Correlation functions and their application for the
analysis of MD results
Introduction. Intuitive and quantitative definitions of correlations
in time and space.
Velocity-velocity correlation function.
the decay in the correlations in atomic motion
Data analysis for different types of simulations
We may be interested in:
Equilibrium properties of the model system.
Structure and properties of the system in a metastable state.
Dynamic processes in the system far from equilibrium.
Issues relevant to th
Kinetic Monte Carlo:
from transition probabilities to transition rates
With MD we can only reproduce the dynamics of the system for 100 ns. Slow thermallyactivated processes, such as diffusion, cannot be modeled. Metropolis Monte Carlo samples
Mobility of atoms and diffusion. Einstein relation.
In MD simulation we can describe the mobility of atoms through the
mean square displacement that can be calculated as
1 N r
MSD r ( t )
( ri ( t ) ri ( 0 ) 2
N i =1
The MSD contains information on
Introduction to interatomic potentials (I)
In order to use Molecular Dynamics or Monte Carlo methods we have to define the rules that
are governing interaction of atoms in the system. In classical and semi-classical simulations
these rules are often expre
University of Virginia, Department of Materials Science and Engineering
Spring 2014, Tuesday and Thursday, 3:30 - 4:45 pm, Wilsdorf Hall 101
MSE 4270/6270: Introduction to Atomistic Simulations
Instructor: Leonid V. Zhigilei
Office: Wilsdorf Hall 303D
MSE 4270/6270: Introduction to Atomistic Simulations, Spring 2014
Homework #2 Running simulations with MSE627-MD
Objective: Become familiar with the MSE627-MD code, pick an appropriate timestep for
integration, understand the partitioning of the thermal e
Objective: Getting experience with Metropolis Monte Carlo simulations, using
Ising model to study compositional ordering and segregation in binary alloys.
1. Review computer code that implements a simple Ising model, mse627-mc.f90,
(if you fin
Homework #5 (page 1 of 2)
Objective: Understanding the relation between microscopic mechanisms and
continuum description of diffusion.
1. Using the same FCC crystal that you used in homework #3 (5x5x5 unit cells, 500
atoms, afcc = 5.78 ), perform two simu
Homework #1 (page 1 of 2)
Simple MD code with Velocity Verlet algorithm
Write the simplest possible one-dimensional molecular dynamics code for two particles
connected by a spring (Force = k(x2-x1-x0) where x=x2-x1 is the distance between particles,
Homework #3 (150 points), page 1 of 2
Objective: Building initial system with MSE627-CG code. Understand the connection
between the temperature and velocity distribution. Analysis of melting and phase
transformations in terms of evolution of kinetic and p
The length-scale of MD is limited a large fraction of the atoms is on the surface or feel
the presence of the surface. How to reproduce interaction of atoms in the MD computational
cell with the surrounding material?
1. Free boundaries
Introduction to the Science and Engineering of Materials
MSE 209: Introduction to the Science
and Engineering of Materials
Spring 2010 MSE 209 - Section 1
Instructor: Leonid Zhigilei
Monday and Wednesday, 08:30 9:45 am
Olsson Hall 009
MSE 2090: Introduction to Materials Science
Chapter 1, Introduction