Soft-Mode Damping and Ultrasonic Attenuation at a Structural Phase Transition

Abstract

The soft-mode damping and the ultrasonic attenuation at a displacive phase transition has been calculated with the help of a model Hamiltonian. The soft-mode damping parameter $\Gamma$ is finite at the transition temperature, whereas the ultrasonic attenuation $\alpha$ is singular. For sound frequencies $\omega \ll \Gamma$, the ultrasonic attenuation is proportional to the sound frequency squared with critical exponents $\eta =0.5\mathrm{} \mathrm{and} 1.5$, respectively, for weakly damped and strongly overdamped soft-mode frequencies. A comparison is made with previous calculations based on the Silvermann model.