The Raman frequencies of the lattice modes (147 cm 1 and 207 cm 1 / are analyzed for the˛-ˇtran-sition in quartz according to a power-law formula with the critical exponent by using the experimental data. The temperature dependence of the Raman frequency is associated with the order parameter (polarization P ) for this transition in the quartz crystal. The damping constant of the lattice modes studied here is calculated using the Raman frequencies at various temperatures for the˛-ˇtransition in quartz (T c D 846 K) using the soft mode -hard mode and the energy fluctuation models. Our calculations for the damping constant (bandwidths) give an evidence that the lattice mode of the 147 cm 1 exhibits a soft mode behavior for the˛-ˇtransition in quartz.
Temperature and pressure dependencies of the thermal expansivity (a p ), isothermal compressibility (j T ) and the specific heat (C p -C v ) are studied for piezoelectric materials, in particular, for b-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 (a p , j T and C p -C v ) are obtained and the Pippard relations (C p -C v vs. Va p and a p vs. j T ) close to the transition from the b-quartz to the b-cristobalite are examined.
The temperature dependence of the 501 cm −1 frequency of the vibrational mode is analyzed for SiO 2 -moganite. The experimental data for the heating and cooling cycles of moganite from the literature is used for our analysis. The coexistence of α-β moganite is obtained over a finite temperature interval, and the α-β moganite transition at around 570 K is studied, as observed experimentally.
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