Modeling of electron-stimulated mobility and disordering of adsorbed particles

The electron-stimulated mobility and the electron-stimulated disordering of adsorbed particles is studied for a two-dimensional lattice gas model on a square lattice using kinetical Monte Carlo simulations. Pairwise nearest-neighbor repulsive interactions are considered which induce c(2 × 2) ordering of the lattice gas at low temperatures around half coverage. Adsorbed particles are allowed to perform thermally activated as well as electron-induced jumps to nearest-neighbor sites. The calculations are performed taking full advantage of the numerical power of a supermassive parallel computer.

It was found that the electron-induced mobility of adatoms causes the complete breakdown of the c(2 × 2) ordering at low temperatures if the fraction of electron-induced jumps exceeds a critical value. The breakdown of the ordering is accompanied by substantial changes of the chemical and tracer surface diffusion coefficients.     

Backward-to-forward jump rates on a tilted periodic substrate

Driven diffusion of a Brownian particle along a one-dimensional lattice is investigated numerically on decreasing its damping constant. The notions of multiple jumps, jump reversal, and backward-to-forward rates are discussed in detail. In particular, we conclude that in the underdamped limit backward jumps are suppressed relative to forward jumps more effectively than previously assumed. The dependence of such a drive-controlled mechanism on the damping constant and the temperature is interpreted analytically.     

Diffusion in concentrated lattice gases

Journal of Statistical Physics - The diffusion of many particles on a lattice is an example of a correlated random-walk process. Recently the waiting-time distributions for two consecutive jumps of...     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

Long jump rates in surface diffusion: W on W(110)

We have reexamined the diffusion of W adatoms on W(110) using the field ion microscope. The diffusivity is in good agreement with previous results and reveals no unusual features, but from observations of the distribution of displacements, corrected for diffusion during temperature transients, we have for the first time been able to measure the temperature dependence of rates for nearest-neighbor and double jumps, as well as for vertical and horizontal transitions. Activation energies and frequency factors for all the long jumps are significantly larger than for single jumps, and a simple model is proposed to account for our observations.     

Vacancy diffusion in the Cu(001) surface I: an STM study

We have used the indium/copper surface alloy to study the dynamics of surface vacancies on the Cu(0 0 1) surface. Individual indium atoms that are embedded within the first layer of the crystal, are used as probes to detect the rapid diffusion of surface vacancies. STM measurements show that these indium atoms make multi-lattice-spacing jumps separated by long time intervals. Temperature dependent waiting time distributions show that the creation and diffusion of thermal vacancies form an Arrhenius type process with individual long jumps being caused by one vacancy only. The length of the long jumps is shown to depend on the specific location of the indium atom and is directly related to the lifetime of vacancies at these sites on the surface. This observation is used to expose the role of step edges as emitting and absorbing boundaries for vacancies.     

Percolation mechanism of the diffusion of impurity atoms in dense surface layers

The molecular dynamics method is used to study the migration of an impurity atom on an unfilled square lattice. The calculations are performed on a lattice containing 2¹² × 2¹⁴ sites at various values of the ratio p of the frequencies of jumps impurity and lattice atoms and various relative concentrations of vacancies ? _V . In the limit of vanishingly small concentrations of vacancies, ? _V ? 1, the present simulation results are in agreement with our previous analytical results. With increasing ? _V , the diffusion coefficient of impurity atoms predicted by the simulations exceeds the result of the analytical theory, a behavior that can be explained by the growing influence of vacancy clusters, voids on the surface, in which the impurity atom can travel long distances. This is most clearly seen in the case of highly mobile impurity atoms (p ? 1), where within the characteristic time of displacement of impurity atoms, lattice atoms remain practically immobile, and the problem appears to be closely related to the percolation problem. In this case, up to ? _V ≈ 0.3, the diffusion coefficient is independent of p; then, such a dependence appears, and the diffusion coefficient increases sharply with ? _V .     

Experimental study of lattice distortion in ellipsoid-like nano-crystallites of copper

The elastic state of embedded inclusions is of considerable importance to the properties of materials. The non-uniform lattice distortion in the inclusions in which the interfaces are shaped with variable curvature cannot be measured by usual experimental methods. In this paper, the lattice distortions in an ellipsoid-like nano-crystallite of copper were measured by means of the peak finding method in the central part of the HRTEM image. The effects of contrast delocalization are studied by HRTEM image simulations, which show that the measured spacings of peaks in the middle part of the crystallite can be considered approximately equal to the true spacings of columns. With the HRTEM method, our measured results show that the nano-crystallite is expanded in the short axis direction and compressed in the long axis direction. The results calculated with the elasticity theory incorporating interface tension consist with the experimental results of HRTEM.     

Modification of the donor-acceptor-pair luminescence in doped multi-thin film structures

A single crystal multi-thin film structure consisting of films with both donor and acceptor doping to almost compensation, and separated by intrinsic semiconductor layers of a thickness governed by the Bohr radius of the donor electron, is analyzed with respect to a possible modification of the Donor-Acceptor-Pair (DAP) luminescence band.Pronounced jumps in the DAP-distribution curve and consequently in the luminescence intensity band with spacings of the intrinsic layer thickness are manifested, which are the result of Coulomb interaction between donors of the one and acceptors of the neighbouring doped films. This photoluminescence property, not yet documented in the literature, can advantageously be used for the analysis of doped superlattice films. Doping layers of the described kind may even be introduced as probes in order to study the initial steps of diffusion or migration of impurity atoms into the bulk in luminescence active semiconductor materials.     

Diffusion in a heterogeneous medium for low concentrations

The equations describing diffusion on a heterogeneous lattice for low concentrations are considered taking into account lattice site blocking. It is shown that lattice site blocking cannot be disregarded in the case of a strongly heterogeneous lattice even for low concentrations. It is established that the equation with a fractional time derivative holds only in a bounded time interval. Anomalous diffusion, which is described by the equation with a fractional time derivative at the initial stage, must be described over long time periods by an ordinary diffusion equation with a concentration-dependent diffusion coefficient.     

Kinetics of the diffusion of an impurity atom on a fcc(111) surface

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is performed. The case of small surface coverages of both vacancies and impurity atoms is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, when the frequency of jump ω of the imurity atom is small, the diffusion coefficient of the impurity depends linearly on ω, whereas in the opposite case, a saturation occur and its dependence on the frequency of jumps of the impurity atom disappears.     

Das Energiespektrum und die mittlere freie Bahn der deformierenden Excitonen in Molekularkristallen

A study is made of the energy spectrum of a deforming exciton and its temperature dependence in molecular crystals. The mean free path and diffusion coefficient of the deforming exciton with respect to multi-phonon collisions with crystal lattice vibrations are theoretically determined. The possibility of distinguishing the propagation of excitation in molecular crystals in the form of deforming excitons from that in the form of non-deforming excitons and from the propagation of excitation by random jumps from one molecule to another is discussed on the basis of the theoretically derived temperature dependence of the diffusion coefficient of the deforming exciton.     

Site stability and pipe diffusion of hydrogen under localised shear in aluminium

This paper studies the effect of a plastic shear on the tetrahedral vs. octahedral site stability for hydrogen, in aluminium. Based on Density Functional Theory calculations, it is shown that the tetrahedral site remains the most stable site. It transforms into the octahedral site of the local hexagonal compact structure of the intrinsic stacking fault. The imperfect stacking is slightly attractive with respect to a regular lattice site. It is also shown that the shearing process involves a significant decrease of the energetic barrier for hydrogen jumps, at half the value of the Shockley partial Burgers vector, but not in the intrinsic stacking fault. These jumps involve a displacement component perpendicular to the shearing direction which favours an enhancement of hydrogen diffusion along edge dislocation cores (pipe diffusion). The magnitude of the boost in the jump rate in the direction of the dislocation line, according to Transition State Theory and taking into account the zero point energy correction, is of the order of a factor 50, at room temperature. First Passage Time Analysis is used to evaluate the effect on diffusion which is significant, by only at the nanoscale. Indeed, the common dislocation densities are too small for these effects (trapping, or pipe diffusion) to have a signature at the macroscopic level. The observed drop of the effective diffusion coefficient could therefore be attributed to the production of debris during plastic straining, as proposed in the literature.     

Lattice-assisted proton hopping in oxides at low temperatures

Stimulated diffusion of protons in oxides such as ABO₃ crystals and rutile TiO₂ is discussed in the context of quantum Brownian motion. A self-consistent lattice-assisted proton hopping (LAPH) model is developed by going from white noise (characteristic of the standard stochastic theory of superionic conduction) to colored noise in the Markovian limit. This model differs from the commonly used ion jump models in that the hydrogen diffusion rate prefactor is identified as a quantity proportional to the frequency of phonon assistance. Application of the quantum fluctuation–dissipation theorem suggests that the dynamic activation energy for diffusion is a function of a bath-mode frequency. The LAPH model can predict enhanced rates of barrier jumping at room temperature compared to thermally activated proton diffusion. This indicates that low-temperature solid oxide devices are potential candidates for use in hydrogen energy research. The LAPH model offers a valid explanation for the mechanism of high protonic mobility recently observed for TiO₂ in a picosecond transient pump-probe experiment. This unexpected dominant lattice relaxation channel must be considered as a new classical-like (but low-temperature) proton transfer mechanism. For vibration-assisted protonic jumps to occur at low temperature, the phonon assistance must be classified as a low-frequency vibration specific to each lattice.     

Theoretical description of adatom migration in two-dimensional highly-ordered states

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c() state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c() ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. Received 24 June 1998     

A Monte Carlo study of ionic transport in a simple cubic random alloy via the interstitialcy mechanism: effects of non-collinear and direct interstitial jumps

Self-diffusion and ionic conduction via the interstitialcy mechanism in a simple cubic, binary random alloy AB were investigated as a function of composition using Monte Carlo simulation. It was found that allowance for non-collinear jumps (partly) replacing concurrent collinear site exchanges leads to a reduction in diffusion correlation effects. This goes along with a shift of the diffusion percolation threshold to lower concentrations of the (more) mobile component B. Even stronger changes of mass and charge transport compared to an exclusively collinear interstitialcy scheme are observed for additional contributions of direct interstitial jumps. It is remarkable that for both extensions of interstitialcy mediated diffusion, the Haven ratio appears to be greater than unity in certain composition ranges poor in B. All results rely on the calculation of tracer and interstitialcy correlation factors in the simplest possible three-dimensional lattice structure. Yet they may have more general relevance to the interpretation of tracer self-diffusion data and ionic conductivity measurements on crystalline materials.     

Atomistic Modeling of Point Defects and Diffusion in Copper Grain Boundaries

The atomic structure of several symmetrical tilt grain boundaries (GBs) in Cu and their interaction with vacancies and interstitials as well as self-diffusion are studied by molecular statics, molecular dynamics, kinetic Monte Carlo (KMC), and other atomistic simulation methods. Point defect formation energy in the GBs is on average lower than in the lattice but variations from site to site within the GB core are very significant. The formation energies of vacancies and interstitials are close to one another, which makes the defects equally important for GB diffusion. Vacancies show interesting effects such as delocalization and instability at certain GB sites. They move in GBs by simple vacancy-atom exchanges or by long jumps involving several atoms. Interstitial atoms can occupy relatively open positions between atoms, form split dumbbell configurations, or form highly delocalized displacement zones. They diffuse by direct jumps or by the indirect mechanism involving a collective displacement of several atoms. Diffusion coefficients in the GBs have been calculated by KMC simulations using defect jump rates determined within the transition state theory. GB diffusion can be dominated by vacancies or interstitials, depending on the GB structure. The diffusion anisotropy also depends on the GB structure, with diffusion along the tilt axis being either faster or slower than diffusion normal to the tilt axis. In agreement with Borisov's correlation, the activation energy of GB diffusion tends to decrease with the GB energy.     

Direct absorption of gas-phase atomic hydrogen by si(100): A narrow temperature window

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1D nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase jumps. Our conclusions are confirmed by the analysis of two variants of this model.     

High-temperature transport in fluorites

The high-temperature fluorites are amongst the simplest materials to show superionic conductivity. In this paper the recent experimental and theoretical studies of the nature of disorder and transport in the halide fluorites is reviewed. The majority of the evidence is in favour of anion motion by discrete jumps and not by a cooperative liquid-like diffusion. It is also clear that the anions do not appreciably occupy the cube-centre interstitial sites of the lattice. The exact nature and extent of the disorder has still to be resolved, although the number of mobile defects appears to be relatively small.