Application of Focal Curves to the Evaluation of Conic Diffraction Lines

Abstract

Micro diffraction methods like the Kossel or X-ray rotation tilt techniques generate diffraction patterns consisting of conic sections. Extracting information about lattice parameters, orientation or stresses from those patterns generally requires additional information. As a consequence, it is necessary to make high precision measurements of the pattern center and the detector-sample distance. By modeling the focal curves of a diffraction pattern it is possible to determine these parameters from only a single exposure. The focal curves of the conic sections in the detected image intersect (ideally) at the inspected sample point. This point is also the apex of all diffraction cones. The use of the geometry of the focal curves leads to an improved accuracy for the determination of lattice constants, residual stress and strain tensors by avoiding mechanical frames and their accompanying measurement errors. Therefore, by using this analysis route it is possible to extract three-dimensional crystal information out of a single two-dimensional diffraction pattern.