Integer Model of a Hexagonal Close-Packed Crystal Lattice and Calculation of the Number of Bonds Broken by an Arbitrary Plane

Abstract

An algorithm for calculating the number of broken interatomic bonds for a hexagonal close-packed crystal lattice cut by an arbitrary plane is proposed. This challenge occurs in surface energy calculation, modeling strength and surface properties, the crystal growth simulation, and other problems of solid-state and surface physics. The dimension and complexity of this problem are so great that it cannot be solved without involving a computer with a proper software. In the paper, the geometry of the HCP lattice was analyzed. This made it possible to represent the lattice as an integer discrete space and to construct an integer metric in it. Such representation allowed us to develop an exact, fully integer algorithm for solving the problem. The algorithm was implemented as a PC application. In addition to the number of broken bonds, the application calculates the reticular density, builds 3D models of the HCP lattice cross-section by a given plane. The analysis of the time complexity of the algorithm and test results are also given.