The contribution of the long-range strain field of dislocations in metals to their electrical resistivity

Abstract

A method is described for calculating the electrical resistivity produced by weak long-range inhomogeneities, modelled by fluctuations of an equivalent refractive index. The theory is applicable when the variance of the refractive index is very much less than unity and when the scale length of the fluctuations is much larger than an electron's wavelength. There is no limit to how large the scale length may be (in contrast to the usual situation regarding the Born approximation) which makes the method of particular use for investigating the electrical resistivity produced by scattering from the strain field of dislocations in metals. Such a calculation is described in which the effects of correlations are included through an adjustable parameter, rho c, an outer cut-off radius. It is found that the resistivity is negligible if scattering from regions within a few Burgers' lengths from dislocation lines is ignored, however large rho c is taken to be. It is concluded that dislocation resistivity must be due to core scattering, except possibly in those rather special situations when the strain fields of dislocations tend to reinforce each other at large distances.