On Using Monte Carlo Simulations for Sampling Crystallite Orientations from Given Texture Data

An approach based on Monte Carlo simulations for sampling crystallite orientations from known texture data is developed. A randomized algorithm is proposed to reconstruct the orientation distribution function by a given set of pole densities. The algorithm fills up the orientation space with lots of uniformly distributed points and tries to evaluate the reconstructable function specifically at these points. This leads to a sparse quadratic programming problem, which is a discrete statistical analogue of the fundamental equation of Texture Analysis. The resulted distribution is represented as a weighted sample of orientations, with the weights equal to the reconstructed distribution function values. By means of randomized weight-based selections, such a sample can be reduced to an unweighted one with appropriately distributed orientations. A theoretical substantiation of the methods is presented in the paper in the weak probabilistic sense. Several examples of practical applications are provided as well.