Specific Heat of Mercury and Thallium between 0.35 and 4.2°K

Abstract

The specific heat of mercury and thallium were measured between 0.35 and 4.2°K. In the normal state below 0.7°K the mercury results are given by: $C_n=1.79T+5.23\mathrm{}{T}^3$ mJ/mole deg. The coefficient $\alpha$ of the $T^3$ term corresponds to a value of the Debye parameter ${\Theta }_0$ of 71.9°K. For temperatures higher than 0.7°K, the lattice specific heat deviates above the $T^3$ law. A plot of $\Theta \mathrm{}\left(T\right)\mathrm{}$ is given. Below 0.6°K, the specific heat of thallium in the normal state is given by: $C_n=1.47T+4.03\mathrm{}{T}^3$ mJ/mole deg. The corresponding value of ${\Theta }_0$ is 78.5°K. Above 0.6°K, the lattice specific heat of thallium shows a deviation below the pure $T^3$ law, a result contrary to that found for most solids. This would imply a deviation in the dispersion curve above the linear portion. A similar effect was observed in the specific heat of graphite which was explained on the basis of bond-bending modes of vibration. It is suggested that similar modes may explain this behavior for thallium. In the superconducting state the specific heat of both materials can be represented by a sum of the normal lattice term and a superconducting electronic term $C_{\mathrm{es}}$ of the form a$\gamma T_c\exp (-\frac{b{T}_c}{T})$. For mercury, values are obtained for a=15 and $b=1.64\mathrm{}$ with $T_c=4.16\mathrm{}°$K; for thallium a=9 and $b=1.52\mathrm{}$ with $T_c=2.38\mathrm{}°$K. In the case of thallium the critical field as a function of temperature $H_c\mathrm{}\left(T\right)\mathrm{}$ is determined, with $H_c\mathrm{}\left(0\right)=176.5\mathrm{}$ G.