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.
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Acknowledgments
The author acknowledges Sunil K. Sinha (University of California–San Diego) for introducing him to this problem and for recommending the harmonic lattice as a starting point, and acknowledges Stina N. Anacona, Stephan Rosenkranz, Ray Osborn, and John F. Mitchell (Argonne National Laboratory) for providing single-crystal diffuse scattering data from La1.2Sr1.8Mn2O7. This work was supported by an award from Research Corporation. Experimental work at beamline 1ID-C of the Advanced Photon Source at Argonne National Laboratory was supported by the United States Department of Energy under Contract No. W-31-109-ENG-38.
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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.
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Campbell, B.J. Quantitative Local Atomic Displacements from Huang Scattering Normalized by Thermal Diffuse Scattering. Metall Mater Trans A 41, 1130–1136 (2010). https://doi.org/10.1007/s11661-009-9893-2
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DOI: https://doi.org/10.1007/s11661-009-9893-2