Theory of transport properties of pure, single crystal zinc

Abstract

Pseudopotential calculations have been performed by Tomlinson and Swihart to obtain phonon frequencies and polarization vectors, the Fermi surface, band velocities, and multi-orthogonalized-plane-wave electron-phonon matrix elements for pure zinc. These results are then used to determine the electrical and thermal resistivities which result from the scattering of electrons by thermal phonons. The same interaction also contributes to the attenuation of ultrasonic waves and the finite lifetimes of quasiparticle states near the Fermi surface, and these effects are also calculated. The Fermi surface and electron wave functions are based on the extremely accurate fit to de Haas-van Alphen data obtained by Stark and Falicov. Tomlinson and Swihart also make use of their resulting nonlocal pseudopotential for the matrix elements. The phonon model used is based on a pseudopotential calculation, and agrees well with neutron-diffraction data for frequencies at all high-symmetry points and for the polarization vectors where they have been determined. We solve the Boltzmann equation by the variational method, where we assume that the trial distribution function can be well represented as an expansion in up to six spherical harmonics. Solution in terms of different types of trial functions and in terms of anisotropic scattering times are presented for comparison.