Phenomenological and Microscopical Description of Scattering from Distorted Materials

Abstract

For the investigation and the control of internal stresses in (distorted) crystalline materials by X-ray or neutron scattering two approaches can be used. According to the phenomenological classification of internal stresses, the line-shifts of X-ray or neutron reflections are related to macrostresses (stress of the 1 st kind) being constant within the whole scattering crystal volume. Line broadening is formally described in terms of microstresses being constant within different grains or subgrains (internal stress of the 2 nd kind) and/or significantly varying within the individual grains or subgrains (internal stress of the 3 rd kind). The concept of averaged crystal lattice may be used to describe the scattering by the crystal with the size L in the following case. When mean quadratic fluctuations of the displacements in the matrix remain finite and are of the order of interatomic distance d. If in this case the latter are tending to infinity it is not possible to use the concept of such average crystal for the whole crystal. But even in this case usually it is possible to use such concept for relatively large regions of the crystal with the size L2. In that case the intensity maximums correspond to mean lattice parameters in the L2 regions. Due to the deviation of these parameters for different L2 regions the intensity maximums are displaced with respect to each other. The resulting intensity distribution becomes much broader. The described above microscopical and phenomenological concepts present different viewpoints on the same phenomenon. The comparison of the results obtained by the above two approach enables us to understand the connection between different types of stresses and strains in the crystal with the type of the defects in it.