Experimental determination of triplet phases and enantiomorphs of non-centrosymmetric structures. I. Theoretical considerations

Information on the triplet phase sum Φ_Σ of the structure factor product F(-h)F(h - g)F(g) can be deduced from the rocking curve of a ψ-scan experiment scanning through a three-beam position. For non-centrosymmetric structures, four typical profiles can be observed. For Φ_Σ = 0, 180°, asymmetric profiles result, whereas a nearly symmetrical decrease or increase of the two-beam intensity appears for Φ_Σ = ±90°. In a first approximation this behaviour can be explained by the interference between the directly diffracted wave of h and the 'Renninger Umweg' wave of g and h - g. Their phase relationship and the amplitudes are governed by a spatial resonance term, which causes a phase shift of 180° and a continuously turning on and off of the Umweg wave amplitude scanning through the three-beam position. This interference can be displayed by a phase-vector diagram which outlines the main features of the ψ-scan profiles. The semi-quantitative results are confirmed by calculation based on the dynamical theory. The distinction between Φ_Σ = ±90° allows the experimental determination of enantiomorphs.