Search

In this article we investigate the complex 1D mesoscopic model of adatom diffusion and the evolution of an ordered phase on the substrate surface. The analysis of the theoretical model is compared with the experimental results of the spreading of Au adatoms on Si(111)-(7×7) surface. The steady state solutions and their stability conditions are determined within the concept of the traveling-wave solution. It is shown that the formation of the ordered phase (5×2) and the difference in the diffusion of Au on (7×7) and on (5×2) structure results in a sharp edge of diffusion front which corresponds to the coverage of a saturated (5×2) phase. This edge moves linearly in time and α can be determined by experiment. The system of model equations enables the damped waves solution or temporary evolution of two steps.

A novel growth low temperature morphology is observed in the growth of Pb/Si(1 1 1) related to the kinetics of Quantum Size effects. This morphology is globally observed over mesoscopic distances. Bilayer height rings nucleate first at the island perimeter which spread out towards the center. With Monte Carlo simulations the morphology is reproduced with highly anisotropic diffusion (i.e., radial diffusion out of a ring of one lattice constant is slower than azimuthal diffusion by at least 10−5 at 180 K). This shows that both kinetics and energetics are responsible for the uniform height island formation and the similar temperature “window” ∼180 K independent of the initial Si interface.

We use Monte Carlo simulations to study the mobility and collective diffusion of mutually interacting adparticles on stepped surfaces. We consider the case of nearest–neighbor repulsive interactions together with different binding and activation energies at the step edges in the disordered phase. To complement previous work that focused on diffusion across steps, here we concentrate on diffusion along the steps in the case of strong step binding. We find that the collective diffusion behavior is dictated by a complex interplay between enhanced or suppressed diffusion along the lower step edge positions, binding at step edges, and interactions between adparticles. Diffusion along the lower step edge positions plays a particularly important role at low coverages, while at high coverages diffusion is governed mainly by adparticle interactions.

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

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.

Surface diffusion is studied in a two barrier system, i.e. a system with two different activation energies. The dynamic and thermodynamic properties of the system of interacting ad-atoms on an fcc(1 1 1) surface are studied using Monte-Carlo simulations, the Bortz–Kalos–Lebowitz algorithm and the Metropolis algorithm. The results are compared with our previous analytical calculations in the same system. Numerical results fit well to the analytical results for high temperatures. At low temperatures, contrary to previous analytical calculation (based on quasi-chemical approximation), we observe a sharp local minimum at a coverage Θ =0.5 in the case with repulsive interaction and a large difference between activation energies. The Monte-Carlo simulations result in a higher occupation of deep sites, formation of an ordered phase and in lower diffusion coefficient in comparison with the analytical results.

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.

The collective diffusion coefficient is studied for a system of particles adsorbed on a surface with two non-equivalent adsorption sites. The non-equilibrium conditions are characterized by the non-equilibrium distribution of atoms between adsorption sites with different energy of adsorption. The determination of the diffusion coefficient is based on the general theory published in [J. Phys. Condens. Matter. 12 (2000) 6343] and links to the former studies of the diffusion coefficient and phase diagrams of the same systems in equilibrium. Our analysis shows that non-equilibrium conditions strongly influence the step-like dependence of diffusion coefficient on coverage, as determined in equilibrium conditions for non-interactive adparticles, and that the diffusion coefficient can even have an opposite behavior. Far from equilibrium the appearance of a local maximum is observed. These deviations reflect the influence of the state of the adparticle system on their collective behavior.

Despite its importance in theoretical studies of surface diffusion there has been limited experimental progress in developing methods to measure the dynamic structure factor S(q,t). In this work we study gases adsorbed on single-crystal surfaces and show that their equilibrium dynamics is measurable in a diffraction experiment through density fluctuations described by the dynamic correlation function . Using a lattice-gas model with nearest-neighbor repulsive interaction, we demonstrate how to separate out the microscopic dynamics caused by diffusion and adsorption-desorption from the form of . Our analytical results show that decays as an exponential with a time constant {tau}(q). Significant deviations from the hydrodynamic dependence of 1/{tau}(q)=D{sub c}q{sup 2} are found with and without desorption. These deviations have important consequences in extracting diffusion constants from experiments. (c) 2000 The American Physical Society.

The interrelation between the surface symmetry and diffusion of adsorbed atoms is studied theoretically on a model face-centred cubic (fcc) (111) surface within the lattice-gas approximation. Diffusion proceeds through two non-equivalent sites on the fcc(111) surface. Short-range repulsive interaction between particles in the nearest-neighbour non-equivalent sites is considered. This repulsion leads to a modification of the occupation numbers of both kinds of site and to changes in the energy barrier height for diffusion. The chemical surface diffusion coefficient, D, has been found to be strongly dependent on coverage, Θ, the interaction strength between adatoms, and the difference between the activation energies, ΔE. In the case of a small ΔE value, the diffusion coefficient D increases with Θ, as was expected for repulsive interaction. In our model the increase of D at Θ=0.5 is reduced for higher values of ΔE and a local maximum of D(Θ) is observed.

We study the temperature and coverage dependence of an effective diffusion barrier assuming an Arrhenius shape of the chemical diffusion coefficient for a system of interacting particles. The previously published model of the diffusion of an fcc (111) surface with bivariate trap is used. The presence of two nonequivalent occupation sites and interaction result in a non-Arrhenius shape of the diffusion coefficient and a coverage- and temperature-dependent effective diffusion barrier. The temperature dependence of effective energy Ea shows a minimum at low temperatures (at approximately 150 K) for strong interactions. The coverage dependence of Ea has a deep minimum in the vicinity of Θ=1/2, even in a system without interaction.

Diffusion on a fcc(111) surface will be studied theoretically. Diffusion proceeds through non-equivalent hcp and fcc sites with different adsorption energy. Repulsive interaction between particles in the first neighbour sites and change of saddle point energy due to interaction are included. In this model the repulsion to the next neighbour site results in the inadequately increased diffusion coefficient. The large difference of adsorption energy between hcp and fcc sites depresses diffusion at higher coverages and diffusion coefficient has maximum at Θ=1/2. Inclusion of the change of the saddle point energy reduces increase of D and results in a tame local minimum, emphasizing a local maximum.

During deposition on a stepped surface the growth mode depends on the conditions such as temperature T, deposition rate F and width of the terraces w. In this work we studied the influence of all the above mentioned characteristics using the kinetic Monte Carlo (kMC) technique. We concentrated on the conditions on the terrace at the moment of the first nucleation. The critical density of monomers for nucleation ηm decreases with the width of the terrace and the nucleation starts at surprisingly low densities of monomers. We tested several definitions of the critical width for nucleation wc used in various articles in the past and we compared our results with results of the analytical steady-state mean-field model (Ranguelov and Altman 2007 Phys. Rev. B 75 245419). To check how the simplified assumption about the steady-state regime during deposition influences the resulting dependence of wc =/~ (D/F)(κ), we set and also solved a time-dependent analytical model. This analytical model as well as kMC predict that wc =/~ (D/F)(1/5). kMC simulation also shows that the Ehrlich-Schwobel barrier has only limited influence on the nucleation on the stepped surface at conditions close to the nucleation regime. For all widths of terraces there is a critical value of the Ehrlich-Schwobel barrier ΔE(c)(ES)/k(B)T ~ 7.3 (ΔE(c)(ES) ~0.11 eV at T = 175 K), and only below this critical value does the Ehrlich-Schwobel barrier affect the final value of the density of nuclei. The results of the kMC are summarized in a semi-empirical analytical formula which describes the dependence of the step-flow growth and nucleation on the terrace width w, diffusion coefficient D and deposition rate F. In our simulations we tested two models of the stepped surface with different thicknesses of the step, both with an Ehrlich-Schwobel barrier on the edge of the terrace.

An analytical expression for the surface diffusion coefficient is derived by summing the fluxes due to single jump events between adjacent sites on a simple square lattice. All microscopic configurations of a layer of interacting particles are included at particular coverages. In a quasi-chemical approach, the nearest-neighbour particle-particle interactions are introduced by adjusting the jump rate as well as by adapting the probability of occurrence of particular configurations consistent with the concentration. The diffusion coefficient is found to be dominated by the latter contribution at medium and high concentrations. A comparison with the results of Monte Carlo simulations shows that an improved approximation can be achieved if the interactions are accounted for not only by changes of the activation energy of diffusion but also by their effect on the equilibrium distribution of the particles.

The formation of the uniform height Pb islands on Si(111) is unusually fast and it is important to understand the driving forces responsible for it. The growth to bigger heights proceeds by bilayer rings nucleating first at the island perimeter, which spread out toward the island center. The rings have sharp growth fronts and it is challenging to explain this unusual morphology with the same set of barriers for island heights of the same stability, since nucleation is restricted to 2 layers. With Monte Carlo simulations, this nucleation morphology is reproduced and the corresponding potential-energy surface (PES) identified. The key barriers of the PES are very fast terrace diffusion (with barrier less than $50\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$), highly anisotropic diffusion (i.e., the azimuthal diffusion within a one-lattice-constant ring is 1000 times faster than radial diffusion toward the island center), and interlayer diffusion barriers for stable versus unstable islands differing by $0.11\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (for diffusion from the island top back to the wetting layer).

We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density rho in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient D(T)(rho) decreases monotonically up to the freezing transition, the collective diffusion coefficient D(C)(rho) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of D(T)(rho) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both D(T)(rho) and the angular diffusion coefficient D(R)(rho) decrease with rho. Also in this case D(C)(rho) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where D(C)(rho) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.

The surface diffusion of potassium on Pd{111} has been studied with photoelectron emission microscopy (PEEM) for coverages up to one monolayer. The coverage dependence of the chemical diffusion coefficient is determined by analysis of the concentration profiles obtained from the PEEM images with the Boltzmann–Matano method. The diffusion coefficient, D, decreases with increasing coverage but a local maximum is found at a coverage of Θ≈0.5 ML. The values of D at low coverages (Θ

We extend a standard theory of second-layer nucleation in the regime of low temperature, where the diffusion is the limiting process. The theory takes into consideration the fluctuations of the adatoms and the distribution of stable clusters on a surface, and yields an expression for the nucleation rate and time evolution of the density of stable clusters. When diffusion is slow, the fluctuations of the monomer distribution play an important role and results differ qualitatively and quantitatively from those obtained using the standard rate-equation approach to nucleation. We argue that in this case the standard theory fails because slow diffusion delays nucleation and the nucleation rate depends on the fluctuations of interatomic distances. It is shown that the final density of stable clusters depends on the fluctuations of the monomer and stable clusters distribution and can be even independent of the deposition rate, as was experimentally observed at low temperatures.

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.

The diffusion of single Pb atoms and the formation of stable clusters containing two and three Pb atoms on a Si(111)−(7×7) reconstructed surface was studied with variable temperature scanning tunneling microscopy (STM). The numbers of single Pb atoms and Pb atoms in clusters were monitored as a function of time. A new and simple statistical model describing diffusion was developed. This model enables us to estimate the diffusion coefficient and the activation energy of diffusion. The main advantage is the avoidance of questionable counting of jump events in successive STM images. For substrate temperatures of 308, 311, and 313 K we obtained diffusion coefficients of 8.1×10−18, 1.2×10−17, and 1.9×10−17 cm2 s−1, respectively, and the activation energy of diffusion equaled E=0.56±0.07 eV. The energy difference ΔE between the binding energies of single Pb atoms at faulted and unfaulted halves of the Si(111)−(7×7) unit cells was estimated to be 27±9 meV.

In this paper is demonstrated that the fading of the given glasses cannot be explained only by the ionization of trapping centres. We must consider the second process (the diffusion of oxygen in glasses) to explain the high fading of glasses on the base of P2O5.

The stochastic theory was applied to the description of the solidification of binary systems. This theory is suitable for the studying of the dependence of kinetic phase diagrams on the technological conditions. The general relations between the concentrations of the liquid and the solid phases and between the rate of the solidification and the thermodynamic potentials of both phases are presented. In the case the stationary solidification of the binary systems our results are compared with the results published in the previous papers. The dependences of the kinetic phase diagrams on the growth rate or on the diffusion are in a good agreement with the Monte-Carlo calculations. [Russian Text Ignored.]