Kinematical Theory of Diffraction

Abstract

Crystal lattice points serve in x-ray diffraction as the scattering centers for incident waves. The spherically scattered wavefronts are detected by their intensities ∔ the amplitude squared at a point of observation far away from the crystal. To account for the diffracted intensity and to understand the diffraction mechanism, diffraction theories were developed under a few simplifying assumptions which often rely on the nature of the crystal. For example, in Laue’s geometrical theory of x-ray diffraction [3.1], the following assumptions were made: (1) The velocity of the x-ray beam traveling through the crystal is the velocity of light. The interaction between the incident and diffracted beams is neglected. (2) The multiple scattering effect is excluded. This means that the scattered waves are not subjected to re-scattering at other lattice points. (3) Absorption plays no role in the diffraction. This theory is therefore valid for diffraction in small crystals.