Thermodynamic relations at solid state phase transitions, applied to the α-β quartz transition

Solid state phase transitions are treated as thermodynamic instabilities. Limiting relations between the specific heat c p , thermal expansion coefficients and elastic compliance elements are obtained for certain phases as the transition is approached. For example, such relations hold for alpha -quartz, but not necessarily for beta -quartz. A criterion is given to show whether the behaviour of the high-temperature phase, in regard to such relations, is different to that of the low-temperature form. For alpha -quartz it is shown, using only elastic constant and thermal expansion data, that c p diverges, while for beta -quartz it remains finite, consistent with experiment. The relations derived for the low-temperature forms are similar to the Pippard relations, but have a different constant of proportionality.