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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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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: 26 October 2021

Finding Transition Pathways

Finding Transition Pathways

7 (p.117) Finding Transition Pathways
Computer Simulations of Dislocations

Vasily Bulatov

Wei Cai

Oxford University Press

As was discussed in Chapter 2, stable and accurate numerical integration of the MD equations of motion demands a small time step. In MD simulations of solids, the integration step is usually of the order of one femtosecond (10−15 s). For this reason, the time horizon ofMDsimulations of solids rarely exceeds one nanosecond (10−9 s). On the other hand, dislocation behaviors of interest typically occur on time scales of milliseconds (10−3 s) or longer. Such behaviors remain out of reach for direct MD simulations. Time-scale limits of a similar nature also exist in MC simulations. For instance, the magnitude of the atomic displacements in the Metropolis algorithm has to be sufficiently small to ensure a reasonable acceptance ratio, which results in a slow exploration of the configurational space. This disparity of time scales can be traced to certain topographical features of the potential-energy function of the many-body system, typically consisting of deep energy basins separated by high energy barriers. The system spends most of its time wandering around within the energy basins (metastable states) only rarely interrupted by transitions from one basin to another. Whereas the long-term evolution of a solid results from transitions between the metastable states, direct MDand MC simulations spend most of the time faithfully tracing the unimportant fluctuations within the energy basins. In this sense, most of the computing cycles are wasted, leading to very low simulation efficiency. Because the transition rates decrease exponentially with the increasing barrier heights and decreasing temperature, this problem of time-scale disparity can be severe.

Keywords:   Contour line, Potential energy landscape, Rare event, Sinclair–Fletcher algorithm, Transition pathway, Transition rate, Transition state theory (TST)

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