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 ${\mathbb{R}}^d$ across length scales. In particular, we propose the use of the local volume-fraction variance ${\sigma }_{{}_V}^2(R)$ associated with a spherical window of radius $R$ as an order metric. We determine ${\sigma }_{{}_V}^2(R)$ 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.

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• Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns
• Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials
• Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks
• Characterizing the Hyperuniformity of Disordered Network Metamaterials
• Communication: Modeling layered mosaic perovskite alloy microstructures across length scales via a packing algorithm
• Irregular Metamaterial Networks
• Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime