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FFT-based modelling of X-Ray Diffraction peaks: application to dislocation loops

Abstract : In this work, we propose and test an original numerical method of simulation of X-ray diffraction peaks by single crystals. This method is based on the use of Fast Fourier Transform (FFT) algorithms for the calculation of mechanical fields resulting from external loading and / or linear defects such as dislocation loops. These defects are modeled by stress-free strain fields (eigenstrains) in a periodic microstructure subjected to thermomechanical loadings. In the first part, we present an improved approach by FFT-type algorithms which allows to accurately obtain the local mechanical fields without numerical oscillation at material's discontinuities. This improvement is due to the use of a discrete and periodic Green operator. This is obtained by solving the Lippmann-Schwinger equation in the Fourier space and using an appropriate spatial discretization. The fourth order modified Green operator allows to calculate the values of the strain and stress fields at all voxels. We also propose a third order periodic green operator to compute the displacement field. The computed displacement field is then corrected by a sub-voxelization method which removes the artifacts appearing in the case of dislocation loops inclined with respect to the reference grid. Numerical examples on reference cases show the effect of the Green operators for the calculation of local mechanical fields without oscillation and the efficiency of the sub-voxellization method. The final displacement field obtained is the input data of the simulation of X-ray diffraction patterns. The method of simulation of X-ray diffraction peaks of FCC (Face-Centered Cubic) single crystals is then presented. The diffracting material is modelled by a representative volume containing dislocation loops in (111) slip planes. We calculate the amplitude then the intensity of the diffracted beam near a node of the reciprocal lattice. This 3D distribution of the diffracted intensity is processed to obtain 1D diagrams that will be analyzed. The simulations demonstrate foremost the elimination of the artifacts on the diffraction diagrams which are due to the oscillations of the uncorrected mechanical fields. The diffraction peaks are analyzed by different statistical methods (Fourier transform of intensity, method of moments, etc.) which allow to evaluate the distribution parameters of dislocations (density, polarization factor, etc.) and compare them with their theoretical values.
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https://hal.univ-lorraine.fr/tel-02976248
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Submitted on : Friday, October 23, 2020 - 1:52:11 PM
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  • HAL Id : tel-02976248, version 1

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Komlavi Sényo Eloh. FFT-based modelling of X-Ray Diffraction peaks: application to dislocation loops. Materials Science [cond-mat.mtrl-sci]. Université de Lorraine, 2020. English. ⟨NNT : 2020LORR0097⟩. ⟨tel-02976248⟩

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