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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.

One of the goals for growing low dimensional structures is to explore their electronic structure variation with size due to confinement. Recent experiments in Pb adsorption on Pb islands of stable and unstable height at low temperatures have shown a spectacular variation in the nucleated island density (∼60 times) as a function of height. With Monte Carlo simulations we can faithfully reproduce the observed morphologies with a single assumption that i c is different on stable and unstable islands. This shows that confinement can result in large oscillations of nucleation rates and adsorption.

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.

Pb diffusion on the Si(1 1 1)-7 × 7 surface was studied with 16 different energy barriers. As a part of general problem of diffusion in the unit cell, some characteristics of diffusion (as frequency factor, effective energy barrier or differences in binding energy) was found analytically as a steady state solution of the master equation. The probability distribution of the occupation of particular sites was compared with the result of the Monte Carlo simulation and the STM experiment. Starting from the values obtained with the semi-empirical extended Huckel approximation, the diffusion barriers were adjusted to obtain a reasonable coherence with the experiment. The results of MC simulation and the analytical solution agree quite well and reproduce the dynamics of a Pb atom in the 7 × 7 unit cell.

A careful study of electrochemical lithiation of a composite graphite electrode at elevated temperatures was performed using a potentiostatic intermittent titration technique. Special emphasis was placed on the stage 4 to stage 3 phase transition, occurring in the range of x (in Li x C6) between 0.12 and 0.22 (this corresponds to the partial dimensionless intercalation level θ ranging from 0 to 1). An abrupt increase in the Li chemical diffusion coefficient, D chem, when approaching the relative coverage level θ=1/3, and a specific non-Arrhenius shape of the plot of D chem vs. the inverse of the absolute temperature were observed. These two features of the phase transition seem to be in agreement with a recent thermodynamic model for adatoms diffusing on a surface with two considerably different barrier energy sites.

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.

We investigated phase diagram of a system of particles adsorbed on a lattice with two non-equivalent sites, the number of which in the elementary cell and adsorption energy is different. The repulsive lateral interaction between particles in the nearest neighbour non-equivalent sites is considered. The existence of phase transition was found, depending on the parameters of the system (the difference in adsorption energies and interaction energy) and on surface geometry. The phase diagram for repulsive interaction differs considerably from the phase diagram of an ordinary lattice gas with equivalent sites and shows non-monotonic dependence of the critical temperature T c on adparticle surface coverage θ .

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.

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.

The effect of deviations from equilibrium at the solid–liquid interface during steady-state directional solidification of binary alloys has been analysed. The analysis includes the solute trapping region wherein freezing is accompanied by an increase in the chemical potential of the solute as well as the domain in which solidification is associated with a decrease in chemical potential of both the components. The limits to constitutional undercooling and the interface liquid compositions at various interface velocities in the solute trapping region have been derived using a thermodynamic approach.

The effective energy barrier for diffusion, E a , has been previously determined as a function of coverage and temperature within a two-barrier model of diffusion, assuming an Arrhenius form of chemical diffusion coefficient. To determine the diffusion coefficient at a given temperature and coverage, we used previously published results based on the lattice gas model of non-interacting adatoms. The presence of two non-equivalent sites for adsorption and diffusion of atoms on a surface (with energy barriers E 1 , E 2 ) results in substantial changes to E a within coverage Θ , with a step-like shape having a value close to Θ =1/3. The temperature dependence of E a shows a slight minimum, and the Arrhenius shape (with constant E a ) seems to be good approximation of the relatively small differences in energy barriers E 1 , E 2 . We obtain considerable deviation from such an Arrhenius behaviour of diffusion when there is a large difference in the energy barriers.

We calculated the surface diffusion coefficient D as a function of coverage in the quasi-chemical approximation of a system of particles on a square lattice with two non-equivalent binding sites characterized by different activation energies E1 and E2 for diffusion. A short-range repulsive interaction between particles in the nearest neighbour non-equivalent sites is considered, resulting in the modification of these energies by δE. The thermodynamic and kinetic parts of D have been calculated separately, in order to estimate their contribution to the diffusivity at different concentrations. It has been found that D exhibits a step-like increase at a critical coverage Θc which varies from Θc=0.33 for δE=0 to Θc=0.5 for E1=E2. The origin of the concentration dependence of D is discussed in terms of the repulsion strength between particles and their jump-rate through the sites existing on the surface.

The chemical surface diffusion coefficient D has been determined for a lattice-gas model where diffusion proceeds through two non-equivalent lattice sites with different activation energies, E1 and E2. By calculating the thermodynamic factor as well as jump diffusion rate we obtain the coverage dependence of D as a function of the energy difference E1 − E2. No lateral interactions are considered. Depending on the sign of E1 − E2, the diffusion coefficient shows either a maximum or a step-like increase at a particular coverage, both of which develop into discontinuities in the limits of either E1 − E2 → ± ∞. In the case of the step-like behaviour of D, the variation of D can be classified as being due to a kind of diffuse phase transition between a low and a high diffusivity state, which in the limits is shown to be of first order.

The kinetics of the crystallization process in amorphous hydrogenated Si (a-Si:H) thin films induced by XeCl and ArF excimer laser pulses has been studied both experimentally and theoretically. Time-resolved reflectivity spectroscopy (TRR) has been used to monitor phase changes as a function of pulse energy density. The time of the recrystallization process, tr, has been determined experimentally. Independently of the wavelength of applied laser radiation, a strong minimum has been found in the tr versus energy density (E) curves. The theoretical simulations have been done with the non-equilibrium thermal model which includes a nucleation process. The results clearly demonstrate that the crystallization from the phase interface dominates for energy densities close to the melting threshold in contrast to the high energy density region where the nucleation and solidification in the subsurface region prevails.

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.

In this paper, we report the models of fast recrystallization processes in a-Si thin films. An important feature of the modeling of nucleation in a-Si films is the capability of allowing description of non-equilibrium solidification including the distribution of small crystalline clusters which can be responsible for visible photoluminescence. We integrate the results of the description of nucleation and growth on the phase interface of c-Si from a-Si or l-Si. The transient time, nucleation rate and growth rate were determined as a function of temperature and the position of local extremes of these functions were stated. The solidification velocity was calculated from the nucleation rate and growth rate with respect to the temperature distribution in a system. The suitability of the particular approximations and models is discussed.

By calculating the jump diffusion rate (Г) and the thermodynamical factor (Kd) for a layer of non-interacting particles on a lattice with the non-equivalent bond sites we show that the diffusion coefficient D = ГK d exhibits specific features as a function of coverage, such as steps or maxima at critical coverages, which correspond to phase transformations in the adlayer. The chemical potential of the adlayer is derived analytically from the free energy. The difference of binding energy between the two kinds of sites is described by a parameter k and it is shown that the chemical potential (or the thermodynamic factor) at the critical coverage indicates the existence of a diffuse phase transition which develops for k → 0 into a first-order point phase transition.

The capability of the laser-induced thermal desorption technique (LITD) to detect the migration of adsorbed oxygen on a semiconductor surface is demonstrated. The surface diffusion coefficient of oxygen on Ge{100}(2 × 1) has been measured for a constant initial coverage in a wide temperature range (220–650 K). The experimental results show that after an initial stage of fast refilling of the depleted area the diffusion process strongly slows down. In the first stage the data can be fitted by the solution of Fick's second law. Within this approximation of a constant diffusion coefficient, an extremely low activation energy (∼ 0.04 eV) is obtained. The observations suggest that the second stage in the refilling process is connected with an irreversible chemical reaction between adsorbate and substrate.

The linear theory of stability was applied to the study of the marginal stability of stationary directional solidification in binary systems with respect to the kinetic material parameter Γ characterizing the rate of phase transformation. The theory is not restricted to dilute solutions. It was determined that for any value of Γ there exists a critical value ω crit of the frequency of front perturbation and undercooling on the solidification front ΔT crit such that for undercooling ΔT ΔT crit the solidification process is stable. ω crit and ΔT crit depend on Γ. At lower values of Γ the solidification process is more stable. ω crit increases with increase of Γ. In this paper the quantitative dependences ΔT crit ( Γ ) and ω crit ( Γ ) are proposed for a particular type of materials. The transport properties of materials do not change these quantitative results. Stability analysis is general, but our particular calculations are limited to regular solutions.

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.

A dynamical description of surface diffusion is presented for a surface containing two non-equivalent bonding sites with different binding energies. Diffusion proceeds via single hopping events between adjacent sites which can be of both kinds. Dynamical coupling is introduced by assuming that the hopping rates into and out of one type of site depend on whether the adjacent site of the other kind is occupied or empty. The derivation starts out from the microscopic difference equations accounting for the single jump events for all possible configurations. These are then transformed into differential equations with continuous functions and solved by the method of finite differences. The activation energies for individual jumps serve as adjustable parameters. It is shown that the widely observed dependence of the diffusion coefficient on coverage also follows naturally from this model, although direct particle-particle interactions in the usual sense are specifically excluded. The influence of the substrate-adsorbate interaction and of the surface geometry on the diffusion process is also discussed.

Recent experiments on epitaxial growth of metals on graphene have shown a strong dependence of island densities on coverage. These investigations cannot be explained by the standard mean-field nucleation theories. To understand them, we extend to higher coverage the former theory of rate equations developed for the initial state of nucleation, in a system where adsorbate interaction is included. We account for that, in the case of high coverage, the repulsive interaction influences both the attachment of monomers to clusters and the mobility of atoms. In our work we analyze the modification of the dependence of the island density on coverage, temperature and F/D ratio. In some regimes our theory results in the experimentally observed substantial growth of island density with coverage for a high deposited amount and a weak dependence on deposition rate F. We also find out the local maxima in temperature dependence of island density, as a consequence of long-range repulsive interactions.

It is well-known that eutectics do not necessarily grow at the eutectic temperature, or with the eutectic composition. Thus, the eutectic point can be shifted due to nonequilibrium conditions in the system. This fact was observed in many experiments. We try to explain this behaviour on the basis of the study of phase transformation kinetics. We construct the kinetic phase diagrams within the framework of the nucleation theory as well as of the theory of growth on the phase interface. Our models are based on the molecular model of the difference in chemical potential of components for the liquid and solid phases. The proposed model describes the position of the eutectic point very well.

Results of the space experiments show the shift of the eutectic point in the PbCl 2 -AgCl system in the direction of the higher concentration of AgCl with an increase of the undercooling of the melt. In our paper we endeavour to explain this phenomenon on the basis of the study of nucleation kinetics in the system. Using the statistical methods of calculations of the probability of first critical nucleus creation in the system, a kinetic phase diagram is constructed, which corresponds to the experimental data. A molecular model (based on the energy of intermolecular binding) of the difference of chemical potential in liquid and solid phase is proposed in our work. This model describes the position of the eutectic point and the shape of the liquidus line in the equilibrium phase diagram very well.

The homogeneity of n-type Sn and S doped and semi-insulating Fe doped InP crystals is studied by luminescence topography, low temperature luminescence, and Raman scattering. As in GaAs nonrelational striations and faceting are the main sources of inhomogeneous impurity distribution in doped crystals and dislocations in semi-insulating ones. The fluctuations in free carrier concentration influencing the luminescence intensity are independently proved by Raman scattering spectra. Die Homogenitat von n-leitenden, Sn- und S-dotierten In P-Kristallen sowie von semi-isolierendcn, Fe-dotierten InP-Kristallen wird mittcls Lumineszenztopografie. Tieftemperaturlumineszenz und Ramanstreuung untersucht. Wie im GaAs bilden Striations und Fazettenbildung die Hauptquellen fur inhomogene Strorstellenvertcilung in dotiertcn Kristallen und Vcrsetzungen in semi-isolierenden. Die Fluktuationen der Konzentration freier Trager, die die Lumineszenzintcnsitat beeinflussen, werden unabhangig mittels Ramanstreuspektren uberpruft.

The influence of radiant heat transport and impurity distribution in a semi-transparent crystal-melt system on the morphological stability of a planar interface during the crystallization of semi-transparent binary dilute melt is studied in the framework of the linear theory. Our analysis shows that the influence of radiation on stability is complex. If radiant transport of heat is sufficiently strong, and the physical properties of liquid and solid phases differ considerably, radiation will influence the loss of stability of the crystal-melt interface. The loss iof stability can also occur when the impurity is absent. It is very evident in the case N S » N L α L >α S . In addition, radiation can enhance or reduce the stability of interface through the dependence on the relation between α S , α L and λ S , λ L for the case in which the values of N S,L are small. If λ S = λ L and λ S = λ L , the stability of interface is not influenced by radiation, though the radiation undercooling exists ( N S . L = 16 n 2 bT 3 m /(3 λ S . L α S , L . ), n is refractive index, b is Stefan-Boltzmann constant, T m is the equilibrium temperature of melting, α S.L is mean value of absorption coefficient, λ S.L is heat diffusivity and the indexes S, L correspond to the solid or liquid phases).

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).

The parameters ${\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t}$ and $\ensuremath{\Delta}{E}_{s}$ for Ag/Ag(111) describing the interlayer diffusion probability $p=({\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t}{e}^{\ensuremath{-}(\ensuremath{\Delta}{E}_{s}/kT)})$ have been measured by different methods. Different results are obtained for the prefactor ratio ${\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t},$ with ${\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t}g1$ extracted at low temperatures $Tl150\mathrm{K}$ while ${\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t}\ensuremath{\sim}1$ is extracted at higher temperatures $T=300\mathrm{K}.$ We examine as a possible reason for the discrepancy, the dependence of the step-edge barrier on the type of microscopic site (i.e., kinks vs straight-step sites) or whether long-range interactions play a role. Both factors can lead to non-Arrhenius temperature dependence. In addition we examine the conditions necessary for a steady state to hold in island decay experiments which are used to conclude ${\ensuremath{\nu}}_{s}/{\ensuremath{\nu}}_{t}\ensuremath{\sim}1$ and when such conditions are fulfilled for Ag/Ag(111).

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 suppressed by frequent interparticle collisions. We also study the role of memory effects for many-particle diffusion.

We investigate the thermodynamic properties of a system of particles adsorbed on a lattice with two nonequivalent sites, with different unit cell numbers and adsorption energies. We include lateral interactions between particles in the nearest-neighbor nonequivalent sites. We use the decoration-iteration transformation in order to reduce the problem to the Ising spin square ferromagnet in a magnetic field. The phase diagram of the system for the case of repulsive interaction differs considerably from the phase diagram of an ordinary lattice gas with equivalent sites and shows nonmonotonic dependence of the critical temperature ${T}_{c}$ on adparticle surface coverage $\ensuremath{\theta}.$ Using the real-space renormalization group method we also calculate adsorption isotherms and coverage dependencies of the isothermal susceptibility for attractive and repulsive interactions. These functions exhibit features characteristic for systems with simultaneous repulsive and attractive interactions. Results from Monte Carlo simulations are in good agreement with theory.

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.

I: Surface Diffusion at Equilibrium. Quasielastic Helium Scattering Studies of Surface Diffusion: The Diffusion Barrier A.P. Graham, J.P. Toennies. Experimental Aspects of Metal Particle Diffusion on a Silicon Surface J. Slezak, et al. Surface Dynamics of Stepped Si(001) Studied by Temporal LEED Spectroscopy K. Kammler. Electric Current Induced Asymmetry of Surface Diffusion - Instability of Vicinal Crystal Surfaces S.S. Stoyanov, et al. Memory Effects and Memory Functions in Surface Diffusion T. Hjelt, et al. Driven Diffusion in a Model of the O/W(110) System M.A. Zaluska-Kotur, et al. Surface Diffusion and Real-Space Renormalization Group A.A. Tarasenko, et al. Surface Diffusion Near Phase Transitions F. Nieto, et al. II: Surface Diffusion from Profile Evolution Methods. Surface Heterodiffusion in Adsorbed and Coadsorbed Overlayers of Li, Sr, and Cu on the W and Mo (112) Surfaces A.T. Loburets, et al. Metal Heterodiffusion on Metallic Surfaces: Case of Pb on Cu C. Cohen, et al. Step Effects on Surface Diffusion: A Comprehensive Study of CO on Pt(111) X. Xiao. Adsorption, Desorption, and Diffusion of Potassium on Metal and Oxide Surfaces G. Kerner, et al. III: Surface Diffusion Under Non-equilibrium Conditions. Dynamics of Interacting Adparticles Under Non-Equilibrium Conditions Z. Chvoj. Statistical-Mechanical Description of Nonequilibrium Processes in Interacting Lattice Gases V.S. Vikhrenko, et al. Model Studies of Collective Diffusion I. Vattulainen. Study of Non-Equilibrium Surface Diffusion From an Initial Step-Concentration Profile With a New Probability-Based Continuum Method M.R. Dudek, M.C. Tringides. IV: Diffusion Mechanisms in Growth Processes. Diffusion on and IN Surfaces: The Atomic Slide Puzzle J.W.M. Frenken, et al. Decay of Two-Dimensional Islands on Ag(110) K. Morgenstern, et al. Surface Morphology and dynamics: Using Ab-initio Total Energies to make the Most of STM Data P.J. Feibelman. Substrate-Mediated Interaction on Ag(111) Surfaces From First Principles K.A. Fichthorn, M. Scheffler. Diffusion of Adatoms and Small Clusters on Missing-Row-Reconstructed Surfaces F. Montalenti, R. Ferrando. Effects of Adsorbates on Submonolayer Growth M. Kotrla, et al. Surfactants in Semiconductor Heteroepitaxy: Thermodynamics and/or Kinetics? I. Markov. V: Substrate Effects and Surface Diffusion. Nonlinear Diffusion and Sliding Friction S.C. Ying, et al. Selective Activation Dynamics: A Minimal Path Approach L.Y. Chen, et al. Long Jumps in Surface Diffusion Investigated by Stochastic Equations R. Ferrando, et al. Analytical Kinetic Theory of Single-Particle and Collective Surface Diffusion S.Y. Krylov. Adatom Island Diffusion on Metal FCC(100) Surfaces O.S. Trushin, et al. Paths, Barriers, and Prefactors for Adatom Descent from Ag Clusters on Ag(111) T.S. Rahman, et al. Correlated Diffusion of Adatoms and Islands on the Low indexed Surfaces of Noble Metals and Alloys A.E. Evangelakis.

The direct evolution of submonolayer two-dimensional Au phases on the $\mathrm{Si}(111)\ensuremath{-}(7\ifmmode\times\else\texttimes\fi{}7)$ surface was studied in real time using the spectroscopic photoemission and low energy electron microscope located at the synchrotron radiation source ELETTRA. A finite area covered by 1 monolayer (ML) of gold with a steplike transition zone was prepared by evaporation in situ. Subsequent annealing resulted in the spread of the Au layer and the formation of laterally extended $\mathrm{Si}(111)\ensuremath{-}(5\ifmmode\times\else\texttimes\fi{}1)\ensuremath{-}\mathrm{Au}$ and $\mathrm{Si}(111)\ensuremath{-}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}\mathrm{Au}$ surface reconstructions. At a temperature around 970 K, the boundary of the gold-covered region propagates on the clean $\mathrm{Si}(111)\ensuremath{-}(7\ifmmode\times\else\texttimes\fi{}7)$ and exhibits a nonlinear dependence on time. The ordered $\mathrm{Si}(111)\ensuremath{-}(5\ifmmode\times\else\texttimes\fi{}1)\ensuremath{-}\mathrm{Au}$ plateau develops a separated front moving with constant velocity. Two values of the Au diffusion coefficients were estimated at a temperature of about 985 K: (1) ${D}_{7\ifmmode\times\else\texttimes\fi{}7}=5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}{\mathrm{cm}}^{2}{\mathrm{s}}^{\ensuremath{-}1}$ as the average diffusion coefficient for Au on a clean $\mathrm{Si}(111)\ensuremath{-}(7\ifmmode\times\else\texttimes\fi{}7)$ surface in the concentration range from 0.4 ML up to 0.66 ML and (2) ${D}_{5\ifmmode\times\else\texttimes\fi{}1}=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}{\mathrm{s}}^{\ensuremath{-}1}$ as the lower limit for the diffusion of single Au atoms on the $\mathrm{Si}(111)\ensuremath{-}(5\ifmmode\times\else\texttimes\fi{}1)\ensuremath{-}\mathrm{Au}$ ordered phase.

We present a theoretical investigation of the influence of domain boundaries on the Ge/Si(111)-5 × 5 phase using both large-scale DFT simulations and an analytical model. It is shown that different boundary types modify the atomic and electronic structure of the adjoining 5 × 5 domains in very different ways. A simple theoretical model, that describes the energy interaction J between the boundaries and the 5 × 5 phase, is presented and the interaction energy decay J(x) ≈ x(-n) for different domain boundaries is estimated. Additionally, the influence of the boundaries on the atomic and electronic structure of adatoms in the parental 5 × 5 phase is analyzed and it is argued that the presence of domain boundaries may strongly affect not only the physical but also the chemical properties of the Ge/Si(111)-5 × 5 phase.

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 have extended a recently proposed correlated cluster mean-field (CCMF) theory to two-dimensional binary alloys with interactions up to the next-nearest neighbors and investigated their critical behavior. A very good agreement with results from the renormalization group theory was obtained for the critical temperatures of a simple model. We finally successfully compared our results obtained using the CCMF with the results of Monte Carlo simulations for the case of ordering in a random Fe(0.5)Co(0.5) overlayer on the Cu(001) substrate. The proposed theory represents a numerically efficient alternative to existing approaches like the cluster variation method and Monte Carlo simulations.

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 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.

It is derived the method of the calculation of the solidification rate and the concentration of components in the solid phase during the solidification process of the n-component melt at the given undercooling. The calculations are performed in the framework of the stochastic theory of the kinetic phase diagrams, which were derived in the case of the steady-state processes. This is the question of the generalization of relations derived for the binary systems. [Russian Text Ignored].

In this work the influence of time dependence of temperature on kinetic processes during nucleation on a simple model is studied. The nucleation rate and the average effective radius of nuclei R is counted. It is proved that in the case of oscillating temperature the nucleation rate also oscillates and the rate of growth of radius R is directly proportional to frequency of temperature change.

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.]

This paper deals with the behaviour of ferromagnetic alloys in the region of magnetic phase transition. The temperature dependences of spontaneous magnetization, magnetic susceptibility and specific heat are discused. The theoretical results are compared with experimental data.