Electron-Phonon Interactions in Solid Alkali Metals. I. Scattering and Transport Coefficients

Abstract

Electron-phonon scattering in all the solid alkali metals at high temperature is studied in a calculation allowing detailed numerical assessment of anisotropy. The primary result sought and obtained is a conclusive accounting for the divergence of Li from the other alkali metals in having a large positive electron-diffusion thermopower. Animalu-Heine-Abarenkov pseudopotentials are used. The phonon dynamics is contained in a three-force-constant dynamical matrix fitted to elastic constants listed by Huntington, which reproduces the experimental structure factors for Na and for K to within 10% and 5%, respectively, and allows uniform treatment of all the alkalis. The electronic free path $l(\ensuremath{\epsilon}, \stackrel{^}{k})$ and $\frac{\ensuremath{\partial}\mathrm{ln}l(\ensuremath{\epsilon}, \stackrel{^}{k})}{\ensuremath{\partial}\mathrm{ln}\ensuremath{\epsilon}}$ are computed for $\stackrel{^}{k}$ in the principal symmetry directions, appropriate averages giving estimates for several transport-property coefficients. The anisotropy as calculated is very marked for Li and appreciable for Na, and gives Hall coefficients in satisfactory accord with those accurately known. The thermopower coefficients $\ensuremath{\xi}$ agree in sign and, except for Cs, semiquantitatively in magnitude with experiment, the decisive role being filled by the pseudopotentials. Estimated resistivities are, not unexpectedly, unsatisfactory. Analysis for Na, using scattering amplitudes fitted to resistivity, indicates strongly that most of such quantitative discrepancies as remain are primarily ascribable to slight but important inaccuracies in the pseudopotentials. A more thorough reinvestigation will, however, be required to account for the behavior of Cs.