The Scattering of X-rays by Crystals

Abstract

Scattering of X-rays by Crystals (Rocksalt and Calcite), Metal (Aluminum) and Amorphous Solid (Glass).---Both homogeneous rays (${\mathrm{K}}_{a}$ of Mo obtained by preliminary reflection from a rocksalt crystal) and heterogeneous rays direct from a Mo or W target (70 to 110 kv.) were used, and scattering curves were obtained by measuring the ionization for various angles of scattering. On account of the small intensity of the scattered radiation, incident beams of 15\ensuremath{'} to 3\ifmmode^\circ\else\textdegree\fi{} width and a scattered beam of 6\ifmmode^\circ\else\textdegree\fi{} width were required even with a sensitive Compton electrometer. For angles from 50\ifmmode^\circ\else\textdegree\fi{} to 150\ifmmode^\circ\else\textdegree\fi{} the curves obtained for the crystals are of the same shape as those for Al and glass, each curve showing a minimum at about 100\ifmmode^\circ\else\textdegree\fi{}; but for angles below 50\ifmmode^\circ\else\textdegree\fi{} the crystal curves fall below the others and each shows a maximum at a larger angle, between 15\ifmmode^\circ\else\textdegree\fi{} and 30\ifmmode^\circ\else\textdegree\fi{}, depending on the wave-length. In addition to the general scattering at all angles, there appear, for the crystalline substances, maxima corresponding to the Laue spots. When correction for the absorption of the crystal is made, for which a formula is given, the scattering in a particular direction is found not to depend on the orientation of the crystal. This indicates that the atoms are isotropic. As was to be expected the scattered radiation was softer than the primary. For the width of x-ray beams used the total energy scattered in all directions was an appreciable fraction (0.70 for homogeneous Mo ${\mathrm{K}}_{a}$ rays on calcite) of the energy reflected in a first order spectrum line. Comparison with the Debye theory shows fair agreement only in the case of rocksalt for angles greater than 60\ifmmode^\circ\else\textdegree\fi{}. For calcite there is no agreement and the prediction that the scattering by amorphous substances should be quite different from that by crystals is not verified. Applying the Thomson formula, however, the number of electrons per molecule for each crystal has been calculated from the relative amount of energy scattered at 90\ifmmode^\circ\else\textdegree\fi{} and comes out of the right order of magnitude.