Computation of Defects in Materials

Abstract

Abstract The purpose of this project is to investigate and assess, using the MATLAB computer language, some numerical methods used in several elds of computational molecular dynamics. First a theoretical model of a one-dimensional chain of atoms was studied. The atoms in this chain would interact based on the Lennard-Jones potential energy function. Several algorithms were investigated that found con gurations of the chain where the total potential energy was lowest. Aspects of the one-dimensional chain were then carried over into a model of a two-dimensional system of atoms. For this model a full simulation of the movement of the atoms in the system was used to study the system. It was found that one of the simplest atom con gurations, a square lattice pattern, was unstable. In the simulation, this structure evolved over time into several disconnected regions, called grains," of a more stable triangular-hexagonal lat- tice pattern. These structures are similar to crystal grains in real-world polycrystalline materials. Some basic computational thermodynamics (more specically, Langevin dynamics) was also used in the simulation. It was found that by regulating the temperature, or average kinetic energy, of the system, the formation of grains could be controlled to some degree.