[Paper Review] Local structure characterization in particle systems

Rachael S. Skye, Erin Teich|arXiv (Cornell University)|Jan 9, 2026

Material Dynamics and Properties0 citations

TL;DR

A survey of local-structure metrics for particulate systems, detailing how to compute them from particle positions and highlighting software tools.

ABSTRACT

Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we discuss can all be computed from the positions of particles, and are thus most useful when there is access to this information, either from simulation or experimental imaging. For each metric, we provide derivations, intuition regarding its implications, example uses, and references to software packages that compute the metric. Our survey encompasses characterization techniques ranging from the simplest to the most complex, and will be useful for students getting started in the structural characterization of particle systems.

Motivation & Objective

• Motivate the need to characterize local neighborhoods in particle systems across contexts.
• Survey a suite of local-structure metrics that operate on particle positions.
• Provide derivations, intuition, and example uses for each metric.
• Highlight software packages that implement these metrics for easy adoption by researchers.
• Position these tools to aid students and researchers in structural analysis of soft matter.

Proposed method

• Define the local environment as the set of vectors from a central particle to its nearest neighbors.
• Enumerate simple to complex metrics that can be computed from local environments.
• Present how each metric is derived, interpreted, and used to distinguish structures.
• Compare software implementations across freud, OVITO, pyscal, and mdapy (and reference a table of methods).
• Illustrate crystallization detection and orientational order through representative metrics and examples.
• Discuss how harmonic order parameters and bond orientational diagrams capture rotational symmetry of local environments.

Experimental results

Research questions

• RQ1 What local-environment metrics best characterize short-, medium-, and long-range order in particulate systems?
• RQ2 How do coordination number, radial distribution function, bond orientational order, and harmonic order parameters distinguish crystal, liquid, and disordered phases?
• RQ3 What are practical considerations (neighbor definitions, noise robustness, and cutoffs) when applying these metrics?
• RQ4 How do different software packages implement these metrics, and what are the pros/cons for researchers?
• RQ5 Can these metrics jointly detect crystallization and defects such as stacking faults?

Key findings

• A progression of metrics from basic (CN) to more information-rich (g(r), bond orientational order) enables crystallization detection.
• g(r) provides information on short- to long-range order but lacks angular information, requiring complementary metrics.
• Bond orientational order diagrams reveal local symmetry differences between fcc and bcc environments and can indicate stacking faults.
• Harmonic order parameters (psi_l) quantify rotational symmetry and are effective in 2D and quasi-2D systems for phase identification (e.g., hexatic transition).
• The survey connects metrics to practical software implementations across freud, OVITO, pyscal, and mdapy for accessible analysis.