On the relationship and distinction between atomic density and coordination number in describing crystal defects

Crystal defects are often described through broken atomic bonds, through counting the nearest neighbor coordination number. In this work, we highlight that the intrinsic heterogeneities in interatomic spacing due to a crystal defect, which is overlooked in broken-bond models, can 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, shows much better correlations with the grain boundary properties. The atomic density field is shown to simultaneously capture bond depletion and spacing variations, thereby covering and unifying both structural and volumetric information. Our results establish the coarse-grained atomic density field as a principled surrogate for describing grain boundary thermodynamics, motivating the augmentation of broken-bond rules in predictive theories of interfacial energetics, excess properties, segregation, and phase behavior, and providing a direct bridge from atomistic to mesoscale models, with potential applications extending to other microstructural defects.