Calculations of the integrated diffracted intensity for Renninger experiments, i.e. calculations of 0-scan profiles scanning through three-beam positions, are reported. The fundamental equations of the dynamical theory are solved by means of an eigenvalue procedure and boundary conditions consistent with the diffraction geometry. It is shown that for noncentrosymmetric structures the three-beam 0-scan profiles bear information on both the magnitude, defined in the range 0 < -<-180°, and the sign of the triplet phase involved in the three-beam interference. In general, the 0-scan profiles can be separated into two parts: a phase-dependent part ('ideal' profile) due to the interference effect and a symmetric phase-independent Umweganregung or Aufhellung profile due to the mean energy flow in a three-beam case. Both parts can be calculated by summing up the 0-scan profiles for +~b and -~b, one profile being reversed with respect to the three-beam point. As a result, the experimentally best suited three-beam cases for triplet phase determination should involve structure factors of nearly equal magnitude. In a recent paper (Hiimmer, Weckert & Bondza, 1989) we reported on the direct measurements of triplet phases by means of three-beam interference experiments for two non-centrosymmetric structures. It was shown that the shape of the 0-scan intensity profile is related to the triplet phase so that the sign of the triplet phase and not only its cosine can be determined. For example, the 0-scan profiles for triplet phases near +90 or -90 ° show typical differences. In order to distinguish experimentally between triplet phases of +90 or -90 ° it is essential that the structure factors involved in the three-beam case have approximately the same magnitudes. If this criterion is not fulfilled then phase-independent effects of Aufhellung or Umweganregung superimposed on the interference effect are dominant and it is difficult to extract any phase information.In order to provide a reliable theoretical basis for the experimental results we resumed our calculations based on Laue's dynamical theory of three-beam Xray diffraction (cf. Hfimmer & Billy, 1982). We investigated systematically the influence of the magnitude of the structure factors and we varied systematically the value of the triplet phase to get an idea of the precision of the triplet phases determined from 0-scan profiles, when unavoidable phase-independent Umweganregung or AuJhellung effects are present, as is the case in most three-beam experiments.Alternative mathematical descriptions of threebeam diffraction related to experimental phase determination are, for example, those of Thorkildsen (1987) who used Takagi-Taupin equations and of who used a modified two-beam approximation.
Computational detailsThe fundamentals for calculating 0-scan profiles near a three-beam case have already been outlined in a former paper (Hfimmer & Billy, 1982). Below, this paper is referred to as HBI. In some details we have changed and improved the computing program, to t...