All Times EDT
Keywords: Crystallographic Texture, Orientation Distribution Function, Bayesian Inference, Directional Statistics
Polycrystalline materials, such as metals, are comprised of individual crystallites that are heterogeneously oriented. The distribution of orientations of the crystallites is characterized via the orientation distribution function (ODF), which is of practical importance since the macroscale response of a polycrystalline material to an applied stimulus, such as the yield strength of a metal sample, directly depends on the ODF. Not only must ODFs account for the unit length constraint of the data, they also must account for known symmetries associated with the materials and how they are processed. Data is available in the form of 4-dimensional unit vectors, quaternions, that describe crystallite orientation measured through electron backscatter diffraction. Common methods for recovering ODFs from such data are based on non-parametric kernel density estimation, which is computationally inexpensive but often lacks interpretability. In contrast, we propose to model the ODF as a mixture of symmetric Bingham distributions, which is both flexible and interpretable in the context of the application. Bayesian inference is performed on the number of mixture components, the mixture weights, and the scale and location parameters that define the symmetric Bingham distribution. Posterior inference is made possible by a reversible jump Markov chain Monte Carlo algorithm enabling sampling over the resulting varying-dimensional parameter space. We discuss this model and implementation along with the analysis of various orientation datasets, providing interpretation of parameter estimates and their uncertainty, while comparing the results with the corresponding kernel density estimates.