Lattice Dynamics of Gold

The complete phonon dispersion relations for gold in the high-symmetry directions have been measured at room temperature by the coherent inelastic scattering of neutrons. It is found that the forces in gold are not homologous with the other noble metals, the frequencies of gold lying appreciably higher than those "scaled" from copper and silver. An analysis of the data in terms of different force-constant models reveals that a general tensor force is required for the first-neighbor interaction, whereas for neighbors beyond the first either general tensor or axially symmetric forces give an excellent fit to the data. The axially symmetric model alone does not adequately describe the data even when forces extending to ninth-nearest neighbors are included in the fit. In addition, simple screened-pseudopoential models were fit to the data and these results also indicate the need for the first-neighbor interaction to be general. Frequency distribution functions and related thermodynamic quantities were calculated from the various force-constant models. The Debye temperature ${\Theta }_C$ versus temperature curves obtained show an anomaly at low temperatures consistent with the ${\Theta }_C\mathrm{}\left(T\right)\mathrm{}$ obtained from specific-heat measurements. The relation between this anomaly and the character of the dispersion curves is given.