Characterizing dislocation loops in irradiated polycrystalline Zr alloys by X-ray line profile analysis of powder diffraction patterns with satellites

Abstract

This work extends the convolutional multiple whole profile (CMWP) line profile analysis (LPA) procedure to determine the total dislocation density and character of irradiation-induced dislocation loops in commercial polycrystalline Zr specimens. Zr alloys are widely used in the nuclear industry as fuel cladding materials in which irradiation-induced point defects evolve into dislocation loops. LPA has long been established as a powerful tool to determine the density and nature of lattice defects in plastically deformed materials. The CMWP LPA procedure is based on the Krivoglaz–Wilkens theory in which the dislocation structure is characterized by the total dislocation density ρ and the dislocation arrangement parameter M. In commercial Zr alloys irradiation-induced dislocation loops broaden the peak profiles, mainly in the tail regions, and occasionally generate small satellites next to the Bragg peaks. In this work, two challenges in powder diffraction patterns of irradiated Zr alloys are solved: (i) determination of the M values from the long tail regions of peaks has been made unequivocal and (ii) satellites have been fitted separately, using physically well established principles, in order to exclude them from the dislocation determination process. Referring to the theory of heterogeneous dislocation distributions, determination of the total dislocation density from the main peaks free of satellites has been justified. The dislocation loop structure has been characterized by the total dislocation density of loops and the M parameter correlated to the dipole character of dislocation loops. The extended CMWP procedure is applied to determine the total dislocation density, the dipole character of dislocation loops, and the fractions of 〈a〉- and 〈c〉-type loops in proton- or neutron-irradiated polycrystalline Zr alloys used in the nuclear energy industry.

Towards quantitative inference of nanoscale defects in irradiated metals and alloys

“…More recently, the convolutional multiple whole profile (CMWP) X-ray diffraction Line Profile Analysis (XLPA) method [67,68] has been developed to characterize dislocation loops in irradiated materials [69,70]. Through calculation of the broadening of X-ray diffraction (XRD) peaks, the type, density, and size distribution of dislocation loops can be determined.…”

Dislocation Density Transients and Saturation in Irradiated Zirconium

“…Although the Wilkens model is formally derived assuming that a dislocation configuration is composed of straight lines, the model is in fact able to mimic the statistical properties of distributions of curved dislocations (Kamminga and Delhez, 2000;Groma and Borbély, 2004). When compared to transmission electron microscope (TEM) measurements of irradiated Zircaloy-2, the cmwp software was able accurately follow the dislocation density evolution as a function of dose (Seymour et al, 2017), and the cmwp approach has now become an accepted tool for determining dislocation densities (Ungár et al, 2021b;Topping et al, 2018) as well as other microstructural features (Ungár et al, 2021a) in irradiated Zircaloys. The cmwp software evaluates parameters describing effects of both the specimen size and dislocation broadening of diffraction intensity peaks by first employing a statistical Monte Carlo optimisation followed by the Marquardt-Levenberg non-linear least squares algorithm, see Ribárik et al (2020).…”

White Laue and powder diffraction studies to reveal mechanisms of HCP-to-BCC phase transformation in single crystals of Mg under high pressure

“…However, non-basal slip can also be activated with an increase of non-hydrostatic component of applied pressure and in favorable orientation of the crystal 31 , 32 . While active slip modes and change of dislocation density can be measured by monochromatic diffraction methods 33 , 34 , this lies beyond the scope of this work. We thus estimate only the slip-induced local misorientation that can be readily inferred from size of Laue reflections.…”