Lattice Dynamics, Heat Capacities, and Debye-Waller Factors for Be and Zn Using a Modified Axially Symmetric Model

It is noted in this paper that the total energy of the electron-ion system in the metallic state arises from an electron self-energy term as well as volume-dependent pairwise interaction terms among the ions. The Slutsky-Garland model used by Schmunk et al. to analyze the experimental dispersion curves of Be does not give the proper elastic behavior. The experimental dispersion curves for beryllium and zinc measured by Schmunk et al. and Borgonovi et al., respectively, are analyzed using a model consistent with the elastic behavior. For beryllium, the calculated dispersion curves agree well with the neutron inelastic-scattering data and the elastic constants of Smith and Arbogast. For zinc, the calculated frequencies are within the experimental uncertainties with the exception of the transverse branches along the [$0\overline{1}\overline{1}0$] direction which describes atomic motions perpendicular to the basal planes. The experimental data on Zn indicate high dispersion and fluctuations in frequency $\omega$ versus wave number $q$. The calculated elastic constants agree within a few percent with the experimental data of Alers and Neighbours at 300°K, with the exception of ${\mathrm{C}}_{44}$ and ${\mathrm{C}}_{13}$, which are low by 19% and 27%, respectively. The Debye-Waller factor and the specific heat for both metals are compared with available experimental data. It is found that the calculated specific heat for zinc is in excellent agreement with experiment over the whole temperature range. However, for beryllium, the calculated values are low for small temperatures; the discrepancy could be attributed to heavy impurities in beryllium. The anisotropy in the Debye-Waller factor for zinc is in good agreement with x-ray and Mössbauer experiments.