Diffusion, adatom

Bonig L, Liu S and Metiu FI 1996 An effective medium theory study of Au islands on the Au(IOO) surface reconstruction, adatom diffusion, and island formation Surf. Sot 365 87... 

The plasma potential is the maximum value with which ions can be accelerated from the edge of the sheath towards the substrate, located at the grounded electrode. This may cause ion bombardment, which may induce ion-surface interactions such as enhancement of adatom diffusion, displacement of surface atoms, trapping or sticking of incident ions, sputtering, and implantation see Section 1.6.2.1. 

Calculate the activation energy for diffusion of a Pt adatom on Pt(100) via direct hopping between fourfold sites on the surface and, separately, via concerted substitution with a Pt atom in the top surface layer. Before beginning any calculations, consider how large the surface slab model needs to be in order to describe these two processes. Which process would you expect to dominate Pt adatom diffusion at room temperature ... 

The interpretation of this data on metals in terms of microscopic mechanisms of surface atom transport is not totally understood. The original papers[ 11] proposed that during surface transport the controlling process was adatom terrace diffusion between steps with the adatom concentration being that in local equilibrium with the atomic steps. This may indeed be the case, but in light of other experiments on adatom diffusion[13] and exchange processes at steps[14] the possibility of step attachment/detachment limited kinetics caimot be raled out. 

For A/-kinetics, on the other hand, adatoms diffuse rapidly along steps, and we can expect a tendency to wash out the variation of the terrace adatom flux onto the step. Thus, at the very least, we can say that step fluctuations in this system should form more slowly than for /-kinetics, i.e.. 

We begin our discussion with the diffusion of a Si adatom over a flat terrace. This problem has previously been addressed with ab initio calculations for the case of symmetric dimers. The main result is that diffusion is highly anisotropic on the surface, with fast diffusion taking place over the top of the dimers with a saddle point energy of about 0.60 eV. Slow adatom diffusion is predicted to take place across the dimer rows with a barrier of 1.0 eV. Experiments based on a number counting of the island density are in agreement with these results. ... 

We adopt the following simple picture. Initially, we assume that steps are far enough apart that the effects of step repulsions can be ignored. The relevant physics for evaporation involves the detachment of adatoms from step edges, their surface diffusion on the adjacent terraces, and their eventual evaporation. This is quite well described by a generalization of the classical BCF model "- which considers solutions to the adatom diffusion equation with boundary conditions at the step edges. 

Fig. 4.24 A careful mapping of the adatom position of a Re adatom on a W (123) surface (some of these images are shown in Fig. 4.23 ) demonstrates the discrete random nature of the atomic jumps in adatom diffusion.

Adatom diffusion, at least under the low temperature of field ion microscope measurements, almost always follows the direction of the surface channels. Thus adatoms on the W (112) and Rh (110) surfaces diffuse in one direction along the closely packed atomic rows of the surface channels. Such one-dimensional surface channel structures and random walks can be directly seen in the field ion images, and thus the diffusion anisotropy is observed directly through FIM images. Unfortunately, for smoother surfaces such as the W (110) and the fee (111), no atomic or surface channel structures can be seen in field ion images. But even in such cases, diffusion anisotropy can be established through a measurement of the two-dimensional displacement distributions, as discussed in the last section. Because of the anisotropy of a surface channel structure, the mean square displacements along any two directions will be different. In fact this is how diffusion anisotropy on the W (110) surface was initially found in an FIM observation.120... 

Map showing the exchange of an adatom with a lattice atom in cross channel adatom diffusion on the fee 110 plane. 

Because the adatoms diffuse relatively rapidly along the surface and the ledges to the kinks, many more atoms reach the kinks by these routes than by direct impingement from the vapor. Note the close similarity between this crystal growth process on a vicinal surface and the climb of dislocations depicted in Fig. 11.2. 

Therefore, when A >> /Jx2), rj y/(x2)/X 1 and the efficiency is very low. This is the case where the ledge spacing is much greater than the adatom diffusion distance on the surface and very few adatoms reach the ledge sinks before jumping back into the vapor phase. On the... 

Solution. The rate at which adatoms diffuse into a unit length of ledge is... 

The scheme of nucleating and growth of particles at deposition of M/SC from gaseous phase on a substrate is submitted in work [43]. The atoms adsorbed from a gas phase (adatoms) diffuse over a surface. During diffusion adatoms are partly desorbed and in part are stabilized on a surface, forming nuclei of a new phase. Such nuclei arise by collision of diffusing adatoms and their aggregation into stable primary clusters or as a result of... 

In this expression vd is a frequency of adatom vibration over the surface, a0 the jump distance, of the order of the surface lattice parameter, and fsD the activation energy of adatom diffusion [42]. Thus,... 

Based on the TLK (terrace, ledge and kink) model, growth on a perfect vicinal and singular surface proceed by a sequence of steps involving adsorption from vapor to form a surface adatom. This adatom diffuses to a kink site of the surface and incorporate into the crystal at the kink site. In order to determine the growth rate, the rate of formation of stable cluster must be determined. This is the rate at which cluster of radius r grow by the addition of one incremental atom from the adlayer. The rate is given by. 

This causes a diffusion flux, I>sd(cads - fo,ads) /, of adatoms towards the step edge, where the adatoms are rapidly incorporated into kink positions. Therefore, the adatom concentration at the step edge is kept at the equilibrium value Co,ads- At room temperatures, where the average kink distance, i k (cf. eq. (2.5)), is low and smaller than the mean displacement of adatoms, diffusion along the steps can be neglected and the diffusion process can be treated as linear. The incorporation of atoms in the step results in a step propagation with a rate Vsd [cm s ] determined by the flux Dsd Acads/Asd [mol cm s ] and the area 0 hU) occupied by one mole. 

This system of differential equations differs in boundary condition (8.33) from the well-known adatom diffusion model of Me deposition on native substrate [8.10-8.12]. Principally, it allows Arto be described as a function of and t. The relation between AF, q, and the local" cathodic current density in the range 0 < jr < < tep. iQc), is given by... 

Figure 15 Illustration of dimer formation on a crystallite surface from two adatoms diffusing from the support onto the crystallite surface.

The Monte Carlo model is based on a technique originally used to model the leaching of silver from a Au - 50 at.% Ag alloy, examining the evolution of nano-porosity [10], For NiAl alloys two key processes are assumed to be taking place during leaching, namely adatom diffusion (Ni or Al) and A1 dissolution. These processes are assumed to occur at known rates that serve as the inputs for the model. Both diffusion and dissolution of adatoms are assumed to proceed at a rate described by the following Arrhenius relationships respectively ... 

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