The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

Abstract

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.