Effective conductivity for interface scattering in metal-matrix composites

The contribution to the resistivity of metal-matrix composites resulting from electrons scattering from the surface of the embedded phase has long been recognized, but quantitative assessments of this effect are practically unknown. We present a theory that can serve as a starting point for such investigations. The theory focuses on an effective local conductivity for scattering, which rises steadily from a minimum at the scattering surface to the matrix value several mean-free-path lengths into the bulk. By making suitable assumptions, we are able to give a closed-form expression for this local conductivity, which is insensitive to the geometry of the scattering surface. Our analytical results compare favorably with recent numerical calculations for the scattering of electrons from the external surface of a long cylinder.