Fall 2000 | Instructors: Sidney Yip, Ju Li | TA: Jingli Liu | Syllabus (ps,doc)

Lecture Outline

1. Overview [1,ps,pdf]
   9/6: atomistic simulation, multiscale modeling, materials science
   

   A. Simulation Methodology

2. Elements of Molecular Dynamics [4,ps,pdf]
   9/8: atomic tranjectories, Newtonian dynamics, simulation model
   9/11: equations of motion, integration algorithm, predictor-corrector
   9/13: force cutoff, min. image, pbc, Verlet list, initialization
   9/15: flow chart, eq. and time-dep properties, unique features, limitations
   

3. Elements of Monte Carlo [2]
   9/18: probability distribution sampling, importance sampling
   9/20: Metropolis method, kinetic/dynamic interpretation
   

4. Interatomic Potential Functions [6]
   9/22: overview: class. pot vs. electronic structure methods
   9/25: pair potentials
   9/27: empirical many-body potentials for metals (EAM)
   9/29: potentials for covalent bonding
   10/2: ab-initio approach - density-functional theory (LDA)
   10/4: tight-binding (LCAO) approximation
   

   Lab Sessions on Code Development and Property Calculations [2]
   10/6: description of MD Code [JL]
   10/11: applications of Code - various property calculations [JL]
   

   B. Statistical Processes

5. Basic Principles [1]
   10/13: Phase-space sampling, Liouville equation, canonical distrib.
   

6. Thermodynamic Equilibrium and Stability [3]
   10/16: thermodyn potentials and derivatives, phase transitions
   10/18: van der Waals eq. of state, critical behavior
   10/20: universal binding and eq. of state
   

7. Free Energy Calculations [4]
   10/23: overview of approaches, harmonic methods
   10/25: thermodynamic integration and adiabatic switching
   10/27: reversible scaling
   10/30: application of reversible scaling
   

8. Strength, Deformation and Toughness [7]
   11/1: free energy expansion, tij, Cijkl, Bijkl
   11/3: atomistic local strain, microcanonical vs. canonical ensembles
   11/6: stability criteria for homogeneous deformation, P-R method
   11/8: unifying Born's melting and stability criteria
   11/13: lattice vibration formalism, dispersion curves, dos, soft modes
   11/15: fracture simulations, Griffith criterion, BDT, Rice-Peierls model
   11/17: dislocaton simulations, core and kink energetics, mobility
   

9. Linear Response Theory of Fluctuations and Transport [3]
   11/20: Green-Kubo formulas, density correlation functions
   11/22: hydrodynamics, kinetic theory, mode-coupling theory
   11/27: thermal conductivity simulations
   11/29: summary and review
   

   12/1: Quiz
   

   C. Selected Applications [3]

   Recent topics in materials modeling - melting, glass transitions, stability, defect mobility, and fracture.
   12/4: melting
   12/6: supercooled liquids and amorphized solids
   12/8: ASCI program on dislocation dynamics
   12/11: Project presentation I
   12/13: Project presentation II
   

Books

1. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (review).

2. D. Frenkel, B. Smit, eds. Understanding Molecular Simulation: From Algorithms to Applications (review).

3. D.C. Rapaport, The Art of Molecular Dynamics Simulation (review).

4. A.P. Sutton, Electronic Structure of Materials (review).

Problem Sets and Solutions

• problems (ps,pdf,doc)

• PS1 (due 9/20)

• PS2 (due 10/2)

• PS3 (due 10/6)

• PS4 (due 10/13)

• PS5 (due N/A)

• Quiz

Supplementary Materials

• Hong Kong/Taiwan Lectures

• 3.320 Atomistic Computer Modeling of Materials

• WebElements; NIST constants; unit conversion

• Modeling Codes on the Internet

Links

Project Exhibition