Dynamical Theory of X-Ray Diffraction

The kinematical theory of X-ray diffraction follows closely the secondary ex-tinction theory, which can be applied to situations involving very weak or no interaction between the incident wave and the diffracted wave. The theory is therefore suited for diffractions from small and imperfect crystals. If the diffraction from a large perfect crystal is concerned, the primary extinction becomes important. This is because the atomic planes in a perfect crystal are well ordered. Once the atomic planes are set to the exact Bragg diffraction position for an incident wave, they are also perfectly aligned for the reflected wave to be diffracted back into the direction of the incident wave. In analogy with the optics of the visible spectrum, a phase lag of about π/2 of the reflected wave in the incident-wave direction relative to the incident wave results. Namely, the phase difference between the twice-reflected wave and the incident wave leads to the modification of the amplitude of the incident wave. Similar modification takes place for the diffracted wave. Thus, the interaction between the incident and the diffracted waves via multiple reflection dominates the diffraction process. If a relatively strong reflection is involved, this multiple reflection effect cannot be ignored. Moreover, the phase lag of the reflected wave occurs for each plane of atoms inside the crystal. The resultant phase lags of the incident and diffracted waves modify their phase velocities in the crystal, thus changing the index of refraction.