V.N. Kuzovkov

Kinetic oscillations in the catalytic CO oxidation on Pt single crystal surfaces: Theory and simulation

A simple lattice gas model is studied for the description of the kinetic oscillations in the CO oxidation on the Pt(100) and Pt(110) surfaces. It takes CO diffusion and surface reconstruction into account and exhibits very interesting phenomena such as synchronized oscillations and mesoscopic pattern formation. The model uses only few parameters, the CO gas phase concentration y, the CO diffusion constant D, the surface phase propagation velocity V, and the ratio of the O2 sticking coefficients on the two surface phases. This enables the study of the whole parameter regime and the theoretical stability analysis for the kinetic oscillations. It can be shown that it is only the ratio of the O2 sticking coefficients on the reconstructed and non–reconstructed surfaces which determines the type of oscillations and the parameter range where these oscillations exist.

THE KINETICS OF CAF2 METALLIZATION INDUCED BY LOW-ENERGY ELECTRON IRRADIATION

Abstract Results of experimental and theoretical studies on metal colloid growth after irradiation and subsequent heating of CaF 2 are presented. Samples at a temperature of 200 K were irradiated in UHV for 30 min with 2.5 keV electrons. After irradiation samples were heated at a rate of about 1 K/min and colloid formation was investigated by optical extinction spectroscopy. Colloid radii as well as the amount of metal were determined from a Mie scattering analysis. A steep rise in colloid size was observed between 260 and 270 K. The concentration of F centers not aggregated into colloids was below the detection limit for all temperatures. A microscopic theory of F and H center aggregation taking into account defect creation, interaction, diffusion, and annihilation of dissimilar defects is presented. Theory successfully reproduces the main experimental observations of small colloid formation at low temperatures during irradiation and the onset of colloid growth at a temperature where F centers become mobile.

SPONTANEOUS SYMMETRY BREAKING IN A NO + CO SURFACE REACTION MODEL

Abstract A simple lattice gas model for the catalytic CO + NO → CO 2 + 1 2 N 2 surface reaction is studied by means of a model involving a stochastic cluster approximation. The cluster approximation on an infinite square lattice gives a reactive interval from a second-order phase transition at y1 = 0.171 to a first-order phase transition at y2 = 0.319. The subdivision of the lattice into two chequerboard-like sublattices leads to a third phase transition at yCO = 0.227 where the reactive interval ends. This point is the left-hand limit of the domain of spontaneous symmetry breaking where a phase transition from dynamical disorder to static order occurs.

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

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 analysed 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. Consequences for perturbation approaches, the problem of self-averaging quantities and numerical scaling are discussed.

Forced oscillations in a self-oscillating surface reaction model

A microscopic lattice gas model for the catalytic COu2006+u2006O2 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.

A stochastic approach to surface reactions including energetic interactions: I. Theory

A stochastic model to describe surface reaction systems is introduced. The reactions may include mono- and bimolecular steps (i.e. adsorption, desorption, reaction and diffusion steps). Furthermore, energetic interactions between the adsorbed particles are allowed. The temporal evolution of the system is described by master equations using the Markovian behaviour of these systems. The resulting infinite chain of equations is truncated at a certain level by using an improved superposition approximation. The equations are solved in a small lattice region exactly and their solution is connected to continuous functions which represent the behaviour of the system for large distances. We define a standard model which can be used to model various surface reaction systems in a unique manner. This gives the possibility for a better and easier comparison between different models.

A LOTKA-TYPE MODEL FOR OSCILLATIONS IN SURFACE REACTIONS

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 predict the system behaviour correctly. Simple approximations which do not account for long-range correlations (such as mean-field approximations) fail in the prediction of the system behaviour. The correlation analysis (an advanced stochastic description) is in overall good agreement with the results of the simulation and therefore is an alternative to computer simulation. Moreover, it is not restricted to using a finite lattice and does not need a large amount of computing time.

A stochastic approach to surface reactions including energetic interactions: II. Application to the reaction

We study a stochastic model for the reaction with energetic interactions between the particles. The reaction system includes adsorption, desorption, reaction and diffusion steps which depend on energetic interactions. The temporal evolution of the system is described by master equations using the Markovian behaviour of the system. We study the system behaviour at different values of the energetic parameters and at varying diffusion and desorption rates. The location and the character of the phase transition points will be discussed in detail. The role of the constants used in situ mean field theories such as kinetic constants etc are discussed in view of the new theories. All such constants, if they are at all meaningful, are functions of correlation functions and not constants. This has important implications for the analysis of experiments.

Defining percolation kinetically on an infinite lattice

Abstract Percolation is a structural, geometric concept. We show that it can be defined in a purely kinetic way via a chemical reaction. The A + 1 2 B 2 → 0 reaction on a square lattice is chosen. The analysis is done for site percolation on an infinite lattice where a fraction S of sites is active. The approach is via stochastic master equations describing the reaction events. A reactive state is obtained for S > S , where S is the kinetically defined critical occupation probability. For S S no reaction occurs for t → ∞ on the finite clusters. S is found to be S ≈ 0.63 .

The microscopic theory of diffusion-controlled defect aggregation

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.