An optical transform and Monte Carlo study of the disorder in β-cristobalite SiO₂

A previously reported lattice-dynamical model of β-cristobalite [Hua, Welberry, Withers & Thompson (1988). J. Appl. Cryst. 21, 458–465], which assumed the Wyckoff C9 structure but gave a satisfactory qualitative description of observed diffuse intensity in electron diffraction patterns, is shown to give atomic displacements which are much too small to be consistent with the 147° Si—O—Si angle observed in other forms of silica. Monte Carlo simulations of a modified model in which this angle is constrained to be close to 147° have been carried out and optical diffraction patterns obtained from the resulting lattice realisations. The diffraction patterns are very similar in appearance to those calculated for the simple C9 model, but the displacements are now consistent both with the expected geometry and also with mean-square atomic displacements derived from X-ray powder studies. In this simulation the oxygen atoms are distributed uniformly around an annulus which encircles the 16(c) sites of the Fd3m C9 structure. The hypothesis of Wright & Leadbetter [Philos. Mag. (1975). 31, 1391–1401], that the oxygen atoms preferentially occupy the six 96(h) sites which occur around this annulus, has been tested and it is concluded that if such ordering exists it is not very pronounced.