?-? Transition in Quartz: Temperature and Pressure Dependence of the Thermodynamic Quantities for ?-Quartz and ?-Cristobalite as Piezoelectric Materials
Temperature and pressure dependencies of the thermal expansivity (?p), isothermal compressibility (?T) and the specific heat (Cp ? Cv) are studied for piezoelectric materials, in particular, for ?-quartz. By analyzing the temperature (at 1atm) and pressure (at 848K) dependence of the observed volume V from the literature, the thermodynamic functions (?p, ?T and Cp ? Cv) are obtained and the Pippard relations (Cp ? Cv vs. V?p and ?p vs. ?T) close to the transition from the ?-quartz to the ?-cristobalite are examined.
thermodynamic quantities ?-quartz ?-cristobalite piezoelectricity pippard relations