Method to generate all the geometrical ambiguities of powder indexing solutions

A new algorithm is reported that returns all the lattices with the same set of d spacings as that of a given lattice. The algorithm is useful for quickly checking lattice parameters obtained for a considered powder diffraction pattern and assessing the reliability of the results of powder indexing. The proposed algorithm was implemented as a new function in the powder indexing software Conograph (http://sourceforge.jp/projects/conograph/ ; http://research.kek.jp/people/rtomi/ConographGUI/web_page.html ). Examples of real cases are reported to explain how the algorithm can be used.