Examination of the Iterative Series-Expansion Method for Quantitative Texture Analysis

Abstract

Three-dimensional orientation distributions of grains in polycrystalline aggregates are referred to as crystallographic textures. Commonly, they are computed from two-dimensional centro-symmetric pole figures by employment of series expansion techniques or so called direct inversion methods. Both approaches lead to inaccuracies which are due to the absence of the odd coefficients and by truncation errors in the first case and to the under-determination of the set of linear equations combining cells in the pole figures and in the three-dimensional orientation space in the second case. For both types of calculation methods various correction procedures were suggested. In case of the series expansion methods the introduction of the non-negativity condition was reported to considerably improve the obtained solution. However, before large series of experimental data can be processed by such a method, its reliability has to be checked by use of analytical tools. Hence, in the present study a recently introduced iterative series-expansion method which accounts for the non-negativity condition is examined by use of standard functions.