Effects of Stress on Superconducting Sn, In, Tl, and Al

Abstract

Hydrostatic pressures of 0 to 100 atmos obtained with helium gas pressure, and of 1.9\ifmmode\times\else\texttimes\fi{}${10}^{3}$ atmos obtained by an ice expansion bomb technique are used to measure the pressure displacement of critical temperature ${T}_{c}$. The coefficient ($\frac{\ensuremath{\partial}{T}_{c}}{\ensuremath{\partial}p}$) for Sn, In, Tl, and Al is -4.7\ifmmode\pm\else\textpm\fi{}0.2, -4.0\ifmmode\pm\else\textpm\fi{}0.2, +0.6\ifmmode\pm\else\textpm\fi{}0.3, and -2.0\ifmmode\pm\else\textpm\fi{}0.2 in units of ${10}^{\ensuremath{-}5}$ \ifmmode^\circ\else\textdegree\fi{}K/atmos, respectively. The temperature dependence of $R=\frac{{(\frac{\ensuremath{\partial}{H}_{c}}{\ensuremath{\partial}p})}_{T}}{{(\frac{\ensuremath{\partial}{H}_{c}}{\ensuremath{\partial}p})}_{{T}_{c}}}$ above 1\ifmmode^\circ\else\textdegree\fi{}K is described by $R=0.61+0.029{T}^{2}$ for Sn, and $R=0.77+0.020{T}^{2}$ for In. This result is discussed in connection with the similarity principle, $\frac{{H}_{0}}{{T}_{c}}=\mathrm{constant}$. From an analysis combining stress and isotope effects, it is seen that ${T}_{c}$, or ${H}_{c}$, is more sensitive to volume changes, holding zero-point lattice vibration amplitude fixed, than to zero-point amplitude changes, holding $V$ fixed: ${(\frac{\ensuremath{\partial}{H}_{c}}{\ensuremath{\partial}\mathrm{ln}V})}_{{q}^{2}}=5.5\ifmmode\times\else\texttimes\fi{}{(\frac{\ensuremath{\partial}{H}_{c}}{\ensuremath{\partial}\mathrm{ln}{q}^{2}})}_{V}$ for Sn. Zero-pressure critical field data are also presented for the subject metals.