ON THE X-RAY DIFFRACTION BY PERFECT ABSORBING CRYSTALS. Alfonso E. Merlini, 21027 Ispra (Va), Italy

Previous measurements of the (111) intensities diffracted by a perfect Ge crystal in the Bragg case, at frequencies of the incident radiation close to the K absorption edge, were considerably higher than those calculated by the dynamical theory of X-ray diffraction¹. The theory was modified so that the Kramers-Kronig dispersion relations be satisfied for each value of the glancing angle of the incident beam. In this way the photoelectric absorption contribution to the real part of the form factor depends on the glancing angle as the imaginary part does. is equal to the product of the intensity of the internal wavefield at the absorbing K-electrons by the contribution predicted by the anomalous dispersion theory of the individual atom (for simplicity the effects of the crystal field on the matrix elements of the absorption transition are neglected). The corresponding Darwin-Prins curves are higher than those foreseen by the present form of the dynamical theory of absorbing crystals and the integrated intensities are 20-30% greater. For example the relative calculated integrated intensities of the (111) Bragg reflection by a thick Ge crystal for a frequency of the incident beam 7.64 eV higher than the frequency of the absorption edge are about 1.58, 1.44 and 1.12 by taking the absorption contributions to the real part of the form factor equal to 0, and , respectively. The dynamical theory in its present form is a good approximation if the absorption contribution to the real part of the form factor is much smaller than its basic part. It is proposed that this theory be modified to take into proper account the dispersion relations. An important conclusion is that [[circleplus]] 0 (the effect of the anomalous dispersion is wiped out) in that part of the interference region where the absorption is small.Since the internal wavefield depends on the absorption contribution to the real part of the form factor, a consistent value of this contribution can be obtained either by a numerical solution of the equation of or by an iteration procedure(applicable for incident frequencies a few eV away from the absorption edge) of the same equation. A comparison with the above mentioned experimental results is satisfactory. The proposed modified theory can be readily extended to the Laue case, to different absorption phenomena and to the diffraction of other types of radiation by perfect crystals.

1) A. E. Merlini, Il Nuovo Cimento 15 D (1993) 169.