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.
Highlights
X-ray diffraction (XRD) is one of the most powerful non-destructive tools to investigate materials, as their wavelength is commensurate with the distance between atoms within a crystal [1,2,3,4,5,6,7,8,9].Successive improvements of both the X-ray sources and detectors have led to a tremendous increase in the quantity of data recorded per unit time, allowing real time in situ or in operando measurements [10,11]
We have shown that the use of a periodized Green operator in the fast Fourier transform (FFT)-based method improves the final displacement field solution in a representative volume containing discontinuities, artifacts due to the voxelization of the dislocation loop planes are still present with respect to analytical solutions
These artifacts have unwanted consequences on the tails of diffraction peaks simulated by using this displacement field as input data
Summary
X-ray diffraction (XRD) is one of the most powerful non-destructive tools to investigate materials, as their wavelength is commensurate with the distance between atoms within a crystal [1,2,3,4,5,6,7,8,9].Successive improvements of both the X-ray sources (from X-ray tubes to third generation synchrotrons) and detectors (from photographic plates and gas counters to fast two-dimensional arrays) have led to a tremendous increase in the quantity of data recorded per unit time, allowing real time in situ or in operando measurements [10,11]. It is possible to determine the 3D grain microstructure of a bulk material with a submicron resolution (using topo-tomography), to follow the evolution of the elastic strain state of the grains of a polycrystal during mechanical tests (3D-XRD, far field diffractometry), or to measure the distribution of strains within a few grains in real time (2D diffractometry) [12,13]. Such experiments result in terabytes of data recorded within a few days, which need to be analyzed efficiently. The classical techniques used to analyze the 1D or 2D diffraction patterns recorded during tests performed on polycrystalline specimens such as the Rietveld method, the square sines method to measure internal stresses, or CMWP (convolutional multiple whole profile) fitting for Materials 2018, 11, 1669; doi:10.3390/ma11091669 www.mdpi.com/journal/materials
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