Diffusion of oxygen on tungsten (110)

2001

We study the nature of nonequilibrium effects in the collective diffusion coefficient DC(θ) vs the coverage θ as extracted from Boltzmann–Matano analysis of spreading coverage profiles. We focus on the temporal behavior of the profiles and study how the corresponding nonequilibrium effects in DC(θ) depend on the initial density gradient and the initial state from which the spreading starts. To this end, we carry out extensive Monte Carlo simulations for a lattice-gas model of the O/W(110) system. Studies of submonolayer spreading from an initially ordered p(2×1) phase at θ=12 reveal that the spreading and diffusion rates in directions parallel and perpendicular to rows of oxygen atoms are significantly different within the ordered phase. Aside from this effect, we find that the degree of ordering in the initial phase has a relatively small impact on the overall behavior of DC(θ). Also, although we find that nonequilibrium effects are clearly present in submonolayer spreading profiles, DC(θ) determined from such data approaches its asymptotic equilibrium behavior much more rapidly than in the case of full spreading. Nevertheless, in both cases there are noticeable deviations from equilibrium results that persist even at very long times and are strongest in ordered phases and in the vicinity of phase boundaries. These conclusions are confirmed by complementary studies of the temporal behavior of the order parameter φ(θ). Finally, we use DC(θ) and φ(θ) to determine the locations of phase boundaries and find such data to be clearly time dependent during full spreading. We conclude that nonequilibrium effects seem to be an inherent feature in profile evolution studies of surface diffusion in all cases where ordering plays a prominent role. This warrants particular care to be taken with profile spreading experiments.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Density profile evolution and nonequilibrium effects in partial and full spreading measurements of surface diffusion

Nikunen

2001

“…When these simulations were extended to much longer times ͑be-yond 10 6 MCS͒, these minor peaks vanished while all other structures in the data remained unchanged. What makes this finding interesting is the fact that Butz and Wagner 42 have conducted BM spreading experiments to consider the diffusion of oxygen on a W͑110͒ surface. While their studies are not fully comparable to ours due to the temperature range of 760-880°C in their study ͑corresponding to the disordered phase͒, some features of their findings may be compared to ours.…”

Section: B Boltzmann-matano Spreading: Even Terrace Widthsmentioning

confidence: 99%

“…The studies in Ref. 42 were conducted over large times ͑4-45 min͒ and large distances ͑several micrometers͒. Hence the experimental data are presumably influenced by nonequilibrium conditions ͑see Fig.…”

Section: B Boltzmann-matano Spreading: Even Terrace Widthsmentioning

confidence: 99%

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

Mašín

et al. 2007

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.

“…The BM method has been applied to a number of experiments [55][56][57][58][59][60][61] and simulation studies 44,45,[62][63][64][65] during the last few decades.…”

Section: Nonequilibrium Studiesmentioning

confidence: 99%

Effects of quenched impurities on surface diffusion, spreading, and ordering of O/W(110)

Nikunen

2002

We study how quenched impurities affect the surface diffusion and ordering of strongly interacting adsorbate atoms on surfaces. To this end, we carry out Monte Carlo simulations for a lattice-gas model of O/W͑110͒, including small concentrations of immobile impurities which block their adsorption sites. We examine the behavior of the diffusion coefficients and order parameters as a function of coverage corresponding to various ordered phases at low temperatures. The effects of impurities are examined under both equilibrium and nonequilibrium conditions, and the results are compared to recent studies on a completely clean surface. We find that even minute impurity concentrations affect the diffusion behavior considerably in equilibrium. The effects are strongest in ordered phases and close to phase boundaries, where quenched impurities lead to a reduction of order, which in turn leads to significant changes in the collective diffusion and phase behavior. As the impurity concentration is increased to a level of a few percent of the total surface area, the reduction in order becomes particularly prominent at high coverages. Further studies under nonequilibrium conditions reveal that nonequilibrium effects are strong in the absence of impurities, while for surfaces covered by impurities the nonequilibrium effects are relatively weaker.