Mobility, interdiffusion, and tracer diffusion in lattice-gas models of two-component alloys

Kehr, K. W.; Binder, Kurt; Reulein, SM

doi:10.1103/physrevb.39.4891

Cited by 105 publications

(75 citation statements)

References 42 publications

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“…As a result of this, we can consider the atom-vacancy multicomponent system as a one-component system with a well-defined selfdiffusion coefficient. 5,21 The connection between macroscopic phenomena of self-diffusion and microscopic transitions of atom vacancy is given by 22 …”

Section: Theorymentioning

confidence: 99%

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Impurity diffusion activation energies in Al from first principles

2009

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Activation energies for vacancy-mediated impurity diffusion in face-centered-cubic aluminum have been computed ab initio for all technologically important alloying elements, as well as for most of the lanthanides. The so-called five-frequency rate model is used to establish the limiting vacancy interchange process. Many elements were shown to be limited by Al-vacancy interchanges. For these elements we showed that the diffusion activation energy is rather close to that for Al self-diffusion, and additionally the diffusion preexponential factor is of the same order as that for Al self-diffusion. The diffusion activation energy is shown to exhibit a linear relation with the solute partial molar volume in Al. In contrast, transition metals are shown to deviate strongly from these generalities. Diffusion of transition-metal atoms is limited by solute-vacancy interchanges that require remarkably high activation energies. Transition-metal diffusivities in Al show strong trends with the number of d-valence electrons but not with partial molar volume.

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Section: Theorymentioning

confidence: 99%

“…In the limit of dilute solution and at equilibrium vacancy concentration, there will be one relevant diffusion coefficient for the solute X only. 21 Our calculations pertain to this limit. If X features metallic bonding and does not break the close-packed character of the Al matrix, the diffusion will be mediated through vacancy jumps.…”

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confidence: 97%

Impurity diffusion activation energies in Al from first principles

2009

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“…Reference 47 gives only a simple approximate analysis, and Ref. 74 gives only a partial ͑exact͒ analysis, prompting our more complete analysis of this problem. 75 In the above, A could be CO͑ads͒, and B could be O͑ads͒ ͑for COoxidation͒ or NO͑ads͒ ͑for the NOϩCO reaction͒, etc.…”

Section: Appendix C: Chemical Diffusion In Mixed Adlayersmentioning

confidence: 99%

“…From general considerations of transport theory, 47,74 gradients in the coverages induce diffusive fluxes, J A and J B , for species A and B, respectively. Arranging coverages and fluxes into two-component vectors, and J, then these are related by 8 ͑jamming͒.…”

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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“…Despite this fact, there has been little consideration of chemical diffusion in mixed adlayers, which are of relevance to these surface reaction systems. The primary exceptions are some analyses for LG models of ideal mixed adlayers ͑i.e., noninteracting adlayers except for exclusion of double-site occupancy͒ where both species are mobile, [10][11][12] and of stochastic mesoscale mean-field models 13 and simplistic LG models, [14][15][16][17] where one species is mobile and the other͑s͒ are immobile. In the latter case, one must effectively consider a percolative-type transport problem.…”

Section: Introductionmentioning

confidence: 99%

Chemical diffusion of CO in mixed CO+O adlayers and reaction-front propagation in CO oxidation on Pd(100)

Liu

Evans

2006

The Journal of Chemical Physics

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Within the framework of a realistic atomistic lattice-gas model, we present the theoretical formulation and simulation procedures for precise analysis of the chemical diffusion flux of highly mobile CO within a nonuniform interacting mixed CO+O adlayer on a Pd(100) surface. The approach applies in both regimes of relatively immobile unequilibrated and fairly mobile near-equilibrated O adlayer distributions. Spatiotemporal behavior in surface reactions is controlled by chemical diffusion in mixed adlayers. Thus, we naturally integrate the above analysis with a previously developed multiscale modeling strategy to describe mesoscale reaction front propagation in CO oxidation on Pd(100). This treatment avoids using a simplified prescription of chemical diffusion and reaction kinetics as in traditional mean-field reaction-diffusion equation approaches. KeywordsAtomistic lattice-gas model, chemical diffusion flux, reaction-diffusion equation, reaction-front propagation, computer simulation, diffusion in gases, oxidation, palladum, reaction kinetics, surface reactions, carbon monoxide Within the framework of a realistic atomistic lattice-gas model, we present the theoretical formulation and simulation procedures for precise analysis of the chemical diffusion flux of highly mobile CO within a nonuniform interacting mixed CO+O adlayer on a Pd͑100͒ surface. The approach applies in both regimes of relatively immobile unequilibrated and fairly mobile near-equilibrated O adlayer distributions. Spatiotemporal behavior in surface reactions is controlled by chemical diffusion in mixed adlayers. Thus, we naturally integrate the above analysis with a previously developed multiscale modeling strategy to describe mesoscale reaction front propagation in CO oxidation on Pd͑100͒. This treatment avoids using a simplified prescription of chemical diffusion and reaction kinetics as in traditional mean-field reaction-diffusion equation approaches.

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Mobility, interdiffusion, and tracer diffusion in lattice-gas models of two-component alloys

Cited by 105 publications

References 42 publications

Impurity diffusion activation energies in Al from first principles

Impurity diffusion activation energies in Al from first principles

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

Chemical diffusion of CO in mixed CO+O adlayers and reaction-front propagation in CO oxidation on Pd(100)

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