Two-beam dynamical diffraction solution of the phase problem: A determination with x-ray standing-wave fields

Using the dynamical theory of Bragg diffraction, we show that there is a direct relationship between the phase of the x-ray standing-wave field and the phase of the structure factor. For an experimental demonstration, we monitor the Ga and As K fluorescence and resonant Raman scattering yields, while scanning through the (111) and (200) Bragg diffraction rocking curves of GaAs perfect single crystals. The phases of the (111) and (200) GaAs structure factors are determined from the phases of the modulations in these secondary yields. With the use of monochromatized synchrotron radiation, with a variable photon energy between 10 and 15 keV, the effect of anomalous dispersion on the structure-factor phases is clearly seen in the vicinity of the Ga and As K absorption edges. We use this feature, in conjunction with the measured absorption spectrum, for directly determining the dispersion parameters f and f for atoms which appear in single-crystal structures.