OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 3 2022 The X-ray diffraction analysis was carried out by the synchrotron X-ray diffraction method in transmission using the beamline P07 of Petra III source of Deutsches Elektronen-Synchrotron (DESY). The wavelength of the radiation used was 0.14235 nm. It corresponds to energy of 87.1 keV. A 2D PerkinElmer XRD 1621 detector was used to record the diffraction patterns. The screen resolution of the detector was 2048 × 2048 px. The screen area was 409.6 mm × 409.6 mm. The distance from the sample to the detector was 1.05 m. The resulting diffraction patterns were reduced to a one-dimensional form by azimuthal integration using the pyFAI library [10]. Examples of the obtained two-dimensional and one-dimensional diffraction patterns are shown in Fig. 1. For peak profi le analysis, one-dimensional diffraction patterns were described by a function of the following form: 10 7 i 1 i 0 (2 ) (2 ) (2 ) , j pattern i j I I a (1) where the fi rst sum determines the contribution to the intensity of ten diffraction maxima, and the second sum is a 7th order polynomial to describe the background. In turn, the profi le of each of the diffraction maxima was described by the pseudo-Voigt function, which is generally written as: 0 (2 ) (2 ) (1 ) (2 ) , i I I L G (2) where I0 – the value of the maximum intensity of the diffraction peak; η – Lorentz function contribution; L(2θ) and G(2θ) – Lorentz and Gauss functions, respectively. These functions look like: 2 2 2 0 0.5 [1 ] (2 ) 0.5 [1 ] (2 2 ) A L A (3) and 2 0 2 (2 2 ) (2 ) exp , 0.5 [1 ] / ln 2 G A (4) where 2θ0 – angular position corresponding to the maximum value of the peak intensity; β – full width at half maxima (FWHM); A – diffraction peak asymmetry parameter (–1 ≤ A ≤ 1). The instrumental contribution was taken into account by using the Caglioti function. The parameters of the function were determined by analyzing the diffraction pattern of the HEA sample after cold rolling and long-term annealing at 400 C. To carry out X-ray diffraction analysis the classical Williamson-Hall model was used. According to this model, the peak broadening depends on the parameters of the sample microstructure as follows: 0.9 2 , K K D (5) where 2sin K – reciprocal coordinate; cos 2 K ; ε – relative lattice distortion; λ – wavelength; D – average «visible» size of CSRs. As noted in the introduction, the anisotropy of the elastic properties of materials causes a high error in the approximation of diffraction data using the classical methods of peak profi le analysis. Therefore, in this work, in addition to the classical Williamson-Hall model, several other models were used. In some cases, the approximation error can be reduced by introducing a correction based on the assumption that crystal lattice distortions in one of the directions depend on the elastic modulus of the crystal along this direction [11]. This model can be written in the following way:
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