Elastic Constants of Palladium from 4.2-300°K

Abstract

Elastic constant measurements have been made on a single crystal of palladium in the temperature range 4.2-300\ifmmode^\circ\else\textdegree\fi{}K. Extrapolation of the data to absolute zero gives ${c}_{11}=2.341\ifmmode\pm\else\textpm\fi{}0.027\ifmmode\times\else\texttimes\fi{}{10}^{12} \mathrm{dyne} {\mathrm{cm}}^{\ensuremath{-}2},$ ${c}_{12}=1.761\ifmmode\pm\else\textpm\fi{}0.027\ifmmode\times\else\texttimes\fi{}{10}^{12} \mathrm{dyne} {\mathrm{cm}}^{\ensuremath{-}2},$ ${c}_{44}=0.712\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\times\else\texttimes\fi{}{10}^{12} \mathrm{dyne} {\mathrm{cm}}^{\ensuremath{-}2}.$ The corresponding value of Debye temperature is ${\ensuremath{\theta}}_{0}=275\ifmmode\pm\else\textpm\fi{}8\ifmmode^\circ\else\textdegree\fi{}$K, which compares well with the calorimetric figure of ${\ensuremath{\theta}}_{0}=274\ifmmode\pm\else\textpm\fi{}3\ifmmode^\circ\else\textdegree\fi{}$K. Both shear constants show an anomalous temperature dependence. This dependence can be correlated with the temperature variation of the contribution to $C={c}_{44}$ and ${C}^{\ensuremath{'}}=\frac{1}{2}({c}_{11}\ensuremath{-}{c}_{12})$, resulting from the presence of holes in the $d$ band of palladium.