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°K. Extrapolation of the data to absolute zero gives $c_{11}=2.341\mathrm{}\pm 0.027\times {10}^{12} \mathrm{dyne} {\mathrm{cm}}^{-2\mathrm{}},$ $c_{12}=1.761\mathrm{}\pm 0.027\times {10}^{12} \mathrm{dyne} {\mathrm{cm}}^{-2\mathrm{}},$ $c_{44}=0.712\mathrm{}\pm 0.003\times {10}^{12} \mathrm{dyne} {\mathrm{cm}}^{-2\mathrm{}}.$ The corresponding value of Debye temperature is ${\theta }_0=275\mathrm{}\pm 8°$K, which compares well with the calorimetric figure of ${\theta }_0=274\mathrm{}\pm 3°$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 $C^{\prime }=\frac{1}{2}(c_{11}-c_{12})$, resulting from the presence of holes in the $d$ band of palladium.