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Use of Topotactic Phase Transformations To Obtain Solutions of the Crystal Structures of Highly Disordered Materials Published as part of a Crystal Growth and Design virtual special issue Honoring Prof. William Jones and His Contributions to Organic Solid-State Chemistry Logan C. Lorson, Onkei Tai, and Bruce M. Foxman* Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02453-2700, United States S Supporting Information *

ABSTRACT: A straightforward procedure is outlined for prediction of the complete three-dimensional coordinate set for a highly disordered phase. For a mother and daughter phase, where one of the pair has an “unsolvable” structure, one needs only to (a) establish the topotaxy using previously published techniques, (b) obtain the topotactic transformation matrix, φ, between the ordered and highly disordered phase, and (c) apply the transpose of φ−1 to obtain a trial set of coordinates for refinement using the reflection data set of the highly disordered phase. For the inclusion compound [Fe(η-C5H5)]· 3(NH2)2CS (1), which contains highly disordered ferrocene molecules above 160 K (polymorph 1_I), we found a more ordered structure at low temperature. At 135 K (polymorph 1_II), two ferrocene moieties are present in the thiourea channel in an approximately 1:1 ratio. One is nearly orthogonal (87.0°) to the channel axis, while the other is tipped 16.2° from that direction. Using steps (a−c) outlined above, a trial structure may be obtained for 1_I, and refinement leads to R1 = 4.25%. The structure of 1_1, containing 12-fold disordered ferrocene molecules, is similar to that found at temperatures below the phase transition, with a greater amount of the orthogonal orientation (55:45 vs 51:48), consistent with, but lower than, amounts found using solid-state NMR techniques. The low temperature polymorph is a trill, with an approximately 3:1:1 ratio of twin components. The exact alignment of the mother phase and the three daughters has been established using the methods of topotactic analysis described previously.

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solid-state reaction of bis(p-methoxy)-trans-stilbene, first described in a 1984 paper by Theocharis, Jones and Rao, served as an opportunity for B.M.F. to write to Professor Bill Jones with some questions about the paper.10 We enjoyed a short, polite, and pleasant exchange, which began a long friendship and exchange of ideas. I have always enjoyed my interactions with Bill and have never failed to be impressed by his work, which is always characterized by the highest standards and highest originality. His superior mentorship of young scientists serves as an example to us all. In a recent paper,7 we described a procedure that may be used to experimentally establish the three-dimensional relationship between a mother and daughter phase, i.e., a parent and an end-phase in certain solid-state transformations. The procedure applies to any process involving a crystal-to-crystal transformation where relative orientations of mother and daughter phases are observable: specifically, the crystal must remain on the diffractometer during the transformation. The procedure uses a

INTRODUCTION Crystal-to-crystal phase transitions provide a unique opportunity to study molecular motion in solids, including the bond-making/bond-breaking processes that occur in solid-state reactions. Yet, in spite of many interesting and revealing investigations, our knowledge about first-order phase transitions in molecular crystals remains incomplete. Professor Jack Dunitz has elegantly summed up the present status in a recent essay,1 which, in addition to highlighting great science, will serve to stimulate young scientists to solve new, and old, problems in the field. The present contribution reports a different approach to the use of phase transitions: to predict, in optimal cases, the structure of a material which has remained elusive at the atomic coordinate level. Topotactic crystal-to-crystal phase transformations, including those processes involving either molecular reorientation or a chemical reaction, have been an important focus of our research for over four decades.2−7 “In topotaxy, a single crystal of a starting material is converted into a pseudomorph8 containing one or more products in a definite crystallographic orientation; the conversion takes place throughout the entire volume of the crystal.”9 The topotactic © XXXX American Chemical Society

Received: October 3, 2017 Revised: November 13, 2017 Published: November 20, 2017 A

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between 150 and 170 K (uncalibrated temperature, Oxford Cryosystems 700 Plus), from the trigonal system to a likely monoclinic phase. Initial crystallization attempts led to large (∼2 mm) prismatic crystals, which required cutting before mounting on the diffractometer. For several prismatic crystals, we found that the daughter phase was severely twinned and/or composed of multiple misoriented zones, and various attempts did not provide data from which an acceptable structure could be obtained. After several months of crystallization attempts, a small number of acicular crystals appeared among the prismatic crystals, and, suspecting a new polymorph, we examined the new material. It became immediately clear that the new morphology had the same unit cell as observed previously at temperatures above the phase transition; the low-temperature unit cell, though twinned, could be readily indexed, and the structure could be solved. The cell constants for polymorph 1_I and 1_II are listed in Table 1. A re-examination of several data

readily available program, TOPO, which can provide the data required to prepare two-frame animations of the phase transitions or solid-state reactions.11 A transformation matrix, the topotactic transformation matrix, which relates the mother and daughter unit cells, is included in the output of TOPO. Our recent paper7 includes a tutorial-style approach and applications to the phase transitions in cyanopyridinium perchlorate, ferrocenium tetrafluoroborate, and ferrocenium hexafluorophosphate. On the basis of the prior examples, crystals containing the ferrocene or ferrocenium moiety appeared to provide a rich opportunity for further study. Moreover, since for the present work we preferred to investigate a commensurate inclusion compound, the thiourea clathrate seemed ideal,12 as most of (but not all)13 such compounds are commensurate. The present work centers on the polymorphic phase transition and structures in the thiourea-ferrocene clathrate system. A study conducted by Clement et al. in 1974 demonstrated the existence of thiourea-metallocene clathrates with ferrocene and nickelocene as guest molecules.14 A rhombohedral unit cell was found at room temperature, and a reversible phase transition was reported to occur at 162 K. However, no crystal structures were determined. Additionally, the authors proposed that the size of the guest metallocene may play a prominent role in the stability of the clathrate. Observations indicated that the thiourea clathrate containing nickelocene was much more easily destabilized than that of ferrocene, while a thiourea clathrate of ruthenocene could not be formed. A later study suggested that the ferrocene guest molecules are, in fact, only weakly held in the thiourea tunnels.15 In 1978 Hough and Nicholson carried out a partial X-ray structure determination of the thiourea-ferrocene clathrate at 295 K and a study of the behavior of individual reflections at 105 K.16 At 295 K the clathrate crystallizes in the rhombohedral space group R3̅c. The partial structure solution (R = 0.079) of the [Fe(η-C5H5)]· 3(NH2)2CS clathrate 1 included the thiourea host molecules, the iron atoms from each ferrocene molecule, as well as partial modeling of a set of disordered Cp carbon atom positions. However, the Cp carbon atom positions were not listed, and no mention was made of their deposition as supporting information. The present contribution reports complete determinations of the structures of 1 at 260 and 135 K. During the analysis of the phase transition in 1, we also observed that the ferrocene moiety in the room-temperature mother phase (hereafter 1_I) was highly disordered; we were initially unable to model the disorder. A successful structure determination of the lowtemperature daughter phase (hereafter 1_II) at 135 K led us to hypothesize that, given that the mother and daughter phases are related by the topotactic transformation matrix φ,17 one might be able to use the inverse transform of the φ matrix to generate the coordinates of the mother phase from those of the daughter phase.18 In the present contribution we review the theoretical aspects of the procedure and show that it leads to a highly satisfactory solution of the crystal structure of polymorph 1_I. Further, we comment on the likely general applicability of the method.

Table 1. Crystallographic Data for Compound 1 compound

1_I

1_II

chemical formula a, Å b, Å c, Å α, deg β, deg γ, deg V, Å3 Z, Z’ formula wt g/mol space group T, K λ, Å ρcalc, g cm−3 μ, mm−1 θmax; transmission factors Ra Rwb Sc no. reflections (all; I > 2σ(I)) no. parameters

C10H10Fe·3CH4N2S 16.3194(5) 16.3194(5) 12.3630(4) 90 90 120 2851.43(15) 6, 0.1667 414.40 R3̅c 260(1) 0.71073 1.448 1.129 30.05°; 0.79−0.80 0.0425 0.1330 1.008 934, 791 104

FeC10H10·3CH4N2S 10.1295(6) 16.1683(11) 12.4035(7) 90 114.037(4) 90 1855.2(2) 4, 1 414.40 P21/a 135(1) 0.71073 1.484 1.157 30.15°; 0.79−0.80 0.0456 0.1226 0.988 5357, 3771 283 1/2

a

R = ∑ ∥Fo| − |Fc||/∑ Fo

b

R w = ⎡⎣∑ w(|Fo| − |Fc|)2 /∑ w |Fo|2 ⎤⎦

1/2

c

S = ⎡⎣∑ w(|Fo| − |Fc|)2 /(n − m)⎤⎦

sets collected at 120 K for the prismatic crystals verified that these represented the same phase as found for the acicular habit; however, the data for the prismatic crystals were always of relatively poor quality. Thus, we abandoned our study of the prismatic crystals, and the remainder of this report focuses solely on the structure and phase transition of the crystals of acicular habit. Photomicrographs of each habit may be viewed in Figure S1 (Supporting Information). Below we first describe the solution of the structure for polymorph 1_II, followed by that of the 1_I form. The discussion concludes with a presentation of the detailed topotactic relationships between 1_1 and 1_II, as well as “before-and-after” animations of the process. (A). Structure of [Fe(η-C5H5)]·3(NH2)2CS (1_II) at 135 K. While previous studies indicated a phase transition at 162 K, no information on the unit cell or space group of the

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RESULTS AND DISCUSSION Crystals of the thiourea-ferrocene clathrate, [Fe(η-C5H5)]· 3(NH2)2CS, were prepared in a manner similar to that previously described,16 except using toluene-methanol mixed solvent media instead of benzene-methanol solutions. Preliminary experiments verified that a phase transition occurred B

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low-temperature form of 1 was noted.14,16 At 135 K, 1_II is monoclinic, space group P21/a (Table 1). The nonstandard setting of space group P21/c was chosen, since it seemed likely that the channel axis of the trigonal mother phase (c) would then correspond to the c axis of the P21/a setting; that assumption later proved to be correct. Inspection of the individual frames of diffraction data, as well as observations during the course of solution and refinement of the structure, strongly suggested that the structure was twinned. During the refinement, processing of the data with ROTAX19 revealed that the crystal was a trill; i.e., it was triply twinned. For twins, our general laboratory procedure involves (a) solution and refinement of the data with ROTAX, (b) reprocessing of the frames with CELL_NOW20 and TWINABS21 to produce a (b) hklf4 and (c) hklf5 file. Conventional refinement using these two files is then carried out, and the three models [(a) through (c)] are compared. Experience suggests that it is very difficult to predict which of the three models will be best in an individual case. In this case, the refinement using ROTAX was superior; on many occasions the ability to vary the twin overlap parameter in the Crystals for Windows22 software leads to substantive improvement. The crystal is a (∼3:1:1) TLQS23 conservative twin17 rotated about the 110 and 1̅10 reciprocal directions. The twin laws and corresponding obliquities24 are (1̅ 1 0)/[3̅ 1 1̅], 0.45°, (0.507, −0.493, 0.501/−1.507, −0.507, −0.501/0, 0, 1)̅ and (1 1 0)/[3 1 1], 0.45°, (−0.507, −0.493, −0.501/1.507, −0.507, 0.501/0, 0, 1). Final refined values of each component were 0.602(4), 0.206(4), and 0.192(4). If conservative twinning,17 i.e., preservation of the trigonal symmetry of 1_I in the resultant monoclinic 1_II crystal by twinning, was fully achieved, one would expect an equal distribution of the three components. Such a distribution is most often seen in TLS23 (merohedral or pseudomerohedral) twins; kinetic factors may intervene to change the distribution. In order to explore the latter idea, we examined a second crystal at several temperatures. The same twin laws were found, with little variation in the twin law scale factors with temperature (119−135 K). However, at 135 K the final refined values of each component were 0.722(6), 0.192(6), and 0.086(5), supporting the idea that kinetic factors may well influence the relative amounts of each component. We note that approximate 3-fold relationships are maintained in the trilled crystals, with the angles between (110) and (0 1̅ 0) and (1̅ 1 0) and (0 1̅ 0) both measuring 119.78°, and the angle between (1̅ 1 0) and (1 1 0) at 120.44°. Complete details of the solution and refinement appear in the Supporting Information. An initial solution of the structure indicated that 1_II was disordered; however, the disorder could be resolved in a straightforward manner. Figure 1 shows the asymmetric unit, which contains three ordered thiourea molecules and one ferrocene molecule involved in an approximate 50:50 disorder. The figure shows major component atoms C(201)−C(204) and C(206)−C(209) in red with refined occupancy 0.516(4), and minor component atoms C(101)−C(110) in yellow; occupancies of major and minor components were constrained to sum to 1.0. Atoms C(105) and C(107) (green) lie in nearly the same position as the corresponding major component atoms; the two disordered molecules are shown separately in Figure S3 (Supporting Information). In this case disorder could not be resolved, and these atoms were assigned an occupancy factor of 1.0. The two ferrocene moieties lie at an angle of 76.8° to one another (calculated using the vectors between upper and lower Cp ring centroids for each molecule). Using the same vectors,

Figure 1. View of the asymmetric unit of polymorph 1_II. C atoms in green are associated with both disordered ring sets and have fixed occupancies of 1.0; atom C(105) is in the upper left and C(107) at lower right. More complete numbering is available in Supporting Information (Figure S2).

we find that the minor component ferrocene is tilted 16.2° from a parallel orientation in the channel, while the major component ferrocene is nearly orthogonal (87.0°) to the channel axis. Close inspection of the crystal packing along the c axis (Figure 2), retaining the yellow/red color scheme, reveals the parallel/perpendicular orientations along the channel axis. Previously, compound 1 has been studied at various temperatures by calorimetry,25 Mössbauer26,27 and solid-state NMR spectroscopy,27−29 as well as by molecular modeling.30 Studies of 1 by adiabatic calorimetry revealed heat capacity anomalies, associated with phase transitions, at 147.2, 159.79, 171.4, 185.5, and 220 K.25 The largest (by far) of these occurs at 159.79 K. We also collected data at uncalibrated temperatures of 100, 120, 150 K for 1_II, and 160 and 180 K for 1_I. Refinements using data from the other temperatures were identical within experimental error to the results presented here; no evidence for dynamic disorder was found within the temperature ranges studied. Mössbauer and 2H solid-state NMR studies by the Hendrickson group showed that there were three ferrocene orientations tipped ∼17° from an orientation parallel to the channel axis, and three perpendicular, with a ratio of 0.48:0.52 at 110 K, respectively and 0.40:0.60 at 155 K.27 We noted no variation of population within the temperature ranges studied; however, we are nonetheless impressed with the agreement between the crystallographic data and Hendrickson’s results.27 Although the structure is monoclinic, the observed trilling fits well with the observation of three each, C3-related parallel and perpendicular orientations.27 (B). Structure of [Fe(η-C5H5)]·3(NH2)2CS (1_I) at 260 K. First attempts to solve the structure of 1_I followed conventional approaches to disorder-modeling. Positions of the Fe atom on a Wyckoff 6a site (32 symmetry) at (0, 0, 0.25) and a half-thiourea molecule on a Wyckoff 18e site (2 symmetry) at (x, x, 0.75) were consistent with the 1:3 stoichiometry. Difference electron-density maps showed numerous peaks around the Fe atom. As noted by Hough and Nicholson,16 it was possible to begin a modeling study, and to account for the electron density, but the models were not C

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Figure 2. View of the unit cell of 1_II down the c axis (a vertical, b horizontal). Close inspection of the disordered ferrocene moieties shows the minor yellow component, tipped 16.2° from parallel to the channel, and the red major component, nearly perpendicular (87.0°) to the channel.

structurally sensible. Thus we set that approach aside and attempted a solution that, at least in part, involved a spherical distribution of electron density. Using readily available tools in the Oxford University Crystals for Windows software,22 we refined the structure as having (in part) a spherical distribution of electron density for the cyclopentadienyl C atoms, along with partial atoms embedded in the sphere.31 The amounts of electron density in the sphere and the partial atoms were constrained to sum to that of 10 C and 10 H atoms. While this gave relatively low values for R1 (5−6%), the solution for the partial atoms was again not sensible in a structural chemical sense. In both of the above models, we noted a likely further disorder of the Fe atom: values of U33 were as large as 4 times those of U11, suggesting disorder in the Fe atom positions. We set the spherical-distribution model aside as well. We then decided to explore whether a set of coordinates could be generated for 1_1 using the methods of topotaxy. As suggested in the Introduction, in any crystal-to-crystal process, reaction, or phase transition, one has the opportunity, if the process is observed during a single diffractometer session, to obtain the exact orientation relationship between the pair of unit cells observed.7 The procedure, using the current version (4.40) of our available program TOPO,11 involves reading in a pair of .p4p or .cif files that contain the orientation matrices for Phase 1 and Phase 2, R1, and R2, respectively. The product of the inverse of the orientation matrix for Phase 2 and the orientation matrix for Phase 1 gives the topotactic transformation matrix φ; the φ matrix may be used to transform the direct space axial parameters of unit cell 1 to unit cell 2.7,17

The fractional coordinates associated with Phases 1 and 2 transform contravariantly to the unit cell parameters;18 thus we can transform the coordinates as follows, ⎛ x2 ⎞ ⎛ x1⎞ ⎜y ⎟ −1⎜ y ⎟ ⎜ 2 ⎟ = ϕ̅ ⎜ 1 ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ z2⎠ ⎝ z1⎠

where the bar indicates the transform of matrix φ. The coordinates of polymorph 1_II were then multiplied by the transpose of the inverse topotactic transformation matrix, (−0.29240015, −1.02595031, 0.00465608/ −0.65292293, −0.07470173, −0.00103417/0.33493739, −0.00935831, −1.00324917). Conveniently, both φ and its inverse are part of the TOPO program output,11 and the Oxford University Crystals for Windows software provides an option for coordinate transformation.22 Once the new coordinate set was generated, redundant atoms, specifically those associated with 2-1/2 of the original three thiourea moieties, had to be removed; these of course were symmetry-related to those of the half-molecule in the Wyckoff 18e position. The derived Fe atom position (1/3, 2/3, −0.097) was displaced ca. 0.17 Å from the Wyckoff 6a position (1/3, 2/3, −0.0833) and therefore was assigned a fixed occupancy of 0.5. Cyclopentadienyl C atoms, involved in a 2-fold disorder in 1_II, were now initially set to occupancies of 0.0833 (= 0.5/6). When the parameter files were completely updated using the predicted new coordinates, and the occupancies were adjusted, refinement was carried out using isotropic displacement parameters for the ring C atoms, and the refined occupancies of the two ferrocene orientations were constrained to sum to 1/6. The atom numbering scheme is

φ = R−12R1 D

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containing the mother phase data, and a second file containing all three daughter orientation matrices (in its present form the program TOPO (version 4.40) can read any sequence of twin component orientation matrices in a single *.p4p file). The TOPO-guided analysis of the topotaxy reveals a rather complicated set of relationships, as follows: Twin Component Topotaxy 1 (010)m || (1̅00)d ; (2̅10)m || (010)d ; cm || −cd 2 (110)m || (010)d ; (110)m || (01̅0)d ; cm || cd 3 (100)m || (100)d ; (010)m || (13̅0)d ; cm || −cd

identical to that employed in polymorph 1_II. Bond length, vibration, and angle restraints for the C−C and Fe−C distances were also included. Complete details appear in the deposited .cif files and/or Supporting Information. The final value of R1 was a satisfactory 4.25%. The final electron density difference map had only three peaks above 0.3 e−/Å3, with the largest (0.5 e−/Å3) near composite atom C(105) (see section A), and two at ∼0.35 e−/Å3 near S(1) and atom C(204) in the perpendicular ring of the ferrocene moiety. Figure 3 shows the packing of the disordered system viewed down the crystallographic c axis. Intervector angles for the two

The before-and-after paired illustrations are shown in Figure 4a−c for transformations of each of the three components (see also the animations of each of the three motherdaughter pairs in Supporting Information download files FcTU3_1.pptx through FcTU3_3.pptx). The interplanar angles in the daughter phase 1_II, e.g., (100)d − (1 3̅ 0)d, 59.78° and (010)d − (1 3̅ 0)d, 29.22°, consistent with the small obliquity observed, help to facilitate the trilling.

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CONCLUSIONS We have described a straightforward procedure for prediction of the complete three-dimensional coordinate set for a highly disordered phase. For a mother and daughter phase, where one of the pair has an “unsolvable” structure, one needs only to (a) establish the topotaxy using previously published techniques, (b) obtain the topotactic transformation matrix φ between the ordered and highly disordered phase,7,8,17 and (c) apply the transpose of φ−1 to obtain a trial set of coordinates for refinement using the reflection data set of the highly disordered phase.18 For the inclusion compound [Fe(ηC5H5)]·3(NH2)2CS (1),16 which contains highly disordered ferrocene molecules above 160 K (polymorph 1_I), we found a more ordered structure at low temperature. At 135 K (polymorph 1_II), two ferrocene moieties are present in the thiourea channel in an approximately 1:1 ratio. One is nearly orthogonal (87.0°) to the channel axis, while the other is tipped 16.2° from that direction. Using steps (a−c) outlined above, a trial structure may be obtained for 1_I, and refinement leads to R1 = 4.25%. The structure of 1_I, containing 12-fold disordered ferrocene molecules, is similar to that found at temperatures below the phase transition, with a greater amount of the orthogonal orientation 0.555(7):0.445(7) at 260 K vs 0.516(4):0.484(4) at 135 K. The small, barely significant increase above the phase transition is consistent with, but lower than, amounts found using solid-state NMR techniques (63:37). The low temperature polymorph is a trill, with an approximately 3:1:1 ratio of twin components. The exact alignment of the mother phase and the three daughters has been established using the methods of topotactic analysis described previously.7,8,17 The question of general applicability remains to be answered; however, we can provide some immediate insight from recent experiments. Experiments using single crystals of the [C6H12]· 3(NH2)2CS clathrate predict the structure of the roomtemperature,32 12-fold disordered phase, and are in excellent agreement with the powder X-ray diffraction results obtained by the Harris group for all three phases.33 However, when attempts are made to carry out predictive studies using [C6H11Br]· 3(NH2)2CS, also highly disordered at room temperature, no

Figure 3. View of the unit cell of 1_I down the c axis. The 2-folddisordered ferrocene molecules in 1_II are now each involved in symmetry-generated 6-fold disorder, yielding an overall 12-fold disorder for the ferrocene guest. The red rectangle corresponds to the unit cell outline in Figure 2. Further details of the alignment appear in section C of this paper.

ferrocene moieties have changed slightly. The two parent molecules now lie at an angle of 70.5°, the minor component ferrocene is tilted 18.4° from a parallel orientation in the channel, and the major component ferrocene moiety remains nearly orthogonal (87.6°) to the channel axis. The final values of the minor (∥)/major (⊥) occupancies are 0.0741/ 0.0925(11), a ratio of ∼44.5:55.5, and similar to that found for 1_II. Solid-state NMR studies above the transition temperature suggested that the parallel/perpendicular ratio was 37:63.28,29 (C) Topotactic Relationships between 1_I and 1_II. Experimental verification of the topotaxy, along with the preparation of static and dynamic overlay figures, proceeds in a manner similar to those examples discussed previously.7 In the present case there are three processes to consider, involving transformations from the mother phase to each of the three twin-component daughters. One must start with a *.p4p file E

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Figure 4. (a) Aligned projections down −c of polymorphs 1_II (above), and 1_I, Twin Law I [60.0%]; (b) aligned projections down c of polymorphs 1_II (above), and 1_I, Twin Law 2 [60.0%]; (c) aligned projections down -c of polymorphs 1_II (above), and 1_I, Twin Law 3 [60.0%].

satisfactory solution may be obtained for the room-temperature material.34 This is a likely consequence of the fact that the lowtemperature form has axial Br exclusively, while the roomtemperature form is either a mixture of axial and equatorial forms, and/or there has been significant reorientation of the guest. Once again, the results are consistent with those obtained recently by the Harris group.35

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Experimental detail for X-ray data collection, solution, and refinement for polymorphs of 1_I and 1_II; topotactic transformation matrix and inverse from output of program TOPO and *.p4p files for compounds 1_I and 1_II (twin component 1). Interested readers may obtain a copy of program TOPO, which must be run on a PC in a DOS window, at http://www.xray.chem.brandeis.edu (PDF)

ASSOCIATED CONTENT

Accession Codes

S Supporting Information *

CCDC 1577933−1577934 contain the supplementary crystallographic data for this paper (polymorphs 1_I and 1_II). These data can be obtained free of charge via www.ccdc.cam.ac.uk/ data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre,

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b01406. Files FcTU3_1.pptx, FcTU3_2.pptx, FcTU3_3.pptx, providing animations associated with the observed phase transformation (ZIP) F

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(22) Betteridge, P. W.; Carruthers, J. R.; Cooper, R. I.; Prout, K.; Watkin, D. J. J. Appl. Crystallogr. 2003, 36, 1487; Prout, C. K.; Pearce, L. J. CAMERON, Chemical Crystallography Laboratory, Oxford, UK, 1996. (23) Donnay, G.; Donnay, J. D. H. Can. Mineral. 1974, 12, 422−425. (24) Foxman, B. M. OMEGA v2.10, A Program for Calculation of Twin Laws; Brandeis University, 2017; http://www.xray.chem.brandeis.edu/ . (25) Sorai, M.; Ogasahara, K.; Suga, H. Mol. Cryst. Liq. Cryst. 1981, 73, 231−254. (26) Gibb, T. C. J. Phys. C: Solid State Phys. 1976, 9, 2627−2642. (27) Lowery, M. D.; Wittebort, R. J.; Sorai, M.; Hendrickson, D. N. J. Am. Chem. Soc. 1990, 112, 4214−4225. (28) Nakai, T.; Terao, T.; Imashiro, F.; Saika, A. Chem. Phys. Lett. 1986, 132, 554−557. (29) Heyes, S. J.; Clayden, N. J.; Dobson, C. M. J. Phys. Chem. 1991, 95, 1547−1554. (30) Drew, M. G. B.; Lund, A.; Nicholson, D. G. Supramol. Chem. 1997, 8, 197−212. (31) Schröder, L.; Watkin, D. J.; Cousson, A.; Cooper, R. I.; Paulus, W. J. Appl. Crystallogr. 2004, 37, 545−550. (32) Nguyen, A. N. Senior Honors Thesis, Brandeis University, 2014. (33) Pan, Z.; Desmedt, A.; MacLean, E. J.; Guillaume, F.; Harris, K. D. M. J. Phys. Chem. C 2008, 112, 839−847. (34) Batson, I. S. Senior Honors Thesis, Brandeis University, 2016. (35) Palmer, B. A.; Kariuki, B. M.; Morte-Ródenas, A.; Harris, K. D. M. Cryst. Growth Des. 2012, 12, 577−582.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bruce M. Foxman: 0000-0001-5707-8341 Author Contributions

The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Drs. David Watkin and Richard Cooper for helpful discussions on refinement/twinning and matrix transformation issues. The approach described here had its origins in thoughts that developed during the final months of a grant from the National Science Foundation (DMR-0504000), and we are grateful for the support of the initiation of a new direction in our program.

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REFERENCES

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DOI: 10.1021/acs.cgd.7b01406 Cryst. Growth Des. XXXX, XXX, XXX−XXX