Restoration of the Orientation Distribution Functions from Direct Pole Figures Using Superposition of Normal Distributions and Arbitrarily Defined Cells (Comparative Analysis)

A comparative study of the orientation distribution functions (ODFs) calculated from direct pole figures (DPFs) is carried out using a superposition of a large number of positive standard Gaussian normal distributions with the same scattering (Texxor software) and the method of arbitrarily defined cells (ADC) (LaboTex software) in order to identify the advantages and shortcomings of each method. The comparison is performed for the Santa Fe reference orientation (the previously calculated total DPFs were used as the experimental DPFs) and the measured incomplete DPFs characterizing the recrystallization textures of 6016 aluminum alloy with a high degree of sharpness. The RP factor is used as a criterion for evaluating the calculation errors for both programs: the difference between the intensities of the experimental and calculated DPFs averaged over each and all measured DPFs and assigned to the corresponding experimental values on the pole figure. The values of the RP factors depend on the method of the ODF reconstruction and the experimental errors of the measured pole figures of the materials under study. It is shown that the values of the RP (0.5) factor (normalized intensities used in the calculation, ≥0.5) for Santa Fe are 0.3 (Texxor) and 2.6% (LaboTex). The corresponding maximum values of the orientation density of ODF differ insignificantly (5.1 and 4.5, respectively). However, for measured incomplete DPFs of the recrystallization texture of aluminum alloy, they differ substantially (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 recovery using the Texxor software is preferable compared to that with LaboTex.