Elastic anomalies at structural phase transitions : a consistent perturbation theory. I. One component order parameter

Abstract

The perturbation theory of elastic anomalies near structural phase transitions is revisited.It is shown that expressions more often used to interpret ultrasonic attenuation anomalies are not correct,particularly below the phase transition temperature T c .A consistent perturbation theory is worked out and it is shown that the sound wave attenuation coefficient takes a form less simple in the general case than that usually assumed.The explicit results for the temperature and frequency dependence of the sound attenuation coefficient are given for two extreme cases:order-disorder systems and displacive systems.It is found that for the order-disorder transitions,which are not too far from the tricritical point the main part of the sound attenuation anomaly can be described by the Landau-Khalatnikov (LK) formula with the order parameter exhibiting a non-mean field bahaviour.For displacive transitions for both LK and fluctuation, contributions have the same temperature dependence and the same order of magnitude within the perturbative region.As a result the low frequency sound frequency sound attenuation ciefficient has the same «critical index»for the two phases but different «critical amplitudes»,the ratio of the amplitudes A T Tc going to zero when the tricritical point is approached.At tricritical phase transition the «critical index» in the low-temperature phase is different from that in the high-temperature one.