Instructor

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.

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