Main text: Handouts and lecture notes (Handouts will appear in this page as course progresses).
Books for the course (including books placed on reserve circulate) are listed here.
Grading: Term project 55%, Homework 45%
The course introduces students to atomic-level computational methods commonly used in Materials Science, Physics, Chemistry, and Mechanical Engineering. The molecular dynamics and Monte Carlo methods are discussed in depth, from the introduction to the basic concepts to the overview of the current state-of-the-art. Some of the emerging methods for mesoscopic and multiscale modeling are also discussed in the context of real materials-related problems (mechanical and thermodynamic properties, phase transformations, microstructure evolution during processing). Success stories and limitations of contemporary computational methods are considered.
The emphasis of the course is on getting practical experience in designing and performing computer simulations. Pre-written codes implementing atomistic computational methods will be provided. Students will use and modify the pre-written codes and write their own simulation and data analysis codes while working on their homework assignments and term projects. A set of example problems for term project will be provided, although students are encouraged to choose a project relevant to their thesis research.
Recent research articles in the area of atomistic modeling will be discussed, with each student leadong a discussion of a recent research paper. Students will learn to assess the quality and significance of published computational results.
Topics that will be covered include:
article by R. LeSar and D. C. Chrzan
article by R. Gomperts, E. Renner, and M. Mehta
article by U. Landman
NSF White Paper on "Matter by design"
White House Materials Genome Initiative
DOE Report on Mesoscale Science
overview of modeling projects funded by EU FP7 in 2007-13
roadmapping study for connecting materials models and simulations across length/time scales, TMS and NIST, 2015
- Spatial and temporal hierarchy of microstructure and dynamics in materials
- Types of models: quantum mechanical, atomistic, mesoscopic, continuum
- Multiscale approaches
- Example of continuum modeling: Conduction/diffusion equation
- Atomistic models: Molecular dynamics
- Ordinary differential equations for particle dynamics
- The basics of classical molecular dynamics
First MD papers by Gibson et al.
Papers on the quest for the record time (milliseconds) MD simulations Nature'08
and record length-scale (trillions of atoms) MD simulations IJMPC'08
Paper on MD simulation of human crowds PRL'14
- Initial conditions, creating lattice structures, introducing defects
- Defining and maintaining temperature and pressure
Handouts on pressure
- Boundary conditions (free, periodic, stochastic, conducting, non-reflecting)
- Methods for constant temperature or/and pressure simulations
- Tricks of the trade (neighbor lists, force/energy tables, potential cutoffs, etc.)
Article on tabulated potentials by Wolff and Rudd (pdf, 178 Kb)
Article on cell-linked neighbor list method by Mattson and Rice (pdf, 480 Kb)
- Monte Carlo methods
- The basics of Monte Carlo
- Monte Carlo integration, thermodynamic averages
- Importance sampling, Metropolis scheme
- Lattice Monte Carlo, Ising model
- Multi-state Potts models (grain coarsening, recrystallization)
- Kinetic Monte Carlo (surface processes, thin film growth)
- (extracurricular) Direct Simulation Monte Carlo
Handouts by Alexey Volkov
- Interatomic potentials
Handouts on EAM and Tersoff potentials by Prof. Robert A. Johnson
2015 Review paper by Akimov and Prezhdo
- Introduction, Born-Oppenheimer approximation
- Pair potentials and their limitations
- Calculation of elastic constants from potential function
- Potentials for ionic systems, ceramics
- Many-body potentials for metallic systems
- Many-body potentials for covalently bounded systems
- Forces from "first principles" (time permitting)
- Analysis of the simulation results
- Mesoscopic methods (time permitting)
- Discrete dislocation dynamics
- Strain and stress fields for edge and screw dislocations in an isotropic medium
- The equation of motion in Newtonian Dislocation Dynamics
- Examples from 2D and 3D simulations
- Current problems
- Coarse-grained models for organic materials
- Mesoscopic models for nanofibrous and carbon nanotube materials
Bridging the scale gaps between different simulation levels
- Simultaneous integration of the models
- Sequential integration of the models (hierarchical approach)
- Examples of combined methods (MD-FEM, MD-MC, etc.)
Codes to be provided
- MSE627-MD code for MD/MC simulation
- MSE627-CG crystal generator (FCC, BCC, diamond)
- MSE627-MC Ising model for binary alloys
Objective: To get experience in designing and performing computer simulations.
Parts of the project:
- Design (or adapt an idea from literature) a simulation that is of scientific or computational interest to you
- Choose and justify a computational approach appropriate for the problem of interest
- Write the code (or parts of the code that have not been supplied)
- Run simulations and analyze the results
- Prepare a report; include electronic copies of your code
- Present your results to the class (mini-symposium)
February 1st - decide in the topic/title of your project and inform the instructor
March 1st - prepare the first draft of the introduction (with references to relevant papers) and discuss progress with instructor (optional)
May 5th and 6th (tentative dates) - turn in a report; give a presentation to the class at a mini-symposium
A set of example problems for term projects can be found here.
A problem chosen for the term project should have some science content and be doable in the timeframe of one semester. Students are encouraged to choose a project relevant to their thesis research. If the intention is to continue computational work in the future, the term project may be a well-defined part of a larger research project.
link to the topics of the term projects
"The purpose of computation is insight, not numbers."
Computational Materials Group
Materials Science & Engineering