Elastic stiffness and ultrasonic attenuation of superconductor ${\mathrm{MgB}}_2$ at low temperatures

Temperature dependencies of elastic constants and ultrasonic attenuation of a polycrystalline ${\mathrm{MgB}}_2$ showing high-$T_c$ superconductivity are reported. An electromagnetic acoustic resonance method detected the specimen’s resonance frequencies, from which we derived the elastic constants for nonporous ${\mathrm{MgB}}_2$ using micromechanics calculation. The bulk and shear moduli extrapolated to 0 K are determined to be 96.6 GPa and 74.2 GPa, respectively, which gives the Debye temperature ${\Theta }_D=819\mathrm{}\mathrm{K}$ and the coupling constant $\lambda \approx 0.76–0.89$ with McMillan formula. In the temperature behavior of ultrasonic attenuation, two anomalous peaks are observed near 30 K.