Z. Chvoj

Irreversible thermodynamics and true thermal state dynamics in view of generalised solid-state reaction kinetics

Reaction dynamics of processes involving solids are extensively studied by thermal analysis methods. They are often solved almost naively by analogy with apparently gradientless homogeneous reactions. Other oversimplified approximations involve the regular shape of reacting particles that are assumed to be circles or spheres regardless of their true texture (stereology). This model never matches the results of traditional morphology observations. This article points the direction where a more rigorous solution should go by introducing a more actual state of the sample but, unfortunately, is yet unable to show the practical way how to actually bring in the challenge of entire introducing fluxes incorporation which solution makes difficult mathematical problem but it enables wide options of state of the system. Practical examples are illustrated on the flux-dependent growth of dendrites.

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

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 OW(110), where steps are described by an additional binding energy EB 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 p(2x1) phase, whose periodicity Lp 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 [p(2x1) and p(1x2)], and the step-induced ordering due to the enhanced binding at the lower step edge position. The latter case favors the p(2x1) 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 (LLp is noninteger), the mismatch gives rise to frustration, which eliminates the effect of steps provided that EB 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 (LLp is an integer), 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 p(2x1) and p(1x2) structures on a flat surface. This effect is particularly strong for narrow terraces, yet it persists up to about L approximately 25Lp for small EB and up to about L approximately 500Lp for EB, 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.

Theoretical approaches to collective diffusion on stepped surfaces

We study collective diffusion of adsorbed particles on stepped surfaces using analytic and numerical techniques. We employ the Langmuir lattice gas model where the distribution of adatoms on the surface is solely determined by the difference in adsorption energy of atoms on terraces and along step edges. For the system in equilibrium, we consider the master equation approach for collective diffusion across the steps within the dynamic mean field approximation. We demonstrate that results obtained for the collective diffusion coefficient Dc(Θ) are sensitive to the choice of relevant slow variables for inhomogeneous systems such as stepped surfaces. Next, we consider diffusion across steps in situations where the system is not in equilibrium such as during spreading or ordering. To this end, we consider a phenomenological theory using balance between particle fluxes across a stepped surface within the linear response theory. This allows us to derive expressions for effective diffusion coefficients in the limit of large and small coverages, where the results agree well with Dc(Θ) in the corresponding limits.

Non-equilibrium effects in profile spreading on stepped surfaces

Abstract We study non-equilibrium effects in spreading and collective diffusion of adatoms on stepped surfaces through Monte Carlo simulations of a lattice-gas model. The spreading density profiles are analyzed by the Boltzmann–Matano method to determine the temporal behavior of the effective collective diffusion coefficients. We find that the presence of steps induces considerable non-equilibrium effects in diffusion. For spreading along the steps, we find that these deviations can be explained by the slow approach of the different adparticle concentrations on terraces and at step edges towards equilibrium. For spreading across the steps, however, we find no such dependence, indicating the breakdown of the linear response theory at early times.

Dynamics of adsorbed atoms under non-equilibrium conditions

This paper deals with the determination of the tracer (DT ) and chemical (Dch ) surface diffusion coefficients in the presence of a gradient of the coverage . The lattice gas model and quasi-chemical approximation are taken as accepted in the theory. The results are discussed with respect to the interaction energy of particles, which influences the equilibrium energy of atoms as well as the saddle-point energy. Such interactions break the symmetry of jumps in the systems with gradient grad . This model predicts a decrease of DT with the square of the gradient of the coverage .Dch depends on the coefficient of proportionality of the difference between the mean jump rate in the direction of grad and that in the opposite direction. It has been found that, in the case of repulsive interaction, the coverage dependencies of DT and Dch have local maxima, whose positions depend on the rates of change of the saddle-point energy and of the equilibrium energy of the atoms due to the interaction. For attractive interaction, DT either decreases with or increases depending on the saddle-point energy changes. At low temperatures our results differ substantially from those of the calculations made within dynamical mean-field theory.

Nonequilibrium effects in diffusion of interacting particles on vicinal surfaces

We study the influence of nonequilibrium conditions on the collective diffusion of interacting particles on vicinal surfaces. To this end, we perform Monte Carlo simulations of a lattice-gas model of an ideal stepped surface, where adatoms have nearest-neighbor attractive or repulsive interactions. Applying the Boltzmann-Matano method to spreading density profiles of the adatoms allows the definition of an effective, time-dependent collective diffusion coefficient D(C) (t)(theta) for all coverages theta. In the case of diffusion across the steps and strong binding at lower step edges we observe three stages in the behavior of the corresponding D(xx,C) (t)(theta). At early times when the adatoms have not yet crossed the steps, D(xx,C) (t)(theta) is influenced by the presence of steps only weakly. At intermediate times, where the adatoms have crossed several steps, there are sharp peaks at coverages theta<1L and theta>1-1L, where L is the terrace width. These peaks are due to different rates of relaxation of the density at successive terraces. At late stages of spreading, these peaks vanish and D(xx,C) (t)(theta) crosses over to its equilibrium value, where for strong step edge binding there is a maximum at theta=1L. In the case of diffusion in direction along the steps the nonequilibrium effects in D(yy,C) (t)(theta) are much weaker, and are apparent only when diffusion along ledges is strongly suppressed or enhanced.

Prefactors for interlayer diffusion on Ag/Ag(111)

Interlayer diffusion controls the transfer of atoms between layers in a film and is the key factor determining whether growth is layer-by-layer or two-dimensional. Analysis of recent experimental data on Ag/Ag(111) taken at two sets of temperatures provides similar values for the step edge barrier ?Es but not for the ratio of the prefactors ?s/?t where ?t is the prefactor for diffusion on a terrace and ?s the prefactor at a step edge site. A prefactor ratio larger than 1, 1

The surface collective diffusion coefficient and diffuse phase transformations

>?s/?t > 1, is extracted from the measurements at low temperature (T ?s/?t > 1, in good agreement with the low temperature experiments.

Many-particle diffusion in continuum: Influence of a periodic surface potential

We study the temperature dependence of the collective diffusion coefficient Dc(T) of adsorbed particles during a diffuse first-order phase transformation. In the case where the phase transformation proceeds within a finite temperature interval where two phases coexist, the temperature dependence of the collective diffusion coefficient can show a local extremum in the vicinity of the critical temperature. The local extremum depends on the difference of the diffusion coefficients of the two phases and on the course of the phase transformation. The analytical behaviour of Dc(T) in the vicinity of the critical temperature Tc is characteristic for the evolution of the phase transformation. Results are given for two typical examples.

Stability, interaction and influence of domain boundaries in Ge/Si(111)-5 × 5.

We study the diffusion of Brownian particles with a short-range repulsion on a surface with a periodic potential through molecular dynamics simulations and theoretical arguments. We concentrate on the behavior of the tracer and collective diffusion coefficients DT(θ) and DC(θ), respectively, as a function of the surface coverage θ. In the high friction regime we find that both coefficients are well approximated by the Langmuir lattice-gas results for up to θ≈0.7 in the limit of a strongly binding surface potential. In particular, the static compressibility factor within DC(θ) is very accurately given by the Langmuir formula for 0⩽θ⩽1. For higher densities, both DT(θ) and DC(θ)show an intermediate maximum which increases with the strength of the potential amplitude. In the low friction regime we find that long jumps enhance blocking and DT(θ) decreases more rapidly for submonolayer coverages. However, for higher densities DT(θ)/DT(0) is almost independent of friction as long jumps are effectively suppresse...