Acoustic Phonon Dispersion in the Incommensurate Phase of SiO₂ (Quartz)

Abstract

Ultrasonic and Brillouin scattering measurements were performed near the incommensurate (INC) transition of SiO₂ (quartz). The decrease of the LA sound velocity in the INC phase was found to be much less for 10 MHz than for 27 GHz, being remarkably different from other crystals which undergo INC phase transitions. The dispersion in the INC phase can be well characterized by a simple Landau-Khalatnikov type relaxation with a relaxation time τ (T)= (2.6 ± 0.5 )× 10^-12 (T_i- T)^-1s.A small but critical decrease of the TA velocity as T → T_c (=T_i -1.4 K) was also detected by the ultrasonic measurement.