An apparent paradox in crystal structure analysis

Abstract

A Commonly used test for the correctness of a crystal structure deduced from X-ray diffraction data is to perform a Fourier synthesis using the observed structure amplitudes (|F _o|) and the calculated phases (α_c) in the Fourier coefficients (namely |F _o|exp iα_c) and to verify that this diagram gives peaks of the right magnitudes at the assumed positions of atoms and none elsewhere. It was thought worth while examining what would happen if the amplitudes and the phases that are fed in belong to different structures. The tests that were carried out are briefly described here, together with an explanation of the results observed and their relation to the methods of structure analysis.