Low-Temperature Heat Capacities of Indium and Tin

Abstract

The heat capacity of indium has been measured between 0.08 and 4.2\ifmmode^\circ\else\textdegree\fi{}K in the normal state ($H=1000$ Oe) and between 0.1\ifmmode^\circ\else\textdegree\fi{}K and the critical temperature in the superconducting state. At $T<~0.8\ifmmode^\circ\else\textdegree\fi{}$K, ${C}_{n}=0.00101{T}^{\ensuremath{-}2}+1.69T+1.42{T}^{3}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$ and at $T<~0.35\ifmmode^\circ\else\textdegree\fi{}$K, ${C}_{s}=1.22{T}^{3}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$. The absence of the hyperfine contribution to ${C}_{s}$ is a consequence of the long spin-lattice relaxation time. Below 0.35\ifmmode^\circ\else\textdegree\fi{}K, where the superconducting-state lattice heat capacity can be measured, the normal-state lattice heat capacity is only a small part of ${C}_{n}$ and calorimetric measurements alone cannot exclude the possibility that the lattice heat capacities in the two states are equal. However, the excellent agreement between the elastic constants and the apparent normal-state lattice heat capacity supports the conclusion that they are not. The apparent discrepancy in the lattice heat capacities is less than that reported by Bryant and Keesom but the difference is largely accounted for by differences in analysis of the normal-state data and by their assumption that the measured ${C}_{s}$ included the nuclear quadrupole term. The measurements of ${C}_{s}$ extend to temperatures well below that at which the electronic contribution becomes negligible and therefore permit a comparison with theoretical studies of the superconducting-state lattice heat capacity. The heat capacity of tin was measured only below 1\ifmmode^\circ\else\textdegree\fi{}K. Below 0.45\ifmmode^\circ\else\textdegree\fi{}K, ${C}_{s}=0.246{T}^{3}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$, in good agreement with the elastic constants. Within the experimental error, ${C}_{n}=1.78T+0.246{T}^{3}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$.