In strong magnetic fields, most metals have highly anisotropic transport coefficients, and these have long been known to be much influenced by sample inhomogeneities. This paper reports a detailed theoretical study of such effects. Various approximations for calculating the effective transport coefficients of inhomogeneous solids are rederived from a unified point of view; these are then used for a variety of model calculations appropriate to metals with open Fermi surfaces. A small concentration of crystallites with open orbits embedded in a free-electron metal is shown to give rise to a strictly linear transverse magnetoresistance (TMR) at strong magnetic fields. The linear coefficient is strongly dependent on the orientation of the open orbit in the plane perpendicular to the magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. Extended-orbit crystallites in a free-electron metal produce a TMR which is initially linear, but saturates at sufficiently strong field. The Hall coefficient ${R}_{H}$ is unchanged from its free-electron value to first order in the concentration of defects. A striking geometrical effect is predicted, the TMR from open-orbit crystallites saturating in geometries such that current distortions are unable to propagate parallel to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. The TMR and Hall coefficient of a free-electron metal containing a larger concentration of open-orbit crystallites is calculated in the effective-medium theory (EMT). The TMR is found to saturate at strong fields, in agreement with previous results of Stachowiak, while the Hall coefficient falls off as 1/${\mathrm{H}}^{2}$ at strong fields, except in flat-plate samples with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ perpendicular to the plate, in which case it is predicted to saturate at its free-electron value for a sufficiently large concentration of open-orbit crystallites, but to fall off quadratically for lower concentrations. In contrast, calculations within a non-self-consistent approximation give a strictly linear TMR and a Hall coefficient which saturates at a value below the free-electron coefficient. Possible explanations for the discrepancy are discussed. Calculations in the EMT for a model polycrystal with extended-orbit crystallites reveal a broad field region of quasi-linear magnetoresistance, as found previously by Stachowiak, and a reduced Hall coefficient, as well as a conspicuous geometrical effect. The possible relation of these model calculations to experiments of polycrystalline noble metals is examined, but no quantitative theory for these metals is given.
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