Abstract
Deviations of crystal diffraction line profiles from those predicted by the dynamical theory of diffraction for perfect crystals provide a window into the microscopic distributions of defects within non-perfect crystals. This overview provides a perspective on key theoretical, computational, and experimental developments associated with the analysis of diffraction line profiles for crystals containing statistical distributions of point defect clusters, e.g., dislocation loops, precipitates, and stacking fault tetrahedra. Pivotal theoretical developments beginning in the 1940s are recalled and discussed in terms of their impact on the direction of theoretical and experimental investigations of lattice defects in the 1960s, the 1970s, and beyond, as both experimental and computational capabilities advanced. The evolution of experimental measurements and analysis techniques, as stimulated by theoretical and computational progress in understanding the distortion fields surrounding defect clusters, is discussed. In particular, consideration is given to determining dislocation loop densities and separate size distributions for vacancy and interstitial type loops, and to the internal strain and size distributions for coherent precipitates.
Highlights
The impact of lattice vibrations, lattice defects, and lattice microstructure on the diffraction line profiles of crystals is the subject of longstanding interest within the crystallography, crystal physics, and materials science communities
Differing significantly in their underlying origins, these two cases turned out some 25 years later to describe the two main regimes of the diffuse scattering from defect clusters in crystals
These regimes are (1) the so-called Huang scattering region at small q very close to Bragg reflections, which is generated by the r−2 falloff of the long-range displacement fields of small clusters, and (2) the so-called Stokes–Wilson scattering region generated by the Crystals 2019, 9, 257; doi:10.3390/cryst9050257
Summary
The impact of lattice vibrations, lattice defects, and lattice microstructure on the diffraction line profiles of crystals is the subject of longstanding interest within the crystallography, crystal physics, and materials science communities. Straight dislocations in deformed materials inherently produce distributions of local elastic strains that induce distributions of Bragg-like (but not δ-function) scattering peaks at positions corresponding to varying local strains, which result in line broadening at the full-width at half-maximum. As discussed below, this signature is to be distinguished from the diffuse scattering distributions generated at the base of a single true Bragg reflection by statistically random spatial distributions of relatively small defect clusters within an otherwise undeformed crystal. There is not an attempt to be comprehensive in this overview; rather, selected investigations illustrating the threads of progress leading to the present state of diffuse scattering line-profile analysis are presented and discussed in terms of a perspective on their impact on the direction of scientific research in the field of defect physics
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