Quantitative Local Atomic Displacements from Huang Scattering Normalized by Thermal Diffuse Scattering

Abstract

The three-dimensional (3-D) pattern of atomic displacements at the core of a small defect or defect cluster embedded in a bulk crystal is possible to measure in principle, but difficult to obtain in practice, especially if quantitative displacements are desired. Here, it is demonstrated that a least-squares fit to the single-crystal X-ray Huang-scattering distribution surrounding an intense Bragg peak is a practical means of obtaining quantitative displacements when thermal diffuse scattering is used as an internal intensity standard. After fitting a model based on local Kanzaki forces embedded within an elastic continuum, the use of finite-defect and point-defect methods of computing and interpreting the pattern of local displacements are compared and contrasted. To make the analysis general with regard to both crystal symmetry and defect symmetry, numerical Fourier transforms are employed rather than pursuing analytical expressions for the displacements.