Remarks on the use of Boltzmann's equation for electrical conduction calculations in metal matrix and in situ composites

Abstract

The Boltzmann equation and its solutions are cental to the development of microscopic models describing the longitudinal and transverse electrical conductivity of metal matrix and in situ composites. Such solutions are needed to describe electron and phonon scattering and transport phenomena in the matrix due to the presence of a second filamentary phase, and to describe electrical conductivity at cryogenic and higher temperatures. In this paper, we derive solutions to the Boltzmann equation in the relaxation time approximation in cylindrical coordinates. It is shown that one solution for the electric field parallel to the fibre direction leads to an expression for composite conductivity at cryogenic and higher temperatures. We also present a solution for the case in which the electric field is normal to the fibre direction.