The Effect of Crystal Defects on 3D High-Resolution Diffraction Peaks: A FFT-Based Method

Abstract

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.

Development of a new consistent discrete green operator for FFT-based methods to solve heterogeneous problems with eigenstrains

“…Optimal choices of the DGO truncation order k and reference medium for heterogeneous materials containing rigid inclusions and voids will be investigated in a future work. Furthermore, the numerical method based on DGO will be applied to simulate Synchrotron high-resolution diffraction peaks on real microstructures, as described in first promising results (Jacques, 2016;Eloh et al, 2018). To be well understood, such diffraction peaks need very accurate predictions of local displacement fields in the course of plastic deformation, which are only reachable with the new DGO k .…”

“…It will be shown that the numerical oscillations near materials discontinuities originate from the commonly used Continuous Green Operator (CGO). This work is also focused on the development of a new DGO to compute the displacement field, which was recently already used to simulate X-rays diffraction peaks in other contributions (Jacques, 2016;Eloh et al, 2018). Our starting point is the numerical resolution of the Lippmann-Schwinger equation using a DGO adapted to the numerical iterative scheme for heterogeneous materials with eigenstrains developed by Anglin et al (2014).…”

Data-Driven Analysis of Neutron Diffraction Line Profiles: Application to Plastically Deformed Ta

“…Nevertheless, both the modest number of cases considered (5) and the approximations made in generating the virtual profiles limited the general applicability of their approach. Since then, several continuum-based methods have been proposed to more accurately generate virtual profiles [51][52][53][54] .…”

“…Recently, improvements to the speed and accuracy of virtual diffraction algorithms 6,[50][51][52][53][54][55] and to the efficiency of mesoscale simulations 56 have enabled the rapid generation of hundreds of diffraction profile-microstructure pairs 52 . For example, Bamney et al 52 developed two strainbased virtual diffraction algorithms, one using the Stokes-Wilson approximation 34 , the other using differential strains to include the effects of spatially correlated strains on broadening.…”