Ultrasonic study of incommensurate phase transitions in ferroelectrics

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Abstract
Many ferroelectric crystals with incommensurately modulated structure have been studied using ultrasonic methods both by the present authors and by other researchers. This review article is devoted to the analysis of the experimental data from ultrasonic studies of ferroelectrics with an incommensurate phase. The phase transition from a normal to an incommensurate phase is accompanied by strong anomalies in ultrasonic velocity and attenuation. In incommensurate phase transitions, the amplitudon manifests itself in the same way as a conventional soft mode at a normal phase transition and the phason cannot generally give a significant contribution into the elastic anomalies with the exception of the shear stiffness c55 in some crystals whose anomaly in the incommensurate phase is due to the contribution of the phason with large wave vector K. An asymmetry behaviour in the phase transition region of shear waves with the same strain but with different propagation direction has been observed. The nature of this asymmetry is discussed including the possible contribution of gapless phasons. Order parameter relaxation times, coupling coefficients and incommensurability parameters have been deduced from the experimental results.