Analytical Solutions for Representing Fiber Textures as Axial Pole Figures

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Abstract
An axial or inverse pole figure represents the density of a fiber axis over the crystallographic triangle for the crystal system. This function can be represented by a series over this triangle and the coefficients are defined by a least‐squares solution. In a second method, the values of the density at a collection of points over the triangle can be calculated without using a series. Both these methods are easier to set up, have much greater flexibility in the data selection and weighting, and give impoved results over those obtained by using Legendre polynomials. Expressions for calculating the standard deviation for all three cases are given.

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