Cluster diffusion

Cullinan presented an extension of Cussler s cluster diffusion the-oiy. His method accurately accounts for composition and temperature dependence of diffusivity. It is novel in that it contains no adjustable constants, and it relates transport properties and solution thermodynamics. This equation has been tested for six very different mixtures by Rollins and Knaebel, and it was found to agree remarkably well with data for most conditions, considering the absence of adjustable parameters. In the dilute region (of either A or B), there are systematic errors probably caused by the breakdown of certain implicit assumptions (that nevertheless appear to be generally vahd at higher concentrations). 

However, when the concentration or mobility of ion pairs is significant compared with the individual ions then the measured diffusion coefficients for both constituents approach that of the ion pairs and not the free ions and as a consequence the apparent t+, and hence t, approach 0.5. In fact it is no longer valid to apply the above equation in order to determine transport numbers. Generally, in the presence of mobile ion pairs or more complex mobile ion clusters, diffusion coefficients and t+ measurements... 

STEP FLUCTUATIONS FROM EQUILIBRIUM ANALYSIS TO STEP UNBUNCHING AND CLUSTER DIFFUSION IN A UNIFIED PICTURE... 

Fig. 4.22 On the surface of a solid, there are a wide variety of atomic processes. A formation of a surface vacancy-adatom pair, or their recombination B association or dissociation of adatoms with an atomic cluster and cluster diffusion C diffusion of a surface vacancy, especially toward the lattice step D falling off a lattice step of an adatom E diffusion of a substitutional or interstitial impurity atom and its interaction with an adatom F diffusion of an adatom and its long range interactions with other adatoms G diffusion, dissociation and activation of a ledge atom H dissociation and activation of a kink atom into an adatom, a ledge atom, or an adatom on the layer above.

In a molecular dynamic simulation147 of bulk atomic diffusion by a vacancy mechanism, two atoms may occasionally jump together as a pair. The temperature of the simulation is close to the melting point of the crystal. In FTM studies of single atom and atomic cluster diffusion, the temperature is only about one tenth the melting point of the substrate. All cluster diffusion, except that in the (1 x 1) to (1 x 2) surface reconstruction of Pt and Ir (110) surfaces already discussed in Section 4.1.2(b), are consistent with mechanisms based on jumps of individual atoms.148,149 In fact, jumps of individual atoms in the coupled motion of adatoms in the adjacent channel of the W (112) surface can be directly seen in the FTM if the temperature of the tip is raised to near 270 K.150... 

Fig. 4.32 Two-jump mechanism of diatomic cluster diffusion on the W (110) surface with the [110] and [001] intermediate bond configurations.

CCA) process, where particles and clusters diffuse across each other and... 

In this manner the water molecules move cooperatively instead of individually. The cluster, instead of an individual water molecule, becomes the kinetic unit. As the entire cluster diffuses through the fixed matrix these different water molecules experience different environments. 

In Refs. [208, 217-219] the dynamical scaling description of cluster sizes distribution in the cluster-cluster diffusion-limited aggregation (DLA) model was considered. As it was mentioned above, this model was applicable completely for PDMDAAC radical polymerization description by the following reason. The estimated according to the Eq. (4) value... 

Meakin, P Vicsek, F. Dynamic cluster-size distribution in cluster-cluster aggregation effects of cluster diffusivity. Phys. Rev. B, 1984, 31(1), 564-569. 

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