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.
This article is based on a presentation given in the symposium entitled “Neutron and X-Ray Studies of Advanced Materials”
which occurred February 15–19, 2009 during the TMS Annual Meeting in San Francisco, CA, under the auspices of TMS, TMS Structural
Materials Division, TMS/ASM Mechanical Behavior of Materials Committee, TMS: Advanced Characterization, Testing, and Simulation
Committee, and TMS: Titanium Committee.