THEORY OF ULTRASONIC-ATTENUATION AT INCOMMENSURATE PHASE-TRANSITIONS

Acoustic properties below incommensurate phase transitions are severely influenced by phason modes. These unique massless Goldstone modes may lead to coexistence anomalies within the whole phase of broken continuous symmetry. The present theory, based on an order parameter model appropriate for a universality class containing the A2BX4 family, employs an extended renormalization scheme. Within this scheme, critical behavior of the Goldstone modes is governed by a fixed point, permitting an exact treatment of the anomalies induced by them. With regard to the coefficient of sound attenuation, the hydrodynamic behavior is not altered by the phason modes, but they lead to a singularity of the scaling function, which describes the crossover from the critical region to the coexistence regime. Determining the universal scaling function and revealing its coexistence anomaly constitute a main result of our study, which explicitly takes fluctuation contributions of the phason and amplitudon modes into account. The sound velocity is predicted to display a minimum in its temperature dependence below the maximum sound attenuation at the same frequency. A treatment of the high-temperature phase is also included. Application to experiments on Rb2ZnCl4 and K2SeO4 reveals agreement with our theoretical predictions over several orders of magnitude of the scaling variable.