Experimental Establishment of MotherâDaughter ... - ACS Publications

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Experimental Establishment of Mother−Daughter Orientation Relationships and Twinning Effects in Phase Transitions: A Great Legacy from Jack Gougoutas and Peggy Etter Published as part of the Crystal Growth & Design Margaret C. (Peggy) Etter Memorial virtual special issue Shai R. Posner, Logan C. Lorson, Aaron R. Gell, and Bruce M. Foxman* Department of Chemistry, MS 015, Brandeis University, Waltham, Massachusetts 02453-2700, United States S Supporting Information *

ABSTRACT: A simple procedure, with an available program, may readily be used to establish the three-dimensional relationships between a mother and daughter phase, where mother and daughter are either two different phases of a material or a reactant and product in a solid-state transformation. The only requirements are that (i) the process involves a crystal-to-crystal transformation, and (ii) the experiment must be carried out without changing the alignment of the mother crystal. Application of the method supports the inferred alignment of mother and daughter phases in the published structures of two polymorphs of 4-cyanopyridinium perchlorate monohydrate 1. A new low-temperature, monoclinic polymorph of ferrocenium tetrafluoroborate 2 is produced when the known orthorhombic polymorph is cooled from 173 to 120 K. The major features of the transformation include “conservative twinning” and a modulation of the structure along the crystallographic b direction upon cooling. Redetermination of the structure of the low-temperature polymorph of ferrocenium hexafluorophosphate 3 reveals that the phase change is accompanied by reproducible four-component twinning, providing a proper explanation for the previously reported, very high R-factor of 12.4%. Included tutorial information on the process will assist the reader in obtaining topotactic relationships, as well as in preparing figures and animations describing phase transitions or reactions.

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INTRODUCTION Crystal-to-crystal two-phase transformationseither involving reactions or solely phase changespresent a dual challenge: one must not only determine the detailed orientation between mother and daughter phases, but also, more often than not, resolve the complex twinning phenomena that accompany the process. In this case mother and daughter phases are either two different structures determined as part of a phase transition study or are reactant and product, respectively, in a solid-state reaction. In the present work, we reflect on how the orientation challenge was met over 40 years ago by Jack Gougoutas and Peggy Etter, and provide protocols, as well as a convenient program, for obtaining the orientation relationships between mother and twinned daughter phases. Finally, we examine two illustrative examples of twinning that occur during phase transitions. In the 1970s, we began an investigation of crystal-to-crystal solid-state transformations, focusing on a series of solid-state polymerization reactions discovered by Walton and Whyman.1 As we repeated Walton and Whyman’s studies, with a view to learning about the crystallographic nature of the transformations, it soon became apparent that the reactions could be described as topotactic crystal-to-crystal transformations.2 In © 2015 American Chemical Society

a topotactic process, a single crystal of a starting material is converted into a pseudomorph3 containing one or more products in a definite crystallographic orientation; the conversion takes place throughout the entire volume of the crystal.2 At that time, the literature did not contain many papers describing topotactic processes in molecular crystals. Fortunately, the group led by J. Z. Gougoutas produced an extensive series of papers on both the synthetic and crystallographic aspects of topotactic transformations, mainly concerning organic polyvalent iodine compounds.3,4 We read the papers avidly and learned a great deal by comparing and contrasting our work to that of Professor Gougoutas and his students. One of my favorite papers at that time, remaining high (and highly recommended) on my (BF) list even today, was a single-author paper by Peggy Etter, a detailed study of the topotactic reactions of two polymorphs of 1-methoxy-1,2-benziodoxolin3-one.3 The elegant paper described, in detail, how irradiation of the orthorhombic polymorph led to formation of four “conservatively twinned”5 crystalline product phases, ordered Received: April 8, 2015 Revised: May 26, 2015 Published: June 3, 2015 3407

DOI: 10.1021/acs.cgd.5b00487 Cryst. Growth Des. 2015, 15, 3407−3416

Crystal Growth & Design

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volume of the crystal.2 Thus, topotaxy pertains to either a single crystal to single crystal process (a solitary daughter phase is produced) or a process during which the mother phase is converted into more than one daughter (twinned phases are produced). Thus, in order to keep the discussion general, we will term the processes described in the manuscript as “crystalto-crystal”. In fact, in the present work, all the transformations studied involve twinned product phases. The important point is that, for topotactic transformations, the diffraction properties of the daughter phase allow the orientation(s) of the mother and daughter phases(s) to be established experimentally, as described in the following discussion. In the 1970s the alignment of mother and daughter phases in molecular crystals was established through examination of aligned Weissenberg or precession photographs.3−7 The analysis led to the following interlattice relationship, which is important in interpreting the topotaxy observed in the experiment (symbols from the 1976 article are used here):3

such that iodine-containing planes of the reactant and each of the four product lattices are mutually parallel and have virtually the same ∼4 Å interplanar spacing.3 In 1978, I (BF) met Peggy at ICCOSS V, held here at Brandeis, and we began a friendship and a set of inspiring scientific dialogues that lasted until her untimely passing in 1992. After some initial success in topotactic thermal reactions,6,7 we turned our attention to γray-induced radical reactions in solids. The bulk of the transformations involved solid-state oligomerization reactions that led to amorphous materials.8,9 However, most recently, we explored γ-ray induced, stereospecific oligomerizations of crotonate salts and established that the geometric course of hydrogen atom transfer in the solid state is topochemical, stereospecif ic, and not the result of a random process.10,11 In the second decade of the new millennium, our 60Co γ-ray source was in its eighth-to-ninth half-life, and it was not feasible to acquire a new source, forcing a phaseout of further projects in solid-state radical chemistry. We then decided to return to studies of crystal-to-crystal, thermally induced reactions and/or phase transformations. At the outset, we faced a dilemma: in the 1970s the alignment of reactant and product (“mother” and “daughter”) phases was established using X-ray photographic techniques, viz., comparison of axial relationships of carefully aligned samples on Weissenberg or precession photographs, taken before and after the transformation. While a modern diffractometer produces no shortage of images, one does not work with aligned samples, and thus the images cannot be used directly to establish relative orientations. However, using the approach described by Gougoutas et al.4,5 and by Etter,3 it is straightforward to carry out analyses identical to those done in the 1970s. The technique is simple and its application provides an opportunity to experimentally establish the orientation relationship between a mother phase and one or more daughter phases or twin orientations. In the present contribution we describe the methodology, simple mathematics, and a program (available from the authors) that simplifies the calculation steps and provides all necessary information to establish orientation relationships and provide an accurate method to visually overlay mother and daughter packing diagrams. Taking a lead from Peggy Etter’s presentation style, the paper combines the scientific results with a tutorial approach.3

bi = φija j

where φij is the topotactic transformation matrix, while bi and aj are the direct basis set vectors for the product and reactant lattices, respectively. We refer the interested reader to Etter’s paper for other elements of the theory and an interesting historical account of how φij was derived from observations on X-ray photographs.3 In the present day, our approach first centered on the use of the original CAD-4 command set, as implemented in the CAD4PC software,12 which may still be run on a modern PC! For example, after entering the orientation matrix (taken from a *.p4p file obtained using our Bruker-Nonius Kappa-Apex2 instrument) for a mother phase, we could use the HB command (hkl to “bisecting setting” angles: θ, φ, χ) to get the setting angles of, for example, 100, 010, and 001 for the mother phase. Then, after cooling our crystal, and observing appearance of the daughter unit cell, we enter the orientation matrix of the daughter crystal into CAD4-PC and use the BH command (“bisecting setting” to hkl), along with the original 100, 010, and 001 angles settings from the mother phase. The resultant values show the correspondence between mother and daughter vectors before and after the transformation. While this worked beautifully, we imagined that the use of an older, though elegant, program would discourage general adoption by the community. Further, we had not yet solved the problem of how to obtain the topotactic transformation matrix, φij. The orientation matrix for a crystal mounted on a diffractometer has been part of standard printed output for many decades and now appears in one or more files, either in one or both of *.cif or *.p4p files. Thus, we decided to write a program that, in its initial incarnation, would read *.p4p files each of a mother and daughter phase, automatically calculate angles between all nine combinations of 100, 010, and 001 mother vs daughter vectors, and further, allow (a) the calculation of the corresponding values for h, k, and l for a daughter phase referenced to the mother phase; (b) the calculation of the corresponding values for h, k, and l for a mother phase referenced to the daughter phase; and (c) the angle between a specific h, k, l combination in the mother phase and any chosen h, k, l combination in the daughter phase. Finally, the program would provide the opportunity to perform the calculations either in reciprocal space or direct space. After reading in two *.p4p files, the program automatically calculates the diffractometer coordinates (cmx, cmy, cmz) for an axial hkl set

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RESULTS AND DISCUSSION Gougoutas’ original paper on the specification of topotactic alignments appeared in 1972 and presented an elegant, straightforward methodology for specifying the orientation of mother and daughter phases.5 A later detailed analysis of the topotaxy of 1-methoxy-1,2-benziodoxolin-3-one, along with a step-by-step methodology, and an appendix containing the mathematical relationships was published by Etter in 1976.3 These two papers are essential reading for any scientist interested in establishing, by experiment, the alignment of a mother phase and one or more daughter phases arising from a crystal-to-crystal solid-state transformation. Despite their importance, the papers have been cited only 15 and 11 times, respectively. As we returned to the field of topotactic transformations in 2010, we sought to use modern diffractometry to solve the problem. It is important here to repeat the definition of topotaxy so that a critical point may be addressed. In topotaxy, a single crystal of a starting material is converted into a pseudomorph3 containing one or more products in a definite crystallographic orientation; the conversion takes place throughout the entire 3408



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Table 1. Program TOPO Output for the Transformation between Polymorphs 1_I and 1_II

(in reciprocal or direct space) of the mother crystal, using Rm, the orientation matrix for the mother crystal:

and this information also appears in the program output. Below, we illustrate how the technique and program (TOPO) may be used, by applying the method to three literature examples: (A) 4-cyanopyridinium perchlorate monohydrate 1, where the authors correctly hypothesized the mother−daughter alignment but did not experimentally establish the orientation relationships or topotactic transformation matrix between mother and daughter phases;14 (B) ferrocenium tetrafluoroborate 2, a correct structure determination carried out at 173 K, which undergoes a previously undiscovered phase transition between 173 and 120 K;15 and (C) ferrocenium hexafluorophosphate 3,16 which reportedly undergoes a phase transition at 143 K, and our results are at variance with the published structure at low temperature.16b In addition to the two chosen examples, compounds containing ferrocene or ferrocenium cations have a rich history of phase transformations, and preliminary experiments on a number of compounds15−18 suggested that the present examples would illustrate many of the important features that we wished to explore. (A). 4-Cyanopyridinium Perchlorate Monohydrate. A search of the Cambridge Structural Database19 for phase transitions revealed many examples. 4-Cyanopyridinium perchlorate monohydrate was chosen, as the correspondence between mother and daughter phases appeared to be correct,

⎛ hm ⎞ ⎛ cmx ⎞ ⎜ ⎟ ⎜c ⎟ ⎜ my ⎟ = R m⎜ k m ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ cmz ⎠ ⎝ lm ⎠

After getting the coordinates, we then use the inverse of the orientation matrix for the daughter crystal, R−1d, to obtain the correspondence between the indices of the mother crystal referenced to the daughter unit cell: ⎛ hd ⎞ ⎛ cmx ⎞ ⎜ ⎟ −1 ⎜ c ⎟ ⎜ kd ⎟ = R d⎜ my ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ cmz ⎠ ⎝ ld ⎠

With the above information in hand, one can obtain direction cosines and calculate angles between mother and daughter vectors as well. As we wrote the program in g95 Fortran 95,13 it became obvious that calculation of the topotactic transformation matrix was a simple affair: φij = R−1dR m 3409



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this is shown in Figure S-1, Supporting Information. Figure 1 shows the result, with both phases correctly aligned according

although the alignment was not established experimentally. Further, we thought that the present example would allow the orientation relationships between the two known enantiotropic polymorphs to be established without carrying out two complete data collections. Enantiotropic polymorphs undergo reversible phase transformations upon variation of T and P.20 The salt was synthesized from HClO4 and 4-cyanopyridine, and recrystallized from water. A single crystal was mounted on a glass fiber using epoxy cement. The Bruker Apex2 software (Evaluate Unit Cell option) was used to collect only 36 frames (10 s, 0.3° scans for each set) at 294 K and at 260 K. Unit cells consistent with literature values were readily found in each case, and the *.p4p files (cn294.p4p and cn260.p4p, available in Supporting Information), containing orientation matrices, were saved in each case. These were read by the program TOPO, and the initial results appear in Table 1 (only part of the dialogue and output are shown). The user simply provides the mother and daughter *.p4p files, and the program prints the topotactic transformation matrix and calculates intervector angles; the angles between mother and daughter reciprocal axes (or direct-space planes) are highlighted for the 100, 010, and 001 reciprocal lattice vectors. Clearly, for the settings observed for mother and daughter unit cells during the experiment, (a*)m is parallel to (−a*)d, and (b*)m is parallel to (−b*)d. The two 001 directions are not parallel; thus, the user needs to learn what the 001m direction corresponds to in the daughter phase; the result is obtained using the “md” option. We learn that the −102d reciprocal lattice vector is parallel to 001m (or (001)m is parallel to (−102)d).21 The authors observed that 1 transforms from the orthorhombic system, space group Pnma, with (polymorph 1_I) a = 16.436, b = 7.664, c = 7.537 Å; V = 949.4 Å3, to the monoclinic system (polymorph 1_II), space group P21/c, a = 17.825, b = 7.617, c =15.163 Å; β = 115.08°; V = 1864.6 Å3. The topotactic transformation matrix, with a determinant of approximately 2 and a doubling of the c axis, is consistent with that observation.14 The authors present packing diagrams along the c axis that show the correct alignment of mother and daughter phase; the same diagrams are readily produced with Mercury using the structures deposited in the CSD (PEXVOE (Pnma) and PEXVOE01 (P21/c)).19,22 Since no experimental verification was provided, we must assume that an educated, “visual best fit” was the method used. In fact, our analysis demonstrates that, experimentally (refer to Table 1), planes (100)m and (100)d are parallel, while (010)m and (010)d are parallel. We strongly recommend that experimental verification of alignment always be carried out whenever a phase transition is studied without changing the crystal position between the mother and daughter measurements. As an example of how to use the results for experimental verification, let us examine how we might use the data to correctly produce a different (experimentally verified) view, for example, along the b direction. To produce the best diagrams, it is important to keep all positive and negative signs as they appear in the output. Thus, planes (1 0 0)m and (−1 0 0)d are parallel, and planes (0 0 1)m and (−1 0 2)d are parallel. Using the CSD PEXVOE.cif and PEXVOE01.cif files,19 we open two instances of Mercury.22 In the first, using PEXVOE, we create red (1 0 0)m and blue (0 0 1)m planes, while in the second (PEXVOE01) we create red (1 0 0)d and blue (−1 0 2)d planes. We will use the two sets to correctly align the two polymorphs. The two plane sets must have the same orientation; for clarity,

Figure 1. Aligned projections down b of polymorphs 1_I (above; c across, a down) and 1_II (below; c across, -a down).

to the experimental observations. Rather than creating an overlay of the two structures, a two-frame “movie” shows the resulting molecular displacements quite effectively. To create the “movie”, one enters each drawing into a two-slide Power Point presentation, moving either drawing left or right and up or down as necessary in order to obtain an appropriate superposition. The two drawings may then be cycled in Power Point (see Supporting Information, file cg5b00487_si_004.pptx). Significant changes in hydrogen bonding are apparent from viewing the two frames; indeed, the authors discuss this in detail in their presentation.14 The authors of the original paper discovered that the lowtemperature polymorph (LT) was twinned, with twin law (−1 0 −1/0 −1 0/0 0 1); the scale factor(s) for the twin components was not reported in the paper or in the original deposited cif file (CCDC 605278).19 We find the LT form 1_II to be a TLQS (non-merohedral) twin,23 with a low obliquity of 0.092°.24,25 Obliquity (ω) is a measure of the degree of nonmerohedry; briefly, ω may be defined as the angle between a twin axis [hkl] and the normal to the twin plane (h′ k′ l′).24 Twins with obliquity greater than ca. 5° are rarely observed.23 Polymorph 1_II is likely an example of a Lonsdale twin, where the twinning may be due to geometrical relationships between the parent crystal and the (secondary) twin individual of the product rather than between the main and secondary twin individuals themselves.26 Gougoutas discusses the special case of a Lonsdale twin in the context of solid-state reactivity;5 specifically, that when the reactant crystal structure contains several crystallographically equivalent lattice networks of identical molecular arrangements, growing product phases may be produced in a twin relationship. The geometrical 3410



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relationship necessarily would be a point-group symmetry operation of the reactant lattice.5 Gougoutas terms this phenomenon conservative twinning, and we have found his concept to be extremely useful, both in our earlier studies of solid-state reactivity,6,7 as well as in recent studies of twins produced during a phase transition. (B). Ferrocenium Tetrafluoroborate. In order to illustrate application of the techniques of topotactic analysis to a new example, we grew crystals of ferrocenium tetrafluoroborate 2. The structure determination of 2 had been carried out at 173 K in 2007. We examined the unit cell dimensions near room temperature and found a similar, Ccentered orthorhombic unit cell to that found by Lerner et al.15 At 173 K, our measurements also agreed with the earlier findings. However, at 120 K, a new unit cell was observed; the new cell appeared to be orthorhombic, C-centered, with a = 14.890, b = 23.781, c = 12.008 Å, representing a quadrupled unit cell compared to the 173 K unit cell (cf. values in Table 2).

Figure 2. View of the cation and anion in polymorph 2_I (50% probability ellipsoids).

Table 2. Crystallographic Data for Compound 2 compound

2_I

2_II

chemical formula a, Å b, Å c, Å β, 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

C10H10BF4Fe 7.4665(4) 11.9467(5) 12.0974(7) 90 1079.09(6) 4, 0.25 272.84 Cccm 173(1) 0.71073 1.679 1.417 27.97 0.76−0.83 0.0419 0.1127 1.041 689, 562 42

C10H10BF4Fe 7.0121(2) 12.0018(4) 12.6356(5) 94.0046(19) 1060.79(4) 4, 1 272.84 P2/n 120(1) 0.71073 1.708 1.442 30.06 0.76−0.83 0.0350 0.0887 1.000 4735, 3445 105

Figure 3. View of the cations and anion in polymorph 2_II (50% probability ellipsoids). For a complete description of the disorder not shown here, see Figure S-2.

one-half ferrocenium cation on a crystallographic center of symmetry, and a tetrafluoroborate anion on a general position. In both structures the Fe and the C atoms are disordered; the disorder is evident in the published 173 K structure as well.15 We were unable to successfully model the disorder in the 173 K structure. In 2_I, the Fe atom and C atoms have large U33 components ≈ 3−4× those of the U11 or U22 (Figure 2), while in 2_II, the corresponding atoms have large U22 ≈ 1.5−2× those of the U11 or U33 components (Figure 3). As described below, analysis of the topotaxy shows that (001)m is parallel to (0 −1 0)d; thus, while the disorder is maintained, it appears to be somewhat less in the low-temperature polymorph. A large peak near Fe(1) indicated the presence of ca. 3.7% of a minor component of a disordered ferrocenium cation related to the major component by the noncrystallographic operation (x, −y, z). The structure was refined with the noncrystallographic symmetry constraint applied to the ferrocenium ion associated with Fe(1). For clarity, the disordered molecule is not shown in Figures 3 and 4, but is illustrated in Figure S-2. Experimental verification of the topotaxy provides additional insight, both to the value of the technique itself, and to the structural aspects of the phase transition. For the structure 1 polymorphs, the authors could infer the alignment from either inspection of the structures or an examination of the similarity of cell constants. In the present case, the cells for the two polymorphs appear similar, but the alignment is more complex.

R = ∑||Fo| − |FC||/∑Fo. bRw = [∑w(|Fo| − |FC|)2/∑w|Fo|2]1/2. cS = [∑w(|Fo| − |FC|)2/(n − m)]1/2.

a

The structure was originally solved in space group Ccca, but a better solution could be obtained in the unlikely/rare space group C222; in both cases there were problems with systematic absences. Considering that the 120 K polymorph was likely a conservative twin,5 a satisfactory solution was found in the twinned monoclinic space group C1121/a, which was then transformed to a standard setting in space group P2/n (Table 2). The crystal is a (∼1:1) TLQS conservative twin5 rotated about the 101 reciprocal direction, with very small obliquity (ω = 0.02°) and twin law (0.5 0 0.5/0 −1 0/1.5 0 −0.5). The small obliquity appears to be an important influence on the nearly equal abundance of the twin components. In the 173 K structure (Polymorph 2_I) the asymmetric unit (Figure 2) contains one-quarter each of a ferrocenium cation on a crystallographic 2/m position, and a tetrafluoroborate anion on a crystallographic 222 position. The asymmetric unit of the 120 K structure (Polymorph 2_II, Figure 3) contains one-half ferrocenium cation on a crystallographic 2 position, 3411



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establish the orientation relationships between the mother and daughter phases. The cell constants (Table 3) are in good agreement with values obtained earlier.16 Our results for polymorph 3_I differ Table 3. Crystallographic Data for Compound 3

Figure 4. Aligned projections down b of polymorphs 2_I (above; c across, reciprocal 1 −1 0 down) and 2_II (below; b across, c down).

compound

3_I

3_II

chemical formula a, Å b, Å c, Å β, 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

C10H10PF6Fe 13.4125(2) 9.5318(2) 9.4855(2) 93.200(1) 1210.79(3) 4, 1 331.00 P21/c 295(1) 0.71073 1.816 1.431 30.00°; 0.84−0.85 0.0456 0.1598 0.995 3519, 1945 212

C10H10PF6Fe 13.3922(5) 9.2457(3) 9.3076(3) 96.840(2) 1144.27(4) 4, 1 331.00 P21/c 120(1) 0.71073 1.921 1.514 30.05°; 0.83−0.84 0.0364 0.0772 0.961 3333, 2280 165

R = ∑||Fo| − |FC||/∑Fo. bRw = [∑w(|Fo| − |FC|)2/∑ w|Fo|2]1/2. cS = [∑w(|Fo| − |FC|)2/(n − m)]1/2.

a

Use of TOPO (output available in Supporting Information) shows that the alignment pairs are (1 0 0)d and (−1 −3 0)m; (0 1 0)d and (0 0 −1)m; (001)d and (1 −1 0)m. A view of corresponding pairs in MERCURY22 suggested that the most interesting view was that based on the (010) and (001) daughter planes, presented in Figure 4. Inspection of Figure 4 reveals that polymorph 2_II shows a modulation of the structure along the crystallographic b direction. This is most apparent when the correctly overlaid structures are cycled (as a two-frame “movie”) in Power Point (see cg5b00487_si_005.pptx in Supporting Information). (C). Ferrocenium Hexafluorophosphate. Ferrocenium hexafluorophosphate 3 is trimorphic; X-ray structure determinations of a high-temperature form at 360 K,16a a roomtemperature form at 299 K,16a and a low-temperature form at 143 K16b have been carried out. In this paper we will adopt the polymorph number assignments presented previously and attach the prior Roman numeral identifications to our compound number (thus HT form 3_III, RT form 3_I, LT form 3_II). We decided to reinvestigate only the roomtemperature to low-temperature transition. We were intrigued both by the high R-factor for the published structure of 3_II and by the authors’ comments that “The overall quality of X-ray data collected on organometallic crystals that undergo twophase transitions within a small temperature interval cannot be compared with those obtainable with normal, well-behaving, crystals”, and other subsequent comments in footnote 8b.16b It seemed very likely that the low-temperature phase was twinned. Tools such as DIRAX,27 used in the past, had led us to explain twinning, and fortunately, a few decades ago, allowed us to better understand complex diffraction patterns for crystals undergoing solid-state reactions.28 Thus, we decided to reexamine the phase transition by carrying out the structure determination at 295 and 120 K in order to experimentally

from the published structure16a only in that we modeled disorder in the Cp ring bonded to Fe(1) (see Figures 5 and S-

Figure 5. View of the cations and anion in polymorph 3_I (50% probability ellipsoids). For a complete description of the disorder not shown here, see Figure S-3.

3). The asymmetric units of both polymorphs contain two halfmolecules of cation, each on crystallographic centers of symmetry, and one anion on a general position. For polymorph 3_II (Figure 6), routine solution of the structure led to a conventional R-value of ca. 12%, very similar to that observed previously.16b Simulated precession photographs (Figure 7) suggested a possible tripling of the a axis, but trial solutions showed little improvement over the smaller cell. A plot of Fo vs Fc showed many reflections for which Fo > Fc, a likely indication of twinning. Thus, we carried out a ROTAX analysis of the structure,29 a standard option in the Oxford University Crystals for Windows package.30 Among the ROTAX choices was a rotation about the reciprocal 100 direction, a common twinning direction for a monoclinic crystal. Application of the corresponding twin law led to a preliminary R-value ca. 5.3%. However, it was clear that the model was incomplete, as the Fo 3412



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reproducibility required testing. Thus, a new crystal was grown and selected, and the experiment was repeated in full. The fresh crystal was measured at 240 K, 120 K and, again, at 240 K after the low-temperature experiment. The two 240 K results were identical, confirming the idea that the transition is enantiotropic, and the crystals remain undamaged after a return to room temperature. At 120 K, the crystal is again polymorph 3_II, a four-component twin, with scale factors for the components very similar to the previous observation: 0.8023(18), 0.1428(15), 0.0273(9), and 0.0275(13). The reproducible, four-component twinning is clearly not an example of a Lonsdale26 or conservative twin,5 as the transformation occurs from monoclinic P21/c to the same crystal system and space group. At this time we have no speculation to offer on the reason for such complex twinning. The analogous salt, Co(C5H5)2PF6, is isomorphous,16b and preliminary experiments suggest that it undergoes a very similar twinning upon cooling.32 Experimental verification of the topotaxy, along with the preparation of static and dynamic overlay figures, must proceed in a manner different from the previously discussed examples. In the present case there are four processes to consider, involving transformations from the mother phase to each of the four twin-component daughters. One must start with a *.p4p file containing all four daughter orientation matrices and edit the file to produce four *.p4p files, each with the appropriate daughter matrix ordered first in the list (in its present form the program only reads the first orientation matrix). Apart from that procedural issue, we proceed as before. The TOPO-guided analysis of the topotaxy reveals a rather complicated set of relationships, as shown in Table 4. The before-and-after paired illustrations are shown in Figure 8a−d for transformations of each of the four components (see also the animations of each change in Supporting Information, files cg5b00487_si_006.pptx through cg5b00487_si_009.pptx). The four twin laws and their scale factors are ([1 0 0/0 1 0/0 0 1], 0.7769(15); [1 0 0.343/0 −1 0/0 0 −1], 0.1526(12); [−1 −0.168 −0.166/0 0 1/0 1 0], 0.0365(8); [−1 0.173 −0.173/0 0 −1/0 −1 0], 0.0340(11)). Now, recall that β for the mother crystal is 93.2° and for the daughter phase is 96.8°. For component 1, the major motion is reorientation of c or a*, an axial shift of ca. 3.6°, while for component 2, the sense is reversed relative to the mother crystal, and c or a* must reorient by ∼10° (i.e., 3.2 + 6.8°, which is readily confirmed in the TOPO output files in the Supporting Information). The reorientation difference likely accounts for the larger amount of twin component 1, relative to that for component 2, found in the product. The latter two twin laws, equal within experimental error, are related (approximately) to one another through application of the second twin law, which suggests that twin operations 3 and 4 are a consequence of a minor third component being “twinned” by the second operation, to produce an equal amount of component 4. The four twin laws represent a closed set by multiplication. As mentioned earlier,

Figure 6. View of the cations and anion in polymorph 3_II (50% probability ellipsoids).

Figure 7. Simulated hk0 precession images of polymorphs 3_I (294 K) and 3_II (120 K) (h down, k across).

vs Fc plot was still unsatisfactory. Repeated attempts, using various trial twin laws, demonstrated that two additional twin laws, representing rotations about [0 1 1] and [0 1 −1], were required to complete the description. Adding twin laws for components 3 and 4 reduced the conventional R factor to 4.4% and 3.9%, respectively. The same set of twin laws could be found using CELL_NOW,31 but the ROTAX procedure provided a more efficient and straightforward solution in this particular case. The option to vary the overlap parameter manually (“twintolerance” parameter in CRYSTALS;28,29 final value 0.016 Å−1) also worked extremely well in the present example. The final result, a four-component twin, had scale factors of 0.7769(15), 0.1526(12), 0.0365(8), and 0.0340(11) for the major component, and rotations about 100, [0 1 1] and [0 1 −1], for the latter three components, respectively. The final conventional R-factor, after modeling disorder for the Cp ring bonded to Fe(1), was 0.0364. The obliquities for the latter three rotations are 0.19°, 4.58°, and 4.58°, respectively. The low percentage of the twins arising from [0 1 1] and [0 1 −1] rotations corresponds well to the observation that twins with obliquity greater than ca. 5° are rarely observed.23 The fourcomponent twinning seemed so unusual and rare to us that its Table 4 twin component 1 2 3 4

topotaxy (1 (1 (1 (1

0 0 0 0

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0)m 0)m 0)m 0)m

|| || || ||

(−1 0 0)d; (0 1 0)m || (0 1 0)d; (0 0 1)m || (1 0 −12)d (−1 0 0)d; (0 1 0)m || (0 −1 0)d; (0 0 1)m || (−1 0 4)d (1 0 0)d; (0 1 0)m || (−1 0 6)d; (0 0 1)m || (0 −12 1)d (1 0 0)d; (0 1 0)m || (1 0 −6)d; (0 0 1)m || (0 12 1)d DOI: 10.1021/acs.cgd.5b00487 Cryst. Growth Des. 2015, 15, 3407−3416


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Figure 8. (a) Aligned projections down b of polymorphs 3_I (above; a across, c down) and 3_II, Twin Law 1 [77.7%] (below; a across, c down). (b) Aligned projections down b of polymorphs 3_I (above; a across, c down) and 3_II, Twin Law 2 [15.3%] (below; -a across, c down). (c) Aligned projections of polymorphs 3_I (above; down b; a across, c down) and 3_II, Twin Law 3 [3.6%] (below; down c, a across, b down). (d) Aligned projections of polymorphs 3_I (above; down b; a across, c down) and 3_II, Twin Law 4 [3.4%] (below; down -c, a across, b down).

product in a solid-state transformation. The only requirements are (i) the process involves a crystal-to-crystal transformation, and (ii) the experiment must be carried out without changing the alignment of the mother crystal (or, alternatively, a partially transformed crystal containing both the mother and daughter phases may be used). We strongly recommend that the procedure, or any analogous procedure, be carried outand reportedfor all crystal-to-crystal phase transitions or solidstate reactions studied henceforth. Minimally, the requirements

the small amounts observed for the latter two components correspond well to the observation that twins with obliquity greater than ca. 5° are rarely observed.23

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CONCLUSIONS

We have described a simple procedure that may readily be used to establish the three-dimensional relationships between a mother and daughter phase, where mother and daughter are either two different phases of a material or a reactant and 3414



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for new papers should include orientation matrix data (in *.cif or *.p4p) in the Supporting Information. We note that many (but certainly not all!) solid-state reactions are single-phase transformations, and thus topotactic, with no (or very small) changes in orientation. The present technique has important applications, particularly in two-phase solid-state reactions. Future papers will examine new phase transitions as well as examples of solid-state oligomerization reactions. The results obtained demonstrate the utility of the method, using published data (polymorphs 1_I and 1_II),14 newly discovered phase transitions (polymorphs 2_I15 and 2_II), or incorrect analyses in the literature (correct polymorph 3_I16a and incorrect 3_II16b). The provided tutorial information on assembling correct overlay diagrams and/or two-frame animations will guide the interested reader to prepare figures describing transitions or reactions. In appropriate cases, the products of the transformations should be viewed as conservative twins,5 a special case of Lonsdale twinning.26 The results suggest, not surprisingly, that the relative abundance of a twin orientation also depends on the amount of reorientation of the unit cell, as well as the obliquity associated with a given twin law.

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(2) Dent Glasser, L. S.; Glasser, F. P.; Taylor, H. F. W. Q. Rev. 1962, 16, 343−60. (3) Etter, M. C. J. Am. Chem. Soc. 1976, 98, 5331−5339 Etter defines a pseudomorphic transformation as “one in which the morphology of the reactant crystal does not change during reaction. In a single crystal to single crystal pseudomorphic transformation, the diffraction pattern of the reacting crystal changes but the dimensions and shape of the crystal itself does not (color and density changes often occur also)”. (4) (a) Gougoutas, J. Z.; Clardy, J. C. J. Solid State Chem. 1972, 4, 230−242. (b) Gougoutas, J. Z.; Lessinger, L. J. Solid State Chem. 1973, 7, 175−185. (c) Gougoutas, J. Z.; Lessinger, L. J. Solid State Chem. 1974, 9, 155−164. (d) Gougoutas, J. Z.; Lessinger, L. J. Solid State Chem. 1975, 12, 51−62. (e) Gougoutas, J. Z.; Naae, D. G. J. Solid State Chem. 1976, 16, 271−281. (f) Gougoutas, J. Z.; Chang, K. H.; Etter, M. C. J. Solid State Chem. 1976, 16, 283−291. (g) Etter, M. C. J. Solid State Chem. 1976, 16, 399−411. (h) Etter, M. C. J. Am. Chem. Soc. 1976, 98, 5326−5331. (i) Gougoutas, J. Z. J. Am. Chem. Soc. 1977, 99, 127−132. (j) Gougoutas, J. Z.; Naae, D. G. J. Phys. Chem. 1978, 82, 393−401. (k) Gougoutas, J. Z.; Johnson, J. J. Am. Chem. Soc. 1978, 100, 5816−5820. (l) Gougoutas, J. Z. J. Am. Chem. Soc. 1979, 101, 5672−5675. (5) Gougoutas, J. Z. Isr. J. Chem. 1972, 10, 395−407 In “conservative twinning”, the symmetry of the daughter phase conserves the symmetry of the mother phase via twinning; the concept is fully illustrated later in the present manuscript. (6) Cheng, K.; Foxman, B. M. J. Am. Chem. Soc. 1977, 99, 8102− 8103. (7) Cheng, K.; Foxman, B. M.; Gersten, S. W. Mol. Cryst. Liq. Cryst. 1979, 52, 77−82. Foxman, B. M.; Jaufmann, J. D. J. Polym. Sci., Polym. Symp. 1983, 70, 31−43. (8) Jaufmann, J. D.; Case, C. B.; Sandor, R. B.; Foxman, B. M. J. Solid State Chem. 2000, 152, 99−104 and references therein. (9) Vela, M. J.; Buchholz, V.; Enkelmann, V.; Snider, B. B.; Foxman, B. M. Chem. Commun. 2000, 2225−2226. (10) Hickey, M. B.; Schlam, R. F.; Guo, C.; Cho, T. H.; Snider, B. B.; Foxman, B. M. CrystEngComm 2011, 13, 3146−3155. (11) Shang, W.; Hickey, M. B.; Enkelmann, V.; Snider, B. B.; Foxman, B. M. CrystEngComm 2011, 13, 4339−4350. (12) Schagen, J. D.; Straver, L.; van Meurs, F.; Williams, G. CAD4 Version 5.0; Enraf-Nonius: Delft, The Netherlands, 1989; Chapters II and VIII; see also: http://www.nonius.nl/cad4/manuals/user/ chapter02.html and http://www.nonius.nl/cad4/manuals/user/ chapter08.html. (13) Vaught, A. G95; Mesa, Arizona, 2006; see also http://www.g95. org/index.shtml. (14) Czupiński, O.; Wojtaś, M.; Pietraszko, A.; Jakubas, R. Solid State Sci. 2007, 108−115. (15) Scholz, S.; Scheibitz, M.; Schodel, F.; Bolte, M.; Wagner, M.; Lerner, H. W. Inorg. Chim. Acta 2007, 360, 3323−3329 CCDC refcode: AFALID; original deposition number (for accessing Uij’s): CCDC 632409. (16) (a) Webb, R. J.; Lowery, M. D.; Shiomi, Y.; Sorai, M.; Wittebort, R. J.; Hendrickson, D. N. Inorg. Chem. 1992, 31, 5211−5219. (b) Grepioni, F.; Cojazzi, G.; Draper, S. M.; Scully, N.; Braga, D. Organometallics 1998, 17, 296−307. (17) Paulus, E. S.; Schafer, L. J. Organomet. Chem. 1978, 144, 205− 213. Cotton, F. A.; Daniels, L. M.; Pascual, I. Acta Crystallogr. Sect. C: Cryst. Struct. Commun. 1998, 54, 1575−1578. (18) Hough, E.; Nicholson, D. G. J. Chem. Soc., Dalton Trans. 1978, 15−18. (19) Allen, F. H. Acta Crystallogr. Sect. B: Struct. Sci. 2002, 58, 380− 388. (20) Bernstein, J. Polymorphism in Molecular Crystals; Oxford Science: Oxford, UK, 2002; pp 34−38. (21) Experience to date suggests that, from experiment to experiment, and compound to compound, variations in the observed values of interplanar/interaxial angles may range from as little as 0.3° up to ca. 2°. In part, this depends on (a) the mechanical stability of the mounted crystal; (b) the quality/”singleness” of the crystal at the

ASSOCIATED CONTENT

S Supporting Information *

Crystallographic information (*.cif) files for polymorphs of 2 and 3, including those establishing reproducibility of the transitions for 3. Experimental detail for X-ray data collection, solution, and refinement for polymorphs of 2 and 3, including reproducibility of the transitions for 3; output of program TOPO and *.p4p files for compounds 1−3; figures providing tutorial information and illustration of disorder (32 pages). Power Point files providing animations associated with the observed phase transformations. Interested readers may obtain a copy of program TOPO, which must be run on a PC in a DOS window, at http://xray.chem.brandeis.edu. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.5b00487.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 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 issues, Rob Hooft and Victor Young for kick-starting our ideas on how to approach problems in topotaxy in the 21st Century, Victor Young (again), Simon Parsons, Larry Falvello, Peter White and Howard Flack for helpful discussions on twinning and obliquity, Dan Frankel, Martin Adam, Holger Ott, and Daniel Stern for discussions of CAD-4 and Apex2 diffractometry, and the referees for very helpful suggestions. The present approach 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

(1) Walton, R. A.; Whyman, R. J. Chem. Soc. A 1968, 1394−1398. 3415



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temperatures measured; and (c) the number of data used to obtain the orientation matrix. (22) Macrae, C. F.; Bruno, I. J.; Chisholm, J. A.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Rodriguez-Monge, L.; Taylor, R.; van de Streek, J.; Wood, P. A. J. Appl. Crystallogr. 2008, 41, 466−470. (23) Donnay, G.; Donnay, J. D. H. Can. Mineral. 1974, 12, 422−425 The Donnays’ specification of TLQS (twin-lattice quasi-symmetry; (Friedel’s non-merohedral twinning concept) strongly implies that obliquity also be specified. (24) Friedel, G. Bull. Soc. Fr. Mineral. 1920, 43, 246−295 See also: http://reference.iucr.org/dictionary/Twin_obliquity. (25) Le Page, Y. J. Appl. Crystallogr. 1982, 15, 255−259. Buerger, M. J. Z. Kristallogr., Kristallgeom., Kristallphys., Kristallchem. 1960, 113, 52−56 We thank Dr. Howard Flack for providing a copy of the Le Page program CREDUC81, which provides a convenient and thorough calculation of obliquities. (26) Lonsdale, K. Acta Crystallogr. 1966, 21, 5−7. (27) Duisenberg, A. J. M. J. Appl. Crystallogr. 1992, 25, 92−96. (28) Schlam, R. Ph.D. Thesis, Brandeis University, 1999. (29) Cooper, R. I.; Gould, R. O.; Parsons, S.; Watkin, D. J. J. Appl. Crystallogr. 2002, 35, 168−174. Parsons, S. Acta Crystallogr. Sect D: Biol. Crystallogr. 2003, 59, 1995−2003. (30) Betteridge, P. W.; Carruthers, J. R.; Cooper, R. I.; Prout, K.; Watkin, D. J. J. Appl. Crystallogr. 2003, 36, 1487. (31) Sheldrick, G. M. CELL_NOW, Version 2008/4; Georg-AugustUniversität Göttingen: Göttingen, Germany, 2008. (32) Lorson, L. C. Senior Honors Thesis, Brandeis University, 2013.

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