Lattice dynamics of cristobalite

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Abstract
Dispersion relations are calculated in a number of symmetry directions for α-cristobalite, using three force constants describing bond stretching, and bond bending at both silicon and oxygen atoms. A Keating representation is used for the first two, but for stability a Born potential was used to describe bending at the oxygen atom. The calculation shows that very-low-frequency zone-boundary transverse acoustic modes arise naturally in the perfect crystal, giving a density of states at low frequencies that explains the low-temperature heat capacity.