X-ray Powder Diffraction Pattern Indexing for Pharmaceutical Applications

Crystal-structure determination using X-ray diffraction from single crystals is a well-developed technique (1). A single crystal structure provides full structural characterisation of the form at the atomic scale. The main drawback to single crystal diffraction is the need to grow a sufficiently large and defect-free crystal for analysis, which is not practical for all crystal forms. Furthermore, a single crystal is not always representative of the polycrystalline material from which it was obtained. X-ray powder diffraction (XRPD) is an ensemble analysis that is generally representative of a powder material, and utilises powder samples that are often easier to produce than single crystals. For these reasons, XRPD is used routinely for the characterisation of crystalline solids.

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The XRPD pattern of a crystal form at a given thermodynamic state point serves as a fingerprint for the form under the given conditions. Information encoded in the XRPD pattern includes whether a material is a single phase or a mixture of phases; the size, shape and symmetry of the unit cell; the position of the molecules in the unit cell; and the crystallite strain, among other information. Despite the wealth of information available, routine interpretation of XRPD patterns is often limited to a qualitative visual comparison that, at best, underutilises the available information and, at worst, leads to incorrect conclusions. Extracting information from an XRPD pattern beyond visual interpretation adds significant value and greatly enhances understanding of crystal forms. XRPD indexing is one method that can be used to extract information and aid the interpretation of XRPD patterns.

XRPD indexing is the process of determining the size, shape and symmetry of the crystallographic unit cell for a crystalline component responsible for a set of peaks in an XRPD pattern. Indexing gets its name from the assignment of Miller index labels to each of the peaks in a pattern. The size and shape of the unit cell is determined as part of the indexing procedure. Generally, the unit-cell information is of greater interest than the Miller index labels. Indexing makes use only of the positions of the observed peaks. Peak positions are determined by the crystal symmetry and dimensions, as well as the X-ray wavelength utilised. Other techniques, such as Rietveld refinement, may be used to extract additional information using the peakintensity information (2); however, that is beyond the scope of this article.

Figure 1 is a graphical presentation of a successful indexing solution for lactose monohydrate. The XRPD pattern, shown in black, has many resolved reflections, good signal-to-noise and a small diffuse background. These characteristics are the result of utilising a diffractometer with high-quality optics and a crystalline specimen with adequate crystallite size and quality. Highquality data, such as those shown in Figure 1, significantly improve the likelihood of producing a correct indexing solution. The red bars below the pattern indicate the peak positions consistent with the tabulated unit cell and X-rays generated by the copper K-alpha transition. Agreement between the allowed peak positions and the observed peaks indicates a consistent unitcell determination. The published crystal structure of lactose monohydrate (3) is in excellent agreement with the trialindexing solution in this example. If a single crystal structure is not available for a given form, consistency between allowed and observed peak positions without excessive unobserved peaks provides evidence for a correct indexing solution.

Figure 1: Indexing solution for lactose monohydrate.

Applications of indexing

Mixtures.Mixtures that are mistakenly designated as single forms can be time consuming and expensive, particularly in the later stage of development. This problem can be avoided early in the development process by indexing the XRPD pattern of the form(s) of interest. All of the allowed peak positions are identified once an indexing solution is obtained. Therefore, an XRPD pattern is known to be representative of a single crystalline phase once it is indexed. Mixtures of forms have peaks at positions that are incompatible with an indexing solution for one form. Consequently, mixtures of forms cannot be indexed using a single unit cell. It is advisable to have the XRPD patterns of all crystalline forms indexed to avoid unpleasant surprises during development.

It is important to note that an XRPD pattern that is not successfully indexed does not necessarily mean that the pattern is representative of a mixture. Poor data quality, significant peak overlap, elongated or compressed unit cells, preferred orientation artifacts and/or several weak reflections are all potential reasons why an XRPD pattern of a single phase may not index successfully. A successful indexing attempt reveals that the XRPD pattern is representative of a single crystalline phase. Although an unsuccessful attempt may be indicative of a mixture, it is not conclusive. Additional techniques are necessary to determine if the material is a mixture of forms.

Density estimates. Form stability has been correlated with density (4). Because indexing yields accurate unit-cell dimensions, the density of each form can be calculated provided that the contents of the unit cell are known. This can be useful when multiple anhydrous forms are discovered to determine the most and least dense crystal forms.

Variable hydrates, solvates and/or cocrystals. Multiple components may be incorporated into a crystal framework, resulting in hydrates, solvates and/or cocrystals. Multicomponent crystal forms can be stoichiometric or nonstoichiometric. Stoichiometric forms have a fixed ratio of water, solvent and/or coformer molecules per API. These fixed ratios are the result of discrete positions for molecules within the crystal structure. Because the crystal structures of stoichiometric forms are fixed, the XRPD peak positions occur at consistent diffraction angles. In contrast, nonstoichiometric forms have a range of compositions owing to flexible crystal frameworks that expand or contract to accommodate different amounts of water, solvent and/or coformer. As the crystal structure changes, the unit-cell geometry changes, and the XRPD pattern changes.

Stoichiometric cocrystals of p-coumaric acid and nicotinamide are examples for illustration. Table I presents the unitcell information for p-coumaric acid (5), nicotinamide (6) and two cocrystals containing different stoichiometries of the same two components (7). Indexing solutions for the components were taken from the Cambridge Structural Database (CSD) (5,6). XRPD patterns for each of the cocrystals were successfully indexed. The volume per asymmetric unit for the 1:1 cocrystal (345 ų) is in agreement with the sum of the volume per asymmetric unit for the components (339 ų ). The 1:1 stoichiometry was confirmed using single crystal-structure determination. The volume per asymmetric unit for the 2:1 cocrystal (538 ų) is in agreement with the weighted sum of its components (533 ų). The 2:1 stoichiometry was confirmed using solution ¹H NMR. In this example, each of the components and the cocrystals share the same space group (P2₁/c, no. 14). This coincidence is not necessary for the stoichiometry estimation.

Table I: Cocrystal stoichiometry determination.

The XRPD peak positions of variable hydrates, solvates and/or cocrystals may appear slightly shifted due to minor unit-cell changes, or they may appear at significantly different diffraction angles if the unit-cell changes are large and/or anisotropic. XRPD patterns for a variable composition form may appear to be different and, therefore, may be mistakenly designated as distinct forms when in reality they represent state points in one form with variable properties. Anisotropic cell changes may cause overlapping peaks to become resolved as the cell composition changes, and the "new" peak may be incorrectly sighted as evidence of a new form. Indexing a series of patterns for a variable form may be used to show that a material maintains its symmetry and has continuous changes in unit-cell geometry. This continuity is evidence for a variable form. In contrast, changes in cell symmetry and/or discrete changes in unit- cell parameters are evidence for multiple forms.

Comparisons with single crystal data

Unit cells generally expand with increasing temperature. Indexing can be used to account for thermal expansion when comparing a calculated XRPD pattern that was generated from a single crystal data collection at low temperature to an experimental XRPD pattern that was collected at room temperature. Single crystal data are often collected at low temperatures to improve the quality of the structure (1). Anisotropic thermal expansion may cause a calculated XRPD pattern from a single crystal structure to differ from the experimental XRPD pattern. When the experimental XRPD pattern is indexed, the unit-cell parameters can be compared with the unit-cell parameters from the single crystal structure determination to assess whether the forms are the same. Forms with different symmetries are necessarily different. If the indexing solution from the single crystal structure and the XRPD indexing solution share the same symmetry and similar unit-cell parameters, however, the differences may be attributed to thermal expansion.

Figure 2: Comparison of room temperature X-ray powder-diffraction (XRPD) pattern (red) and calculated XRPD pattern from the single crystal structure at 120 K (blue) for the 1:1 cocrystal of p-coumaric acid and nicotinamide. The maximum intensity of both patterns is scaled to 10,000 counts for ease of comparison.

Figure 2 presents two XRPD patterns for the 1:1 cocrystal of p-coumaric acid and nicotinamide discussed previously. The experimental powder pattern in red was collected at room temperature; whereas, the pattern calculated from the single crystal structure at 120 K is in blue. Although the patterns share similarities, peak shifting and changes in relative peak intensity make the patterns look different, particularly at higher scattering angles, 2θ. Unitcell data corresponding to the same state points are given in Table II. The unit cells share the same space group, which is a necessary condition for being of the same form. Also, the unitcell lengths are in similar proportions but are somewhat longer at room temperature. In other systems, one or more of the cell parameters may shrink with increasing temperature. An overall increase in volume of a few percent upon warming from 120 K to room temperature is common. The example in Table II includes a shear component, which also contributes to changes in XRPD patterns for triclinic and monoclinic crystals.

Table II: Comparison with single crystal structure for 1:1 p-coumaric acid/nicotinamide cocrystal.

Preferred orientation effects

XRPD relies on a uniform distribution of crystallites to produce a representative pattern. Crystals with anisotropic morphologies, such as needles or plates, tend to align relative to the specimen holder during XRPD analysis, which leads to a nonuniform distribution of crystal orientations. As a result, peaks may become significantly stronger, weaker, or even too weak to be observed. This phenomenon is called preferred orientation. Because preferred orientation is a result of the interaction between crystals with a particular morphology and a specimen holder with a particular geometry, changes in the specimen, specimen preparation, specimen holder and/or diffractometer geometry may lead to XRPD patterns with different relative peak intensities. These differences can be mistakenly attributed to multiple forms. Indexing of XRPD patterns may be used to show that the unit-cell symmetry and geometry are consistent, indicating that the same crystal form is present despite preferred orientation effects.

Indexing software

Several programs are available to index XRPD patterns, such as DICVOL (8), ITO (9), TOPAS (Bruker Corporation) (10), TREOR (11) and X-Cell (Accelrys) (12). SSCI has developed its own proprietary indexing algorithm, which was designed specifically with pharmaceutical crystal forms in mind. Indexing packages use various methods to generate trial unit cells that are tested for consistency with the experimental pattern. Most of the trial unit cells are found to be inconsistent with the peak positions and are rejected. XRPD patterns for materials with unit cells of higher symmetry (cubic, hexagonal, tetragonal) are relatively easier to index because fewer degrees of freedom are necessary to account for the peaks. Such high-symmetry unit cells are common for inorganic materials. Unit cells of lower symmetry (orthorhombic, monoclinic, triclinic) are more challenging to index. Triclinic unit cells are particularly difficult because there are no restrictions on any of the unit-cell lengths or angles. The overwhelming majority of pharmaceutical solids, however, crystallise in orthorhombic, monoclinic, or triclinic crystal classes. More than 96% of crystal structures of pharmaceutically relevant molecules solved at SSCI adopt one of these three crystal classes. Therefore, indexing programs that focus on the lower symmetry crystal classes are recommended for pharmaceuticals.

Indexing routines should be used by individuals with experience in diffraction and crystallography. Most indexing software packages will output a best solution for any input pattern, but it is up to the user to determine if the proposed solution is consistent with the input pattern. Because unit cells are not unique, a common problem is reporting the correct unit cell in a nonstandard way. Another common problem is that a trial unit cell, which is a fraction of the correct cell, is reported, and a higher symmetry is not recognised. Alternatively, too high a symmetry can be reported. Powder patterns of mixtures are not indexable in principle, but indexing programs generally produce a nonsensible trial solution for mixture patterns that should be rejected by the user. Some indexing packages, however, are able to successfully index a crystalline material in the presence of a crystalline impurity. Knowledge of the molecular volume, degree of hydration and/or solvation, chirality of the compound and common space groups can aid an expert in evaluating trial indexing solutions. For instance, although there are 230 space groups, the frequencies at which they occur are far from equal. Work at SSCI on pharmaceutically relevant molecules has shown that over 90% of chiral molecules are found to adopt one of four space groups (P2₁, P2₁2₁2₁, C2, or P1) and more than 90% of nonchiral molecules adopt one of four space groups as well (P2₁/c, P-1, C2/c, or Pbca). Although indexing solutions have been determined for APIs in other space groups, these are less common. Proposed indexing solutions outside of the common space groups should be scrutinised.

Conclusion

XRPD indexing can be used to extract information from high-quality XRPD patterns and add value to their interpretation. It can be used to identify patterns that represent single phases as well as to determine if patterns represent the same or different forms. Indexing of XRPD patterns for crystalline forms should be a routine part of solid form screening and analysis.

Richard B. McClurg*, PhD, is a research fellow, richard.mcclurg@aptuit.com, and Jared P. Smit, PhD, is a research investigator, jared.smit@aptuit.com, both at SSCI, a division of Aptuit LLC, 3065 Kent Ave., West Lafayette, IN, USA 47906.

*To whom all correspondance should be addressed.

Submitted: 2 May 2012. Accepted: 18 Sept. 2012.

References

1. W. Massa, Crystal Structure Determination (Springer, Berlin, Germany, 2nd ed. 2004).

2. R. A. Young, "Introduction to the Rietveld method," in The Rietveld Method, R. A. Young, Ed., (Oxford University Press, New York, NY, 1993), pp. 1-38.

3. C. A. Beevers and H. N. Hansen, Acta Cryst., B27, 1323–1325 (1971).

4. A. Burger and R. Ramberger, Mikrochim. Acta, 72 (3–4) 273–316 (1979).

5. R. F. Bryan and P. G. Forcier, Mol. Cryst. Liq. Cryst., 60 (3) 157–165 (1980).

6. Y. Miwa et al., Acta Cryst., B55, 78–84 (1999).

7. Results from research at SSCI, a division of Aptuit, West Lafayette, IN, USA, not previously published.

8. A. Boultif and D. Louër, J. Appl. Cryst., 37 (5) 724–731 (2004).

9. J. W. Visser, J. Appl. Cryst., 2 (3) 89–95 (1969).

10. A. A. Coelho, J. Appl. Cryst., 36 (1) 86–95 (2003).

11. P. E. Werner, L. Erikson, and M. Westdahl, J. Appl. Cryst., 18 (5) 367–370 (1985).

12. M. A. Neumann, J. Appl. Cryst., 36 (2) 356–365 (2003).