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https://hdl.handle.net/2142/68648
Description
Title
Studies of Surface Diffusion
Author(s)
Reed, David Allen
Issue Date
1980
Department of Study
Metallurgy and Mining Engineering
Discipline
Metallurgical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Materials Science
Language
eng
Abstract
Several different topics, all concerned with surface diffusion are considered. First, the relationship between the diffusion coefficient D and the jump rate (GAMMA) is examined. It is shown that in analogy to alloy diffusion, the diffusivity is given by
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
Here (lamda) is the jump length, (mu) is the chemical potential, (theta) is the coverage, and ((PAR-DIFF)(mu)/kT/(PAR-DIFF)ln(theta))(,T) is a thermodynamic factor. This latter may be deduced from adsorption isotherms, or from observations of concentration fluctuations in a small area element of the surface. To illustrate the importance of this factor, computer simulations have been done for several different interatomic potentials. For some of these, the thermodynamic factor has a strong dependence on coverage, so that the courses of D and (GAMMA) with coverage are not even qualitatively similar.
The temperature dependence of D and (GAMMA) at constant coverage have also been investigated. It is demonstrated that the activation energy for diffusion and jumping may be significantly different.
The time correlation (rho) of concentration fluctuations as a measure of the diffusion coefficient is examined next. The standard relation between (rho) and D for dilute systems is found inadequate for surface diffusion; an improved relation is derived and tested via computer simulation. It works well for Langmuir layers and a nearest neighbor repulsive potential but discrepancies between the true diffusion coefficient and that deduced from concentration fluctuations as large as a factor of five are found for interactions producing superlattice formation. Likewise, the activation energy for diffusion, deduced from an Arrhenius plot, is not correctly measured under those conditions.
Also investigated by Monte Carlo methods are several problems important in field ion microscopic studies of the motion of individual atoms. Corrections to the estimated mean-square displacement, to account for the boundaries of the surface, are discussed for one- and two- dimensional diffusion under a variety of conditions. The accuracy of and optimal conditions for measuring the pair potential of adatoms from their pair separation distribution is also considered. Finally, experiments to establish the fundamental step length in surface diffusion are tested by Monte Carlo simulations.
In an application of some of these notions, the diffusion of two rhenium adatoms in the same channel of the (211) plane of tungsten is investigated. The activation energy, 23.3 kcal/mole, is considerably higher than that for cross-channel dimers. In-channel trimers were found not to move at the highest temperature in this study (435(DEGREES)K), while other clusters which contain no more than two adatoms per channel exhibited behavior similar to simple in-channel dimers. These observations allow some comparisons between atomic interactions along and across channels.
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