Surface Diffusion Rate Research Articles

Effect of H on Si molecular-beam epitaxy

In Si crystal growth by molecular-beam epitaxy (MBE) at low temperatures there is known to be an epitaxial thickness: an initially crystalline regime before the deposited film becomes amorphous. The predominant impurity in MBE is hydrogen, but the role of background H in low-temperature MBE has not previously been assessed. Here the effect of deliberate dosing of the Si surface with atomic H during low-T growth is studied. The epitaxial thickness is shown to be sensitive to very small additional H fluxes (≊10−9 Torr, i.e., an increase in H only marginally above ambient). With further increases in dose rate, the epitaxial thickness decreases as hepi=h0−k(ln PH). Using secondary-ion-mass spectrometry data on the segregated H at the interface, we argue that breakdown in epitaxy is not caused directly by the surface concentration of adsorbed impurities. It is deduced that very small concentrations of H may influence the Si surface diffusion rate. The possible effect of background H adsorption on previous experiments on Si steps and surface diffusion is discussed.

Influence of Atmosphere on the Final‐Stage Sintering Kinetics of Ultra‐High‐Purity Alumina

The influence of sintering atmosphere on the final‐stage sintering of ultra‐high‐purity alumina has been investigated. Model final‐stage microstructures were tailored via a latex sphere impregnation and burnout technique. Critical experiments have been conducted to quantitatively examine the influence of the oxygen partial pressure on the final‐stage sintering kinetics. Samples were sintered at 1850°C in either dry hydrogen (Po2∼ 3 × 10−17 atm) or wet hydrogen Po2∼ 5 × 10−10 to 2 × 10−11 atm), and their microstructures were characterized as a function of sintering time, Sintering in dry hydrogen decreased the susceptibility of the final‐stage microstructure to pore/boundary breakaway. In the kinetic analysis, the variation in the number of pores per grain, Ng, was taken into account. It was found that in both atmospheres, the densification rate was controlled by grain boundary diffusion, and that sintering in dry hydrogen increased the densification rate by a factor of 2.25. In addition, it was determined that the grain growth rate in both atmospheres was controlled by the rate of surface diffusion of matter around the pores and that sintering in dry hydrogen enhanced the grain growth rate by a factor of 5.6. The overall effect of the dry hydrogen atmosphere was that it enhanced the coarsening rate relative to the densification rate by a factor of 2.5, and consequently shifted the grain size‐density trajectory to much lower densities for a given grain size.

Kinetics of Radical Processes in Organic Crystals during High-Pressure Shearing

The kinetic dependencies of radical generation and recombination during shearing under high pressure of an organic polycrystalline compound, arylindandione dimer, were investigated using modified EPR spectroscopy. The radicals were created as a result of dimer splitting at shear deformation. A statistical model of brittle crushing and a semiphenomenological theory of radical kinetics were proposed. The theory describes well the functional dependence of EPR spectral parameters on the shearing angle, shear rate, and pressure, as well as on shearing by impact. Comparison with experimental data enabled us to determine the parameters of the radical kinetics: grain dimensions, multiplicity of grains split during shearing, radical density on the grain surface, and the radical surface diffusion rate constant. The work reveals the broad capabilities of the EPR method in investigating microscopic parameters of destruction of solids by mechanical stresses.

Monte Carlo study of the temperature dependence of domain-growth kinetics in a system with a nonconserved order parameter and a zero-temperature equilibration fixed point.

We have investigated the relationship between the proportionality factor in the Lifschitz-Allen-Cahn scaling relation and the microscopic kinetics of nonequilibrium transport in a Monte Carlo model of domain growth in a two-dimensional, quenched, chemisorbed overlayer with a nonconserved order parameter and a zero-temperature equilibration fixed point. We have identified two components of the proportionality factor, which reflect the two temperature dependences of domain growth in this system. The primary temperature dependence arises from the rate of surface diffusion. In addition, we find a factor, \ensuremath{\alpha}, which decreases with increasing temperature due to the influence of thermal fluctuations. We also find that the proportionality factor has a time dependence, which arises from the rate of surface diffusion. We have found that this time dependence can influence the apparent form of the growth law. We discuss why the observed time dependence of diffusion should be a general phenomenon present in both simulations and experiments of domain growth in quenched systems.

Snow crystals, natural and man made

Abstract A short history of observations on the shapes of snow crystals starts in ancient China, summarizes the remarkable but little-known essay by Kepler in 1611, includes contributions by Descartes and Hooke, and ends with the beautiful collections of microphotographs by Bentley and Humphreys (1931) and Nakaya (1954). Modern observations from aircraft and mountain observatories reveal that the dominant crystal habits, hexagonal plates, columns, needles and dendritic stellar forms, and transition from one to another, are strongly correlated with air temperature, with the supersaturation of the vapour having only a secondary influence. There follows a review of laboratory experiments to determine the nature and origin of natural ice-forming nuclei and the properties of artificial nuclei, such as silver iodide, through the study of epitaxial growth of ice crystals on single crystalline substrates. Growth of snow crystals under carefully controlled conditions in laboratory cloud chambers has established that the crystal habit changes sharply six times over the temperature range 0 to—25°C. The author argues that the basic habit is determined in the very early stages of growth by the relative rates of surface diffusion of water molecules across the basal and prism faces. He deduces the average migration distance, xs, for molecules on the basal face from measurements on the velocity of growth layers and of that on the prism faces from measurements on the axial ratios of small crystals. In both cases, xs, varies rapidly between 1 and 6 μm with temperature, and the two curves intersect at three temperatures that correspond to transitions between crystal habits. A theory is developed to explain the transition from regular plates to dendritic stellar crystals; the corners sprout when material from the vapour phase arrives at corners more rapidly than it can be carried away by surface diffusion and occurs only when the diameter of the plate exceeds a critical value dc, ∝ Ds, /Dv, = αx2 p, /Dv, where Ds, Dv, are the coefficients of surface and volume diffusion and xp, is the surface migration distance on the (prism) edge of the plate. The predictions of the theory are compared with observations on natural snow crystals. Equations are derived for the growth rates of snow crystals as they fall through the atmosphere. The predicted maximum attainable diameters of the various shapes are in good agreement with observations.

Scanning electrochemical microscopy. 14. Scanning electrochemical microscope induced desorption: a new technique for the measurement of adsorption/desorption kinetics and surface diffusion rates at the solid/liquid interface

Scanning electrochemical microscope induced desorption (SECMID) is introduced as a new technique for the measurement of adsorption/desorption kinetics and surface diffusion rates at the solid/liquid interface, which is generally applicable to the study of reversible processes involving electroactive adsorbates. The method utilizes the ultramicroelectrode (UME) probe of a scanning electrochemical microscope, located close to the sample surface, to perturb the equilibrium of the solid/liquid interfacial adsorption/desorption process under investigation and to measure the resulting flux of adsorbate desorbing from the surface. This is achieved through the application of a potential step to the UME such that the solution component of the adsorbate is electrolyzed at a diffusion-limited rate. The resulting UME current is a measure of the rate of diffusion through solution, the adsorption/desorption kinetics, and the rate of surface diffusion. A theoretical treatment of the chronoamperometric (current-time) response of SECMID is developed, and experimental strategies for obtaining both a&rption/desorption kinetics and surface diffusion rates are delineated. Particular emphasii is given to the a&rption/desorption of H+ on hydrous metal oxides. The applicability of the technique is illustrated with experiments on the adsorption/dwrption of H+ on rutile (001) and aluminosilicate, albite (NaA1Si308), (010) surfaces. Iatroduction Adsorption/desorption processes and surface diffusion are key steps in the general scheme of reactions at the solid/liquid interface,' and thus dynamic measurements of their rates are of fundamental importance in understanding a variety of interfacial reactions in the physical2 and biological3 sciences. Although a number of techniques are available for measuring adsorption/ desorption kinetics at the electrode/electrolyte interface? kinetic measurements of the elementary steps involved in such processes on insulating materials in contact with liquids are more difficult, and comparatively few studies in this area have therefore been rep~rted.~g' Notable exceptions include the use of relaxation methods,2b-6 employing either pressure jump or electric field pulses, and the stopped-flow technique' for kinetic measurements on suspensions of powdered material. Additionally, total internal reflection fluorescent methods have been used to study adsorption/desorption kinetics and surface diffusion rates of fluorescent-labeled molecules at the solid/liquid Relaxation methods have provided useful insights into the mechanisms of a number of rapid adsorption/desorption processe~.~~-~ However, since, in general, this approach can only be applied to adsorbents in the form of suspensions, which comprise various crystal faces (and amorphous material), the measured characteristics represent an average of the behavior of individual faces, possibly with very different adsorptive characteristics. This is in marked contrast to surface studies at both the electrode/ electrolyte9 and gas/solidIo interfaces, where well-defined surfaces (e&, single crystals) are often used.

Model predictions of feature-size-dependent step coverages by PVD aluminum: surface diffusion

The three-dimensional ballistic transport and reaction model (BTRM), a flux-based model which predicts the evolution of film profiles during low pressure deposition processes, is discussed and the governing equations for finite trenches are presented. The equations governing the evolution of deposited films are material balances on species adsorbed on the surface and include surface diffusion and non-cosine flux distributions. Simulations of aluminum physical vapor deposition (PVD) indicate that surface diffusion can result in feature-size-dependent step coverages. A single parameter in the governing equation for aluminum PVD the ratio of a characteristic rate of surface diffusion to a characteristic deposition rate, governs the effect of diffusion on step coverage in this process. Step coverage can be increased for a given process and given trench dimensions by increasing the surface diffusion or decreasing the deposition rate. According to the BTRM, the diffusivity should be scared by the square of the feature size to maintain a target step coverage for given operating conditions. The assumed forms for the angular distributions of fluxes from the source to the feature do not cause feature-size-dependent step coverages in the absence of surface diffusion, although they do impact step coverage for specified feature geometry and dimensions.

Surface diffusion of organic vapor mixtures through porous glass

This study reports the experimental results of surface diffusion on porous glass for four vapor mixtures, i.e. benzene/hexane, benzene/cyclohexane, benzene/acetone and benzene/methanol, at 308 K. For all components, the surface diffusion flux was changed by the presence of the accompanying component. This suggests that interaction among permeants plays a significant role in the surface diffusion of the mixtures. To discuss the interaction quantitatively, the adsorption equilibrium and surface diffusion coefficients, which determine surface diffusion rates, were obtained experimentally. For the adsorption equilibrium, an extended BET equation was derived by introducing interaction terms among different components; the equation expressed the experimental results of the adsorption equilibrium well. For the surface diffusion coefficients, the hopping model was extended to a binary system by considering the changes in the potential barrier of hopping due to the interaction between a diffusing molecule and an adsorbed molecule; the extended model explained the dependence of the surface diffusion coefficients on the amounts adsorbed up to monolayer capacities. These results show that interaction among components affects both the adsorption equilibrium and the surface diffusion coefficients. Furthermore, correlations were found between the interaction term in the expression of surface diffusion coefficients and the corresponding interaction term in the expressions of the adsorption equilibrium.

Slow adsorption kinetics of H2O on Si(111)7 × 7

The kinetics of H2O adsorption on Si(111)7 × 7 was studied at H2O vapor pressures of 2 × 10−11 to 4 × 10−8 Torr by the flash desorption technique. The surface coverage was found to depend not only on the surface exposure, i.e., on the P × t product, but also on the vapor pressure P or the exposure time t per se. Within the water vapor pressure interval mentioned above the sticking coefficient varied between 8 × 10−2 and 9 × 10−3, respectively. A possible mechanism includes creation of a 2D hydrosilicate phase forming islands on terraces between the steps and/or strips along the steps. Stoichiometry of this hydrosilicate phase should demand surface diffusion to or from the new 2D phase. The surface diffusion rate αt−12 may be responsible for the observed dependence of surface coverage both on the Pt product and on P or t in addition.

Surface crystallization kinetics in soda-lime-silica glasses

A review of previous research on surface nucleation in glasses demonstrates that these are mostly qualitative and that strong discrepancies exist regarding the nucleation mechanism. In this article, the surface crystallization kinetics of several glasses — a Na20.3Ca0.6SiO2 (devitrite), a non-stoichiometric devitrite, and two commercial soda-lime-silica (a float and a microscope slide) glasses — were determined in a wide range of temperatures and time. An analysis of the average number of crystals per crystallization arises from a fixed number of special sites, Ns. The number of crystals nucleated strongly depends on the unit area, Ns, crystal growth rates and viscosity data indicates that the surface nucleation rates are very high and that surface condition (e.g., fire polished versus mechanically polished or as-received; clean versus dirty), on the chemical composition of the parent glass, and also on the nature of the crystallizing phase. However, Ns does not depend on time or temperature. The experimental evidence indicates that the surfaces ‘per se’ do not alter the thermodynamic barrier for nucleation (the interfacial energy or the chemical potential). The enhanced nucleation rates at the external surfaces are the result of the catalytic effect of some (unknown) solid impurity particles and faster surface diffusion rates.

The effects of steps, coupling to substrate vibrations, and surface coverage on surface diffusion rates and kinetic isotope effects: Hydrogen diffusion on Ni

We have applied canonical variational transition state theory with semiclassical transmission coefficients to investigate the dynamical effects of metal motions, surface defects (namely, steps), and surface coverage on the diffusion of H on the Ni(100) surface. We have used the embedded diatomics-in-molecules (EDIM) method to represent the hydrogen–hydrogen, hydrogen–metal, and metal–metal interactions. The roles of metal motions, surface defects, and coverage in the overall diffusion rates and kinetic isotope effects are discussed in detail, and comparisons with experimental data are made.

Regulation of Ca 2+ transport in brain mitochondria. I. The mechanism of spermine enhancement of Ca 2+ uptake and retention

Spermine enhances electrogenic Ca 2+ uptake and inhibits Na +-independent Ca 2+ efflux in rat brain mitochondria. As a result, Ca 2+ retention by brain mitochondria increases greatly and the external free Ca 2+ level at steady-state can be lowered to physiologically relevant concentrations. The stimulation of Ca 2+ uptake by spermine is more pronounced at low concentrations of Ca 2+, effectively lowering the apparent K m for Ca 2+ uptake from 3 μM to 1.5 μM. However, the apparent V max is also increased. At low Ca 2+ concentrations, Ca 2+ uptake is diffusion-limited. Spermine strongly inhibits Ca 2+ binding to anionic phospholipids and it is suggested that this increases the rate of surface diffusion which reduces the apparent K m for uptake. The same effect could inhibit the Na +-independent efflux if the rate of efflux is limited by Ca 2+ dissociation from the efflux carrier. In brain mitochondria (but not in liver) the spermine effect depends on the presence of ADP. In a medium that contains physiological concentrations of P i, Mg +, K +, ADP and spermine, brain mitochondria sequester Ca 2+ down to 0.1 μM and below, depending on the matrix Ca 2+ load. Moreover, brain mitochondria under the same conditions buffer the external medium at 0.4 μM, a concentration at which the set point becomes independent of the matrix Ca 2+ content. Thus, mitochondria appear to be capable of modulating calcium oscillations in brain cells.

Spin-orbit state specific laser probing of the desorption kinetics and islanding behavior of In on Si(100)

The adsorption and desorption characteristics of In on Si(100) are investigated. Laser-induced fluorescence is used to probe specific spin-orbit states of the desorbing or scattered In atoms. The sticking coefficients of both In ( 2P 1 2 ) and In ( 2P 3 2 ) are determined to be unity ( > 0.9). State specific desorption measurements show that the two spin-orbit states have the same desorption parameters. This indicates that both spin-orbit states originate from the same “bath” of In atoms on the surface. Isothermal desorption measurements, also using Auger spectroscopy, find that at surface temperatures below 820 K, and for coverages θ < 0.5 ML, In desorbs by a half order mechanism. This is in contrast to the results of Knall et al. [Surf. Sci. 209 (1989) 314] who observe a first order behavior. The 1 2 order desorption indicates two-dimensional In islands on the surface. We observe a first order desorption only for temperatures > 820 K. For θ > 0.5 ML, desorption takes place by a 2 3 order mechanism, whereas Knall et al. report a zero order. These differences are discussed in terms of possible differences in surface diffusion rates. The 2 3 order indicates indirect desorption from three-dimensional islands in terms of possible differences in surface diffusion rates. The first order desorption energy for In from Si(100) (θ < 0.5 ML, T > 820 K), is 2.5 ± 0.2 eV with a pre-exponential factor of 10log A = 14 ± 1 (s −1 . An activation energy, for the 2 3 order regime, which is attributed to diffusion of In from three-dimensional islands onto the surface, is 1.9 ± 0.1 eV, 10log A = 10.5 ± 0.5 log ML 1 3 s −1) .

Studies of adsorbate structure and dynamics on catalytic surfaces with NMR spectroscopy: CO on metals

NMR studies of adsorbed CO illustrate the methodology of NMR spectroscopy and demonstrate results attainable in a comprehensive application to a heterogeneous catalytic system. This review is divided into two sections: adsorbate structure and dynamics. CO adsorbs on dispersed metals in at least three forms: linear- and bridge-bonded CO on metal particles and multicarbonyls on isolated metal atoms. Broadline 13C NMR spectra of CO on Ru and Rh reveal distinct powder patterns for each type, which provides quantitative site distributions of the site geometries. High resolution spectra obtained by magic-angle spinning provide isotropic shifts which support the separation of the overlapping broadline components. The metallic character of the dispersed metal particles is revealed through susceptibility broadening and large Knight shifts. Further details of the adsorbed states are available through analysis of the various nuclear dipolar couplings; examples include measurements of the CO bond length, the local density of CO on the metal particles, and the intramolecular distance in dicarbonyls. The rates of surface diffusion and site exchange have been characterized by the application of three different methods — relaxation studies, lineshape narrowing, and spin-population labeling — which together allow measurements of rate constants spanning 8 orders of magnitude.

Thiophene hydrodesulfurization on fresh, spent, and treated catalysts

Thiophene hydrodesulfurization was explored as a means of characterizing activity of spent catalysts which have been subjected to severe treatment to remove coke and contaminant metals. Samples of a commercial trilobe catalyst in fresh, spent and treated states were examined. A Langmuir-Hinshelwood model was used to correlate intrinsic rate data. The fresh and spent catalysts exhibited highest and lowest activities respectively. Coke and metals removal partially restored activity on a unit weight basis. The adsorption parameter in the rate model was much higher for spent and treated catalysts than for fresh catalyst. The treatment restored the effectiveness factor to the level of the fresh catalyst. Application of simple diffusion-reaction theory to explain measured effectiveness factors yielded a tortuosity factor of 1.4 for the fresh catalyst, but yielded uncharacteristically low values (τ<1) for spent and treated catalysts. This theory, which is based upon assumptions of uniform pellet activity and diffusivity, may be invalid for these latter two catalysts because of nonuniform deactivation. Low tortuosity factors might also be the result of high surface diffusion rates - a possible consequence of increased adsorption in the latter two catalysts. A means of applying diffusion-reaction theory to Langmuir-Hinshelwood kinetics when adsorption-desorption constants are unknown was demonstrated.

Low-temperature Ge heteroepitaxy on GaAs(001)

It is shown through the use of low-energy electron diffraction and high-energy x-ray photoelectron diffraction that very nearly layer-by-layer epitaxial growth of ultrathin Ge films can be achieved on GaAs(001). Superior overlayer uniformity has been attained by minimizing the surface defect density on the substrate and growing at a low enough substrate temperature to prevent high rates of surface diffusion and the resulting agglomeration of adatoms. When these two conditions are achieved, clustering is minimized during the initial stages of epitaxy. We have found that the first monolayer of Ge intermixes with the substrate to a limited extent when grown at 220 °C. Partial third-layer formation occurs as a result of the deposition of two monolayer equivalents (ML eq), and some fifth-layer formation occurs during the deposition of the fourth ML eq, but is limited in extent. These films exhibit less clustering but are also not as well ordered as those grown at 320 °C.

The passivation of FeCrRu alloys in acidic solutions

Electrochemical and surface analytical techniques have been used to study the spontaneous passivation of Fe40CrRu alloys in 0.5 M solutions of sulphuric and hydrochloric acids. Passivation is achieved much more readily in alloys containing 0.2 w/o Ru than in alloys containing 0.1 w/o Ru, and for both these alloys passivation is more rapid in 0.5 M H 2SO 4 than in 0.5 M HCl. The increase in the rate of hydrogen evolution and the simultaneous lowering of the rate of anodic dissolution caused by ruthenium addition has been directly demonstrated for Fe40Cr-0.1Ru in 0.5 M H 2SO 4. These processes combine to produce a positive shift in the potential of the alloy, and the conventional passivation process in stainless steels then occurs at the passivation potential of Fe40Cr. Auger analysis shows that ruthenium is only a minor constituent of the passive surfaces of alloys containing 0.2 w/o Ru. Higher ruthenium concentrations (and evidence for a ruthenium redistribution process) are found on the passive surfaces of alloys containing 0.1 w/o Ru, where larger amounts of dissolution occur before the onset of passivation. A qualitative model to explain these observations is suggested. This presumes that the rate of surface diffusion of ruthenium atoms during selective dissolution is an important factor in determining the geometry of the ruthenium distribution, and hence its efficiency in promoting spontaneous passivation.

Characterization of gold surfaces for use as substrates in scanning tunneling microscopy studies

We have used scanning tunneling microscopy to characterize the surface of epitaxial gold on mica in air. We find that these surfaces are simple to prepare, are relatively inert to exposure to air or to water, and have atomically flat terraces extending for up to several hundred angstroms. The observed topography is consistent with the Au(111) surface. It is possible to produce bumps on the surface of less than 100 Å in size in a controlled manner by pulsing the tip voltage while scanning. Self-diffusion of gold is observed in the decay of written features and well as in the movement of existing terrace edges. In some cases, a periodicity in both the geometry of terrace edges and the spatial variation of surface diffusion rates suggest the presence of the 22×1 surface reconstruction.

Copper-catalyzed etching of silicon by F2: Kinetics and feature morphology

The copper-catalyzed fluorination of silicon is first order in [F2] and in [Cu]s until the coverage reaches ∼4 monolayers. Above ∼4 monolayers the reaction rate is zero order in copper, suggesting a limited number of catalytically active Cu/Si sites. Copper islands form at high coverages, above saturation, and provide a reservoir of catalyst. The limited rate of surface diffusion of copper leads to anisotropic etching and feature size-dependent etch depths. The copper compounds, CuF2 and CuO, and copper silicides, Cu5Si and Cu3Si, all catalyzed the F2-Si reaction which suggests that they are all converted to the same active species. The results can be explained by mechanisms involving copper fluorides or copper silicides as active intermediates.

Surface diffusion of H, D, and T on a metal surface: The role of metal motions in the kinetic isotope effects

Canonical variational transition state theory and a multidimensional semiclassical tunneling method were used to calculate the surface diffusion rate constants of H, D, and T on the (100) surface of a model metal, nominally Cu. In the present study, we especially examined the influence of metal motions on the kinetic isotope effect for this process. We have employed the embedded cluster approach with a cluster size of 28 metal atoms. The adsorbate–substrate and substrate–substrate interactions are modeled by pairwise potential functions. The results show that including the metal zero-point motions has a negligible effect on the kinetic isotope effect predicted by the rigid-lattice model, but the inclusion of nonzero metal vibrational amplitudes in the semiclassical tunneling path has a large effect. We call this phonon-assisted tunneling. In the low-temperature region, where phonon-assisted tunneling is most important, the isotope effects were found to be smaller than those predicted by the rigid-lattice model, whereas at higher temperatures, they are found to be larger than the lattice predictions. This occurs despite the fact that the phonon–adsorbate interactions decrease the effective reduced masses of the adsorbates in the tunneling region.