On the Relationship and Distinction Between Atomic Density and Coordination Number in Describing Grain Boundaries

TL;DR

This paper shows that atomic density, as a coarse-grained descriptor, better captures grain boundary properties in materials than traditional coordination number, unifying structural and volumetric information for improved modeling.

Contribution

It introduces atomic-density fields as a comprehensive descriptor for grain boundaries, surpassing coordination number by capturing bond depletion and spacing variations.

Findings

Density-based descriptors correlate with thermodynamics and kinetics.

Density fields unify structural and volumetric information.

Results suggest augmenting broken-bond rules in models.

Abstract

Crystal defects are often rationalized through broken-bond counting via the nearest neighbor coordination number. In this work, we highlight that this perspective overlooks intrinsic heterogeneities in interatomic spacing that decisively shape defect properties. We analyze excess free volume, energy, and entropy for a large set of BCC-Fe grain boundaries relaxed by molecular statics and demonstrate that an atomic-density field, as a systematically coarse-grained field variable, provides a more comprehensive descriptor. Unlike coordination alone, the density field simultaneously captures bond depletion and spacing variations, thereby unifying structural and volumetric information. Our results establish density-based descriptors as principled surrogates for grain-boundary thermodynamics and kinetics, offer a direct bridge from atomistic data to mesoscale models, and motivate augmenting broken-bond rules in predictive theories of interfacial energetics, excess properties, segregation and phase behavior.