A note on the reading of Kossel patterns

Abstract

A Kossel pattern, as recorded on a flat photographic plate, is best regarded as a gnomonic projection of a “spherical Kossel pattern”, recorded on a sphere centred at the source point. The spherical Kossel pattern is identical (at arbitrary scale) with the circles of intersection of the “X-ray Fermi sphere” (a sphere of radius 1 λ centred at the origin of reciprocal space) with the Brillouin planes, which form the boundaries of Brillouin zones. By this visualization one readily identifies the characteristic features in a Kossel pattern which are of value for revealing crystal orientation and lattice structure, for simple and sometimes sensitive measurement of lattice parameters, and for sensitive detection of strain. Two Kossel conies, one well observed ( i.e., a complete or nearly complete ellipse, or a hyperbola with both branches visible) will suffice to determine the orientation for a known crystal. Two well observed will give the lattice parameter as well if the characteristic X-ray wave-length is known, and three suffice to determine the lattice structure. However, special features such as Kossel-line intersections provide superior information which should be exploited as far as possible.