Specific Heat of Gallium and Zinc in the Normal and Superconducting States

Abstract

By using a ${\mathrm{He}}^{3}$ cryostat the specific heat of gallium has been measured between 0.35\ifmmode^\circ\else\textdegree\fi{}K and 4.3\ifmmode^\circ\else\textdegree\fi{}K, and that of zinc between 0.42\ifmmode^\circ\else\textdegree\fi{}K and 4.2\ifmmode^\circ\else\textdegree\fi{}K. Measurements on Ga in the normal state indicate that the coefficient of the electronic specific heat, $\ensuremath{\gamma}$, is 0.601 millijoule/mole ${(\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{2}$ while the Debye characteristic temperature $\ensuremath{\theta}$ at 0\ifmmode^\circ\else\textdegree\fi{}K is 317\ifmmode^\circ\else\textdegree\fi{}K. For Zn, $\ensuremath{\gamma}=0.640$ millijoule/mole ${(\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{2}$; $\ensuremath{\theta}=309\ifmmode^\circ\else\textdegree\fi{}$K. The electronic specific heat in the superconducting state, ${C}_{\mathrm{es}}$, for both metals for $T$ well below the transition temperature, ${T}_{c}$ can be represented by the expression ${C}_{\mathrm{es}}=a\ensuremath{\gamma}{T}_{c}{e}^{\ensuremath{-}\frac{b{T}_{\mathrm{c}}}{T}}$. For Ga, ${T}_{c}=1.087\ifmmode^\circ\else\textdegree\fi{}$K, $a=7.0$, and $b=1.35$. The zinc sample measured has a broad transition, ${T}_{c}$ taken as 0.852\ifmmode^\circ\else\textdegree\fi{}K. Also for Zn, $a=6.4$ and $b=1.27$. The magnetic threshold field curves are calculated from these specific heat results. The critical field at 0\ifmmode^\circ\else\textdegree\fi{}K for Ga is 59.4 gauss and for Zn, 53.4 gauss.In comparing these measurements with the calorimetric results of other superconductors a definite variation is noted in the parameters $a$, $b$, $\frac{({C}_{\mathrm{es}}\ensuremath{-}{C}_{\mathrm{en}})}{\ensuremath{\gamma}{T}_{c}}$ at ${T}_{c}$, and $\frac{\ensuremath{\gamma}{{T}_{c}}^{2}}{{V}_{m}{{H}_{0}}^{2}}$. There appears to be a correlation between the magnitudes of these quantities and the transition temperature.