An electron diffraction and lattice-dynamical study of the diffuse scattering in β-cristobalite, SiO₂

Strong diffuse scattering has been observed on electron diffraction photographs of β-cristobalite. This is observed to be in the form of diffuse planes normal to the six (110) directions. A simple Born–von Karman force model including nearest-neighbour Si–O, O–O and Si–Si interactions has been used to calculate lattice-dynamical properties for β-cristobalite assuming the structure to be the simple Wyckoff [Z. Kristallogr. (1925), 62, 189–200] C9 structure. The force-model parameters used were obtained by fitting to the infrared and Raman frequencies of α-cristobalite and are very similar to those obtained by Barron, Huang & Pasternak [J. Phys. C (1976), 9, 3925–3940] for quartz. Calculated thermal diffuse scattering patterns obtained are in good agreement with the observed patterns, and may be interpreted in terms of low-lying relatively dispersionless branches of the phonon dispersion curve diagrams. These branches correspond to motions of the structure involving coupled rotations of the tetrahedra in columns along the (110) directions, the motion in neighbouring columns being virtually uncoupled.