Bragg-surface three-beam dynamical X-ray diffraction

Three-beam diffraction with a symmetric Bragg reflection and a surface diffraction is studied based on the dynamical theory of X-ray diffraction. The difficulty involved in the boundary conditions for the surface diffraction is overcome by treating the Bragg–surface diffraction as either a Bragg–Laue or a Bragg–Bragg case with the inclination angle α between the crystal surface and the surface-diffracted beam being very small, about 10−5 rad. The geometry of the dispersion surface, the number of permitted modes of wave propagation, the linear absorption coefficient, the excitation of the beam and the diffracted intensity are calculated for the Ge (000) (222) (31\overline 1) Bragg–surface diffraction of Cu Kα1. It is found that the calculated relative integrated intensity ratio among the Bragg–surface 31\overline 1 case and the Bragg–Bragg 113 and 51\overline 1 cases is in good agreement with the integrated intensity ratio obtained experimentally.