Crystallite Orientation Analysis from Incomplete Pole Figures

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Abstract
The use of incomplete pole figures results in the loss of orthogonality relations among the associated Legendre functions, and necessitates explicitly evaluating integrals of products of these functions. The required indefinite integrals of associated Legendre functions and their products have been evaluated for cubic crystallographic symmetry and orthotropic physical symmetry through sixteenth order.The solution has been particularized for {200}, {222}, and {110} back-reflection pole figures, where data are confined to the region not exceeding 60 degrees from the sheet normal direction.Data obtained from a sample of low—manganese steel sheet are used to illustrate the method, and results are compared to those obtained using complete pole figures obtained with a composite sample of the same material.The method described makes it possible to study crystallite orientation distribution as a function of distance from the sheet surface, by a series of pole figure measurements on the surface after successive material removals by polishing and etching.