Small-angle scattering by dislocations

It is shown that the small-angle scattering of X-rays or neutrons by dislocations within a deformed metal, which are partially ordered into wall-like structures, is characterized by several factors. Principally these are associated with: (i) a single dislocation or dipole; (ii) the dislocation configuration in the plane of the wall; and (iii) the distribution of dislocations across the wall thickness. With the assumption of isotropic elasticity, small-angle scattering will be sensitive only to the edge components of the dislocations. The scattered intensity is dominated by scattering from dislocations that lie perpendicular to the scattering vector, q, and reaches a maximum when q is normal to the slip plane of these dislocations. Above a particular |q|, the scattered intensity is sensitive only to the total edge dislocation content of the scattering dislocations (i.e. scattering is incoherent), while, below this value, the scattering is dominated by how the dislocations are distributed in walls. For walls normal to their slip planes, the configuration factor will reflect the dislocation distribution in the plane of the wall, while, for walls parallel to their slip planes, the distribution in the thickness direction will be visible. Therefore, even though a deformed material is composed of complicated dislocation structures, only those segments conforming to these rather strict prescriptions will be singled out for scattering, and, by adjusting the beam/slip system geometry, many parameters of the microstructure can be determined experimentally.