Sensitivity of short-range trio interactions to lateral relaxation of adatoms: Challenges for detailed lattice-gas modeling

Sathiyanarayanan, Rajesh; Stasevich, Timothy J.; Einstein, T. L.

doi:10.1016/j.susc.2008.01.022

Cited by 12 publications

(13 citation statements)

References 42 publications

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“…10). To the extent that this value of Ed is reliable, 29 there remains a discrepancy between the NN-Ising theory and experiment a mystery. One possible explanation is the existence of other significant many-body interactions that make the calculated E d effective rather than actual.…”

Section: Discussionmentioning

confidence: 99%

“…Another possible explanation we are currently exploring suggests that calculated trio interaction energies can vary significantly between LDA and GGA calculations, whereas pair interactions remain unchanged. We are currently looking further into this issue for Pt on Pt systems, 29 where more asymmetry between A-and B-steps exists, and where results for kink-formation energies (which are directly related to E a and E b ) are known to be worse for GGA than for LDA. 25,30 In closing, we believe first-principle calculations such as the ones described here will prove useful in determining the limits of lattice gas models applied to all sorts of systems.…”

Section: Discussionmentioning

confidence: 99%

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Extended lattice gas interactions of Cu on Cu(111) and Cu(001):Ab initioevaluation and implications

2006

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We present ab-initio calculations of a variety of different lattice-gas interaction energies between Cu adatoms on Cu(001) and Cu(111). We find the next-nearest-neighbor (NNN) interactions to be negligible on Cu(111), explaining the success of the nearest-neighbor (NN) Ising model when describing the Cu(111) step stiffness. On Cu(001), however, we find that NNN interactions are roughly (1/7) the attractive NN interaction strength. On both surfaces, we find longer-range pair interactions to be small, although there are relatively large trio interactions. On Cu(111) these include two orientation dependent trios composed of adatoms forming a NN-triangle. We calculate the interaction energies of these trios and show that they can account for the difference in formation energies between A-and B-steps. On Cu(001), we find the trio interaction composed of adatoms forming a NN-isosceles right triangle to be quite large and repulsive. This contradicts our theoretical expectations, which suggest the interaction should be attractive to account for the Cu(001) step stiffness. Finally, by calculating the bulk energy per atom in multiple ways, we show our calculations are self-consistent.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Extended lattice gas interactions of Cu on Cu(111) and Cu(001):Ab initioevaluation and implications

2006

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“…Generally, a more complete set of pair and many-body interactions is determined systematically from ab-initio DFT calculations within a cluster expansion framework. 25,26,[135][136][137][138][139] This larger set of interactions provides the input for Monte Carlo or KMC simulation. The cluster expansion approach was initially developed to describe the configuration-dependent energetics of multi-component bulk metallic alloys, 140 where a rigorous framework for convergence has been developed.…”

Section: Stochastic Lattice-gas Modeling Of Equilibrium Nc Structurementioning

confidence: 99%

“…However, it is recognized that there are practical complications when applied to epitaxial NCs since lateral relaxation of atoms near the step edges, i.e., near the NC periphery, can be quite distinct from that in the NC interior. 137,138 Finally, we mention that novel refinements of conventional cluster expansion approaches may be more effective in some 2D epitaxial systems. 141 For 3D unsupported NCs, again fundamental insights into equilibrium shapes come from application of simple 3D Ising type models with pairwise interactions.…”

Section: Stochastic Lattice-gas Modeling Of Equilibrium Nc Structurementioning

confidence: 99%

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling

et al. 2019

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Self-assembly of ensembles of supported 2D or 3D nanoclusters (NCs) by surface deposition, and of unsupported 3D NCs by solution-phase synthesis, produces intrinsically nonequilibrium systems. Individual nanoclusters can have far-from-equilibrium shapes and composition profiles. The free energy of the ensemble can be lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening is key for, e.g., avoiding catalyst degradation. In this review, we focus on crystalline metallic NCs. Atomistic-level modeling of equilibration processes typically utilizes stochastic lattice-gas models to access appropriate time-and length-scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution. We also discuss modeling of coarsening including diffusion and decay of individual NCs, and unconventional coarsening processes. We describe high-level modeling integrated with STM studies for 2D epitaxial NCs, and developments in modeling for supported and unsupported 3D NCs motivated by in situ TEM studies.

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“…Most aspects of adatom multisite interactions have been discussed in detail with a special focus on phase boundary asymmetries [12,13,14]. A still unresolved issue in such calculations is the influence longer range pair interactions may have on the determination of trio-and quarto parameters.…”

Section: Introductionmentioning

confidence: 99%

Modelling the size of nitrogen c(2x2) islands on Cu(001) with elastic multisite interactions

Kappus¹

2021

Surface Science

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Sensitivity of short-range trio interactions to lateral relaxation of adatoms: Challenges for detailed lattice-gas modeling

Cited by 12 publications

References 42 publications

Extended lattice gas interactions of Cu on Cu(111) and Cu(001):Ab initioevaluation and implications

Extended lattice gas interactions of Cu on Cu(111) and Cu(001):Ab initioevaluation and implications

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling

Modelling the size of nitrogen c(2x2) islands on Cu(001) with elastic multisite interactions

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