Inconsistency of neighborhood based on Voronoi tessellation and Euclidean distance

Voronoi tessellation (VT) is commonly used for spatial segmentation, surface reconstruction, local structure analysis, and so on. In VT two points are neighbors to each other if they share a common bisection-facet (edge in the two-dimensional case). Such definition of neighborhood is different from the concept based on Euclidean distance. In this paper, the inconsistency between Voronoi neighbors and Euclidean neighbors in 2D and 3D cases is discussed. The Voronoi Neighbor Anomaly (VNA) has been defined as that for a given atom, VT identifies farther atoms as neighbors but fail to identify nearer atoms as neighbors. The VNA is theoretically proved to be possible and the conditions are studied in 2D and 3D based on the Delaunay triangles and polyhedrons, respectively. Furthermore, by employing VT and the largest standard cluster analysis (LSCA) to quantify neighborhood between atoms to a MD simulated cooling of liquid metal Ta, the VNA cases are indeed found in the system. It is also shown that as the disordered degree of a system increases, the probability of VNA increases. These findings clarify a potential issue of VT in characterizing local structures, particularly disordered systems. The proposed VNA could be linked to other structural characteristics, which deserves further studies. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The paper discusses the inconsistency between Voronoi neighbors and Euclidean neighbors in 2D and 3D cases in Voronoi tessellation. It is found that as the disorder degree of a system increases, the probability of the Voronoi Neighbor Anomaly (VNA) also increases.