Correlations between the resonant frequency shifts and the thermodynamic quantities for the α-β transition in quartz

The resonant frequency shifts are related to the thermodynamic quantities (compressibility, order parameter and susceptibility) for the α-β transition in quartz. The experimental data for the resonant frequencies and the bulk modulus from the literature are used for those correlations. By calculating the order parameter from the mean field theory, correlation between the resonant frequencies of various modes and the order parameter is examined according to the quasi-harmonic phonon theory for the α-β transition in quartz. Also, correlation between the bulk modulus in relation to the resonant frequency shifts and the order parameter susceptibility is constructed for the α-β transition in this crystalline system.