Historical Perspective on Diffraction Line-Profile Analyses for Crystals Containing Defect Clusters

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.

Perspectives on multiscale modelling and experiments to accelerate materials development for fusion

“…Sand et al [165] estimated the uncounted small defects by looking at the distribution of intensities of defects as a function of size. From this they determined that the count of the smallest defects (1-2 nm) might be low by a factor of 5, in broad agreement with Refs [146,163,164] . Importantly, including this confidence interval brought their theoretical estimate for the number of observable defects in line with experiment, where a simple 'square-root-N' estimator of the error in the observed count would not have done.…”

“…It is regularly quoted that there is a minimum defect size observable in a TEM [146,151,163,164] . While this is true, and agrees with the results obtained using X-ray diffraction and other means of microstructural examination, strictly speaking this is the limit determined by the aperture, and small defects slightly larger than this small size limit may be undetectable due to the faintness of their intensity profile.…”

Dynamic model for an ensemble of interacting irradiation-induced defects in a macroscopic sample

“…Strain field ˆ , stress field σ, and the derivative of strain field can then be computed from the field of displacements. We should note that equation (20) only works for a stationary system that exhibits no translational and rotational motion.…”

“…Molecular dynamics simulations of collision cascades in perfect crystals [8][9][10][11] suggest that the statistics of sizes and numbers of vacancy and interstitial defects formed at low dose, below the cascade overlap dose of ∼ 0.01 dpa, follow a power-law scaling. This means that a considerable, if not dominant, fraction of defects produced by irradiation is not visible in a transmission electron microscope (TEM) [12,19,20]. The fact that the microstructure of an irradiated material contains many defects and defect clusters that are too small to be observed by means of even high resolution experimental methods, makes modelling and simulation a vital tool for understanding the various aspects of microstructural evolution under irradiation that are critical to an informed reactor design effort.…”

X-ray Diffuse Scattering from Ca3NbGa3Si2O14 Single Crystal under External Electric Field Application

“…The diffuse scattering method is widely used in the study of microdefects arising in crystals as a result of various influences, including implantation, radiation, annealing, etc. [ 5 , 6 ]. The diffuse scattering method is also used to study the effect of various growth parameters on the real structure of single crystals [ 7 ].…”