Title
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.
Description
Additional contributors: Brian Vankoten; Mitchell Luskin (faculty mentor)
Funding information
This project was supported by the University of Minnesota's Undergraduate Research
Opportunities Program.
Suggested Citation
Veit, Max.
(2011).
Computation of Defects in Materials.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/115367.