Dislocation scattering: a new Hamiltonian for describing multivalued elastic displacement fields

Abstract

A new procedure for treating the scattering of electrons or phonons by the multivalued elastic displacement fields of dislocations is developed on the basis of the tight-binding model used recently by Kawamura (1978) to describe screw dislocations. It is equivalent, in the continuum limit, to applying a multivalued coordinate transformation to the free-electron Hamiltonian and then seeking a single-valued solution of the resulting eigenvalue equation. This provides a kinematic scattering mechanism that is independent of the details of the lattice potential. Such a mechanism is indicated by the uniformity of the experimental data on dislocation resistivity.