The propagation of electrons in a strained metallic lattice

Abstract

The propagation of electrons in a strained metallic medium is studied by a perturbation technique in which the perturbing potential is proportional to the elastic strain and not, as in the usual treatment, to the displacement. For slowly varying strains the perturbing potential is a deformation potential of the type introduced by Bardeen & Shockley (1950), in which the periodicity of the lattice does not appear explicitly. In the approximation of nearly free electrons, the contribution of the ionic lattice to the deformation potential depends only on the dilatation and not on the shear components. This potential is modified by a flow of electrons from the compressed regions of the lattice to the expanded regions. The resulting potential depends only on the Fermi energy of the electrons and not on their interaction with the lattice of ions. In a higher approximation, the effective mass of the electrons depends on their interaction with the ionic lattice. The contribution of this term is comparable with that already considered, and the shear components of the strain also influence the deformation potential. The method is applied to estimate the electrical resistivity produced by dislocations of edge and screw types present in sodium and copper. In copper screw dislocations add appreciably to the total resistivity.