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Abstract
The acoustic anomalies of gadlinium molybdate Gd2(MoO4)3 observed below To were analyzed by the linear theory which was extended in this paper from Aizu-Dvořák's static theory to the dynamical case in order to include the damping of acoustic modes. The analysis made clear mainly the following. The observed softening of elastic constants is due to both the bilinear interaction with the optical modes oscillating parallel to the direction of the spontaneous value of the order parameters and the order of the transition to be the first but very near to the second. The temperature dependence of the relaxation time of soft optical modes was determined from the data of both the damping constants and the anomalous parts of elastic constants. Anomalous parts of elastic constants were separated into both softenings and step-discontinuities.