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 amplitude from a complete knowledge of the differential cross section or, in the case of a crystal, from the diffracted intensities. The Sayre equation and all the direct methods of phasing following there from are derived as a special case of unitarity for zero excitation error. Dynamical and kinematical scattering are considered, and the relationship between them, S = exp(i tau nzK), is obtained. Applications to the case of electron diffraction including for non-zero excitation error are discussed.