Diffusion Coefficient Of Atoms Research Articles

Nonlinear diffusion of interstitial atoms

A nonlinear kinetic discrete model for interstitial diffusion in a nonuniform system is presented, based on Martin's deterministic model and Hillert's sublattice theory, where the diffusion coefficient of interstitial atoms strongly depends on their local concentration. The nonlinear diffusion of interstitial atoms is characterized by the concentration-dependent correlation coefficient $\ensuremath{\gamma}$ and the relaxation time $\ensuremath{\tau}$, which are determined by the pair interaction energies between interstitial atoms and between interstitial atoms and matrix atoms, respectively. This model exceeds the range of validity of the traditional Fick's law, and allows of an extension of Fick's law to diffusion on the nanoscale.

Transport properties of ground-state aluminium atoms in hollow cathode gas discharge plasma

For investigation of Al atoms transport properties a pulse-periodic longitudinal hollow cathode gas discharge in cylindrical geometry is used. The cathode represents a 20 cm in length and 1.8 cm in inner diameter hollow aluminium cylinder. During the discharge Al atoms are sputtered from the wall into the cathode volume, while in the afterglow phase their concentration decreases due to diffusive losses back to the wall surface. The diffusive loss rates at different buffer gas pressures are measured by using a double-channel time-resolved optical absorption technique with gated photon counting. By relating the experimental loss rates with a diffusion model based on the experimental geometry and a boundary condition of the third kind, the diffusion coefficient of ground-state Al atoms in argon, as well as the reflection coefficient of these atoms from the cathode surface are obtained. The experimental value for the diffusion coefficient at 313 K temperature and 133 Pa argon pressure is D0 = 160 ± 30 cm2s−1. The reflection coefficient was found to be in the range: 0.2 < ρ < 0.82. The result for the diffusion coefficient is compared with theoretical results based on 12-6 Lenard-Jones and rigid-sphere inter-atomic interaction model.

Study on the Critical Time and Diffusion Coefficient in Grain-Boundary Segregation of Phosphorus

The critical times of phosphorus segregation in low alloy steel 12Cr1MoV at different solution temperatures, 1050°C and 1300°C, are studied and the diffusion coefficient of complexes, Dc, and diffusion coefficient of phosphorus, Di, are calculated. Results show that the calculated result with the kinetic equations perfectly fits with the experimental observations. And that the higher the solution temperature, the higher is the segregation level of phosphorus, and also the longer is the critical time. It also shows that in the segregation process, the rate of phosphorus segregation at first is high due to a large diffusivity of the complex, Dc. Then the segregation rate decreases due to decreasing complex concentration gradient. In the de-segregation process, the level of phosphorus segregation decreases with increasing holding time t. But the rate of phosphorus desegregation from grain boundaries to centre is slower compared with that in segregation for the diffusion coefficient of phosphorus atoms, Di, is far lower than that of the complexes, Dc.

Investigation of indium diffusion process in In + ion implanted GaAs

Rutherford backscattering (RBS) has been used to determine diffusion coefficients of indium atoms in semi-insulating (1 0 0) GaAs implanted with 250 keV In + ions at a fluence of 3×10 16 cm −2 and isobarically annealed at 600 and 800 °C temperature. Computer modeling of the indium depth profiles based on Ga vacancy-mediated diffusion has shown good agreement with the RBS experimental results. Self-annealing effect was confirmed to play an important role due to high defect mobility at room temperature ion implantation. Large values of the In diffusion coefficients obtained in the present study, in comparison with the literature data for unimplanted GaAs, confirms strong enhancement of the diffusion process by radiation damage.

Diffusion coefficient of krypton atoms in helium gas at low and moderate temperatures

In the present work, using the Chapman–Enskog method for dilute gases, the diffusion coefficients of ground krypton atoms in a very weakly ionized helium buffer gas are revisited. The calculations are carried out quantum mechanically in the range of low and moderate temperatures. The 1 Σ+ potential-energy curve via which Kr approaches He is constructed from the most recent ab initio energy points. The reliable data points used in the construction are smoothly connected to adequate long- and short-range forms. The calculations of the classical second virial coefficients and the Boyle temperature of the helium–krypton mixture are also discussed. These coefficients and their variations in terms of temperature are analysed by adopting the constructed HeKr potential and the Lennard–Jones form that fits it. The diffusion and elastic cross sections are also explored and the resonance features they exhibit are closely examined. The variation law of the diffusion coefficients with temperature is determined for typical values of density and pressure. The coefficients show excellent agreement with the available experimental data; the discrepancies do not exceed 5%.

Vapor-liquid-solid growth of silicon nanowires by chemical vapor deposition on implanted templates

We show the realization of a distinctive nanoscale metal template for the vapor-liquid-solid growth of semiconductor nanowires. The template is based on the high-dose implantation of metal ions into silicon substrates and subsequent annealing upon which the atoms agglomerate. In case the wafer is amorphized at the surface upon implantation and the metal atoms reside within the amorphized part of the wafer, a high diffusion coefficient (holds for Au) of the metal atoms in amorphous silicon (compared to crystalline silicon) yields agglomeration of metal atoms at the wafer surface and the formation of supercritical metal nanoparticles. We show the implantation of gold (dose at least 1×1016cm−2) and discuss the option to use this type of template formation with other metals, such as gallium, indium, aluminum, and palladium, which are partly easy to be oxidized.

Investigation of the interactions of long-lived excited atoms in the afterglow of gas discharge plasma

When an electric discharge is fired in a gas consisting of atoms or molecules with long-lived excited states there are several inelastic processes releasing fast electrons in the afterglow plasma after the end of the current pulse. Most common among them are the chemiionization and de-excitation electron-atom collisions. Here these processes are investigated by measurements of the reactant particle densities at the entrance and at the exit channels of the reactions. In this way the rate coefficients of the ionising collisions of the couples Ne3P2-Ne3P2, Ar3P2-Ar3P2, Kr3P2-Kr3P2, Xe3P2-Xe3P2 as well as the rate coefficients for chemi-ionization of the ground state mercury atoms by collision with Ne 33P2 and Ar 43P2, 1, 0 atoms were obtained. By similar measurements the rate coefficients for super elastic collisions between electrons and excited heavy rare gases atoms as well as mercury atoms in the electron temperature range 500 - 2000 K were obtained. By monitoring the decay of the excited atom's density and electron's density and temperature the rate coefficients of electron impact induced transfer of excitation between the levels of configuration np5(n + 1) s in Ne, Kr and Xe were determined. In the same way were derived the rate coefficients of the transfer of excitation between Cd 63P2, 1, 0 levels induced by collisions with ground state cadmium and neon atoms. The diffusion coefficients of magnesium atoms in rare gases and their reflection coefficients from the vessel metallic wall are determined. Besides, the diffusion coefficients of metastable Cd 63P2, 0 atoms in neon are also determined.

A predictive equation for solute diffusivity in liquid metals

Determination of diffusion coefficients of elements in liquid metals is of vital importance when studying metallurgical processes involving molten metals. In this study, a predictive diffusion coefficient equation, aimed at describing the diffusivity of solute atoms in liquid metals, has been developed. The prediction of this equation is in reasonably good agreement with the experimental studies. Due to the simple-parameter nature of the equation, it could be very useful in predicting diffusion coefficients of solute atoms in liquid metals when experimental data are scarce.

Diffusion of He interstitials in grain boundaries in α-Fe

Helium diffusion in metals is a complex process due to its very low solubility in solids and its ability to be trapped by vacancy type defects or impurities. The preferential positions and predominant migration mechanisms of He atoms depend on temperature, as well as the presence of other intrinsic or irradiation induced defects that can act as traps for He. This work presents results of a systematic molecular dynamics study of the diffusion mechanisms of He atoms in grain boundaries in α-Fe. Two grain boundaries, Σ11〈1 1 0〉 {3 2 3} and Σ3〈1 1 0〉 {1 1 2}, were used for the current investigations. The low-temperature (about 0 K) equilibrium structures of these grain boundaries were determined using standard molecular dynamics relaxation techniques, with a flexible border condition. The migration of He atoms were followed for 1–14 ns, at temperatures between 600 and 1200 K. The diffusion coefficient of He atoms using the mean square displacements of He atoms, and the effective migration energies were determined. We found that He atoms diffuse rapidly in the Σ11 grain boundary, where the binding energy of a He atom to the boundary is high. He migration is primarily one-dimensional along specific directions, but a few directional changes were observed at higher temperatures. In the Σ3 grain boundary, where the He binding energy is low, He atoms migrate one-dimensionally at low temperature, two-dimensionally at intermediate temperature and three-dimensionally at higher temperature. The different activation energies and diffusion mechanisms in these two representative grain boundaries suggests that the atomic structures of the grain boundaries play an important role in the diffusivity of He.

Solute size effects on the solvation structure and diffusion of ions in liquid methanol under normal and cold conditions

We have performed a series of molecular dynamics simulations of alkali metal (Li+, Na+, K+, Rb+, and Cs+) and halide (F-, Cl-, Br-, and I-) ions in liquid methanol at two different temperatures to investigate the effects of ion size on the hydration structure and diffusion of ions in methanol under normal and cold conditions. Simulations are also carried out for some of the larger cations such as I+, (CH3)4N+, and (C2H5)4N+ and also neutral alkali metal atoms in methanol at both temperatures. With the increase of ion size, the diffusion coefficients of both positive and negative ions are found to show anomalous behavior. For cations, it is found that the maximum of the diffusion coefficient versus ion size curve occurs at the rather large cation of (CH3)4N+ unlike in water where the maximum occurs at the relatively smaller ion of Rb+. For halide ions, the anomalous behavior, i.e., the increase of diffusion with ion size, continues up to iodide ion and no maximum is observed. These results are in good agreement with experimental observations. The diffusion coefficients of neutral atoms are found to be greater in methanol than that in water and they decrease monotonically with solute size, whereas the diffusion coefficients of the corresponding ions are found to be smaller in methanol. Accordingly, an ion experiences a smaller Stokes friction and a higher dielectric friction in methanol than in water. These contrasting effects are believed to be responsible for the shift of the maximum of ion diffusion toward a larger ion size when compared with similar anomalous size dependence in liquid water.

Simulating Liquid GeTe

AbstractOne of the most difficult problems in condensed matter physics is to describe the microscopic liquid state. Owing to the dynamical nature of the liquid state, it is not possible to discuss specific microscopic structures, only ensemble averages can be specified. Such averages can be performed via molecular dynamics simulations. A problematic issue in performing such simulations is computing accurate interatomic forces. Although classical many-body potentials can be use for simulations of covalent materials, one must effectively map quantum phenomena such as hybridization onto such potentials. This mapping is complex and lacking a well-defined prescription. This step can be avoided by employing quantum forces from the pseudopotential-density functional method. Using molecular dynamics with quantum forces, we examine the local atomic order as well as some dynamic and electronic properties of the semiconducting liquid GeTe. Near the melting temperature, the Peierls distortion responsible for the lower temperature crystal phase of GeTe is shown to manifest itself within the liquid structure. At higher temperatures in the liquid, increasing disorder leads to an eventual semiconductor-metal transition. The calculated kinematic viscosity of the liquid is found to agree with the experimental value and is shown to arise from the small diffusion coefficient of the Te atoms. Using an ensemble average, we predict the dc conductivity of the melt to be consistent with recent measurements.

Probe field spectroscopy in three-level Λ systems under arbitrary collisional relaxation of low-frequency coherence

We investigate theoretically the spectrum of weak probe field absorption by three-level atoms with the Λ configuration of levels in the field of a strong electromagnetic wave acting on an adjacent transition and colliding with buffer gas atoms. Analysis is carried out for the general case of arbitrary collisional relaxation of low-frequency coherence at a transition between two lower levels. It is shown that, in the absence of collisional relaxation of low-frequency coherence, the probe field spectrum always exhibits clearly manifested anisotropy with respect to mutual orientation of wavevectors of the strong and probe radiation (even under small Doppler broadening). It is found that the probe field spectrum may acquire under certain conditions supernarrow resonances with a width proportional to the diffusion coefficient for atoms interacting with radiation. This fact may form the basis for a spectroscopic method for measuring transport frequencies of collisions between absorbing and buffer particles. A large-amplitude supernarrow resonance (with an amplitude much larger than the amplitude of the resonance near the line center), which is observed in the far wing of the absorption line, exhibits collisional narrowing (a nonlinear spectroscopic analog of the Dicke effect) at collision frequencies several orders of magnitude lower that the Doppler linewidth. Simple working equations proposed for describing the probe field spectrum are convenient for experimental data processing.

The initial states of wetting and spreading of Sn on Al surfaces

Tin (Sn) deposited on polycrystalline aluminium (Al) surfaces shows a Stranski–Krastanov growth mode which means that before Sn islands nucleate a thin Sn wetting layer is formed. If the wetting layer is removed from the Al surface by sputter cleaning in UHV it reforms by a solid state wetting process. The sources of the Sn atoms forming the wetting layer are the Sn islands, which are not removed from the Al surface due to their size. Nonetheless, it was observed that not every island acts as an Sn emitter. In this work, we show that this selective Sn emission is a consequence of the chemical composition and the crystallographic structure of the Sn islands. Regarding the chemical composition of the Sn islands each residual trace of oxygen has to be removed to facilitate the emission of Sn atoms from the island boundaries. In addition wetting is only initiated if the sputter cleaning process results in a visible damage of the islands, thus increasing the roughness of their surface. From this rough interface Sn atoms can emerge more easily than from a crystallographically smooth surface due to their lower coordination. By monitoring line scans obtained from scanning auger electron spectroscopy the diffusion coefficient of the Sn atoms could be estimated from the progress of the rim of the wetting layer around the islands.

Simulation of copper atom diffusion via the vacancy mechanism in a dilute Fe-Cu alloy

Atomic diffusion in pure $\ensuremath{\alpha}$-Fe and Fe-l at. % Cu crystals via vacancies is investigated by molecular-dynamics computer simulation. In order to generate a large statistical set, modeling is performed for the temperature range of 1000--1800 K. The migration energy and preexponential factors in diffusion coefficients of copper and iron atoms are estimated and compared with the results of a five-frequency model, using different approaches for the frequencies, and Monte Carlo studies, where the energy barriers are obtained by molecular statics. It is concluded that the five-frequency model is valid. The vacancy-copper atom cross-diffusion coefficient is estimated by both molecular-dynamics and Monte Carlo methods and is concluded to be negative over the entire temperature range studied, indicating that under irradiation conditions copper atoms migrate in the direction opposite to the vacancy flux. It has been observed that, at temperatures above 1500 K, about 0.5% of the vacancy jumps are double jumps, when two atoms move simultaneously in a $⟨111⟩$ direction towards the vacancy.

Solidification of Pb overlayer on Cu(111) surface by molecular dynamics simulation

We present molecular dynamics simulation results based on a semi-empirical potential model in analogy to the tight binding theory in the second moment approximation, concerning the structural and dynamical properties of various concentrations Pb adlayers on the Cu(111) surface. We found that the adlayer's character changes from lattice gas to solid as the Pb concentration passes the characteristic value θ c = 37.5%. Specifically, at concentration less than θ c the deposited Pb atoms exhibit lattice gas behaviour, while above θ c 2D liquid like character appears, to recover typical solid behaviour above the saturation concentration that is dictated by the lattice mismatch at θ s = 56.3%. These conclusions are deduced from the calculated structural and dynamical properties of the overlayer, namely the Pb two-dimensional radial distribution function and the velocity autocorrelation functions as well as the atomic diffusion coefficient. It is found that for concentrations up to θ c the adlayer exhibits important expansion with Pb atoms flowing over the substrate and diffusing very fast, while at θ s the Pb adlayer is compressed by as much as − 2.65% with respect to the lattice spacing of the bulk Pb. Our findings are in agreement with available experimental results.

Superheating and Induced Melting at Semiconductor Interfaces

We present ab initio density-functional simulations of the state of several semiconductor surfaces at temperatures near the bulk melting temperatures. We find that the solid-liquid phase-transition temperature at the surface can be altered via a microscopic (single-monolayer) coating with a different lattice-matched semiconducting material. Our results show that a single-monolayer GaAs coating on a Ge(110) surface above the Ge melting temperature can dramatically reduce the diffusion coefficient of the germanium atoms, going so far as to prevent melting of the bulk layers on the 10 ps time scale. In contrast, a single-monolayer coating of Ge on a GaAs(110) surface introduces defects into the bulk and induces melting of the top layer of GaAs atoms 300 K below the GaAs melting point. To our knowledge, these calculations represent the first ab initio investigation of the superheating and induced melting phenomena.

Simulation of Interstitial Atom Diffusion in FCC Metals with Point Defects

This work is devoted to simulation of interstitial atom diffusion in fcc metals with point defects. We used the molecular static and the Monte Carlo methods. An activation barrier set for different configurations of the carbon–vacancy complexes is simulated by the method of the molecular static (MS). Then we calculate atom jump rates for these configurations. The simulation of the carbon and vacancy migration in an fcc metal is realized on the basis of obtained atom jump rates by using the Monte-Carlo (MC) method. In particular, the calculations were made for the system of the nickel-carbon. In the result of that interstitial atom diffusion coefficient has been obtained at different temperatures.

Activation energy of hydrogen, oxygen, and nitrogen diffusion in metals

Significant progress has recently been made in experimental studies of the diffusion of atoms of light elements in metals. In particular, for a number of metals, the diffusion coefficients of tracer atoms of hydrogen (tritium), oxygen, nitrogen, and boron were measured. Previously, such data were available only for carbon. New experimental data enabled us in this work to formulate the problem of developing a theoretical criterion for the reliability of experimental results on the activation energy Q for the interstitial diffusion mechanism. The necessity of formulating such a problem is primarily caused by the fact that the scatter of experimental data on the diffusion of interstitial impurities in metals is often very wide. For example, experimental values of the activation energy Q of hydrogen diffusion in α -Ti are within the range 24‐62 kJ/mol [1]. In this context, in this work, we analyzed experimental data on the diffusion of interstitial atoms in metals that were obtained by reliable methods. It was found that all such data on the activation energy of hydrogen, oxygen, and nitrogen diffusion are consistent with a calculation model [2, 3] based on the theory of elasticity. The calculation accuracy corresponds to the level of a modern precision experiment (on the order of 1%). The corresponding data for carbon and boron were excluded from the analysis. This is because the adequacy of the elastic model of the potential barrier for carbon was not confirmed by the results of measuring the anisotropy of the diffusion coefficients in α -Ti [4, 5]. Data on the diffusion of tracer boron atoms in metals are extremely meager and did not allow us to analyze relationships for boron. Elastic model of the potential barrier. The currently dominant concept of the nature of Q and procedures for calculating Q was formulated in the midtwentieth century [2, 3]. Within this concept, the activation energy Q for the interstitial diffusion mechanism is determined by the elastic energy of crystal strain when an impurity atom is placed at a saddle point; i.e., the larger the diffusant atom, the higher the activation energy Q . The expression for Q has the form [2]

Probe field spectroscopy in two-level systems with arbitrary phase memory in collisions

The spectrum of weak probe field absorption (amplification) by two-level atoms experiencing collisions with buffer gas atoms in a strong resonance laser field is studied theoretically. Analysis is carried out for systems with a weak Doppler broadening under relatively mild constraints on the strong field intensity for the general case of an arbitrary change in the phase of the radiation-induced dipole moment in elastic collisions of gas particles. It is shown that, in spite of uniform broadening of the absorption line, the probe field spectrum exhibits a clearly manifested anisotropy to mutual orientation of the wavevectors of strong and probe radiation. It is found that the width of resonances in the probe field spectrum under definite conditions (that can easily be created in experiments) is proportional to the diffusion coefficient for atoms interacting with radiation. This fact can form the basis of the spectroscopic method for measuring the transport frequencies of collisions between particles absorbing radiation and buffer particles. It is shown that phase memory effects in collisions strongly modify the probe field spectrum both qualitatively and quantitatively. Simple operative formulas proposed for the probe field spectrum are convenient for experimental data processing.

Uptake of Fe, Na and K atoms on low-temperature ice: implications for metal atom scavenging in the vicinity of polar mesospheric clouds

Ice clouds form in the mesosphere between 80 and 90 km, at high latitudes during summer when the temperature falls below 150 K. There is strong evidence that the water-ice particles in these clouds scavenge metal atoms that are produced in the mesosphere by meteoric ablation. In the present study the uptake of Fe, Na and K on an ice film was studied in a fast flow tube over a temperature range of 80-150 K, covering the temperatures over which ice clouds form in the upper mesosphere. The uptake was found to be highly efficient and mostly in the diffusion-limited regime, requiring accurate measurements of the diffusion coefficients of the metal atoms in He: DFeHe = 366 (+/- 17) (T/296 K)(1.85 +/- 0.07), DNaHe 286 (+/- 13) (T/296 K)(1.68 +/- 0.04) and DKHe = 247 (+/- 15) (T/296 K)(1.69 +/- 0.07) Torr cm2 s(-1). Measured values of the diffusion coefficients in N2 are 112 (+/- 4), 125 (+/- 4) and 88 (+/- 4) Torr cm2 s(-1) at 293 K for Fe, Na and K, respectively. The uptake of Na and K was observed to be extremely efficient from 80-150 K, with lower limits of gamma Na > 0.09 and gamma K > 0.05, although it is likely that gamma is much closer to unity. The uptake of Fe on cubic ice is close to unity efficiency above 135 K, but gamma Fe decreases to only 3 x 10(-3) at 80 K. Uptake of Fe on amorphous ice films is much more efficient than on cubic ice films below 130 K. These results are interpreted using quantum calculations of the metal atoms adsorbed onto a 12-H2O model ice surface. Finally, it is shown that the uptake of Fe, Na and K on low-temperature ice is sufficiently fast to explain the substantial depletions in the mesospheric metal layers that are observed in the presence of mesospheric ice clouds.