Dynamic structural disorder in cristobalite: neutron total scattering measurement and reverse Monte Carlo modelling

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Abstract
The atomic structure of cristobalite in both its high-temperature β-phase and low-temperature α-phase has been studied using constrained reverse Monte Carlo modelling of neutron total scattering data. The modelling has shown that the disorder of the β-phase involves rotations and displacements of rigid SiO4 tetrahedra, consistent with the predictions of the `rigid-unit mode' (RUM) model. The structure of the α-phase is significantly different from that of the β-phase, but still has a degree of disorder. The calculated distribution of oxygen atoms in β-cristobalite is continuous rather than based on specific crystallographic sites. There is no evidence for correlations between the Si-O distance and the corresponding Si-O-Si bond angles, contrary to quantum mechanical calculation findings. The three-dimensional diffuse scattering has been calculated from the model configurations, and is found to be in agreement with experimental electron diffraction measurements and the predictions of the RUM model. There is little significant temperature dependence of the structure or diffuse scattering in the β-phase.