A single-exposure method for the determination of lattice spacings and crystal orientation from Kossel diffraction patterns

A single exposure method is described for the calculation of lattice spacings and crystal orientation, from Kossel diffraction patterns. This method is extremely simple from an experimental viewpoint since the only data required are the coordinates of five or more points on each Kossel diffraction curve in an arbitrary orthogonal system and the wavelength of the characteristic X-ray radiation forming the pattern. The method requires the analysis of at least two diffraction curves which can be either elliptical or hyperbolic. The equation of each curve is first derived in the arbitrary system. It is then transformed to a coordinate system in which the coefficients may be equated with those of an equation of the same curve derived in terms of the lattice spacing, the orientation of the crystal planes responsible for the diffraction cone and the X-ray wavelength. The lattice spacings and the directions of the crystal plane normals are calculated. A computer program has been written to handle the lengthy arithmetical operations required for the analysis, and application of the method to a Kossel pattern from a single grain of Swedish iron is described.