Local order metrics for many-particle systems across length scales

Abstract

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of $n$-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance ${\sigma }_N^2(R)$ associated with a spherical sampling window of radius $R$ (which encodes pair correlations) and an integral measure derived from it ${\Sigma }_N(R_i,R_j)$ that depends on two specified radial distances $R_i$ and $R_j$. Across the first three space dimensions ($d=1,2,3$), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale $R$. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of $R$. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius $R$ [S. Torquato {\it et al}., Phys. Rev. X, \textbf{11}, 021028 (2021)] to devise even more sensitive order metrics.

19 pages, 8 figures

References in corpus (20)

• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Anomalous structure and dynamics of the Gaussian-core fluid
• Hyperuniformity of Quasicrystals
• Exactly Solvable Disordered Sphere-Packing Model in Arbitrary-Dimension Euclidean Spaces
• Collective Coordinate Control of Density Distributions
• Disordered Hyperuniform Heterogeneous Materials
• The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero
• Central limit theorems for Poisson hyperplane tessellations
• Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media Beyond the Quasistatic Regime
• Disordered hyperuniformity in two-component non-additive hard disk plasmas
• Manifestations of metastable criticality in the long-range structure of model water glasses
• Local Order Metrics for Two-Phase Media Across Length Scales
• Effective Elastic Wave Characteristics of Composite Media
• Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions
• Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties
• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability

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• Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems
• Communication: Modeling layered mosaic perovskite alloy microstructures across length scales via a packing algorithm