Calculation of Texture Volume Fractions by Integration and Gaussian Fitting

Abstract

The concept of texture volume fractions has proved useful in the assessment of the orientation distributions of polycrystalline samples. Unfortunately, there is more than one method of calculating volume fractions, and the different techniques may give rather different answers. The three most commonly used methods appear to be calculation from the coefficients of the harmonic function, integration over a selected portion of an orientation distribution function (ODF), or decomposition of an ODF into component Gaussian ideal textures by a least squares fitting. The integration and Gaussian fitting methods are examined further here. In particular, the nature of the errors or differences arising from the method of integration or fitting chosen, the differing interpretations of the shape and ‘spread’ of the ideal texture, and the effect of neglecting texture components lying outside of the H⁰ subspace are considered. Integration of a volume enclosed by one or more cylinders defined in Eulerian space seems the most robust technique. It is usually, but not always, acceptable to neglect the effect of texture components lying outside of H⁰. However, it is vital that the ‘spread’ of the ideal texture component be precisely defined, and the texture volume fraction is very sensitive to the magnitude of the spread as well as to the geometric shape assumed for it.