Diffractions des rayons X par les structures en couches désordonnées. I

Abstract

While the approximations in the theoretical treatments of X-ray diffraction by two-dimensional gratings are in many cases valid and justify the application of the resultant formulae (in particular the Laue-Warren formulae) to the interpretation of experimental data, in certain cases a more detailed treatment is required. The present paper is concerned with the variation of the structure factor F within the zone of integration involved in determining the reflected intensity from a random powder of two-dimensional gratings. This integration is resolved into two parts corresponding to integration (a) across, (b) along the diffuse lines which represent two-dimensional layer lattices in reciprocal space; (a) is carried out algebraically, and the results are tabulated numerically for crystals of three simple shapes; (b) must be performed numerically for each individual case in accordance with the variation of F. The application of the formulae derived is discussed in relation to cases for which the variation of F ~ with angle is (i) slow, (ii) rapid and negative, (iii) rapid and positive, and the three types of diffracted bands are indicated. Results obtained by the present method and by the use of the Warren formulae are compared.