Extraction of Crystal Structures Based on Euclidean Voronoi Diagram and Angle Distributions among Atoms

Abstract

The structural configurations of atom constituting materials are one of the fundamental factors in the study of physical properties of materials. Presented in this paper is a mathematical and computational methodology to efficiently classify a given atomic structure of an arbitrary material into groups of atoms in BCC, FCC, and HCP crystal structures. The approach is based on the angle distributions among neighboring atoms efficiently identified by a computational geometry technique called Voronoi diagram. In this paper, the presented mathematical theory was applied to analyze a multi-layer atomic structure in a geometric perspective so that a best condition for thin film growth can be found.