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 50%, Homework 40%, Presentation/discussion of a published research articles 10%
Homework assignments will appear here as the course progresses|
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
- Initial conditions, creating lattice structures, introducing defects
- Defining and maintaining temperature and 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.)
- 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
- Interatomic potentials
- 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
- Equilibrium properties (energy, temperature, pressure, velocity distributions)
- Structural properties (geometrical tessellation, pair correlation functions, atomic-level stresses)
- Dynamic properties (diffusion, time correlation functions)
- 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 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.
Discussion of published research articles
Each student will lead a discussion of a recent research paper in the area of atomistic simulations (10 min). Papers will be posted at least one week before the discussion.
"The purpose of computation is insight, not numbers."
Computational Materials Group
Materials Science & Engineering