MSE 460

Computational Materials Science
Term Offered: Fall
Text(s):  
Instructor(s): Professor Vaclav Vitek, Room 218 LRSM, vitek@lrsm.upenn.edu, 898-7883
Prerequisite(s): Ability to write simple computer code using a programming language (Fortran, C, C++, Matlab)
Basic condensed matter physics (MSE 221 or equivalent)
Thermodynamics (Chem 102 or equivalent)
Structure of materials
Grading:  
Course Home Page URL:  
Course Description: This course will cover fundamentals of atomic level modeling of the structure and properties of materials. Specifically it will cover metals, semiconductors, oxides and other ionic crystals. First, the description of atomic interactions will be introduced. This will include both basics of the density functional theory and approximations in terms of pair potentials, embedded atom method and tight-binding. The methods of computer modeling include molecular statics, molecular dynamics, Monte Carlo and lattice dynamics (phonons). Interpretations of results of such modeling in terms of structures, for example using the radial distribution function, thermodynamic and statistical physics analyses will be an important component of the course.
Course Outline: 1. INTRODUCTION: Why atomic level modeling is essential for modern materials science and nano-engineering.
Structures - basis of understanding of materials properties.
Complex crystal structures
Non-crystalline solids and liquids
Atomic clusters and nano-structures
Lattice defects, surfaces, interfaces, nano-crystals.
Examples: Model of a nano-crystal
Model of a free surface
Model of a grain boundary
Linking structural studies with experiments:
High resolution electron microscopy
Scanning tunneling microscopy and atomic force microscopy
Ion and electron scattering
Field ion microscopy and atom probe
Lattice vibrations - phonons
Examples: Nb-sapphire interface
Atomic force microscope
Computer experiments:
Phase transformations
Bulk, surface and interfacial diffusion
Deformation and fracture
Catalysis.
Examples: Dislocation generation during nanoindentation
Deformation and fracture of a nanotube
Radiation damage
Material deposition to surfaces


2. GENERAL ASPECTS OF ATOMIC LEVEL MODELING:
Energy of a system of particles, equation of motion and equilibrium conditions
Concept of stress in a discrete atomic system.
Link to mechanical and thermodynamic properties of the system studied.
Boundary conditions: finite blocks, periodic and semi-periodic boundary conditions
Methods of interpretation of results:
Graphical representation of structures
Radial distribution function
Voronoi polyhedra
Atomic level stresses

3. DESCRIPTION OF ATOMIC INTERACTIONS AND THE ENERGETICS OF MATERIALS
Pair potentials
Pair potentials in molecules vs pair potentials in condensed matter
Lennard-Jones, Born-Mayer, Morse potentials
Defficiencies of pair-potentials.
Many-body central force potentials for metallic materials
Embedded atom method
Potentials for covalent solids - semiconductors:
Dependence on bond angles
Tersoff and Stilinger-Weber and Brener's potentials for Si, C etc.
Basics of density functional theory

4. METHODS OF COMPUTER MODELING
Molecular statics - minimization of the energy
Steepest descent
Conjugate gradient.
Molecular dynamics (MD)
Verlet algorithm
Constant volume and constant pressure simulations
'Thermostats' and their use in the control of temperature in MD calculations
Some basic concepts of statistical physics
Physical interpretation using statistical physics: fluctuations, correlations, autocorrelations
Monte Carlo
Brief overview of necessary statistical mechanics and equilibrium thermodynamics, Metropolis method
Canonical ensemble: constant volume, temperature, number of particles
Grand canonical ensemble: constant volume, temperature, variable number of particles
Isothermal-isobaric canonical ensemble: constant pressure, temperature, number of particles
Modeling segregation and order/disorder.
Kinetic Monte Carlo
Diffusion in crystalline materials.
Lattice Dynamics
Lattice vibration-phonons
Link to thermodynamic properties of materials.

Assessment tools:

Home assignments that include coding simple molecular statics, molecular dynamics and Monte Carlo codes and interpretation of the results of running the codes for a specific structure.
Quizzes on the studies material.
 


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