Atomistic structural

Now having specified the bulk electrode, the bulk electrolyte, and the interface between them, our aim in this section is to quantify the atomistic structure of the interface and derive an expression that allows us to evaluate its stabUity. Based on (5.5), we wUl extend the ab initio atomistic thermodynamics approach to electrochemical systems. 

Recently a hierarchy of methods has been developed which covers the mapping of polymers to a mesoscopic level as well as the reintroduction of the atomistic structure [43-45]. Section 6 (Kremer, Murat, Hahn) gives some very first attempts to bridge the gap from microscopic to mesoscopic [43,44] and thereafter to the semi-macroscopic regime [45] within a simulation scheme. 

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. 

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... 

The method aims to pass the distribution of structural parameters from the atomistic structure to the coarse-grained. The procedure involves performing an atomistic MD simulation and calculating the... 

Su, X. and Garofalini, S.H., (2004a), Atomistic structure of calcium silicate intergranular films between prism and basal planes in silicon nitride a molecular dynamics study , J. Mater. Res., 19 (3), 752-758. 

A. J. ROSENBERG (M. I. T.) r Throughout your paper you treat the surface as a physical continuum, disregarding its atomistic structure. Chemically we know that we must consider the atomistic nature of the surface I wonder if you might suggest how this aspect of the surface might be incorporated in your treatment. 

Besides issues related to the accuracy of force fields in spatially inhomogeneous systems comprising many chemically distinct components, the basic restriction related to the chemically detailed models is the rather small length and time scales that they can access. This limitation imposes severe restrictions for considering collective phenomena in amphiphilic vesicles, i.e., processes that involve large particle numbers. Typical examples include vesicle assembly, vesicle fusion, phase separation and shape transformations of multicomponent amphiphilic vesicles. For many of these processes, it is expected that the underlying atomistic details of the molecular constituents can be captured by a small number of relevant characteristics and universality classes, comprised of systems with a rather different atomistic structure, can be identified. These phenomena can be successfully investigated via minimal... 

M. Ishimaru, et al., Atomistic structures of metastable and amorphous phases in ion-irradiated magnesium aluminate spinel. J. Phys.-Condens. Matter 14(6), 1237-1247 (2002). 

Debye regards a solid as a continuum, and takes no notice of its atomistic structure. In accordance with a rule derived from the radiation theory for solids, he takes the number of oscillations in a solid body as... 

Coarse-grained models have a longstanding history in polymer science. Long-chain molecules share many common mesoscopic characteristics which are independent of the atomistic structure of the chemical repeat units [4, 5 and 6]. The self-similar structure [7, 8, 9 and 10] on large length scales is only characterized by a single length scale, the chain extension R. 

Consider a climb-dissociated sdge dislocation in spinel. Draw a model for the atomistic structure. 

Figure 13.27 Reprinted in part with permission from Sayle, D.C. and Watson, G.W. (2002) Atomistic structures of 25 000-atom oxide nanoparticles supported on an oxide substrate /. Phys. Chem. B, 106,10793. Copyright 2002 American Chemical Society.

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