Comment on “Surface diffusion near the points corresponding to continuous phase transitions” [J. Chem. Phys. 109, 3197 (1998)] (original) (raw)
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The Journal of Chemical Physics, 2007
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.
Vacuum, 2001
We present two methods of the Monte Carlo analysis of the chemical di!usion processes on solid surfaces. First method is based on the analysis of the decay of sinusoidal adsorbate density perturbations; the second one uses the Boltzmann}Matano procedure applied to the step-like density pro"le. The usefulness of both these methods is shown on extraction of the chemical di!usion coe$cient from the numerical results.We have applied our two methods to various realizations of 2D lattice gas systems, simulating di!usion of adsorbate on surfaces of crystal having hexagonal symmetry of adsorption sites. In particular we were interested in the dependence of the di!usion process on strength and sign of the interactions of the jumping adatom at its activated state. We have compared systems with the same equilibrium properties (same ordered and disordered phase structure) and di!erent interaction-dependent barriers for attractive and repulsive forces.
Many-particle surface diffusion coefficients near first-order phase transitions at low temperatures
Physical Review E, 2012
We analyze the collective surface diffusion coefficient, D c , near a first-order phase transition at which two phases coexist and the surface coverage, θ, drops from one single-phase value, θ + , to the other one, θ −. Contrary to other studies, we consider the temperatures that are sufficiently subcritical. Using the local equilibrium approximation, we obtain, both numerically and analytically, the dependence of D c on the coverage and system size, N , near such a transition. In the twophase regime, when θ ranges between θ − and θ + , the diffusion coefficient behaves as a sum of two hyperbolas, D c ≈ A/N |θ − θ − | + B/N |θ − θ + |. The steep hyperbolic increase in D c near θ ± rapidly slows down when the system gets from the two-phase regime to either of the single-phase regimes (when θ gets below θ − or above θ +), where it approaches a finite value. The crossover behavior of D c between the two-phase and single-phase regimes is described by a rather complex formula involving the Lambert function. We consider a lattice-gas model on a triangular lattice to illustrate these general results, applying them to four specific examples of transitions exhibited by the model.
Long-timescale simulations of diffusion in molecular solids
Physical Chemistry Chemical Physics, 2012
Kinetic processes play a crucial role in the formation and evolution of molecular layers. In this perspective we argue that adaptive kinetic Monte Carlo is a powerful simulation technique for determining key kinetic processes in molecular solids. The applicability of the method is demonstrated by simulating the diffusion of a CO admolecule on a water ice surface, which is an important process for the formation of organic compounds on interstellar dust grains. CO diffusion is found to follow Arrhenius behavior and the corresponding effective activation energy for diffusion is determined to be 50 AE 1 meV. A coarse graining algorithm is applied which greatly enhances the efficiency of the simulations at low temperatures, down to 10 K, without altering the underlying physical processes. Eventually, we argue that a combination of both on-and off-lattice kinetic Monte Carlo techniques is a good way for simulating large-scale processes in molecular solids over long time spans.
Collective surface diffusion near a first-order phase transition
Physical Review B, 2011
For a large class of lattice models we study the thermodynamic factor, Φ, of the collective surface diffusion coefficient near a first-order phase transition between two phases at low temperatures. In a two-phase regime its dependence on the coverage, θ, is Φ ≈ θ/[(θ − θ −)(θ + − θ)N ], where N is the number of adsorption sites and θ ± are the single-phase coverages at the transition. In the crossover between the two-phase and single-phase regimes Φ(θ) is shown to have a more complex behavior. The results are applied to a simple 2D lattice model.
Non-equilibrium surface diffusion in the O/W(110) system
1996
In this Letter, we present results of an extensive Monte Carlo study of the O/W(110) system under non-equilibrium conditions. We study the mean square displacements and long wavelength density fluctuations of adatoms. From these quantities, we define effective and time-dependent values for the collective and tracer diffusion mobilities. These mobilities reduce to the usual diffusion constants when equilibrium is reached. We discuss our results in view of existing experimental measurements of effective diffusion barriers, and the difficulties associated with interpreting non-equilibrium data.
Collective diffusion of O/W(110) at high coverages: Monte Carlo simulations
Surface Science, 2004
The diffusion coefficient of the O/W(1 1 0) system at low temperatures, below critical point, exhibits some interesting properties. It is observed that the activation energy of the diffusion process increases rapidly at the phase transition from disordered to the ordered (2 · 1) phase. It is possible to model this rapid change in the activation energy, by proper choice of the transition probabilities in the lattice gas model. This rapid increase of the activation energy is visible as the change of the scaling of the diffusion curves. In the present work we use the same transition rates to calculate the diffusion coefficient at higher densities from 0.5 to 1. Scaling function shows how the activation energy varies with density. The density dependence of the activation energy changes its character on coming from lower to higher temperatures, what can be related to the changes in the phase diagram.
Non-equilibrium surface diffusion in the system
Surface Science, 1996
In this Letter, we present results of an extensive Monte Carlo study of the O/W(110) system under non-equilibrium conditions. We study the mean square displacements and long wavelength density fluctuations of adatoms. From these quantities, we define effective and time-dependent values for the collective and tracer diffusion mobilities. These mobilities reduce to the usual diffusion constants when equilibrium is reached. We discuss our results in view of existing experimental measurements of effective diffusion barriers, and the difficulties associated with interpreting nonequilibrium data.
Modelling of diffusion from equilibrium diffraction fluctuations in ordered phases
Surface Science, 2008
Measurements of the collective diffusion coefficient D c at equilibrium are difficult because they are based on monitoring low amplitude concentration fluctuations generated spontaneously, that are difficult to measure experimentally. A new experimental method has been recently used to measure time-dependent correlation functions from the diffraction intensity fluctuations and was applied to measure thermal step fluctuations. The method has not been applied yet to measure superstructure intensity fluctuations in surface overlayers and to extract D c . With Monte Carlo simulations we study equilibrium fluctuations in Ising lattice gas models with nearest neighbour attractive and repulsive interactions. The extracted diffusion coefficients are compared to the ones obtained from equilibrium methods. The new results are in good agreement with the results from the other methods, i.e., D c decreases monotonically with coverage h for attractive interactions and increases monotonically with h for repulsive interactions. Even the absolute value of D c agrees well with the results obtained with the probe area method. These results confirm that this diffraction based method is a novel, reliable way to measure D c especially within the ordered region of the phase diagram when the superstructure spot has large intensity.
Monte Carlo study of phase transitions in a confined lattice gas
Physical review. B, Condensed matter, 1989
The phase diagram of a lattice gas confined between two parallel adsorbing walls is investigated via Monte Carlo simulation. For large wall separations, we find a line of first-order capillarycondensation transitions at chemical potentials shifted to smaller values, p(T), than the bulk value p", (T). We also find a line of first-order prewetting transitions, terminating in a prewetting critical point and intersecting the line of capillary-condensation transitions in a triple point where thin-film, thick-film, and "liquid" phases all coexist. Although such a rich phase diagram had been conjectured earlier on the basis of mean-field calculations and thermodynamic arguments, we believe this is the first confirmation by simulation. I. INTR@DUCTION The inAuence of confinement of a Auid on its bulk and surface phase transitions is a subject of considerable recent interest. ' The phase diagram of a Auid confined in slitlike geometry is predicted by mean-field treatments of lattice models and by density-functional theories of continuum Auids' to be extremely rich and a complete exploration of this by Monte Carlo simulation is not feasible. However, one of the main features of confinementthat of bringing the bulk liquid-gas phase transition into competition with those surface phase transitions occurring for an undersaturated bulkis evident in a restricted region of the full phase diagram, which we have explored in detail by simulation. Specifically, consider a Auid in contact with a reservoir at constant chemical potential p and temperature T, and confined between two identical parallel adsorbing walls separated by a finite distance H in the z direction, but of infinite area in the x and y directions. Interactions between the walls and the Auid are represented by an external potential which varies only with z (perpendicular to the walls). Then, if the attractive part of the wall potential is of "moderate" strength so that a first-order wetting transition, with its accompanying prewetting or thickto thin-film transition, ' occurs for a single wall (H=oo) the mean-field analysis of Refs. 2 and 3 suggests that the phase diagram is of the form depicted in Fig. 1(a). The genesis of such a diagram is best understood by reference to the (T,p) phase diagram for lattice-gas adsorption at a single wallsee Fig. 1(b). In this case, the prewetting line AB extends from the point of the wetting transition (T, p",) to the prewetting critical point (T"""p",) where the distinction between thick and thin adsorbed films disappears. Note that T & Tp & T, and T, is the the bulk critical temperature.