Calculation of the Normalization Factor of Incomplete Pole Figures by Cubic Extrapolation

Abstract

The calculation of orientation distribution functions from incomplete pole figures can be carried out by a least squares approximation of the texture coefficients and the normalization factors N h k l to the available experimental data. This procedure is less susceptable to instabilities due to experimental errors if the normalization factors can be calculated independently of the coefficients . In the case of cubic materials, the relationship = 0 to be fulfilled by pole figure values provides an independent condition for the calculation of the normalization factor. This condition can still be improved by taking the slopes of the pole density curves at α = α max⁡ and α = 90° into account. An economic way to consider the slope in the pole figures is to use a cubic spline interpolation.