Diffusion of clusters

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

When diffusing adatoms encounter each other, in most cases they will associate into an atomic cluster if the surface temperature is low enough. Figure 4.31(a) and (b) show formation and diffusion of clusters of various sizes on the W (110) and W (112) surfaces and (c) gives an example of... 

However, the field of force or gradient in the Gibbs energy introduced by Eqs. (11-13) must be, in general, retained to describe the random diffusion of clusters through the distribution of their sizes. The equilibrium concentration of -mers is given by... 

A study was made of the migration of spherical Sb clusters which had been deposited onto graphite surfaces. Good agreement with computer simulations was found, and this fact was used to deduce the diffusivity of clusters, which contained about 2300 Sb atoms, on the substrate. The results were described by ... 

Cooperative diffusion of transient polymer networks, heterogeneity mode related to polymer self-diffusion in diblock copolymers, entanglement mode, chain reptation, viscoelastic relaxation, diffusion of clusters Viscoelastic relaxation, a- and 3-relaxation... 

The peaks in Figure 3.13a (counted from the left) are ascribed to the following modes peak 3 (dominant) to cooperative or translational diffusion, peak 4 to selfdiffusion of the copolymer chain, and peak 5 to the diffusion of clusters of a hydrodynamic radius equal to about 120 nm, as estimated via the Stokes-Einstein relation (Equation 3.27). Peaks 1 and 2 correspond to thermal diffusion and to self-diffusion of solvent molecules, respectively. 

Water molecules combine the tendency to cluster, craze and plasticize the epoxy matrices with the characteristic of easily diffusion in the polymer1 10). The morphology of the thermoset may be adversaly influenced by the presence of the sorbed moisture. The diffusion of the water in glassy polymers able to link the penetrant molecules is, therefore, characterized by various mechanisms of sorption which may be isolated giving useful information on the polymer fine structure. 

The ionization potential (7.9 eV) falls right outside the bracket of experimental IP s reported for carbon clusters with 40 to 100 atoms (6.42 eV IP 7.87 eV, Ref. 11). Inclusion of correlation effects will lower the calculated ASCF IP by 0.25 to 0.50 eV, so that the corrected IP will be at the upper end of the experimental IP>bracket. Due to the diffuseness of the n orbital from which an electron is removed, the correlation error in the ASCF value will be smaller than in cases where an electron is removed from a well localized bond. In these cases a correction of 1 eV is usually applied. 

Room temperature deposition of silver on Pd(lOO) produces a rather sharp Ag/Pd interface [62]. The interaction with a palladium surface induces a shift of Ag 3d core levels to lower binding energies (up to 0.7 eV) while the Pd 3d level BE, is virtually unchanged. In the same time silver deposition alters the palladium valence band already at small silver coverage. Annealing of the Ag/Pd system at 520 K induces inter-diffusion of Ag and Pd atoms at all silver coverage. In the case when silver multilayer was deposited on the palladium surface, the layered silver transforms into a clustered structure slightly enriched with Pd atoms. A hybridization of the localized Pd 4d level and the silver sp-band produces virtual bound state at 2eV below the Fermi level. 

Becerra LR, Klug CA, Slichter CP, Sinfelt JH. 1993. NMR-study of diffusion of CO on alumina-supported Pt clusters. J Phys Chem 97 12014-12019. 

Diffusion of cations in a Nation membrane can formally be treated as in other polymers swollen with an electrolyte solution (Eq. (2.6.21). Particularly illustrative here is the percolation theory, since the conductive sites can easily be identified with the electrolyte clusters, dispersed in the non-conductive environment of hydrophobic fluorocarbon chains (cf. Eq. (2.6.20)). The experimental diffusion coefficients of cations in a Nation membrane are typically 2-4 orders of magnitude lower than in aqueous solution. 

Whatever the advantages of the SCF calculations with the Cl s, they do not always give good results, as is the case for M2 molecules with quintuple and sextuple M-M bonds [135,156], Nevertheless, some deviations from the simple MO scheme can be explained using simpler qualitative arguments. For example, the increased ability of technetium to form d4-d5 complexes and their greater stability in comparison to that of the d4-d4 complexes are explained on the basis of a model of the electrostatic repulsion of M atoms with like charges in a binuclear cluster [10,90,150] or on the basis of different diffusivities of cr, o, n, 5 and S metallic MO s of the clusters [63,141,157]. 

Percolation theory describes [32] the random growth of molecular clusters on a d-dimensional lattice. It was suggested to possibly give a better description of gelation than the classical statistical methods (which in fact are equivalent to percolation on a Bethe lattice or Caley tree, Fig. 7a) since the mean-field assumptions (unlimited mobility and accessibility of all groups) are avoided [16,33]. In contrast, immobility of all clusters is implied, which is unrealistic because of the translational diffusion of small clusters. An important fundamental feature of percolation is the existence of a critical value pc of p (bond formation probability in random bond percolation) beyond which the probability of finding a percolating cluster, i.e. a cluster which spans the whole sample, is non-zero. 

Gold has been used for many years as a minority carrier lifeline controller in Si. As such, it is introduced in a controlled manner, usually by diffusion into transistor structures to decrease the carrier lifetime in the base region in order to increase the switching speed (Ravi, 1981). Conversely, the uncontrolled presence of Au is clearly deleterious to the performance of devices, both because of the increased recombination within the structure and the increase of pipe defects, which can cause shorting of the device. These pipe defects consist of clusters of metallic impurities at dislocations bounding epitaxial stacking faults. 

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