A phenomenological analysis of ultrasound near phase transitions

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Abstract
Phenomenological predictions for sound attenuation and velocity anomalies near critical points are presented. General symmetry properties of the linear elastic constants and the general properties of the low- and high-frequency behaviours of linear-response functions are used to develop phenomenological equations, where exponents, relaxation times and amplitudes are introduced as parameters to fit to the experimental data. Novel interpretation formulae, which combine the asymptotic high- and low-frequency limits of complex dynamic elastic constants, are constructed. It is shown that causality requirements give new relations between the amplitudes of ultrasonic attenuation and the velocity in the asymptotic limits of high and low frequency.