The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

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.

Martensitic steels are widely used structural materials with outstanding mechanical properties. Their high strength is provided by the non-diffusional phase transformation of fcc γ into thin lamellar bcc plates during fast cooling. Coherency strains between the fcc and bcc lamellae induce large dislocation densities in the range of 10¹⁶ m⁻², well above the densities attainable by conventional plastic deformation. Using high resolution X-ray line profile analysis, scanning electron microscopy, and hardness tests we show that during tensile deformation when the active Burgers vectors are within the lath plane the lath-packets work soften. On the contrary, when the active Burgers vectors are oblique to the lath-plane the lath-packets work harden. The softening and hardening processes in the differently oriented lath-packets produce a composite of hard and soft components on the length scale of lath-packet size. The stress–strain response of the alloy is discussed in terms of the different mean free paths and the different annihilation lengths of dislocations in the softened and hardened lath-packets. The relatively good ductility is shown to be produced by the composite microstructure induced by plastic strain.

Forward modeling of diffraction peaks is a potential way to compare the results of theoretical mechanical simulations and experimental X-ray diffraction (XRD) data recorded during in situ experiments. As the input data are the strain or displacement field within a representative volume of the material containing dislocations, a computer-aided efficient and accurate method to generate these fields is necessary. With this aim, a current and promising numerical method is based on the use of the fast Fourier transform (FFT)-based method. However, classic FFT-based methods present some numerical artifacts due to the Gibbs phenomenon or “aliasing” and to “voxelization” effects. Here, we propose several improvements: first, a consistent discrete Green operator to remove “aliasing” effects; and second, a method to minimize the voxelization artifacts generated by dislocation loops inclined with respect to the computational grid. Then, we show the effect of these improvements on theoretical diffraction peaks.

Polycrystalline copper samples were deformed in the range of strain rate between ~10⁻³ and 10⁷ s⁻¹ using a material testing machine, split Hopkinson pressure bar and electric gun. The quasi-static and Hopkinson bar samples were compressed at the strains of 0.1 and 0.4, and the electric gun samples were compressed at the shock pressures of 19, 25, 35 and 49 GPa. The dislocation structure in the recovered samples was determined using high-resolution X-ray line profile analysis. Compared to the quasi-static and Hopkinson bar tests, different characteristics of the evolution of dislocation density and arrangement were found in the planar plate impacts of the electric gun. The correlation between the flow stresses and the dislocation densities in the samples was discussed using the Taylor equation.