MATLS 4NN3/6NN3: COMPUTATIONAL MODELLING IN MATERIALS ENGINEERING

Instructor

Oleg Rubel

Oleg Rubel
Room:
JHE 359
Tel:
+1-905-525-9140, ext. 24094
E-Mail:
rubelo(a)mcmaster.ca
URL:
http://olegrubel.mcmaster.ca

Course structure

12 weeks, 3 hrs/week: 1 hr lecture, 2hrs hands on session (tutorials)

Module 1 (week 1–2): Fundamentals of density functional theory (DFT)

  • elements of quantum mechanics
  • ab initio approaches in historical perspective
  • DFT shortcut
  • self consistency problem
  • basis set
  • pseudopotentials
  • software (Wien2k, VASP, ABINIT)
  • Tutorial: VESTA building and visualization of simple crystal structures
  • Tutorial: ABINIT under Windows/Linux, analysis tools

Module 2 (week 3–4): Prediction of basic material structure

  • equilibrium structure
  • phase stability
  • phase diagram
  • convergence and accuracy
  • Tutorial: stable structure of Fe (bcc and fcc phases, magnetism)

Module 3 (week 5–6): Mechanical properties

  • elastic properties
  • equation of state (EOS)
  • strength and fracture toughness
  • Tutorial: lattice constant and bulk modulus of Si, convergence test, MATLAB code for EOS fit

Module 4 (week 7–10): Optical and electrical properties

  • band structure
  • transport coefficients
  • Tutorial: Band structure of GaAs and Si (direct vs indirect semiconductors)
  • Tutorial: Charge transport and effective mass
  • Tutorial: Band gap engineering in (InGa)N
  • polarization
  • piezoelectric properties
  • Tutorial: Electromechanical coupling in ferroelectric ceramics PbTiO3

Module 5 (week 11–12): Structural defects and impurities

  • supercells
  • structure relaxation
  • formation energy
  • defect electronic states
  • Tutorial: Solubility of C in fcc-Fe and bcc-Fe
  • special topic project (6NN3)

Graduate students (6NN3) are required to develop an individual or a small group project
where they apply the learned techniques to solving a problem in materials science of their
choice. At the end, students are asked to write a report paper in the form of a wiki page.

Learning Outcomes

  • Basic knowledge of quantum-mechanical concepts used in computational modelling of materials.
  • Use existing DFT programs for the quantitative simulation of intrinsic material properties.
  • Ability to develop structural models that capture relevant interactions for a material property in question.
  • Know how to interpret computational results and compare between computational and experimental results.
  • Efficiently utilize Linux-based multiprocessor servers for solving demanding computational and data-intensive problems.
Activities
Contribution to the final grade
4NN3 6NN3
Assignments (1 per module)
50%
40%
Final exam
50%
40%
Special topic project
--
20%

Prerequisites and relevance to other courses

The material covered is largely self-contained, but an earlier exposure to quantum me-
chanics and solid state physics (MATLS 3Q03 Materials for Electronic Applications) is
desirable. No extensive programming knowlege is required.

Recommended texts include but not limited to the following titles

  • June Gunn Lee, Computational materials science: an introduction (CRC Press, Taylor & Francis Group, 2012).
    ISBN: 978-1-4398-3616-3
  • David S. Sholl and Janice A. Steckel, Density functional theory: a practical introduction (John Wiley & Sons, 2009).
    ISBN: 978-0-470-37317-0
  • Efthimios Kaxiras, Atomic and electronic structure of solids (Cambridge University Press, 2003).
    ISBN-13: 978-0521523394

Notes: The text by Lee gives a great introduction to the quantum mechanics and DFT. The text by Sholl and Steckel complements with a good set of examples, but is more shallow in terms of the DFT theory. The book by Kaxiras is more general and cover many aspects apart from DFT.

Course notes