Diffusion of particles on a heterogeneous surface: A case of adsorption-induced surface reconstruction

The influence of surface reconstruction on diffusion of particles adsorbed on the surface is investigated in the framework of symmetrical four-position model. The analytical expressions for free energy and diffusion coefficients are obtained assuming the lateral interaction between particles is negligibly small.The critical behavior of the system is described by the Ising spin model. The coverage dependencies of the tracer, jump and chemical diffusion coefficients are calculated for some representative temperatures. The dependencies show clearly strong influence of the surface reconstruction on the thermodynamic and kinetic phenomena: diffusion coefficients become anisotropic on the reconstructed surface. To check the analytical results we have used Monte Carlo simulations of the diffusion on this lattice.     

Surface diffusion of particles adsorbed on an inhomogeneous lattice with two non-equivalent sites

We investigate surface diffusion in a system of particles with the nearest neighbor pairwise lateral interaction adsorbed on a two-dimensional inhomogeneous lattice of square symmetry with deep and shallow sites. General analytical expressions for the chemical and jump diffusion coefficients have been derived in case of strong inhomogeneity. The expressions are valid for the inhomogeneous lattices with different geometries and dimensionalities. We have calculated the coverage dependencies of the tracer, jump and chemical diffusion coefficients for different temperatures using the real-space renormalization group (RSRG) method and compared the data with the numerical results obtained by the MC simulations. The coincidence between the data obtained by these quite different methods is rather good.     

Diffusion in heterogeneous lattices

We present here the results of our investigations of particle diffusion over different heterogeneous lattices with deep and shallow adsorption sites. A general analytical expression for chemical diffusion coefficient has been derived for a number of inhomogeneous lattices of different dimensionality and symmetry. We have calculated coverage dependencies of diffusion coefficients. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.     

Complete hyperelliptic integrals of the first kind and their non-oscillation

Let be a real polynomial of degree , and be an oval contained in the level set . We study complete Abelian integrals of the form

where are real and is a maximal open interval on which a continuous family of ovals exists. We show that the -dimensional real vector space of these integrals is not Chebyshev in general: for any 1$">, there are hyperelliptic Hamiltonians and continuous families of ovals , , such that the Abelian integral can have at least zeros in . Our main result is Theorem 1 in which we show that when , exceptional families of ovals exist, such that the corresponding vector space is still Chebyshev.

     

The Real Period Function of A3 Singularity and Perturbations of the Spherical Pendulum

We prove that the Hessian matrix of the real period function () associated with the real versal deformation f (x)=±x ⁴+₂ x ²+₁ x+₀ of a singularity of type A ₃, is nondegenerate, provided that ³ does not belong to the discriminant set of the singularity. We explain the relation between this result and the perturbations of the spherical pendulum.     

Li-impurity effect in optical spectra of KTaO<Subscript>3</Subscript>:Er<Superscript>3+</Superscript> crystals

The optical properties of one-dimensional photonic crystals based on porous anodic aluminum oxide films have been studied by measuring transmittance and specular reflectance spectra in the visible and UV spectral regions. Angular dependences of the spectral positions of optical stop bands are obtained. It is shown that the reflectance within the first stop band varies from point to point on the sample surface, reaching a level of 98–99% at some points. The dispersion relation for electromagnetic waves in the model of infinite periodic structure is calculated for the samples under study. The possibility of using models with an infinite or finite number of layers to calculate reflectance spectra near the first optical stop band is discussed.     

Electrochemical impedance spectroscopy of mesoporous Al-stabilized TiO<Subscript>2</Subscript> (anatase) in aprotic medium

High-frequency electrochemical impedance spectroscopy was used to investigate the mesoporous film of Al-stabilized TiO₂ on F-doped SnO₂ support in 1 M Li(CF₃SO₂)₂N in ethylene carbonate/dimethoxyethane (1:1 v/v). Kinetic parameters, viz. charge transfer resistance and chemical diffusion coefficient, were determined. Charge transfer resistance increased with time of contact of electrode in the above aprotic electrolyte solution. The increase followed exponential dependence, whereas the double layer capacitance, simultaneously, decreased exponentially with time. These effects were discussed in terms of the solid–electrolyte interface, which undergoes chemical changes upon contact with the electrolyte solution. Adel Attia is currently on leave from the Department of Physical Chemistry, National Research Center, El-Tahrir St., Dokki 12622, Cairo, Egypt.     

Crystal and molecular structure of 5-amino-1,2,3,4-thiatriazole

The crystal structure of 5-amino-1,2,3,4-thiatriazole has been determined from three-dimensional counter data and refined by full-matrix least-squares techniques. The crystals belong to the monoclinic space groupP2₁/n witha = 3.780(2),b = 10.179(5),c = 10.139(5) Å, = 91.78(4) °, andD _x = 1.74 g cm^–3 forZ = 4. The finalR factor for 572 observed reflections is 0.042. This structure represents the first X-ray structure determination of an ammosubstituted thiatriazole, although electron diffraction and CNDO calculations have been carried out on related systems. The results show that the discrepancy between the observed reactivity and that calculated might be due to the fact that 5-substitution appreciably affects the -system of the heteroaromatic ring.