alpha-beta Transition in Quartz: Temperature and Pressure Dependence of the Thermodynamic Quantities for beta-Quartz and beta-Cristobalite as Piezoelectric Materials

Temperature and pressure dependencies of the thermal expansivity (alpha(p)), isothermal compressibility (j(T)) and the specific heat (C-p - C-v) are studied for piezoelectric materials, in particular, for beta-quartz. By analyzing the temperature (at 1 atm) and pressure (at 848 K) dependence of the observed volume V from the literature, the thermodynamic functions (ap, jT and C-p - C-v) are obtained and the Pippard relations (C-p - C-v vs. Vap and ap vs. j(T)) close to the transition from the beta-quartz to the beta-cristobalite are examined.