Knowledge Bank

The properties of materials are functions of their internal structure. Most engineering materials, including metals, are polycrystalline and composed of microscopic crystals. The crystallographic texture, the description of the orientations of the crystallites in a material, is a key structural indicator of the deformation behavior. Estimating the orientation distribution function (ODF) of a sample allows materials scientists to identify the probability a crystal in a sample is oriented in a certain direction. The current process, which employs a Fourier series expansion over a generalized spherical harmonic basis, leaves much to be desired and is poorly understood by much of the community that uses it. Some limitations include bias introduced by ad-hoc parameters and poor accuracy for small sample sets. The purpose of this study is to develop an algorithm to estimate the ODF using a mixture model that would be free from ad-hoc parameters. To accomplish this, the algorithm uses a mixture of symmetrized Bingham distributions. Using these distributions, it employs a Estimation Maximization (EM) approach to estimate the distribution and reevaluate the data to improve subsequent estimations. It also used a minimum message length (MML) criterion to prevent overfitting, or making too specific estimations based on insufficient data. This algorithm is compared with a similar algorithm developed in tandem using a mixture of symmetrized Bingham distributions but using a Markov Chain Monte Carlo (MCMC) approach instead.