Analysis of the IR-Raman Modes and the Heat Capacity Near the alpha-Inc-beta Transitions in Quartz

Abstract

This study gives our analysis for the temperature dependence of the infrared frequency and the integrated intensity of the 695 cm(-1) mode near the alpha-beta transition at 847.5 K and the temperature dependence of the Raman scattering cross section of the 355 cm(-1) mode near the beta-INC (incommensurate) transition which occurs within a small temperature (similar to 1.3 K) interval in relation to the order parameter in quartz. Both analyses are performed according to a power-law formula for the order parameter Q with the critical index beta using the experimental data from the literature. We also analyze the temperature dependence of the heat capacity C p according to the renormalization-group expression including first-order corrections to scaling term close to the alpha-INC-beta transitions in quartz by using the literature data. From our analyses, values of the critical exponent beta for the frequency and the integrated intensity of the 695 cm(-1) infrared mode and for the Raman scattering cross section of the 355 cm(-1) mode as a measure of the order parameter, are extracted. From the analysis of C p , the values of the critical exponent alpha are also extracted. Additionally, by means of scaling relations the critical exponent gamma of the isothermal compressibility kappa T and the renormalized components ( beta R , alpha R and gamma R ) are predicted for the alpha-INC-beta transitions in quartz. Our analyses given here indicate that weakly first-order transition occurs from the alpha phase to the incommensurate (INC) phase, which changes to the nearly second-order transition to the beta phase with increasing temperature in quartz, as also observed experimentally.