Longitudinal Electrical Conductivity of Metal Matrix Composites at Cryogenic Temperature in the Presence of a Longitudinal Magnetic Field. Part 1. Solution of the Linearized Boltzmann Equation. Part 2. Application of the Solution to Metal Matrix Composites,

摘要

We solve the Boltzmann equation in the relaxation time approximation with parallel E and B fields parallel to the continuous fibres reinforcing a metal matrix. It is shown that this solution is identical to that described by us elsewhere, except for the addition of the cyclotron frequency. The addition of the cyclotron frequency term shows that the electrons follow helical paths as they drift down the composite. The boundary considered is either the external or the internal surface of a cylinder representing the fibre. To apply this solution to metal-matrix composite materials we assumed that the cylindrical fibres are non-conducting cylinders in a matrix of pure crystalline metal. The electron mean free path is never greater than half the fibre separation distance. In a companion paper we discuss the application of this solution to metal-matrix composites. Keywords: Metal matrix composites, Fiber reinforced composites, Linearized Boltzmann equation. (JES)