Description of Crystallite Orientation in Polycrystalline Materials Having Fiber Texture

Abstract

The distribution of plane‐normal orientations in a polycrystalline sample can be investigated by x‐ray diffraction measurements. Our problem is to deduce from such a set of data the maximum amount of information concerning the distribution of crystallite orientations within the sample. We restrict our attention to samples having fiber texture. The plane‐normal distribution function is expanded in a series of Legendre polynomials, the coefficients of which are to be evaluated from the experimental diffraction data. The crystallite distribution function is expanded in a series of spherical harmonics, the coefficients of which may be obtained by the solution of a set of simultaneous linear equations. Certain simplifications arising from symmetry within the unit cell, or in the crystallite distribution, are examined. The effects of series termination errors are investigated, and relations are presented which permit one to estimate the number of terms which will be required to achieve a specified degree of accuracy. If diffraction from a particular plane is too weak to measure, the present treatment permits the construction of its plane‐normal distribution from diffraction data for other planes. Also, the effect of overlapping reflections can be accounted for. Finally, one can obtain information concerning the distribution of orientations for a subset of crystallites in the sample, for example, those having a specified c‐axis orientation.