantaneous orientations of the surrounding SO42- ions. The ionic motion of Li2SO4, a fast ionic conductor, is enhanced by the rotational motion of the translationally static counter ions.
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    Aronsson, R.; Jansson, B.; Knape, H. E. G.; Lundén, A.; Nilsson, L.; Sjöblom, C.-A.; Torell, L. M. Fast ion conductors with rotating sulphate ions. J. Phys., Colloq. 1980, 41, C6-35– C6-37,  DOI: 10.1051/jphyscol:1980609
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    Boerjesson, L.; Torell, L. M. Reorientational motion in superionic sulfates: A Raman linewidth study. Phys. Rev. B 1985, 32, 2471– 2477,  DOI: 10.1103/PhysRevB.32.2471
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    Reorientational motion in superionic sulfates: a Raman linewidth study
    Boerjesson, L.; Torell, L. M.
    Physical Review B: Condensed Matter and Materials Physics (1985), 32 (4), 2471-7CODEN: PRBMDO; ISSN:0163-1829.
    Raman spectra of 2 superionic conducting crystals, fcc. Li2SO4 and bcc. LiAgSO4, were recorded at 300-1400 cm-1 across the entire temp. range of stability of each compd. Comparison of polarized and depolarized spectral bandwidths for the sym. A1 sulfate internal mode permits a component due to the sulfate-ion reorientation to be sepd., which confirms the plastic behavior of the superionic phases of the 2 crystals. For Li2SO4, the reorientation time derived corresponds well with the value 2 ps recently reported on the basis of computer-simulation studies. The measurements are precise enough to yield the temp. dependence of the reorientation time in each type of crystal. The Arrhenius activation energies are significantly different: 0.40 and 0.72 eV for fcc. Li2SO4 and bcc. LiAgSO4, resp. These values are sufficiently close to the contrasting activation energies for cation diffusion, 0.34 and 0.52 eV, resp., to support the paddle-wheel migration postulate for this type of plastic crystal.
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    Lundén, A. Enhancement of cation mobility in some sulphate phases due to a paddle-wheel mechanism. Solid State Ion. 1988, 28–30, 163– 167,  DOI: 10.1016/S0167-2738(88)80026-2
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    Jansen, M. Volume Effect or Paddle-Wheel Mechanism─Fast Alkali-Metal Ionic Conduction in Solids with Rotationally Disordered Complex Anions. Angew. Chem., Int. Ed. 1991, 30, 1547– 1558,  DOI: 10.1002/anie.199115471
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    Witschas, M.; Eckert, H.; Wilmer, D.; Banhatti, R.; Funke, H.; Fitter, J.; Lechner, R. E.; Korus, G.; Jansen, M. Anion Rotation and Cation Transport in the Rotor Phase α-Sodium Orthophosphate: Paddle-Wheel Mechanism Redefined in View of New Experimental Results. Z. Phys. Chem. 2000, 214, 643– 673,  DOI: 10.1524/zpch.2000.214.5.643
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    Anion rotation and cation transport in the rotor phase α-sodium orthophosphate: paddle-wheel mechanism redefined in view of new experimental results
    Witschas, M.; Eckert, H.; Wilmer, D.; Banhatti, R. D.; Funke, K.; Fitter, J.; Lechner, R. E.; Korus, G.; Jansen, M.
    Zeitschrift fuer Physikalische Chemie (Muenchen) (2000), 214 (5), 643-673CODEN: ZPCFAX; ISSN:0044-3336. (R. Oldenbourg Verlag)
    The high-temp. phase of sodium ortho-phosphate, α-Na3PO4, is characterized by a dynamic rotational disorder of its polyat. anions and, at the same time, by a considerable translational mobility of its cations. During the past decade, there has been considerable controversy about the question of whether both kinds of motion are dynamically coupled. To resolve this issue we have probed anionic and cationic motion individually over a wide range of exptl. time scales. Coherent quasielastic neutron scattering as well as temp.-dependent 17O NMR lineshape and relaxation spectroscopy serve to characterize the rotational motion of the anions, whereas the cation motion is probed by high-frequency cond. and 23Na NMR relaxation measurements. On the picosecond timescale, the combined interpretation of the neutron scattering and elec. cond. data suggests strong dynamic coupling between the rotation of the phosphate groups about one of the four threefold P-O axes and the spatial fluctuations of nearby sodium ions. On more extended time scales, the NMR data indicate an addnl., slower process, corresponding to dynamic jump reorientations of the C3 axis of rotation. This process appears to be coupled to the translational Na+ transport dynamics as suggested by a strong correspondence between the 17O and 23Na NMR relaxation characteristics and the elec. conductivities in the dc plateau region. The Na+ transport process can be viewed as highly correlated, not unlike the chain mechanism obsd. in AgBr.
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    Kniaź, K.; Fischer, J. E.; Zhu, Q.; Rosseinsky, M. J.; Zhou, O.; Murphy, D. W. C60 orientational ordering in superconducting Na2RbC60. Solid State Commun. 1993, 88, 47– 50,  DOI: 10.1016/0038-1098(93)90767-H
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    Fullerene (C60) orientational ordering in superconducting sodium rubidium fulleride (Na2RbC60)
    Kniaz, Krzysztof; Fischer, John E.; Zhu, Qing; Rosseinsky, Matthew J.; Zhou, Otto; Murphy, Donald W.
    Solid State Communications (1993), 88 (1), 47-50CODEN: SSCOA4; ISSN:0038-1098.
    The C60 mols. in Na2RbC60 are orientationally ordered in a manner essentially the same as in pure C60. Fits to data at both 300 K and 27 K are significantly better in space group Pa‾3 (simple cubic) than in Fm‾3m (merohedral disorder) or by assuming uniform spherical shells of charge (complete disorder). The anomalously low Tc of this compd. cannot be attributed to excess orientational disorder, and therefore remains a mystery.
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    Tanigaki, K.; Hirosawa, I.; Manako, T.; Tsai, J. S.; Mizuki, J.; Ebbesen, T. W. Phase transitions in Na2AC60 (A = Cs, Rb, and K) fullerides. Phys. Rev. B 1994, 49, 12307– 12310,  DOI: 10.1103/PhysRevB.49.12307
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    Phase transition in Na2AC60 (A = Cs, Rb, and K) fullerides
    Tanigaki, K.; Hirosawa, I.; Manako, T.; Tsai, J. S.; Mizuki, J.; Ebbesen, T. W.
    Physical Review B: Condensed Matter and Materials Physics (1994), 49 (17), 12307-10CODEN: PRBMDO; ISSN:0163-1829.
    The ternary system fullerides Na2AC60 (A = Cs, Rb, and K) were studied by differential scanning calorimetry at 100-450 K. All show reproducible phase transitions at the transition temps. of 299 K (ΔH = 2.5 ± 0.5 J/g) for Na2CsCo60, 313 K (ΔH = 2.7 ± 0.5 J/g) for Na2RbC60, and 305 K (ΔH = 3.1 ± 0.5 J/g) for Na2KC60. Orientational ordering of the fullerene unit is responsible for the obsd. phase transitions (Tsc-fcc.) from a high-temp. fcc. to a low-temp. simple-cubic (s.c.) phase. The obsd. Tsc-fcc. and enthalpy can be compared to those for pristine C60 which has Tsc-fcc. = 256.5 K (ΔH = 8 ± 0.5 J/g). The obsd. behavior is discussed in terms of the balance between the C603--C603- intermol. interaction and the C603--A+ Coulombic interaction as a function of lattice parameter.
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    Saito, T.; Maniwa, Y.; Oda, H.; Kume, K.; Kosaka, M.; Hirosawa, I.; Tanigaki, K. NMR Studies on Orientational Ordering Phase Transition in Na2CsC60. J. Phys. Soc. Jpn. 1995, 64, 4513– 4517,  DOI: 10.1143/JPSJ.64.4513
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    NMR studies on orientational ordering phase transition in Na2CsC60
    Saito, Takahito; Maniwa, Yutaka; Oda, Hitoshi; Kume, Kiyoshi; Kosaka, Mayumi; Hirosawa, Ichiro; Tanigaki, Katsumi
    Journal of the Physical Society of Japan (1995), 64 (12), 4513-17CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
    Na-contg. alkali metal fulleride, Na2CsC60, was studied by 13C and 23Na NMR below and above the fcc. to simple cubic (s.c.) phase transition temp., Tm. The C60 mols. rotate faster than the rotational correlation time of 1.6 × 10-5 sec at ⪆140 K and 2.4 × 10-9 sec around 300 K. Using 23Na NMR spectra broadened by the 2nd-order quadrupole interaction, the elec. field gradient at Na sites, e2qQ/h, is 940 ± 20 kHz and <0.1 kHz below and above Tm, resp. Apparently the Na atoms in the s.c. phase have a covalent character with C60 mols. Probably Na2CsC60 is the 1st metallic plastic crystal.
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  27. 27
    Skripov, A. V.; Babanova, O. A.; Soloninin, A. V.; Stavila, V.; Verdal, N.; Udovic, T. J.; Rush, J. J. Nuclear Magnetic Resonance Study of Atomic Motion in A2B12H12 (A = Na, K, Rb, Cs): Anion Reorientations and Na+ Mobility. J. Phys. Chem. C 2013, 117, 25961– 25968,  DOI: 10.1021/jp4106585
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    27
    Nuclear Magnetic Resonance Study of Atomic Motion in A2B12H12 (A = Na, K, Rb, Cs): Anion Reorientations and Na+ Mobility
    Skripov, Alexander V.; Babanova, Olga A.; Soloninin, Alexei V.; Stavila, Vitalie; Verdal, Nina; Udovic, Terrence J.; Rush, John J.
    Journal of Physical Chemistry C (2013), 117 (49), 25961-25968CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    To study the reorientational motion of icosahedral [B12H12]2- anions in A2B12H12 (A = Na, K, Rb, Cs) and the translational diffusion of Na+ cations in Na2B12H12, the authors have measured the 1H, 11B, and 23Na NMR spectra and spin-lattice relaxation rates in these compds. at 170-580 K. For cubic compds. K2B12H12, Rb2B12H12, and Cs2B12H12, the measured 1H and 11B spin-lattice relaxation rates are governed by thermally activated reorientations of the [B12H12]2- anions. The activation energy of this reorientational motion decreases with increasing cation radius, changing from 800 meV for K2B12H12 to 549 meV for Rb2B12H12 and 427 meV for Cs2B12H12. For Na2B12H12, the 1st-order transition from the low-temp. monoclinic to the high-temp. cubic phase near 520 K is accompanied by a 2 orders of magnitude increase in the reorientational jump rate, and the corresponding activation energy changes from 770 meV for the low-T phase to 270 meV for the high-T phase. Measurements of the 23Na NMR spectra and spin-lattice relaxation rates show that the transition from the low-T to the high-T phase of Na2B12H12 is also accompanied by the onset of the fast translational diffusion of Na+ ions. Just above the transition point, the lower limit of the Na+ jump rate estd. from the 23Na spin-lattice relaxation data is 2 × 108 s-1, and the corresponding activation energy for Na+ diffusion is ∼410 meV.
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    Udovic, T. J.; Matsuo, M.; Unemoto, A.; Verdal, N.; Stavila, V.; Skripov, A. V.; Rush, J. J.; Takamura, H.; Orimo, S.-i. Sodium superionic conduction in Na2B12H12. Chem. Commun. 2014, 50, 3750– 3752,  DOI: 10.1039/C3CC49805K
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    28
    Sodium superionic conduction in Na2B12H12
    Udovic, Terrence J.; Matsuo, Motoaki; Unemoto, Atsushi; Verdal, Nina; Stavila, Vitalie; Skripov, Alexander V.; Rush, John J.; Takamura, Hitoshi; Orimo, Shin-ichi
    Chemical Communications (Cambridge, United Kingdom) (2014), 50 (28), 3750-3752CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
    Impedance measurements indicate that Na2B12H12 exhibits dramatic Na+ cond. (∼0.1 S cm-1) above its order-disorder phase-transition at ≈529 K, rivaling that of current, solid-state, ceramic-based, Na-battery electrolytes. Superionicity may be aided by the large size, quasispherical shape, and high rotational mobility of the B12H122- anions.
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  29. 29
    Kweon, K. E.; Varley, J. B.; Shea, P.; Adelstein, N.; Mehta, P.; Heo, T. W.; Udovic, T. J.; Stavila, V.; Wood, B. C. Structural, Chemical, and Dynamical Frustration: Origins of Superionic Conductivity in closo-Borate Solid Electrolytes. Chem. Mater. 2017, 29, 9142– 9153,  DOI: 10.1021/acs.chemmater.7b02902
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    Structural, Chemical, and Dynamical Frustration: Origins of Superionic Conductivity in closo-Borate Solid Electrolytes
    Kweon, Kyoung E.; Varley, Joel B.; Shea, Patrick; Adelstein, Nicole; Mehta, Prateek; Heo, Tae Wook; Udovic, Terrence J.; Stavila, Vitalie; Wood, Brandon C.
    Chemistry of Materials (2017), 29 (21), 9142-9153CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Li2B12H12, Na2B12H12, and their closo-borate relatives exhibit unusually high ionic cond., making them attractive as a new class of candidate electrolytes in solid-state Li- and Na-ion batteries. However, further optimization of these materials requires a deeper understanding of the fundamental mechanisms underlying ultrafast ion conduction. To this end, we use ab initio mol. dynamics simulations and d.-functional calcns. to explore the motivations for cation diffusion. We find that superionic behavior in Li2B12H12 and Na2B12H12 results from a combination of key structural, chem., and dynamical factors that introduce intrinsic frustration and disorder. A statistical metric is used to show that the structures exhibit a high d. of accessible interstitial sites and site types, which correlates with the flatness of the energy landscape and the obsd. cation mobility. Furthermore, cations are found to dock to specific anion sites, leading to a competition between the geometric symmetry of the anion and the symmetry of the lattice itself, which can facilitate cation hopping. Finally, facile anion reorientations and other low-frequency thermal vibrations lead to fluctuations in the local potential that enhance cation mobility by creating a local driving force for hopping. We discuss the relevance of each factor for developing new ionic cond. descriptors that can be used for discovery and optimization of closo-borate solid electrolytes, as well as superionic conductors more generally.
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  30. 30
    Udovic, T. J.; Matsuo, M.; Tang, W. S.; Wu, H.; Stavila, V.; Soloninin, A. V.; Skoryunov, R. V.; Babanova, O. A.; Skripov, A. V.; Rush, J. J.; Unemoto, A.; Takamura, H.; Orimo, S.-I. Exceptional Superionic Conductivity in Disordered Sodium Decahydro-closo-decaborate. Adv. Mater. 2014, 26, 7622– 7626,  DOI: 10.1002/adma.201403157
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    30
    Exceptional Superionic Conductivity in Disordered Sodium Decahydro-closo-decaborate
    Udovic, Terrence J.; Matsuo, Motoaki; Tang, Wan Si; Wu, Hui; Stavila, Vitalie; Soloninin, Alexei V.; Skoryunov, Roman V.; Babanova, Olga A.; Skripov, Alexander V.; Rush, John J.; Unemoto, Atsushi; Takamura, Hitoshi; Orimo, Shin-ichi
    Advanced Materials (Weinheim, Germany) (2014), 26 (45), 7622-7626CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Sodium decahydro-closo-decaborate forms a disordered, fcc. phase above about 360 K, possessing a vacancy-rich Na+ cation sublattice. This cation sublattice is highly mobile within the spacious corridors formed by the large B10H102- anions and exhibits remarkable superionic cond. (e.g., σ = 0.01 Scm-1 at 383 K) to substantially lower temps. than for Na2B12H12. This cond. is more than an order of magnitude higher than that of all other solid-state Na-based complex-hydride materials investigated to date in this temp. region. This discovery represents a major advancement in the field of solid-state Na+ fast-ion conduction at technol. relevant device temps.
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  31. 31
    Tang, W. S.; Unemoto, A.; Zhou, W.; Stavila, V.; Matsuo, M.; Wu, H.; Orimo, S.-i.; Udovic, T. J. Unparalleled lithium and sodium superionic conduction in solid electrolytes with large monovalent cage-like anions. Energy Environ. Sci. 2015, 8, 3637– 3645,  DOI: 10.1039/C5EE02941D
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    Unparalleled lithium and sodium superionic conduction in solid electrolytes with large monovalent cage-like anions
    Tang, Wan Si; Unemoto, Atsushi; Zhou, Wei; Stavila, Vitalie; Matsuo, Motoaki; Wu, Hui; Orimo, Shin-ichi; Udovic, Terrence J.
    Energy & Environmental Science (2015), 8 (12), 3637-3645CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    Solid electrolytes with sufficiently high conductivities and stabilities are the elusive answer to the inherent shortcomings of org. liq. electrolytes prevalent in today's rechargeable batteries. We recently revealed a novel fast-ion-conducting sodium salt, Na2B12H12, which contains large, icosahedral, divalent B12H122- anions that enable impressive superionic cond., albeit only above its 529 K phase transition. Its lithium congener, Li2B12H12, possesses an even more technol. prohibitive transition temp. above 600 K. Here we show that the chem. related LiCB11H12 and NaCB11H12 salts, which contain icosahedral, monovalent CB11H12- anions, both exhibit much lower transition temps. near 400 K and 380 K, resp., and truly stellar ionic conductivities (>0.1 S cm-1) unmatched by any other known polycryst. materials at these temps. With proper modifications, we are confident that room-temp.-stabilized superionic salts incorporating such large polyhedral anion building blocks are attainable, thus enhancing their future prospects as practical electrolyte materials in next-generation, all-solid-state batteries.
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    Dimitrievska, M.; Stavila, V.; Soloninin, A. V.; Skoryunov, R. V.; Babanova, O. A.; Wu, H.; Zhou, W.; Tang, W. S.; Faraone, A.; Tarver, J. D.; Trump, B. A.; Skripov, A. V.; Udovic, T. J. Nature of Decahydro-closo-decaborate Anion Reorientations in an Ordered Alkali-Metal Salt: Rb2B10H10. J. Phys. Chem. C 2018, 122, 15198– 15207,  DOI: 10.1021/acs.jpcc.8b04385
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    Nature of Decahydro-closo-decaborate Anion Reorientations in an Ordered Alkali-Metal Salt: Rb2B10H10
    Dimitrievska, Mirjana; Stavila, Vitalie; Soloninin, Alexei V.; Skoryunov, Roman V.; Babanova, Olga A.; Wu, Hui; Zhou, Wei; Tang, Wan Si; Faraone, Antonio; Tarver, Jacob D.; Trump, Benjamin A.; Skripov, Alexander V.; Udovic, Terrence J.
    Journal of Physical Chemistry C (2018), 122 (27), 15198-15207CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The ordered monoclinic phase of the alkali metal decahydro-closo-decaborate salt Rb2B10H10 is stable from ∼250 K all the way up to an order-disorder phase transition temp. of ≈762 K. The broad temp. range for this phase allowed for a detailed quasielastic neutron scattering (QENS) and NMR study of the protypical B10H102- anion reorientational dynamics. The QENS and NMR combined results are consistent with an anion reorientational mechanism comprised of 2 types of rotational jumps expected from the anion geometry and lattice structure, namely, more rapid 90° jumps around the anion C4 symmetry axis (e.g., with correlation frequencies of ≈2.6 × 1010 s-1 at 530 K) combined with order of magnitude slower orthogonal 180° reorientational flips (e.g., ≈3.1 × 109 s-1 at 530 K) resulting in an exchange of the apical H (and apical B) positions. Each latter flip requires a concomitant 45° twist around the C4 symmetry axis to preserve the ordered Rb2B10H10 monoclinic structural symmetry. This result is consistent with previous NMR data for ordered monoclinic Na2B10H10, which also pointed to 2 types of anion reorientational motions. The QENS-derived reorientational activation energies are 197(2) and 288(3) meV for the C4 4-fold jumps and apical exchanges, resp., between 400 and 680 K. Below this temp. range, NMR (and QENS) both indicate a shift to significantly larger reorientational barriers, for example, 485(8) meV for the apical exchanges. Subambient diffraction measurements identify a subtle change in the Rb2B10H10 structure from monoclinic to triclinic symmetry as the temp. is decreased from around 250 to 210 K.
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  33. 33
    Famprikis, T.; Dawson, J. A.; Fauth, F.; Clemens, O.; Suard, E.; Fleutot, B.; Courty, M.; Chotard, J.-N.; Islam, M. S.; Masquelier, C. A New Superionic Plastic Polymorph of the Na+ Conductor Na3PS4. ACS Materials Letters 2019, 1, 641– 646,  DOI: 10.1021/acsmaterialslett.9b00322
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    A New Superionic Plastic Polymorph of the Na+ Conductor Na3PS4
    Famprikis, Theodosios; Dawson, James A.; Fauth, Francois; Clemens, Oliver; Suard, Emmanuelle; Fleutot, Benoit; Courty, Matthieu; Chotard, Jean-Noel; Islam, M. Saiful; Masquelier, Christian
    ACS Materials Letters (2019), 1 (6), 641-646CODEN: AMLCEF; ISSN:2639-4979. (American Chemical Society)
    Na3PS4 is one of the most promising Na+ conductors, relevant for applications that can leverage its high ionic cond., such as solid-state batteries. At present, 2 cryst. phases of the material have been identified and it had been thought to melt >500°. In contrast, we show that it remains solid above this temp. and transforms into a 3rd polymorph, γ, exhibiting fast-ion conduction and an orthorhombic crystal structure based on diffraction, ab initio simulations, impedance spectroscopy and thermal anal. We show that the fast Na+-conduction is assocd. with rotational motion of the thiophosphate polyanions pointing to a plastic crystal. These findings are of major importance for the development and understanding of new polyanion based solid electrolytes.
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  34. 34
    Saha, S.; Rousse, G.; Courty, M.; Shakhova, Y.; Kirsanova, M.; Fauth, F.; Pomjakushin, V.; Abakumov, A. M.; Tarascon, J. M. Structural Polymorphism in Na4Zn(PO4)2 Driven by Rotational Order–Disorder Transitions and the Impact of Heterovalent Substitutions on Na-Ion Conductivity. Inorg. Chem. 2020, 59, 6528– 6540,  DOI: 10.1021/acs.inorgchem.0c00612
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    Structural Polymorphism in Na4Zn(PO4)2 Driven by Rotational Order-Disorder Transitions and the Impact of Heterovalent Substitutions on Na-Ion Conductivity
    Saha, Sujoy; Rousse, Gwenaelle; Courty, Matthieu; Shakhova, Yaroslava; Kirsanova, Maria; Fauth, Francois; Pomjakushin, Vladimir; Abakumov, Artem M.; Tarascon, J. M.
    Inorganic Chemistry (2020), 59 (9), 6528-6540CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
    Solid electrolytes have regained tremendous interest recently in light of the exposed vulnerability of current rechargeable battery technologies. While designing solid electrolytes, most efforts concd. on creating structural disorder (vacancies, interstitials, etc.) in a cationic Li/Na sublattice to increase ionic cond. In phosphates, the ionic cond. can also be increased by rotational disorder in the anionic sublattice, via a paddle-wheel mechanism. Herein, we report on Na4Zn(PO4)2 which is designed from Na3PO4, replacing Na+ with Zn2+ and introducing a vacancy for charge balance. We show that Na4Zn(PO4)2 undergoes a series of structural transitions under temp., which are assocd. with an increase in ionic cond. by several orders of magnitude. Our detailed crystallog. study, combining electron, neutron, and X-ray powder diffraction, reveals that the room-temp. form, α-Na4Zn(PO4)2, contains orientationally ordered PO4 groups, which undergo partial and full rotational disorder in the high-temp. β- and γ-polymorphs, resp. We furthermore showed that the highly conducting γ-polymorph could be stabilized at room temp. by ball-milling, whereas the β-polymorph can be stabilized by partial substitution of Zn2+ with Ga3+ and Al3+. These findings emphasize the role of rotational disorder as an extra parameter to design new solid electrolytes. Temp.-driven structural transitions in Na4Zn(PO4)2, involving rotational disorder of PO4 groups, are responsible for increasing Na-cond. in the high-temp. phases, which are stabilized at room temp. by ball-milling and chem. substitutions.
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    Geirhos, K.; Lunkenheimer, P.; Michl, M.; Reuter, D.; Loidl, A. Communication: Conductivity enhancement in plastic-crystalline solid-state electrolytes. J. Chem. Phys. 2015, 143, 081101,  DOI: 10.1063/1.4929554
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    Communication: Conductivity enhancement in plastic-crystalline solid-state electrolytes
    Geirhos, K.; Lunkenheimer, P.; Michl, M.; Reuter, D.; Loidl, A.
    Journal of Chemical Physics (2015), 143 (8), 081101/1-081101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Finding new ionic conductors that enable significant advancements in the development of energy-storage devices is a challenging goal of current material science. Aside of material classes as ionic liqs. or amorphous ion conductors, the so-called plastic crystals (PCs) are good candidates combining high cond. and favorable mech. properties. PCs are formed by mols. whose orientational degrees of freedom still fluctuate despite the material exhibits a well-defined cryst. lattice. The cond. of Li+ ions in succinonitrile, the most prominent mol. PC electrolyte, can be enhanced by several decades when replacing part of the mols. in the cryst. lattice by larger ones. Dielec. spectroscopy reveals that this is accompanied by a stronger coupling of ionic and reorientational motions. These findings, which can be understood in terms of an optimized revolving door mechanism, open a new path towards the development of better solid-state electrolytes. (c) 2015 American Institute of Physics.
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    Vaalma, C.; Buchholz, D.; Weil, M.; Passerini, S. A cost and resource analysis of sodium-ion batteries. Nat. Rev. Mater. 2018, 3, 18013,  DOI: 10.1038/natrevmats.2018.13
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    Haynes, W. CRC Handbook of Chemistry and Physics, 97th ed.; CRC Press, 2016; pp 14– 17.
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    Meilander, B. E.; Nilsson, L. Thermal Expansion of Lithium Sulphate. Z. Naturforsch A 1983, 38, 1396– 1399,  DOI: 10.1515/zna-1983-1218
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    Egami, T.; Billinge, S. J. L. Underneath the Bragg peaks: Structural analysis of complex materials, 2nd ed.; Elsevier: Amsterdam, 2012.
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    Terban, M. W.; Billinge, S. J. L. Structural analysis of molecular materials using the pair distribution function. Chem. Rev. 2022, 122, 1208– 1272,  DOI: 10.1021/acs.chemrev.1c00237
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    Structural Analysis of Molecular Materials Using the Pair Distribution Function
    Terban, Maxwell W.; Billinge, Simon J. L.
    Chemical Reviews (Washington, DC, United States) (2022), 122 (1), 1208-1272CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. This is a review of at. pair distribution function (PDF) anal. as applied to the study of mol. materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorg. crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to mol. materials such as carbons, pharmaceuticals, polymers, liqs., coordination compds., composites, and more. Here, an overview of applications toward a wide variety of mol. compds. (org. and inorg.) and systems with mol. components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material prepn., high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful ref. to practitioners for PDF applications in a wide realm of mol. sciences, and help new practitioners to get started with this technique.
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    Prill, D.; Juhás, P.; Schmidt, M. U.; Billinge, S. J. L. Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs. J. Appl. Crystallogr. 2015, 48, 171– 178,  DOI: 10.1107/S1600576714026454
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    Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs
    Prill, Dragica; Juhas, Pavol; Schmidt, Martin U.; Billinge, Simon J. L.
    Journal of Applied Crystallography (2015), 48 (1), 171-178CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)
    The methods currently used to calc. at. pair distribution functions (PDFs) from org. structural models do not distinguish between the intramol. and intermol. distances. Owing to the stiff bonding between atoms within a mol., the PDF peaks arising from intramol. atom-atom distances are much sharper than those of the intermol. atom-atom distances. This work introduces a simple approach to calc. PDFs of mol. systems without building a supercell model by using two different isotropic displacement parameters to describe at. motion: one parameter is used for the intramol., the other one for intermol. atom-atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calcns. were done with the DiffPy-CMI complex modeling infrastructure. The new modeling approach produced remarkably better fits to the exptl. PDFs, confirming the higher accuracy of this method for org. materials.
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    Terban, M. W.; Russo, L.; Pham, T. N.; Barich, D. H.; Sun, Y. T.; Burke, M. D.; Brum, J.; Billinge, S. J. L. Local structural effects due to micronization and amorphization on an HIV treatment active pharmaceutical ingredient. Mol. Pharmaceutics 2020, 17, 2370– 2389,  DOI: 10.1021/acs.molpharmaceut.0c00122
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    Local Structural Effects Due to Micronization and Amorphization on an HIV Treatment Active Pharmaceutical Ingredient
    Terban, Maxwell W.; Russo, Luca; Pham, Tran N.; Barich, Dewey H.; Sun, Yan T.; Burke, Matthew D.; Brum, Jeffrey; Billinge, Simon J. L.
    Molecular Pharmaceutics (2020), 17 (7), 2370-2389CODEN: MPOHBP; ISSN:1543-8384. (American Chemical Society)
    Processing procedures for inducing domain size redn. and/or amorphous phase generation can be crucial for enhancing the bioavailability of active pharmaceutical ingredients (APIs). It is important to quantify these reduced coherence phases and to detect and characterize assocd. structural changes, to ensure that no deleterious effects on safety, function, or stability occur. Here, X-ray powder diffraction (XRPD), total scattering pair distribution function (TSPDF) anal., and solid-state NMR spectroscopy (SSNMR) have been performed on samples of GSK2838232B, an investigational drug for the treatment of human immunodeficiency virus (HIV). Prepns. were obtained through different mech. treatments resulting in varying extents of domain size redn. and amorphous phase generation. Completely amorphous formulations could be prepd. by milling and microfluidic injection processes. Microfluidic injection was shown to result in a different local structure due to dispersion with dichloromethane. Implications of combined TSPDF and SSNMR studies to characterize mol. compds. are also discussed, in particular, the possibility to obtain a thorough structural understanding of disordered samples from different processes.
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    Adams, S.; Rao, R. P. High power lithium ion battery materials by computational design. Phys. Status Solidi A 2011, 208, 1746– 1753,  DOI: 10.1002/pssa.201001116
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    High power lithium ion battery materials by computational design
    Adams, Stefan; Rao, R. Prasada
    Physica Status Solidi A: Applications and Materials Science (2011), 208 (8), 1746-1753CODEN: PSSABA; ISSN:1862-6300. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Empirical bond length-bond valence (BV) relations provide insight into the link between structure of and ion transport in solid electrolytes and mixed conductors. Building on our earlier systematic adjustment of BV parameters to the bond softness, here we discuss how the squared BV mismatch is linked to the abs. energy scale and used as a general Morse-type interaction potential for analyzing low-energy ion migration paths in ion conducting solids or mixed conductors by either an energy landscape approach or mol. dynamics (MD) simulations. For a wide range of lithium oxides we could thus model ion transport revealing significant differences to an earlier geometric approach. This novel BV-based force-field has then been applied to investigate a range of mixed conductors, focusing on cathode materials for lithium ion battery (LIB) applications to promote a systematic design of LIB cathodes that combine high energy d. with high power d. To demonstrate the versatility of the new BV-based force field it is applied in exploring various strategies to enhance the power performance of safe low cost LIB materials including LiFePO4, LiVPO4F, LiFeSO4F, etc.
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    Chen, H.; Wong, L. L.; Adams, S. SoftBV – a software tool for screening the materials genome of inorganic fast ion conductors. Acta Cryst. B 2019, 75, 18– 33,  DOI: 10.1107/S2052520618015718
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    SoftBV - a software tool for screening the materials genome of inorganic fast ion conductors
    Chen, Haomin; Wong, Lee Loong; Adams, Stefan
    Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2019), 75 (1), 18-33CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
    The identification of materials for advanced energy-storage systems is still mostly based on exptl. trial and error. Increasingly, computational tools are sought to accelerate materials discovery by computational predictions. Here are introduced a set of computationally inexpensive software tools that exploit the bond-valence-based empirical force field previously developed by the authors to enable high-throughput computational screening of exptl. or simulated crystal-structure models of battery materials predicting a variety of properties of technol. relevance, including a structure plausibility check, surface energies, an inventory of equil. and interstitial sites, the topol. of ion-migration paths in between those sites, the resp. migration barriers and the site-specific attempt frequencies. All of these can be predicted from CIF files of structure models at a minute fraction of the computational cost of d. functional theory (DFT) simulations, and with the added advantage that all the relevant pathway segments are analyzed instead of arbitrarily predetd. paths. The capabilities and limitations of the approach are evaluated for a wide range of ion-conducting solids. An integrated simple kinetic Monte Carlo simulation provides rough (but less reliable) predictions of the abs. cond. at a given temp. The automated adaptation of the force field to the compn. and charge distribution in the simulated material allows for a high transferability of the force field within a wide range of Lewis acid-Lewis base-type ionic inorg. compds. as necessary for high-throughput screening. While the transferability and precision will not reach the same levels as in DFT simulations, the fact that the computational cost is several orders of magnitude lower allows the application of the approach not only to pre-screen databases of simple structure prototypes but also to structure models of complex disordered or amorphous phases, and provides a path to expand the anal. to charge transfer across interfaces that would be difficult to cover by ab initio methods.
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    Petříček, V.; Dušek, M.; Palatinus, L. Crystallographic Computing System JANA2006: General features. Z. Kristallogr. 2014, 229, 345– 352,  DOI: 10.1515/zkri-2014-1737
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    Crystallographic Computing System JANA2006: General features
    Petricek, Vaclav; Dusek, Michal; Palatinus, Lukas
    Zeitschrift fuer Kristallographie - Crystalline Materials (2014), 229 (5), 345-352CODEN: ZKCMAJ; ISSN:2194-4946. (Oldenbourg Wissenschaftsverlag GmbH)
    JANA2006 is a freely available program for structure detn. of std., modulated and magnetic samples based on X-ray or neutron single crystal/ powder diffraction or on electron diffraction. The system has been developed for 30 years from specialized tool for refinement of modulated structures to a universal program covering std. as well as advanced crystallog. The aim of this article is to describe the basic features of JANA2006 and explain its scope and philosophy. It will also serve as a basis for future publications detailing tools and methods of JANA.
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    Chupas, P. J.; Qiu, X.; Hanson, J. C.; Lee, P. L.; Grey, C. P.; Billinge, S. J. L. Rapid acquisition pair distribution function analysis (RA-PDF). J. Appl. Crys. 2003, 36, 1342– 1347,  DOI: 10.1107/S0021889803017564
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    Rapid-acquisition pair distribution function (RA-PDF) analysis
    Chupas, Peter J.; Qiu, Xiangyun; Hanson, Jonathan C.; Lee, Peter L.; Grey, Clare P.; Billinge, Simon J. L.
    Journal of Applied Crystallography (2003), 36 (6), 1342-1347CODEN: JACGAR; ISSN:0021-8898. (Blackwell Publishing Ltd.)
    An image-plate (IP) detector coupled with high-energy synchrotron radiation was used for at. pair distribution function (PDF) anal., with high probed momentum transfer Qmax ≤ 28.5 Å-1, from cryst. materials. Materials with different structural complexities were measured to test the validity of the quant. data anal. Exptl. results are presented for cryst. Ni, cryst. α-AlF3, and the layered Aurivillius type oxides α-Bi4V2O11 and γ-Bi4V1.7Ti0.3O10.85. Overall, the diffraction patterns show good counting statistics, with measuring time from one to tens of seconds. The PDFs obtained are of high quality. Structures may be refined from these PDFs, and the structural models are consistent with the published literature. Data sets from similar samples are highly reproducible.
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    Kieffer, J.; Ashiotis, G.; Deschildre, A.; Nawaz, Z.; Wright, J. P.; Karkoulis, D.; Picca, F. E. The fast azimuthal integration Python library: pyFAI. J. Appl. Crys. 2015, 48, 510– 519,  DOI: 10.1107/S1600576715004306
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    Juhás, P.; Davis, T.; Farrow, C. L.; Billinge, S. J. L. PDFgetX3: A rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions. J. Appl. Crys. 2013, 46, 560– 566,  DOI: 10.1107/S0021889813005190
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    PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions
    Juhas, P.; Davis, T.; Farrow, C. L.; Billinge, S. J. L.
    Journal of Applied Crystallography (2013), 46 (2), 560-566CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
    PDFgetX3 is a new software application for converting x-ray powder diffraction data to an at. pair distribution function (PDF). PDFgetX3 was designed for ease of use, speed and automated operation. The software can readily process hundreds of x-ray patterns within a few seconds and is thus useful for high-throughput PDF studies that measure numerous data sets as a function of time, temp. or other environmental parameters. In comparison to the preceding programs, PDFgetX3 requires fewer inputs and less user experience and it can be readily adopted by novice users. The live-plotting interactive feature allows the user to assess the effects of calcn. parameters and select their optimum values. PDFgetX3 uses an ad hoc data correction method, where the slowly changing structure-independent signal is filtered out to obtain coherent x-ray intensities that contain structure information. The output from PDFgetX3 was verified by processing exptl. PDFs from inorg., org. and nanosized samples and comparing them with their counterparts from a previous established software. In spite of the different algorithm, the obtained PDFs were nearly identical and yielded highly similar results when used in structure refinement. PDFgetX3 is written in the Python language and features a well documented reusable code base. The software can be used either as a standalone application or as a library of PDF processing functions that can be called from other Python scripts. The software is free for open academic research but requires paid license for com. use.
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    Yang, X.; Juhás, P.; Farrow, C.; Billinge, S. J. L. xPDFsuite: an end-to-end software solution for high throughput pair distribution function transformation, visualization and analysis. arXiv Preprint (Condensed Matter, Materials Science) , February 13, 2015. arXiv:1402.3163. https://arxiv.org/abs/1402.3163
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    Coelho, A. A.; Chater, P. A.; Kern, A. Fast synthesis and refinement of the atomic pair distribution function. J. Appl. Crys. 2015, 48, 869– 875,  DOI: 10.1107/S1600576715007487
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    Coelho, A. A. TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. J. Appl. Crystallogr. 2018, 51, 210– 218,  DOI: 10.1107/S1600576718000183
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    TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++
    Coelho, Alan A.
    Journal of Applied Crystallography (2018), 51 (1), 210-218CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)
    TOPAS and its academic variant TOPAS-Academic are nonlinear least-squares optimization programs written in the C++ programming language. This paper describes their functionality and architecture. The latter is of benefit to developers seeking to reduce development time. TOPAS allows linear and nonlinear constraints through the use of computer algebra, with parameter dependencies, required for parameter derivs., automatically detd. In addn., the objective function can include restraints and penalties, which again are defined using computer algebra. Of importance is a conjugate gradient soln. routine with bounding constraints which guide refinements to convergence. Much of the functionality of TOPAS is achieved through the use of generic functionality; for example, flexible peak-shape generation allows neutron time-of-flight (TOF) peak shapes to be described using generic functions. The kernel of TOPAS can be run from the command line for batch mode operation or from a closely integrated graphical user interface. The functionality of TOPAS includes peak fitting, Pawley and Le Bail refinement, Rietveld refinement, single-crystal refinement, pair distribution function refinement, magnetic structures, const. wavelength neutron refinement, TOF refinement, stacking-fault anal., Laue refinement, indexing, charge flipping, and structure soln. through simulated annealing.
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    Rietveld, H. M. A. Profile Refinement Method for Nuclear and Magnetic Structures. J. Appl. Crystallogr. 1969, 2, 65– 71,  DOI: 10.1107/S0021889869006558
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    Profile refinement method for nuclear and magnetic structures
    Rietveld, H. M.
    Journal of Applied Crystallography (1969), 2 (Pt. 2), 65-71CODEN: JACGAR; ISSN:0021-8898.
    A structural refinement method for neutron diffraction is presented which makes direct use of the profile intensities obtained from the powder diagram. It is applicable to nuclear structures and to magnetic structures which can be described on the nuclear unit cell or a multiple thereof. Equations for the measured profiles to be used in the least sqs. treatment are cor. for asymmetry and preferred orientation; the angular dependence of the half widths of the peaks is given by the formula of Caglioti, et al. (1958). The magnetic contribution to the profile equation is expressed by calcg. only one av. cross section for each set of equiv. reflections. It is possible to introduce constraint functions, linear or quadratic, between parameters used in the least sqs. treatment. Results of the use of this method are given for a series of compds. In all instances it has proved superior to any other method involving integrated neutron powder intensities, single or overlapping.
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    Dinnebier, R. E.; Leineweber, A.; Evans, J. S. O. Rietveld Refinement: Practical Powder Diffraction Pattern Analysis Using TOPAS, 1st ed.; De Gruyter STEM: Berlin, 2019.  DOI: 10.1515/9783110461381 .
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  • Abstract

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    Figure 1

    Figure 1. Variable-temperature PXRD of Na4P2S6 upon heating (bottom) and cooling (top) across the β–γ phase transition: contour plot of diffractograms (the color code, red to purple/blue, indicates the ranges from low to high diffraction intensities, respectively) and exemplary diffractograms (black) at 520 °C (β), 620 °C (γ), and 520 °C (β after heating above the phase transition). The selected diffractograms are additionally depicted in Supporting Information Figure S1.

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    Figure 2

    Figure 2. (a) Temperature-dependent volume expansion and contraction across the β → γ phase transition relative to the room-temperature unit cell volume, Vrt, of Na4P2S6. (b) Differential scanning calorimetry (DSC) curve.

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    Figure 3

    Figure 3. (a) Experimental synchrotron PDF with PDFs simulated from the fitted structure models and P2S64– anion only and (b) Rietveld fit of the PXRD pattern for γ-Na4P2S6 at 650 °C. The gray shaded region in (a) represents the unphysical interatomic distance range that is more highly affected by systematic errors from data processing. (c) Illustration of the PDF-refined γ-structure with a static approximation of the P2S64– anions in a 2 × 2 × 2 cell, and (d) in a single unit cell. (e) Overlay of bond valence energy landscape (red surface) and the crystal structure visualizing the three-dimensional Na+ conducting pathways.

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    Figure 4

    Figure 4. (a) Arrhenius plot of ionic conductivity and activation energies derived from impedance spectroscopy. The heating and cooling segments are indicated by orange and blue circles. The activation energy was extracted from the orange (heating) data points, since the cooling data points possibly describe a mixed ionic–electronic conducting (MIEC) phase. The error bars arise from the standard deviation of ionic conductivity measured on three distinct pellets. (b) Mean-squared displacements (MSDs) of Na, P, and S at 1000 K from AIMD simulations. (c) Arrhenius plot of the ionic conductivity and activation energy from AIMD simulations.

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    Figure 5

    Figure 5. (a) Scheme of the definition of the azimuthal angle (ϕ) and polar angle (θ) with respect to the P–P handle and scheme of the P–P orientation in Cartesian octants. (b) Orientation heat map of all P2S64– in a 2 × 2 × 2 cell at 1000 K in a 300 ps simulation. (c) ϕ and (d) θ as a function of time of an exemplary P2S64– at 1000 K.

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      Innovative rechargeable batteries that can effectively store renewable energy, such as solar and wind power, urgently need to be developed to reduce greenhouse gas emissions. All-solid-state batteries with inorganic solid electrolytes and electrodes are promising power sources for a wide range of applications because of their safety, long-cycle lives and versatile geometries. Rechargeable sodium batteries are more suitable than lithium-ion batteries, because they use abundant and ubiquitous sodium sources. Solid electrolytes are critical for realizing all-solid-state sodium batteries. Here we show that stabilization of a high-temperature phase by crystallization from the glassy state dramatically enhances the Na(+) ion conductivity. An ambient temperature conductivity of over 10(-4) S cm(-1) was obtained in a glass-ceramic electrolyte, in which a cubic Na(3)PS(4) crystal with superionic conductivity was first realized. All-solid-state sodium batteries, with a powder-compressed Na(3)PS(4) electrolyte, functioned as a rechargeable battery at room temperature.
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      Hayashi, Akitoshi; Noi, Kousuke; Tanibata, Naoto; Nagao, Motohiro; Tatsumisago, Masahiro
      Journal of Power Sources (2014), 258 (), 420-423CODEN: JPSODZ; ISSN:0378-7753. (Elsevier B.V.)
      Sulfide solid electrolytes with cubic Na3PS4 phase has relatively high sodium ion cond. of over 10-4 S cm-1 at room temp., and all-solid-state sodium batteries Na-Sn/TiS2 with the electrolyte operated as a secondary battery at room temp. To improve battery performance, cond. enhancement of sulfide electrolytes is important. In this study, the cond. is enhanced by optimizing prepn. conditions of Na3PS4 glass-ceramic electrolytes. By use of cryst. Na2S of purity of 99.1%, cubic Na3PS4 crystals were directly pptd. by ball milling process at the compn. of 75Na2S·25P2S5 (mol%). The glass-ceramic electrolyte prepd. by milling for 1.5 h and consecutive heat treatment at 270° for 1 h showed the highest cond. of 4.6 × 10-4 S cm-1, which is twice as high as the cond. of the cubic Na3PS4 glass-ceramic prepd. in a previous report. All-solid-state Na-Sn/NaCrO2 cells with the newly prepd. electrolyte exhibited charge-discharge cycles at room temp. and kept about 60 mAh per g of NaCrO2 for 15 cycles.
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    6. 6
      Krauskopf, T.; Culver, S. P.; Zeier, W. G. Local Tetragonal Structure of the Cubic Superionic Conductor Na3PS4. Inorg. Chem. 2018, 57, 4739– 4744,  DOI: 10.1021/acs.inorgchem.8b00458
      6
      Local Tetragonal Structure of the Cubic Superionic Conductor Na3PS4
      Krauskopf, Thorben; Culver, Sean P.; Zeier, Wolfgang G.
      Inorganic Chemistry (2018), 57 (8), 4739-4744CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
      The sodium superionic conductor Na3PS4 is known to crystallize in one of two different structural polymorphs at room temp. (i.e., cubic or tetragonal, depending on the synthetic conditions). Exptl., the cubic structure is known to exhibit a higher ionic cond. than the tetragonal structure, despite theor. studies suggesting that there should be no difference at all. Employing a combination of Rietveld and pair distribution function (PDF) analyses, as well as electrochem. impedance spectroscopy, the authors study the open question of how the crystal structure influences the ionic transport in Na3PS4. Despite the av. structures of Na3PS4 prepd. via ball-milling and high-temp. routes being cubic and tetragonal, resp., the structural anal. by PDF indicates that both compds. are best described by the structural motifs of the tetragonal polymorph on the local scale. Ultimately, the high ionic cond. of Na3PS4 prepd. by the ball-milling approach is independent of the crystal structure. Even in ionic conductors differences can be obsd. between the av. and local crystal structures, and it reasserts that the high ionic cond. in Na3PS4 is not related to the crystal structure but rather differences in the defect concn.
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    7. 7
      Rush, L. E.; Holzwarth, N. A. W. First principles investigation of the structural and electrochemical properties of Na4P2S6 and Li4P2S6. Solid State Ion. 2016, 286, 45– 50,  DOI: 10.1016/j.ssi.2015.12.015
      There is no corresponding record for this reference.
    8. 8
      Rush, L. E. J. First-Principles Investigation of Electronic Properties in Sodium-Ion Electrolytes for Solid-State Battery Materials. Thesis, Wake Forest University, Winston-Salem, NC, USA, 2017.
      There is no corresponding record for this reference.
    9. 9
      Fincher, T.; LeBret, G.; Cleary, D. A. Single-Crystal Structure Determination of Na4P2S6·6 H2O. J. Solid State Chem. 1998, 141, 274– 281,  DOI: 10.1006/jssc.1998.7992
      9
      Single-crystal structure determination of Na4P2S6.6H2O
      Fincher, T.; LeBret, G.; Cleary, D. A.
      Journal of Solid State Chemistry (1998), 141 (1), 274-281CODEN: JSSCBI; ISSN:0022-4596. (Academic Press)
      The single-crystal structure of Na4P2S6.6H2O is reported. TGA (23.6% wt. loss) showed that Na4P2S6.6H2O converted to Na4P2S6 as it was heated from room temp. to 80°. The room temp. IR spectrum of Na4P2S6.6H2O was analyzed in terms of the symmetry of the P2S6-4 group. Na4P2S6.6H2O crystd. in the monoclinic space group P21/c with a 25.4761(4), b 7.10350(10), and c 20.3282(3) Å, β 113.482°, Z = 8, dc = 1.565. The single crystal structure was also solved at -60°. The low temp. crystal data were a 25.3961(3), b 7.06480(10), and c 20.22160(10) Å, β 113.431(1)°, Z = 8, dc = 1.586. At. coordinates are given. (c) 1998 Academic Press.
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    10. 10
      Kuhn, A.; Eger, R.; Nuss, J.; Lotsch, B. V. Synthesis and Structural Characterization of the Alkali Thiophosphates Na2P2S6, Na4P2S6, K4P2S6, and Rb4P2S6. Z. Anorg. Allg. Chem. 2014, 640, 689– 692,  DOI: 10.1002/zaac.201300575
      10
      Synthesis and Structural Characterization of the Alkali Thiophosphates Na2P2S6, Na4P2S6, K4P2S6, and Rb4P2S6
      Kuhn, Alexander; Eger, Roland; Nuss, Juergen; Lotsch, Bettina V.
      Zeitschrift fuer Anorganische und Allgemeine Chemie (2014), 640 (5), 689-692CODEN: ZAACAB; ISSN:0044-2313. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Four compds. in the ternary systems Na-P-S, K-P-S, and Rb-P-S, Na2P2S6, Na4P2S6, K4P2S6, and Rb4P2S6 were prepd. and structurally characterized using single-crystal x-ray diffraction. Na2P2S6 crystallizes in the monoclinic space group P21/m with a 6.6752(3), b 7.7968(4), c 9.0379(4) Å, and β 90.151(1)° in a new structure type that can be described as a distorted Tl2P2S6 structure. The monoclinic structure of Na4P2S6 [space group C2/m, a 6.725(2), b 11.222(2), c 7.542(2) Å, and β 107.03(3)°] is a stuffed variant of the FePS3 structure. K4P2S6 and space group Rb4P2S6 are isotypic and crystallize in the K4P2Se6 structure type [space group P21/c, a = 13.243(3) / 13.538(3), b = 11.946(2) / 12.310(3), c 8.396(2) / 8.751(2) Å, and β = 91.44(3) / 92.46(3)° for K4P2S6 / Rb4P2S6].
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    11. 11
      Scholz, T.; Schneider, C.; Eger, R.; Duppel, V.; Moudrakovski, I.; Schulz, A.; Nuss, J.; Lotsch, B. V. Phase formation through synthetic control: polymorphism in the sodium-ion solid electrolyte Na4P2S6. J. Mater. Chem. A 2021, 9, 8692– 8703,  DOI: 10.1039/D0TA11008F
      11
      Phase formation through synthetic control: polymorphism in the sodium-ion solid electrolyte Na4P2S6
      Scholz, Tanja; Schneider, Christian; Eger, Roland; Duppel, Viola; Moudrakovski, Igor; Schulz, Armin; Nuss, Juergen; Lotsch, Bettina V.
      Journal of Materials Chemistry A: Materials for Energy and Sustainability (2021), 9 (13), 8692-8703CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
      The development of all-solid-state sodium batteries for scalable energy storage solns. requires fast sodium conducting solid electrolytes. To fast-track their discovery, candidate materials need to be identified that are synthesized from abundant resources via cheap and green synthesis routes. Their ion conducting mechanism has to be understood and adapted to meet the stringent requirements for long-term operation in all-solid-state batteries. Here, structure and properties of the sodium hexathiohypodiphosphate Na4P2S6 obtained by two different synthesis methods are compared: a solid-state reaction and a pptn. route from aq. soln. Combined investigations using powder X-ray diffraction (PXRD), precession electron diffraction (PED), differential scanning calorimetry (DSC), solid-state NMR spectroscopy (ssNMR), and Raman spectroscopy reveal that the solid-state synthesized material is characterized by a Na+ and vacancy disorder-driven enantiotropic phase transition at 160 °C (α- to β-Na4P2S6), which is accompanied by a symmetry change of the P2S64- anion. Pptd. Na4P2S6 already crystallizes in a β-like polymorph at room temp., likely assisted by inter- and intralayer defects. Bond-valence and nudged elastic band (NEB) calcns. were employed to identify a low energy, 2D conduction network in β-Na4P2S6, suggesting facile 2D long-range Na+ diffusion. Electrochem. impedance spectroscopy reveals a higher ionic cond. at room temp. in pptd. β-like Na4P2S6 (2 x 10-6 S cm-1) compared to the solid-state α polymorph (7 x 10-7 S cm-1). The activation energy is around 0.4 eV for both materials. The findings highlight that even subtle structural changes can significantly impact the sodium-ion diffusion in solid electrolytes and at the same time reveal an intricate interplay between phase formation and synthetic control.
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    12. 12
      Timmermans, J. Plastic crystals: A historical review. J. Phys. Chem. Solids 1961, 18, 1– 8,  DOI: 10.1016/0022-3697(61)90076-2
      12
      Plastic crystals: a historical review
      Timmermans, J.
      Physics and Chemistry of Solids (1961), 18 (), 1-8CODEN: PCSOA7; ISSN:0369-8726.
      Properties of plastic crystals are classified and reviewed.
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    13. 13
      Lunkenheimer, P.; Michl, M.; Loidl, A. Nonlinear Dielectric Response of Plastic Crystals. Nonlinear Dielectric Response of Plastic Crystals; Springer, 2018; pp 277– 300.
      There is no corresponding record for this reference.
    14. 14
      MacFarlane, D. R.; Forsyth, M. Plastic Crystal Electrolyte Materials: New Perspectives on Solid State Ion. Adv. Mater. 2001, 13, 957– 966,  DOI: 10.1002/1521-4095(200107)13:12/13<957::AID-ADMA957>3.0.CO;2-#
      14
      Plastic crystal electrolyte materials: new perspectives on solid state ionics
      MacFarlane, Douglas R.; Forsyth, Maria
      Advanced Materials (Weinheim, Germany) (2001), 13 (12-13), 957-966CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH)
      Plastic crystal materials have long been known but have only relatively recently become of interest as solid-state ion conductors. Their properties are often assocd. with dynamic orientational disorder or rotator motions in the cryst. lattice. This paper describes recent work in the field including the range of org. ionic compds. that exhibit ion conduction at room temp. Cond. in some cases is high enough to render the compds. of interest as electrolyte materials in all solid state electrochem. devices. Doping of the plastic crystal phase with a small ion such as Li+ in some cases produces an even higher cond. In this case, the plastic crystal acts as a solid state "solvent" for the doped ion and supports the conductive motion of the dopant via motions of the matrix ions. These doped materials are also described in detail.
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    15. 15
      Tsang, T.; Farrar, T. C. Nuclear Magnetic Relaxation Studies of Internal Rotations and Phase Transitions in Borohydrides of Lithium, Sodium, and Potassium. J. Chem. Phys. 1969, 50, 3498– 3502,  DOI: 10.1063/1.1671574
      15
      Nuclear magnetic relaxation studies of internal rotations and phase transitions in borohydrides of lithium, sodium, and potassium
      Tsang, Tung; Farrar, Thomas C.
      Journal of Chemical Physics (1969), 50 (8), 3498-502CODEN: JCPSA6; ISSN:0021-9606.
      Proton spin-lattice relaxation times, T1, have been measured as a function of temp. for KBH4, NaBH4, and LiBH4. For NaBH4 and KBH4, 23Na and 11B relaxation measurements were also made. In all cases, the magnetization recovery is approx. exponential. Correlation times, τc, derived from the T1 data were used to calc. activation energies, V, for BH4- ion reorientations. For the cubic phase of KBH4, V = 14.8 ± 0.4 kj./mole (3.55 ± 0.1 kcal./mole) (± always refers to root mean sq. error) from measurements on proton and 11B. For NaBH4, V was 11.2 ± 0.5 and 14.8 ± 0.7 kj./mole (2.7 ± 0.1 and 3.5 ± 0.2 kcal./mole) for the high-(cubic) and low-temp. (tetragonal) phases; and anomaly in τc was observed at temps. slightly below the phase transition, and may be interpreted as a relatively sudden change in V assocd. with the phase transition. In LiBH4, a rather broad min. was observed for the proton T1 vs. temp.; this has been interpreted as due to 2 inequiv. BH4- tetrahedra with activation energies of 20 ± 1 and 16 ± 1 kj./mole (4.7 ± 0.3 and 3.8 ± 0.3 kcal./ mole). The proton and 11B nuclei are relaxed by magnetic dipolar interactions, but quadrupolar fluctuations are the dominating relaxation mechanism for 23Na in the cubic phase of NaBH4.
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    16. 16
      Matsuo, M.; Nakamori, Y.; Orimo, S.-I.; Maekawa, H.; Takamura, H. Lithium superionic conduction in lithium borohydride accompanied by structural transition. Appl. Phys. Lett. 2007, 91, 224103,  DOI: 10.1063/1.2817934
      16
      Lithium superionic conduction in lithium borohydride accompanied by structural transition
      Matsuo, Motoaki; Nakamori, Yuko; Orimo, Shin-ichi; Maekawa, Hideki; Takamura, Hitoshi
      Applied Physics Letters (2007), 91 (22), 224103/1-224103/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      The elec. cond. of LiBH4 measured by a.c. complex impedance increased by 3 orders of magnitude due to structural transition from orthorhombic to hexagonal at ∼390 K. The hexagonal phase exhibited a high elec. cond. of about 10-3 S/cm. The cond. calcd. from the Nernst-Einstein equation using the correlation time obtained from 7Li NMR agreed with the measured elec. cond. The elec. cond. in the hexagonal phase is due to Li superionic conduction.
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    17. 17
      Hagemann, H.; Gomes, S.; Renaudin, G.; Yvon, K. Raman studies of reorientation motions of [BH4]− anions in alkali borohydrides. J. Alloys Compd. 2004, 363, 129– 132,  DOI: 10.1016/S0925-8388(03)00468-7
      There is no corresponding record for this reference.
    18. 18
      Nilsson, L.; Thomas, J. O.; Tofield, B. C. The structure of the high-temperature solid electrolyte lithium sulphate at 908 K. J. phys., C, Solid state phys. 1980, 13, 6441– 6451,  DOI: 10.1088/0022-3719/13/35/004
      18
      The structure of the high-temperature solid electrolyte lithium sulfate at 908 K
      Nilsson, Leif; Thomas, John O.; Tofield, Bruce C.
      Journal of Physics C: Solid State Physics (1980), 13 (35), 6441-51CODEN: JPSOAW; ISSN:0022-3719.
      The structure of the high-temp., plastic phase of Li2SO4 was detd. from neutron powder diffraction at 908 K. The structure is fcc., a = 7.07 Å, with the SO42- ion situated at the origin and the O atoms rotationally disordered about the S atom. The Li+ ions occupy the ± (1/4, 1/4, 1/4) positions. The large isotropic temp. factors [B(SO4) = 17.5 Å2 and B(Li) = 33 Å2] suggest that the Li+ ions occupy a statistical distribution of sites instantaneously displaced from ± (1/4, 1/4, 1/4), in short-range correlation with the instantaneous orientations of the surrounding SO42- ions. The ionic motion of Li2SO4, a fast ionic conductor, is enhanced by the rotational motion of the translationally static counter ions.
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    19. 19
      Aronsson, R.; Jansson, B.; Knape, H. E. G.; Lundén, A.; Nilsson, L.; Sjöblom, C.-A.; Torell, L. M. Fast ion conductors with rotating sulphate ions. J. Phys., Colloq. 1980, 41, C6-35– C6-37,  DOI: 10.1051/jphyscol:1980609
      There is no corresponding record for this reference.
    20. 20
      Boerjesson, L.; Torell, L. M. Reorientational motion in superionic sulfates: A Raman linewidth study. Phys. Rev. B 1985, 32, 2471– 2477,  DOI: 10.1103/PhysRevB.32.2471
      20
      Reorientational motion in superionic sulfates: a Raman linewidth study
      Boerjesson, L.; Torell, L. M.
      Physical Review B: Condensed Matter and Materials Physics (1985), 32 (4), 2471-7CODEN: PRBMDO; ISSN:0163-1829.
      Raman spectra of 2 superionic conducting crystals, fcc. Li2SO4 and bcc. LiAgSO4, were recorded at 300-1400 cm-1 across the entire temp. range of stability of each compd. Comparison of polarized and depolarized spectral bandwidths for the sym. A1 sulfate internal mode permits a component due to the sulfate-ion reorientation to be sepd., which confirms the plastic behavior of the superionic phases of the 2 crystals. For Li2SO4, the reorientation time derived corresponds well with the value 2 ps recently reported on the basis of computer-simulation studies. The measurements are precise enough to yield the temp. dependence of the reorientation time in each type of crystal. The Arrhenius activation energies are significantly different: 0.40 and 0.72 eV for fcc. Li2SO4 and bcc. LiAgSO4, resp. These values are sufficiently close to the contrasting activation energies for cation diffusion, 0.34 and 0.52 eV, resp., to support the paddle-wheel migration postulate for this type of plastic crystal.
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    21. 21
      Lundén, A. Enhancement of cation mobility in some sulphate phases due to a paddle-wheel mechanism. Solid State Ion. 1988, 28–30, 163– 167,  DOI: 10.1016/S0167-2738(88)80026-2
      There is no corresponding record for this reference.
    22. 22
      Jansen, M. Volume Effect or Paddle-Wheel Mechanism─Fast Alkali-Metal Ionic Conduction in Solids with Rotationally Disordered Complex Anions. Angew. Chem., Int. Ed. 1991, 30, 1547– 1558,  DOI: 10.1002/anie.199115471
      There is no corresponding record for this reference.
    23. 23
      Witschas, M.; Eckert, H.; Wilmer, D.; Banhatti, R.; Funke, H.; Fitter, J.; Lechner, R. E.; Korus, G.; Jansen, M. Anion Rotation and Cation Transport in the Rotor Phase α-Sodium Orthophosphate: Paddle-Wheel Mechanism Redefined in View of New Experimental Results. Z. Phys. Chem. 2000, 214, 643– 673,  DOI: 10.1524/zpch.2000.214.5.643
      23
      Anion rotation and cation transport in the rotor phase α-sodium orthophosphate: paddle-wheel mechanism redefined in view of new experimental results
      Witschas, M.; Eckert, H.; Wilmer, D.; Banhatti, R. D.; Funke, K.; Fitter, J.; Lechner, R. E.; Korus, G.; Jansen, M.
      Zeitschrift fuer Physikalische Chemie (Muenchen) (2000), 214 (5), 643-673CODEN: ZPCFAX; ISSN:0044-3336. (R. Oldenbourg Verlag)
      The high-temp. phase of sodium ortho-phosphate, α-Na3PO4, is characterized by a dynamic rotational disorder of its polyat. anions and, at the same time, by a considerable translational mobility of its cations. During the past decade, there has been considerable controversy about the question of whether both kinds of motion are dynamically coupled. To resolve this issue we have probed anionic and cationic motion individually over a wide range of exptl. time scales. Coherent quasielastic neutron scattering as well as temp.-dependent 17O NMR lineshape and relaxation spectroscopy serve to characterize the rotational motion of the anions, whereas the cation motion is probed by high-frequency cond. and 23Na NMR relaxation measurements. On the picosecond timescale, the combined interpretation of the neutron scattering and elec. cond. data suggests strong dynamic coupling between the rotation of the phosphate groups about one of the four threefold P-O axes and the spatial fluctuations of nearby sodium ions. On more extended time scales, the NMR data indicate an addnl., slower process, corresponding to dynamic jump reorientations of the C3 axis of rotation. This process appears to be coupled to the translational Na+ transport dynamics as suggested by a strong correspondence between the 17O and 23Na NMR relaxation characteristics and the elec. conductivities in the dc plateau region. The Na+ transport process can be viewed as highly correlated, not unlike the chain mechanism obsd. in AgBr.
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    24. 24
      Kniaź, K.; Fischer, J. E.; Zhu, Q.; Rosseinsky, M. J.; Zhou, O.; Murphy, D. W. C60 orientational ordering in superconducting Na2RbC60. Solid State Commun. 1993, 88, 47– 50,  DOI: 10.1016/0038-1098(93)90767-H
      24
      Fullerene (C60) orientational ordering in superconducting sodium rubidium fulleride (Na2RbC60)
      Kniaz, Krzysztof; Fischer, John E.; Zhu, Qing; Rosseinsky, Matthew J.; Zhou, Otto; Murphy, Donald W.
      Solid State Communications (1993), 88 (1), 47-50CODEN: SSCOA4; ISSN:0038-1098.
      The C60 mols. in Na2RbC60 are orientationally ordered in a manner essentially the same as in pure C60. Fits to data at both 300 K and 27 K are significantly better in space group Pa‾3 (simple cubic) than in Fm‾3m (merohedral disorder) or by assuming uniform spherical shells of charge (complete disorder). The anomalously low Tc of this compd. cannot be attributed to excess orientational disorder, and therefore remains a mystery.
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    25. 25
      Tanigaki, K.; Hirosawa, I.; Manako, T.; Tsai, J. S.; Mizuki, J.; Ebbesen, T. W. Phase transitions in Na2AC60 (A = Cs, Rb, and K) fullerides. Phys. Rev. B 1994, 49, 12307– 12310,  DOI: 10.1103/PhysRevB.49.12307
      25
      Phase transition in Na2AC60 (A = Cs, Rb, and K) fullerides
      Tanigaki, K.; Hirosawa, I.; Manako, T.; Tsai, J. S.; Mizuki, J.; Ebbesen, T. W.
      Physical Review B: Condensed Matter and Materials Physics (1994), 49 (17), 12307-10CODEN: PRBMDO; ISSN:0163-1829.
      The ternary system fullerides Na2AC60 (A = Cs, Rb, and K) were studied by differential scanning calorimetry at 100-450 K. All show reproducible phase transitions at the transition temps. of 299 K (ΔH = 2.5 ± 0.5 J/g) for Na2CsCo60, 313 K (ΔH = 2.7 ± 0.5 J/g) for Na2RbC60, and 305 K (ΔH = 3.1 ± 0.5 J/g) for Na2KC60. Orientational ordering of the fullerene unit is responsible for the obsd. phase transitions (Tsc-fcc.) from a high-temp. fcc. to a low-temp. simple-cubic (s.c.) phase. The obsd. Tsc-fcc. and enthalpy can be compared to those for pristine C60 which has Tsc-fcc. = 256.5 K (ΔH = 8 ± 0.5 J/g). The obsd. behavior is discussed in terms of the balance between the C603--C603- intermol. interaction and the C603--A+ Coulombic interaction as a function of lattice parameter.
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    26. 26
      Saito, T.; Maniwa, Y.; Oda, H.; Kume, K.; Kosaka, M.; Hirosawa, I.; Tanigaki, K. NMR Studies on Orientational Ordering Phase Transition in Na2CsC60. J. Phys. Soc. Jpn. 1995, 64, 4513– 4517,  DOI: 10.1143/JPSJ.64.4513
      26
      NMR studies on orientational ordering phase transition in Na2CsC60
      Saito, Takahito; Maniwa, Yutaka; Oda, Hitoshi; Kume, Kiyoshi; Kosaka, Mayumi; Hirosawa, Ichiro; Tanigaki, Katsumi
      Journal of the Physical Society of Japan (1995), 64 (12), 4513-17CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
      Na-contg. alkali metal fulleride, Na2CsC60, was studied by 13C and 23Na NMR below and above the fcc. to simple cubic (s.c.) phase transition temp., Tm. The C60 mols. rotate faster than the rotational correlation time of 1.6 × 10-5 sec at ⪆140 K and 2.4 × 10-9 sec around 300 K. Using 23Na NMR spectra broadened by the 2nd-order quadrupole interaction, the elec. field gradient at Na sites, e2qQ/h, is 940 ± 20 kHz and <0.1 kHz below and above Tm, resp. Apparently the Na atoms in the s.c. phase have a covalent character with C60 mols. Probably Na2CsC60 is the 1st metallic plastic crystal.
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    27. 27
      Skripov, A. V.; Babanova, O. A.; Soloninin, A. V.; Stavila, V.; Verdal, N.; Udovic, T. J.; Rush, J. J. Nuclear Magnetic Resonance Study of Atomic Motion in A2B12H12 (A = Na, K, Rb, Cs): Anion Reorientations and Na+ Mobility. J. Phys. Chem. C 2013, 117, 25961– 25968,  DOI: 10.1021/jp4106585
      27
      Nuclear Magnetic Resonance Study of Atomic Motion in A2B12H12 (A = Na, K, Rb, Cs): Anion Reorientations and Na+ Mobility
      Skripov, Alexander V.; Babanova, Olga A.; Soloninin, Alexei V.; Stavila, Vitalie; Verdal, Nina; Udovic, Terrence J.; Rush, John J.
      Journal of Physical Chemistry C (2013), 117 (49), 25961-25968CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      To study the reorientational motion of icosahedral [B12H12]2- anions in A2B12H12 (A = Na, K, Rb, Cs) and the translational diffusion of Na+ cations in Na2B12H12, the authors have measured the 1H, 11B, and 23Na NMR spectra and spin-lattice relaxation rates in these compds. at 170-580 K. For cubic compds. K2B12H12, Rb2B12H12, and Cs2B12H12, the measured 1H and 11B spin-lattice relaxation rates are governed by thermally activated reorientations of the [B12H12]2- anions. The activation energy of this reorientational motion decreases with increasing cation radius, changing from 800 meV for K2B12H12 to 549 meV for Rb2B12H12 and 427 meV for Cs2B12H12. For Na2B12H12, the 1st-order transition from the low-temp. monoclinic to the high-temp. cubic phase near 520 K is accompanied by a 2 orders of magnitude increase in the reorientational jump rate, and the corresponding activation energy changes from 770 meV for the low-T phase to 270 meV for the high-T phase. Measurements of the 23Na NMR spectra and spin-lattice relaxation rates show that the transition from the low-T to the high-T phase of Na2B12H12 is also accompanied by the onset of the fast translational diffusion of Na+ ions. Just above the transition point, the lower limit of the Na+ jump rate estd. from the 23Na spin-lattice relaxation data is 2 × 108 s-1, and the corresponding activation energy for Na+ diffusion is ∼410 meV.
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    28. 28
      Udovic, T. J.; Matsuo, M.; Unemoto, A.; Verdal, N.; Stavila, V.; Skripov, A. V.; Rush, J. J.; Takamura, H.; Orimo, S.-i. Sodium superionic conduction in Na2B12H12. Chem. Commun. 2014, 50, 3750– 3752,  DOI: 10.1039/C3CC49805K
      28
      Sodium superionic conduction in Na2B12H12
      Udovic, Terrence J.; Matsuo, Motoaki; Unemoto, Atsushi; Verdal, Nina; Stavila, Vitalie; Skripov, Alexander V.; Rush, John J.; Takamura, Hitoshi; Orimo, Shin-ichi
      Chemical Communications (Cambridge, United Kingdom) (2014), 50 (28), 3750-3752CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
      Impedance measurements indicate that Na2B12H12 exhibits dramatic Na+ cond. (∼0.1 S cm-1) above its order-disorder phase-transition at ≈529 K, rivaling that of current, solid-state, ceramic-based, Na-battery electrolytes. Superionicity may be aided by the large size, quasispherical shape, and high rotational mobility of the B12H122- anions.
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    29. 29
      Kweon, K. E.; Varley, J. B.; Shea, P.; Adelstein, N.; Mehta, P.; Heo, T. W.; Udovic, T. J.; Stavila, V.; Wood, B. C. Structural, Chemical, and Dynamical Frustration: Origins of Superionic Conductivity in closo-Borate Solid Electrolytes. Chem. Mater. 2017, 29, 9142– 9153,  DOI: 10.1021/acs.chemmater.7b02902
      29
      Structural, Chemical, and Dynamical Frustration: Origins of Superionic Conductivity in closo-Borate Solid Electrolytes
      Kweon, Kyoung E.; Varley, Joel B.; Shea, Patrick; Adelstein, Nicole; Mehta, Prateek; Heo, Tae Wook; Udovic, Terrence J.; Stavila, Vitalie; Wood, Brandon C.
      Chemistry of Materials (2017), 29 (21), 9142-9153CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Li2B12H12, Na2B12H12, and their closo-borate relatives exhibit unusually high ionic cond., making them attractive as a new class of candidate electrolytes in solid-state Li- and Na-ion batteries. However, further optimization of these materials requires a deeper understanding of the fundamental mechanisms underlying ultrafast ion conduction. To this end, we use ab initio mol. dynamics simulations and d.-functional calcns. to explore the motivations for cation diffusion. We find that superionic behavior in Li2B12H12 and Na2B12H12 results from a combination of key structural, chem., and dynamical factors that introduce intrinsic frustration and disorder. A statistical metric is used to show that the structures exhibit a high d. of accessible interstitial sites and site types, which correlates with the flatness of the energy landscape and the obsd. cation mobility. Furthermore, cations are found to dock to specific anion sites, leading to a competition between the geometric symmetry of the anion and the symmetry of the lattice itself, which can facilitate cation hopping. Finally, facile anion reorientations and other low-frequency thermal vibrations lead to fluctuations in the local potential that enhance cation mobility by creating a local driving force for hopping. We discuss the relevance of each factor for developing new ionic cond. descriptors that can be used for discovery and optimization of closo-borate solid electrolytes, as well as superionic conductors more generally.
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    30. 30
      Udovic, T. J.; Matsuo, M.; Tang, W. S.; Wu, H.; Stavila, V.; Soloninin, A. V.; Skoryunov, R. V.; Babanova, O. A.; Skripov, A. V.; Rush, J. J.; Unemoto, A.; Takamura, H.; Orimo, S.-I. Exceptional Superionic Conductivity in Disordered Sodium Decahydro-closo-decaborate. Adv. Mater. 2014, 26, 7622– 7626,  DOI: 10.1002/adma.201403157
      30
      Exceptional Superionic Conductivity in Disordered Sodium Decahydro-closo-decaborate
      Udovic, Terrence J.; Matsuo, Motoaki; Tang, Wan Si; Wu, Hui; Stavila, Vitalie; Soloninin, Alexei V.; Skoryunov, Roman V.; Babanova, Olga A.; Skripov, Alexander V.; Rush, John J.; Unemoto, Atsushi; Takamura, Hitoshi; Orimo, Shin-ichi
      Advanced Materials (Weinheim, Germany) (2014), 26 (45), 7622-7626CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Sodium decahydro-closo-decaborate forms a disordered, fcc. phase above about 360 K, possessing a vacancy-rich Na+ cation sublattice. This cation sublattice is highly mobile within the spacious corridors formed by the large B10H102- anions and exhibits remarkable superionic cond. (e.g., σ = 0.01 Scm-1 at 383 K) to substantially lower temps. than for Na2B12H12. This cond. is more than an order of magnitude higher than that of all other solid-state Na-based complex-hydride materials investigated to date in this temp. region. This discovery represents a major advancement in the field of solid-state Na+ fast-ion conduction at technol. relevant device temps.
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    31. 31
      Tang, W. S.; Unemoto, A.; Zhou, W.; Stavila, V.; Matsuo, M.; Wu, H.; Orimo, S.-i.; Udovic, T. J. Unparalleled lithium and sodium superionic conduction in solid electrolytes with large monovalent cage-like anions. Energy Environ. Sci. 2015, 8, 3637– 3645,  DOI: 10.1039/C5EE02941D
      31
      Unparalleled lithium and sodium superionic conduction in solid electrolytes with large monovalent cage-like anions
      Tang, Wan Si; Unemoto, Atsushi; Zhou, Wei; Stavila, Vitalie; Matsuo, Motoaki; Wu, Hui; Orimo, Shin-ichi; Udovic, Terrence J.
      Energy & Environmental Science (2015), 8 (12), 3637-3645CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      Solid electrolytes with sufficiently high conductivities and stabilities are the elusive answer to the inherent shortcomings of org. liq. electrolytes prevalent in today's rechargeable batteries. We recently revealed a novel fast-ion-conducting sodium salt, Na2B12H12, which contains large, icosahedral, divalent B12H122- anions that enable impressive superionic cond., albeit only above its 529 K phase transition. Its lithium congener, Li2B12H12, possesses an even more technol. prohibitive transition temp. above 600 K. Here we show that the chem. related LiCB11H12 and NaCB11H12 salts, which contain icosahedral, monovalent CB11H12- anions, both exhibit much lower transition temps. near 400 K and 380 K, resp., and truly stellar ionic conductivities (>0.1 S cm-1) unmatched by any other known polycryst. materials at these temps. With proper modifications, we are confident that room-temp.-stabilized superionic salts incorporating such large polyhedral anion building blocks are attainable, thus enhancing their future prospects as practical electrolyte materials in next-generation, all-solid-state batteries.
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    32. 32
      Dimitrievska, M.; Stavila, V.; Soloninin, A. V.; Skoryunov, R. V.; Babanova, O. A.; Wu, H.; Zhou, W.; Tang, W. S.; Faraone, A.; Tarver, J. D.; Trump, B. A.; Skripov, A. V.; Udovic, T. J. Nature of Decahydro-closo-decaborate Anion Reorientations in an Ordered Alkali-Metal Salt: Rb2B10H10. J. Phys. Chem. C 2018, 122, 15198– 15207,  DOI: 10.1021/acs.jpcc.8b04385
      32
      Nature of Decahydro-closo-decaborate Anion Reorientations in an Ordered Alkali-Metal Salt: Rb2B10H10
      Dimitrievska, Mirjana; Stavila, Vitalie; Soloninin, Alexei V.; Skoryunov, Roman V.; Babanova, Olga A.; Wu, Hui; Zhou, Wei; Tang, Wan Si; Faraone, Antonio; Tarver, Jacob D.; Trump, Benjamin A.; Skripov, Alexander V.; Udovic, Terrence J.
      Journal of Physical Chemistry C (2018), 122 (27), 15198-15207CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The ordered monoclinic phase of the alkali metal decahydro-closo-decaborate salt Rb2B10H10 is stable from ∼250 K all the way up to an order-disorder phase transition temp. of ≈762 K. The broad temp. range for this phase allowed for a detailed quasielastic neutron scattering (QENS) and NMR study of the protypical B10H102- anion reorientational dynamics. The QENS and NMR combined results are consistent with an anion reorientational mechanism comprised of 2 types of rotational jumps expected from the anion geometry and lattice structure, namely, more rapid 90° jumps around the anion C4 symmetry axis (e.g., with correlation frequencies of ≈2.6 × 1010 s-1 at 530 K) combined with order of magnitude slower orthogonal 180° reorientational flips (e.g., ≈3.1 × 109 s-1 at 530 K) resulting in an exchange of the apical H (and apical B) positions. Each latter flip requires a concomitant 45° twist around the C4 symmetry axis to preserve the ordered Rb2B10H10 monoclinic structural symmetry. This result is consistent with previous NMR data for ordered monoclinic Na2B10H10, which also pointed to 2 types of anion reorientational motions. The QENS-derived reorientational activation energies are 197(2) and 288(3) meV for the C4 4-fold jumps and apical exchanges, resp., between 400 and 680 K. Below this temp. range, NMR (and QENS) both indicate a shift to significantly larger reorientational barriers, for example, 485(8) meV for the apical exchanges. Subambient diffraction measurements identify a subtle change in the Rb2B10H10 structure from monoclinic to triclinic symmetry as the temp. is decreased from around 250 to 210 K.
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    33. 33
      Famprikis, T.; Dawson, J. A.; Fauth, F.; Clemens, O.; Suard, E.; Fleutot, B.; Courty, M.; Chotard, J.-N.; Islam, M. S.; Masquelier, C. A New Superionic Plastic Polymorph of the Na+ Conductor Na3PS4. ACS Materials Letters 2019, 1, 641– 646,  DOI: 10.1021/acsmaterialslett.9b00322
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      A New Superionic Plastic Polymorph of the Na+ Conductor Na3PS4
      Famprikis, Theodosios; Dawson, James A.; Fauth, Francois; Clemens, Oliver; Suard, Emmanuelle; Fleutot, Benoit; Courty, Matthieu; Chotard, Jean-Noel; Islam, M. Saiful; Masquelier, Christian
      ACS Materials Letters (2019), 1 (6), 641-646CODEN: AMLCEF; ISSN:2639-4979. (American Chemical Society)
      Na3PS4 is one of the most promising Na+ conductors, relevant for applications that can leverage its high ionic cond., such as solid-state batteries. At present, 2 cryst. phases of the material have been identified and it had been thought to melt >500°. In contrast, we show that it remains solid above this temp. and transforms into a 3rd polymorph, γ, exhibiting fast-ion conduction and an orthorhombic crystal structure based on diffraction, ab initio simulations, impedance spectroscopy and thermal anal. We show that the fast Na+-conduction is assocd. with rotational motion of the thiophosphate polyanions pointing to a plastic crystal. These findings are of major importance for the development and understanding of new polyanion based solid electrolytes.
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    34. 34
      Saha, S.; Rousse, G.; Courty, M.; Shakhova, Y.; Kirsanova, M.; Fauth, F.; Pomjakushin, V.; Abakumov, A. M.; Tarascon, J. M. Structural Polymorphism in Na4Zn(PO4)2 Driven by Rotational Order–Disorder Transitions and the Impact of Heterovalent Substitutions on Na-Ion Conductivity. Inorg. Chem. 2020, 59, 6528– 6540,  DOI: 10.1021/acs.inorgchem.0c00612
      34
      Structural Polymorphism in Na4Zn(PO4)2 Driven by Rotational Order-Disorder Transitions and the Impact of Heterovalent Substitutions on Na-Ion Conductivity
      Saha, Sujoy; Rousse, Gwenaelle; Courty, Matthieu; Shakhova, Yaroslava; Kirsanova, Maria; Fauth, Francois; Pomjakushin, Vladimir; Abakumov, Artem M.; Tarascon, J. M.
      Inorganic Chemistry (2020), 59 (9), 6528-6540CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)
      Solid electrolytes have regained tremendous interest recently in light of the exposed vulnerability of current rechargeable battery technologies. While designing solid electrolytes, most efforts concd. on creating structural disorder (vacancies, interstitials, etc.) in a cationic Li/Na sublattice to increase ionic cond. In phosphates, the ionic cond. can also be increased by rotational disorder in the anionic sublattice, via a paddle-wheel mechanism. Herein, we report on Na4Zn(PO4)2 which is designed from Na3PO4, replacing Na+ with Zn2+ and introducing a vacancy for charge balance. We show that Na4Zn(PO4)2 undergoes a series of structural transitions under temp., which are assocd. with an increase in ionic cond. by several orders of magnitude. Our detailed crystallog. study, combining electron, neutron, and X-ray powder diffraction, reveals that the room-temp. form, α-Na4Zn(PO4)2, contains orientationally ordered PO4 groups, which undergo partial and full rotational disorder in the high-temp. β- and γ-polymorphs, resp. We furthermore showed that the highly conducting γ-polymorph could be stabilized at room temp. by ball-milling, whereas the β-polymorph can be stabilized by partial substitution of Zn2+ with Ga3+ and Al3+. These findings emphasize the role of rotational disorder as an extra parameter to design new solid electrolytes. Temp.-driven structural transitions in Na4Zn(PO4)2, involving rotational disorder of PO4 groups, are responsible for increasing Na-cond. in the high-temp. phases, which are stabilized at room temp. by ball-milling and chem. substitutions.
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    35. 35
      Geirhos, K.; Lunkenheimer, P.; Michl, M.; Reuter, D.; Loidl, A. Communication: Conductivity enhancement in plastic-crystalline solid-state electrolytes. J. Chem. Phys. 2015, 143, 081101,  DOI: 10.1063/1.4929554
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      Communication: Conductivity enhancement in plastic-crystalline solid-state electrolytes
      Geirhos, K.; Lunkenheimer, P.; Michl, M.; Reuter, D.; Loidl, A.
      Journal of Chemical Physics (2015), 143 (8), 081101/1-081101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Finding new ionic conductors that enable significant advancements in the development of energy-storage devices is a challenging goal of current material science. Aside of material classes as ionic liqs. or amorphous ion conductors, the so-called plastic crystals (PCs) are good candidates combining high cond. and favorable mech. properties. PCs are formed by mols. whose orientational degrees of freedom still fluctuate despite the material exhibits a well-defined cryst. lattice. The cond. of Li+ ions in succinonitrile, the most prominent mol. PC electrolyte, can be enhanced by several decades when replacing part of the mols. in the cryst. lattice by larger ones. Dielec. spectroscopy reveals that this is accompanied by a stronger coupling of ionic and reorientational motions. These findings, which can be understood in terms of an optimized revolving door mechanism, open a new path towards the development of better solid-state electrolytes. (c) 2015 American Institute of Physics.
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    36. 36
      Vaalma, C.; Buchholz, D.; Weil, M.; Passerini, S. A cost and resource analysis of sodium-ion batteries. Nat. Rev. Mater. 2018, 3, 18013,  DOI: 10.1038/natrevmats.2018.13
      There is no corresponding record for this reference.
    37. 37
      Haynes, W. CRC Handbook of Chemistry and Physics, 97th ed.; CRC Press, 2016; pp 14– 17.
      There is no corresponding record for this reference.
    38. 38
      Meilander, B. E.; Nilsson, L. Thermal Expansion of Lithium Sulphate. Z. Naturforsch A 1983, 38, 1396– 1399,  DOI: 10.1515/zna-1983-1218
      There is no corresponding record for this reference.
    39. 39
      Egami, T.; Billinge, S. J. L. Underneath the Bragg peaks: Structural analysis of complex materials, 2nd ed.; Elsevier: Amsterdam, 2012.
      There is no corresponding record for this reference.
    40. 40
      Terban, M. W.; Billinge, S. J. L. Structural analysis of molecular materials using the pair distribution function. Chem. Rev. 2022, 122, 1208– 1272,  DOI: 10.1021/acs.chemrev.1c00237
      40
      Structural Analysis of Molecular Materials Using the Pair Distribution Function
      Terban, Maxwell W.; Billinge, Simon J. L.
      Chemical Reviews (Washington, DC, United States) (2022), 122 (1), 1208-1272CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. This is a review of at. pair distribution function (PDF) anal. as applied to the study of mol. materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorg. crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to mol. materials such as carbons, pharmaceuticals, polymers, liqs., coordination compds., composites, and more. Here, an overview of applications toward a wide variety of mol. compds. (org. and inorg.) and systems with mol. components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material prepn., high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful ref. to practitioners for PDF applications in a wide realm of mol. sciences, and help new practitioners to get started with this technique.
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    41. 41
      Prill, D.; Juhás, P.; Schmidt, M. U.; Billinge, S. J. L. Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs. J. Appl. Crystallogr. 2015, 48, 171– 178,  DOI: 10.1107/S1600576714026454
      41
      Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs
      Prill, Dragica; Juhas, Pavol; Schmidt, Martin U.; Billinge, Simon J. L.
      Journal of Applied Crystallography (2015), 48 (1), 171-178CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)
      The methods currently used to calc. at. pair distribution functions (PDFs) from org. structural models do not distinguish between the intramol. and intermol. distances. Owing to the stiff bonding between atoms within a mol., the PDF peaks arising from intramol. atom-atom distances are much sharper than those of the intermol. atom-atom distances. This work introduces a simple approach to calc. PDFs of mol. systems without building a supercell model by using two different isotropic displacement parameters to describe at. motion: one parameter is used for the intramol., the other one for intermol. atom-atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calcns. were done with the DiffPy-CMI complex modeling infrastructure. The new modeling approach produced remarkably better fits to the exptl. PDFs, confirming the higher accuracy of this method for org. materials.
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    42. 42
      Terban, M. W.; Russo, L.; Pham, T. N.; Barich, D. H.; Sun, Y. T.; Burke, M. D.; Brum, J.; Billinge, S. J. L. Local structural effects due to micronization and amorphization on an HIV treatment active pharmaceutical ingredient. Mol. Pharmaceutics 2020, 17, 2370– 2389,  DOI: 10.1021/acs.molpharmaceut.0c00122
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      Local Structural Effects Due to Micronization and Amorphization on an HIV Treatment Active Pharmaceutical Ingredient
      Terban, Maxwell W.; Russo, Luca; Pham, Tran N.; Barich, Dewey H.; Sun, Yan T.; Burke, Matthew D.; Brum, Jeffrey; Billinge, Simon J. L.
      Molecular Pharmaceutics (2020), 17 (7), 2370-2389CODEN: MPOHBP; ISSN:1543-8384. (American Chemical Society)
      Processing procedures for inducing domain size redn. and/or amorphous phase generation can be crucial for enhancing the bioavailability of active pharmaceutical ingredients (APIs). It is important to quantify these reduced coherence phases and to detect and characterize assocd. structural changes, to ensure that no deleterious effects on safety, function, or stability occur. Here, X-ray powder diffraction (XRPD), total scattering pair distribution function (TSPDF) anal., and solid-state NMR spectroscopy (SSNMR) have been performed on samples of GSK2838232B, an investigational drug for the treatment of human immunodeficiency virus (HIV). Prepns. were obtained through different mech. treatments resulting in varying extents of domain size redn. and amorphous phase generation. Completely amorphous formulations could be prepd. by milling and microfluidic injection processes. Microfluidic injection was shown to result in a different local structure due to dispersion with dichloromethane. Implications of combined TSPDF and SSNMR studies to characterize mol. compds. are also discussed, in particular, the possibility to obtain a thorough structural understanding of disordered samples from different processes.
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    43. 43
      Adams, S.; Rao, R. P. High power lithium ion battery materials by computational design. Phys. Status Solidi A 2011, 208, 1746– 1753,  DOI: 10.1002/pssa.201001116
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      High power lithium ion battery materials by computational design
      Adams, Stefan; Rao, R. Prasada
      Physica Status Solidi A: Applications and Materials Science (2011), 208 (8), 1746-1753CODEN: PSSABA; ISSN:1862-6300. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Empirical bond length-bond valence (BV) relations provide insight into the link between structure of and ion transport in solid electrolytes and mixed conductors. Building on our earlier systematic adjustment of BV parameters to the bond softness, here we discuss how the squared BV mismatch is linked to the abs. energy scale and used as a general Morse-type interaction potential for analyzing low-energy ion migration paths in ion conducting solids or mixed conductors by either an energy landscape approach or mol. dynamics (MD) simulations. For a wide range of lithium oxides we could thus model ion transport revealing significant differences to an earlier geometric approach. This novel BV-based force-field has then been applied to investigate a range of mixed conductors, focusing on cathode materials for lithium ion battery (LIB) applications to promote a systematic design of LIB cathodes that combine high energy d. with high power d. To demonstrate the versatility of the new BV-based force field it is applied in exploring various strategies to enhance the power performance of safe low cost LIB materials including LiFePO4, LiVPO4F, LiFeSO4F, etc.
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    44. 44
      Chen, H.; Wong, L. L.; Adams, S. SoftBV – a software tool for screening the materials genome of inorganic fast ion conductors. Acta Cryst. B 2019, 75, 18– 33,  DOI: 10.1107/S2052520618015718
      44
      SoftBV - a software tool for screening the materials genome of inorganic fast ion conductors
      Chen, Haomin; Wong, Lee Loong; Adams, Stefan
      Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2019), 75 (1), 18-33CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
      The identification of materials for advanced energy-storage systems is still mostly based on exptl. trial and error. Increasingly, computational tools are sought to accelerate materials discovery by computational predictions. Here are introduced a set of computationally inexpensive software tools that exploit the bond-valence-based empirical force field previously developed by the authors to enable high-throughput computational screening of exptl. or simulated crystal-structure models of battery materials predicting a variety of properties of technol. relevance, including a structure plausibility check, surface energies, an inventory of equil. and interstitial sites, the topol. of ion-migration paths in between those sites, the resp. migration barriers and the site-specific attempt frequencies. All of these can be predicted from CIF files of structure models at a minute fraction of the computational cost of d. functional theory (DFT) simulations, and with the added advantage that all the relevant pathway segments are analyzed instead of arbitrarily predetd. paths. The capabilities and limitations of the approach are evaluated for a wide range of ion-conducting solids. An integrated simple kinetic Monte Carlo simulation provides rough (but less reliable) predictions of the abs. cond. at a given temp. The automated adaptation of the force field to the compn. and charge distribution in the simulated material allows for a high transferability of the force field within a wide range of Lewis acid-Lewis base-type ionic inorg. compds. as necessary for high-throughput screening. While the transferability and precision will not reach the same levels as in DFT simulations, the fact that the computational cost is several orders of magnitude lower allows the application of the approach not only to pre-screen databases of simple structure prototypes but also to structure models of complex disordered or amorphous phases, and provides a path to expand the anal. to charge transfer across interfaces that would be difficult to cover by ab initio methods.
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    45. 45
      Petříček, V.; Dušek, M.; Palatinus, L. Crystallographic Computing System JANA2006: General features. Z. Kristallogr. 2014, 229, 345– 352,  DOI: 10.1515/zkri-2014-1737
      45
      Crystallographic Computing System JANA2006: General features
      Petricek, Vaclav; Dusek, Michal; Palatinus, Lukas
      Zeitschrift fuer Kristallographie - Crystalline Materials (2014), 229 (5), 345-352CODEN: ZKCMAJ; ISSN:2194-4946. (Oldenbourg Wissenschaftsverlag GmbH)
      JANA2006 is a freely available program for structure detn. of std., modulated and magnetic samples based on X-ray or neutron single crystal/ powder diffraction or on electron diffraction. The system has been developed for 30 years from specialized tool for refinement of modulated structures to a universal program covering std. as well as advanced crystallog. The aim of this article is to describe the basic features of JANA2006 and explain its scope and philosophy. It will also serve as a basis for future publications detailing tools and methods of JANA.
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    46. 46
      Chupas, P. J.; Qiu, X.; Hanson, J. C.; Lee, P. L.; Grey, C. P.; Billinge, S. J. L. Rapid acquisition pair distribution function analysis (RA-PDF). J. Appl. Crys. 2003, 36, 1342– 1347,  DOI: 10.1107/S0021889803017564
      46
      Rapid-acquisition pair distribution function (RA-PDF) analysis
      Chupas, Peter J.; Qiu, Xiangyun; Hanson, Jonathan C.; Lee, Peter L.; Grey, Clare P.; Billinge, Simon J. L.
      Journal of Applied Crystallography (2003), 36 (6), 1342-1347CODEN: JACGAR; ISSN:0021-8898. (Blackwell Publishing Ltd.)
      An image-plate (IP) detector coupled with high-energy synchrotron radiation was used for at. pair distribution function (PDF) anal., with high probed momentum transfer Qmax ≤ 28.5 Å-1, from cryst. materials. Materials with different structural complexities were measured to test the validity of the quant. data anal. Exptl. results are presented for cryst. Ni, cryst. α-AlF3, and the layered Aurivillius type oxides α-Bi4V2O11 and γ-Bi4V1.7Ti0.3O10.85. Overall, the diffraction patterns show good counting statistics, with measuring time from one to tens of seconds. The PDFs obtained are of high quality. Structures may be refined from these PDFs, and the structural models are consistent with the published literature. Data sets from similar samples are highly reproducible.
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    47. 47
      Kieffer, J.; Ashiotis, G.; Deschildre, A.; Nawaz, Z.; Wright, J. P.; Karkoulis, D.; Picca, F. E. The fast azimuthal integration Python library: pyFAI. J. Appl. Crys. 2015, 48, 510– 519,  DOI: 10.1107/S1600576715004306
      There is no corresponding record for this reference.
    48. 48
      Juhás, P.; Davis, T.; Farrow, C. L.; Billinge, S. J. L. PDFgetX3: A rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions. J. Appl. Crys. 2013, 46, 560– 566,  DOI: 10.1107/S0021889813005190
      48
      PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions
      Juhas, P.; Davis, T.; Farrow, C. L.; Billinge, S. J. L.
      Journal of Applied Crystallography (2013), 46 (2), 560-566CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
      PDFgetX3 is a new software application for converting x-ray powder diffraction data to an at. pair distribution function (PDF). PDFgetX3 was designed for ease of use, speed and automated operation. The software can readily process hundreds of x-ray patterns within a few seconds and is thus useful for high-throughput PDF studies that measure numerous data sets as a function of time, temp. or other environmental parameters. In comparison to the preceding programs, PDFgetX3 requires fewer inputs and less user experience and it can be readily adopted by novice users. The live-plotting interactive feature allows the user to assess the effects of calcn. parameters and select their optimum values. PDFgetX3 uses an ad hoc data correction method, where the slowly changing structure-independent signal is filtered out to obtain coherent x-ray intensities that contain structure information. The output from PDFgetX3 was verified by processing exptl. PDFs from inorg., org. and nanosized samples and comparing them with their counterparts from a previous established software. In spite of the different algorithm, the obtained PDFs were nearly identical and yielded highly similar results when used in structure refinement. PDFgetX3 is written in the Python language and features a well documented reusable code base. The software can be used either as a standalone application or as a library of PDF processing functions that can be called from other Python scripts. The software is free for open academic research but requires paid license for com. use.
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    49. 49
      Yang, X.; Juhás, P.; Farrow, C.; Billinge, S. J. L. xPDFsuite: an end-to-end software solution for high throughput pair distribution function transformation, visualization and analysis. arXiv Preprint (Condensed Matter, Materials Science) , February 13, 2015. arXiv:1402.3163. https://arxiv.org/abs/1402.3163
      There is no corresponding record for this reference.
    50. 50
      Coelho, A. A.; Chater, P. A.; Kern, A. Fast synthesis and refinement of the atomic pair distribution function. J. Appl. Crys. 2015, 48, 869– 875,  DOI: 10.1107/S1600576715007487
      There is no corresponding record for this reference.
    51. 51
      Coelho, A. A. TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. J. Appl. Crystallogr. 2018, 51, 210– 218,  DOI: 10.1107/S1600576718000183
      51
      TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++
      Coelho, Alan A.
      Journal of Applied Crystallography (2018), 51 (1), 210-218CODEN: JACGAR; ISSN:1600-5767. (International Union of Crystallography)
      TOPAS and its academic variant TOPAS-Academic are nonlinear least-squares optimization programs written in the C++ programming language. This paper describes their functionality and architecture. The latter is of benefit to developers seeking to reduce development time. TOPAS allows linear and nonlinear constraints through the use of computer algebra, with parameter dependencies, required for parameter derivs., automatically detd. In addn., the objective function can include restraints and penalties, which again are defined using computer algebra. Of importance is a conjugate gradient soln. routine with bounding constraints which guide refinements to convergence. Much of the functionality of TOPAS is achieved through the use of generic functionality; for example, flexible peak-shape generation allows neutron time-of-flight (TOF) peak shapes to be described using generic functions. The kernel of TOPAS can be run from the command line for batch mode operation or from a closely integrated graphical user interface. The functionality of TOPAS includes peak fitting, Pawley and Le Bail refinement, Rietveld refinement, single-crystal refinement, pair distribution function refinement, magnetic structures, const. wavelength neutron refinement, TOF refinement, stacking-fault anal., Laue refinement, indexing, charge flipping, and structure soln. through simulated annealing.
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    52. 52
      Rietveld, H. M. A. Profile Refinement Method for Nuclear and Magnetic Structures. J. Appl. Crystallogr. 1969, 2, 65– 71,  DOI: 10.1107/S0021889869006558
      52
      Profile refinement method for nuclear and magnetic structures
      Rietveld, H. M.
      Journal of Applied Crystallography (1969), 2 (Pt. 2), 65-71CODEN: JACGAR; ISSN:0021-8898.
      A structural refinement method for neutron diffraction is presented which makes direct use of the profile intensities obtained from the powder diagram. It is applicable to nuclear structures and to magnetic structures which can be described on the nuclear unit cell or a multiple thereof. Equations for the measured profiles to be used in the least sqs. treatment are cor. for asymmetry and preferred orientation; the angular dependence of the half widths of the peaks is given by the formula of Caglioti, et al. (1958). The magnetic contribution to the profile equation is expressed by calcg. only one av. cross section for each set of equiv. reflections. It is possible to introduce constraint functions, linear or quadratic, between parameters used in the least sqs. treatment. Results of the use of this method are given for a series of compds. In all instances it has proved superior to any other method involving integrated neutron powder intensities, single or overlapping.
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    53. 53
      Dinnebier, R. E.; Leineweber, A.; Evans, J. S. O. Rietveld Refinement: Practical Powder Diffraction Pattern Analysis Using TOPAS, 1st ed.; De Gruyter STEM: Berlin, 2019.  DOI: 10.1515/9783110461381 .
      There is no corresponding record for this reference.
    54. 54
      Coelho, A. A. Whole-profile structure solution from powder diffraction data using simulated annealing. J. Appl. Crystallogr. 2000, 33, 899– 908,  DOI: 10.1107/S002188980000248X
      54
      Whole-profile structure solution from powder diffraction data using simulated annealing
      Coelho, A. A.
      Journal of Applied Crystallography (2000), 33 (3, Pt. 2), 899-908CODEN: JACGAR; ISSN:0021-8898. (Munksgaard International Publishers Ltd.)
      Techniques and methods to facilitate the soln. of structures by simulated annealing were developed from the starting point of a space group and lattice parameters. The simulated-annealing control parameters were systematically studied and optimum values characterized and detd. Most significant is the inclusion of electrostatic-potential penalty functions in a nonlinear least-squares Rietveld refinement procedure. The long-range electrostatic potentials are calcd. using a general real-space summation which can be used for all space groups. A general weighting scheme for penalty functions negates the need to det. weighting schemes exptl. Also studied and improved is the nonlinear least-squares minimization procedure used in the refinement of structural parameters. The behavior and success of the techniques were tested on x-ray diffraction powder data against the known structures of AlVO4 in P1 with 18 atoms in the asym. unit, K2HCr2AsO10 in P31 with 15 atoms in the asym. unit excluding H, and [Co(NH3)5CO3]NO3·H2O in P21 with 15 atoms in the asym. unit excluding H. At. coordinates are given.
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    55. 55
      Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
      55
      Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
      Kresse, G.; Furthmueller, J.
      Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    56. 56
      Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15– 50,  DOI: 10.1016/0927-0256(96)00008-0
      56
      Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
      Kresse, G.; Furthmuller, J.
      Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
      The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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    57. 57
      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
      57
      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    58. 58
      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
      58
      A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
      Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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    59. 59
      Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953– 17979,  DOI: 10.1103/PhysRevB.50.17953
      59
      Projector augmented-wave method
      Blochl
      Physical review. B, Condensed matter (1994), 50 (24), 17953-17979 ISSN:0163-1829.
      There is no expanded citation for this reference.
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    60. 60
      Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758– 1775,  DOI: 10.1103/PhysRevB.59.1758
      60
      From ultrasoft pseudopotentials to the projector augmented-wave method
      Kresse, G.; Joubert, D.
      Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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    61. 61
      Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511– 519,  DOI: 10.1063/1.447334
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      A unified formulation of the constant-temperature molecular-dynamics methods
      Nose, Shuichi
      Journal of Chemical Physics (1984), 81 (1), 511-19CODEN: JCPSA6; ISSN:0021-9606.
      Three recently proposed const. temp. mol. dynamics methods [N., (1984) (1); W. G. Hoover et al., (1982) (2); D. J. Evans and G. P. Morris, (1983) (2); and J. M. Haile and S. Gupta, 1983) (3)] are examd. anal. via calcg. the equil. distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N-1/2 from the canonical distribution (N the no. of particles). The results for the const. temp.-const. pressure ensemble are similar to the canonical ensemble case.
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    62. 62
      Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985, 31, 1695– 1697,  DOI: 10.1103/PhysRevA.31.1695
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      Canonical dynamics: Equilibrium phase-space distributions
      Hoover
      Physical review. A, General physics (1985), 31 (3), 1695-1697 ISSN:0556-2791.
      There is no expanded citation for this reference.
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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsenergylett.1c02815.

    • Additional details on diffraction experiments, Raman spectroscopy, pair distribution function analysis, impedance spectroscopy, photographs of impedance samples, and AIMD simulation results (PDF)

    • Single-cell γ-Na4P2S6 structure obtained from PDF refinement (CIF)

    • 2 × 2 × 2 supercell γ-Na4P2S6 structure obtained from PDF refinement (CIF)

    • γ-Na4P2S6 structure obtained from Rietveld refinement (CIF)


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