Case Studies

Abstract

We have discussed in the preceding chapter three approaches to account for the intensities of multiple diffractions. The applicability of these three approaches depends, as in two-beam diffraction, on both perfection of the crystal quality and experimental conditions. Kinematical theory is valid for diffraction from small crystals and imperfect crystals. Cases involving weak reflections and short-wavelength radiation, according to the discussion given in Sect. 5.1, can also be treated kinematically. In these kinematical diffraction situations, the interaction among the diffracted beams in crystals is limited by the crystal imperfection, the lack of space, and the weak wavefield amplitudes, so that dynamical effects are not appreciable in the diffraction process. On the contrary, diffraction from perfect and large crystals, and from planes of strong reflections should be considered from the dynamical viewpoint, since the perfect lattice and strong wavefields provide favorable situations for wave interaction in crystals. The other approach, the quantum theory of diffraction, has not so far been frequently used, because in the usual diffraction experiments the kinematical and dynamical theories give a satisfactory account for experimental observations, except when the diffraction process involves to a great extent excitations of electrons, atoms and molecules, such as photoelectric transitions, phonon interactions, Compton scattering and so forth.