Diffusion Atomistic

Rosenfeld, G., Morgenstem, K., andComsa, G., in Surface Diffusion Atomistic and Collective Processes, M.C. Tringides andM. Scheffler, eds., NATO-AS 1 Series, PlenumPress, New York (1997). 

Surface Diffusion Atomistic and Collective Processes, ed. M. C. Tringides (Plenum Press, 1997). 

Lan Langelaar, M.H., Boerma, D.O., in "Surface Diffusion Atomistic and Collective Processes", Vol. 

Tringides., M. C. (1997) Surface Diffusion - Atomistic and CdUecdve Processes, NATO Advanced Science Institute Series B Physics, vol. 360, Plenum Press, New York. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

As computer power continues to increase over the next few years, there can be real hope that atomistic simulations will have major uses in the prediction of phases, phase transition temperatures, and key material properties such as diffusion coefficients, elastic constants, viscosities and the details of surface adsorption. 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

Cygan RT, Wright K, Fisler DK, Gale JD, Slater B (2002) Atomistic models of carbonate minerals bulk and surface structures, defects, and diffusion. Mol Simul 28 475-495 Davis AM, Hashimoto A, Clayton RN, Mayeda TK (1990) Isotope mass fractionation during evaporation of Mg2Si04. Nature 347 655-658... 

The prediction of a time-dependent centre of mass diffusion coefficient has recently been corroborated by a combined atomistic simulation and an NSE approach on PB ([55]). The dynamic structure factor from simulation and experiment obtained at 353 K are displayed in Fig. 3.11. 

The diffusion coefficient for a given ion in a crystal is determined, as we have seen, by the atomistic properties of the ion in the structural sites where the vacancy (or interstitial) participating in the migration process is created (see eq. 4.71). The units of diffusion (and/or self-diffusion ) are usually cm sec . Pick s first law relates the diffusion of a given ion A (Jf) to the concentration gradient along a given direction X ... 

In the discussion of atomistic aspects of electrodepKJsition of metals in Section 6.8 it was shown that in electrodeposition the transfer of a metal ion M"+ from the solution into the ionic metal lattice in the electrodeposition process may proceed via one of two mechanisms (1) a direct mechanism in which ion transfer takes place on a kink site of a step edge or on any site on the step edge (any growth site) or (2) the terrace-site ion mechanism. In the terrace-site transfer mechanism a metal ion is transferred from the solution (OHP) to the flat face of the terrace region. At this position the metal ion is in an adion state and is weakly bound to the crystal lattice. From this position it diffuses onto the surface, seeking a position with lower potential energy. The final position is a kink site. 

This bimodal dynamics of hydration water is intriguing. A model based on dynamic equilibrium between quasi-bound and free water molecules on the surface of biomolecules (or self-assembly) predicts that the orientational relaxation at a macromolecular surface should indeed be biexponential, with a fast time component (few ps) nearly equal to that of the free water while the long time component is equal to the inverse of the rate of bound to free transition [4], In order to gain an in depth understanding of hydration dynamics, we have carried out detailed atomistic molecular dynamics (MD) simulation studies of water dynamics at the surface of an anionic micelle of cesium perfluorooctanoate (CsPFO), a cationic micelle of cetyl trimethy-lainmonium bromide (CTAB), and also at the surface of a small protein (enterotoxin) using classical, non-polarizable force fields. In particular we have studied the hydrogen bond lifetime dynamics, rotational and dielectric relaxation, translational diffusion and vibrational dynamics of the surface water molecules. In this article we discuss the water dynamics at the surface of CsPFO and of enterotoxin. 

The results in sections 2 and 3 describe the adsorption isotherms and diffusivities of Xe in A1P04-31 based on atomistic descriptions of the adsorbates and pores. The final step in our modeling effort is to combine these results with the macroscopic formulation of the steady state flux through an A1P04-31 crystal, Eq. (1). We make the standard assumption that the pore concentrations at the crystal s boundaries are in equilibrium with the bulk gas phase [2-4]. This assumption cannot be exactly correct when there is a net flux through the membrane [18], but no accurate models exist for the barriers to mass transfer at the crystal boundaries. We are currently developing techniques to account for these so-called surface barriers using atomistic simulations. 

Experiments have shown that Aoxide spinel formation is on the order of 10 4cm at ca. 1000°C [C.A. Duckwitz, H. Schmalzried (1971)]. Using Eqns. (10.45) and (10.46) with the accepted cation diffusivities (on the order of 10 10 cm2/s), one can estimate from j% that each A particle crosses the boundary about ten times per second each way. In other words, quenching cannot preserve the atomistic structure of a moving interface which developed during the motion by kinetic processes. This also means that heat conduction is slower than a structural change on the atomic scale, unless one quenches extremely small systems. 

Microscopic and mechanistic aspects of diffusion are treated in Chapters 7-10. An expression for the basic jump rate of an atom (or molecule) in a condensed system is obtained and various aspects of the displacements of migrating particles are described (Chapter 7). Discussions are then given of atomistic models for diffusivities and diffusion in bulk crystalline materials (Chapter 8), along line and planar imperfections in crystalline materials (Chapter 9), and in bulk noncrystalline materials (Chapter 10). 

Equations 3.71 and 3.72 can be further developed in terms of the self-diffusivity using the atomistic models for diffusion described in Chapters 7 and 8. The resulting formulation allows for simple kinetic models of processes such as dislocation climb, surface smoothing, and diffusional creep that include the operation of vacancy sources and sinks (see Eqs. 13.3, 14.48, and 16.31). 

Macroscopic treatments of diffusion result in continuum equations for the fluxes of particles and the evolution of their concentration fields. The continuum models involve the diffusivity, D, which is a kinetic factor related to the diffusive motion of the particles. In this chapter, the microscopic physics of this motion is treated and atomistic models are developed. The displacement of a particular particle can be modeled as the result of a series of thermally activated discrete movements (or jumps) between neighboring positions of local minimum energy. The rate at which each jump occurs depends on the vibration rate of the particle in its minimum-energy position and the excitation energy required for the jump. The average of such displacements over many particles over a period of time is related to the macroscopic diffusivity. Analyses of random walks produce relationships between individual atomic displacements and macroscopic diffusivity. 

The fundamental process in atomistic diffusion models is the thermally activated jump between neighboring sites of local minimum energy. The duration of any jump is typically very short compared to the particle s residence time in a minimum-energy site. Therefore, the average jump rate—the basis for any model of atomistic diffusive motion—is essentially inversely proportional to the average residence time. 

Equation 7.52 is of central importance for atomistic models for the macroscopic diffusivity in three dimensions (see Chapter 8). For isotropic diffusion in a system of dimensionality, d, the generalized form of Eq. 7.52 is... 

The structure of crystalline surfaces is described briefly in Sections 9.1 and 12.2.1 and in Appendix B. All surfaces have a tendency to undergo a roughening transition at elevated temperatures and so become general. Even though a considerable effort has been made, many aspects of the atomistic details of surface diffusion are still unknown.6... 

Described in Section 2.1.1 the formal kinetic approach neglects the spatial fluctuations in reactant densities. However, in recent years, it was shown that even formal kinetic equations derived for the spatially extended systems could still be employed for the qualitative treatment of reactant density fluctuation effects under study in homogeneous media. The corresponding equations for fluctuational diffusion-controlled chemical reactions could be derived in the following way. As any macroscopic theory, the formal kinetics theory operates with physical quantities which are averaged over some physically infinitesimal volumes vq = Aq, neglecting their dispersion due to the atomistic structure of solids. Let us define the local particle concentrations... 

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