Inversion of Pole Figures for Materials Having Cubic Crystal Symmetry

Abstract

X-ray diffraction measurements on anisotropic polycrystalline samples give a set of functions (pole-figures) describing the orientation distribution of individual plane-normals. From the set of these plane-normal distributions it is possible to deduce the orientation distribution of all crystallites in the sample (inversion of pole-figures) by a procedure described in a previous paper, in which the crystallite distribution function is expanded in a series of generalized Legendre functions. The expansion coefficients Wlmn which characterize the crystallite distribution have to satisfy restrictions imposed by the crystallographic and statistical symmetry elements existing in the sample. When the crystallites belong to the cubic crystal class, it is required not only that some of Wlmn be identically equal to zero but also that the remaining nonzero Wlmn be linearly related to each other (for given l and m). The matrix equation expressing the linear dependence among Wlmn is solved numerically by a computer and the result is presented in a table.