High-Magnetic-Field Specific Heat of a Low-Dislocation-Density Alloy Superconductor

The Specific heat $C$ of a well-annealed alloy V-5 at.% Ta, measured at $1.4\le T\le 5$ °K in steady magnetic fields, displays sharp, bulk, superconducting transitions at upper critical fields $H_{c2\mathrm{}}$ a factor $\approx 10$ larger than the calorimetrically derived thermodynamic critical fields $H_c$. The transitions are similar to those observed earlier by Morin ${\mathit{et}\mathit{al}.\mathrm{}}^1$ in ${\mathrm{V}}_3$Ga, but in the present case it is unlikely that the bulk nature of the high-field transitions can be attributed to a nearly complete occupation of the specimen volume by dislocation-centered high-field superconducting filaments of diameter comparable to the penetration depth, since electron transmission microscopy studies on an identically prepared specimen indicate that in at least 95% of the specimen volume the mean separation between dislocations is greater than 1.4×${10}^{-4\mathrm{}}$ cm. However, the present data are explicable on the basis of the Ginzburg-Landau-Abrikosov-Gor'kov theory with a parameter $\kappa \approx \frac{H_{c2\mathrm{}}}{\sqrt{2}{H}_c}\approx 7$. The transition specific heat jumps $\frac{\Delta C\left(T_s\right)}{\gamma T_s}=1.44,1.15,1.10,0.94\mathrm{}$ occur at $T_s=4.30,4.09,3.85,3.37\mathrm{}$ °K in fields $H=0,1,2,4\mathrm{}$ kG, respectively, where $\gamma \equiv$ normal state electronic specific heat coefficient = 9.20 mJ/mole ${\left(\mathrm{K}\mathrm{°}\right)}^2$. The $\Delta C\left(T_s\right)$ values are in fair agreement with those calculated via Ehrenfest's equation for second-order phase transitions using Abrikosov's theoretical value of ${\left(\frac{\partial I}{\partial H}\right)}_T$ at $T_s$ for $\kappa =7\mathrm{}$, where $I\equiv$ magnetization. For $\left(\frac{T_s}{T}\right)\ge 1.8$, $\frac{C_{\mathrm{es}}}{\gamma T_s}=a \exp (-\frac{b{T}_s}{T})$ with $a=8.95,6.24,5.01,4.7;b=1.48,1.28,1.17,1.1\mathrm{}$; for $H=0,1,2,4\mathrm{}$ kG, respectively, where $C_{\mathrm{es}}$ is the electronic contribution to the specific heat. The exponential temperature dependence of $C_{\mathrm{es}}$ down to 1.4°K suggests an essentially everywhere finite, field-dependent, high-field energy gap in accord with Abrikosov's vortex model.