We studied ultrasonic-wave velocities, both longitudinal and shear, in ${\mathrm{Y}}_1{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$, between 5 and 295 K, during both cooling and warming. Both waves, especially the longitudinal, show thermal hysteresis. The results suggest a hysteretic phase change that occurs between 160 and 70 K during cooling and between 170 and 260 K during warming. This phase-change hypothesis explains anomalies in several physical properties. The phase change agrees with thermodynamic-instability predictions. We confirmed the hysteresis in Ho-Ba-Cu-O, where it is smaller than in Y-Ba-Cu-O, and in Eu-Ba-Cu-O, where it is larger. In a companion perovskite, BaTi${\mathrm{O}}_3$, we observed zero hysteresis. At $T_c$, 91 K, sound velocities show no measurable change in either magnitude or slope. This continuity disputes the current popular view that, contrary to thermodynamics, elastic stiffness increases upon cooling through $T_c$ into the superconducting state. We believe that stiffening results from the usual thermal effects after a phase transformation from a stiffer phase.

• Received 23 May 1988

DOI:https://doi.org/10.1103/PhysRevB.38.11857