The Use of Finite Mixture Models and EM-Algorithm to Analyze Grain Structure in HPT-Nanostructured Metallic Materials

Abstract

Analysis of grain size distribution’s histograms of Nb and Ni subjected to high-pressure torsion at cryogenic temperatures and Nb3Sn layers formed in Nb/Cu – Sn composite wires after the diffusion annealing has been carried out using statistical analysis method based on the application of finite mixture models and using an expectation – maximization algorithm with the estimation of fitting accuracy by the Bayesian information criterion. It has been established that the approximation by the model with a single component of logarithmic standard distribution is the most suitable for all examined experimental distributions in contrast to the model with two components. Besides, the use of the proposed approach allows to practically eliminate an influence of the additional errors in the experimental data which seem to be introduced at transmission electron microscopy image processing and constructing histograms of grain size distributions.