The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Low energy electron diffraction and auger electron spectroscopy studies of the structure of adsorbed gases on solid surfaces

Low energy electron diffraction (LEED) studies of the structure of adsorbed molecules on crystal surfaces revealed that ordered surface structures predominate under most conditions of the experiments. In the absence of chemical reactions with the substrate, the degree of ordering depends on the heats of adsorption, ΔH_ads, and the activation energies for surface diffusion, ΔE_D1. Since ΔH_ads is usually markedly larger than ΔE_D1, small changes of substrate temperature facilitate ordering without appreciable increase in desorption rates. The surface structures of adsorbed gases that have been reported so far have been tabulated. For molecules whose size is compatible with the interatomic distance of the substrate, rules of ordering can be proposed that permit prediction of the structure of the adsorbed layer that is likely to form. These rules indicate close packing due to attractive interactions in the adsorbed layer, and that the rotational multiplicity of the substrate is likely to be maintained by the adsorbate structure. When molecules whose dimensions are larger than the substrate interatomic distance are adsorbed, the conditions that control ordering are more complex and simple rules may not be readily applicable.The surface structures of adsorbed gases have also been studied on high Miller Index substrate surfaces. These surfaces are characterized by ordered steps separated by terraces of low index surface orientation. Many gases have different ordering characteristics on stepped surfaces than on low index crystal faces due to the stronger substrate-adsorbate interactions in these surfaces. The dissociation of diatomic molecules at steps induces the formation of new types of surface structures (frequently one-dimensional) and the dehydrogenation of hydrocarbons at steps induces the formation of ordered carbonaceous surface structures that would not nucleate on low index substrate planes.So far, mostly work function changes upon adsorption gave indication of the magnitude of charge transfer upon adsorption and on forming of new surface chemical bonds. Most recently, chemical shifts of the Auger transitions of the substrate atoms and of the adsorbed molecules upon chemisorption, have been found to provide additional information on charge redistribution during adsorption.     

Fractal analysis and atomic force microscopy measurements of surface roughness for Hastelloy C276 substrates and amorphous alumina buffer layers in coated conductors

In coated conductors, surface roughness of metallic substrates and buffer layers could significantly affect the texture of subsequently deposited buffer layers and the critical current density of superconductor layer. Atomic force microscopy (AFM) is usually utilized to measure surface roughness. However, the roughness values are actually relevant to scan scale. Fractal geometry could be exerted to analyze the scaling performance of surface roughness. In this study, four samples were prepared, which were electro polished Hastelloy C276 substrate, mechanically polished Hastelloy C276 substrate and the amorphous alumina buffer layers deposited on both the substrates by ion beam deposition. The surface roughness, described by root mean squared (RMS) and arithmetic average (R_a) values, was analyzed considering the scan scale of AFM measurements. The surfaces of amorphous alumina layers were found to be fractal in nature because of the scaling performance of roughness, while the surfaces of Hastelloy substrates were not. The flatten modification of AFM images was discussed. And the calculation of surface roughness in smaller parts divided from the whole AFM images was studied, compared with the results of actual AFM measurements of the same scan scales.     

First-principles studies of the oxygen adsorption on unreconstructed and reconstructed Ni(1 1 0) surfaces

First-principles calculations have been performed to investigate the adsorption of oxygen on unreconstructed and reconstructed Ni(1 1 0) surfaces. The energetics, structural, electronic and magnetic properties are given in detail. For oxygen adsorption on unreconstructed surface, (n×1)(n=2,3) substrate with oxygen atom on short-bridge site is found to be the most stable adsorption configuration. Whereas energetically most favorable adsorption phase of reconstructed surface is p(n×1) substrate with oxygen atom located at long-bridge site. Our calculations suggest that the surface reconstruction is induced by the oxygen adsorption. We also find there are redistributions of electronic structure and electron transfer from the substrate to adsorbate. Our calculations also indicate surface magnetic moment is enhanced on clean surfaces and oxygen atoms are magnetized weakly after oxygen adsorption. Interestingly, adsorption on unreconstructed surface does not change surface magnetic moment. However, adsorbate leads to reduction of surface magnetic moment in reconstructed system remarkably.     

Numerical study on surface acoustic wave method for determining Young's modulus of low-k films involved in multi-layered structures

The surface acoustic waves (SAWs) technique is becoming an attractive tool for accurately and nondestructively characterizing the mechanical property of the brittle low dielectric constant (low-k) thin film. The theoretical equations for describing SAWs propagating on the multi-layered structure are derived in this study. The dispersion features of SAWs propagating on different structures of low-k/SiO₂/Si substrate, SiO₂/low-k/Si substrate, low-k/Si substrate, and low-k/Cu/Si substrate are investigated to instruct an accurate and facile fitting process for determining Young's modulus of low-k films. The dependence of dispersion relation on the film thickness, elastic modulus of low-k materials as well as frequency are provided and discussed in detail. The study shows an obvious influence of layered structure on the dispersion relation of SAWs. For a fixed structure, the dispersion curvature increases with the decrease of Young's modulus of low-k films.     

A DFT study the solvent effects of H2 adsorption on Cu(h k l) surface

Density functional theory (DFT) combined with conductor-like solvent model (COSMO) have been performed to study the solvent effects of H₂ adsorption on Cu(h k l) surface. The result shows H₂ can not be parallel adsorbed on Cu(h k l) surface in gas phase and only vertical adsorbed. At this moment, the binding energies are small and H₂ orientation with respect to Cu(h k l) surfaces is not a determining parameter. In liquid paraffin, when H₂ adsorbs vertically on Cu(h k l) surface, solvent effects not only influences the adsorptive stability, but also improves the ability of H₂ activation; When H₂ vertical adsorption on Cu(h k l) surface at 1/4 and 1/2 coverage, H-H bond is broken by solvent effects. However, no stable structures at 3/4 and 1 ML coverage are found, indicating that it is impossible to get H₂ parallel adsorption on Cu(h k l) surfaces at 3/4 and 1 ML coverages due to the repulsion between adsorbed H₂ molecules.     

Method of systems of equations of P-adic coverages for fractal analysis of events

Self-similarity in high-energy multiparticle production processes is discussed. A parton shower and hadronization are assumed to give rise to a set of particle with a fractal structure. It is noted that the box counting (BC) and P-adic coverage (PaC) methods determine the fractal dimension with permissible 1/k ranges. A new method of systems of equations of P-adic coverages (SePaC) is proposed that extends the PaC method to fractals with permissible m/k ranges. The SePaC method is shown to determine the fractal dimension of a shower with a prescribed accuracy, the number of fractal levels, the type of the cascade (random or regular), and its structure.     

Sensitivity of surface plasmon dispersion and damping to alkali adsorption

I have studied the sensitivity to alkali adsorption of the linear coefficients of surface plasmon dispersion and damping, through the use of self-consistent surface potential barriers which have been shown by Lang to give a good account of the work function changes due to such adsorption. The coefficient of dispersion increases strongly with alkali adsorption on an r_S = 2 substrate, while the coefficient of damping changes less.     

High-resolution H atom scattering from NaCl(001)

The NaCl(001) surface is studied using an H atom beam at energies of 76.3 and 86.3 meV. Elastic diffractive scattering is investigated under different incident angles and crystal orientations. Selective adsorption resonances are measured, determining experimentally the energy levels of the H atom bound to the surface. The energy spectrum is reproduced reasonably by a Morse potential with a well depth D = 29.2 meV and a range parameter k = 0.04 nm^?1.     

Low temperature adsorption of water on cleaved GaAs(110) surfaces

The adsorption and desorption of water on UHV-cleaved GaAs(110) surfaces was studied using synchrotron-excited photoelectron spectroscopy. Water was adsorbed at T = 100 K. Desorption was studied during heating to room temperature. At low coverages, dissociated species are observed followed by molecular adsorption. Molecular water is desorbed at T = 160 K. The dissociated species are also mainly desorbed after heating to room temperature. The chemical changes are accompanied by substrate binding-energy shifts, reflecting the movement of the Fermi level at the surface.     

Combined SANS and SAXS study of the action of ultrasound on the structure of amorphous zirconia gels

In the present work, we have studied for the first time the combined effect of both sonication and precipitation pH on the structure of amorphous zirconia gels synthesized from zirconium(IV) propoxide. The techniques of small-angle neutron and X-ray scattering (SANS and SAXS) and low temperature nitrogen adsorption provided the integral data on the changes in the microstructure and mesostructure of these materials caused by ultrasonic (US) treatment. Amorphous ZrO₂·xH₂O synthesized under ultrasonic treatment was found to possess a very structured surface, characterized by the surface fractal dimension 2.9–3.0, compared to 2.3–2.5 for the non US-assisted synthesis, and it was also found to possess a higher specific surface area, while the sizes of the primary particles remain unchanged.     

X-ray photoemission study of physically absorbed SF6

The physical adsorption of octahedral SF₆ on Ru(001) has been studied with X-ray photoelectron spectroscopy (XPS) in an attempt to see effects on the energy levels resulting from the conformation of the molecule on the surface. Near 80 K surface coverages up to a monolayer have been studied at various steady state pressures of SF₆. Kinetic studies, core level binding energies, and peak areas indicate that the surface species studied was a physically adsorbed monolayer of sf₆. The sticking coefficient of SF₆, at ? 80 K is approximately unity. Also, a multilayer structure was observed at the highest pressures of SF₆. The binding energy of the F(ls) peak for monolayer coverage is centered at 688.2 ± 0.2 eV relative to the Ru Fermi level. while the multilayer F(ls) peak is shifted more than 3.5 eV to higher binding energy. The F(ls) linewidth for one monolayer has a full width at half maximum of 1.75 ± 0.1 eV. The F(ls) linewidth of the multilayer peak narrows with increasing coverage. Its narrowest observed linewidth was 1.35 eV ± 0.1 eV or approximately the same as that found in the gas phase. One of the mechanisms which may account for the F(ls) linewidth with monolayer coverage is a difference in F(ls) binding energy between those F atoms in contact with the substrate and those further away. This may be due to the variation in chemical environment and relaxation effects as a function of distance from tlie substrate. A classical image force calculation including finite screening effects of the substrate indicates that there is a differential binding energy, ΔW. between the F ligands; ΔW = 0.85 ± 0.25 eV, for realistic ranges of adsorption distances from the substrate and screening lengths in the substrate. The observed broadening of the monolayer F(ls) level is consistent with a ΔW of 0.7 ± 0.1 eV, indicating the possible existence of such a mechanism. Adsorption of a monolayer of SF₆ onto the Ru covered with a monolayer of oxygen shifts the F(ls) peak to lower binding energy by 0.8 eV. Similar effects due to oxygen have been observed previously in the physical adsorption of Xe on W(111).     

Theoretical study of CO and Pb adsorption on the Ni(1 1 1) and Ni3Al(1 1 1) surfaces

Adsorption of CO molecules and Pb atoms on the Ni(1 1 1) and Ni₃Al(1 1 1) substrates is studied theoretically within an ab initio density-functional-theory approach. Stable adsorption sites and the corresponding adsorption energies are first determined for stoichiometric surfaces. The three-fold hollow sites (fcc for Pb and hcp for CO) are found most favourable on both substrates. Next, the effect of surface alloying by a substitution of selected topmost substrate atoms by Pb or Ni atoms on the adsorption characteristics is investigated. When the surface Al atoms of the Ni₃Al(1 1 1) substrate are replaced by Ni atoms, the Pb and CO adsorption energies approach those for a pure Ni(1 1 1) substrate. The Pb alloying has a more substantial effect. On the Ni₃Al(1 1 1) substrate, it reduces considerably adsorption energy of CO. On the Ni(1 1 1) substrate, CO binding strengthens slightly upon the formation of the Ni(1 1 1)p(2×2)-Pb surface alloy, whereas it weakens drastically when the Ni(1 1 1)-Pb surface alloy is formed.     

Quantum waveguide theory of a fractal structure

The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123$N=123$. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model.     

Surface characterization and microstructure of ITO thin films at different annealing temperatures

In this study, the electron beam evaporation method is used to generate an indium tin oxide (ITO) thin film on a glass substrate at room temperature. The surface characteristics of this ITO thin film are then investigated by means of an AFM (atomic force microscopy) method. The influence of postgrowth thermal annealing on the microstructure and surface morphology of ITO thin films are also examined. The results demonstrate that the film annealed at higher annealing temperature (300 °C) has higher surface roughness, which is due to the aggregation of the native grains into larger clusters upon annealing. The fractal analysis reveals that the value of fractal dimension D_f falls within the range 2.16-2.20 depending upon the annealing temperatures and is calculated by the height-height correlation function.     

Sulphur overlayers on Ir(100) and its effect on the adsorption of CO: a DFT study

Ordered sulphur overlayers adsorbed on Ir(100) surface are studied with differentcoverage ranging from 0.11 to 1.0 ML. Calculations indicate that atomic S adsorbsfavourably in hollow sites, forming strong covalent bonds with the substrate surface andthe adsorption energy is nearly unchanged at lower coverages(θ _S ≤ 0.50 ML). In good agreement withexperimental observations, the p(2 × 2)-S and c(2 × 2)-Sare predicted to be the most stable overlayers. The obtained surface electronic structuremodifications induced by sulphur adsorption are coverage-dependent and the results are inaccordance with the rectangular band and the Hammer-Nørskov models. Moreover, the effectof sulphur on the adsorption of CO is discussed in the p(2 × 2)?(S + CO)overlayer on Ir(100).     

Isothermal adsorption kinetics on heterogeneous surfaces

Adsorption kinetics on energetically heterogeneous surfaces under isothermal conditions is analyzed using the uniform energy distribution model. Considering the quasi-equilibrium of surface diffusion between the adsorption sites with different energy, the kinetic equations dΘ/dt=(k_ap−A_dK_diff)(1−Θ) for first-order adsorption and dΘ/dt=k_ap(1−Θ)²−A_dK_diffΘ(1−Θ) for dissociative adsorption are obtained, where K_diff is a coefficient describing the surface diffusion equilibrium, which depends on the coverage and the energy distribution. Under isochoric conditions with p decreasing due to adsorption, surface diffusion accelerates the rate towards equilibrium significantly, as observed in static calorimetric adsorption experiments. An approximate solution in Lagergren form is derived for this condition.     

Adsorption thermodynamics of interacting particles on diffusion-limited aggregates

Grand canonical Monte Carlo simulations have been performed in order to study adsorption thermodynamics of pairwise interacting particles on fractal surfaces. Diffusion-limited aggregates (DLA) have been used as a substrate where interacting particles are adsorbed. In order to obtain aggregates with different morphologies, DLA clusters are generated on different strongly correlated surfaces. Adsorption isotherm, adsorption energy and differential heat of adsorption were calculated for attractive and repulsive nearest-neighbor (NN) lateral interactions. For the case of repulsive couplings and low temperatures, four novel ordered phases has been found in the adsorbate, each one corresponding to the formation of a chessboard-like structure on sites with one, two, three and four NN sites, respectively. The values of coverage at which these ordered phases emerge are not symmetrical around θ=0.5. This is a consequence of the non-equivalence between vacancy and particle in the case of adsorption on fractal structures. The influence of ordered structures on thermodynamic quantities associated to the adsorbed monolayer has been analyzed and discussed in the context of the Lattice-Gas model.