Bulk-modulus anomalies at the superconducting transition of single-phase Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

We report sound-velocity measurements on polycrystalline single-phase Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ with a $T_c$ of 90 K. The sound velocity is found to increase as the temperature is reduced from room temperature in contrast to the decrease observed in ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$. At $T_c$ there is no discontinuity in the sound velocity within experimental resolution, as expected from thermodynamic arguments and the small value of $\frac{d{T}_c}{\mathrm{dP}}$. As the temperature is lowered below $T_c$ the sound velocity increases at a greater rate. A similar increase below $T_c$ is observed in ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$. The magnitude of the sound-velocity increase below $T_c$ is much larger than observed in conventional superconductors.