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.