The Nuts and Bolts of First-Principles Simulation

1. The Nuts and Bolts of First-Principles Simulation 1: Computational MaterialsScience: an Overview Durham, 6th-13th December 2001 CASTEP Developers’ Groupwith support from the ESF k Network

2. Outline • What would we like to achieve? • Lengthscales and timescales • Techniques • Dislocations • Aim of first principles calculations • The density functional theory plane wave pseudopotential approach • Surface diffusion on aluminium • Zeolite acid catalysts Lecture 1: Computational Materials Science

3. What would we like to achieve? • Computers get cheaper and more powerful every year. • Experiments tend to get more expensive each year. • IF computer simulation offers acceptable accuracy then at some point it should become cheaper than experiment. • This has already occurred in many branches of science and engineering. • Is it possible to achieve this for materials modelling? (Physics, chemistry, biology..) Lecture 1: Computational Materials Science

4. Lengthscales • Materials modelling can describe many things from the atomic scale to entire engineering components. • This covers lengthscales from Ångstroms to many metres - a range of 1012. • This range of lengthscales encompasses a few atoms to 1036 atoms! Lecture 1: Computational Materials Science

5. Timescales • The timescales of interest in materials modelling range from the atomic timescale - of the order of 10-12 seconds, to the lifetime of a material, for a geological specimen this could be millions of years. • Hence, the range of timescales of interest is 1025! Lecture 1: Computational Materials Science

6. Techniques • Clearly the range of lengthscales and timescales of interest are beyond the capability of a single modelling technique. • Techniques: • Continuum modelling • Structural units (for instance groups of atoms that can be regarded as composite units) • Atomistic approaches: empirical, semi-empirical, first principles techniques: density functional theory, ab initio approaches, quantum Monte Carlo,…... Lecture 1: Computational Materials Science

7. Dislocations b Lecture 1: Computational Materials Science

8. Dislocations Elastic energy in long-range strain field. Can be calculated from elastic constants Core energy, depends on atomic positions in highly strained region. Can only be calculated with an atomistic model Lecture 1: Computational Materials Science

9. Dislocations • The elastic strain energy dominates unless dislocations are very close together. • In metallic systems the core energy does not vary greatly as dislocation moves,.... Can obtain an excellent description of the behaviour of entire material by considering only the elastic energy of the dislocations. • In other systems the core energy does vary significantly as dislocation moves,.... Need to compute this energy in order to model behaviour of entire material. Lecture 1: Computational Materials Science

10. Aim of first principles calculations Atomic Numbers Solve the quantum mechanical equations for the electrons Predict physical and chemical properties of systems Lecture 1: Computational Materials Science

11. The density functional theory plane wave pseudopotential approach • Whole periodic table. • Systems containing hundreds of atoms (on large enough computers). • Structural optimisation. • Finite temperature simulations (molecular dynamics) on picosecond timescales. Lecture 1: Computational Materials Science

12. Diffusion of Al adatom on Al(001) Hop over bridge site Exchange mechanism (Feibelman) Lecture 1: Computational Materials Science

13. Zeolite acid catalysts Lecture 1: Computational Materials Science