Coherent scattering theory for the electronic band structure and quantum-state lifetimes in a dilute substitutional Mg alloy

Abstract

The virtual crystal approximation is used to formulate the Schrödinger equation for the electronic band structure of a dilute substitutional alloy and to analyze the effect of coherent scattering on the lifetime τ _k of an electron quantum state. Both coherent and incoherent scattering theory yield essentially the same functional and numerical relationship connecting τ _k ,C, and |V _O|, whereC is the impurity concentration and |V _O| is the typical Fourier transform of the impurity perturbation potential. Electron quantum interference data for Mg-Zn and Mg-Cd alloys are interpreted using this formulation. A consistent picture of these alloys results which contains the following features. (1) The impurity atoms in both types of alloys are partially ordered in the Mg lattice. (2) The perturbation potentials for both Zn and Cd are somewhat larger than predicted by simple pseudopotential theories, with the perturbation for Zn being about 6.5 times larger than for Cd. (3) A standing charge density wave commensurate with the lattice and having aC-dependent amplitude is present in these alloys.