Diffusion of dysprosium on the (112) surface of molybdenum

Loburets, A. T.; Наумовец, А.Г.; Vedula, Yu. S.

doi:10.1016/s0039-6028(97)00830-3

Cited by 47 publications

(30 citation statements)

References 32 publications

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“…However, the problem is that the Boltzmann-Matano analysis can be applied to any profile to obtain D C ( ), and the equilibrium results are found only in the limit where scale invariance holds true, namely at long times when coverage profiles (x,t) collapse to a single scaling function when expressed as (x/ͱt). Recent experimental measurements 18,20 for (x/ͱt) have indeed shown that the asymptotic long-time region is very difficult to achieve, and the observed deviations from scale invariance 18,20 are a clear evidence of the nonequilibrium character of profile evolution. The obvious question that then arises is how closely related is the effective D C ( ) to its equilibrium counterpart.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…This is typically the case in profile evolution measurements of surface diffusion, 4,[15][16][17][18][19][20][21] where the equilibrium theory is often used to analyze the measurements. In situations where there are no ordered phases present, recent careful studies have shown 21,22 that very good agreement with the equilibrium results can be obtained when spreading occurs in the submonolayer regime without ordering effects.…”

Section: Introductionmentioning

confidence: 99%

“…In situations where there are no ordered phases present, recent careful studies have shown 21,22 that very good agreement with the equilibrium results can be obtained when spreading occurs in the submonolayer regime without ordering effects. However, in the case of strong interactions leading to ordered phases, experiments clearly indicate 18,20 that the diffusion behavior can be affected by nonequilibrium effects, leading to diffusion coefficients that depend on the time scale during which the spreading data are collected.…”

Section: Introductionmentioning

confidence: 99%

“…A case in point is the well-established BoltzmannMatano ͑BM͒ method, 6,23,24 which is commonly used 4,[14][15][16][17][18][19][20][21][22]25 to extract the collective diffusion coefficient D C ( ) as a function of coverage from scaled coverage ͑density͒ profiles. We have recently shown 26 through Monte Carlo simulations of a lattice-gas model of O/W͑110͒ that nonequilibrium effects can play a noticeable role under conditions where there are several ordered phases present at different coverages.…”

Section: Introductionmentioning

confidence: 99%

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

Nikunen

Vattulainen

Ala-Nissilä

2001

The Journal of Chemical Physics

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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.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Nikunen

Vattulainen

Ala-Nissilä

2001

The Journal of Chemical Physics

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“…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

Vattulainen

Ala-Nissilä

2002

The Journal of Chemical Physics

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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.

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Surface diffusion on metals, semiconductors, and insulators

Seebauer¹,

Jung²

Adsorbed Layers on Surfaces. Part 1: Adsorption on Surfaces and Surface Diffusion of Adsorbates

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Diffusion of dysprosium on the (112) surface of molybdenum

Cited by 47 publications

References 32 publications

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

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

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

Surface diffusion on metals, semiconductors, and insulators

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