THE PHASE PROBLEM IN THE ANALYSIS OF X-RAY-DIFFRACTION DATA IN TERMS OF ELECTRON-DENSITY DISTRIBUTIONS

The refinement of electron-density distributions for noncentrosymmetri c crystals from X-ray diffraction data may lead to a very good fit bet ween model and data but to totally meaningless electron densities. Thi s is to a large extent because varying certain parameters, or combinat ion of parameters, in the model mainly leads to a change in the phases of the structure factors. A formal analysis of why this happens, when using multipole models, is given as well as specific examples using r eal data: the contributions of odd-order multipoles, which are invaria nt under crystal-class symmetry operations, are poorly determined. The importance of applying constraints on the models is stressed. The con clusions of this analysis can be carried over to refinements of anharm onic atomic vibrations.