SOLUTION OF THE PHASE PROBLEM IN CRYSTALLOGRAPHY AND APPLICATION TO DYNAMICAL ELECTRON-DIFFRACTION

Unitarity, a fundamental principle of scattering theory, leads to the prediction of an essentially unique set of phases for the scattering a mplitude from a complete knowledge of the differential cross section o r, in the case of a crystal, from the diffracted intensities. The Sayr e equation and all the direct methods of phasing following therefrom a re derived as a special case of unitarity for zero excitation error. D ynamical and kinematical scattering are considered, and the relationsh ip between them, S = exp(i tau n(z)K), is obtained. Applications to th e case of electron diffraction including for non-zero excitation error are discussed.