Transport in nearly-free-electron metals. II. Phonon-limited relaxation time at high temperature

The problem of electron transport at high temperatures has been attacked for a model divalent metal, using principally a two-plane-wave approximation and taking into account the Fermi-surface distortion. The electron mean free path is found as a function of position on the Fermi surface for phonon scattering only. The limiting high-temperature form of phonon-scattering structure factor is used and the effective electron-relaxation time is found by a somewhat novel iteration scheme that converges rapidly. Without loss of generality the electric field is chosen to act along a symmetry direction of the lattice. For the purpose of this application the phonon dispersion and anisotropy are disregarded. Simple consideration of two sets of Brillouin zones shows that their effects can be roughly superimposed for the usual nearly-free-electron metal. For a reasonably chosen set of material parameters the calculated dependence of electron relaxation time as a function of $\overrightarrow{\mathrm{k}}$ is used to find the conductivity.