The Electronic and Lattice Specific Heats in W, Mo, and Re

Abstract

Calorimetric measurements have been made in the temperature range 1\ifmmode^\circ\else\textdegree\fi{}K to 77\ifmmode^\circ\else\textdegree\fi{}K on W, Mo, and Re. At the lowest temperatures for W and Mo the specific heat could be resolved into a lattice ${T}^{3}$ function together with an electric term, $\ensuremath{\gamma}T$. It was found that at the lowest temperatures (a), for W, $\ensuremath{\theta}=250\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}\mathrm{to} 380\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$ and $\ensuremath{\gamma}=(1.8\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ cal/mole-${\mathrm{deg}}^{2}$ (b), for Mo, $\ensuremath{\theta}=445\ifmmode^\circ\else\textdegree\fi{}$K and $\ensuremath{\gamma}=(5.1\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ cal/mole-${\mathrm{deg}}^{2}$. These new measurements on tungsten indicate the need for revising previously quoted data.The measured lattice specific heat of tungsten agreed approximately with the theoretical computations made by Fine. The measured lattice specific heat of molybdenum varied with temperature in the manner predicted by Fine for the body-centered cubic lattice of tungsten. The measured electronic specific heat of tungsten was in moderate agreement with the theoretical computation of Manning and Chodorow, and the measured electronic specific heats of W and Mo were considerably less than those of most other transition elements except Cr, a result which may be approximately explained by assuming a $d$ band similar to that calculated by Slater. The question of the $d$-band shape is discussed in detail in the light of recent experimental results.Pure rhenium powder has been measured in the temperature range 68\ifmmode^\circ\else\textdegree\fi{}K to 77\ifmmode^\circ\else\textdegree\fi{}K. At these temperatures the Debye temperature $\ensuremath{\theta}$ was found equal to 262\ifmmode^\circ\else\textdegree\fi{}K.