Local Order Metrics for Two-Phase Media Across Length Scales

Abstract

The capacity to devise order metrics for microstructures of multiphase heterogeneous media is a highly challenging task, given the richness of the possible geometries and topologies of the phases that can arise. This investigation initiates a program to formulate order metrics to characterize the degree of order/disorder of the microstructures of two-phase media in d-dimensional Euclidean space R d across length scales. In particular, we propose the use of the local volume-fraction variance σ 2V (R) associated with a spherical window of radius R as an order metric. We determine σ 2 V (R) as a function of R for 22 different models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short-and long-range order. We find that the local volume-fraction variance as well as asymptotic coefficients and integral measures derived from it provide reasonably robust and sensitive order metrics to categorize disordered and ordered two-phase media across all length scales.