We have used a modified vibrating reed technique to measure the temperature dependence of the sound velocity and attenuation for modes corresponding to the Young's modulus and $c_{44}$ shear modulus of single crystals of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. The Young's sound velocity shows a tremendous softening during the superconducting transition—a smeared discontinuity of as high as 190 ppm. Below the transition, the temperature dependences of both sound velocities harden considerably. The discontinuities of the sound velocities and their temperature derivatives at $T_c$ are related to the specific-heat jump at the superconducting transition.

• Received 10 August 1988

DOI:https://doi.org/10.1103/PhysRevB.39.827