Phase determination using high-order multiple diffraction of X-rays

The effect of invariant phases on the intensity profiles of high-order N-beam X-ray diffractions, with N > 3, is investigated. Theoretically, the second-order Bethe approximation and the graphic analysis of the structure-factor multiplets involved in the dispersion equation of the dynamical theory of X-ray diffraction are employed to reveal the dominant invariant phases in the multiple diffraction processes. It is shown that the phases of the triplets or the quartets are the effective phases which affect the multiply diffracted intensities. Experimentally, the intensity profiles of four-, five-, six- and eight-beam cases provide clear evidence to support the theoretical considerations.