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Dr P D Bristowe

This course deals with the modelling of materials at the atomic level. It follows on from the Pt II course on “Introduction to Materials Modelling” by treating the two main technqiues of Molecular Dynamics and Monte Carlo in more depth. In particular it provides a proper thermodynamic and statistical mechanical foundation to these methods and describes how the simulations can be performed in different thermodynamic ensembles and how quantities such the free energy can be calculated. A key ingredient is the choice of interatomic interaction or force field and varous descriptions appropriate to different classes of materials are considered including the Born model for ionic crystals and the Embedded Atom Method for metals.

The last part of the course moves from classical methods to quantum mechanical technques and introduces the basics of Density Functional Theory. DFT is now commonly used in materials science to compute ground state properties such as equilibrium atomic structures, electronic band structures, bond strengths, formation enthalpies, elastic constants, magnetic moments, atomic charges and much more. It goes significantly beyond the nearly free electron model, the tight-binding method and the LCAO method discussed at Pt II.

Three of the lectures will illustrate specific applications of Molecular Dynamics, Monte Carlo and DFT to problems in material science.

The lecture course will cover:

  • Scope and objectives of atomistic modelling
  • Stochastic simulations (Monte Carlo)
  • An application of Monte Carlo to grain boundary segregation
  • Force fields for molecular systems
  • Interatomic pair potentials for noble gas and ionic solids
  • Interatomic many-body potentials for covalent and metallic solids
  • Deterministic simulations (Molecular Dynamics)
  • Analysing and visualising data from atomistic simulations
  • An application of Molecular Dynamics to fast-ion conduction
  • Atomistic modelling from first principles (Density Functional Theory)
  • Setting up and performing first principles simulations
  • An application of first principles simulations to thin-film adhesion