Jump to ContentJump to Main Navigation
Computer Simulations of Dislocations$
Users without a subscription are not able to see the full content.

Vasily Bulatov and Wei Cai

Print publication date: 2006

Print ISBN-13: 9780198526148

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198526148.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 December 2021

Fundamentals Of Atomistic Simulations

Fundamentals Of Atomistic Simulations

2 (p.27) Fundamentals Of Atomistic Simulations
Computer Simulations of Dislocations

Vasily Bulatov

Wei Cai

Oxford University Press

Fundamentally, materials derive their properties from the interaction between their constituent atoms. These basic interactions make the atoms assemble in a particular crystalline structure. The same interactions also define how the atoms prefer to arrange themselves in the dislocation core. Therefore, to understand the behavior of dislocations, it is necessary and sufficient to study the collective behavior of atoms in crystals populated by dislocations. This chapter introduces the basic methodology of atomistic simulations that will be applied to the studies of dislocations in the following chapters. Section 1 discusses the nature of interatomic interactions and introduces empirical models that describe these interactions with various degrees of accuracy. Section 2 introduces the significance of the Boltzmann distribution that describes statistical properties of a collection of interacting atoms in thermal equilibrium. This section sets the stage for a subsequent discussion of basic computational methods to be used throughout this book. Section 3 covers the methods for energy minimization. Sections 4 and 5 give a concise introduction to Monte Carlo and molecular dynamics methods. When put close together, atoms interact by exerting forces on each other. Depending on the atomic species, some interatomic interactions are relatively easy to describe, while others can be very complicated. This variability stems from the quantum mechanical motion and interaction of electrons [15, 16]. Henceforth, rigorous treatment of interatomic interactions should be based on a solution of Schrödinger’s equation for interacting electrons, which is usually referred to as the first principles or ab initio theory. Numerical calculations based on first principles are computationally very expensive and can only deal with a relatively small number of atoms. In the context of dislocation modelling, relevant behaviors often involve many thousands of atoms and can only be approached using much less sophisticated but more computationally efficient models. Even though we do not use it in this book, it is useful to bear in mind that the first principles theory provides a useful starting point for constructing approximate but efficient models that are needed to study large-scale problems involving many atoms.

Keywords:   Cauchy pressure, Elastic constants, Hamiltonian, Initial condition, Kinetic energy, Local energy, Minimization, Partition function

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .