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Ferroelectric Crystals of Globular Molecules: Cambridge Structural Database Mining and Computational Assessment

Cite this: Cryst. Growth Des. 2023, 23, 12, 8607–8619
Publication Date (Web):November 14, 2023
https://doi.org/10.1021/acs.cgd.3c00713

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

CC-BY 4.0.
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Abstract

Hybrid or organic molecular ferroelectrics hold the potential to serve as lead-free alternatives to conventional inorganic ferroelectrics. In particular, the variants composed of globular, often cage-like molecules can host attractive properties such as multiaxial ferroelectricity, Curie temperatures above room temperature, and orientationally disordered plastic mesophases, in addition to supporting low-temperature synthesis. Here, we present the results of a screening study of the Cambridge Structural Database (CSD) leading to the discovery of 54 candidate ferroelectrics, including molecular crystals and molecular salts, many of which are likely to host plastic mesophases, along with 16 previously reported ferroelectrics. With over 1.2 million entries in the CSD, the screening procedure involved many steps, including considerations of molecular geometry and size, space group, and hydrogen bonding pattern. Out of the candidate systems, many of them were identified to be likely to also host plastic mesophases due to their resemblance to highly symmetric close-packed crystal structures. The spontaneous polarization and electronic band gaps were predicted by using density functional theory. Among the candidate ferroelectrics, 17 exhibited a spontaneous polarization greater than 10 μC/cm2, with five of them being reported at room temperature.

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Synopsis

54 candidate ferroelectric crystals composed of globular molecules are identified by screening the Cambridge Structural Database. The spontaneous polarization and electronic band gap are predicted for all materials using density functional theory, revealing 17 candidate systems with polarization exceeding 10 μC/cm2. To assess the likelihood of plastic mesophase behavior, we compared the crystal structures of candidate systems with close-packed structures that allow for multiple facile slip planes.

1. Introduction

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Ferroelectric molecular crystals are potential alternatives to conventional inorganic ferroelectrics. (1–4) These materials can be synthesized with low-cost and low-energy methods such as coprecipitation, slow evaporation, spin coating, and 3D printing. (5–11) Furthermore, the abundance of available molecular species allows for tailoring of the properties of molecular crystals while eliminating the need for scarce or toxic elements. The ferroelectric molecular crystals can be formed solely through van der Waals and/or hydrogen bonding, and such systems are referred to as molecular crystals. Alternatively, they can also contain an additional ionic component originating from charged molecular species, which are termed ionic molecular crystals.
Of particular interest are (ionic) molecular crystals consisting of globular molecules. Their globular shape reduces the steric hindrance of rotational motion, making polarization switching through rotation possible. In some materials, rotational switching can also occur in combination with displacive mechanisms. (12) These materials can show rapid switching with frequencies of up to 263 kHz. (13–15) Moreover, molecular rotations in response to an applied electric field or mechanical force can result in large shear piezoelectric responses. (16) These types of molecular crystals can also crystallize in pseudo high-symmetry structures, thus allowing multiaxial polarization, with as many as 24 equivalent axes. (17–28) Multiaxial polarization allows the spontaneous polarization to be aligned in a desired direction in polycrystalline materials and could allow for multibit storage in single crystals. (29)
Ferroelectric (ionic) molecular crystals, in particular those of globular molecules, can also host orientationally disordered mesophases. (5,28,30–34) These phases can be highly ductile, or “plastic”, which can arise from reduced intermolecular interactions, and increased symmetry yielding many facile slip planes. (34) This subgroup of molecular crystals is called plastic crystals, and the materials can be molded and fused, in contrast to the rigidity and brittleness observed for most molecular crystals and inorganic ceramics. (35)
Ferroelectric plastic crystals can exhibit a rich phase diagram, (36,37) with multiple competing crystalline phases and the existence of plastic ferroelectric mesophases. This is exemplified by quinuclidinium perrhenate, which displays a ferroelectric phase with partial orientational disorder. (5) A key advantage of these materials is that they can exhibit low coercive fields. For instance, values in the 2–5 kV/cm range have been reported for compounds such as 1-azabicyclo[2.2.1]heptanium perrhenate and quinuclidinium perrhenate. (5,38) These values are comparable to that of BaTiO3, a well-known inorganic ferroelectric material. (39) Plastic crystals can also exhibit high Curie temperatures, which are essential for technological applications such as FeRAM and piezoelectric sensing. An example of this is 4-fluoro-1-azabicyclo[2.2.2]octan-1-ium perrhenate which has a Curie temperature of 466 K. (40,41)
In 2020, Horiuchi and Ishibashi compiled a catalog of approximately 80 reported ferroelectric crystals composed of small molecules. (11) This number is very small compared to the collection of approximately 1.2 million organic structures in the Cambridge Structural Database (CSD), (42) which potentially conceals numerous undiscovered ferroelectrics composed of small globular molecules, including plastic crystals. We recently screened this database, leading to the identification of six new candidates for organic proton-transfer ferroelectric materials. (43) In this paper, we provide a comprehensive account of our screening process for molecular ferroelectrics of globular molecules including an assessment of the potential to have plastic mesophases. For all of the systems uncovered, we used density functional theory (DFT) computations for geometry optimization and to predict the spontaneous polarization and the electronic band gaps. These newly identified systems are not only of interest in themselves but also serve as template structures for further crystal engineering, e.g., by substituting molecular species or halides to fine-tune functional properties.

2. Methods

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2.1. Mining the CSD for Ferroelectric Plastic Crystals

To identify candidate ferroelectrics composed in part or fully by small globular molecules, which also could be candidate plastic crystals in the CSD, we employed a systematic filtering process involving five distinct steps, as illustrated in Figure 1. (44) To execute this procedure, we utilized the CSD Python API 3.0.12 (42) and the Molcrys (45) package developed by us, based on the Atomic Simulation Environment (46) and Networkx. (47)

Figure 1

Figure 1. Overview of the screening procedure to identify ferroelectric plastic crystals in the CSD. The numbers on the left indicate the number of structures remaining after each filtering step.

Step 1 excluded structures that were nonpolar, polymeric, or disordered, as well as less accurate structures with an R-factor ≥0.075.
Step 2 excluded structures with unit cells containing more than 150 atoms. Thus, we avoided time-consuming DFT computations associated with complex and large structures.
Step 3 excluded all material systems composed solely of C and H. This choice was based on the premise that polar covalent bonds or charge transfer between species is needed for high polarization, requiring electronegativity differences.
Step 4 considered the shape of the molecules, removing all structures except those that contained 10 or fewer non-hydrogen atoms, consisted of extended linear segments, or did not contain at least one molecule with a globular or semiglobular geometry. These criteria were motivated by the fact that steric hindrance for molecular rotations should be small in the final structures. The criteria for identifying extended linear segments, such as an aliphatic side group, are detailed in the Supporting Information along with the criteria for globularity.
Step 5 excluded structures where the globular molecules were connected by more than two hydrogen bonds as three directional intermolecular bonds would most likely hinder molecular rotations in all directions.
Following the application of filters, the initial pool of structures was reduced to 75. For each of these, we computed the spontaneous polarization and electronic band gaps using DFT. Note that while we identified a diverse range of systems, the screening criteria have caused some candidates to be omitted. For instance, limiting the number of atoms in the unit cell led to the exclusion of the ferroelectric metal-free plastic perovskite [NH3-dabco]NH4I3 which has 198 atoms in its unit cell. Furthermore, the molecular size constraint excluded some known plastic crystals, including derivatives of adamantane, the C60 fullerene, (48–50) and plastic colloidal crystals. (20) However, our primary goal was not to identify all molecular and plastic ferroelectrics but rather to pinpoint several systems of technological interest. Notably, molecular ferroelectrics comprising small molecules typically exhibit a larger density of dipoles, stemming both from individual molecules and intermolecular charge transfer.

2.2. Additional Criteria to Identify Plastic Crystals

While the screening procedure did uncover known plastic crystals, it is likely that many of the candidate systems also have plastic properties. Still, many of the systems would require further investigation to indicate the existence of a mesophase with plastic ductility. The presence of small globular molecules often allows for a rotational switching mechanism. However, in some systems, the switching path may not be clear-cut, necessitating more complex computations or experimental investigations for full evaluation. Second, for a material to host a plastic mesophase may require not only the existence of an orientationally disordered phase but also that this discorded phase has many facile slip planes, in particular, for the ionic systems. The transition to an orientationally disordered mesophase may involve significant repositioning of the molecules and shifts in the crystal structure, and it is not straightforward to assess the nature of the corresponding disordered phase if such a phase exists. Nonetheless, structures that pack in pseudo close-packed high-symmetry structures are more likely to host a plastic mesophase, as many slip planes would be available with the transition of a high orientational disorder. To assess the similarity to high-symmetry structures, we compared the overlap of radial distribution function (RDF) formed by the center-of-position of each molecule with those of reference structures, representing each molecule/atom as a Gaussian function, g(r)=exp[(rrdist.)2/2σ2], with a small broadening σ to obtain a smooth radial distribution function. The RDFs were scaled so that the first peak positions were set to unity using a Gaussian broadening of σ = 0.1 for the ionic, and σ = 0.07 for the molecular crystals, i.e., in units effectively corresponding to the average center-to-center separations of the molecules. The overlap between the RDFs of the template structures and a given molecular crystal was performed with a scaled-distance cutoff of 2.3. The degree of overlap O was evaluated as follows
M=0rcutdr|RDF(r)RDFtemplate(r)|
(1)
A=0rcutdrRDF(r)
(2)
B=0rcutdrRDFtemplate(r)
(3)
O=[1+M2/(M(A+B))2]1
(4)
For the ionic molecular crystals, the overlap was defined as the sum of the overlap for cations and anions combined and the overlap for cations and anions treated separately, i.e., O = 0.5 Oanions, cations + 0.25 (Oanions + Ocations).
In addition to this structure analysis, we also identified materials systems for which an orientationally disordered phase had been reported in the CSD. Since our initial CSD screening excluded disordered structures, all structures within each refcode family were investigated for competing disordered phases. In addition, to identify systems in which the disordered phase had been reported with a different refcode, we performed a structure search using Conquest. (51)

2.3. Density Functional Theory Calculations

The DFT computations were carried out using the VASP software package (52–55) with the projector augmented plane wave method (PAW) pseudopotentials. (56,57) The plane wave cutoff was set to 530 eV for all computations. A Γ-centered Monkhorst–Pack k-point grid with a spacing of 1/15 Å–1 was used to sample the Brillouin zone. All structures were relaxed until the forces were reduced to below 0.01 eV/Å.
The spontaneous polarization was computed using the Berry phase method. (58,59) Rather than identifying nonpolar reference structures, which is the conventional procedure, we gradually increased the spacing between slabs of materials. In this case, the appropriate polarization branch can be identified by a nondiverging dipole element dipole per slab. The supercell size, i.e., the slab thickness, was converged to obtain a reliable description of the dipole moments.
For both relaxation and polarization calculations, the vdW-DF-cx functional was employed, (60) based on the accurate lattice constants determined in our earlier benchmarking study of exchange–correlation functionals for ferroelectric plastic crystals. (16)

3. Results and Discussion

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Among the 75 systems identified through the screening of the CSD, 16 have previously been reported to have ferroelectric properties. (5,17,37,40,41,61–69) Five more have been studied for their piezoelectric and/or dielectric properties but have not explicitly been reported as ferroelectric (CSD refcodes: ZZZVPE02, BOXCUO, QIMXER, BOBVIY12, and BOCKEK06). (70–74) Table 1 provides a summary of the available experimental results along with the computed values for spontaneous polarization and electronic band gaps for both the earlier reported ferroelectric and dielectric/piezoelectric materials. Table 2 lists the computed values for the other systems found in the screening. For three of these systems, the DFT computations did not yield a finite band gap. For these systems, we also computed the band gaps at the HSE06 hybrid functional level by Heyd, Scuseria, and Ernzerhof (76) which also showed an absence of a band gap.
Table 1. Overview of Earlier Reported Plastic Ferroelectrics That Were Discovered in the CSD Screening, Including Curie and Melting Temperatures, Tc and Tmelt. [K], Coercive Field Ec [kV/cm], Experimental and Computed Spontaneous Polarization, Pexp. and Pcalc. [μC/cm2], Computed Electronic Bandgap Eg [eV], Crystallographic Space Group, Alignment of Dipoles, and Chemical Compositiona
CSD refcodeTcTmelt.EcPexp.Pcalc.EgSpg.alignment (deg)chem. comp.
Trimethyl-X-Y
DIRKEU01 (61)295 (61) 67 (61)2.0 (61)5.50.3Pma2 (CH3)4N+, FeCl4
Cyclic Organic Molecules
RUJBAC (62)454 (62)  1.1 (62)1.71.9P2166, 114; 362C6H12F2N+, PbI42–
BUJQIJ (40)470 (40) 10.8 (40)0.48 (40)2.74.6P2176; –C6H13FN+, I
BUJQOP (40)470 (40) 9.4 (40)0.40 (40)2.84.6P2176; −C6H13FN+, I
Dabco-Based
SIWKEP (63)374 (63) 30 (63)9.0 (63)8.0 (16)3.6Cm C6H13N2+, ReO4
TEDAPC28 (64)378 (37)  4 (64)5.95.2Pm21n C6H13N2+, ClO4
WOLYUR08 (65)374 (65)  5 (65)6.25.3Pm21n C6H13N2+, BF4
BILNES (66)390 (66)   15.94.5R3r52; −C7H16N22+, NH4+, 3Br
BILNOC (66)446 (66) 6–12 (66)22 (66)22.44.0R3r52; −C7H16N22+, NH4+, 3I
Quinuclidinium-Based
LOLHIG02 (41)466 (41)  11.4 (41)12.7 (16)4.4Pn3; −C7H13FN+, ReO4
OROWAV (5)367 (5) 340 (5)5.2 (5)7.3 (16)4.5Pmn215; −C7H14N+, ReO4
YASKIP (17)322 (17) 255 (17)6.7 (17)6.5 (16)2.9Pmn216; –C7H14N+, IO4
SIYWUT (67,68)  1000 (68)1.7 (68)5.6 (16)5.3P41113; –C7H14NO+, Cl
ABIQOU (68)    5.2 (16)5.0P41113; –C7H14NO+, Br
MIHTEE (69)400 (69)492 6.96 (69)10.24.6P6185(R)-C7H13NO
QIVQIY (69)400 (69)  6.72 (69)10.24.5P6585(S)-C7H13NO
Other Dielectric/Piezoelectric Properties Characterized
ZZZVPE02 (70) 367 (34)  17.26.4R3m0(CH3)3BH3N
BOXCUO (71)     0P63mc (CH3)4P+, FeCl4
QIMXER (72)    9.14.7Cmc21 C6H13N2+, Cl
BOBVIY12 (73)    6.73.8Pmc21 C6H13N2+, I
BOCKEK06 (74)    12.24.8P1 C6H13N2+, HF2
a

Melting points are retrieved from the CSD unless a reference is listed. The alignment of dipoles is expressed as the angle between molecular dipoles and the polarization axis, as explained in Section 3.3. The lowest temperature structure is listed for refcode families with more than one entry.

Table 2. Overview of Candidate Ferroelectric Plastic Crystals That Were Discovered in the Screening of the CSDa
 CSD refcodeTstruct.Tmelt.Pcalc.EgSpg.alignment (deg)chem. comp
Trimethyl-X-Y
M(olecular)ZZZVPQ01RT 3.05.8R3mr0(CH3)3SO3N
 LINZOXRT 6.44.4Ama263(CH3)3NH3Al
 TMAMBF11100 (RT)415 (34)20.37.4R3m0(CH3)3BF3N
 CAVJOZ193 0.042.8P63mc (CH3)3Cl2Nb
 TBUHLB051802547.34.9Pmn2119, 32, 33(CH3)3BrC
 ETIPAY1601835.55.3Pna2120(CH3)3CH2ClSi
I(onic)WAGGAMRT 11.02.7P216, 83; –2(CH3)3OS+, Cr2O72–
 GEPZIK1231853.97.6P63 (CH3)3HN+, F, 6HF
 ZISCUC300 7.00.2Cm70; –(CH3)3CH2ClN+, FeCl4
 YODGONRT 3.15.0Pmn21 (CH3)4N+, OCN
 VUGNUGRT 0.125.3Pmn21 (CH3)4N+, N3
 XAKBUG223 4.52.6Abm2103; –(CH3)4N+, OsFO4
 MIWBEC293 13.40.2Pca2153; –(CH3)4N+, FeCl3NO
 ORUKUK100 12.93.0Pna21 (CH3)4N+, Cl3F4
 ZOYGUPRT4843.14.1P2168; –(CH3)4N+, C5H7O4
 SEYLAJ12331712.15.2P31 (CH3)4N+, OH, 4H2O
 PEVXOE100  0Cmc21 (CH3)4P+, O2, 2NH3
 PEVXUK100  0Cmc21 (CH3)4As+, O2, 2NH3
 XENFAZ2954938.41.7P2117, 161; –2(CH2O)3NH3C+, HgI42–
Dabco-Based
MLOLWEORT4297.63.4Cc18, 161; –C6H12N2, 2CH4N2S
 HUSRES150 7.94.8Pca21–; 14C6H12N2, C2H5O5P
IUSAFIG295 0.43.4Pna2195; −C6H13N2O2+, NO3
 VAGVAA01150 12.85.1Pna21 C6H14N22+, 2Cl
 GASBIO123 11.24.2Pca21 C6H14N22+, 2I, H2O
 NAKNOF03150 13.46.8P1 C6H14N22+, 2BF4, H2O
Hexamine-Based
MINEYUY/TAZPAD100 (RT) 0.93.8R3m0C6H12N3P
IHMTAABRT 11.64.8P63mc C6H12N4, NH4+, BF4
 BOHNUH01295 10.64.9R3m83; −C6H13N4+, Br
 TOZTAF296 17.34.3Cc138; 89C6H13N4+, C4H5O5
Boron Clusters
MSASSOURT3787.73.5Cc80CH10B6S2
 OTOLAM150 11.55.5Pnn20C2H14B8
IUTUZAM90 3.24.8P2156; −CH14B9, C3H10N+
 LUWHOD340 7.84.4P42 B10H102–, 2NH4+, NH3
Cyclic Organic Molecules
IWAQBOH295 8.15.7Pn C4H11N2+, BF4
 CUWZOM100 0.45.5P2152; −C5H11FN+, Cl
 AMINIT293 6.84.5P21126; 88C5H12N+, H2AsO4
 EVULAI100 13.24.7P2139C6H15N2S+, Cl
 FENYECRT4074.93.5Cc55; 85C7H5O3, C4H10N+
 HAJXEW123 16.55.6Pn16; –C6H18N33+, ClO4, 2Cl
 OBEXEY2004167.64.8Cmc21 C9H20N+, N3
Cage-like Organic Molecules
MEQAXOL140 9.15.4Pna2148C5H9O3P
 BAPFAB150 4.15.3P2120, 56C6H7FO3
 BAPFOP150 0.75.4P2120C6H7FO3
 NOCPIE01100 (RT) 14.94.5P2151, 63C7H10O3
 MIRHUQ180388 (sublim.)11.34.6P2129, 31C8H15PS
 XIBVIN1804431.34.2C277C8H15PS
 BESWON130 4.55.7P3170C9H16O
 FEJFABRT 7.42.1Pmc2134; −C6H10N2, CBr4
IPINRAI173 5.35.8Pna2160; −C6H9F3N+, Cl
 QAZFUV100 11.55.2Cmc2154; −C6H12N+, Cl
 JEBVOC293>5338.24.4P2170; −C9H14N+, Cl
Other
IHUPTUI100 0.43.7P2186; –C6H18N3S+, TaF6
 VAJKUMRT5131.73.2P2185; 43C6H18N3S+, SF5O
 OTIJUZ123393 (75)2.65.1Pc43, 120; –2C6H18OPSi+, S2O72–
a

Values have been listed for the melting temperatures Tmelt. [K], computed spontaneous polarization Pcalc. [μC/cm2], computed electronic bandgap Eg [eV], crystallographic space group, alignment of dipoles, and chemical composition. Melting points are retrieved from the CSD unless a reference is listed. Tstruct. is the temperature at which the structure was determined (RT) and indicates that the structure is also reported at room temperature. The alignment of dipoles is expressed as the angle between molecular dipoles and the polarization axis, as explained in Section 3.3. The lowest temperature structure is listed for refcode families with more than one entry.

Figure 2 shows an overview of the molecular and ionic molecular crystals among the previously reported and candidate ferroelectrics. Among the 16 known ferroelectrics, 14 are ionic molecular crystals. For the candidate systems, 20 are classified as molecular, while 35 are ionic molecular crystals.

Figure 2

Figure 2. Overview of the candidate ferroelectrics, reported ferroelectrics, and materials with reported dielectric/piezoelectric properties identified in the screening. The outer circle indicates the number of structures in each of these groups, and the inner circle indicates the number of molecular and ionic molecular crystals.

Figure 3 illustrates a selection of the molecular entities found in these identified systems, which include globular molecules, neutral and charged molecules, and ions. In total, the systems encompass 30 different anionic molecules, 31 cations, and 25 neutral molecules.

Figure 3

Figure 3. Examples of globular molecules and the anions, cations, and neutral molecules that are combined in the identified structures. In the top panel, carbon atoms are shown in gray, nitrogen in blue, oxygen in red, fluorine in yellow, boron in beige, and hydrogens as white. Other elements are labeled.

Figure 4 outlines the seven distinct groups of systems identified based on the composition and geometry of the globular molecules. Three candidate systems do not fit into any of these categories and are listed as “Other” in Table 2.

Figure 4

Figure 4. Examples of structures found in each of the eight groups of systems. ETIPAY, MIHTEE, SASSOU, EQAXOL, and FEJFAB are molecular crystals; the remaining are ionic.

Figure 5 compares the computed spontaneous polarization values with experimentally measured values for the previously reported ferroelectric molecular crystals. (5,17,40,41,61–66,68,69) While slightly larger, the computed values overall agree well with the experimental. The larger computed values can be attributed to extrinsic factors such as defects, grain orientation and boundaries, and electronic leakage which can reduce the experimental spontaneous polarization. (77,78) Additionally, atomic vibration and molecular librations may also cause spontaneous polarization to be reduced at a finite temperature. Moreover, the structures used for assessment with DFT were the ones in the CSD determined at the lowest temperature, while remaining the same polymorphs identified in the screening.

Figure 5

Figure 5. Computed spontaneous polarization compared to the experimentally measured values. Spontaneous polarization is reported for 14 out of the 16 known ferroelectrics identified in the screening.

3.1. Candidate Ferroelectric Plastic Crystals

3.1.1. Trimethyl-X-Y Systems

One group of (ionic) molecular crystals identified in our screening is characterized by the presence of trimethyl-X-Y building blocks, where X denotes an atom and Y a chemical group or atom, as exemplified by the two structures in Figure 4. Among the 22 systems, only one, DIRKEU01, has previously been reported as ferroelectric. ZZZVPE02 has been reported to have a piezoelectric coefficient d33 in the range of 10–16 pC/N and a pyroelectric coefficient of ≈25.8 μC/m2 K. (70) Another compound, BOXCUO has been reported to have switchable dielectric and magnetic properties, (71) but this is one of the compounds for which DFT indicated a lack of electronic band gap.
Among the 19 remaining systems identified, seven are composed of neutral molecules, while the rest are formed from various combinations of 12 different anions and seven different cations. Tetramethylammonium is the most common cation, found in eight out of the 22 systems. The many possible combinations of molecules, and the fact that six of the systems exhibit computed spontaneous polarization values exceeding 10 μC/cm2 (Table 2), indicate that the trimethyl-X-Y systems hold significant promise. The highest value is found for TMAMBF11 at 20.3 μC/cm2.

3.1.2. Dabco-Based Systems

Crystals composed of various derivatives of 1,4-diazabicyclo[2.2.2]octane (dabco) in combinations with anions such as ClO4 and ReO4 have been found to have found to exhibit properties such as low coercive fields and rapid ferroelectric switching with frequencies up to 263 kHz. (13,15,24,63,79) Li et al. reported a Curie temperatures as high as 540 K for N-fluoroethyl-N-ZnI3-1,4diazabicyclo[2.2.2]octonium. (80)
In our screening, we identified 13 dabco-based systems, out of which five have previously been reported as ferroelectrics. (37,63–66) Two of these, BILNES and BILNOC, can be classified as organic metal-free perovskites, (66) Figure 4. In addition to the reports of ferroelectric properties, the dielectric response of QIMXER, BOBVIY12, and BOCKEK06 have been characterized by Szafrański et al. (72–74) For the five previously identified ferroelectrics, we computed spontaneous polarization values ranging from 5.9 for TEDAPC28 to 22.4 μC/cm2 for BILNOC, which can be compared to 0.4–13.4 μC/cm2 for the additional systems identified. Interestingly, two of them, LOLWEO and HUSRES, are not ionic, but cocrystals of charge-neutral molecules.

3.1.3. Quinuclidinium-Based Systems

Several systems containing variations of the quinuclidinium molecule have been studied in recent years. (6,18,21,28,67–69,81,82) Notably, Tang et al. reported a Curie temperature of 466 K for [F-C7H13N]ReO4. (41) Another material of interest is [C7H14N]IO4, for which You et al. found 12 equivalent directions of polarization. (17) The reported coercive fields of these compounds are rather high, ranging from 255 to 1000 kV/cm. (68) All seven quinuclidinium-based systems found in this study have previously been reported as ferroelectrics (5,17,38,41,67–69) (Table 1). Five are plastic ionic crystals, while the two remaining are plastic molecular crystals and stereoisomers with identical compositions. The computed spontaneous polarizations of the quinuclidinium systems range from 5.2 to 12.7 μC/cm2.

3.1.4. Hexamine-Based Systems

In our screening, we identified four hexamine-based crystal structures, none of which, to the best of our knowledge, have been reported as ferroelectrics in the past. Figure 3 shows the two variations of the hexamine molecule that we found, the regular hexamine molecule, and a derivative where a nitrogen atom has been substituted by phosphorus. Three structures are ionic molecular crystals with spontaneous polarizations ranging from 10.6 to 17.3 μC/cm2 (Table 2). One of these, HMTAAB, features a perovskite-like structure; see Figure 4. The nonionic molecular crystal with a spontaneous polarization of 0.9 μC/cm2 occurs with two different refcodes in the CSD; TAZPAD and INEYUY. The large spontaneous polarization values of the ionic hexamine-based systems should encourage further experimental characterization and optimization of these types of systems.

3.1.5. Boron Cluster Systems

While boron clusters have been extensively studied for their characteristic chemistry, biological application, and magnetic, optical, and electronic properties, (83–86) their ferroelectric characteristics have not received particular attention. Our screening study identified four systems containing boron clusters (Table 2). Two of them, SASSOU and LUWHOD, were measured at room temperature or higher and have spontaneous polarizations just below 8 μC/cm2. The highest spontaneous polarization value is computed for OTOLAM, at 11.5 μC/cm2. The combination of large polarization and room temperature stability renders the boron cluster-based systems interesting for further investigations.

3.1.6. Systems Containing Cyclic Organic Molecules

Ten of the systems identified contain cyclic organic molecules, both aromatic and nonaromatic, and we chose to group these together. All ten are ionic molecular crystals, including three earlier reported ferroelectrics (40,62) (Table 1), two of them have the same composition and are stereoisomers. The third, RUJBAC, is an organic–inorganic hybrid perovskite. (62) All three have spontaneous polarization below 3 μC/cm2, coercive fields around 10 kV/cm, (40) and exhibit Curie temperatures exceeding 450 K. (40,62) Among the seven candidates identified here, all but one have spontaneous polarizations exceeding those of earlier reported ferroelectrics. HAJXEW has the largest value of 16.5 μC/cm2 (Table 2). Three of the candidates identified, WAQBOH, AMINIT, and FENYEC have been reported as stable at room temperature, with the latter melting above 400 K.

3.1.7. Systems Based on Organic Cage-like Molecules

We found 11 crystal structures containing organic cage-like molecules, none of which have previously been reported as ferroelectric. Seven of these are molecular crystals, while four are ionic (Table 2). Even though there are no reported room temperature structures for MIRHUQ and XIBVIN, their reported sublimation and melting temperatures are high: 388 and 443 K, respectively. JEBVOC is reported to have a melting temperature of exceeding 533 K.
Finally, three of the candidate ferroelectrics do not fit into any of the defined groups. HUPTUI and VAJKUM have similar crystal structures and are built up of tris(dimethylamino)sulfonium molecule and an octahedral inorganic anion. For these systems, the computed spontaneous polarizations are below 3 μC/cm2.

3.2. Comparison of Candidate and Previously Reported Ferroelectrics

The previously reported ferroelectrics frequently contain cage-like organic molecules, such as dabco and quinuclidinium derivatives, combined with halogen, FeCl4, or XO4 anions. The molecules in the identified candidates are by comparison generally smaller: 25 systems consist of molecules with five or fewer carbon atoms (not counting structures of boron clusters). The smaller volume of the asymmetric unit allows for larger spontaneous polarization. The lower molecular weights of the smaller molecules of the candidate systems could, however, lead to reduced melting points. Overall, the candidates display a more diverse set of anions that include entities such as HF2, CNO, FeCl3NO, and SF5O.

3.3. Polarization and Alignment of Molecules

Molecules in plastic crystals often pack in complex arrangements, and the direction of the individual molecular dipoles does not necessarily align with the direction of the spontaneous polarization. (16) In Tables 1 and 2, the “dipolar” direction relative to the polarization direction is listed. Often, the unit cell holds several equivalent molecules that align at the same angle with the polarization axis, as given by space group symmetry. Mirror or rotational symmetries cause the polarization contributions perpendicular to the polarization axis to cancel out. For many of the molecules, their dipolar direction is thus evident from their symmetry, but not all molecules have a clear dipole direction due to their low symmetry, and even for symmetric molecules, the direction with respect to the high symmetry direction is not always clear-cut. For these molecules, we obtain an effective “dipole” direction from the moments of the electronegativity relative to the center of electronegativity and compute its relative angle to the overall spontaneous polarization direction.
Figure 6 illustrates the alignment of the molecular dipoles relative to the polarization axis for MIWBEC. In the cases where the molecules are symmetrical or have a negligible dipole, no alignment is listed. In these systems, interspecies charge transfer is the dominant contribution to spontaneous polarization. Examples of such systems are six of the dabco-based systems, SIWKEP, TEDAPC28, WOLYUR08, VAGVAA01, GASBIO, and NAKNOF03. Despite negligible molecular dipoles, their spontaneous polarizations are in the range 5.0–18.4 μC/cm2. For systems where the molecular dipoles run counter to the overall polarization, an interesting prospect opens up for realignment of the dipoles by application of an electric field. This could both increase the spontaneous polarization and allow for multibit storage, assuming that the electric field required to realign the dipoles is smaller than the coercive field of the ferroelectric material.

Figure 6

Figure 6. Illustration of the alignment of dipoles in MIWBEC (tetramethylamine molecules omitted for simplicity). The dipoles align along two directions, both 53°, on the polarization axis.

3.4. Plastic Properties of the Candidate Ferroelectrics

While the screening study can identify candidate ferroelectric plastic crystals, truly predicting whether the systems can transition to a plastic mesophase demands more involved simulations, such as molecular dynamics. This is not feasible for the large pool of candidate systems identified in this study, but out of the 16 identified known ferroelectrics, eight are reported to be plastic crystals, namely ABIQOU, SIYWUT, MIHTEE, QIVQIY, DIRKEU01, OROWAV, YASKIP, and LOLHIG02. (5,17,24,61,68,69) WOLYUR08, TEDAPC28, and SIWKEP are reported to have rotationally disordered high-temperature phases, but their mesophase ductility has not been investigated. Furthermore, the high-temperature phases of BUJQIJ and BUJQOP have not been resolved due to poor XRD data, (40) which can indicate the high degree of disorder characteristic for plastic crystals. Three candidate systems have been reported to be plastic crystals where all molecules exhibit rotational disorder, namely TMAMBF11, (34) ZZZVPE02, (34) and ZISCUC. (87) LOLWEO has a reported high-temperature phase in which one of the two molecular constituents shows an orientational disorder. Thus, the screening procedure is suited to identify systems with orientationally disordered mesophases.
High ductility is often linked to the existence of many slip systems. Thus, plastic properties are more likely in an orientationally disordered mesophase with a dense packing and high symmetry. High symmetry is particularly acute for the ionically bonded molecular crystals due to their limited number of slip planes. Thus, ionic molecular crystals that are pseudosymmetric to structures such as CsCl and NaCl are more likely to exhibit plastic behavior.
Figure 7 plots the overlap of the RDFs as defined in eqs 14 of systems composed of two molecular entities identified here with the structures of CsCl, NaCl, as well as zincblende. The horizontal line marks the known plastic crystal with the smallest overlap with a reference close-packed structure, namely, ZISCUC with an overlap of 0.83 with the CsCl structure. Structures with a larger overlap are likely to host plastic mesophases. In total, 17 of the systems fulfill these criteria, including all 7 of the materials with previously reported plastic properties. However, it is important to keep in mind that our assessment is quite rough and does not take into account factors such as the available space for rotation; moreover, several of the compounds not fulfilling this criterion may, for instance, exhibit a significant positional shift in the transition to an orientationally disordered mesophase.

Figure 7

Figure 7. Overlap between the ionic molecular crystals identified in the screening with structure types that can allow for plastic properties. The horizontal line marks the lowest overlap calculated for the known plastic crystals identified here. Structures earlier reported as plastic crystals are marked with boldface.

Figure 8 plots the overlap between the molecular crystals and hexagonal close-packed (hcp), body-centered cubic (bcc), and face-centered cubic (fcc) structures. Here, the smallest overlap between a known plastic crystal and a reference structure is ZZZVPE02, which has an overlap of 0.96 with the bcc structure and 0.86 with the hcp structure. The close-packed structures built up of a single molecular species are harder to differentiate than the ones composed of two species using the overlap based on the RDF-overlap.

Figure 8

Figure 8. Overlap between the molecular crystals identified in the screening with structure types that can allow for plastic properties. The horizontal line marks the lowest overlap calculated for the known molecular plastic crystals identified here. Structures earlier reported as plastic crystals are marked with boldface.

This is the case for two of the crystals with reported plastic properties, TMAMBF11 and ZZZVPE02, which show large similarities to both hcp- and bcc-type packing. These two isostructural systems crystallize in the R3m space group, Figure 9, and are reported to have ductility comparable with metals in their plastic phases. (34) A large overlap with the close-packed hcp and fcc structures can indicate plasticity; 14 of the molecular crystals have an overlap larger than 0.86 with the hcp or fcc structures, indicative of plastic properties, including the four reported plastic crystals. Finally, we note that the existence of many slip planes and high symmetry might be less critical for the (nonionic) molecular crystals. Other deformation mechanisms can also be present, such as creep close to the melting temperature. Onset of configurational disorder has been associated with increased plasticity in molecular crystals.

Figure 9

Figure 9. Crystal structure of the plastic molecular crystal ZZZVPE02, isostructural to TMAMBF11.

Overlap with close-packed structures was not evaluated for the 11 structures composed of three molecular entities identified in this study due to their complexity. Out of these, four have perovskite-type structures; RUJBAC, BILNES, BILNOC, and HMTAAB. While these might be less likely to host a plastic mesophase, plastic behavior has earlier been reported for hybrid perovskites. (88–90)

3.5. Thermal Stability

For device applications, thermal stability is an important property and operational temperatures should be significantly below melting and sublimation temperatures. The melting temperature of plastic crystals can be higher than for similar ionic and molecular crystals, due to the high entropy associated with the orientational disorder and increased freedom of movement making melting less favorable, as first reported by Timmermans. (30) The volume change at the phase transition is also small. (91)
For 45 of the 75 systems identified in this study, the crystal structure is ordered with a ferroelectric space group and obtained at ambient temperature. For the four systems, a paraelectric phase is reported at room temperature. Finally, 26 systems lack a reported crystalline room temperature phase in the CSD. The fraction of room temperature investigations is highest for ionic crystals, Figure 10, a result that is in line with the higher stability of the ionic molecular crystals, due to electrostatic interactions.

Figure 10

Figure 10. Overview of the molecular and ionic crystals identified. The outer ring indicates the number of systems, and the inner ring indicates if the potentially ferroelectric phase is reported at room temperature.

3.6. Electronic Band Gap and Multisource Energy Harvesting

Ferroelectric materials with band gaps in the visible range can be of particular interest, as these could be promising for application in multisource energy harvesting devices where piezo- or pyroelectric energy harvesting is combined with the harvesting of solar energy. (92,93) Therefore, we computed the band gaps for all identified systems to find those that could be suitable for such applications.
Tables 1 and 2 list the computed band gaps. Since the computations were performed using the vdW-DF-cx functional, which describes exchange at the generalized-gradient approximation level, (60) we can expect the band gaps to be underestimated. Most of the computed band gaps exceed 4 eV; however, six systems have values smaller than 2 eV. Four of these belong to the trimethyl-X-Y group, which could thus be interesting for multisource energy harvesting.

3.7. Design Strategies for Ferroelectric Plastic Crystals

Novel and improved ferroelectric plastic crystals can be engineered by making new combinations of molecular species. As such, the various species found in the various plastic crystal candidates can be used as building blocks for novel material design; a selection of these is displayed in Figure 3.
Of particular interest are substitutions that are likely to result in similar or isostructural crystals. For systems where this is possible, solid-solution engineering can be used to tweak the material properties. Three examples of pairs of candidates for such alterations are found among the trimethyl-X-Y systems. The compositions between each pair of systems are similar, only differing by the substitution of molecules with similar geometries. PEVXOE and PEVXUK are isostructural and only differ by the substitution of (CH3)4P+ for (CH3)4As+. For ZZZVPE02 and TMAMBF11, the substitution of (CH3)3BH3N to (CH3)3BF3N yields an isostructural material where the computed polarization is increased from 17.2 to 20.3 μC/cm2. A similar effect is seen for YODGON and VUGNUG, where the substitution of N3 for OCN leads to an increase in the spontaneous polarization from 0.13 to 3.1 μC/cm2.
Another example of substitution resulting in similar packing is the earlier reported ferroelectrics TEDAPC28 and SIWKEP, which consist of a dabco molecule and a tetrahedral inorganic ion, ClO4 or ReO4, respectively. This substitution somewhat changes the orientation of molecules, resulting in a different space group. Whereas, we found a spontaneous polarization of 8 μC/cm2 for the ReO4 system, the ClO4 one has a value of 5.9 μC/cm2.
In total, ten different tetrahedral inorganic anions were found in our screening study, such as BF4, FeCl3ON and IO4, but other options also exist and can be considered for the design of new ferroelectric plastic crystals. Substitutions of single atoms in the organic globular molecule can also be a route to engineer the ferroelectric properties. (94) For instance, Lin et al. substituted a hydrogen atom in tetramethylammonium for halogens I, Cl, and Br. The crystal structure was retained, while the number of ferroelectric polar axes increased from 2 for iodine to 6 for chlorine. (95)

4. Conclusions

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Using a CSD-based workflow, we identified 54 candidate ferroelectric molecular crystals. The 17 with spontaneous polarization exceeding 10 μC/cm2 are arguably the ones with the most potential in ferroelectric devices. Among these, five in the trimethyl-X-Y group also display a large variation in electronic band gaps that could make them useful for multisource energy harvesting. Ten likely plastic molecular crystals and ten likely plastic ionic molecular crystals were identified among the candidate systems by comparing the crystal structures of the candidate systems with close-packed crystal structures.
Our study has successfully identified a range of candidate ferroelectric molecular and molecular ionic crystals, including 16 that have been reported as ferroelectrics in the past. The screening criteria used were quite strict, and relaxing some of them, such as the size limitations on both molecules and unit cells, would have expanded the pool. The criteria were based on previously reported ferroelectric molecular and molecular ionic crystals. For this reason, crystal structures that differ significantly from the earlier reported ones could have been overlooked. Still, the identification of the boron cluster-based systems was unexpected, illustrating the potency of the CSD screening. In the design of novel ferroelectric plastic crystals, a good starting point is combining different globular molecular species, e.g., combinations of cations and anions. The various molecular species in the systems identified here and the corresponding crystal structures can serve as inspiration for such design.
In this study, we have not assessed whether the polarizations of the candidate ferroelectrics are switchable, which is a criterion for ferroelectricity. However, all of the candidate systems will necessarily have pyro- and piezoelectric properties as of their polar crystal symmetries. This study and the identified systems should stimulate further theoretical or experimental studies to assess their ferroelectric switchability and other characteristics such as the Curie temperatures and material stability.

Data Availability

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All the relaxed crystal structures used in this study can be accessed through the NOMAD database at https://dx.doi.org/10.17172/NOMAD/2023.06.12-1. All other data are available upon reasonable request. Scripts for computing globularity and Network properties are available in the Molcrys package.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.cgd.3c00713.

  • Description of the screening tools and criteria used for molecular geometries, including the evaluation of the globularity of molecules and the identification of extended linear segments (PDF)

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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
  • Authors
    • Seyedmojtaba Seyedraoufi - Department of Mechanical Engineering and Technology Management, Norwegian University of Life Sciences, 1432 Ås, NorwayOrcidhttps://orcid.org/0000-0003-3800-0412
    • Carl Henrik Görbitz - Department of Chemistry, University of Oslo, 0371 Oslo, Norway
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The computations of this work were carried out on UNINETT Sigma2 high-performance computing resources (grant NN9650K). This work is supported by the Research Council of Norway as a part of the Young Research Talent project FOX (302362).

References

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  • Abstract

    Figure 1

    Figure 1. Overview of the screening procedure to identify ferroelectric plastic crystals in the CSD. The numbers on the left indicate the number of structures remaining after each filtering step.

    Figure 2

    Figure 2. Overview of the candidate ferroelectrics, reported ferroelectrics, and materials with reported dielectric/piezoelectric properties identified in the screening. The outer circle indicates the number of structures in each of these groups, and the inner circle indicates the number of molecular and ionic molecular crystals.

    Figure 3

    Figure 3. Examples of globular molecules and the anions, cations, and neutral molecules that are combined in the identified structures. In the top panel, carbon atoms are shown in gray, nitrogen in blue, oxygen in red, fluorine in yellow, boron in beige, and hydrogens as white. Other elements are labeled.

    Figure 4

    Figure 4. Examples of structures found in each of the eight groups of systems. ETIPAY, MIHTEE, SASSOU, EQAXOL, and FEJFAB are molecular crystals; the remaining are ionic.

    Figure 5

    Figure 5. Computed spontaneous polarization compared to the experimentally measured values. Spontaneous polarization is reported for 14 out of the 16 known ferroelectrics identified in the screening.

    Figure 6

    Figure 6. Illustration of the alignment of dipoles in MIWBEC (tetramethylamine molecules omitted for simplicity). The dipoles align along two directions, both 53°, on the polarization axis.

    Figure 7

    Figure 7. Overlap between the ionic molecular crystals identified in the screening with structure types that can allow for plastic properties. The horizontal line marks the lowest overlap calculated for the known plastic crystals identified here. Structures earlier reported as plastic crystals are marked with boldface.

    Figure 8

    Figure 8. Overlap between the molecular crystals identified in the screening with structure types that can allow for plastic properties. The horizontal line marks the lowest overlap calculated for the known molecular plastic crystals identified here. Structures earlier reported as plastic crystals are marked with boldface.

    Figure 9

    Figure 9. Crystal structure of the plastic molecular crystal ZZZVPE02, isostructural to TMAMBF11.

    Figure 10

    Figure 10. Overview of the molecular and ionic crystals identified. The outer ring indicates the number of systems, and the inner ring indicates if the potentially ferroelectric phase is reported at room temperature.

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