Effect Of Surface Diffusion Research Articles

Sorption Kinetics and Intracrystalline Diffusion of Methanol in Ferrierite: An Example of Disguised Kinetics

Sorption kinetics of methanol in large crystals of ferrierite have been studied in detail by interference microscopy (IFM) and infra-red microscopy (IRM). The IFM measurements yield the transient concentration profiles, thus providing a direct measurement of both the surface resistance to mass transfer and the internal diffusion resistance. It is shown that, for this system, the uptake rate is controlled by the combined effects of surface resistance and diffusion through the 8-ring channels (in the y-direction). Transport through the 10-ring channels (in the z-direction) appears to be blocked by surface resistance. Although the overall uptake curves conform well to the “root t law” the diffusivity values derived from the uptake curves vary widely depending on the assumed direction of diffusion. Even if the correct direction of diffusion is assumed, the diffusivity values derived from the uptake curves are seriously in error as a result of the intrusion of surface resistance. The existence of transport resistances at the crystal surface is clearly apparent from the transient concentration profiles but is not obvious from the uptake curves.

Self- and Interdiffusion in Ternary Cu-Fe-Ni Alloys

Self- and Interdiffusion in Ternary Cu-Fe-Ni Alloys

Continuum approach to self-similarity and scaling in morphological relaxation of a crystal with a facet

The morphological relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition temperature is studied analytically for diffusion-limited (DL) and attachment-detachment-limited (ADL) kinetics with inclusion of the Ehrlich-Schwoebel barrier. The slope profile $F(r,t)$, where $r$ is the polar distance and $t$ is time, is described via a nonlinear, fourth-order partial differential equation (PDE) that accounts for step line-tension energy ${g}_{1}$ and step-step repulsive interaction energy ${g}_{3}$; for ADL kinetics, an effective surface diffusivity that depends on the step density is included. The PDE is derived directly from the step-flow equations and, alternatively, via a continuum surface free energy. The facet evolution is treated as a free-boundary problem where the interplay between ${g}_{1}$ and ${g}_{3}$ gives rise to a region of rapid variations of $F$, a boundary layer, near the expanding facet. For long times and ${g}_{3}∕{g}_{1}<O(1)$ singular perturbation theory is applied for self-similar shapes close to the facet. For DL kinetics and a class of axisymmetric shapes, (a) the boundary-layer width varies as ${({g}_{3}∕{g}_{1})}^{1∕3}$, (b) a universal ordinary differential equation (ODE) is derived for $F$, and (c) a one-parameter family of solutions of the ODE are found; furthermore, for a conical initial shape, (d) distinct solutions of the ODE are identified for different ${g}_{3}∕{g}_{1}$ via effective boundary conditions at the facet edge, (e) the profile peak scales as ${({g}_{3}∕{g}_{1})}^{\ensuremath{-}1∕6}$, and (f) the change of the facet radius from its limit as ${g}_{3}∕{g}_{1}\ensuremath{\rightarrow}0$ scales as ${({g}_{3}∕{g}_{1})}^{1∕3}$. For ADL kinetics a boundary layer can still be defined, with thickness that varies as ${({g}_{3}∕{g}_{1})}^{3∕8}$. Our scaling results are in excellent agreement with kinetic simulations.

Permeation and separation of a carbon dioxide/nitrogen mixture in a methyltriethoxysilane templating silica/α-alumina composite membrane

The experimental and theoretical study of gas permeation and separation characteristics of an MTES (methyltriethoxysilane) templating nano-porous silica/α-alumina composite membrane was conducted using a carbon dioxide/nitrogen binary system. The adsorption equilibriums of carbon dioxide and nitrogen on the MTES templating silica layer were measured using a gravimetric method. The surface diffusion was a dominant transport mechanism on the MTES templating silica layer rather than micro-pore diffusion. On the other hand, the surface diffusion effect of nitrogen was much smaller than that of carbon dioxide. In the separation of the carbon dioxide/nitrogen mixture on the composite membrane, the strong adsorbate on the MTES templating silica layer permeated through the membrane more rapidly than the weak adsorbate due to the surface diffusion and/or the pore-blocking phenomenon. The permeation and separation of multi-component permeation were well predicted by the combined GMS (generalized Maxwell–Stefan) and DGM (dusty gas model) model. The separation characteristics of the composite membrane were tested under various experiment conditions such as feed pressure, temperature, stage cut and sweeping gas flow rate.

A kinetic Monte Carlo simulation of film growth by physical vapor deposition on rotating substrates

Abstract Film growth by physical vapor deposition on rotating substrates is modeled via a kinetic Monte Carlo algorithm on a two-dimensional hexagonal lattice. The motivation is to provide insight on the evolution of porosity during the deposition of thermal barrier coatings (TBCs). The model is implemented on an atomic scale that incorporates the effect of surface diffusion as well as the interplay between surface topography and the changing vapor incidence angle. It is shown that substrate rotation generates voids with a periodicity dependent on the amount of material deposited per revolution. The onset of pore formation and morphology of the pores are linked to the presence of shadowing features on the surface, either in the form of stochastic or crystallographic peaks and valleys evolving during columnar growth, or pre-existing roughness typical of polycrystalline oxide substrates. In addition, various forms of anisotropy develop in the microstructure as a result of the “sunrise–sunset” pattern of vapor incidence characteristic of TBC deposition on, for example, turbine airfoils. Comparison with observations on actual TBCs reveals that the simulations, in spite of their simplicity, capture several key microstructural features characteristic of these complex films.

Modeling and visualization of polycrystalline thin film growth

A novel polycrystalline thin film growth simulator, FACET, has been developed. FACET is a multi-scale model with two major components: an atomic level one-dimensional kinetic lattice Monte Carlo (1D KLMC) model and a real time feature scale two-dimensional facet nucleation and growth model. The 1D KLMC model has been developed to calculate inter-facet diffusion rates. By inputting the diffusion activation energies, the model will calculate the inter-facet atomic flux between {1 0 0}, {1 1 0}, and {1 1 1} facets of FCC materials at any temperature. The results of the 1D KLMC model have been verified by comparison with a full three-dimensional kinetic lattice Monte Carlo (3D KLMC) model. The feature scale polycrystalline thin film nucleation and growth model is based on describing grains in terms of two-dimensional faceted surfaces and grain boundaries. The profile of the nuclei are described by crystallographically appropriate facets. The position and orientation of the nuclei can be randomly selected or preferred textures can be created. Growth rates are determined from different deposition fluxes and surface diffusion effects. Quantitative microstructural characterization tools, including roughness analysis, average grain size analysis, and orientation distribution analysis, were incorporated into the model, which allows the users to design, conduct and analyze the virtual experiments within one integrated graphical user interface. Users can also visualize the nucleation and growth process of the film and obtain the final film microstructure. The effects of thickness, temperature, and deposition flux on thin film microstructures have been studied by FACET.

Effect of pH and concentration on the diffusion of radiostrontium in compacted bentonite—a capillary experimental study

The effects of pH and Sr 2+ solution concentration on diffusion and sorption of Sr 2+ in compacted bentonite ( ρ b=1000±30 kg/m 3) were studied using an “in-diffusion” method at an ionic strength of 0.1 M NaClO 4. The results (distribution coefficients, K d, apparent and effective diffusion coefficients, D a and D e) derived from the capillary method are in good agreement with the literature data obtained for similar bentonite dry densities and fit Fick's second law very well. The results suggest that the diffusion of Sr 2+ in compacted bentonite decreases slightly with increasing pH values and also increases slightly with increasing Sr 2+ solution concentration. The distribution coefficients are weakly dependent on the solution concentrations and show a slight increase with increasing pH values. The average effective diffusion coefficient of Sr 2+ in compacted bentonite is (1.2±0.2)×10 −9 m 2/s, surface diffusion effects are found for the diffusion of Sr 2+ in compacted bentonite.

Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion.

A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i). the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii). kinetic effects are negligible. A recently derived antitrapping current [Phys. Rev. Lett. 87, 115701 (2001)]] is used in the solute conservation equation to recover precisely local equilibrium at the interface and to eliminate interface stretching and surface diffusion effects that arise when the solutal diffusivities are unequal in the solid and liquid. Model results are first compared to analytical solutions for one-dimensional steady-state solidification. Two-dimensional thermosolutal dendritic growth simulations with vanishing solutal diffusivity in the solid show that both the microstructural evolution and the solute profile in the solid are accurately modeled by the present approach. Results are then presented that illustrate the utility of the model for simulating dendritic solidification for the large ratios of the liquid thermal to solutal diffusivities (Lewis numbers) typical of alloys.

Electromigration-induced surface evolution in bamboo lines with transgranular and intergranular edge voids

The evolution of a surface intersected by transgranular (TG) and intergranular (IG) edge voids under isotropic surface diffusion and electric field effects is simulated numerically under both mass-conserving and non-mass-conserving boundary conditions. A surprising similarity is found in the surface topology of transgranular voids between our non-mass-conserving model and Schimschak and Krug's [J. Appl. Phys. 87 (2000) 695] mass-conserving model. The electric field is found to slow the development of an intergranular groove along a positively tilted grain boundary (GB), and to cause thinning or thickening of grains under non-mass-conserving conditions.

Effects of Surface Diffusion of Reflectors on the Acoustic Power from the Stage Area

When a sound source is located near a large plane-surface reflector, the total acoustic power radiated from the source including the reflection depends on the source position. Interference is the cause of this phenomenon, and the musical instruments for bass sound are particularly influenced. The surface diffusion treatment of the stage reflectors may be a solution for improving the problem. In this paper, from the viewpoint of acoustic power from the stage area to the audience area, the effect of surface diffusion of a stage rear-wall is examined by using an analytical model of 2 and 3-dimensional wave theory. As a result of some numerical examples, it is shown that a rear wall tilted more than right angles has a potential of improving the effect.

Selected area growth of II–VI nanostructures using shadow masks

AbstractWe investigate molecular beam epitaxy of II–VI materials through GaAs/AlGaAs epitaxial shadow masks on GaAs(001) substrate. Scanning electron and atomic force microscopy are employed to investigate the effects of surface diffusion, faceting, partial shadow (minimized in the experimental set‐up), and material deposition on the mask (closing of apertures) on the selected area growth of ZnSe and CdSe. The results illustrate that selected area growth of II–VI nanostructures is controlled by the growth geometry. In contrast to the case of III–V materials, we found no macroscopic features (>10 nm) which could be attributed to surface diffusion. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation

Surface diffusion is a (fourth-order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for graphs and derive a priori error estimates for a time-continuous finite element discretization. We also introduce a semi-implicit time discretization and a Schur complement approach to solve the resulting fully discrete, linear systems. After computational verification of the orders of convergence for polynomial degrees 1 and 2, we show several simulations in one dimension and two dimensions with and without forcing which explore the smoothing effect of surface diffusion, as well as the onset of singularities in finite time, such as infinite slopes and cracks.

Systematic study of effects of growth conditions on the (nano-, meso-, micro)size and (one-, two-, three-dimensional) shape of GaN single crystals grown by a direct reaction of Ga with ammonia

A series of experiments have been conducted to systematically study the effects of growth conditions (NH3 flow rate, growth temperature, chamber pressure, and growth location) on the size (nano, meso, or micro) and the shape (one, two, or three dimensional) of GaN single crystal products grown by a direct reaction of Ga with NH3. A growth map with a wider range of experimental parameters was developed; it has three distinct zones. The size and shape of the products in every zone were found to depend on both temperature and NH3 flow rate with other growth conditions fixed. An effective surface diffusion length consisting of the Ga atomic surface diffusion length and the GaN molecular surface diffusion length, and the anisotropy of the Ga surface diffusion length and the GaN growth rate in different growth directions were introduced into the growth model, in such a way that it allowed successful explanation of all observed results. The optimal growth parameters could thus be determined, which conclusively demonstrated that nanowires with uniform diameter, clear crystal structure, length larger than 1 mm, uniform location distribution, and high yield can be obtained. Such a growth map based on in-depth understanding of the growth mechanism provides a clear direction for growing various materials with desired size and shape.

New directions in fluid dynamics: non-equilibrium aerodynamic and microsystem flows.

Fluid flows that do not have local equilibrium are characteristic of some of the new frontiers in engineering and technology, for example, high-speed high-altitude aerodynamics and the development of micrometre-sized fluid pumps, turbines and other devices. However, this area of fluid dynamics is poorly understood from both the experimental and simulation perspectives, which hampers the progress of these technologies. This paper reviews some of the recent developments in experimental techniques and modelling methods for non-equilibrium gas flows, examining their advantages and drawbacks. We also present new results from our computational investigations into both hypersonic and microsystem flows using two distinct numerical methodologies: the direct simulation Monte Carlo method and extended hydrodynamics. While the direct simulation approach produces excellent results and is used widely, extended hydrodynamics is not as well developed but is a promising candidate for future more complex simulations. Finally, we discuss some of the other situations where these simulation methods could be usefully applied, and look to the future of numerical tools for non-equilibrium flows.

Bulk mediated surface diffusion: the infinite system case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.

Slow dynamics of embedded fluid in mesoscopic confining systems as probed by NMR relaxometry.

Mesoscopic media such as porous materials or colloidal dispersions strongly influence the dynamics of the embedded fluid. In the strong-adsorption regime, it was recently proposed that the effective surface diffusion on flat surface is anomalous and exhibits long-time pathology, enlarging the time domain of the embedded-fluid dynamics towards the low-frequency regime. An interesting way to probe such a slow interfacial process is to use the field-cycling NMR relaxometry. This technique is used here to probe the fluid dynamics in two types of interfacial systems: i) a colloidal glass made of thin and flat particles; ii) a fully saturated porous media, the Vycor glass. Experimental results are critically compared to either a simple theoretical model of NMR dispersion involving elementary steps of the fluid dynamics near an interface (loops, trains, tails) or Brownian-dynamics simulations performed inside 3D reconstructions of these confined systems.

Nanostructuring of solid surfaces by ion-beam erosion

Extensive experimental investigations are presented on the self-organized formation of regular ordered nanodot structures on InP and GaSb surfaces during ion-beam erosion. It is demonstrated that hexagonally arranged dots can be formed by Ar+ sputter erosion either at normal or, alternatively, at oblique ion incidence with simultaneous sample rotation. The size, the geometrical shape, and the local ordering of these dots are determined by ion energy and ion-incidence angle. At elevated temperatures, square-pattern ordering can occur instead of hexagonal ordering. The experimental findings are critically discussed within the context of a stochastic partial differential equation, intentionally proposed to describe this pattern formation. Provided that ion-induced effective surface diffusion is the dominant relaxation process, this theory is proved to predict quantitatively the formation of a dot pattern and the magnitude of its spatial period at a nearly glancing ion-incidence angle of 75 degrees from normal approximately. Nevertheless, the current status of this theory does not allow a complete description of self-organized nanodot formation by ion-beam erosion.

Synthesis of ceria based ion conducting mesoporous membranes by soft-chemistry

Ce0.9Gd0.1O1.95 (CGO) nanophase materials and related porous supported membranes were synthesized by a soft-chemistry route. One of the membranes was post-impregnated with Pt nanoparticles. The CGO average crystallite size is in the range 9–22 nm and the specific surface area varies from 43.4 to 6.7 m2/g in the intermediate temperature domain between 500 and 700 °C. The gas permeation properties of Pt-free and Pt post-impregnated CGO porous membranes were studied up to 500 °C. Although, the intrinsic bulk ionic conduction properties of the CGO material cannot be expected to contribute to oxygen transport at such a low temperature, attractive surface diffusion effects have been evidenced, which were clearly enhanced by a dispersion of Pt particles. The observed inversion of O2/N2 selectivity (α>1) compared to the Knudsen selectivity αK(O2/N2)=0.935 was attributed to the effect of the nanophase CGO material. Insertion of Pt nanoparticles increased oxygen surface diffusion at low temperature independently of the CGO effect. The barrier effect of the membranes and the induced solid/gas contact time were considered as key parameters to develop these porous nanophase ceramic membranes.

Parameter Optimization of Molecular Models: Application to Surface Kinetics

A multistep methodology is explored for the optimization of the parameters of molecular models. This methodology is based on response surface methods and circumvents the practically impossible rigorous parameter fitting of computationally intensive molecular models. The approach is demonstrated for the parameters of the catalytic oxidation reaction of CO on platinum modeled by kinetic Monte Carlo simulations. After implementation of an initial reaction mechanism, sensitivity analysis is carried out to determine the key (active) reaction parameters for selected experimental points. Next, solution mapping is used to parametrize the model responses as low-degree polynomials of the active parameters. Finally, optimization of the active parameters is performed using simulated annealing. The optimized parameters are contrasted to those of a continuum-type mean-field model. The effect of surface diffusion in determining intrinsic kinetic parameters is also addressed, and the possibility of bridging the pressure gap via multiscale simulations is discussed.

Step Bunching in a Si(001) Vicinal Face with Electric Current : Effects of Surface Diffusion and Step Kinetics

Step Bunching in a Si(001) Vicinal Face with Electric Current : Effects of Surface Diffusion and Step Kinetics