Local order metrics for two-phase media across length scales

Salvatore Torquato, Murray Skolnick, Jaeuk Kim

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The capacity to devise order metrics to characterize and classify microstructures of multiphase heterogeneous media across length scales is an outstanding but 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 Rd across length scales. In particular, we propose the use of the local volume-fraction variance σV2(R) associated with a spherical window of radius R as an order metric. We determine σV2(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. Such order metrics could be employed to accelerate the discovery of novel heterogeneous materials by tailoring their degree of order/disorder.

Original languageEnglish (US)
Article number274003
JournalJournal of Physics A: Mathematical and Theoretical
Issue number27
StatePublished - Jul 8 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • hyperuniformity
  • length scales
  • order metrics
  • two-phase media


Dive into the research topics of 'Local order metrics for two-phase media across length scales'. Together they form a unique fingerprint.

Cite this