Temperature dependence of the piezoelectric resonance frequency in relation to the anomalous strain near the incommensurate phase of quartz

Abstract

The temperature dependence of the piezoelectric resonance frequency is analyzed by the power-law formula in the vicinity of the critical temperature of the incommensurate (INC) phase in quartz using the experimental data from the literature. By considering the piezoelectric resonance frequency as an order parameter of the INC phase, correlation between the piezoelectric resonance frequency and the strain is constructed, which both decrease linearly with increasing temperature toward T-c in quartz. Our results can explain dynamics of the ordering mechanism in the INC phase (within a very narrow temperature interval between the alpha and beta phases of quartz) and suggest a second order transition from INC to the beta phase in quartz.