Symmetry Information Inherent in Powder Diffraction Data: α- and β-Quartz as Examples

Laue classes of powder diffraction data for tetragonal, hexagonal and cubic crystal families can be derived from interpretation of the concentration of peaks in Patterson functions that are transformed from weighted reciprocal lattices constructed with diffraction data of polycrystalline materials [Ohmasa & Ohsumi (1995). Acta Cryst. A51, 87–91 ]. The method was applied to powder diffraction data of α- and β-quartz, and discrepancies of concentrations of the peaks in both Patterson functions were detected, although the difference of their structures is caused by small shifts of the atomic positions.