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\ifmmode^\circ\else\textdegree\fi{}K. In the normal state below 0.7\ifmmode^\circ\else\textdegree\fi{}K the mercury results are given by: ${C}_{n}=1.79T+5.23{T}^{3}$ mJ/mole deg. The coefficient $\ensuremath{\alpha}$ of the ${T}^{3}$ term corresponds to a value of the Debye parameter ${\ensuremath{\Theta}}_{0}$ of 71.9\ifmmode^\circ\else\textdegree\fi{}K. For temperatures higher than 0.7\ifmmode^\circ\else\textdegree\fi{}K, the lattice specific heat deviates above the ${T}^{3}$ law. A plot of $\ensuremath{\Theta}(T)$ is given. Below 0.6\ifmmode^\circ\else\textdegree\fi{}K, the specific heat of thallium in the normal state is given by: ${C}_{n}=1.47T+4.03{T}^{3}$ mJ/mole deg. The corresponding value of ${\ensuremath{\Theta}}_{0}$ is 78.5\ifmmode^\circ\else\textdegree\fi{}K. Above 0.6\ifmmode^\circ\else\textdegree\fi{}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$\ensuremath{\gamma}{T}_{c}\mathrm{exp}(\ensuremath{-}\frac{b{T}_{c}}{T})$. For mercury, values are obtained for a=15 and $b=1.64$ with ${T}_{c}=4.16\ifmmode^\circ\else\textdegree\fi{}$K; for thallium a=9 and $b=1.52$ with ${T}_{c}=2.38\ifmmode^\circ\else\textdegree\fi{}$K. In the case of thallium the critical field as a function of temperature ${H}_{c}(T)$ is determined, with ${H}_{c}(0)=176.5$ G.