The X-Ray Diffraction Image of a Stacking Fault

Abstract

The spherical wave theory of X-ray Pendellosung fringes in perfect crystals (N. Kato, Acta Cryst, 14: 526, 627, 1961) is extended to the case of crystals including a single stacking fault in an arbitrary way, Kelvin's stationary phase method is used extensively. The stationary phase condition gives us the trajectories of X-ray beams in the crystal. The phase and the amplitude along each trajectory are obtained by straightforward calculation. Based on this crystal wave field, the section patterns in X-ray diffraction topographs are obtained both for the direct and the Braggreflected waves. Characteristic fringe-patterns are expected. Through the image of a fault plane in a single section pattern, the geometrical configuration inside the crystal and the magnitude of the fault vector can be determined. Traverse patterns are also discussed. The fault image based on the plane wave theory (Whelan and Hirsch, Phil. Mag. 2: 1121, 1303, 1957) is also reformulated in the most general Laue case without the use of ad hoc assumptions on the shape of the dispersion surface.