Vibration Spectra and Specific Heats of Cubic Metals. II. Application to Silver

Abstract

The frequency spectrum of silver, and hence its specific heat $C_v$ at constant volume as a function of temperature, are calculated by solving the secular equation derived in Part I of this work for the determination of the frequencies of the normal modes of vibration of a monovalent face-centered cubic metal. The calculations are made with two sets of elastic constants, namely with their values at absolute zero of temperature and at room temperature. The calculated $C_v$ are compared with the experimental data and with the earlier calculations based on a two force-constant model (in contrast to the three appearing in our secular equation) by plotting the corresponding effective Debye temperatures $\Theta$ against temperature. It is found that, except for temperatures below about 7°K, the agreement between theory and experiment is satisfactory. It is shown that the discrepancy between the two sets of values below 7°K can be partly removed by making a choice for the elastic constants slightly different from that actually used in the calculation. However, it appears that the explanation of the entire discrepancy at low temperatures for silver and of a similar one found by Bhatia for sodium lies elsewhere.