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

Three-dimensional orientation distributions of grains in polycrystalline aggregates are referred to ascrystallographic textures. Commonly, they are computed from two-dimensional centro-symmetric polefigures by employment of series expansion techniques or so called direct inversion methods. Bothapproaches lead to inaccuracies which are due to the absence of the odd coefficients and by truncationerrors in the first case and to the under-determination of the set of linear equations combining cellsin the pole figures and in the three-dimensional orientation space in the second case. For both typesof calculation methods various correction procedures were suggested. In case of the series expansionmethods the introduction of the non-negativity condition was reported to considerably improve theobtained 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 recentlyintroduced iterative series-expansion method which accounts for the non-negativity condition isexamined by use of standard functions.