Surface diffusion anisotropic

Despite the insights which the dynamics have provided into surface diffusion, additional studies will be required to hilly characterize surface dynamics. In particular, the role of surface reconstructions on diffusion has not bwn fully explored, and additional studies of the relationship between anisotropic diffusion and step stability are currently needed. 

In marked contrast, the classical continuum theory by mullins describes the sim-ulational data (profile shapes and amplitude decay) above roughening for wires even with small geometries surprisingly well, both for surface diffusion and evaporation-condensation The agreement may be a little bit fortuituous, because of a compensation of the competing effects of the anisotropic surface tension and anisotropic mobility, whereas continuum theory assumes isotropic quantities. In any event, the predicted decay laws with w= 1/4 for surface diffusion and w= 1/2 for evaporation kinetics are readily reproduced in the simulations. 

Evolution by Surface Diffusion and by Vapor Transport. Although calculation of the morphological evolution for particular cases can become tedious, the kinetic equations are straightforward extensions of the isotropic case [11], For the movement of an anisotropic surface by surface diffusion, the normal interface velocity is an extension of Eq. 14.6 which holds for the isotropic case for the anisotropic case,... 

If the surface diffusivity is anisotropic, its surface derivatives must appear as well. 

Fridline D. R. and Bower A. F., Influence of Anisotropic Surface Diffusivity on Electromigration Induced Void Migration and Evolution, J. Appl. Phys. 85, 3168 (1999). 

Let us use the distribution fvinction which corresponds to file (generally) anisotropic surface diffusion of adatoms ... 

These results demonstrate that the mechanism of roughness relaxation at column-structured metal surfaces operates under a surface diffusion control. The anisotropy of coalescence is consistent with an anisotropic smface diffusion process on smooth grains (a= 1). 

The interatomic and intennolecular interactions of adsorbed species and their state on the catalyst surface are the basis of all elementary steps of the catalytic process. The importance and reliability of the modeled results depend on the correct choice of the potential of the interatomic interaction. The question about the type and nature of interatomic forces between adsorbed species is the focus. Interatomic forces are diverse and usually anisotropic. Adsorbed species do not form structures at low coverage. When the number of adsorbed species and the rate of their surface diffusion increase, the probabilities of their interaction and formation of surface polyatomic structures increases. These structures can be rather stable and they form islands of adsorbed species. 

Ochoa-Tapia J.A., del Rio J.A. and Whitaker S. 1993. Bulk and surface diffusion in porous media An application of the surface averaging theorem, Chem. Eng. Sci., 48, 2061-2082. Ochoa-Tapia J.A., Stroeve P. and Whitaker S. 1994. Diffusive transport in two-phase media Spatially periodic models and Maxwell s theory for isotropic and anisotropic systems, Chem. Eng. Sci., 49, 709-726. 

For porous electrodes, an additional frequency dispersion appears. First it can be induced by a non-local effect when a dimension of a system (for example, pore length) is shorter than a characteristic length (for example, diffusion length), i.e. for diffusion in finite space. Second, the distribution characteristic may refer to various heterogeneities as roughness, distribution of pores, surface disorder, anisotropic surface structures. De Levie used a transmission line equivalent circuit to simulate the frequency response in a pore where cylindrical pore shape, equal radius and length for all pores were assumed [14]. 

Surface diffusion is faster than bulk diffusion and may be highly anisotropic due to surface structure. 

A silicon wafer with anisotropically KOH-etched openings was used as shadow mask. The shadow mask is accurately positioned with the help of an optical microscope and fixed using a custom-made wafer holder. A 50-nm-thick TiW-film is deposited by sputtering through the shadow mask. This film serves as adhesion layer and diffusion barrier and covers the rough surface of the CMOS-Al-metallization. A Pt-layer with a thickness of 100 nm was sputtered on top of this TiW-layer. 

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