Kinematical diffraction analysis of the diffuse scattering from grain boundaries along the direction normal to the interface

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Abstract
A kinematical diffraction analysis for determining the intensity of excess diffuse scattering along the direction normal to the interface plane of a grain boundary is developed, taking into account the interaction between the scattering from the grain boundary core and the perfect crystal regions. Grain boundary structures are aperiodic normal to the interface plane, and amplitude-phase diagrams are used to illustrate the nature of the diffraction process and to calculate the intensity profile of the diffuse scattering along the direction normal to the interface. Various models for the boundary structure are described and the diffuse scattering intensity profile is calculated for each model structure. The effects of deviations from these model structures such as segregation and rumpling of atomic planes are described. Comparison of the diffracted intensity profiles calculated for the various model structures gives physical insight into the influence of different characteristics of the boundary structure on the diffraction profiles. It is shown that the rigid body translation between the two crystals neighbouring the boundary and the boundary width can be determined by an analysis of the diffuse scattering intensity profile close to the matrix reflections.