Scattering of X-Rays from Powdered Crystals

Abstract

When monochromatic x-rays are scattered by a powdered crystal, the scattered rays consist partly of those rays which are scattered in special directions and which give rise to the Debye-Scherrer circles in a photograph and partly of those rays which are diffusely scattered and which give rise to the background between the circles. If the scattered rays from a powdered crystal enter a wide window of an ionization chamber, the intensity of the rays per unit solid angle is an average for several Debye-Scherrer circles and the diffuse background between the circles. Coven has experimentally examined this "average scattering" for the case of monochromatic x-rays, but his results are inconclusive. In our experiments we have used not only a wide window (the extreme angular width of the rays entering the window was 6\ifmmode^\circ\else\textdegree\fi{}) but also a wide band of wave-lengths obtained by passing the x-rays from a tungsten target x-ray tube operated at 54.9 kv through 3.25 mm of aluminum or its equivalent. The spectral distribution of the intensity of these rays was obtained by reflection from rocksalt. The scattered intensities at average angles varying from 5\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{} from powdered crystal brickettes of KCl, CaS, NaF and MgO were compared with the scattered intensity at 90\ifmmode^\circ\else\textdegree\fi{} from paraffin. From Jauncey and Harvey's theory of the diffuse scattering from crystals together with the theory of the intensity of the Debye-Scherrer circles, a formula has been obtained for the ionization current produced by the rays entering a narrow window and consisting of a wide band of wave-lengths of known intensity distribution. This formula was then integrated graphically so as to obtain theoretical values for the case of a wide window. The calculation of the theoretical values involves $f$ and ${f}^{\ensuremath{'}\ensuremath{'}}$ values. James and Brindley's $f$ values as obtained from wave mechanics were used. Values of ${f}^{\ensuremath{'}\ensuremath{'}}$ were calculated from data given in James and Brindley's paper and are tabulated for ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Na}}^{+}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, ${\mathrm{K}}^{+}$, neon and argon. Excellent agreement between the theoretical and experimental values of the scattered intensity is shown over the whole range of average angles of scattering for each of the crystals. It is shown that, in experiments on the diffuse scattering of x-rays by crystals, an average wave-length as determined by absorption in aluminum may to a fairly close approximation be treated as if it were a single wave-length and so the $S$ curves obtained for KCl by Harvey and for NaF by Jauncey and Williams are reasonably accurate.