Computational Materials Science

Syllabus

Introduction to materials models for computer simulations

Length and time scales hierarchy in modeling materials structure and processes (quantum mechanical, atomistic, mesoscopic, continuum).

Fundamental background for classical simulations.

Brief review of classical mechanics, statistical physics, methods of numerical integration and solution of differential equations.

Atomic-level simulations

Interatomic interaction potentials. Molecular dynamics method. Monte Carlo method. Initial conditions, crystal lattice construction, defects. Boundary conditions. Methods for constant temperature or/and pressure simulations.

Results analysis

Equilibrium properties, structural, mechanical, dynamical properties. Specific materials properties calculation with realistic interaction potentials and comparison with experiments.

Introduction to first principles calculations

The basics of density functional theory. Structural and elastic properties calculations.

Mesoscopic and continuum simulations

Coarse-grain method. Space discretization. Finite difference and finite element methods. Applications (e.g., dislocation dynamics, electromagnetic wave propagation). Cellular automata.

Combining methods

Concurrent and hierarchical combination of models. Multiple scale simulations.

Learning Outcomes

The course introduces the basic techniques used for the theoretical study of materials using computers. The course combines lectures and laboratory exercises in order for the students to get familiar with appropriate modeling and simulation methods for understanding the materials structure-properties relationship as well as the processes involved in several materials science problems. The learning goals that should be achieved by the end of the course are:

1. Students acquire a fundamental background in state-of-the-art programming, modelling and simulation of materials.
2. Students develop scientific computing and software related technical skills.
3. Students acquire hands-on experience in modeling complex phenomena and in solving challenging problems in materials science.

The course according to the European Qualifications Framework for Lifelong Learning belongs to level 7.

Recommended Bibliography

• J.M. Thijssen, Computational Physics, Cambridge University Press, Cambridge, New York (1999).
• D. Raabe, Computational Materials Science: the Simulation of Materials Microstructures and Properties, Wiley-VCH, Weinheim, New York (1998).
• M. P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1990).
• D. Frenkel, B. Smit, Understanding Molecular Simulation: from Algorithms to Applications, Academic Press, San Diego, (1996).
• K. Ohno, K. Esfarjani, and Y. Kawazoe, Introduction to Computational Materials Science: from Ab Initio to Monte Carlo Methods, Springer-Verlag, Berlin, New York (1999).
• K. Binder, D.W. Heermann, Monte Carlo Simulation in Statistical Physics: an Introduction, Springer, Berlin, New York (1997).
• K. Binder, Monte Carlo and Molecular Dynamics Simulations in Polymer Sciences, Oxford University Press, Oxford, New York (1995).