Multiple scattering of X-rays by amorphous samples

Abstract

An exact expression in the form of a double integral is obtained for the ratio of the intensity of double scattering to that of single scattering 1(2)/1(1) for a diffractometer sample of an amorphous material.By expressing the double scattering in terms of the independent scattering of the atoms, and approximating this quantity by an expression involving two parameters, the double integral is evaluated and tabulated as a function of 20 and the two parameters. With these tabulated values, the ratio 1(2)/1(1) for unmodified scattering only, or for both unmodified and modified scattering, can be obtained for a sample of any composition. For the unmodified scattering from vitreous SiO2 using Rh Ke radiation,

Double diffraction des rayons X par une substance amorphe

“…La Fig une partie correspondant aux grands angles (20> 120 °) pour lesquels ce rapport augmente tr~s rapidement, d'ofi la n6cessit6 d'utiliser le montage par r6flexion: dans ce cas 1(2)/1(1) est au contraire faible (Warren & Mozzi, 1966).…”

“…Une premiere 6tude a 6t6 r6alis6e/~ partir d'un montage diffractom6trique,par r6flexion, sans monochromateur (Warren & Mozzi, 1966); Chonacky & Beeman (1969) ont calcul6 la double diffraction pour 0=0 /t partir d'un montage diffractom6trique par transmission sans monochromateur, et en tenant compte de la divergence du faisceau et de la largeur de la fente de mesure; ces deux corrections sont faibles si l'on utilise un monochromateur. Nous envisageons ici les diff6rentes m6thodes diffractom6triques par transmission et r6flexion; dans tous les cas le faisceau incident est partiellement polaris6 par un monochromateur.…”

Intensity of secondary scattering of X-rays by non-crystalline materials. Transmission gemoetry with an incident-beam monochromator

“…Under these conditions a simple approximation for primary scattering can be used for the conditions described in the Introduction (Warren & Mozzi, 1966). In this approximation two parameters b and q are used to approximate the intensity of primary scattering.…”

“…In the reflection-geometry case, the intensity of secondary scattering is often well under 10%, even for a sample of infinite thickness (Warren & Mozzi, 1966). In the transmission cases the intensity of secondary and higher-order scattering becomes 100% of primary intensity as infinite sample thickness is approached (Dwiggins & Park,197l).…”

“…In the cases when no monochromator was used, Warren & Mozzi (1966) and Dwiggins & Park (1971) developed methods for the reflection-geometry case that require numerical integration over only one variable. Similar methods were developed by Dwiggins & Park (1971) and by Dwiggins (1972) for fixedsample and moving-sample transmission geometry.…”