Low-Temperature Specific Heat of Indium and Tin

Abstract

The heat capacities of indium and tin were measured between 0.4 and 4.2°K. In the normal state, the specific heat could be represented by $A{T}^{-2\mathrm{}}+\gamma T+\alpha T^3+\beta T^5+\mu T^7$. For Sn, in molar millijoule units, $A=0\mathrm{}$; $\gamma$, the coefficient in the electronic term, is 1.80; $\alpha =0.242\mathrm{}$, corresponding to a Debye temperature, ${\theta }_0$, of 200°K; $\beta =0.004\mathrm{}$; and $\mu =0.00014\mathrm{}$. For In, $A$, the coefficient of a nuclear electric quadrupole term, is calculated to be 8.97×${10}^{-4\mathrm{}}$ from resonance data; $\gamma =1.61\mathrm{}$ for one ingot and 1.59 for another; ${\theta }_0=109\mathrm{}° \mathrm{and} 108°$K; and $\beta =0.008\mathrm{}$. In the superconducting state, the specific heat of Sn could be expressed as the normal lattice term plus an electronic term of the form $a\gamma T_c\exp (-\frac{b{T}_c}{T})$, with $T_c=3.70\mathrm{}°$K (0.02 deg lower than found in a magnetic measurement), $a=7.63\mathrm{}$, and $b=1.41\mathrm{}$ when $2<\mathrm{}\frac{T_c}{T}<7\mathrm{}$; the value of $b$ agrees with infrared measurements of the energy gap. This sort of analysis could not be applied to In, for below 0.8°K the total superconducting specific heat was less than the normal lattice term. A possible interpretation is that ${\theta }_0$ is 9% higher in the superconducting state than in the normal metal at 0.4°K; this is not supported, however, by the recent acoustic measurements of the elastic constants by Chandrasekhar and Rayne. The anomaly is not as yet understood, but a few plausible explanations are discussed.