Low-Temperature Thermodynamic Properties of Vanadium. I. Superconducting and Normal States

The specific heat of vanadium (resistivity ratio = 140) has been measured in the superconducting and normal states between 0.5 and 5.4\ifmmode^\circ\else\textdegree\fi{}K. The normal-state specific heat is given by ${C}_{n}=9.82T+0.035{T}^{3}+{C}_{\mathrm{nuc}}$ mJ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{deg}}^{\ensuremath{-}1}$, where the term ${C}_{\mathrm{nuc}}$ arises from the interaction of the nuclear magnetic moments with the applied magnetic field. The coefficient of the cubic term corresponds to a Debye temperature ${\ensuremath{\bigominus}}_{0}$ at 0\ifmmode^\circ\else\textdegree\fi{}K of (382\ifmmode\pm\else\textpm\fi{}10)\ifmmode^\circ\else\textdegree\fi{}K, which is slightly less than the value 399.3\ifmmode^\circ\else\textdegree\fi{}K obtained from elastic measurements. The superconducting specific heat contains a term linear in $T$ which is 0.52% of the normal-state linear term. This indicates the presence of a very small energy gap at the Fermi surface in addition to the normal gap. At all but the lowest temperatures the specific heat is governed by the normal energy gap and is in fair agreement with the BCS prediction. The agreement becomes excellent if the normal energy gap is assumed to be anisotropic with a maximum value of $3.52k{T}_{c}$ and a minimum of $3.20k{T}_{c}$, which is consistent with ultrasonic measurements. The superconducting transition temperature for this sample is (5.379\ifmmode\pm\else\textpm\fi{}0.004) \ifmmode^\circ\else\textdegree\fi{}K with a total transition width of only about 1 mdeg. The intrinsic transition temperature for vanadium is estimated to be (5.414\ifmmode\pm\else\textpm\fi{}0.010) \ifmmode^\circ\else\textdegree\fi{}K.