Understanding and visualizing microstructure and microstructure variance as a stochastic process

The study of microstructure-property relationships is a defining concept in the field of materials science and engineering. Despite the paramount importance of microstructure to the field a rigorous systematic framework for the description of structural variance between samples of materials with the same processing history and between different materials classes has yet to be adopted. Here the authors utilize the formalism of stochastic processes to develop a statistical definition of microstructure and develop measures of structural variance in terms of the measured variance of estimators of higher order probability distributions. Principal component analysis (PCA) of higher order distributions is used to produce visualization of the space spanned by an ensemble of microstructure realizations and for quantification of the structural variance within the ensemble. The structural variance is correlated with the variance in properties and structure/property maps are produced in the PCA space.