The microscopic theory of diffusion-controlled defect aggregation

1998

Abstract The kinetics of diffusion-controlled aggregation of primary Frenkel defects ( F and H centers) in irradiated CaF 2 crystals is theoretically studied. Microscopic theory is based on the discrete-lattice formalism for the single defect densities (concentrations) and the coupled joint densities of similar and dissimilar defects treated in terms of the Kirkwood superposition approximation. Conditions and dynamics of the efficient F center aggregation during crystal heating after irradiation are analyzed.

Anomalous Kinetics of Diffusion-Controlled Defect Annealing in Irradiated Ionic Solids

2017

The authors thanks A. Ch. Lushchik, M. Izerrouken, and V. Lisitsyn for stimulating discussions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euroatom research and training programme 2014-2018 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. R.V. acknowledges the financial support by the MEIC (Ministerio de Economa, Industria y Competitivad; Project ENE2015-70300-C3-1-R). The calculations were performed using facilities of the Stuttgart Supercomputer Center (Project DEFTD 12939).

A Lotka-type model for oscillations in surface reactions

1997

In this paper we introduce a reaction model on a lattice which leads to oscillations. The model consists of two monomolecular and one bimolecular reaction step and is related to the Lotka model. Despite the simple evolution rules, the model shows a complex behaviour (i.e. the appearance of oscillations). This offers us the opportunity to test different types of stochastic approximations and compare them with the results of a Monte Carlo simulation. The simulation is performed on a large lattice (L = 1024) in order to take long-range correlations into account. Comparing the results of this simulation with the stochastic approaches shows that only advanced numerical approximations are able to…

Microscopic theory of colloid formation in solids under irradiation

1996

Results of the first-principles study of diffusion-controlled aggregation of Frenkel defects-interstitial atoms-under irradiation of solids are presented. Conditions of the efficient radiation-induced aggregation of vacancies and interstitials are studied and the scenario of this process is presented.

Kinetic model for surface reconstruction

2002

Institut fu ¨r Physikalische und Theoretische Chemie, Technische Universitat Braunschweig, Hans-Sommer-Strase 10,38106 Braunschweig, Germany~Received 7 December 2001; published 25 July 2002!A microscopic kinetic model for the ab @e.g., hex131 for Pt~100! and 132131 for Pt~110!#surface reconstruction is investigated by means of the mean field approximation and Monte Carlo simulations.It considers homogeneous phase nucleation that induces small surface phase defects. These defects can grow ordecline via phase border propagation in dependence on the chemical coverage by an adsorbate A ~CO!.Anasymmetry in the adsorbate surface diffusion from one surface phase to the other gives rise to two criti…

Statistical characterization of self-assembled charged nanoparticle structures

2013

We propose a novel approach for description of dynamics of nanostructure formation for a system consisting of oppositely charged particles. The combination of numerical solution of analytical Bogolyubov–Born–Green–Kirkwood–Yvon (BBGKY) type equation set with reverse Monte Carlo (RMC) method allows us to overcome difficulties of standard approaches, such as kinetic Monte Carlo or Molecular Dynamics, to describe effects of long-range Coulomb interactions. Moreover, this allows one to study the system dynamics on realistic time and length scales. We applied this method to a simple short-range Lenard–Jones (LJ)-like three- (3D) and two-dimensional (2D) system combining the long-range Coulomb an…

Kinetic Monte Carlo modeling of Y2O3 nano-cluster formation in radiation resistant matrices

2018

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

Radiation-induced defects in sapphire single crystals irradiated by a pulsed ion beam

2020

Abstract The luminescence and thermal stability of defects formed in α-Al2O3 single crystals after powerful (300 keV) pulsed irradiation with C+/H+ ion beam were investigated. It was found by measuring of optical density, photoluminescence, and pulsed cathodoluminescence that ion irradiation induces both single F-, F+-centers and F2-type aggregate centers. An intense thermoluminescence band with a complex shape was observed in the broad temperature range of 350–700 K, its intensity decreases with increasing of the energy density of the ion beam. The thermal stability of the F-type defects produced in α-Al2O3 after irradiation with a pulsed ion beam is comparable to that in neutron-irradiate…

Thermal annealing of radiation damage produced by swift 132Xe ions in MgO single crystals

2020

Abstract The annealing kinetics of the electron-type F+ and F color centers in highly pure MgO single crystals irradiated by 0.23-GeV 132Xe ions with fluences covering three orders of magnitude (Φ = 5 × 1011 –3.3 × 1014 ions/cm2) are studied experimentally via dependence of the optical absorption on preheating temperature. The annealing data are analyzed in terms of the diffusion-controlled bimolecular reactions between F-type centers and complementary interstitial oxygen ions. The behavior of the main kinetic parameters – the migration energies and pre-exponential factors – for different irradiation fluences is discussed and compared with that for other wide-gap binary materials from previ…

The kinetics of defect aggregation: A novel lattice formalism

1995

We introduce a stochastic model for the A + B → O reaction on a discrete lattice. The system may include mono- and bimolecular steps (i. e. reaction and diffusion steps). The resulting infinite chain of equations is truncated at a certain level via a modified Kirkwood approximation.

Evidence for the formation of two types of oxygen interstitials in neutron-irradiated α-Al2O3 single crystals

2021

Authors are indebted to R. Vila for stimulating discussions. Tis work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under Grant agreement No 633053. The views and opinions expressed herein do not necessarily refect those of the European Commission. In addition, the research leading to these results has received funding from the Latvian grant LZP-2018/1-0147 (EV). Institute of Solid State Physics, University of Latvia as the Center of Excellence is supported through the Framework Program for European universities Union Horizon 2020, H2020-WIDESPREAD-01–2016–2017-TeamingP…

Monte Carlo simulations of the periodically forced autocatalyticA+B→2Breaction

2000

The one-parameter autocatalytic Lotka-like model, which exhibits self-organized oscillations, is considered on a two-dimensional lattice, using Monte Carlo computer simulations. Despite the simplicity of the model, periodic modulation of the only control parameter drives the system through a sequence of frequency locking, quasiperiodic, and resonance behavior.

The A + B → 0 reaction on a disordered lattice

1996

Abstract In this paper a stochastic model for the A + B → 0 reaction with creation of particles on a disordered surface is studied for d = 2 and d = 3 spatial dimensions. Densities and correlations of the particles are examined in detail. We find that the stationary state which exists for d = 3 in case of an ordered lattice vanishes in the case of a disordered lattice. A stationary state for d = 2 never exists.

Global Synchronization via Homogeneous Nucleation in Oscillating Surface Reactions

1999

The mechanism leading to globally synchronized oscillations in the $\mathrm{CO}+{\mathrm{O}}_{2}/\mathrm{Pt}\left(110\right)$ reaction system is investigated by means of Monte Carlo simulations. The model considers the reconstruction of the surface via phase border propagation and spontaneous phase nucleation. The reason for global oscillations turns out to be the spontaneous phase nucleation. This nucleation, which is modeled as a weak noise process, results in a random creation of dynamic defects and leads to global synchronization via stochastic resonance. The mechanism of global coupling via the gas phase, as it is proposed to date, does not occur.

Peculiarities of the diffusion-controlled radiation defect accumulation kinetics under high fluencies

2020

We are grateful to A. Lushchik and E. Shablonin for numerous and valuable discussions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

The Two Types of Oxygen Interstitials in Neutron‐Irradiated Corundum Single Crystals: Joint Experimental and Theoretical Study

2021

Pattern Formation Kinetics for Charged Molecules on Surfaces: Microscopic Correlation Function Analysis

2011

The kinetics of pattern formation and phase separation in a system of two types of oppositely charged molecules with competing short- and long-range interactions on surfaces/interfaces is studied combining three methods: a microscopic formalism of the joint correlation functions, reverse Monte Carlo, and nonequilibrium charge-screening factors. The molecular ordering occurs on the background of the Ostwald ripening and thus is strongly nonequilibrium. We have demonstrated how initial random distribution of molecules is changed for loose similar-molecule aggregates, with further reorganization into dense macroscopic domains of oppositely charged molecules. Pattern formation process is charac…

Manifestation of dipole-induced disorder in self-assembly of ferroelectric and ferromagnetic nanocubes

2019

The authors thank Marjeta Maˇcek Kržmanc for many useful discussions. The financial support of M-ERA.NET Project Har-vEnPiez (Innovative nano-materials and architectures for integrated piezoelectric energy harvesting applications) is gratefully acknowledged. D.Z. acknowledges the support of the postdoctoral research program at the University of Latvia (Project No. 1.1.1.2/VIAA/1/16/072). The computing time of the LASC cluster was provided by the Institute of Solid State Physics (ISSP).

Model of the catalyticA+B→0reaction with surface reconstruction

2002

The $A+\stackrel{\ensuremath{\rightarrow}}{B}0$ reaction model with a surface reconstruction is analyzed. It is compared with another similar model for the ${A+1/2B}_{2}\ensuremath{\rightarrow}0$ reaction [V. N. Kuzovkov et al., J. Chem. Phys. 108, 5571 (1998)], which mimics the CO oxidation reaction on the Pt surfaces. The effect of monomer B adsorption instead of dimer ${B}_{2}$ is examined. It is shown that qualitative system features such as reactant concentration oscillations are independent of this substitution.

Kinetics of nanocavity formation based onF-center aggregation in thermochemically reduced MgO single crystals

2001

Division of Materials Science, Office of Basic Energy Sciences, SC 13, U.S. Department of Energy, Germantown, Maryland 20874-1290~Received 9 February 2001; published 19 July 2001!The dynamics of interacting F centers resulting in F aggregates and nanocavities is modeled in thermo-chemically reduced MgO single crystals. We have recently shown that thermal annealing of thermochemicallyreduced MgO with an exceptionally high F-center concentration (6310

The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents

2004

The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes…

Discrete-lattice theory for Frenkel-defect aggregation in irradiated ionic solids

1998

Institut fu ¨r Physikalische und Theoretische Chemie, Technische Universitat Braunschweig, D-38106 Braunschweig, Germany~Received 11 September 1997; revised manuscript received 6 April 1998!A microscopic theory of diffusion-controlled aggregation of radiation Frenkel defects—called in ionic solidsH and F centers—is presented. This is based on a discrete-lattice formalism for the single defect densities~concentrations! and the coupled joint densities of similar and dissimilar defects treated in terms of a modifiedKirkwood superposition approximation. The kinetics of defect aggregation is studied in detail; the cooperativecharacter of this process for both types of complementary defects is sho…

Kinetics of the electronic center annealing in Al2O3 crystals

2018

Authors are greatly indebted to A. Ch. Lushchik, V. Kortov, M. Izerrouken and R.Vila for stimulating discussions. This work has been carried out within the framework of the Eurofusion Consortium and has received funding from the Euroatom research and training programme 2014–2018 under grant agreement No 633053 . The views and opinions expressed herein do not necessarily reflect those of the European Commission. The calculations were performed using facilities of the Stuttgart Supercomputer Center (project DEFTD 12939 ).

Pair and triple correlations in theA+B→Bdiffusion-controlled reaction

1994

An exact solution for the one-dimensional kinetics of the diffusion-controlled reaction A+B\ensuremath{\rightarrow}B is obtained by means of the three-particle correlation functions. Because of a lattice discreteness each site could be occupied by a single particle only which leads to the so-called ``bus effect'': Recombination of any particle A is defined by a spatial configuration of two nearest particles B only surrounding A from its left and right. This results in the unusual algebraic decay law, n(t)\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, which asymptotically (as t\ensuremath{\rightarrow}\ensuremath{\infty}) does not depend on the trap B concentration.

Atomistic theory of mesoscopic pattern formation induced by bimolecular surface reactions between oppositely charged molecules

2011

The kinetics of mesoscopic pattern formation is studied for a reversible A+B⇌0 reaction between mobile oppositely charged molecules at the interface. Using formalism of the joint correlation functions, non-equilibrium charge screening and reverse Monte Carlo methods, it is shown that labyrinth-like percolation structure induced by (even moderate-rate) reaction is principally non-steady-state one and is associated with permanently growing segregation of dissimilar reactants and aggregation of similar reactants into mesoscopic size domains. A role of short-range and long-range reactant interactions in pattern formation is discussed.

Static and dynamic screening effects in the electrostatic self-assembly of nano-particles.

2014

In the description of charge screening in the electrostatic self-assembly of nanoparticles (molecules) embedded into a polar solvent, the static screening effects (a contribution associated with the rapid spatial redistribution of small and highly mobile ions of a solvent) are traditionally treated phenomenologically, using the Yukawa short-range potential for describing the interaction between these particles. However, this model has a limited range of applicability being valid only for infinitely diluted systems and high salt concentrations. During a slow self-assembling process with nanoparticle formation, very dense structural elements (aggregates) are formed, in which the distances bet…

The kinetics of defect accumulation under irradiation: many-particle effects

1993

The kinetics of Frenkel defect accumulation under permanent particle source (irradiation) is discussed with special emphasis on many-particle effects. Defect accumulation is restricted by their diffusion and annihilation, A + B → 0, if the relative distance is less than the critical distance r0. A novel formalism of many-point particle densities based on Kirkwood's superposition approximation is developed to take into account aggregation of similar defects (A−A, B−B). The dependence of the saturation concentration after a prolonged irradiation upon spatial dimension ( = 1, 2, 3), defect mobility and the initial correlation within geminate pairs is analyzed. It is shown that the defect conce…

Reply to "comment on 'Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions' ".

2002

As is well known, a wide class of physical problems, including the kinetics of heterogeneous catalytic reactions, is traditionally described in terms of the master equations ~ME!. The definition of ME allows us not only to perform Monte Carlo ~MC! simulations, but also to develop at the same time appropriate analytical methods @mean field~MF!, cluster approximations, etc. #@ 1#. ME is formally defined when all possible states of a system and the transition rates between these states are specified. This is enough to define only the transition rates K(i! j ) for such elementary processes as particle adsorption, desorption, diffusion, reaction, etc., from the initial state i to the final state…

Global oscillation mechanism in the stochastic Lotka model.

2000

The microscopic one-parameter kinetic model of the oscillatory $A+\stackrel{\ensuremath{\rightarrow}}{B}2B$ reaction (Lotka model) is studied using direct Monte Carlo simulations and analytical methods. Percolation is proposed as the mechanism of global oscillations that are not limited to any finite size of a system. An analytical estimate of the oscillation frequency is derived and compared to computer simulations. We also observe the transition from synchronized oscillations to specific ${f}^{\ensuremath{-}2}$ noise in two dimensions which was previously reported for self-organized critical models.

Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization

2012

We performed kinetic Monte Carlo simulations on a model of a polymerization process in the presence of a periodic oscillatory flow to explore the role of mixing in polymerization reactors. Application of an oscillatory flow field helps overcome the diffusive limitations that develop during a polymerization process due to an increase in the molecular weights of polymer chains, thereby giving rise to high rates of polymerization. A systematic increase in the flow strength results in a "dynamic" coil-stretch transition, leading to an elongation of polymer chains. Reactive ends of stretched (polymer) chains react more frequently than the reactive ends of coiled chains, which are screened by oth…

The kinetics of F-center aggregation under irradiation: many-particle effects in ionic solids

1994

The accumulation kinetics of primary Frenkel defects created in solids under permanent irradiation is calculated using the microscopic formalism of many-particle densities. It is based on the Kirkwood superposition approximation for three-particle densities as described in our previous paper p. N. Kuzovkov and E. A. Kotomin, Physica Scripta 47, 585 (1993)l. This formalism is generalized in this paper by incorporating the elastic attraction between similar defects (called in ionic solids F-centers) which causes their efficient aggregation. It is shown that the aggregation process starts only if the dose rate and elastic attraction energy exceed certain critical values; it also happpens in th…

Dynamic self-assembly of photo-switchable nanoparticles

2012

Nanoparticles functionalized with photo-switchable ligands can be assembled into a broad range of structures by controlled light exposure. In particular, alternating light exposures provide the means to control formation of assemblies of various sizes and symmetries. Here, we use scaling arguments and Kinetic Monte Carlo simulations to study the evolution of reversible aggregates in a solution of periodically irradiated photo-switchable nanoparticles. Scaling estimates of the characteristic size and the mean separation of aggregates agree with the simulations. The transition probabilities in the Kinetic Monte Carlo scheme are derived from a renormalized master equation of the diffusion proc…

Diffusion-controlled annihilation and aggregation of F-centers in thermochemically reduced MgO crystals

2002

Abstract The dynamics of F-center (an oxygen vacancy which has trapped two electrons) aggregation in thermochemically reduced MgO single crystals with an exceptionally high F-center concentration (6×1018 cm−3) is discussed. A theory of the Mg nanocavity formation process is developed based on diffusion-controlled aggregation of elastically interacting F centers and their annihilation at traps. We show that in contrast to the generally accepted viewpoint, the F centers in the bulk are not annealed out at the external sample surface but at internal defects, such as dislocations, subgrain boundaries and impurities. The mutual attraction of the F centers is a key factor controlling the aggregat…

Comparison of the F-type center thermal annealing in heavy-ion and neutron irradiated Al2O3 single crystals

2018

Abstract The optical absorption and thermally stimulated luminescence of Al2O3 (sapphire) single crystals irradiated with swift heavy ions (SHI) 238U with energy 2.4 GeV is studied with the focus on the thermal annealing of the F-type centers in a wide temperature range of 400–1500 K. Its theoretical analysis allows us to obtain activation energies and pre-exponentials of the interstitial oxygen ion migration, which recombine with both types of immobile electron centers (F and F+ centers). A comparison of these kinetics parameters with literature data for a neutron-irradiated sapphire shows their similarity and thus supports the use of SHI-irradiation for modeling the neutron irradiation.

Stochastic model for complex surface-reaction systems with application toNH3formation

1993

A stochastic model is introduced that is appropriate to describe surface-reaction systems. These reaction systems are well suited for the description via master equations using their Markovian behavior. In this representation an infinite chain of master equations for the distribution functions of the state of the surface, of pairs of surface sites, etc., arises. This hierarchy is truncated by a superposition approximation. The resulting lattice equations are solved in a small region which contains all of the structure-sensitive aspects and can be connected to continuous functions which represent the behavior of the system for large distances from a reference point. In the present paper, we …

Oscillation Phenomena Leading to Chaos in a Stochastic Surface Reaction Model

1998

A microscopic lattice gas model for the $\mathrm{CO}+\mathrm{NO}$ reaction on Pt(100) is studied by means of Monte Carlo simulations. It shows different kinetical phenomena such as steady state reaction, damped, regular, and irregular oscillations, as well as a transition into chaotical behavior via the Feigenbaum route. Because of its small number of parameters, each with a specific physical meaning, it enables the investigation of the whole parameter regime leading to a deeper insight to the mechanisms which create the oscillations and chaotical behavior.

Microscopic approach to the kinetics of pattern formation of charged molecules on surfaces.

2010

A microscopic formalism based on computing many-particle densities is applied to the analysis of the diffusion-controlled kinetics of pattern formation in oppositely charged molecules on surfaces or adsorbed at interfaces with competing long-range Coulomb and short-range Lennard-Jones interactions. Particular attention is paid to the proper molecular treatment of energetic interactions driving pattern formation in inhomogeneous systems. The reverse Monte Carlo method is used to visualize the spatial molecular distribution based on the calculated radial distribution functions (joint correlation functions). We show the formation of charge domains for certain combinations of temperature and dy…

Comment on "surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions".

1999

In a recent article Zhdanov studied the oscillating $\mathrm{NO}+{\mathrm{H}}_{2}$ reaction on the Pt(100) single-crystal surface [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)]. We have scrutinized his model and found fundamental errors in the chemical modeling, in the modeling of the surface reconstruction and in the simulation procedure itself.

The non-equilibrium charge screening effects in diffusion-driven systems with pattern formation.

2011

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Huckel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial ordering effects. At long distances the inhomogeneous molecular distribution is limited by diffusion, whereas at short distances (of the order of several coordination spheres) by a balance of short-range (Lennard-Jones) and long-range (Coulomb) interactions. The non-equilibrium charge screening effects in …

Forced oscillations in a self-oscillating surface reaction model

2004

A microscopic lattice gas model for the catalytic CO + O2 reaction on Pt(110) subject to external periodic forcing is studied by means of cellular automaton simulations. Harmonic resonance, subharmonic and superharmonic entrainment, quasiperiodic as well as chaotic behavior are among the observed phenomena in this model when the gas phase concentration of CO as an external control parameter is periodically varied and interacts with the self-oscillating reaction system.

Role of Intrinsic Dipoles in the Evaporation‐Driven Assembly of Perovskite Nanocubes into Energy‐Harvesting Composites

2020

Effect of nonequilibrium charge screening in A + B ? 0 bimolecular reactions in condensed matter

1993

The formalism of many-particle densities developed earlier by the present authors is applied to the study of the cooperative effects in the kinetics of bimolecular A +B--*0 reactions between oppositely charged particles (reactants). It is shown that unlike the Debye-Hiickel theory in statistical physics, here charge screening has essentially a nonequilibrium character. For the asymmetric mobility of reactants (DA=0, D~4:0) the joint spatial distribution of similar immobile reactants A reveals at short distances a singular character associated with their aggregation. The relevant reaction rate does not approach a steady state (as it does in the symmetric case, DA=DB), but increases infinitel…

Effect of reactant spatial distribution in theA+B→0reaction kinetics in one dimension with Coulomb interaction

1996

The effect of nonequilibrium charge screening in the kinetics of the one-dimensional, diffusion-controlled $A+B\ensuremath{\rightarrow}0$ reaction between charged reactants in solids and liquids is studied. The incorrectness of the static, Debye-H\"uckel theory is shown. Our microscopic formalism is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the nonuniform spatial distribution of similar and dissimilar reactants treated in terms of the relevant joint correlation functions. Special attention is paid to the pattern formation due to a reaction-induced non-Poissonian fluctuation sp…

Distinctive features of diffusion-controlled radiation defect recombination in stoichiometric magnesium aluminate spinel single crystals and transpar…

2020

This work has been performed within the framework of the EUROfusion Enabling Research project: ENR-MFE19.ISSP-UL-02 “Advanced experimental and theoretical analysis of defect evolution and structural disordering in optical and dielectric materials for fusion application”. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Research of A.L, E.F.,, V.S and E.S has been partly supported by the Estonian Research Council grant (PUT PRG619); has been also carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The …

Random walk approach to the analytic solution of random systems with multiplicative noise—The Anderson localization problem

2006

We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized diffusion with a noise-induced first-order phase transition. The generalized diffusion manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the Lyapunov exponent $\gamma$, which is the inverse of the localization length, $\xi=1/\gamma$. The appearance of the generalized diffusion arises due to the instability of a fundamental mode corresponding to…

Computer modeling of metal colloid formation in tracks of swift heavy ions in ionic solids

2001

Abstract We present results of computer modelling of the aggregation of primary radiation defects—F centers—in ionic crystals within tracks of swift heavy ions. We study how F-aggregate properties depend on the initial density of primary Frenkel defects in the track and its radius. The mean number of F centers in aggregates is typically very small, about five defects, which greatly complicates detection of expected metal colloids by ESR.

Modeling of primary defect aggregation in tracks of swift heavy ions in LiF

2001

To simulate aggregation of primary F centers created along the path of swift heavy ions in LiF, Monte Carlo simulations were developed. Parameters relevant for defect aggregation as a result of their random hopping, such as the migration energy, temperature in the track, initial defect concentration, and diffusion time, were estimated from available experimental data. It is estimated that in the electronically excited state and under temperature locally increased up to 1200 K F centers are mobile enough to make several tens of hops. Most of the F aggregates formed are extremely small and consist only of two or three F centers. The fraction of larger F clusters ~with more than 10 defects! is…

Void lattice formation in electron irradiated CaF 2 : Statistical analysis of experimental data and cellular automata simulations

2016

Abstract Calcium fluoride (CaF2) is an important optical material widely used in both microlithography and deep UV windows. It is known that under certain conditions electron beam irradiation can create therein a superlattice consisting of vacancy clusters (called a void lattice). The goal of this paper is twofold. Firstly, to perform a quantitative analysis of experimental TEM images demonstrating void lattice formation, we developed two distinct image filters. As a result, we can easily calculate vacancy concentration, vacancy cluster distribution function as well as average distances between defect clusters. The results for two suggested filters are similar and demonstrate that experimen…

Kuzovkov and Kotomin reply.

1995

Front propagation in the one-dimensional autocatalyticA+B→2Areaction with decay

1999

We consider front propagation in the autocatalytic scheme $A+\stackrel{\ensuremath{\rightarrow}}{B}2A,$ where we also allow the A particles to decay, $\stackrel{\ensuremath{\rightarrow}}{A}0,$ with a constant decay rate $\ensuremath{\beta}.$ In a one dimensional, discrete, situation the A domain moves as a pulse, and its dynamics differs from what is found in higher dimensions. Thus the velocity of the pulse tends to a finite value when $\ensuremath{\beta}$ approaches from below the critical value ${\ensuremath{\beta}}_{c},$ at which pulses die out. On the other hand, when approaching ${\ensuremath{\beta}}_{c}$ from above, the mean lifetime of the pulse grows as $T\ensuremath{\propto}(\ensu…

Theory of non-equilibrium critical phenomena in three-dimensional condensed systems of charged mobile nanoparticles.

2014

A study of 3d electrostatic self-assembly (SA) in systems of charged nanoparticles (NPs) is one of the most difficult theoretical problems. In particular, the limiting case of negligible or very low polar media (e.g. salt) concentration, where the long-range NP interactions cannot be reduced to commonly used effective short-range (Yukawa) potentials, remains unstudied. Moreover, the present study has demonstrated that unlike the Debye–Huckel theory, a complete screening of the charges in SA kinetics (dynamic SA) is not always possible. Generally speaking, one has to take into account implicitly how each NP interacts with all other NPs (the true long-range interactions). Traditional theoreti…

Void superlattice formation in electron irradiated CaF2: Theoretical analysis

2010

Abstract CaF2 is widely adopted as deep-UV window material and thin film optical coating. The void superlattice was observed experimentally under electron irradiation at room temperature. We performed kinetic Monte Carlo (kMC) simulations of the initial stages of the process when short- and intermediate-range order of defects in small Ca colloids and larger interstitial aggregates (F2 gas voids) is created. The kMC model includes fluorine interstitial–vacancy pair creation, defect diffusion, similar defect attraction and dissimilar defect recombination. Special attention is paid to the statistical analysis of the defect aggregate distribution functions under different conditions (dose rate,…

Anderson localization problem: An exact solution for 2-D anisotropic systems

2007

Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal-insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two localization lengths arise instead of one length only.

The kinetic MC modelling of reversible pattern formation in initial stages of thin metallic film growth on crystalline substrates

2003

Abstract The results of kinetic MC simulations of the reversible pattern formation during the adsorption of mobile metal atoms on crystalline substrates are discussed. Pattern formation, simulated for submonolayer metal coverage, is characterized in terms of the joint correlation functions for a spatial distribution of adsorbed atoms. A wide range of situations, from the almost irreversible to strongly reversible regimes, is simulated. We demonstrate that the patterns obtained are defined by a key dimensionless parameter: the ratio of the mutual attraction energy between atoms to the substrate temperature. Our ab initio calculations for the nearest Ag–Ag adsorbate atom interaction on an MgO…

Self-organization in the A + B → 0 reaction of charged particles

1992

The formalism of many-particle densities developed earlier by the authors is applied to the study of the self-organization phenomena occuring during the course of the bimolecular A + B → 0 reaction between charged particles, interacting via the Coulomb law. Unlike the Debye-Huckel theory, charge screening has an essentially non-equilibrium character. It is shown that for the asymmetric mobility of reactants (DA = 0, DB ≠ 0) similar immobile reactants A form aggregates characterized by a sharp maximum, observed at short distances, in the joint correlation function XA(r, t). Such an aggregation leads to the accelerated particle recombination n ∝ t-54 (nA = nB = n) instead of the generally acc…

Internal Spatiotemporal Stochastic Resonance in a Microscopic Surface Reaction Model

1999

We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises once homogeneous nucleation in the individual surface phases (reconstructed and non-reconstructed) is added. This nucleation is modelled as a noise process. As a result, synchronization of the kinetic oscillations is obtained. Internal stochastic resonance may t…

Exact analytic solution of the multi-dimensional Anderson localization

2004

The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes…

Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"

2004

We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.

A new approach to the analytic solution of the Anderson localization problem for arbitrary dimensions

2005

Subsequent to the ideas presented in our previous papers [J.Phys.: Condens. Matter {\bf 14} (2002) 13777 and Eur. Phys. J. B {\bf 42} (2004) 529], we discuss here in detail a new analytical approach to calculating the phase-diagram for the Anderson localization in arbitrary spatial dimensions. The transition from delocalized to localized states is treated as a generalized diffusion which manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the Lyapunov exponent $\gamma$, which is the inverse of the localization length, $\xi=1/\gamma$. The appearance of the generalized diffusion arises due to the instability of a fundamental mode cor…

Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization

2002

The Anderson localization problem in one and two dimensions is solved analytically via the calculation of the generalized Lyapunov exponents. This is achieved by making use of signal theory. The phase diagram can be analyzed in this way. In the one dimensional case all states are localized for arbitrarily small disorder in agreement with existing theories. In the two dimensional case for larger energies and large disorder all states are localized but for certain energies and small disorder extended and localized states coexist. The phase of delocalized states is marginally stable. We demonstrate that the metal-insulator transition should be interpreted as a first-order phase transition. Con…

A new synchronization mechanism via Turing-like microscopic structures for CO oxidation on Pt(110)

2002

We discuss an alternative to the traditional gas-phase coupling approach in order to explain synchronized global oscillations in CO oxidation on Pt(110). We use a minimalist microscopic model which includes structural Pt surface reconstruction via front propagation, and large diffusion rates for CO. The synchronization mechanism is associated with the formation of a Turing-like structure of the substrate. By using large parallel microscopic simulations we derive a scaling laws which allow us to extrapolate to realistic diffusion rates, pattern size, and oscillation periods.

Parallelization of Cellular Automata for Surface Reactions

2002

We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T is the computer time used for one single processor and P the number of processors. Two examples are presented to test the algorithm, the simple A+B->0 model and a realistic model for CO oxidation on Pt(110). By using large parallel simulations, it is possible to derive scaling laws which allow us to extrapolate to even larger system sizes and faster diffusion coefficients allowing us to make direct comparisons with experiments.