DOI: 10.1021/cg100338t
Single-Crystal-to-Single-Crystal Reactivity: Gray, Rather than Black or White
2010, Vol. 10 2817–2823
Ivan Halasz*,† Department of Chemistry, Faculty of Science, University of Zagreb, Horvatovac 102a, 10000 Zagreb, Croatia. †Present address: Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany. Received March 15, 2010; Revised Manuscript Received May 17, 2010
ABSTRACT: Single-crystal-to-single-crystal (SCSC) reactions are discussed as a specific case of solid-state reactions. Some shortcomings in the contemporary use of the term are revealed, and directions for research and interpretation of results are suggested.
Introduction Solid-state chemists recognize a special case of solid-state reactions, in which a reactant single crystal yields a product in the form of a single crystal, and this type of conversion is termed a single-crystal-to-single-crystal (SCSC) reaction.1,2 The characteristic which differentiates a SCSC reaction from all other solid-state reactions is that the single crystal maintains its integrity (commonly evaluated on the basis of its shape and transparency) during the reaction.3 Since the majority of solidstate reactions that begin with single crystals result in polycrystalline products, SCSC reactions have for some time been a rarity in solid-state chemistry. This rare status will probably need to be re-evaluated due to an increasing rate of discovery of new systems exhibiting SCSC reactivity. Much interest has been devoted to SCSC reactions based on their potential applications in materials science (e.g. in the reversible sorption and desorption of gases and liquids,4 in the manufacture of highly crystalline organic polymers which would be inaccessible by other routes,5 or as parts of molecular machines6). On the other hand, a large portion of the academic interest in SCSC reactivity arises from the possibilities of mechanistic studies of solid-state reactions, since one is in the position to directly observe how the crystal structure is changing during a reaction via single-crystal-diffraction methods.3b,7,8 Such a direct insight furthers understanding of solid-state reaction mechanisms which, when combined with crystal engineering to obtain desired crystal packing, opens routes to systematic use of the solid state as a medium for conducting chemical reactions.9 That a solid-state reaction might occur by a different pathway and thus yield a different product from the one obtained in solution was recognized as early as in 1918 by Kohlsch€ utter.10 It was later on realized that reactions in crystals can occur wherein a definite relationship is observed between the orientations of crystal lattices of the reactant crystal (mother crystal) and the product crystal (daughter crystal), a phenomenon described by the term topotaxy (such a reaction is said to be topotactic).11,12 In a topotactic reaction, the crystal lattice of the mother crystal determines the orientation of at least one crystallographic axis of the daughter crystal. The distinction between the terms SCSC reaction and topotactic reaction is minor.3a Specifically, a topotactic reaction does not stipulate that the daughter phase
must remain in the form of a single crystal. For example, a crystal may disintegrate but if just one crystallographic axis, e.g. the c axes, of all the newly formed daughter crystallites remains parallel to the c axis of the mother crystal, the reaction is topotactic.13 On the other hand, an SCSC reaction does not necessarily require an orientational relationship between the two lattices, but the daughter phase must be formed as a single crystal.3a There is a bit of confusion in the literature, as some authors use the two terms interchangeably and some prefer to use one rather than the other. Designation of a reaction as a topotactic reaction is more common for inorganic systems, while designation as an SCSC reaction is more common with organic samples. Additionally, if the relative positions and orientations of reacting groups within the mother crystal are such that a specific reaction takes place, the product is said to be formed under the topochemical control.10,14 In such reactions, it is the crystal structure of the mother crystal that determines which chemical reaction can occur most readily and thus directs the formation of often just one product species. Morawetz et al. have listed the criteria whereby a reaction can be classified as a topotactic and/or topochemical reaction.12b In this perspective we will focus on SCSC reactions with an emphasis on the single-crystallinity of the daughter crystal and our examples will be limited to organic solid-state reactions. Our aim here will be to analyze SCSC reactivity in a broader context of solid-state reactions. In doing so we will examine experimental requirements for SCSC designation and, on the other hand, discuss SCSC reactivity regarding the scope of the terms single crystal and polycrystal. Applications and potential benefits of materials exhibiting SCSC reactivity are discussed elsewhere15 and will, thus, not be addressed herein. This Perspective will not describe in detail specific solid-state systems and will also not attempt to give a comprehensive account of single-crystal-to-single-crystal (and topotactic) reactions/transformations, since a number of excellent review articles addressing solid-state reactions, and SCSC reactions as their subset, are available in the literature.16,3a Experimental Requirements for SCSC Reactivity
*E-mail:
[email protected]. Telephone: þ385 1 4606 416. Fax: þ385 1 460 6401.
A solid-state reaction may, in the majority of instances, be classified as an SCSC reaction if the following sequence of events is accomplished: (1) successful crystal structure solution and refinement of the mother single crystal, (2) reaction in the crystal (not necessarily to completion), and (3) successful
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Halasz
Figure 1. The distribution of orientations of coherently scattering domains could in principle determine the position of a sample between A (perfect polycrystal) and B (perfect single crystal). Each line coming out of the sphere represents a crystallographic axis (e.g. the c axis) of one coherently scattering domain. Lines originate in centers of respective spheres, which serve only to give an impression of three dimensionality.
structure solution and refinement of the obtained daughter single crystal. This might seem to oversimplify SCSC reactivity, since it does not consider the structural and chemical properties of a particular system. However, these events constitute the experimental criteria required to categorize a solid-state reaction as an SCSC reaction. Other techniques, e.g. microscopy,17 have also been used to establish SCSC reactivity, but single-crystal diffraction is by far the most frequent one. Can We Quantify the Crystallinity of Solids? For reasons of clarity in this discussion, we define a perfect crystal to be of finite dimensions and within which periodicity is strictly obeyed by whichever chemical entity it is comprised of. We then define (A) a perfect polycrystal (powder) as a collection of a large number18 of microscopic perfect crystals which are randomly oriented relative to one another and (B) a perfect single crystal as a perfect crystal of macroscopic dimensions. Perfect polycrystals and perfect single crystals do not exist in reality. Each real single crystal, which is subjected to a structure determination experiment, has defects19,16f,16g and is mosaic, i.e. consists of many coherently scattering domains slightly differing in their orientation.20 A real polycrystal, apart from possibly possessing a nonrandom distribution of domain orientations, can be constituted only from real microscopic single crystals. For the time being, we neglect the presence of deviations from strict periodicity in a crystal (e.g., defects and lack of order on a crystal’s surface) and concentrate on the distribution of orientations of coherently scattering domains (see Appendix). It is conceivable that some of the microscopic crystals of a real polycrystalline sample align to have the same or similar orientations, thus increasing the preferred orientation of the sample (and that alignment of the microscopic crystals could occur through the entire sample). It is equally conceivable that some of the coherently scattering domains of a real single crystal misalign, introducing more variation in their relative orientations, thus increasing the crystal’s mosaicity (and such misalignment of the domains could also occur throughout the sample). Thus, the distributions of domain orientations in a perfect single crystal and a perfect polycrystal present two extremes (Figure 1) between which there is a gradual change. Increasing the preferred orientation of a polycrystalline sample makes it more single-crystal-like, and oppositely, increasing the mosaicity of a single crystal makes it more polycrystalline-like. Depending upon the variation of relative orientations of coherently scattering domains, a real sample will be closer to either A or B. In other words, every real single crystal (as well as every real polycrystal) could in principle be placed somewhere on the line between A and B. Preferred orientation and mosaicity designate the same phenomenon, but the former is taking a point of view from the side of a perfect polycrystal while the latter from the side of a
perfect single crystal. This notion of crystallinity of a solid sample has significant implications on the potential definition of the term single crystal and thus on the term single-crystalto-single-crystal reaction. During a reaction in a real single crystal, it is a question of how much it may shift toward A (generally, shifting toward B during a reaction is not excluded) and still retain enough of its single-crystallinity to allow for a single-crystal-like data set to be collected and to refine the structure of the daughter crystal. With this in mind, it is clear that the classification of a particular solid-state reaction as an SCSC reaction strongly relies on the method of structure determination used, as well as on the researcher’s judgment as to whether it is appropriate to attempt to refine the structure model with data from the daughter crystal. When it comes to different single-crystal diffraction instruments, the characteristics of the instrument itself may determine whether a sample crystal is suitable as a single crystal or not; similarly, some samples that we are currently in the position to consider as single crystals could not be considered as such 10 years ago. One only has to remember that the size of suitable single crystals is decreasing with the advance of instrumentation and thus the practical usage of the term single crystal is extending to smaller and smaller crystals. Additionally, data processing procedures are becoming increasingly capable of extracting good quality data sets from poor-quality crystals. It is thus conceivable that some solid-state reactions could be in the future classified as SCSC reactions, although contemporary instrumentation and data-processing procedures do not allow such a classification. This would imply the shifting of the single-crystal/polycrystal threshold mark, which is, to begin with, not clearly set (and it would probably be illusory to seek one). To answer the question posed in the section heading, quantifying the crystallinity of a sample requires that it be placed on the A-B line of Figure 1. To our knowledge, there is no methodology that is generally applicable21 for this purpose in the case of a solid sample. Even if there were one, there would still be no simple way to divide samples into two classes and say in this set are single crystals and in that set are polycrystals. When talking about a single crystal and a polycrystal, we are thus dealing with terms with rather diffuse meanings. SCSC Reactivity in Practice The term single crystal is embedded in the chemist’s conceptual framework, and it is common practice to estimate whether a sample is a single crystal purely by visual inspection. However, as we have shown, no clear criteria actually exist to perform such an estimation, and in this context, the integrity of a single crystal (which is said to be retained in an SCSC reaction) is another vague term. A definition of the term single-crystal-to-single-crystal reaction/transformation cannot
Perspective
be given without first having a definition of the term single crystal. We could have a “working” definition of an SCSC reaction based on the experimental requirements listed above, but such a definition will not be of much help if we wanted to understand SCSC reactions better. That single-crystal diffraction is not necessarily an adequate technique for the investigation of solid-state reactions was pointed out by e.g. Thomas16f and Schmidt.14a A feature inherent to X-ray diffraction techniques (for both single crystals and polycrystalline samples) is that the results give the time- and space-averaged crystal structure. This was astonishingly illustrated when the same material was found to have different unit cells and different space groups depending on the radiation wavelength (Cu KR and Mo KR).22,4k Explanation was found in different volumes of coherently scattering domains (about ten times bigger for Cu KR radiation) and thus different structure averaging over space. This example strongly accentuates that the fact of averaging must be kept in mind in all studies and every interpretation of results obtained by X-ray diffraction methods. That is, any change that is observed in the crystal structure is measured as the space- and time-average while the structure may locally exhibit considerable deviations from the average. We find it likely that, since atomic coordinates do not change gradually, but abruptly upon formation of product molecules, any gradual changes in atomic coordinates (as well as perhaps in lattice parameters) as the reaction progresses are a consequence of averaging between coordinates of reactant molecules and product molecules which reside at similar positions in the unit cell. Even though conclusions on absolute atomic movement in various stages of the reaction8 could be valid, further supporting evidence is needed. Explanations for SCSC reactivity are often sought in the similarities between the crystal structures of the mother phase and the daughter phase. The reaction cavity concept states that, among many possible product molecules, the one most likely to be formed is the one which fits best in the cavity that would remain after the reacting molecule(s) are removed from the mother crystal.16c,h In this respect, reactions for which the product molecule approximately fits in the cavity have a greater potential to exhibit SCSC reactivity.23 But this could merely be just one of the prerequisites for SCSC reactivity. We are convinced that the mother crystal’s microstructural (defects) and macrostructural properties (size and morphology), as well as the way the reaction is conducted, greatly influence or even determine its behavior.3a When a product molecule is formed in the mother crystal, its neighbors need to adapt to the change in their surroundings. In fact, the whole crystal adapts to the new environment.24 The misfit of the product molecule in the mother crystal will inevitably exert strain on the mother crystal25 and the pattern and energies of intermolecular interaction will change to a greater or lesser extent. Cooperativity among molecules as product molecules are formed and the daughter crystal grows will influence the overall crystalline behavior,1a,3b,26 as often shown in studies involving calixarenes, a class of compounds frequently studied in the context of SCSC reactivity.4j,l We must also not forget the limitations of diffraction: it does not tell us what is happening locally in the crystal. Large scale movements of molecules on the order of tens of nanometers, presumably due to the stress evolved, have been observed on the surface of crystals even though reaction could have proceeded in an SCSC manner.27 Localized changes within the bulk of a sample cannot at present be well-characterized by
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Figure 2. Crystal breaking during solid-state phase transformation which initiated in an SCSC manner.32,33 The phase boundary (seen in the lower left part of the crystal) could have encountered a defect, or the accumulated strain could have produced the defect by itself, which caused the sudden increase in the rate of the transformation. Reprinted with permission of the publisher (Taylor & Francis Group, http://www.informaworld.com).
diffraction,28 but they could be observable by solid-state NMR spectroscopy.4j,29 That SCSC reactivity is dependent on the characteristics of the reacting crystal and on the experimental conditions may be evidenced by the fact that one can exercise control over such reactions by using a variety of methods, including the following: (i) It has been observed in photochemical solid-state reactions that irradiation of a single crystal with radiation of its absorption tail may promote SCSC reactivity while irradiation with wide range radiation leads to a polycrystalline product.30,1e Also, if there is a large gradient in radiation intensity between the crystal surface and the bulk of the crystal, reaction will advance faster on the surface, increasing the chances of product phase separation.31 (ii) Any mismatch between lattice metrics, densities, and intermolecular interactions will exert strain on the mother crystal, which could cause it to break if an efficient relaxation of strain is hindered. This relates to crystal size, where it is expected that a smaller crystal will relax more efficiently, but also to crystal morphology, as it has been observed that it is more likely for a thin crystal, undergoing a solid state phase transformation, to remain in one piece than for a prismatic one.32 This can be understood if we consider that the accumulating strain can be released through crystal surfaces: thus, in a small or a thin crystal, the surface is always more accessible from the bulk, thus allowing easier dissipation of stress. Regarding the size of reacting crystals, it has been observed that cocrystals of nanoscale dimensions appear intact after a photochemical reaction while bigger crystals show cracks.17a Mnyukh has described beautiful examples of solid-state phase transformations that were initiated and proceeded to a considerable extent in an SCSC manner before the accumulated strain caused crystal cracking (Figure 2).32,33 Had the crystal been thinner or smaller, the transformation potentially could have proceeded in an SCSC manner throughout. We are not aware of any investigations that probe the mechanical properties of organic
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crystals and the effect of these properties on crystal behavior and reactivity. (iii) It seems reasonable to assume that if the reaction is taking place slowly, retention of the single-crystal-like quality of the sample is more likely than if the reaction is taking place rapidly.7c Rapid reactions could also lead to rapid accumulation of strain, thus leading to crystal cracking. In a recent report on solid-state phase transformation of D,L-leucine, it was noted that the number of cracks formed during the transformation were reduced if the transformation proceeded at a slower rate, and it was anticipated that it could be further reduced by additional decreases in transformation rates.34 Therefore, the same chemical reaction in crystals of the same material may or may not proceed in an SCSC manner, depending upon the size or morphology of the crystals or on the way the reaction is conducted. Our understanding of SCSC reactivity will be well founded only when we will be able to understand why a particular change in the way the reaction is conducted results in SCSC reactivity and thus be able to predict which of the experimental conditions need to be modified in a reaction yielding polycrystalline product, in order to observe SCSC reactivity. Consequently, we believe that every solid-state reaction could be made to proceed in an SCSC manner. It boils down to finding the right conditions with which to observe it. A crystal’s characteristics (like its mosaicity) change in the course of every solid-state reaction or phase transition. We believe that this issue should receive more attention than it is given currently. Even though there is no straightforward way to quantify this change, we suggest that reports on SCSC reactivity should at least include information on the mosaicities of the mother and daughter crystals and, if possible, thorough qualitative crystal descriptions during the reaction/ transformation. A great deal about a solid-state reaction/ transformation can be learned just by observing what is happening in the crystal using optical microscopy.32,35,25b For example, one can distinguish if the reaction starts on defects and how it advances. It also allows one to observe if different single crystals behave differently, and importantly, one does not see the averaged image but can distinguish what is happening in the crystal locally, especially if the crystal is transparent. Investigations should also incorporate other techniques which could detect local changes in crystals, such as solid-state NMR spectroscopy. Some reports describe SCSC reactions where the mother crystals cracked during the reaction36 and the crystal structure of the daughter phase was solved by using one of several obtained smaller single crystals. Such a practice could be troublesome. Namely, with advancing instrumental techniques for data collection, we are able to collect single-crystallike data sets with smaller and smaller crystals. Dimensions of crystals that can be used in a single crystal diffraction experiment are now down to 1 μm.37 Crystals of this size constitute what is generally considered a polycrystalline sample.38 Since there is no fundamental difference between a mother single crystal cracking to thousands of tiny single crystals or to several single crystals, one of the thousands of tiny daughter crystals could be used for successful structure determination. Should this be considered as an SCSC reaction? This would clearly be meaningless, and we might quickly conclude that cracking of mother single crystals must preclude any option
Halasz
for SCSC classification. The situation, however, is not as simple. An increase in the mosaicity of the daughter crystal actually shows that the mother crystal cracked but the domains retained similar orientations and still somehow held onto each other.39 This is also the case if a twinned daughter crystal forms.36 A recent study described cracking of a mother single crystal, even quickly after the beginning of the reaction, as a type of nonideal SCSC reaction.40 It must be noted that, in any reaction yielding a polycrystalline product, disintegration of the mother crystal will never happen immediately after the reaction has begun.41 A solid solution with product molecules scattered within the mother crystal or a mother crystal with clusters of product molecules, which are small enough so that the strain they exert can be sustained, will always form initially. The reaction extent when the strain will cause breaking of a particular mother crystal will depend on its microstructural and macrostructural properties. Summary and Outlook We have shown that solid-state reactions that proceed in an SCSC manner and those that yield polycrystals are not the two extremes but that there is rather a whole scope of possible outcomes which will be dependent on crystals’ microstructural and macrostructural properties and the experimental conditions in which the reaction is conducted. The underlying reasons why a particular crystal exhibits SCSC reactivity are many while the current widespread approach to SCSC classification is such that any solid-state reaction for which a daughter crystal (or even a part of it) has been used for data collection using a single-crystal diffractometer is termed an SCSC reaction. Such practice makes SCSC classification directly dependent on the instrument and data processing methodology used, rather than providing an insight into a natural phenomenon. Almost every attempt thus far (that we are aware of) to formulate guidelines for the design of systems exhibiting SCSC reactivity or to explain observed SCSC reactivity has not given due attention to microstructural and macrostructural crystal properties but has put emphasis on similarities between the crystal structures of the mother and daughter crystals.42 We find such an approach to be, at the very least, incomplete. Additionally, techniques that could detect local changes, such as solid-state NMR spectroscopy and optical microscopy, should be more widely exploited in studies of SCSC reactivity. To conclude, we anticipate that SCSC reactivity is not an inherent property of some solid-state reaction but rather that it emerges as a special case in some crystals (not some materials but specific crystals of some materials) when all the conditions are favorable and, thus, needs to be considered in a broader context of solid-state reactivity where the contributions of all the crystals’ properties are to be taken into account. Only after these are well understood will we be able to describe what is happening in crystals on both micro- and macroscale during the reaction, and only then will we be able to fully utilize the solid-state for the preparation of new compounds and new crystals.9 SCSC reactivity could thus play a major role in the future for our understanding of solidstate reactions. Appendix We have previously neglected deviations from strict periodicity but have concentrated only on mosaicity (or preferred
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(2)
(3) (4)
Figure 3. Concepts of perfect single crystal, perfect polycrystal, and perfect amorphous sample and their relationships regarding the distribution of orientations of coherently scattering domains and long-range order.
orientation). Here we will broaden Figure 1 to account for any violations of periodicity. Thus, we define a perfect amorphous sample (C) in which the chemical entities it is comprised of (which include atoms, molecules, molecular complexes as in cocrystals or formula units) assume a completely random orientation and position relative to each other. That is, there is a complete lack of any long-range or short-range order. Of course, a perfect amorphous sample does not exist in reality. Since no real crystal is completely void of defects (at least on its surface), real single crystals and real polycrystals cannot actually lie directly of the A-B line, as was previously assumed, but will be moved from it in the direction of a perfect amorphous sample. Therefore, every sample could in principle be represented by a point within the triangle of Figure 3. If a polycrystal would have more and more defects, it would become closer to an amorphous sample. The same would be valid for a single crystal. A perfect polycrystal can be viewed as a sample in which long-range order is not as long as that in a perfect single crystal. A path from B to C could “visit” A in the following way: imagine only the long-range order in B is reduced (by reducing domain sizes while increasing their number) while periodicity is strictly maintained in each domain. Thus, we arrive to a perfect polycrystal wherefrom C is reached by introducing deviations from periodicity. Acknowledgment. I am truly grateful to Dejan-Kresimir Bucar, Vedran Dunjko, Dr. Krunoslav Uzarevic, Dr. Mirta Rubcic, Arundhuti Sen, Evangelos Krokos, and Lina Zgaga for discussions, support, and comments at various stages of this manuscript. The Ministry of Science, Education and Sports of the Republic of Croatia (Grant No. 119-11913421334) and the Max Planck Society are acknowledged for financial support.
(5)
(6) (7)
(8)
(9)
(10) (11) (12)
(13)
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(1) For some of the pioneering reports on SCSC reactivity, see: (a) Parkinson, G. M.; Thomas, J. M.; Williams, J. O.; Goringe,
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M. J.; Hobbs, L. W. J. Chem. Soc., Perkin Trans. 2 1976, 836– 838. (b) Duesler, E. N.; Wiegers, K. E.; Curtin, D. Y.; Paul, I. C. Mol. Cryst. Liq. Cryst. 1980, 59, 289–298. (c) Iguchi, M.; Nakanishi, H.; Hasegawa, M. J. Polym. Sci., A-1 1968, 6, 1055–1057. (d) Nakanishi, H.; Jones, W.; Thomas, J. M. Chem. Phys. Lett. 1980, 71, 44–48. (e) Enkelmann, V.; Wegner, G.; Novak, K.; Wagener, K. B. J. Am. Chem. Soc. 1993, 115, 10390–10391. SCSC reactivity is readily extended to solid-state phase transformations, since a solid state transformation can be considered as the simplest solid-state reaction where the reactant molecules and product molecules are the same. Thus, one speaks of solid-state phase transformations that proceed in an SCSC manner. (a) Friscic, T.; MacGillivray, L. R. Z. Kristallogr. 2005, 220, 351– 363. (b) Barbour, L. J. Aust. J. Chem. 2006, 59, 595–596. SCSC reactivity was often observed in porous materials during gas or solvent uptake and release: (a) Lee, E. Y.; Suh, M. P. Angew. Chem., Int. Ed. 2004, 43, 2798–2801. (b) Wu, C. D.; Lin, W. B. Angew. Chem., Int. Ed. 2005, 44, 1958–1961. (c) Choi, H. J.; Suh, M. P. J. Am. Chem. Soc. 2004, 126, 15844–15851. (d) Vittal, J. J. Coord. Chem. Rev. 2007, 251, 1781–1795. (e) Ohmori, O.; Kawano, M.; Fujita, M. J. Am. Chem. Soc. 2004, 126, 16292–16293. (f) Deiters, E.; Bulach, V.; Hosseini, M. W. Chem. Commun. 2005, 3906–3908. (g) Halder, G. J.; Kepert, C. J. Aust. J. Chem. 2006, 59, 597–604. (h) Gurunatha, K. L.; Mohapatra, S.; Suchetan, P. A.; Maji, T. K. Cryst. Growth Des. 2009, 9, 3844–3847. (i) Chandler, B. D.; Enright, G. D.; Udachin, K. A.; Pawsey, S.; Ripmeester, J. A.; Cramb, D. T.; Shimizu, G. K. H. Nat. Mater. 2008, 7, 229–235. But it was observed also for nonporous organic solids: (j) Tian, J.; Thallapally, P. K.; Dalgarno, S. J.; Atwood, J. L. J. Am. Chem. Soc. 2009, 131, 13216–13217. (k) Ripmeester, J. A.; Enright, G. D.; Ratcliffe, C. I.; Udachin, K. A.; Moudrakovski, I. L. Chem. Commun. 2006, 4986–4996. (l) Atwood, J. L.; Barbour, L. J.; Jerga, A.; Schottel, B. L. Science 2002, 298, 1000–1002. (a) Nakanishi, H.; Suzuki, Y.; Suzuki, F.; Hasegawa, M. J. Polym. Sci., A-1 1969, 7, 743–752. (b) Nakanishi, H.; Suzuki, Y.; Suzuki, F.; Hasegawa, M. J. Polym. Sci., A-1 1969, 7, 753–766. (c) Nakanishi, H.; Parkinson, G. M.; Jones, W.; Thomas, J. M.; Hasegawa, M. Isr. J. Chem. 1979, 18, 261–265. (d) Nakanishi, H.; Jones, W.; Thomas, J. M.; Hasegawa, M.; Rees, W. L. Proc. R. Soc. London, A 1980, 369, 307– 325. (e) Hasegawa, M. Pure Appl. Chem. 1986, 58, 1179–1188. (f) Lauher, J. W.; Fowler, F. W.; Goroff, N. S. Acc. Chem. Res. 2008, 41, 1215–1229. Garcia-Garibay, M. A. Angew. Chem., Int. Ed. 2007, 46, 8945– 8947. (a) Jones, W.; Nakanishi, H.; Theocharis, C. R.; Thomas, J. M. J. Chem. Soc., Chem. Commun. 1980, 610–611. (b) Kim, J. H.; Hubig, S. M.; Lindeman, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2001, 123, 87– 95. (c) Nakanishi, H.; Jones, W.; Thomas, J. M.; Hursthouse, M. B.; Motevalli, M. J. Phys. Chem. 1981, 85, 3636–3642. See for example: (a) Trzop, E.; Turowska-Tyrk, I. Acta Crystallogr. 2008, B64, 375–382. (b) Turowska-Tyrk, I.; Bakowicz, J.; Scheffer, J. R. Acta Crystallogr. 2007, B63, 933–940. (b) TurowskaTyrk, I.; Labecka, I.; Scheffer, J. R.; Xia, W. Pol. J. Chem. 2007, 81, 813–824. (a) Kaupp, G. Top. Curr. Chem. 2005, 254, 95–183. (b) Scheffer, J. R.; Xia, W. Top. Curr. Chem. 2005, 254, 233–262. (c) Green, B. S; Lahav, M.; Rabinovich, D. Acc. Chem. Res. 1979, 12, 191–197. (d) Friscic, T.; MacGillivray, L. R. In Making Crystals by Design; Braga, D.,Grepioni, F., Eds. Wiley-VCH: 2007; pp 176-192. (e) Friscic, T.; MacGillivray, L. R. Croat. Chem. Acta 2006, 79, 327–333. Kohlsch€ utter, V. Z. Anorg. Allg. Chem. 1918, 105, 1–25. Lotgering, F. K. J. Inorg. Nucl. Chem. 1959, 9, 113–123. This was first observed with inorganic crystals, but it has afterwards been shown also to be valid for organic crystals. (a) Kohlsch€ utter, H. W. Ann. Chem. 1930, 482, 75–107. (b) Morawetz, H.; Jakabhazy, S. Z.; Lando, J. B.; Shafer, J. Proc. Natl. Acad. Sci. 1963, 49, 789–793. The term epitaxy is used when referring to the oriented growth of a crystalline solid phase on some crystalline substrate where the exposed surface of the substrate determines the lattice orientation of the growing phase, but it has mostly been used for growth of the solid phase from melt or vapor and has scarcely been used in describing oriented growth of a solid within a solid. Epitaxy, however, seems to have the same meaning as topotaxy. (a) Schmidt, G. M. J. Pure Appl. Chem. 1971, 27, 647–678. (b) Morawetz, H. Science 1966, 152, 705–711. Kawano, M.; Fujita, M. Coord. Chem. Rev. 2007, 251, 2592– 2605.
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(16) (a) Keating, A. E.; Garcia-Garibay, M. A. In Molecular and Supramolecular Photochemistry; Ramamurthy, V., Schanze, K., Eds.; Marcel Dekker: New York, 1998; Vol. 2, pp 195-248. (b) MacGillivray, L. R.; Papaefstathiou, G. S.; Friscic, T.; Hamilton, T. D.; Bucar, D.-K.; Chu, Q.; Varshney, D. B.; Georgiev, I. G. Acc. Chem. Res. 2008, 41, 280–291. (c) Zimmerman, H. E.; Nesterov, E. E. Acc. Chem. Res. 2002, 35, 77–85. (d) Paul, I. C.; Curtin, D. Y. Acc. Chem. Res. 1973, 6, 217– 225. (e) Desiraju, G. R. Solid State Ionics 1997, 101, 839–842. (f) Thomas, J. M. Pure Appl. Chem. 1979, 51, 1065–1082. (g) Cohen, M. D. Tetrahedron 1987, 43, 1211–1224. (h) Cohen, M. D. Angew. Chem., Int. Ed. 1975, 14, 386–393. (i) Vittal, J. J. Chem. Commun. 2008, 42, 5277–5288. An excellent account of topotaxy in inorganic systems is given in: (j) Figlarz, M.; Gerand, B.; Delahayevidal, A.; Dumont, B.; Harb, F.; Coucou, A.; Fievet, F. Solid State Ionics 1990, 43, 143–170. (17) (a) Bucar, D.-K.; MacGillivray, L. R. J. Am. Chem. Soc. 2007, 129, 32–33. (b) Takahashi, S.; Miura, H.; Kasai, H.; Okada, S.; Oikawa, H.; Nakanishi, H. J. Am. Chem. Soc. 2002, 124, 10944–10945. (c) Miura, H.; Takahashi, S.; Kasai, H.; Okada, S.; Yase, K.; Oikawa, H.; Nakanishi, H. Cryst. Growth Des. 2010, 10, 510–517. (18) It can be argued that to have a perfect polycrystal all possible orientations must be represented with exactly the same mass of material. Since there is infinitely many of them, perfect polycrystals would consequently need to be infinitely big. Within the here used definition of a perfect polycrystal, this is neglected and it is assumed that the number of crystallites is just large enough. The distinguishing feature between a perfect single crystal and a perfect polycrystal is that a perfect polycrystal consists of a large number of crystals while a perfect single crystal consists exclusively of one. Note also that making distinctions between a large number of crystals and just one immediately brings us to the sorites paradox. (19) For the role of defects in solid-state reactions, see: (a) Cohen, M. D.; Ludmer, Z.; Thomas, J. M.; Williams, J. O. Proc. R. Soc. London, A 1971, 324, 459–468. (b) Braun, H.-G.; Wegner, G. Mol. Cryst. Liq. Cryst. 1983, 96, 121–139. (c) Thomas, J. M.; Williams, J. O. Prog. Solid State Chem. 1971, 6, 119–154. (d) Ramachandra Swamy, H.; Guru Row, T. N.; Ramamurthy, V.; Venkatesan, K.; Rao, C. N. R. Curr. Sci. 1982, 51, 381–386. (e) Ramdas, S.; Jones, W.; Thomas, J. M.; Desvergne, J.-P. Chem. Phys. Lett. 1978, 57, 468–470. (20) (a) Authier, A.; Malgrange, C. Acta Crystallogr. 1998, A54, 806–819. (b) Darwin, C. G. Philos. Mag. 1922, 43, 800–829. (c) Bragg, W. L.; Darwin, C. G.; James, R. W. Philos. Mag. 1926, 1, 897–922. (21) Single crystal diffraction experiments can estimate a crystal’s mosaicity based on an angular range of crystal rotation around a diffractometer axis through which a certain reflection is observed on the detector. There are two usual ways of describing the extent of preferred orientation of a polycrystalline sample,: the semiempirical March-Dollase modeling ( (a) March, A. Z. Kristallogr. 1932, 81, 285–297. (b) Dollase, W. A. J. Appl. Crystallogr. 1986, 19, 267– 272. (c) Zolotoyabko, E. J. Appl. Crystallogr. 2009, 42, 513–518. ) and the empirical modeling with spherical harmonic functions (J€arvinen, M. J. Appl. Crystallogr. 1993, 26, 525–531.). The approaches for single crystals and polycrystals operate on opposing parts of the A-B line of Figure 1 and are not compatible. It has also been demonstrated how the preferred orientation of crystallites in a polycrystalline sample can be used in solving the problem of intensity partition due to reflection overlap in a powder diffraction pattern and obtaining a single-crystallike diffraction data set (Wessels, T.; Baerlocher, C.; McCusker, L. B. Science 1999, 284, 477–479.). (22) (a) Enright, G. D.; Brouwer, E. B.; Udachin, K. A.; Ratcliffe, C. I.; Ripmeester, J. A. Acta Crystallogr. 2002, B58, 1032–1035. See also: (b) Stilinovic, V.; Kaitner, B. Acta Crystallogr. 2010, A66, http://dx. doi.org/10.1107/S0108767310013814. (23) Reacting molecules with bulky substitutents seem to be more prone to exhibiting SCSC reactivity: Marubayashi, N.; Ogawa, T.; Hamasaki, T.; Hirayama, N. J. Chem. Soc., Perkin Trans. 1997, 2, 1309–1314. This is expected if we consider that formation of a new bond will have less of an effect on the overall crystal if this is just a small part of the molecule. That is, if the overall change is small, its influence on the surrounding molecules will correspondingly be small. Consider the changes protein crystals can endure, e.g. introduction of heavy atoms or exchange of substrates at the active sites in enzymes by soaking. All these changes in protein crystals are of an SCSC kind. Protein crystals can be very flexible, maybe because only just a tiny bit in them is actually changing and, with all the water in crystals, the molecules have a lot of freedom. For an account on free space accessible
Halasz
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to molecules and the influence of solid-state reactivity, see: Gavezzotti, A. J. Am. Chem. Soc. 1983, 105, 5220–5225. Luty, T.; Eckhardt, C. J. J. Am. Chem. Soc. 1995, 117, 2441–2452. (a) McBride, J. M.; Segmuller, B. E.; Hollingsworth, M. D.; Mills, D. E.; Weber, B. A. Science 1986, 234, 830–835. (b) Kaupp, G. In Making Crystals by Design; Braga, D., Grepioni, F., Eds.; WileyVCH; 2007; pp 87-148. (c) McBride, J. M. Acc. Chem. Res. 1983, 16, 304–312. (a) Eckhardt, C. J.; Luty, T.; Peachey, N. M. Mol. Cryst. Liq. Cryst. 1998, 313, 25–38. (b) Dunitz, J. D. Pure Appl. Chem. 1991, 63, 177–185. (a) Kaupp, G. Angew. Chem., Int. Ed. Engl. 1992, 31, 592–595. (b) Kaupp, G. Angew. Chem., Int. Ed. Engl. 1992, 31, 595–598. (c) Kaupp, G. Curr. Opin. Solid State Mater. Sci. 2002, 6, 131–138. (d) Koshima, H.; Ide, Y.; Ojima, N. Cryst. Growth Des. 2008, 7, 2058–2060. Coppens, P.; Benedict, J.; Messerschmidt, M.; Novozhilova, I.; Graber, T.; Chen, Y.-S.; Voronotsov, I.; Scheins, S.; Zheng, S.-L. Acta Crystallogr. 2010, A66, 179–188. Fattah, J.; Twyman, J. M.; Heyes, S. J.; Watkin, D. J.; Edwards, A. J.; Prout, K.; Dobson, C. M. J. Am. Chem. Soc. 1993, 115, 5636– 5650. (a) Varshney, D. B.; Papaefstathiou, G. S.; MacGillivray, L. R. Chem. Commun. 2002, 1964–1965. (b) Enkelmann, V.; Wegner, G.; Novak, K.; Wagener, K. B. Mol. Cryst. Liq. Cryst. 1994, 240, 121–126. (c) Enkelmann, V. Mol. Cryst. Liq. Cryst. 1998, 313, 15– 23. (d) Novak, K.; Enkelmann, V.; Wegner, G.; Wagener, K. B. Angew. Chem., Int. Ed. Engl. 1993, 32, 1614–1616. Braun, H.-G.; Wegner, G. Makromol. Chem. 1983, 184, 1103–1119. Mnyukh, Y. Fundamentals of Solid State Phase Transformations, Ferromagnetism and Ferroelectricity; Authorhouse: 2001. Mnyukh, Y. Mol. Cryst. Liq. Cryst. 1979, 52, 201–218. Coles, S. J.; Gelbrich, T.; Griesser, U. J.; Hursthouse, M. B.; Pitak, M.; Threlfall, T. Cryst. Growth Des. 2009, 9, 4610–4612. (a) Desiraju, G. R.; Paul, I. C.; Curtin, D. Y. J. Am. Chem. Soc. 1977, 99, 1594–1601. (b) Meyer, W.; Lieser, G.; Wegner, G. Makromol. Chem. 1977, 178, 631–634. See, for example: Xue, D.-X.; Zhang, W.-X.; Chen, X.-M.; Wang, H.-Z. Chem. Commun. 2008, 1551–1553. Some reports of SCSC reactivity state that the crystal has cracked but remained in one piece upon reaction/transformation (e.g. Bardelang, D.; Udachin, K. A.; Anedda, R.; Moudrakovski, I.; Leek, M. D.; Ripmeester, J. A.; Ratcliffe, C. I. Chem. Commun. 2008, 4927–4929. ). Such reports show that formation (growth) of daughter domains was topotactic (epitaxial), thus retaining the mosaicity of the final crystal sufficiently low to allow for a single-crystal-diffraction data set to be collected. The mother crystal actually disintegrated while daughter domains grew with closely similar orientations. Formation of twin domains upon SCSC reaction is also an option. Such cases also give evidence for multiple nucleation sites, such as, for example, in the solid-state UV-photolysis of dimeric cak, H.; Mihalic, p-bromonitrosobenzene ( Halasz, I.; Mestrovic, E.; Ci Z.; Vancik, H. J. Org. Chem. 2005, 70, 8461–8467). The dimer crystallizes in the centrosymmetric P 21/c space group while the monomer crystallizes in the chiral P 21 space group. The daughter crystal showed pronounced mosaicity, and it was observed by refinement of the Flack parameter, x, that an inversion twin had formed. The portions of the crystal belonging to opposite chiralities were found to be equal (x = 0.50(2)). This observation can be explained by many nucleation sites where the chirality of the daughter phase starting to grow at a particular nucleation site was chosen possibly at random while all daughter domains had to grow with approximately similar orientations for the crystal to retain its behavior as a single crystal in a diffraction experiment. Explanations for the topotactic (epitaxial) growth in this case potentially lie in the network of supramolecular interactions, which remains unchanged upon reaction. The network of interactions already present in the mother crystal could have thus determined the least-energy path for growth of daughter domains and served as sort of a template for their orientations. For thorough accounts of twinning in topotactic reactions, see: Gougoutas, J. Z.; Lessinger, L. J. Solid State Chem. 1975, 12, 51–62. Gougoutas, J. Z. J. Am. Chem. Soc. 1977, 99, 127–132. Thorough account of epitaxial growth in solid-state phase transformations is given by Mnyukh.32 Volkringer, C.; Popov, D.; Loiseau, T.; Guillou, N.; Ferey, G.; Haouas, M.; Taulelle, F.; Mellot-Draznieks, C.; Burghammer, M.; Riekel, C. Nat. Mater. 2007, 6, 760–764. Pecharsky, V. K.; Zavalij, P. Y. Fundamentals of Power Diffraction and Structural Characterisation of Materials; Springer: New York, 2005.
Perspective (39) This whole discussion has a bit of a philosophical spirit in it. Saying that a crystal had broken is not easy, since this term does not have clear-cut boundaries. How big would a crack need to be to declare that the crystal had broken? How small is the crack allowed to be, without declaring the crystal as cracked, when even the tiniest misalignment of two domains in a crystal could be declared a crack? Which method should we use to find potential cracks? It is clear that if we just take a more sensitive method, a crack previously unnoticed could be found. The situation is the same with many terms mentioned here, including the terms single crystal, polycrystal, SCSC reaction/transformation, and even crystal (Desiraju, G. R. Nature 2003, 423, 485.). These terms are vague, and there is most probably no way to avoid the vagueness. But additionally, many terms in chemistry are also inherently vague (e.g. homogeneous and
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heterogeneous). For instance, a description of vagueness of the term polymorphism is given in: Desiraju, G. R. Cryst. Growth Des. 2008, 8, 3–5. Since vagueness probably cannot be avoided, our wish here is to point this out so that we are aware of it in the course or our reasoning. The reader is referred to a recent book: van Deemter, K. Not Exactly: in Praise of Vagueness; Oxford University Press: New York, 2010. (40) Khan, M.; Enkelmann, V.; Brunklaus, G. CrystEngComm 2009, 11, 1001–1005. (41) (a) Shalaev, E. Y.; Zografi, G. J. Phys. Org. Chem. 1996, 9, 729–738. (b) Kim, J. H.; Jaung, J. Y.; Jeong, S. H. Opt. Mater. 2002, 21, 395–400. (42) This has been more valid in the last two decades, possibly because of the drastic increase in availability of diffraction methods then in the advent of interest in solid state reactivity in the 1960s and 1970s.
