A local orientational order parameter for systems of interacting particles

Abstract

Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we introduce a quantity $E$ that captures the amount of pairwise informational redundancy among the bonds formed by a particle. Particles with larger $E$ have less diversity in bond angles and thus simpler neighborhoods. We show that $E$ possesses a number of intuitive mathematical properties, such as increasing monotonicity in the coordination number of Platonic polyhedral geometries. We demonstrate analytically that $E$ is, in principle, able to distinguish a wide range of structures and conjecture that it is maximized by the icosahedral geometry under the constraint of equal sphere packing. An algorithm for computing $E$ is described and is applied to the structural characterization of crystals and glasses. The findings of this study are generally consistent with existing knowledge on the structure of such systems. We compare $E$ to the Steinhardt order parameter $Q_6$ and polyhedral template matching (PTM). We observe that $E$ has resolution comparable to $Q_6$ and robustness similar to PTM despite being much simpler than the former and far more informative than the latter.

arXiv comment9 pages, 6 figures. Title changed in this version. Content updated based on reviewer suggestions. The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/journal/jcp

References in corpus (10)

• Structure identification methods for atomistic simulations of crystalline materials
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Robust Structural Identification via Polyhedral Template Matching
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Identification of structure in condensed matter with the topological cluster classification
• A Topological Framework for Local Structure Analysis in Condensed Matter
• Phase diagram of Kob-Andersen type binary Lennard-Jones mixtures
• Lifetimes and Lengthscales of Structural Motifs in a Model Glassformer
• A local order metric for condensed phase environments
• Characterizing Polygonality in Biological Structures

Cited by in corpus (2)

• Dependence of simulated radiation damage on crystal structure and atomic misfit in metals
• On the topology of the space of coordination geometries