Statistical quantification of the microstructural homogeneity of size and orientation distributions

Abstract

Methodologies to quantify the microstructural homogeneity, or uniformity, have been developed based on the proposed statistical homogeneity theory. Two kinds of homogeneities are considered, for the size and orientation distributions, respectively. In the case of size distribution, the homogeneity is quantified using two parameters, H 0.1 and H 0.2, which are defined as the probabilities falling into the ranges of μ ± 0.1μ and μ ± 0.2μ, respectively, where μ is the mean size. Whereas in the case of orientation distribution, three parameters are used to quantify the homogeneity: H R, the mean resultant length that is a simple measure of the angular data concentration, and H 0.1 and H 0.2, which are the probabilities in particular angular ranges of the circular or spherical data. These homogeneity quantities are formularized using the common statistical models, and typical examples are demonstrated.