Geometrical and mathematical ambiguities arising in crystallographic unit cell determination

Indexing programs often propose several possible cells compatible with the same observed X-ray powder diagram. Two types of ambiguity can be distinguished: one of geometrical origin, in which the crystallographic network remains unchanged, and the other of mathematical origin, giving cells without any physical meaning. A list of these ambiguities is presented and a computer program suitable for their detection is proposed. © 1993 Academic Press, Inc.