Crystal Dynamics and Electronic Specific Heats of Palladium and Copper

Using inelastic neutron scattering, the frequency – wave vector dispersion relations for the lattice vibrations in a single crystal of palladium have been determined at 120, 296, 673, and 853 °K. Analyses of the results have given force-constant models from which frequency distributions have been computed. First-neighbor interactions are dominant, but weaker interactions also exist, extending beyond sixth-nearest neighbors. The total lattice specific heat (harmonic plus anharmonic) at constant pressure has been calculated, using the frequency distribution at 296 °K and the shifts in the frequencies with changing temperature. Similar calculations were also carried out for copper, using the room temperature distribution reported by Svensson et al.; the temperature dependence of the frequencies was established by carrying out measurements along major symmetry directions of Cu at 296, 473, and 673 °K. The electronic specific heats of Cu and Pd have been calculated at temperatures between 0 and 900 °K. The electronic specific heat of Cu agrees well enough with the linear relation Ce = γT for T < 700 °K. For Pd, Ce is anomalously high at low temperatures, in agreement with experiments at helium temperature, but tends to saturate for temperatures > 200 °K.