On a physical interpretation of direct-methods relationships

On the basis of Laue's dynamical theory of X-ray diffraction the non-negativity condition for the Karle-Hauptman determinant is obtained. For the three-beam case the validity of the triplet phase relation of direct methods is displayed. The unitary relation and dynamical X-ray scattering amplitude from crystals are used to derive a Sayre-type equation, which for identical atoms reduces to Hughes's equation. These results allow the interpretation of relations between structure amplitudes in direct methods on the basis of dynamical theory.