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Computer Simulations of Dislocations$
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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

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Case Study Of Static Simulation

Case Study Of Static Simulation

Chapter:
3 Case Study Of Static Simulation
Source:
Computer Simulations of Dislocations
Author(s):

Vasily Bulatov

Wei Cai

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198526148.003.0007

Having discussed the basic concepts of atomistic simulations, we now turn to a case study that demonstrates the use of the static simulation techniques and, along the way, reveals some of the realistic aspects of the dislocation core structure and highlights the coupling between continuum and atomistic descriptions of dislocations. Section 3.1 explains how to use simple solutions of the continuum elasticity theory for setting up initial positions of atoms. The important issue of boundary conditions is then discussed in Section 3.2. Section 3.3 presents several practical methods for visualization of dislocations and other crystal defects in an atomistic configuration. This first case study sets the stage for a subsequent exploration of more complex aspects of dislocation behavior, which demands more advanced methods of atomistic simulations to be discussed in Chapters 4 through 7. In Section 1.2 we already considered the atomistic structure of dislocations in simple cubic crystals. In other crystals, the atomistic structure of dislocations is considerably more complicated but can be revealed through an atomistic simulation. This is the topic of this chapter. An atomistic structure is specified by the positions xi of all atoms. In a perfect crystal, xi ´s are completely determined by the crystal’s Bravais lattice, its atomic basis and its lattice constant (Section 1.1). Now assume a dislocation or some other defect is introduced, distorting the crystal structure and moving atoms to new positions x´i . A good way to describe the new structure is by specifying the displacement vector ui ≡x'i −xi for every atom i. The relationship between ui and xi can be obtained analytically if we approximate the crystal as a continuum linear elastic solid. This is certainly an approximation, but it works well as long as crystal distortions remain small. Let us define x as the position of a material point in the continuum before the dislocation is introduced and x´ as the position of the same material point after the dislocation is introduced. Here, x is a continuous variable and the displacement vector u(x)≡x´−x expressed as a function of x is the displacement field.

Keywords:   formula, formula morphism, free extension, freely

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