Elastic constants of the polycrystalline Bi-Pb-Sr-Ca-Cu-O superconductor

For polycrystalline For polycrystalline (Bi-Pb${)}_2$@${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$, we report the 5–295-K elastic constants: shear modulus (G), Young modulus (E), bulk modulus (B), and Poisson ratio (ν). Both G and E show nearly normal temperature variation. During cooling, B softens between 215 and 65 K. The Poisson ratio decreases abruptly at 215 K and decreases almost five percent in the 295–5-K region. In its temperature dependence, this compound resembles ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. However, it shows much lower elastic stiffness. Corrected to the void-free state, we calculate a Debye temperature of 312 K, versus 436 K for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The Poisson ratio, 0.20, agrees well with that of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_7$, 0.21. We use Kresin’s model to interrelate Debye temperature, critical temprature, and electron-phonon interaction parameter for four classes of copper-oxide superconductors. DOI: https://doi.org/10.1103/PhysRevB.39.9689 ©1989 American Physical Society