Specific Heats of Some Cubic Superconducting Titanium-Molybdenum Alloys between 1.1 and 4.3°K

The specific heats of four bcc Ti-Mo alloys have been measured between 1.1° and 4.3°K, and at atomic fractional Mo concentrations between 0.0625 and 0.0860 (sufficient to stabilize the bcc phase). The normal state molar specific heats can be represented by the usual expression $C_n=\gamma T+\beta T^3$, where it is commonly assumed that $\gamma \propto N\left(E_F\right)$, the energy density of electronic states at the Fermi energy, and $\beta \propto {{\theta }_D}^{-3\mathrm{}}$. For each of the alloys the apparent electronic superconducting state specific heat for $1.3<\left(\frac{T_c}{T}\right)<\mathrm{}2.6\mathrm{}$ can be represented as $\frac{C_{\mathrm{es}}}{\gamma T_c}=a\exp (-\frac{b{T}_c}{T})$ where $a=10.5\mathrm{}$, $b=1.52\mathrm{}$, and the superconducting transition temperature, $T_c$, is taken as the midpoint of the rather broad (≈0.45 K°) superconducting transition. The measured values of $T_c$, ${\theta }_D$, and $\gamma$ are all rapidly varying and nearly linear functions of atomic fractional Mo concentration, $f$. At the mean solute concentration $\mathrm{}(f=0.0742\mathrm{}): T_c=2.59\mathrm{}°$K, $\frac{d\ln T_c}{\mathrm{df}}=+16.7\mathrm{}$; ${\theta }_D=337\mathrm{}°$K, $\frac{d\ln {\theta }_D}{\mathrm{df}}=-6.2\mathrm{}$; $\gamma =5.45\mathrm{}$ millijoules/mole ${\left(\mathrm{K}\mathrm{°}\right)}^2$, $\frac{d\ln \gamma }{\mathrm{df}}=\frac{d\ln N\left(E_F\right)}{\mathrm{df}}=+7.7\mathrm{}$. On the basis of the Bardeen-Cooper-Schrieffer theory of superconductivity, the relative variations of $T_c$, ${\theta }_D$, and $N\left(E_F\right)$ indicate that the electron-electron interaction parameter of that theory, $A$, is a relatively slowly varying function of solute concentration ($\frac{d\ln A}{\mathrm{df}}=-3.0\mathrm{}$).