Restoration of the orientation distribution functions from direct polar figures using superposition of normal distributions and arbitrarily defined cells (comparative analysis)

A comparative study of orientation distribution functions (ODF) calculated from direct pole figures (DPF) is carried out using a superposition of a large number of positive standard Gaussian normal distributions with the same scattering (Texxor program) and the method of arbitrary defined cells (ADC) (LaboTex program) to identify the advantages and shortcomings of each method. The comparison was carried out for the Santa Fee reference orientation (the previously calculated total PPF were used as the experimental PPF) and the measured incomplete PPF characterizing the recrystallization textures of 6016 aluminum alloy with a high degree of sharpness. The RP-factor was used as a criterion for evaluating the calculation errors for both programs: the difference between the intensities of the experimental and calculated PPFs averaged over each and all measured PPFs and referred to the corresponding experimental values on the pole figure. The values of the RP-factors depend on the method of the ODF reconstructing and the experimental errors of the measured pole figures of the materials under study. It is shown that the values of RP(0.5)-factor (normalized intensities used in the calculation, ≥0.5) for Santa Fee are 0.3 (Texxor) and 2.6 % (LaboTex) and the corresponding maximum values of the orientational density of ODF differ insignificantly (5.1 and 4.5, respectively). However, for measured incomplete PPF of the recrystallization texture of the aluminum alloy, they differ significantly (61.8 and 95.9), and the RP(0.5)-factor increases to 12.6 and 30.5%, respectively. Since the method of superposition of normal distributions provides a lower value of the RP(0.5)-factor compared to the ADC method, the ODF reconstruction using the Texxor program is preferable compared to LaboTex.

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