Skip to Main Content
Book Chapter

Basics of first-principles simulation of matter under extreme conditions

By
Daniel Y. Jung
Daniel Y. Jung
1
Institute of Mineralogy and Petrology, Department of Earth Science, ETH Zurich, Sonneggstrasse 5, CH-8092 Zurich, Switzerland
Search for other works by this author on:
Artem R. Oganov
Artem R. Oganov
2
Laboratory of Crystallography, Department of Materials, ETHHonggerberg, Wolfgang-Pauli-Strasse’0, CH-8093 Zürich, Switzerland;
Search for other works by this author on:
Published:
January 01, 2005

Abstract

Most of the Earth’s material exists at high pressures and temperatures inside the planet. Since experiments in this p-T regime often turn out to be difficult or plain impossible, it is often necessary to do simulations, which avoid some of the important problems encountered in experiments.

For a more specific look on the topics of this chapter we refer the reader to Kohn (1999), Martin (2004), Oganov et al. (2002), Payne et al. (1992) and Stixrude et al. (1998). In this chapter we describe how to calculate the energy of a crystal with ab initio methods. It will shortly touch the historical origins of today’s methods and will end with the state-of-the-art quantum-mechanical calculations.

When we want to investigate a mineral system we start with the Gibbs free energy. Every system in equilibrium likes to be in the state with the lowest Gibbs free energy G at given pressure and temperature condition. The Gibbs free energy is then given by minimising the following equation:

where E is the energy, p the pressure, V the volume, T the temperature and S the entropy of the system. From statistical mechanics, knowing the energy of different states of the system (i.e. the energies of different vibrational and electronic quantum levels or of different atomic configurations) one can calculate the entropy and the free energy1, the link being provided by the partition function Z:

The total energy of a non-relativistic electron-nuclear system and all its energy levels can be calculated by solving the Schrodinger equation, where H is the Hamilton operator and ψ is the wave function for the N electrons and the M nuclei.

You do not currently have access to this article.

Figures & Tables

Contents

European Mineralogical Union Notes in Mineralogy

Mineral behaviour at extreme conditions

Ronald Miletich
Ronald Miletich
Search for other works by this author on:
Mineralogical Society of Great Britain and Ireland
Volume
7
ISBN electronic:
9780903056465
Publication date:
January 01, 2005

GeoRef

References

Related

Citing Books via

Close Modal
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close Modal
Close Modal