Metastability and Instability of Organic Crystalline Substances

J. Phys. Chem. B 2008, 112, 1435-1444

1435

Metastability and Instability of Organic Crystalline Substances Stanislaw L. Randzio*,† and Andrzej Kutner‡ Polish Academy of Sciences, Institute of Physical Chemistry, Kasprzaka 44/52, 01-224 Warszawa, Poland, and Pharmaceutical Research Institute, Rydygiera 8, 01-793 Warszawa, Poland ReceiVed: September 6, 2007; In Final Form: NoVember 5, 2007

Discovery of an unexpected and thermodynamically paradoxical transition from a crystalline state to an amorphous dense glassy state induced in pure organic substances by a direct absorption of a quantity of heat under atmospheric pressure and its detailed analysis performed with the use of a sensitive scanning transitiometer are described. The obtained results present first experimental precise evidence for understanding the mechanism of such a structural instability of crystalline substances in the form of c-a transition. The observed c-a transition is a purely physical phenomenon, occurring between two nonequilibrium states, a metastable crystalline phase and a dense glass, occurring through a local transient phenomenon of Virtual melting. The metastable state of a crystalline substance can be caused by existence of a number of crystalline imperfections created either during crystallization or by external actions. By measuring extremely sensitive energetic effects, we found the present method to be helpful for quantitative determination of the critical number of imperfections in a crystalline solid, which make it metastable and for an indication under which conditions such a metastable crystalline form becomes unstable. By performing the transitiometric analysis of c-a transitions with two polymorphs of rosiglitazone maleate, we demonstrated to what extent this analysis is important in investigation of stability of crystalline components of drugs.

Introduction Crystalline phases are usually considered as the most stable reference states of matter. However, since Kauzmann1 noticed that despite equilibrium thermodynamic principles a substance in a glassy state can have lower entropy than the entropy of its crystalline state, other similar paradoxes have been reported in the literature. The most known examples involve pressureinduced amorphization of crystalline ice,2-4 multiple Kauzmann paradoxes in metals and their alloys,5 vitrification of minerals,6 semiconductors,7 and metallic alloys8 (sometimes incorrectly9 called “inverse melting”). Theoretical explanations of the observed abnormal effects are based on the role of crystal imperfections in the destabilization of the crystal lattice.10-12 The theory of Virtual melting (VM)13,14 attempted to describe the mechanism of such “paradoxical” transitions. According to this theory the nonequilibrium defects in a crystalline phase, such as vacancies, interstitials, self-interstitials, etc., can create an internal stress and locally lower the equilibrium fusion temperature (Tfus) down to the temperature of virtual melting TVM. If TVM is lower than the glass transition temperature of the substance, the virtual melt transforms immediately to the glassy state. However, such a mechanism of crystal-toamorphous (c-a) transition has never been confirmed by a direct experimental identification of its course. Noticeably, the abovementioned abnormal phenomena have always been induced by external actions, such as high pressure, grinding, or irradiation. However, crystal imperfections can also be created during crystal growth from a solution, and a high concentration of crystal defects itself can lead to nonequilibrium morphologies15 or even can completely destabilize the crystal phase and cause its * To whom the correspondence should be addressed. E-mail: randzio@ ichf.edu.pl. † Polish Academy of Sciences. ‡ Pharmaceutical Research Institute.

amorphization.16 Intuitively one can say that if the defects were so concentrated that their fields overlapped extensively, the material would be amorphous, not crystalline with defects.17 To date no such phenomena have been described for pure organic substances, although amorphizations by milling have been reported for polymers18 and for blended drugs.19 However, there is no basic reasons why such phenomena could not happen in pure organic crystalline substances. Discovery of such phenomena and their detailed investigation could significantly help in understanding formation of multiple metastable phases during crystallization of organic substances, the phenomenon known as monotropic polymorphism, extremely important in pharmaceutical practice.20 Here, we present a detailed description of such thermodynamically paradoxical transitions from a crystalline to a dense glassy state observed under atmospheric pressure in two polymorphic forms of rosiglitazone maleate (RM), an important pharmaceutical substance used as an insulin enhancer. The transition was induced either by a very slow linear or stepwise heating and keeping the sample at the increased temperature for a long time in a sensitive calorimetric detector of a scanning transitiometer,21 without performing any external mechanical action. The transitiometric traces reveal in detail the course of the c-a transition exhibiting that the transition always starts with an endothermic effect, and then it is immediately followed by an important exothermic effect. The transitiometric results thus provide the first direct experimental confirmation of a tentative hypothesis that the c-a transition can occur via virtual melting (VM) and for the first time directly identify its detailed course. The present observations are of general interest from the point of view of examination of structural stability of crystalline substances, otherwise difficult to perform, and are of extreme importance for the pharmaceutical practice. This is because the bioavailability and activity of the drug can dramatically change and create dangerous prob-

10.1021/jp077161a CCC: $40.75 © 2008 American Chemical Society Published on Web 01/12/2008

1436 J. Phys. Chem. B, Vol. 112, No. 5, 2008

Randzio and Kutner

Figure 1. XRPD patterns for the polymorphic forms A (a) and B (b) of rosiglitazone maleate as initial crystalline powders.

lems, if a crystalline component of a drug transforms unexpectedly to a glassy state, during formulation processing, tableting, or storage. Materials and Methods The samples of polymorphic forms A and B of rosiglitazone maleate (RM) (formula C18H19N3O3S. C4H4O, MW 425.51 g/mol, CAS-RN 155141-29-0) were prepared according to known procedures.22,23 A weighted powdered sample of a given crystalline form of RM was placed in the lower part of the measuring transitiometric vessel and tightly closed with a Teflon foil. The upper part of the vessel remained empty. Then, the vessel containing the investigated sample was placed in the calorimetric detector. The reference vessel was of similar construction but contained some additional inert elements in order to compensate the thermal symmetry for properly keeping the baseline in the differential measuring mode. Both temperature ((0.2 K) and energetic ((0.6 µW) scales of the transitiometer used in the present study were calibrated with a number of standard substances.24,25 Prior to transitiometric measurements, the properties of the investigated materials have been carefully analyzed. The crystalline nature of the two polymorphic forms A and B of RM has been determined by XRPD. Figure 1 presents their XRPD

patterns exhibiting clear differences between the long-distance orders in the structures of the two polymorphs. However, their FTIR spectra (Figure 2) do not show significant differences. Figure 3 presents 1H NMR spectra for the initial crystalline powder of the polymorphic form B in a DMSO solution. DSC traces for the two forms (A and B) obtained at a heating rate of 0.17 K/s (Figure 4) revealed that the course of expected equilibrium melting transitions in the two forms have unusual shapes. That is, endothermic effects are followed by slow exothermic phenomena. Formal treatment of the recorded DSC traces resulted in the following data: (a) for the form A, Ttrs,A ) 404.6 K and ∆trsHA ) 110.6 J/g; (b) for the form B, Ttrs,B ) 396.6 K and ∆trsHB ) 103.4 J/g. The heat of fusion rule for the polymorphic systems26 states that, if the higher melting form has the lower heat of fusion, the two forms are enantiotropically related; otherwise they are monotropic. Thus, from the above data one can conclude that the two polymorphs A and B of RM are not enantiotropically related. That is, there is no equilibrium point between them and at least one of the forms is in a metastable state. However, one should be careful with such formal conclusions, because the recorded DSC traces could not be integrated properly. This is because of their unusual shapes. Thus, the enthalpy values cannot be reliably taken as valid.

Metastability of Organic Crystalline Substances

J. Phys. Chem. B, Vol. 112, No. 5, 2008 1437

Figure 2. Solid-state FTIR spectra for the polymorphic forms A (a) and B (b) of rosiglitazone maleate, investigated as initial crystalline powders.

The Crystal-to-Amorphous Transitions. To elucidate the nature of the transitions observed in the DSC measurements, the scanning transitiometric technique21 was used. The energetic sensitivity and the stability of both isothermal and temperature

dynamic modes of a transitiometer are by a factor of at least 105 higher than the corresponding values in the case of conventional DSC. Furthermore, the temperature scanning rates are significantly lower, allowing the investigation of extremely


Randzio and Kutner

Figure 3. 1H NMR spectra for the initial crystalline powder of the polymorphic form B of rosiglitazone maleate in DMSO.

Figure 4. DSC traces for the two polymorphic forms A and B of rosiglitazone maleate recorded at a heating rate of 0.17 K/s.

sensitive energetic states. First, a stepwise temperature scanning technique was used. The investigated sample was heated to a given temperature at a selected rate and then kept for a long time at that temperature. Figure 5 presents an example of such studies performed with the polymorphic form B. From the recorded traces one can see that during the temperature scan from 304.5 ( 0.2 K to 372.0 ( 0.2 K at a rate of 1 ( 0.01

mK/s, nothing happens in particular, except an usual heat flow deviation that appears. This deviation is caused by the difference between the heat capacity of the measuring and reference vessel. However, after about 50 ks from the end of the temperature scan at 372.0 ( 0.2 K, a weak endothermic transition starts, which is followed by an exothermic effect. After completion of the observed transformation, a linear cooling down to 313 K


Figure 5. Transitiometric traces obtained for the polymorphic form B of rosiglitazone maleate when heating from 304.5 ( 0.2 K to 372.0 ( 0.2 K at a rate of 1 ( 0.01 mK/s (1, temperature; 2, heat flow). The c-a transition starts only after keeping the sample about 50 ks at 372.0 ( 0.2 K.

Figure 6. A sample of the polymorphic form B of rosiglitazone maleate before the c-a transition as a crystalline powder (left) and after the c-a transition as a dense glass (right).

Figure 7. Transitiometric traces for the c-a transition in the polymorphic form A of rosiglitazone maleate obtained at various heating rates: 1-0.1 mK/s; 2-0.25 mK/s; 3-1 mK/s; 4-2.5 mK/s.

did not show any transition, demonstrating that the observed transformation was not reversible. After the measuring vessel was opened, it was found that the initially powdered crystalline sample had transformed into a piece of a very dense glass (Figure 6). The volume of the vitrified sample was ca. 4 times smaller than that of its powdered initial crystalline form. Noteworthily, the volume of the initial powdered sample is merely an apparent volume comprising a large free nonoccupied space existing between the fine grains of the crystalline powder.


Figure 8. Dependence of the onset temperature of the c-a transition (beginning of the endothermic effect) on the heating rate obtained for the two polymorphic forms, A (9) and B (2), of rosiglitazone maleate.

Figure 9. Near-equilibrium melting of benzoic acid induced at a temperature scan rate of 1 mK/s. The dashed curves represent heat flow q (1) and temperature T (2) of the full melting transition (liquid phase is the final state), and the full curves represent heat flow q (3) and temperature T (4) of the melting interrupted by stopping the inducing temperature scan after the melting has begun and has not been yet accomplished (equilibrium solid-liquid is the final state).

Figure 10. The c-a transition in the polymorphic form B of rosiglitazone maleate induced at a heating rate of 0.25 mK/s at 372.6 ( 0.2.K continues to a completion (curve 1) despite the fact that the heating (inducing variable) was stopped at 373.8 ( 0.2 K (curve 2), exhibiting its nonequilibrium character.

By transforming into the glassy homogeneous state, this free nonoccupied space practically disappeared, giving rise to important decrease of the volume occupied by the investigated sample. Furthermore, the external shape of the glassy product was nearly cylindrical (Figure 6). However, its external dimensions were much smaller than the internal dimensions of the cylindrical measuring vessel in which the powdered sample was placed. Thus, it was concluded that the transformation had taken


Randzio and Kutner

Figure 11. XRPD patterns for two different glassy samples of the polymorphic form B of rosiglitazone maleate exhibiting their amorphous character.

Figure 12. A comparison of XPRD patterns of the initial crystalline powder (black curve) of the polymorphic form B of rosiglitazone maleate and of its crystalline powder, which was kept at 365.1 K (a few degrees below TVM, the temperature of the virtual melting) for 250 ks (red curve), where the c-a transition was not yet observed.

place entirely in the solid phase, without passing Via any real intermediate liquid phase. This is because the small cylindrical form of the obtained glass proves that the transformation product had no mechanical contact with the internal lateral wall of the experimental vessel. Otherwise, its external diameter would be equal to the internal diameter of the experimental vessel. The initial powdered crystalline sample simply shrunk to the dense glassy state, without passing through a real liquid phase. Thus, the observed transformation is a direct crystal-to-amorphous (ca) transition, for the first time induced in a pure organic crystalline substance by a simple absorption of heat under

atmospheric pressure. The course of this transition could be directly followed by an associated sensitive heat flow trace. Such studies have also been performed for the polymorphic form A, and the results were similar. These initial stepwise transitiometric studies have permitted us to establish possible temperature intervals, in which the observed c-a transitions could be also investigated under the dynamic temperature scanning mode at extremely low heating rates. Figure 7 presents an example of results of such studies performed with the use of polymorphic form A. In order to eliminate the usual instrumental dependence of the magnitude of the recorded heat flow traces on the heating



Figure 13. Solid-state FTIR spectra of the dense glass of the polymorphic form B of rosiglitazone maleate obtained during the c-a transition.

rate, the thermal changes observed during the c-a transitions are presented in Figure 7 in the heat capacity units. Similar traces have also been obtained for the polymorphic form B. Figure 8 presents dependencies of the onset temperatures of the c-a transition (beginning of the endothermic effect) on the temperature scanning rate observed for the two polymorphic forms, A and B. From Figures 7 and 8 one can notice that both the onset temperatures and the shapes of the recorded traces depend on the temperature scanning rate. An increase of the heating rate pushes the transition to higher temperatures but not in a linear way. At the same time, the magnitude of the initial endothermic effect importantly increases with the heating rate. Concomitantly, the exothermic effect always starts relatively fast while later on becomes rather relatively slow. Noticeably, the transitions induced by the lowest temperature scanning rate (0.1 mK/ s) in the two polymorphic forms, A and B, always ended with the external shapes of the glassy products looking exactly the same as that obtained in the temperature stepwise scan experiment presented in Figures 5 and 6. This result can be taken as a proof that the observed c-a transitions occur completely in the solid state also in the continuous heating mode. At higher scanning rates the near cylindrical forms were flattened, most probably because of lower viscosity of the obtained glass at higher temperatures. The two polymorphic forms, when heated above the c-a transition, did not show any further transitions, e.g., recrystallization. It was theoretically suggested that the virtual melt is in equilibrium with the parent crystalline phase and is unstable with respect to the glassy state.14 To check this possibility, an experiment was programmed in such a way that the temperature scan was interrupted just after the beginning of the virtual melting. It is known that in all transitions, where an equilibrium coexistence of phases exists, the transition can be fully controlled by the inducing variable, e.g., stopped at a given extent by interrupting the temperature increase (or isothermal pressure

decrease in volume-expanded transitions) and then pushed back to recrystallization by a temperature decrease (or isothermal pressure increase in volume expanded transitions).21 In order to further prove such a behavior of equilibrium transitions, transitiometric measurements of melting of benzoic acid were performed in the experimental vessel used for the investigation of the c-a transitions in rosiglitazone maleate described above. Figure 9 presents the results obtained, where the dashed lines represent heat flow, q, and temperature, T, of the full melting transition (liquid phase is the final state) and the full lines represent the melting interrupted by stopping the inducing temperature scan after the melting has begun but was not yet accomplished (equilibrium solid-liquid is the final state). One can see that the transition was immediately interrupted when the temperature inducing scan was stopped and the isothermal equilibrium solid-liquid started to be established. Such a technique was previously used for separation of closely spaced polymorphs of theophylline and for an equilibrium preparation of its high temperature form.27 Figure 10 presents results of a similar experiment performed with the polymorphic form B of rosiglitazone maleate. The sample was heated at a rate of 0.25 mK/s up to 373.8 K, and then the inducing temperature scan was stopped. The c-a transition started at 372.6 K and continued until its completion despite the fact that the heating was interrupted before. In order to clearly show the course of the transition in Figure 10, the heat capacity contribution to the calorimetric trace was removed from the total trace (see such a heat capacity contribution in Figure 5). These results clearly demonstrate that there is no equilibrium coexistence between the virtual melt and the parent crystalline phase. Moreover, when cooling from the temperature at which the transition was completed down to room temperature, no transformation was observed. Thus, it can be concluded that the c-a transitions occurring in polymorphic forms A and B of rosiglitazone maleate Via virtual melting are fully irreversible.


Randzio and Kutner

Figure 14. 1H NMR spectra in DMSO of the dense glass of the polymorphic form B of rosiglitazone maleate obtained during the c-a transition.

Properties of the End Glassy Products. The amorphous nature of the vitrified samples was confirmed by XRPD analysis. The respective results are presented in Figure 11. In Figure 12 the XPRD pattern of the original crystalline powder (black curve) of the polymorphic form B of RM is compared to that of its sample, which was kept at 365.1 K (i.e., a few degrees below TVM, the temperature of the virtual melting) for 250 ks (red curve), where the c-a transition was not yet observed. The results in Figures 11 and 12 prove that the loss of crystalline long range order must have happened only during the observed c-a transition. Moreover, it was found that after each experiment, the mass of the vitrified sample was always exactly equal (with precision better than 0.01%) to the respective powdered crystalline sample used for the experiment. However, detailed analysis of the vitrified samples performed with solid-state FTIR spectroscopy (Figure 13) and with 1H NMR spectroscopy in DMSO (Figure 14) revealed traces of chemical changes with respect to the original crystalline forms (cf. with Figures 2b and 3, respectively). However, RM always remained the main component in the glassy state. Because the mass of the sample did not change during the c-a transition, it is plausible that some internal bonds of RM are stabilized by the crystal forces. However, they are weakened and rearrange upon the loss of the long distance order. Discussion It is known that any crystallization process is composed of elementary dynamic acts of competitive nucleation and growth

of mostly metastable forms and of their transformation to a stable form.20 The transformation from a metastable form to a stable crystalline form can also happen only after the completion of crystallization. However, it is also possible that such a transformation is hindered for some reasons and never occurs. The results presented here demonstrate that the latter behavior is the case for the polymorphic forms A and B of RM investigated in the present study. A schematic diagram of such a behavior is presented in Figure 15, where the following inequalities hold: Tamb < TVM < Tg < Tfus. The metastable state of a crystalline substance can originate from the existence of a number of nonequilibrium defects created either during crystallization or by external actions.12 The nonequilibrium defects can create an internal stress and locally lower the melting temperature (Tfus), significantly inducing a local transient phenomenon of virtual melting.13,14 Taking into consideration both this hypothesis and the diagram from Figure 15, we can formulate the following interpretation of transitiometric traces presented in Figure 7, with respect to both their shapes and the temperature, where the transition appears depending on the heating rate. The crystalline powder of either form A or B of RM at ambient temperature is in a metastable state. Upon heating, the TVM temperature is approached and a local melting of the first nonequilibrium grains is induced, giving rise to an endothermic heat flow. This local melt removes the interface friction, reduces the kinetic barrier, increases the molecular mobility, and renders kinetically allowed transformation of the whole metastable crystalline sample into the dense glassy state.14


J. Phys. Chem. B, Vol. 112, No. 5, 2008 1443 polymorphic form B from 396.6 K at temperature scan rate of 0.17 K/s to 371.3 K at 0.1 mK/s. Conclusions

Figure 15. A schematic diagram of appearance of a metastable crystal phase and of crystal-to amorphous transition (a-c) through the mechanism of virtual melting (VM): Tfus, temperature of equilibrium melting/crystallization; Tg, glass transition temperature; TVM, temperature of virtual melting; Tamb, ambient temperature.

This is because, if TVM < Tg, it is the nearest phase of lower entropy on its way to the equilibrium crystal phase. This part of the transition gives rise to an exothermic heat flow. From the heat flow traces presented in Figure 7 it follows that the endothermic effect and the beginning of the exothermic effect are rather fast while the continuation of the exothermic effect, which is associated with the growth of the new dense glassy phase in the whole investigated sample, is rather slow. Generally one can say that out of the slow and fast processes, an increase of the heating rate should rather enhance the fast process. Thus, in the experiments performed with various heating rates, the amount of the virtual melt is increasing with the heating rate, giving rise to an increased endothermic heat flow. For this reason it was difficult to distinguish the transient melting from the expected equilibrium melting of a crystalline substance under the usual relatively high heating rates of conventional DSC, as observed from the results obtained at a heating rate of 0.17 K/s for the two polymorphic forms of RM presented in Figure 4. At the heating rate of 0.17 K/s, the endothermic heat flow is a dominating effect because there is insufficient time to develop the slow exothermic effect associated with the formation and growth of the glassy phase under fast heating conditions. Thus, the DSC traces presented in Figure 4 also represent the c-a transitions between the metastable crystalline forms and their dense amorphous phases, what is a logic extension of the observations from Figure 7. Most plausibly a similar inference is also valid for the literature data on the melting temperature of RM, where the value of 395-396 K was given,28 very close to that obtained presently by DSC for the virtual melting of the polymorphic form B (396.6 K) at a heating rate of 0.17 K/s. Thus, it becomes clear that most likely all the forms of RM obtained and investigated to date are metastable and that the real equilibrium crystalline phase of RM and its properties were not yet reported. Importantly, the c-a transition occurring through the virtual melting is a kinetic (dynamic) phenomenon. On heating, further crystalline defects (such as vacancies) can be formed17 that can increase the internal stress and further decrease the virtual melting temperature TVM. A slower heating allows for more time to form for such defects. Therefore, their number can increase more than during fast heating over the same temperature interval. This can be one of the reasons why the virtual melting temperatures are lowered significantly by the reduction of the heating rate (Figure 8). The TVM value for the polymorphic form A is lowered from 404.6 K at temperature scan rate of 0.17 K/s to 377.1 K at 0.1 mK/s, and for the

The present study for the first time describes and presents a detailed analysis of an unexpected and thermodynamically paradoxical transition from a crystalline state to an amorphous dense glassy state (c-a transition) induced in pure organic substances of pharmaceutical importance by a simple absorption of a quantity of heat under atmospheric pressure. The obtained results bring the first experimentally precise basis for understanding the mechanism of such a structural instability of crystalline substances in the form of c-a transitions. The observed c-a transition is a purely physical phenomenon, occurring between two nonequilibrium states, a metastable crystalline phase and a dense glass. Thus, although the observed c-a transition exhibits changes of both enthalpy and volume, it is not the first-order transition, because according to Ehrenfest classification29 the first-order transitions occur in equilibrium between the states and, moreover, they are reversible. The metastable state of a crystalline substance can be caused by existence of a number of nonequilibrium defects created either during crystallization or by external actions. The nonequilibrium defects create an internal stress and locally lower significantly the melting temperature, inducing a local transient phenomenon of virtual melting, if only the metastable crystalline substance absorbs a sufficient quantity of heat. This local melt removes the interface friction, reduces the kinetic barrier, increases the molecular mobility, and renders the kinetically allowed transformation of the whole metastable crystalline sample into the dense glassy state. This is because it is the nearest phase of lower entropy, if only the temperature of virtual melting is lower than the glass transition temperature of the substance under investigation. Today, neither technique nor theory is available, except for some attempts employing molecular dynamics simulations,16,30 which could quantitatively determine the critical number of imperfections in a crystal solid, making it metastable or unstable. Thus, the best experimental solution to determine such states is the transitiometric investigation of extremely sensitive energetic effects, as it was demonstrated in the present study for two polymorphs of rosiglitazone maleate, an organic substance of high pharmaceutical importance. Acknowledgment. The present contribution is dedicated to Dr. Wieslaw Szelejewski from the Pharmaceutical Research Institute in Warsaw, Poland, on the occasion of his 65th birthday. M. Chodynski, H. Fitak, M. Glice, and K. Leszczynska from the Pharmaceutical Research Institute are greatly acknowledged for providing samples of polymorphs of rosiglitazone maleate, and M. Malecki from the Institute of Physical Chemistry PAS for help in preparation of the manuscript. S.L.R. acknowledges K. Kamienska-Trela from the Institute of Organic Chemistry PAS for a kind discussion on the solid FTIR spectra of crystalline and amorphous samples of the form B of rosiglitazone maleate and W. D. Nix from the Stanford University for providing his notes on imperfections in crystalline solids. References and Notes (1) Kauzmann, W. Chem. ReV. 1948, 43, 219-256. (2) Mishima, O.; Calvert, L. D.; Whalley, E. Nature 1984, 310, 393395. (3) Mishima, O. Nature 1996, 384, 546-549.

1444 J. Phys. Chem. B, Vol. 112, No. 5, 2008 (4) Tse, J. S.; Klug, D. D.; Tulk, C. A.; Swainson, I.; Svensson, E. C.; Loong, C.-K.; Shpakov, V.; Belosludov, V. R.; Belosludov, R. V.; Kawazoe, Y. Nature 1999, 400, 647-649. (5) Cahn, R. W. Nature 1995, 373, 475-476. (6) Richet, P. Nature 1988, 331, 56-58. (7) Marque´s, L. A.; Pelaz, L.; Herna´ndez, J.; Barbolla, J.; Gilmer, G. H. Phys. ReV. B 2001, 64, 045214. (8) Sinkler, W.; Michaelsen, C.; Borman, R. A. J. Mater. Res. 1997, 12, 1872-1884. (9) Stillinger, F. H.; Debenedetti, G. Biophys. Chem. 2003, 105, 211220. (10) Rehn, L. E.; Okamoto, P. R.; Pearson, J.; Bhadra, R.; Grimsditch, M. Phys. ReV. Lett. 1987, 59, 2987-2990. (11) Fecht, H. J.; Johnson, W. L. Nature 1988, 334, 50-51. (12) Kelly, A.; Groves, G. W.; Kidd, P. Crystallography and crystal defects, revised edition; John Wiley & Sons: Chichester, 2000. (13) Fecht, H. J. Nature 1992, 356, 133-135. (14) Levitas, V. I. Phys. ReV. Lett. 2005, 95, 075701. (15) Rohrer, G. S.; Rohrer, C. L.; Mullins, W. W. J. Am. Ceram. Soc. 2001, 84, 2099-2104. (16) Hsieh, H.; Yip, S. Phys. ReV. Lett. 1987, 59, 2760-2763. (17) Nix; W. D. Personal communication, July 2007.

Randzio and Kutner (18) Font, J.; Muntasell, J.; Cesari, E. Mater. Res. Bull. 2001, 36, 16651673. (19) Gupta, M. K.; Vanwert, A.; Bognar, R. H. J. Pharm. Sci. 2003, 92, 536-551. (20) Kitamura, M. Pure Appl. Chem. 2005, 77, 581-591. (21) Randzio, S. L. Chem. Soc. ReV. 1996, 25, 383-392 (http:// www.transitiometry.com). (22) Pool, C. R.; Roman, R. S.; Brighwell, M. D.; Tremper, A. W. Patent WO 9405659, Chem. Abstr. 120, 323564. (23) Craig, A. S.; Giles, R. G.; Ho, T. C. T.; Sasse, M. J. Patent WO 2004085435, Chem. Abstr. 141, 320076. (24) Randzio, S. L.; Stachowiak, C.; Grolier, J.-P. E. J. Chem. Thermodyn. 2003, 35, 639-648. (25) Randzio, S. L.; Orlowska, M. Biomacromolecules 2005, 6, 30453050. (26) Burger, A.; Ramberger, R. Mikrochim. Acta 1979, 2, 259-271. (27) Legendre, B.; Randzio, S. L. Int. J. Pharm. 2007, 343, 41-47. (28) Bhushan, R.; Gupta, D.; Jain, A. J. Planar Chromatogr.sMod. TLC 2006, 19, 288-296. (29) Ehrenfest, P. Proc. Acad. Sci. Amsterdam 1933, 36, 153-157. (30) Nishihira, K.; Motooka, T. Phys. ReV. B 2002, 66, 233310.

Metastability and Instability of Organic Crystalline Substances

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