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

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.