Interplay between steps and nonequilibrium effects in surface diffusion for a lattice-gas model of O∕W(110)

Abstract

Dependence of the self-diffusion coefficient on the sorbate concentration: A two-dimensional lattice gas model with and without confinement J. Chem. Phys. 111, 1658 (1999); 10.1063/1.479425 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. The authors consider the influence of steps and nonequilibrium conditions on surface diffusion in a strongly interacting surface adsorbate system. This problem is addressed through Monte Carlo simulations of a lattice-gas model of O / W͑110͒, where steps are described by an additional binding energy E B at the lower step edge positions. Both equilibrium fluctuation and Boltzmann-Matano spreading studies indicate that the role of steps for diffusion across the steps is prominent in the ordered phases at intermediate coverages. The strongest effects are found in the p͑2 ϫ 1͒ phase, whose periodicity L p is 2. The collective diffusion then depends on two competing factors: domain growth within the ordered phase, which on a flat surface has two degenerate orientations ͓p͑2 ϫ 1͒ and p͑1 ϫ 2͔͒, and the step-induced ordering due to the enhanced binding at the lower step edge position. The latter case favors the p͑2 ϫ 1͒ phase, in which all adsorption sites right below the step edge are occupied. When these two factors compete, two possible scenarios emerge. First, when the terrace width L does not match the periodicity of the ordered adatom layer ͑L / L p is noninteger͒, the mismatch gives rise to frustration, which eliminates the effect of steps provided that E B is not exceptionally large. Under these circumstances, the collective diffusion coefficient behaves largely as on a flat surface. Second, however, if the terrace width does match the periodicity of the ordered adatom layer ͑L / L p is an integer͒, collective diffusion is strongly affected by steps. In this case, the influence of steps is manifested as the disappearance of the major peak associated with the ordered p͑2 ϫ 1͒ and p͑1 ϫ 2͒ structures on a flat surface. This effect is particularly strong for narrow terraces, yet it persists up to about L Ϸ 25L p for small E B and up to about L Ϸ 500L p for E B , which is of the same magnitude as the bare potential of the surface. On real surfaces, similar competition is expected, although the effects are likely to be smaller due to fluctuations in terrace widths. Finally, Boltzmann-Matano spreading simulations indicate that even slight deviations from equilibrium conditions may give rise to transient peaks in the collective diffusion coefficient. These transient structures are due to the interplay between steps and nonequilibrium conditions and emerge at coverages, which do not correspond to the ideal ordered phases.

Surface diffusion near first-order phase transitions for a model on a triangular lattice

“…Clearly, the theoretical formulae are in very good agreement with the numerical values within the intervals of their validity. Thus, formula (11) is very accurate in the two-phase regions, formula (12) in the crossover regions and formula (14) in the single-phase regions. Since the crossover and single-phase regions are very narrow, the coverage dependences of Φ n within them are detailed in the insets to figures 5-8.…”

“…Remark. In fact, in [16] we derived formula (12) only for the case g α ± = 1. However, one may readily refine its derivation given there to extend it to general g α ± .…”

“…Note that, by equation (12), in either crossover region the thermodynamic factor has the general form Φ n (θ…”

Many-particle surface diffusion coefficients near first-order phase transitions at low temperatures

“…One of the intriguing problems that has attracted particular attention is the presence of phase transitions and their effects on surface diffusion. Since lattice gases can be used to model such transitions, they have provided a convenient framework also in this regard [7,8,[11][12][13][14][15][16][17][18][19][20]. However, below critical temperatures ordered phases may arise due to lateral interactions, and sophisticated arguments should be applied to analyze surface diffusion [7].…”

Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

“…When, however, adsorption sites are not equivalent, collective diffusion does depend strongly on the adsorbate density even in the absence of interactions other than the site blocking. [15][16][17][18][19][20][21][22] Adsorption sites may be nonequivalent due to interactions with the substrate 23,24 or because the surface is stepped. 25,26 In this work we discuss the collective diffusion in 2D systems in which interactions are limited to the site blocking only, but the local site potential-energy landscape changes from site to site, i.e., when the underlying substrate is not homogeneous.…”