Temperature dependence of transverse and longitudinal optic modes in theαandβphases of quartz

The temperature dependence of the infrared reflectivity spectra ($A_2-$ and $E$-type vibrational modes) of quartz is reported in the $\alpha$ and $\beta$ phases with emphasis on the vicinity of the $\alpha \to \beta$ phase transition. Spectra have been fitted with a four-parameter dispersion model based on the factorized form of the dielectric function that allows the temperature dependence of the TO and LO frequencies and damping to be determined. Two $A_2$ and three $E$ modes (among the six $E$ modes studied here) are forbidden in the $\beta$ phase, and they critically lose their polar character at the approach of the phase transition. The frequencies of a number of modes critically soften or harden in the $\alpha$ phase, in the vicinity of $T_c=846\mathrm{}$ K. A comparison with thermal lattice expansion indicates that this critical behavior might be understood in term of pure volume effect. In the $\alpha$ phase, mode dampings diverge in the vicinity of the transition whereas in the range 300-700 K and in the $\beta$ phase, phonon lifetimes appear limited by anharmonic three-phonon coupling.