Correlated random walk in lattices: Tracer diffusion at general concentration

Tahir-Kheli, Raza; Elliott, R. J.

doi:10.1103/physrevb.27.844

Cited by 179 publications

(137 citation statements)

References 19 publications

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“…13,46,[48][49][50]52 Results at T ϭ590 K shown in Fig. 2͑b͒ reveal that indeed most of the coverage dependence of f T ( ,T) comes from the memory effects arising from the interparticle interactions.…”

Section: B Coverage Dependence Of F Tmentioning

confidence: 99%

“…This quantity is closely connected to earlier analytical works for the Langmuir gas model, [46][47][48][49][50][51] where in the high coverage limit →1,…”

Section: Directional Correlations In Single-particle Jumpsmentioning

confidence: 99%

“…20,[42][43][44][45] However, in the special case of the Langmuir gas model, 12 in which the only interaction between diffusing particles is the exclusion of double occupancy of lattice sites, the corresponding correlation factor f T L ( ) can be analytically estimated in various lattice geometries. [46][47][48][49][50][51][52] For the Langmuir gas, ⌫( )ϭ (1Ϫ ), where is the bare single-particle jump rate and (1Ϫ ) represents the blocking effect of occupied sites. The decomposition corresponding to Eq.…”

Section: B Coverage Dependence Of F Tmentioning

confidence: 99%

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Memory effects and coverage dependence of surface diffusion in a model adsorption system

et al. 1999

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We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W͑110͒ via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors in tracer and collective diffusion. We show that memory effects can be very pronounced deep inside the ordered phases and in regions close to first and second order phase transition boundaries. Particular attention is paid to the details of the time dependence of memory effects. The memory effect in tracer diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly influenced by both the critical effects related to long-wavelength fluctuations and the local order in the overlayer. We also analyze the influence of the memory effects on the effective diffusion barriers extracted from the Arrhenius analysis. For tracer diffusion, we find that the contribution from memory effects can be as large as 50% to the total barrier. For collective diffusion, the role of memory effects is in general less pronounced. ͓S0163-1829͑99͒03011-8͔

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Section: B Coverage Dependence Of F Tmentioning

confidence: 99%

“…This quantity is closely connected to earlier analytical works for the Langmuir gas model, [46][47][48][49][50][51] where in the high coverage limit →1,…”

Section: Directional Correlations In Single-particle Jumpsmentioning

confidence: 99%

Section: B Coverage Dependence Of F Tmentioning

confidence: 99%

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Memory effects and coverage dependence of surface diffusion in a model adsorption system

et al. 1999

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“…In ͑ii͒, generalized tracer diffusion coefficients, D tr , appear corresponding to a single species diffusing through a ''bath'' of the other species which generally has a different hop rate. 56,73 Condition ͑iii͒ indicates that the flux for species ␣ induced by a gradient in the coverage of the other species must vanish as ␣ →0; ͑iv͒ follows since diffusion cannot occur when ϭ1. It should be noted that the case h A ϭh B is exactly solvable in terms of the tracer diffusion coefficient for a noninteracting single-species lattice gas.…”

Section: Appendix C: Chemical Diffusion In Mixed Adlayersmentioning

confidence: 99%

From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations

Evans

Liu

Tammaro

2002

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant "hydrodynamic" regime of rapid diffusion of (at least some) reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations (RDEs) describing mesoscale spatialpattern formation in surface reactions. Formulation and implementation of these RDEs requires detailed analysis of chemical diffusion in mixed reactant adlayers, as well as development of novel hybrid and parallel simulation techniques. Disciplines Mathematics | Physics CommentsThe following article appeared in Chaos 12, 1 (2002) Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant ''hydrodynamic'' regime of rapid diffusion of ͑at least some͒ reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations ͑RDEs͒ describing mesoscale spatial pattern formation in surface reactions. Local adsorption, desorption, and reaction processes occurring in surface reactions, when combined with surface diffusion, produce a diverse variety of spatiotemporal pattern formation. A key feature of these systems is that both the hysteresis often observed in the reaction kinetics, and the characteristic length of spatial patterns on the order of m, are controlled by the very rapid surface diffusion of at least some reactant adspecies. Many aspects of these phenomena have been successfully elucidated via mean-field reaction-diffusion equation modeling, in which the effects of adlayer ordering are neglected or treated approximately. A more fundamental approach is presented here based on atomistic lattice-gas "LG… models. One could attempt direct simulation of atomistic LG models, but this approach is complicated by the large separation of time and length scales "due to adspecies hop rates many orders of magnitude above other rates…. Thus, we have developed another more appropriate strategy to ''exactly'' connect-the-length-scales from these atomistic LG models to the mesoscale pattern formation. Specifically, we treat directly this ''hydrodynamic'' regime of large hop rates utilizing special simulation models and procedures, coupled with a correct description of chemical diffusion in mixed reactant adlayers. This leads to development of exact reaction-diffusion equations for the hydrodynamic regime. In this report, we pay particular attention to recent developments in the description of chemical diffusion, which has a complicated tensorial nature since the presence of one adspecies can interfere with the diffusion of coadsorbed adspecies.

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“…Elliott [16], Holdsworth and Elliott [17] and eventually to the most efficient model of Moleko, Allnatt and Allnatt [18], but they are introduced by hand in diffusion models of interacting alloys. Inspired by the Manning method they are based on a tagging process of the atoms.…”

Section: Introductionmentioning

confidence: 99%

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

Barbe

Nastar

2006

Philosophical Magazine

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International audienceWe present an improvement of the self-consistent mean field (SCMF) approximation of the L._ij, which extends its applications to alloys presenting high jump frequency ratios. The theory uses a vacancy-atom exchange model which depends on temperature and local composition through thermodynamic and kinetic parameters. Kinetic correlations due to the vacancy mechanism are represented by a time dependent effective Hamiltonian. In the case of high jump frequency ratios it is shown that long return paths of the vacancy need to be considered, which is shown to be equivalent to introduce many-body long-range effective interactions. We compare this theory to existing formalisms and Monte Carlo simulations for systems both without and with atomic interactions

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Correlated random walk in lattices: Tracer diffusion at general concentration

Cited by 179 publications

References 19 publications

Memory effects and coverage dependence of surface diffusion in a model adsorption system

Memory effects and coverage dependence of surface diffusion in a model adsorption system

From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

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