Superconductivity ofα- andβ-Mercury

Precise critical field measurements and a direct measurement of ${\left(\frac{\partial H}{\partial P}\right)}_T$ as a function of temperature were made on physically identical samples of $\alpha$- and $\beta$-Hg. The purpose of these measurements was to obtain data on the effects of crystal structure on the properties of superconductors, and to permit calculation of various thermodynamic quantities difficult to obtain in any other way. The critical fields of the two phases were found to be identical when expressed in terms of the reduced variables $\frac{H}{H_0}$ and $\frac{T}{T_c}$. No generalizations of this type could be found to explain the pressure effects. The advantages of an $H^2$ vs $T^2$ and ($\frac{\partial H^2}{\partial P}$) vs $T^2$ analysis for extrapolation to absolute zero are stressed. The critical fields of several representative superconductors are compared with the critical field predicted by the Bardeen-Cooper-Schrieffer theory, using a plot that emphasizes the detailed shape of the curves at low temperatures. This plot also can be interpreted in terms of the $\frac{\theta }{T_c}$ dependence of the width of the energy gap. The agreement between calorimetric and critical field determinations of the electronic specific heat in the normal state is shown to be improved by using the $H^2-T^2$ extrapolation. The volume dependence of the reduced energy gap is shown to be very small for those superconductors for which pressure effect data are available.