A New Method for yhe Determination of the Texture of Materials of Cubic Structure From Incomplete Reflection Pole Figures

Abstract

The main characteristics of a new method of texture analysis are presented as well aa a comparative study of the results obtained with three different methods.

Quantitative Texture Analysis from X-ray Diffraction Spectra

“…The detailed comparisons between the numerical results of the ODF analysis from diffraction spectra, by the present method and the classic HM, are summarized in Table 1. The accuracy criterion of recalculated intensity is given by the parameter R (Ruer & Baro, 1977),…”

“…The orientation distribution function (ODF) of a polycrystalline material is generally determined from polefigure data by the various pole-figure inversion methods such as the harmonic method (HM) (Bunge, 1965;Roe, 1965), the vector method (VM) (Ruer & Baro, 1977;Vadon, 1981) and the WIMV method (Matthies & Vinel, 1982). Recently, X-ray (or neutron) diffraction spectra have been used to determine the ODFs of some polycrystalline materials (Wenk, Matthies & Lutterotti, 1994).…”

Determination of the Complete Orientation Distribution Function by the Zero‐Range Method

“…1) The discretization method (vector method) (Williams, 1968 andRuer andBaro, 1977) 2) The series expansion method (harmonic method) (Bunge, 1965 and Roe, 1965) 3) The probabilistic method (Imhof, 1977) 4) The integral transformation method (inversion formula) (Mat- thies, 1979) Each of these methods has its specific advantages and disadvantages but in principle they all provide the complete solution to Eq. (4) which is unique if the pole figures are known for all crystal directions h, i.e.…”

“…(18), only in Z but not outside, the approximation function f(g) is defined in the whole orientation space. An approximation to the complete ODF f(g) in the non-zero-range is thus given by fLL(g) fL(g) + fiL(g) (20) as is shown schematically in Figure 2.…”

Improvements in the Quantitative Evaluation of Three-Dimensional Texture. II. The Pole-Figure-Multiplying Method

“…However, the uncertainty range off(g) is limited by the positivity condition (Bunge & Esling, 1979), and a good approximation to f(g) can be obtained from only one incomplete pole figure by the use of an 'iterative-expansion method' (Dahms & Bunge, 1989). Ruer & Baro (1977) suggested the vector method to analyze the ODF to solve the problem of the zone of negative values. Using vectors to stand for the ODF and the pole figures and with the help of their geometric relationship, they always obtain a non-negative ODE In paper I (Yu, Guo, Hendrix, Xu & He, 1995), we show that the number of pole figures should increase as the resolution of each pole figure increases.…”