Dynamical Theory of X-Ray Diffraction

Abstract

The kinematical theory of x-ray diffraction, thus far discussed in the previous chapter, is based on assumptions which are only valid for diffraction in small crystals. When diffraction occurs in large and perfect crystals, multiple scattering results. In other words, the crystal lattice is so regular over a large volume that the reflected wave of a reflection must be further reflected back into the direction of the incident wave. The phase difference between the twice- reflected wave and the incident wave modifies considerably the amplitude of the incident wave within the crystal. If the reflection is relatively strong, the diffracted intensity should be of the same order of magnitude as that of the incident beam. Thus interaction between the incident and the scattered waves is definitely enhanced and the effect of interaction resulting from multiple scattering can no longer be neglected. Moreover, according to the optics of the visible spectrum, the phase of the scattered wave in the forward direction is retarded by about a quarter of a period from that of the incident wave. This slight modification of phase between the scattered and the incident waves happens for the reflection at each plane of atoms. The phase velocity of the resultant wave passing through the crystal is then modified. The velocity of the radiation traveling through the crystal is therefore not the velocity of light. This implies the existence of a correction to the index of refraction for x-rays in crystals.