Local Structure in Amorphous Phases of Piroxicam from Powder X-ray

The PDF transforms show the loss of crystalline order induced by the grinding process ..... Andres Lust , Clare J. Strachan , Peep Veski , Jaakko Aalt...
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Local Structure in Amorphous Phases of Piroxicam from Powder X-ray Diffractometry Agam R.

Sheth,†

Simon

Bates,‡

Francis X.

Muller,§

and David J. W.

Grant*,†

Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Weaver-Densford Hall, 308 Harvard Street SE, Minneapolis, Minnesota 55455-0343, SSCI Inc., 3065 Kent Avenue, West Lafayette, Indiana 47906-1076, and GlaxoSmithKline Pharmaceuticals, P.O. Box 1539, 709 Swedeland Road, King of Prussia, Pennsylvania 19406-0939

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 2 571-578

Received July 15, 2004

ABSTRACT: The local structures of amorphous phases of piroxicam were studied to explain differences in their recrystallization behavior, which we reported earlier (Sheth, A. R.; Bates, S.; Muller, F. X.; Grant, D. J. W. Polymorphism in piroxicam. Cryst. Growth Des., in press). The differences between the structures of form I (PI) at 25 and at 160 °C are consistent with anisotropic thermal expansion (Rx ) 2.85 × 10-5 K-1, Ry ) 1.96 × 10-5 K-1, Rz ) 5.26 × 10-6 K-1, volume thermal expansivity of the unit cell ) 4.92 × 10-5 K-1, increase in unit cell volume ) 2.01%). Cryogenic grinding was employed to produce the respective amorphous forms, PAI from PI and PAII from PII. Pairwise distribution function (PDF) transforms were utilized to compare atom to atom correlations in PAI and PAII and to understand differences in their recrystallization behavior on the basis of their local structure. PDF transforms showed that PAI and PAII are types of amorphous material, which may be termed random ordered network (RON) amorphous. PAI and PAII were found to possess similar short-range interactions. The presence of PI-like residual long-range order in PAI explains recrystallization to PI. However, the absence of PII-like residual longrange order in amorphous PAII appears counterintuitive and suggests that PAII could recrystallize to a crystalline form different from the initial crystalline form. Introduction Amorphous forms prepared by grinding, unlike those prepared from the melt, usually possess characteristics of the original polymorph, that is, “polymorphic memory”, which would direct recrystallization to the original polymorph. A powder X-ray diffraction (PXRD) pattern that is X-ray amorphous due to grinding may originate from different types of material. The most common X-ray amorphous form is disordered crystalline or nanocrystalline material. This type of X-ray amorphous pattern can be modeled by increasing the random-stress (disordered crystalline) or by reducing the crystal size (nanocrystalline) of the corresponding crystal structure. This disordered crystalline or nanocrystalline material is usually unstable and will usually recrystallize to the original crystalline form. Disordered crystalline or nanocrystalline material is the X-ray amorphous form with the strongest “memory” of the original crystalline polymorph. As the disorder is increased, the induced dislocations can approach a sufficiently high density to transform the crystalline phase to an amorphous phase. A number of theoretical models have been proposed to describe the local order within amorphous materials,1 the most notable of which are the random closed packed (RCP) model and the continuous random network (CRN) model. More recently, the CRN model has been extended to incorporate variable chemical bonding in the chemically ordered network (CON) model.2 In the RCP model, the molecules may pack with a local coordination * Corresponding author. Phone: (612) 624-3956. Fax: (612) 6250609. E-mail: [email protected]. † University of Minnesota. ‡ SSCI Inc. § GlaxoSmithKline Pharmaceuticals.

different from that in any of the crystalline polymorphs. In addition, an infinite number of local packing arrangements may occur corresponding to an infinite number of possible local amorphous structures. In contrast, the CRN model describes systems with strong directional covalent bonding. In the original model, each molecule has a single local bonding and coordination requirement with respect to its nearest neighbors (NN). Hence, the local coordination of the molecule will be the same in the crystalline and amorphous forms, corresponding to a single local amorphous structure. The CON model has extended the CRN model to include the possibility of variable local molecular coordination and bonding, which depend on the local chemical stoichiometry. These models of local amorphous structure are ideal concepts that are not directly applicable to molecular organic systems with strong anisotropy and variable molecular bonding schemes, although they have successfully predicted some material properties. We designate this type of amorphous material as random ordered network (RON) amorphous to distinguish it from the models previous mentioned. In RON amorphous materials, the molecules have either strong directional covalent bonding or hydrogen bonding and more than one possible intermolecular bonding network. Furthermore, these systems will be dominated by molecular shape anisotropy and bonding anisotropy.3 In the amorphous phase, the local molecular packing takes precedence over any longer range packing considerations. The molecules tend to achieve the highest local packing density with the largest number of NN molecules permitted by bonding requirements and shape anisotropy. The local packing arrangements are typi-

10.1021/cg049757i CCC: $30.25 © 2005 American Chemical Society Published on Web 11/09/2004

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Figure 1. Molecular structure of piroxicam, 4-hydroxy-2methyl-N-2-pyridinyl-2H-1,2-benzothiazine-3-carboxamide.5

cally different from those in any of the crystalline polymorphs and may be separated from the crystalline packing by a large energy barrier that depends on the degree of anisotropy present.3 Unlike the characteristic NN distance predicted for the RCP and CRN models, the RON amorphous material will have a number of discrete molecular NN distances reflecting the molecular anisotropy. In the simplest case of dominant shape anisotropy, these NN distances correspond to the length, width, and height of the molecule and will appear as three distinct halos in a powder X-ray pattern. The concept of local anisotropy as a cause of stable shortrange ordered clusters is similar to the concepts of jamming and cooperative clusters in glasses and liquid crystals. The RON amorphous material is locally anisotropic but, in common with all amorphous materials, is macroscopically isotropic. The RON amorphous material will be thermodynamically more stable, meaning that it is less likely to recrystallize, than the disordered nanocrystalline X-ray amorphous material on account of the large energy barrier between the local amorphous molecular packing and the longer range crystal packing. On further grinding, the RON amorphous material may disorder to a locally more isotropic amorphous state that is characterized by a single average NN molecular spacing, as predicted by many of the simpler models of amorphous materials. However, due to the significant shape anisotropy of the piroxicam molecule (Figure 1), it is unlikely that a locally isotropic amorphous solid could be produced. “Memory” of longer-range crystalline order, which is expected to be present, has been proposed as a dominant driving force for recrystallization of amorphous forms produced by grinding. Polymorphic “memory” in amorphous material results in the presence of long-range atom-atom correlations characteristic of one of the crystalline polymorphs within the disordered amorphous solid. From the discussion above, the local amorphous packing is separated from any longer-range crystalline order by a significant energy barrier. Thus, these longer-range crystallographic correlations must be physically separate from the locally amorphous regions. As a result of polymorphic memory, this polymorph will most likely be the first crystalline phase formed on recrystallization, although this form may be less stable than the final crystalline form according to Ostwald’s rule of stages.4 The use of pairwise distribution function transforms (PDF) of experimental PXRD data is a common technique for the identification of characteristic atom to atom distances within both amorphous and crystalline materials. Piroxicam (Figure 1), an enolic acid and oxicam derivative, is a potent, long-acting, nonsteroidal anti-

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inflammatory drug.5 In a previous article, we reported that cryogrinding piroxicam forms I (PI) and II (PII) resulted in amorphous piroxicam PAI from form I and amorphous piroxicam PAII from form II.6 We also reported that, because of differences in recrystallization behavior of PAI and PAII,6 PAI appeared to retain some polymorphic memory of PI in contrast to PAII, which was characterized by a complete loss of polymorphic memory of PII. This loss of polymorphic memory due to grinding is counterintuitive. To the best of our knowledge, this is the first study of “polymorphic memory” upon grinding of organic molecular crystals. Some differences in PXRD patterns of PI at 25 °C and at higher temperatures, such as 160 °C, were also reported.6 In the present work, we have redetermined the crystal structure of PI at 25 °C and have also determined it at 160 °C. We have also studied the nature of the crystalline to amorphous transformation of PI and PII and have analyzed the local structure of their disordered phases to explain the differences in the nature of PAI and PAII reported previously.6 Materials and Methods Piroxicam (Sigma Chemical Company, St. Louis, MO) was found to correspond to PI by comparison of diffraction angles using PXRD and was used as received. PII was prepared from PI as described previously.6 The crystal structure of PI (reference code BIYSEH)7 was downloaded from the Cambridge Structural Database (CSD), version 5.24,8 using established software (Conquest,9 version 1.5, Cambridge Crystallographic Data Center, Cambridge, U.K.). The crystallographic information file of the crystal structure of PII was kindly provided by Professors F. Vrecer, M. Vrbinc, and A. Meden.10 Samples of PI recrystallized from various solvents had PXRD patterns with similar peak positions but with different relative peak intensities. A similar observation was also made when comparing PXRD patterns of the same sample of PI obtained on different occasions. Furthermore, when the averaged experimental PXRD pattern of PI was compared with the PXRD pattern calculated from its reported crystal structure, BIYSEH,6,7 the peak positions matched but the relative peak intensities were found to differ. Due to consistent discrepancies between the measured PXRD pattern and the PXRD pattern calculated from the BIYSEH single-crystal structure, the crystal structure of PI was therefore redetermined. Much of the observed variation in peak intensity between the different experimental (measured) PXRD patterns of PI appeared to arise from the effects of the relatively large crystal size on sample preparation. To reduce the sample preparation error as far as possible, the 2θ values of the experimental PXRD patterns were initially shifted to align the major peaks and were then averaged. The correct 2θ shift of the experimental PXRD patterns was determined by first identifying families of diffraction peaks and then shifting the data in 2θ until the spacing of the peaks in a single family was constant in Q (Q ) 4π sin(θ)/λ) or sin(θ).11 The crystal unit cell of the averaged experimental PXRD pattern was determined using a reverse Monte Carlo indexing approach with restricted parameter searching.11 The unit cells searched were automatically restricted to those that supported the allowed packing of the piroxicam molecule as determined by close packing rules.12 DASH13 was used to pack the piroxicam molecules into the indexed unit corresponding to the averaged experimental PXRD pattern. As a final step to determine any scale factors and microstructural properties, MAUD14 was used for Rietveld refinement of the molecular packing solution from DASH. Because of the similarity of the experimental PXRD pattern of PI at 160 °C to that calculated from BIYSEH, only the final Rietveld refinement step (MAUD)14 was required to determine

Local Structure in Amorphous Phases of Piroxicam the final structure of PI at 160 °C. In addition to the scale factors and microstructure, the unit cell lattice parameters were also refined in the Rietveld pass. During this refinement, the relative atomic coordinates were not changed from the original BIYSEH crystal structure. The crystal structure of PII was also redetermined by Rietveld refinement (MAUD14) of the published structure of PII.10 PXRD patterns of PI and PII cryoground for 12, 24, 36, 48, and 60 min were collected as previously described.6,15 Cryogrinding PI or PII for 60 min results in X-ray amorphous PAI or PAII, respectively.6 Cryogrinding PI and PII for intermediate time periods, that is, 12, 24, 36, and 48 min, results in PXRD patterns showing decreasing crystallinity with increasing time of cryogrinding.6,15 The PDF transform, which is a Fourier sine transform of the reduced structure factor representation of the PXRD data, is a powerful tool for studying crystalline-amorphous relationships.16 The PDF transform shows the instantaneous atom to atom distances for a material in real space. By examining PDF transforms of the crystalline material after different times of cryogrinding, it is possible to identify changes in the crystalline form that arise from the stresses induced by cryogrinding. In published reports, PDF transforms are usually applied to powder synchrotron X-ray diffraction patterns or powder neutron diffraction patterns with data collected to relatively high 2θ values. For molecular organic systems, the electronic form factor and the Debye-Waller thermal parameters cause the PXRD data to fall off sharply with increasing 2θ, often with little measurable intensity above 40° 2θ, when using laboratory X-ray diffraction systems with Cu KR radiation (λ ≈ 1.5406 Å). This intensity falloff beneficially allows the use of data collected over a relatively narrow 2θ range and beneficially minimizes the introduction of truncation ripples in the Fourier sine transform. However, the reduced measurement range reduces the spatial resolution of the resulting pairwise distribution function. The presence of significant noise levels within the experimental PXRD data can lead to the appearance of spurious correlations within the PDF transform. This problem is especially serious when analyzing amorphous materials and can be minimized by averaging the results of multiple measurements. In the present work, the PDF transform was calculated by first transforming the experimental PXRD data to a reduced structure factor representation in Q. The method presented by Warren17 was used to correct and normalize the measured X-ray intensity to electron units and then to transform the data into the reduced structure factor representation using the molecular structure to remove the form factor dependence.17 The reduced structure factor data are transformed into the PDF representation of the experimental PXRD pattern through a weighted Fourier sine transform.17 The convergence term was refined until the truncation peaks diminished to a minimum without loss of the essential information in the PDF transform. The robustness and characteristics of the PDF transform derived from short-range PXRD data using this method are demonstrated in Figures 2 and 3 where two very different measurements on form III (transmission parallel beam and reflection Bragg Brentano) give essentially the same PDF result. The calculated PDF pattern consists of a series of peaks as a function of distance, r (Å). For a molecule such as piroxicam, with a single heavy atom, S, the peaks will typically correspond to the S to S atom distances within the structure. These distances can be confirmed by comparing the peak positions with atom distances determined from the crystal structure.

Results and Discussion Table 1 lists select crystallographic parameters of form I7 (reference code BIYSEH7,8), form I redetermined here at 25 and at 160 °C, form II,10 and form II redetermined here. The crystal structure of PI redetermined at 25 °C was found to provide a better reproduction of the average experimental PXRD pattern than

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Figure 2. Experimental powder X-ray diffraction data of form III. The data in (a) red were collected using transmission parallel beam geometry, while the data in (b) black were collected using reflection Bragg-Brentano geometry.

Figure 3. Pairwise distribution function (PDF) transforms of the powder X-ray diffraction patterns in Figure 2: (a) PDF transform of PXRD data collected using transmission parallel geometry; (b) PDF transform of PXRD data collected using reflection Bragg-Brentano geometry. The peak positions present in both PDF transforms are the same, although the resolution in the transmission measurement is poorer.

BIYSEH. The structure of PI redetermined at 25 °C possesses lattice constants that are almost the same as those of the original structure, BIYSEH. Taking into account the shift in the origin and performing symmetry operations permitted by the P21/c space group, the atomic positions in the structure of PI redetermined at 25 °C are slightly different from those of BIYSEH but the overall molecular packing is essentially unchanged. The hydrogen bond network is also identical. The difference in relative intensities among various PXRD patterns of PI can be attributed to particle statistics due to the large crystallite size of PI on crystallization and to random effects arising from slight shifts in atomic positions between BIYSEH and the structure of PI redetermined here at 25 °C. Our previous article6 reported that differences between the PXRD patterns of PI at 25 and at 160 °C arise from expansion or contraction of the crystal lattice of

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Table 1. Crystallographic Parameters of Form I7 (reference code BIYSEH7,8), Form I Redetermined Here at 25 °C and Determined here at 160 °C, Form II,10 and Form II Redetermined Here original form I7 (BIYSEH7,8)

form I redetermined here at 25 °C

form I determined here at 160 °C

original form II10

form II redetermined here

monoclinic P21/c

monoclinic P21/c

monoclinic P21/c

monoclinic P21/c

monoclinic P21/c

7.127(2) 15.136(7) 13.949(6) 90 97.35(4) 1491.15 1.48

7.136(3) 15.164(4) 13.976(4) 90 97.414(15) 1499.6 1.47 [100] 1.04

7.219(2) 15.285(4) 14.006(4) 90 98.181(17) 1529.7 1.44 [100] 0.925

17.5877(4) 11.8592(3) 6.93840(10) 90 97.5614(9) 1434.60(5) 1.534

17.582(7) 11.907(4) 6.960(2) 90 97.056(5) 1446.0 1.52 [001] 1.21

0.19

0.11

crystal system space group unit cell dimensions a (Å) b (Å) c (Å) R, γ (deg) β (deg) volume (Å3) theoretical density (g/cm3) March-Dollase preferred orientation parameter quality of Rietveld model RB

PI under increasing or decreasing temperatures. In the structure of PI at 160 °C, the molecular packing is unchanged, but as shown in Table 1, the unit cell dimensions are slightly larger resulting in an increased unit cell volume. Figure 4 compares the PDF transforms of PI at 25 and at 160 °C and clearly shows that the thermally expanded lattice of PI at 160 °C has the same molecular packing as that of PI at 25 °C. The changes in the crystal lattice of PI from 25 to 160 °C are thus consistent with its expansion through increasing temperature. Knowledge of the crystal structures of PI at 25 and 160 °C enables calculation of its thermal expansivity (also known as thermal expansion coefficient), R, in a particular crystallographic direction, i. Under constant pressure, the thermal expansivity is defined as

Ri )

( )

1 ∆Li Li ∆T

where Li represents the lattice parameter along the crystallographic axis, i, and ∆Li is the change in this lattice parameter corresponding to a temperature range, ∆T, where T is the temperature in kelvin.18 The lattice parameters, a, b, and c in Table 1, refer to the x, y, and

Figure 4. Pairwise distribution function transforms of form 1 (PI) at 25 °C (red, a) and at 160 °C (black, b) from measured (experimental) powder X-ray diffraction data. The molecular packing of PI from 25 to 160 °C is similar, but the absolute peak positions due to thermal expansion of the crystal lattice are different.

0.05

z axes, respectively. Using the above expression, we obtain the following values of thermal expansivity of PI in each of the crystallographic directions, x, y, and z: Rx ) 2.85 × 10-5, Ry ) 1.96 × 10-5, and Rz ) 5.26 × 10-6 K-1. The above values show that the thermal expansion of PI from 25 to 160 °C is anisotropic, the thermal expansivity being largest along the x axis and least along the z axis. From 25 to 160 °C, the volume expansivity of the unit cell is 4.92 × 10-5 K-1. The increase in unit cell volume of 2.01% is also consistent with thermal expansion. Analysis of the local structures of the two amorphous forms PAI and PAII begins with the determination of the PDF transforms of the known crystalline polymorphs (the crystal structure of PI redetermined here at 25 °C, the crystal structure of PI determined here at 160 °C, and the crystal structure of PII redetermined here) and the cryoground material at different stages of grinding. Where the crystal structure is known, the PDF can be directly calculated. Figure 5 compares the PDF transform of PI calculated from the redetermined structure at 25 °C with that determined by measurement. The good agreement demonstrates the precision of the PDF determination from measured PXRD data using the method outlined under Materials and Methods. Figure 6 shows the PDF transforms of PII derived from two different PXRD patterns and that calculated from its

Figure 5. Comparison of PDF transform of form I calculated from the crystal structure redetermined at 25 °C (red, a) with that from the average measured powder X-ray diffraction pattern of form I (black, b).

Local Structure in Amorphous Phases of Piroxicam

Figure 6. Pairwise distribution function transforms of form II calculated from the redetermined single crystal structure (blue, a) and from two different measured powder X-ray diffraction patterns (black, b, and red, c). The differences mainly arise from particle statistics with some peak movement due to the differences in temperature at which the data were collected.

Figure 7. Pairwise distribution function transforms of form I at various stages of cryogrinding: (a) 12 min (red); (b) 60 min (black). Traces for PDF transforms after cryogrinding for 24, 36, and 48 min are also presented. The greater loss of characteristic crystalline peaks at higher atom to atom distances is consistent with the reduction in crystal size.

single-crystal structure redetermined here. The agreement is not as close as that for PI reflecting the influence of particle statistics on the PDF determination. Minor peak shifts occur as a result of the temperature difference between the single crystal data and the measured PXRD data. Although the PDF transforms show some variation in resolution and peak intensity, depending on the instrumentation used to collect the data, the peak positions remain consistent with theoretical predictions and uniquely identify each crystalline polymorph. Figure 7 shows the PDF transforms of PI at 12, 24, 36, 48, and 60 min of cryogrinding. The material cryoground for 60 min has a PXRD pattern consistent with X-ray amorphous material with two broad halos and no sharp diffraction peaks (Figure 11). The PDF transforms show the loss of crystalline order induced

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Figure 8. Pairwise distribution function transforms of form I (PI) showing nearest neighbor (NN) molecular packing distances at various stages of cryogrinding: (a) 12 min (red); (b) 60 min (black). Traces for PDF transforms after cryogrinding for 24, 36, and 48 min are also presented. The NN molecular packing distances change from PI to the amorphous phase. The new NN distances of 4.9, 7.9, and 12.3 Å correspond to molecular length, width, and height and represent random close packing governed by molecular shape anisotropy.

by the grinding process as the characteristic peaks become progressively weaker. Initially, the peaks disappear from the longer atom to atom distances, indicating a reduction of crystal size. The PDF transform provides a useful alternative method for the determination of the crystal size corresponding to the atom to atom distances at which the PDF peaks disappear. Along with the loss of the characteristic crystalline PDF peaks, an oscillation of a much longer length scale appears, corresponding to about 18.5 Å with very broad peaks. This 18.5 Å harmonic arises from the low Q termination error in the sine Fourier transform due to the relatively large initial value of 2θ (5°). This termination error can be removed by measuring to lower angles or by damping mathematically. Figure 8 shows a detailed presentation of the first few PDF peaks corresponding to the nearest neighbor (NN) interactions. As PI is ground, the local NN molecular configuration changes significantly from the crystal packing to a new amorphous packing. The crystalline to amorphous transformation in PI is a continuous process with a gradual loss of crystalline order and with gradual build up of amorphous local order. The three NN peaks correspond to approximate atom to atom distances of 4.9, 7.9, and 12.3 Å. The piroxicam molecule as arranged in the crystal structure of PI redetermined at 25 °C has approximate length 11.5 Å, width 6.0 Å, and height 4.0 Å, which are in close correspondence with the three NN distances determined from the PDF transform. These distances indicate that the average local structure of the PAI amorphous phase is random close packed governed by the molecular shape anisotropy. In addition to the NN peaks, some longer atom to atom correlation remains. Figure 9 shows the use of the convergence function to remove the high Q termination oscillations from the PDF to gain access to any residual structure. The further damping of the high Q termination ripples moves the first NN peak from 4.9

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Figure 9. Pairwise distribution function transforms of X-ray amorphous piroxicam obtained by cryogrinding form I for 60 min (PAI). Both the longer harmonic oscillation at 18.5 Å and the shorter harmonic oscillations at 2.2 Å result from truncation errors in the Fourier sine transform. The (a) red curve is before increasing the convergence parameter, and the (b) black curve is after increasing the convergence parameter to obtain optimum damping. The high-frequency oscillations are removed by the convergence function to reveal local longer range atom to atom correlations. The removal of the high Q truncation error causes the first nearest neighbor (NN) peak to move from 4.9 to 5.7 Å, which is more consistent with NN molecular packing.

Figure 10. Pairwise distribution function transforms of X-ray amorphous piroxicam obtained by cryogrinding form I for 60 min (PAI, red, a) and that calculated from the single crystal structure of form I (blue, b). After removal of the Fourier sine transform truncation oscillations, the residual longer range atom to atom correlations correlate strongly with the original form I crystal structure.

to 5.7 Å, making it more consistent with molecular height spacing. After all the Fourier sine transform truncation peaks are removed, the remaining residual longer range atom to atom correlations between 20 and 50 Å show a strong correlation with the original form I crystal structure as shown in Figure 10. These form I-like longer-range interactions are likely to influence the recrystallization of PAI toward a crystalline form similar to form I. Resemblance of PAI to PI in its longrange order explains the observation that PAI first

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Figure 11. Measured powder X-ray diffraction (PXRD) data of form I cryoground for 60 min (PAI, blue, a) shown with the results of modeling this X-ray amorphous phase as a disordered crystalline material (red, b). The calculated pattern was modeled using the MAUD Rietveld program.14 The lack of agreement between the disordered crystalline model and the measured PXRD data indicates that PAI is not a disordered crystalline or nanocrystalline material.

Figure 12. Pairwise distribution function transforms of form II at various stages of cryogrinding: (a) 12 min (red); (b) 60 min (black). Traces for PDF transforms after cryogrinding for 24, 36, and 48 min are also presented. The greater loss of characteristic crystalline peaks at higher atom to atom distances is consistent with the reduction in crystal size. Spontaneous reordering of the molecular packing takes place before formation of the X-ray amorphous material, PAII.

crystallizes predominantly to PI, which we reported in a previous article.6 Figure 11 illustrates the X-ray amorphous PXRD pattern of PAI. To rule out the possibility that PAI is actually a disordered crystalline or nanocrystalline material, attempts were made to model the measured PXRD data using the Rietveld program MAUD.14 No model of crystalline order could be found that allowed a good description of the measured PXRD data. Figure 11 also shows results of the best model. Figure 12 shows the PDF transforms of PII at various stages of cryogrinding. PII undergoes a spontaneous rearrangement of molecular packing in contrast to the gradual transition seen for PI. On cryogrinding PII, the

Local Structure in Amorphous Phases of Piroxicam

Figure 13. Measured powder X-ray diffraction (PXRD) pattern of form II after cryogrinding for 48 min (black, a) and that calculated from form II modeled as a mixture of nanocrystalline material with 2 nm crystal size and crystalline material (red, b).

initial loss of intensity of the crystalline peaks is accompanied by the build up of diffuse X-ray amorphous intensity, which is different in profile from that of final amorphous form, PAII. Modeling this process using Rietveld refinement (MAUD14) clearly indicates that the amorphous form produced initially from PII is actually a nanocrystalline material with an effective crystal size of about 2 nm. Figure 13 compares the measured PXRD patterns of PII after cryogrinding for 48 min with that calculated from PII modeled as a nanocrystalline material (2 nm crystal size). The amorphous component, which comprises about 92% of the material, differs only in its effective crystal size from the form II crystalline material, which comprises the remaining 8% of the material. The spontaneous transformation of this material to the final X-ray amorphous form, PAII, on further cryogrinding corresponds to a phase transition from nanocrystalline to amorphous. An intermediate nanocrystalline form was not observed for form I. This structural transformation to the final X-ray amorphous form from form II further indicates a significant energy barrier that would slow recrystallization of PAII to the original form II. The PDF transform of PAII is very different from that at intermediate grinding times. The three NN peaks spontaneously jump to their new positions and the low Q truncation harmonic suddenly changes, indicating a different overall distribution of diffraction intensity. Figure 14 compares the measured PXRD patterns on either side of the X-ray amorphous transition. These PXRD patterns differ, also indicating that a spontaneous structural change takes place when form II is cryoground to an X-ray amorphous state. Figure 15 compares the PDF transforms of PAI and PAII and shows that these materials possess essentially the same local amorphous structure. This short-range order exhibits three distinct length scales and is characteristic of RON amorphous material. This amorphous form is the same for PAI and PAII and is typical of random local packing governed by molecular shape anisotropy. The three length scales correspond to NN ordering along the height, width, and length of the

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Figure 14. Measured powder X-ray diffraction (PXRD) data of form II after cryogrinding for (a) 48 min (red) and (b) 60 min (black). The appreciable difference between these PXRD patterns indicates a spontaneous structural change during cryogrinding form II to X-ray amorphous.

Figure 15. Comparison of pairwise distribution function transforms of X-ray amorphous piroxicam obtained by cryogrinding (a) form I for 60 min (PAI, black) and (b) form II for 60 min (PAII, red). Deviations between the two curves at higher atom to atom distances, shown by arrows, indicate different residual long-range order.

organic molecule. However, deviations in the PDF transforms at larger atom to atom distances indicate that the residual order in PAI is not the same as that in PAII. A detailed comparison of the residual long-range atom to atom correlations in PAII with PDF calculated from PII finds no relationship. In view of the spontaneous structural change occurring before PAII is formed, it is not surprising that no residual long-range order of PII remains in PAII. The residual long-range atom to atom correlations in PAII were also found not to be strongly correlated to the other two polymorphs, forms I and III. A weak correlation was observed with the crystal structure of PI at 160 °C, which may be a consequence of the spontaneous molecular reorganization that occurs when PII is cryoground to PAII. We previously reported that PAII recrystallized to form III and not to the original PII.6 Although melt-quenching piroxicam produces an amorphous phase, melt-quenched piroxicam was not used in this study because piroxicam

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was found to undergo chemical degradation upon melting.6 However, melt-quenched piroxicam was also found to recrystallize to form III. The recrystallization behavior of PAII previously reported6 is therefore consistent with the observation in the present work that all residual memory of PII is lost during amorphization. However no evidence in the measurements in the present work independently suggests that PAII would recrystallize to form III. The PII to PAII phase transition is a spontaneous process that indicates the presence of a significant energy barrier between the two phases, which might retard recrystallization of PAII to PII. Using Rietveld refinement (MAUD),14 we also found that PAII, like PAI, is not a disordered crystalline or nanocrystalline material. Conclusions The redetermined structure of PI at 25 °C differs only slightly in atomic positions from the published structure but can reproduce the relative peak intensities of experimental PXRD patterns of PI better than BIYSEH. The crystal structure of PI at 160 °C has the same molecular packing as that at 25 °C but has slightly larger lattice parameters consistent with thermal expansion of its crystal lattice. PI undergoes anisotropic thermal expansion from 25 to 160 °C along each crystallographic axis. PI and PII on cryogrinding resulted in, not disordered crystalline or nanocrystalline material, but RON amorphous material, PAI and PAII, respectively. PAI and PAII have the same local amorphous NN order but differ in their residual longer-range order, suggesting differences in the mechanics of their respective recrystallization processes. In addition, the PII to PAII phase transition is a spontaneous molecular rearrangement that is likely to place an energy barrier to recrystallization of the original PII structure. The difference between the nature of PAI and PAII previously reported6 can similarly be explained. The residual memory of PI in PAI explains its observed recrystallization to PI, as previously reported.6 Loss of polymorphic memory of PII in PAII was found, which is unusual, because amorphous forms prepared by grinding are expected to retain memory of the original polymorph. The above study also highlights the importance of PDF transforms in understanding crystalline-amorphous relationships. Acknowledgment. We thank Pofessors F. Vrecer, M. Vrbinc, and A. Meden (ref 10) for kindly providing the CIF file of the crystal structure of piroxicam form II and GlaxoSmithKline, through Dr. Fran Muller, for gifts of piroxicam and for the award of a studentship to A.R.S. We also thank Dr. Igor Ivanisevic, SSCI, Inc., for kindly providing SSCI software for this work. References (1) Gersten, J. I.; Smith, F. W. The Physics and Chemistry of Materials; John Wiley: New York, 2001.

Sheth et al. (2) Micoulaut, M. The slope equations: a universal relationship between local structure and glass transition temperature. Eur. Phys. J. 1998, B1 (3), 277-294. (3) Tanaka, H. A simple physical model of liquid-glass transition: intrinsic fluctuating interactions and random fields hidden in glass-forming liquids. J. Phys.: Condens. Matter 1998, 10 (14), L207-L214. (4) Ostwald, W. Lehrbuch der Allgemeinen Chemie, vol. 2; W. Engelmann: Leipzig, Germany, 1896; p 444. Ostwald, W. Z. Phys. Chem. 1897, 22, 289-330. Ostwald, W. Grundriss der Allgemeinen Chemie; W. Engelmann: Leipzig, Germany, 1899. (5) Majerus, P. W.; Broze, G. J.; Miletich, J. P.; Tollefsen, D. M. In Goodman and Gilman’s The Pharmacological Basis of Therapeutics, 9th ed.; Hardman, J. G., Limbird, L. E., Eds.; McGraw-Hill: New York, 1996; pp 640-641. The Merck Index, 13th ed.; Merck & Co., Inc.: Whitehouse Station, NJ, 2001; p 7588. The United States Pharmacopoeia XXVI (USP26/NF21, twenty-sixth revision). The United States Pharmacopoeial Convention, Inc.: Rockville, MD, 2003. (6) Sheth, A. R.; Bates, S.; Muller, F. X.; Grant, D. J. W. Polymorphism in piroxicam. Cryst. Growth Des., published online Sept 1, http://dx.doi.org/10.1021/cg049876y. (7) Kojic-Prodic, B.; Ruzic-Toros, Z. Structure of the antiinflammatory drug 4-hydroxy-2-methyl-N-2-pyridyl-2H-1 λ6, 2-benzothiazine-3-carboxamide 1,1-dioxide (piroxicam). Acta Crystallogr. 1982, B38, 2948-2951. (8) Cambridge Crystallographic Data Center. The Cambridge Structural Database; University Chemical Laboratory: Cambridge, UK 1996. Allen, F. H. The Cambridge Structural Database: a quarter of a million crystal structures and rising. Acta Crystallogr. 2002, B58, 380-388. Allen, F. H.; Motherwell, W. D. S. Applications of the Cambridge Structural Database in organic chemistry and crystal chemistry. Acta. Crystallogr. 2002, B58, 407-422. (9) Bruno, I. J.; Cole, J. C.; Edgington, P. R.; Kessler, M.; Macrae, C. F.; McCabe, P.; Pearson, J.; Taylor, R. New Software for searching the Cambridge Structural Database and visualizing crystal structures. Acta. Crystallogr. 2002, B58, 389-397. (10) Vrecer, F.; Vrbinc, M.; Meden, A. Characterization of piroxicam crystal modifications. Int. J. Pharm. 2003, 256, 3-15. (11) SSCI XRPD Pattern Match and Indexing Software, version 1.6.4; SSCI, Inc.: West Lafayette, IN, March 2004. (12) Gavezzotti, A. Are crystal structures predictable? Acc. Chem. Res. 1994, 27 (10), 309-314. (13) DASH, version 2.2 (May 2003) Cambridge Crystallographic Data Center, 12 Union Road, Cambridge, U.K. David, W. I. F.; Shankland, K.; Shankland, N. Chem. Commun. 1998, 931-932. (14) MAUD (Materials Analysis using Diffraction), version 1.9992; Luca Lutterotti, University of Trento: Italy. (15) Sheth, A. R.; Lubach, J. W.; Munson, E. J.; Muller, F. X.; Grant, D. J. W. Mechanochromism of piroxicam accompanied by intermolecular proton-transfer probed by spectroscopic methods and solid phase changes, manuscript in preparation. (16) Billinge, S. J. L.; Thorpe, M. F. Local Structure from Diffraction; Plenum Press: New York, 1998. (17) Warren, B. E. X-ray Diffraction; Dover Publications: New York, 1990. (18) Touloukian, Y. S.; Kirby, R. K.; Taylor, R. E.; Lee, T. Y. R. Thermal ExpansionsNonmetallic solids; Thermophysical Properties of Matter, Vol. 13; Plenum Press: New York 1977.

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