Soft-mode damping and ultrasonic attenuation at a structural phase transition

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 Γ is finite at the transition temperature, whereas the ultrasonic attenuation α is singular. For sound frequencies ωΓ, the ultrasonic attenuation is proportional to the sound frequency squared with critical exponents η=0.5 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. © 1970 The American Physical Society.