Electrical resistivity of dislocations in metals

Abstract

The transport equation for electrons in a dislocated crystal is solved in a way which allows explicitly for a complex (many sheets, open or closed) Fermi surface. Assuming resonance scattering of Fermi electrons by the dislocation core, and assuming negligible interband scattering the author obtains simple expressions for dislocation limited resistivity in metals of arbitrary bandstructure. The dislocation limited mobility mu of electrons or holes in metals of arbitrary bandstructure and containing randomly oriented dislocations of density beta (length per unit volume) is given by the universal expression mu beta =3e/8h(cross)=5.70*10¹⁴ V^-1 s^-1. Experimental data on dislocation resistivity for seventeen metals from ten subgroups of the periodic table are reviewed and comparison is made with calculated values. Good overall agreement of theory with experiment, encompassing a range from 10^-19 to 10^-14 Omega cm³ of dislocation specific resistivity, provides strong evidence both for the existence of dislocation resonances and, for multiband metals, the minor importance of interband scattering by the dislocation core.