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

Abstract

A previously reported lattice-dynamical model of β -cristobalite [Hua, Welberry, Withers & Thompson (1988). J. Appl. Cryst. 21 , 458–465], which assumed the Wyckoff C 9 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 C 9 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 Fd 3 m C 9 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.