Influence of Conduction Electrons on the Lattice Specific Heat and Elastic Moduli of Alpha-Phase Alloys of the Noble Metals

Measurements near 0°K of the lattice specific heat and the elastic moduli $C_{\mathrm{ij}}$ of $\alpha$-phase alloys of the noble metals imply a change in Debye temperature $\Theta$ which is a function only of the electron/atom ratio when the solute is iso-electronic with the solvent. An attempt is made to estimate the variation in $\Theta$ by calculating the dependence of the shear moduli on the total kinetic energy of the electron system. The band structure is assumed rigid and the energy surfaces, which are defined using a nearly-free-electron model, are chosen so that the shape of the model Fermi surface resembles that which has been measured for the pure metals. The calculated variation with electron density is too large, particularly for $C_{44}$, and the observed change in $\Theta$ cannot be reproduced. This is probably due to the use of a rigid-band model, which predicts a decrease in the density of states with increasing electron/atom ratio for a Fermi surface which contacts the zone boundary, and is consequently unable to explain the observed changes in either the lattice or the electronic heat capacities.