Ultrasonic Study of NaNO2. III. Critical Behavior of Elastic Stiffness Constants at the Normal-to-Incommensurate Phase Transition

Abstract

Two coupling terms between the order parameter Q ( q ) with wave vector q and strain e i , (a) γ i ( q ) Q ( q ) Q (- q ) e i and (b) η i ( q ) Q ( q ) Q (- q ) e i 2 , give rise to the anomalous behavior of the elastic stiffness at the phase transition. The coupling (b) causes a similar critical stiffness constant in both longitudinal and transverse waves. On the other hand, (a) brings about the softening of the stiffness constant only in longitudinal waves. Using these characteristics the anomaly caused through (a) is isolated under a minimum assumption and then, γ i ( q ) for i=1–3 are estimated. Contrary to a simple theoretical prediction, the above anomaly is not proportional to that of the specific heat. It is partly due to the disregard of the q -dependence of γ i ( q ). This effect should be taken into account in the study of the elastic anomaly in the other substances.