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.
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.