Local Order Metrics for Two-Phase Media Across Length Scales, Murray Skolnick, G3 (3961621)
A two-phase heterogeneous material has a microstructure that consists of two domains made up of different materials or “phases.” Such two-phase materials are abound in natural and synthetic contexts, including, for example, composites, porous media, foams, cellular solids, colloidal suspensions, polymer blends, geological media, and biological media. The task of devising numerical order metrics to rigorously characterize the degree of order (or disorder) in such materials across length scales is highly challenging due to the rich range of topologies and geometries exhibited by these systems. In this work, we propose the use of the variance of the distribution of local volume-fractions of a phase as such a metric—the principle being that a larger local volume-fraction variance indicates greater disorder. Moreover, by varying the size of the environment in which we measure the local volume-fraction, we are able to assess order at specific length scales in the microstructure. Overall, we find that the local volume-fraction variance is a reasonably robust and sensitive order metric that is able to rank the relative order of a set of model two-phase materials in a manner that is consistent with intuition and prior knowledge of these models.