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 ${0.3}^{\circ }K$ to $T_c$, at pressures of 0, 3100, 5400, and 7200 psi. The data are extrapolated to $T=0\mathrm{}$, yielding the values (at zero pressure) $H_0=104.93\mathrm{}\pm 0.2$ G, $\gamma =1.349\mathrm{}\pm 0.015$ mJ/mole °${\mathrm{K}}^2$ and $T_c=1.1793\mathrm{}\pm 0.003$ °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 $\frac{d\ln H_0}{d\ln V}=19.2\mathrm{}\pm 0.4$, $\frac{d\ln T_c}{d\ln V}=16.4\mathrm{}\pm 1.1$, and $\frac{d\ln \gamma }{d\ln V}=6.65\mathrm{}\pm 3$. These results are in fair agreement with earlier $H_c\mathrm{}(P,T)\mathrm{}$ measurements of Al, although our result for $\frac{d\ln \gamma }{d\ln V}$ is about a factor of 3 larger than has been obtained from thermal expansion measurements.