Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media

The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The analysis is based on geometrical optics. The discrete-scale approach uses the Monte Carlo ray-tracing applied directly to real 3D geometry measured by computed tomography. The continuum-scale approach is based on a set of continuum-scale radiative transfer equations and associated radiative properties, and employs the Monte Carlo ray-tracing for computations of radiative fluxes and for computations of the radiative properties. The model two-phase media are reticulate porous ceramics and a particle packed bed, each composed of semitransparent solid and fluid phases. The results obtained by the two approaches are in good agreement within the limits of statistical uncertainty. The continuum-scale approach leads to a reduction in computational time by approximately one order of magnitude, and is therefore suited to treat radiative transfer problems in two-phase media in a wide range of engineering applications.     

Synthesis of nanoporous structures in metallic materials under laser action

We defined conditions of the laser-aided formation of nanoporous structures with nanopores ranging in size from 40 to 50 nm using laser pulses of 10.6 μm wavelength at a pulse-repetition rate of up to (4-5)×10³ Hz for a model metallic material (a two-component alloy “brass of 62%”). It has been established that the exposure to a uniform laser light at depths of up to 25-30 μm results in the formation of nanopores with a relatively uniform distribution across the surface. The resulting pattern contains both solitary pores and ramified porous channels. The nanopores are uniformly distributed within a subgrain, being fairly stable in size and shape. The nanopore size and shape feature larger non-uniformity on the subgrain boundary. The resulting metallic structures show promise for use as catalysts and ultrafiltration membranes.     

Overcoming apparent susceptibility-induced anisotropy (aSIA) by bipolar double-pulsed-field-gradient NMR

Double-Pulsed-Field-Gradient (d-PFG) MR is emerging as a powerful new means for obtaining unique microstructural information in opaque porous systems that cannot be obtained by conventional single-PFG (s-PFG) methods. The angular d-PFG MR methodology is particularly important since it can utilize the effects of microscopic anisotropy (μA) and compartment shape anisotropy (csA) in the E(ψ) profile at the different t_m regimes to provide detailed information on compartment size and eccentricity. An underlying assumption is that the PFGs that are imparted to weigh diffusion are the only gradients present; however, in realistic systems and especially where there are randomly oriented anisotropic pores, susceptibility effects may induce strong internal gradients. In this study, the effects of such internal gradients on E(ψ) plots obtained from angular d-PFG MR and on microstructural information that can be obtained from s-PFG and d-PFG MR were investigated. First, it was found that internal gradients induce a bias in the s-PFG MR results, thus creating an anisotropy that is not related to microstructure, termed apparent-Susceptibility-Induced-Anisotropy (aSIA). We then show that aSIA effects are also manifest in different ways in the angular d-PFG MR experiment in controlled phantoms and in realistic systems such as quartz sand, emulsions, and biological systems. The effects of aSIA in some cases completely masked the effects of μA and csA; however, we subsequently show that by introducing bipolar gradients to the d-PFG MR (bp-d-PFG), the effects of aSIA can be largely suppressed, restoring the E(ψ) plots that are expected from the theory along with the microstructural information that it conveys. We conclude that when specimens are characterized by strong internal gradients, the novel information on μA and csA that is manifest in the E(ψ) plots can indeed be inferred when bp-d-PFG MR is used, i.e. when bipolar gradients are applied.     

Scaling of submonolayer island growth with reversible adatom exchange in surfactant-mediated epitaxy

Surfactant-mediated epitaxial growth is studied with a realistic model, which includes three main kinetic processes: diffusion of adatoms on the surfactant terrace, exchange of adatoms with their underneath surfactant atoms, and reexchange in which an exchanged adatom resurfaces to the top of the surfactant layer. The scaling behavior of nucleus density and island size distributions in the initial stage of growth is investigated by using kinetic Monte Carlo simulations. The results show that the temperature dependence of nucleus density and island size distributions governed by the reexchanging-controlled nucleation at high temperatures exhibits similar scaling behavior to that obtained by the standard diffusion-mediated nucleation at low temperatures. However, at intermediate temperatures, the exchanging-controlled nucleation leads to an increase of nucleus density with temperature, while the island size distribution scales to a monotonically decreasing function, showing nonstandard scaling behavior.     

Some insights in superdiffusive transport

In a wide range of systems, the relaxation in response to an initial pulse has been experimentally found to follow a nonlinear relationship for the mean squared displacement, of the kind 〈x²(t)〉∝t^α$〈x^2(t)〉\propto t^{\alpha }$, where α$\alpha$ may be greater or smaller than 1. Such phenomena have been described under the generic term of anomalous diffusion. “Lévy flights” stochastic processes lead to superdiffusive behaviour (1<α<2)$(1<\alpha <2)$ and have been recently proposed to model—among the others—the subsurface contaminant spread in highly heterogeneous media under the effects of water flow. In this paper, within the continuous-time random walk (CTRW) approach to anomalous diffusion, we compare the analytical solution of the approximated fractional diffusion equation (FDE) with the Monte Carlo one, obtained by simulating the superdiffusive behaviour of an ensemble of particle in a medium. We show that the two are neatly different as the process approaches the standard diffusive behaviour. We argue that this is due to a truncation in the Fourier space expansion introduced by the FDE approach. We propose a second-order correction to this expansion and numerically solve the CTRW model under this hypothesis: the accuracy of the results thus obtained is validated through Monte Carlo simulation over all the superdiffusive range. The same kind of discrepancy is shown to occur also in the derivation of the fractional moments of the distribution: analogous corrections are proposed and validated through the Monte Carlo approach.     

Penetration of ammonia molecule into ice film; activation energy analysis using Xe molecular beam irradiation

We have investigated the barrier energy for an ammonia molecule to penetrate into ice film by the use of infrared spectroscopy and Xe supersonic beam. After the ice film on a Pt(1 1 1) surface is exposed to ammonia molecules, an umbrella mode of ammonia molecules adsorbed on the ice film has been observed in infrared spectra. After the irradiation of accelerated Xe beam, we observed an energy shift of the mode of ammonia. The shifted mode is assigned to that of ammonia molecules at the interface between the ice film and the Pt(1 1 1) surface. This indicates that the collision with Xe beam induced the penetration of an ammonia molecule to the interface through the ice film. Using this feature, we estimate a barrier for penetration as 0.28 ± 0.03 eV which is much smaller than the one previously reported for bulk ice.     

Ionic diffusion on a lattice: Effects of the order-disorder transition on the dynamics of non-equilibrium systems

We examine the behaviour of the concentration profiles of particles with repulsive interactions diffusing on a host lattice. At low temperature, the diffusion process is strongly influenced by the presence of ordered domains. We use mean field equations and Monte-Carlo simulations to describe the various effects which influence the kinetic behaviour. An effective diffusion coefficient is determined analytically and is compared with the simulations. Finite gradient effects on the ordered domains and on the diffusion are discussed. The kinetics studied is relevant for superionic conductors, for intercalation and also for the diffusion of particles adsorbed on a substrate. Received: 26 June 1997 / Revised: 18 September 1997 / Accepted: 10 November 1997     

Method for independent control of particle size and distance in rhodium epitaxy on TiO2(110)-(1×2) surface An STM study

A method for independent control of the particle size and distance is presented for rhodium epitaxy on TiO₂(110)-(1×2) surface. The real space imaging of the surface morphology was performed by scanning tunneling microscopy. The amount of the deposited rhodium was checked by Auger electron spectrometry. The method consists of two steps: (i) evaporation of 0.001–0.050 ML equivalent of rhodium at room temperature with a post-annealing at 1100 K (“seeding”); (ii) post-deposition of rhodium for growing of the Rh nanoparticles formed in step (i) (“growing”). The mechanism of this procedure is based on the large difference of the surface diffusion coefficient between Rh adatoms and Rh nanocrystallites larger than 1–2 nm. In the first step the average distance between the metal particles is controlled in the range 5–200 nm, the second step determines the particles size (2–50 nm). This work demonstrates that the diffusion processes of metal nanoparticles of different sizes and the growing modes of the crystallites can be studied in detail by application of seeded surfaces.     

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.     

Physical characterization of a new composition of oxidized zirconium-2.5 wt% niobium produced using a two step process for biomedical applications

Zirconium and particularly Zr-2.5 wt%Nb (Zr2.5Nb) alloy are useful for engineering bearing applications because they can be oxidized in air to form a hard surface ceramic. Oxidized zirconium (OxZr) due to its abrasion resistant ceramic surface and biocompatible substrate alloy has been used as a bearing surface in total joint arthroplasty for several years. OxZr is characterized by hard zirconium oxide (oxide) formed on Zr2.5Nb using one step thermal oxidation carried out in air. Because the oxide is only at the surface, the bulk material behaves like a metal, with high toughness. The oxide, furthermore, exhibits high adhesion to the substrate because of an oxygen-rich diffusion hardened zone (DHZ) interposing between the oxide and the substrate.In this study, we demonstrate a two step process that forms a thicker DHZ and thus increased depth of hardening than that can be obtained using a one step oxidation process. The first step is thermal oxidation in air and the second step is a heat treatment in vacuum. The second step drives oxygen from the oxide formed in the first step deeper into the substrate to form a thicker DHZ. During the process only a portion of the oxide is dissolved. This new composition (DHOxZr) has approximately 4-6 μm oxide similar to that of OxZr. The nano-hardness of the oxide is similar but the DHZ is approximately 10 times thicker. The stoichiometry of the oxide is similar and a secondary phase rich in oxygen is present through the entire thickness. Due to the increased depth of hardening, the critical load required for the onset of oxide cracking is approximately 1.6 times more than that of the oxide of OxZr. This new composition has a potential to be used as a bearing surface in applications where greater depth of hardening is required.