A quantitative description of the morphological aspects of materials structures suitable for quantitative comparisons of 3D microstructures

While several laboratories can produce 3D models of microstructure from serial sectioning or tomography, the more widespread practice is to attempt to infer 3D shapes from 2D sections of different orientations. We have developed a forward modeling approach that, given a 3D particle shape, produces statistically representative 2D sections whose projections are characterized by 2D moment invariants (MI). Since the sectioning plane is random, each particle will produce a statistical distribution of 2D moments and an ensemble of particles in a microstructure will produce its own characteristic distribution of 2D moments and can be used as a representation of the microstructure. This distribution can be represented as a point in a metric space. We use the Hellinger distance as the measure for this space, which allows us to quantify the similarity of two microstructures. Example applications include: determination of a 3D shape by computing the Hellinger distance between MI density maps derived from random 2D section micrographs and the density map database; automated detection and quantification of rafting in cuboidal microstructures; and quantitative comparison of pairs of microstructures.