Rigid-unit phonon modes and structural phase transitions in framework silicates

The rigid-unit mode model provides many new insights into the stability and physical properties of framework silicates. In this model the SiO4 and AlO4 tetrahedra are treated as very stiff, to a first approximation as completely rigid, in comparison with intertetrahedral forces. In this paper we apply the model to several important examples. The model is reviewed by a detailed study of quartz, and it is shown that the alpha-beta phase transition involves a rigid-unit mode that preserves the Si-O-Si bond angle. The model is used to explain the phase transitions in cristobalite and the different feldspar, sodalite, and leucite structures. We also use the model to explain the nature of the high-temperature disordered phases of cristobalite and tridymite, to interpret the observations of streaks of diffuse scattering in electron diffraction patterns, to interpret the structures in the kalsilite-nepheline solid solution, to explain volume anomalies in the cubic leucite structures, and to explain qualitatively the negative linear thermal expansion in cordierite. The results for the highest symmetry sodalite structure show that there is a rigid-unit mode at every wave vector, a finding with significant implications for the understanding of the sorption and catalytic behavior of zeolites.