Specific Heat and Grüneisenγof Noble Metals

It has been found after an elaborate study of the phenomenological electron-gas models that, although all models show good agreement of the calculated Debye $\Theta$ and Grüneisen parameter $\gamma$ with experimental data for copper and silver, none is able to reproduce the anomalous low-temperature behavior of the Debye $\Theta$ of gold. The calculations were carried out using Houston's method as modified by Horton and Schiff for temperatures below $\frac{\Theta }{10}$ down to 1°K and using the root-sampling technique above $\frac{\Theta }{10}$ up to 300°K. It is difficult to comment on the low-temperature calculated values of $\gamma$ because of the large scatter in the experimental $\gamma$ values determined by different people. An interesting point to note is that, while the use of old pressure-derivative data of Daniels and Smith to calculate $\gamma$ gives quite satisfactory results, the recent data of Hiki and Granato do not give as good agreement. Merits and demerits of the models used are discussed, and it is suggested that the data for the pressure derivative of elastic constants should be reinvestigated.