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
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 Å3) is in agreement with the sum of the volume per asymmetric unit for the components (339 Å3 ). The 1:1 stoichiometry was confirmed using single crystal-structure determination. The volume per asymmetric unit for the
2:1 cocrystal (538 Å3) is in agreement with the weighted sum of its components (533 Å3). 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.