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An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions pp 13–36Cite as

A Stochastic Model for the Description of Surface Reaction Systems

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Part of the book series: Lecture Notes in Physics ((LNP,volume 856))

Abstract

The most important concept for surface reactions is the adsorption site. For simple crystal surfaces the adsorption sites form a lattice. Lattices form the basis for the description of surface reactions in kinetic Monte Carlo. We give the definition of a lattice and discuss related concepts like translational symmetry, primitive vectors, unit cells, sublattices, and simple and composite lattices. Labels are introduced to describe the occupation of the adsorption sites. This leads to lattice-gas models. We show how these labels can be used to describe reactions and other surfaces processes and we make a start with showing how they can also be used to model surfaces that are much more complicated than simple crystal surfaces. Kinetic Monte Carlo simulates how the occupation of the sites changes over time. We derive a master equation that gives us probability distributions for what processes can occur and when these processes occur. The derivation is from first principles. Some general mathematical properties of the master equation are discussed and we show how a lattice-gas model simplifies the master equation so that it becomes feasible to use it as a basis for kinetic Monte Carlo simulations.

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Notes

  1. 1.

    Parts of Sect. 2.2.2 have been reprinted with permission from X.Q. Zhang, A.P.J. Jansen, Kinetic Monte Carlo method for simulation reactions in solutions, Phys. Rev. E 82, 046704 (2010). Copyright 2010, American Physical Society.

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Authors and Affiliations

  1. ST/SKA, Eindhoven University of Technology, Eindhoven, Netherlands

    A. P. J. Jansen

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Jansen, A.P.J. (2012). A Stochastic Model for the Description of Surface Reaction Systems. In: An Introduction to Kinetic Monte Carlo Simulations of Surface Reactions. Lecture Notes in Physics, vol 856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29488-4_2

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