Critical Field of Superconducting Aluminum as a Function of Pressure and Temperature above 0.3°K

Precise measurements have been made of the critical field of superconducting Al from ${0.3}^{\ensuremath{\circ}}K$ to ${T}_{c}$, at pressures of 0, 3100, 5400, and 7200 psi. The data are extrapolated to $T=0$, yielding the values (at zero pressure) ${H}_{0}=104.93\ifmmode\pm\else\textpm\fi{}0.2$ G, $\ensuremath{\gamma}=1.349\ifmmode\pm\else\textpm\fi{}0.015$ mJ/mole \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{2}$ and ${T}_{c}=1.1793\ifmmode\pm\else\textpm\fi{}0.003$ \ifmmode^\circ\else\textdegree\fi{}K. These values are used to calculate the superconducting electronic entropy and the deviation of the critical-field curve from a parabolic law. The results are compared with previous experimental work and with the Bardeen-Cooper-Schrieffer theory as extended by Clem to include effects of energy-gap anisotropy. The present work gives better agreement with previous calorimetric measurements of the thermodynamic properties of superconducting Al than do earlier published critical-field measurements. The shape of the critical-field curve shows no pressure dependence to within the experimental accuracy. Assuming that the shape of the critical-field curve is entirely independent of pressure, we find $\frac{d\mathrm{ln}{H}_{0}}{d\mathrm{ln}V}=19.2\ifmmode\pm\else\textpm\fi{}0.4$, $\frac{d\mathrm{ln}{T}_{c}}{d\mathrm{ln}V}=16.4\ifmmode\pm\else\textpm\fi{}1.1$, and $\frac{d\mathrm{ln}\ensuremath{\gamma}}{d\mathrm{ln}V}=6.65\ifmmode\pm\else\textpm\fi{}3$. These results are in fair agreement with earlier ${H}_{c}(P,T)$ measurements of Al, although our result for $\frac{d\mathrm{ln}\ensuremath{\gamma}}{d\mathrm{ln}V}$ is about a factor of 3 larger than has been obtained from thermal expansion measurements.