Silicon diffusion in molybdenum disilicide: correlation effects

Correlation factors for silicon diffusion by a vacancy mechanism in the silicon sublattice of the tetragonal MoSi₂ structure have been calculated by combining an analytical and a Monte Carlo approach. The ratio of the silicon diffusivity perpendicular to the tetragonal axis to that parallel to the tetragonal axis is also deduced. An effect of forward correlation of tracer atom jumps in the silicon sublattice with the corresponding partial correlation factor of 1.5 appears at small frequencies of silicon atom jumps along the tetragonal axis with respect to the jump frequencies in the silicon layer perpendicular to the tetragonal axis of the MoSi₂ structure. The anisotropy of silicon diffusion in MoSi₂ measured by Salamon et al. is explained in terms of correlation effects of silicon diffusion on its own sublattice.     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

A Monte Carlo study of ionic transport in a simple cubic random alloy via the interstitialcy mechanism: effects of non-collinear and direct interstitial jumps

Self-diffusion and ionic conduction via the interstitialcy mechanism in a simple cubic, binary random alloy AB were investigated as a function of composition using Monte Carlo simulation. It was found that allowance for non-collinear jumps (partly) replacing concurrent collinear site exchanges leads to a reduction in diffusion correlation effects. This goes along with a shift of the diffusion percolation threshold to lower concentrations of the (more) mobile component B. Even stronger changes of mass and charge transport compared to an exclusively collinear interstitialcy scheme are observed for additional contributions of direct interstitial jumps. It is remarkable that for both extensions of interstitialcy mediated diffusion, the Haven ratio appears to be greater than unity in certain composition ranges poor in B. All results rely on the calculation of tracer and interstitialcy correlation factors in the simplest possible three-dimensional lattice structure. Yet they may have more general relevance to the interpretation of tracer self-diffusion data and ionic conductivity measurements on crystalline materials.     

Correlation effects for cation diffusion via vacancy-pairs in fluorite-related oxides

Recent research has suggested that diffusion via vacancy-pairs could be an important contribution to cation diffusion in fluorite-related oxides, such as yttria-stabilized zirconia. In this paper, a combination of analytical development and Monte Carlo computer simulation is used to analyze various diffusion correlation effects for cation and oxygen ion diffusion via tightly bound vacancy-pairs in the fluorite structure. It is shown that the application of sum-rule relations provides exact expressions for the collective correlation functions. It is also shown that a formalism inspired by Manning's diffusion kinetics formalism gives accurate expressions for tracer correlation factors when tested against Monte Carlo simulation results. It is also shown that the tracer correlation factors follow the impurity-form, thereby simplifying an interpretation of the diffusion isotope effect.     

Front Propagation Dynamics with Exponentially-Distributed Hopping

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.     

Fractal walk and walk on fractals

The one-dimensional walk of a particle executing instantaneous jumps between the randomly distributed “atoms” at which it resides for a random time is considered. The random distances between the neighboring atoms and the time intervals between jumps are mutually independent. The asymptotic (t → ∞) behavior of this process is studied in connection with the problem of interpretation of the generalized fractional diffusion equation (FDE). It is shown that the interpretation of the FDE as the equation describing the walk (diffusion) in a fractal medium is incorrect in the model problem considered. The reason is that the FDE implies that the consecutive jumps (fractal walk) are independent, whereas they are correlated in the case under consideration: a particle leaving an atom in the direction opposite to the preceding direction traverses the same path until arriving at the atom.     

Monte Carlo simulation of phosphorus diffusion in α-iron via the vacancy mechanism

Monte Carlo simulations of the vacancy and phosphorus (P) atom diffusion in body centred cubic (bcc) iron are presented. The input parameters for the calculations, namely the activation energies of atomic jumps, have been obtained using a potential set developed recently for a dilute Fe–P alloy using ab initio data. The diffusion coefficients entering equations for the fluxes of vacancies and solute atoms are evaluated. The results show that, in the temperature range of practical importance for P segregation, P atoms move down the vacancy gradient; hence, under irradiation conditions, vacancies should drag P atoms towards sinks of point defects. This is because of the high binding energy between a P atom and a vacancy in the first and second nearest neighbour sites from each other, which allows a vacancy to move around a P atom without loss of bonding and, hence, co-migrate with it.     

Atom transport in random two sublattice structures: analogue of the random alloy sum rule

A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.     

Kinetics of the diffusion of an impurity atom on a fcc(111) surface

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is performed. The case of small surface coverages of both vacancies and impurity atoms is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, when the frequency of jump ω of the imurity atom is small, the diffusion coefficient of the impurity depends linearly on ω, whereas in the opposite case, a saturation occur and its dependence on the frequency of jumps of the impurity atom disappears.     

The Manning factor for direct exchange and ring diffusion mechanisms

Abstract

In this paper, we consider lattice-based diffusion kinetics for the direct exchange and ring mechanisms as possible proxy diffusion mechanisms for diffusion in liquid alloys. For these mechanisms, we assessed the Manning factor that arises from the Darken–Manning relation relating the interdiffusion coefficient and tracer diffusion coefficients and which can be obtained experimentally. The maximum values of the Manning factor for these two mechanisms occur when the exchange only takes place between the atoms of different type but not between the atoms of the same type. These values have strong composition dependence and reach a value of 2 (ignoring tracer correlation factors) for the direct exchange mechanism at equal compositions of the two components in binary alloys. But for the three atom ring mechanism, these values as a function of composition have a much more complicated form that sits below the direct exchange mechanism for compositions between 10 and 90%. When all exchanges (allowed by a mechanism) occur with approximately the same probability, then the Manning factor is about unity for all compositions.     

Quantitative study of diffusion jumps in atomistic simulations of model gas–polymer systems

Microscopic mechanisms underlying the diffusion of particles in polymeric and other systems include ‘jumps’ that are said to provide for a substantial contribution to the overall particle displacement. Such jumps have been observed in molecular simulations and experimentally, leading to important qualitative conclusions. An efficient method has been proposed for the identification and quantitative processing of jumps, and successfully employed in simulations of gas–liquid alkane systems. In the present work, the same method is applied in equilibrium Molecular Dynamics simulations of methane-like molecules dispersed in polymer-like alkanes, at atmospheric pressure and temperature well above the polymer melting point. The systems studied were prepared and equilibrated and a linear diffusion regime was confirmed by means of various criteria. The occurrence of distinct jump events was clearly revealed and their average length and frequency were calculated. In this way, a random-walk-type diffusion coefficient, D _s,?jumps, of the penetrants, was obtained and found to be lower than the overall diffusion coefficient D _s,?MSD calculated by the mean square displacement method. This is a strong indication that the overall diffusion is a combination of longer jumps with other microscopic mechanisms such as smoother and more gradual displacements effected upon the diffusing particle by its surroundings.     

Atomic quantum zeno effect for ensembles and single systems

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.     

Kinetics of shape equilibration for two dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time. Received 7 December 1998 and Received in final form 18 March 1999     

Long jumps in the surface diffusion of large molecules

We have studied the diffusion of the two organic molecules DC and HtBDC on the Cu(110) surface by scanning tunneling microscopy. Surprisingly, we find that long jumps, spanning multiple lattice spacings, play a dominating role in the diffusion of these molecules--the root-mean-square jump lengths are as large as 3.9 and 6.8 lattice spacings, respectively. The presence of long jumps is revealed by a new and simple method of analysis, which is tested by kinetic Monte Carlo simulations.     

Contribution a la theorie atomique de la diffusion chimique

Here we present an analysis and a development of the atomic theory of chemical diffusion as proposed by Manning for a binary system a/b.The general expression for the flux of a tracer in a concentration gradient is first established. This expression of the flux is identified with that deduced in the phenomenological theory. Thus a relationship between the partial correlation factors of vacancies with each of the a and b species is obtained.The effect of “vacancy flow” can be described in terms of these correlation factors. Thus the vacancy flow on species A leads to a correlation of the vacancy jumps with species B and vice versa.We shall see that the Nernst-Einstein equation can be extended to the case of chemical diffusion and that the ratio of the intrinsic diffusion coefficients is equal to the ratio of the mean jump frequencies W_A and W_B.Also, the activation energies of intrinsic diffusion coefficients are related very simply to the activation enthalpies of atomic jumps.In conclusion, we shall see that chemical diffusion in a binary system a/b can be completely described if either the thermodynamic factor and the coefficients of self diffusion, or the thermodynamic factor and the coefficients of intrinsic diffusion are known as functions of the concentration.     

General theory of microscopic dynamical response in surface probe microscopy: from imaging to dissipation

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature.     

Kinetics of the diffusion of an impurity atom on a square lattice

An analytical study of the migration of an embedded impurity atom over a solid surface under the influence of the diffusion of vacancies is presented. The case of small surface coverages of both vacancies ϑ _v and impurity atoms ϑ _i , with ϑ _i ≪ ϑ _v ≪ 1, is considered. It is shown that the realization of multiple collisions of a single impurity atom with vacancies imparts a Brownian character to its motion. At long times, the dependence of the mean square displacement on the time differs little from the linear, whereas the spatial density distribution is close to the Gaussian, features that makes it possible to introduce a diffusion coefficient. For the latter, an analytical expression is derived, which differs from the product of the diffusion coefficient of vacancies and their relative concentration only by a numerical factor η. The dependence of the diffusion coefficient of an impurity atom on the ratio of the frequency of its jumps to the frequency of jumps of vacancies is analyzed. In the kinetic mode, at ω ≪ 1, the diffusion coefficient of impurity atoms depends linearly on ω, whereas at ω ≫ 1, a saturation is observed; i.e., the dependence on the frequency of jumps of the impurity atom disappears. Nevertheless, the value of η remains less than unity, and no total entrainment of impurity atoms with vacancies occurs.     

Muonium quantum diffusion and localization in cryocrystals

We review our recent study of atomic muonium ( ⁺e^– or Mu, a light isotope of the hydrogen atom) diffusion in the simplest solids-van der Waals cryocrystals. We give experimental evidence of the quantum-mechanical nature of the Mu diffusion in these solids. The results are compared with the current theories of quantum diffusion in insulators. In solid nitrogen bothT ⁷ andT ^–7 temperature dependences of the Mu hop rate are observed directly for the first time, which is taken as a confirmation of a two-phonon scattering mechanism. In solid xenon and krypton, by contrast, the one-phonon interaction is dominant in the whole temperature range under investigation due to extremely low values of the Debye temperatures. Particular attention is dedicated to processes of inhomogeneous quantum diffusion and Mu localization. It is shown that at low temperatures static crystal disorder results in an inhomogeneity of the Mu quantum diffusion which turns out to be inconsistent with diffusion models using a single correlation time _c . Conventional trapping mechanisms are shown to be ineffective at low temperatures in insulators. The localization effects in Mu quantum diffusion are studied in detail in solid Kr. In all the cryocrystals studied muonium atom turns out to be localized at low temperatures.     

A model for quantum jumps in magnetic resonance force microscopy

We propose a simple model which describes the statistical properties of quantum jumps in a single-spin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.     

Etude des mouvements moléculaires en milieu liquide à partir du profil des bandes de vibration dans l'infrarouge et des fonctions de corrélation

We have studied the fundamental bands of chloroform and bromoform, both pure and in solution in various solvents; also the first harmonics of v ₁, and a few other harmonics and combination bands. The correlation functions of v ₁ and v ₂ and band moments of v ₁ have been calculated. The comparison of our results with those obtained in microwave and far IR and Raman spectra offers an opportunity to discern, in widths and correlation functions, what can be attributed to vibration and what originates in rotational diffusion. Our results are interpreted with the assumption that rotational diffusion is produced by small angles jumps and that the vibrational effect is very important. The v ₁ band shows an additional widening not accounted for in existing theories.