A general method for locating the X-ray source point in Kossel diffraction

A development of a conic fitting procedure is described which enables the X-ray source point in Kossel diffraction to be determined solely by analysis of shadows cast on the recording film and so dispenses, in subsequent analysis of the pattern, with the need to have prior knowledge of the crystal structure of the specimen or to have accurately manufactured cameras. The technique involves a conic fitting analysis of the shadows cast by spheres positioned between the recording film and X-ray source. Two or more shadows provide data from which the pattern centre and specimen to film distance are evaluated, so locating the X-ray source. The technique has been used in conjunction with new experiments in the development of suitable procedures for adaptation of Kossel diffraction for use in scanning electron microscopes. The paper includes a numerical analysis of errors involved in source location and in subsequent evaluation of lattice spacing and the technique is tested with studies on iron, copper and copper-bismuth alloy. It is shown that the standard deviation of errors in locating the X-ray source amounts to 1 part in 3000 and in lattice-spacing measurement, to 1 part in 7000. The lattice parameters found for the three materials tested were for iron 2.8653±0.0005 Å, for copper 3.61715±0.0005 Å, for copper-bismuth 3.6155±0.0005 Å. The crystal volume yielding the patterns for which these data were obtained is estimated as 260 × 10^-9 mm³.