Phonon properties ofA−15superconductors obtained from heat-capacity measurements

Abstract

The heat capacities of ${\mathrm{Nb}}_3$Al, ${\mathrm{Nb}}_3$Sn, and ${\mathrm{Nb}}_3$Sb were measured between 2 and 400 K. Their superconducting transition temperatures $T_c$ are 18.5, 17.9, and 0.2 K, respectively. The higher-temperature entropy was analyzed, and it was found that phonon-mode softening occurs on cooling for the two high-$T_c$ compounds, but not for ${\mathrm{Nb}}_3$Sb. Geometric mean phonon frequencies ${\omega }_g$ are also evaluated for these compounds and for ${\mathrm{V}}_{3}X$, where $X=\mathrm{Si},\mathrm{Ga},{\mathrm{Ga}}_{0.5}{\mathrm{Sn}}_{0.5}, \mathrm{and} \mathrm{Sn}$. As is shown, ${\omega }_g$ is an appropriate phonon average for evaluating McMillan's expression for the electron-phonon mass enhancement. Average phonon properties cannot reliably be used to calculate $T_c$ values for these $A-15$ materials. It is suggested that, for the higher electronic density-of-states materials, select phonon modes strongly couple to the electronic system and influence the magnitude of $T_c$ to a greater extent than average-phonon correlations would indicate. This view is supported by the observation that the higher-density-of-states materials exhibit the more pronounced phonon-mode softening on cooling.