Two-wave approximation in surface effects in asymmetric Laue crystals

Abstract

This paper is a study of surface effects, e.g. roughness or asymmetrical cut, in the Laue diffraction of X-rays by crystals, based on the Takagi-Taupin equations. By means of Riemann-Green integrals, first a formal solution has been obtained when the entrance and the exit surfaces are arbitrary. Then a coordinate transformation mapping a propagation domain with arbitrary boundaries into a rectangular domain with straight boundaries is given. Potential measurement errors in \gamma-ray wavelength and silicon lattice-parameter measurements by double-crystal diffractometry and X-ray interferometry, respectively, are outlined and anticipated by studying, in the two-wave approximation, the reflection peak shift and extra phase originating from an asymmetrically cut crystal. A relationship between analyser displacement, interferometer-signal phase and relative uncertainty in lattice-parameter measurement is also given.