Configurational diffusion atoms

A common and important problem in theoretical chemistry and in condensed matter physics is the calculation of the rate of transitions, for example chemical reactions or diffusion events. In either case, the configuration of atoms is changed in some way during the transition. The interaction between the atoms can be obtained from an (approximate) solution of the Schrodinger equation describing the electrons, or from an otherwise determined potential energy function. Most often, it is sufficient to treat the motion of the atoms using classical mechanics,... 

In anticipation of the work we will do quantitatively below, let s first work up a qualitative understanding of the process. We begin by imagining the diffusing atom to occupy one of the wells as depicted in fig. 7.21. By virtue of thermal excitation, it is known that the atom is vibrating about within that well. The question we pose is how likely is it that the diffusing atom will reach the saddle point between the two wells The answer to that question allows us to determine the flux across the saddle point, and thereby, the rate of traversal of the saddle configuration which can then be tied to the diffusion constant. 

There has been an explosion in the application of atomistic and molecular modeling to corrosion and electrochemistry in the past decade. The continued increasing computational power has allowed the development and implementation of atomistic and molecular modeling frameworks that would have been impractical even a short time ago. These frameworks allow the application of fundamental physics at the appropriate scale on assemblies of atoms of a size that provides a more realistic basis than ever before. In some cases, that level is the determination of the electronic structure based on quantum mechanics. Such is the case when determining the energetics of surface structures and reactions. In other cases, the appropriate scale requires the forces between atoms or ions to be calculated, and the effects those forces have on the configuration of atoms and how it changes with time. Surface and solution diffusion are prime examples. 

This value of diffusivity is in the range of configurational diffusion. The carbon particle was assumed to be exposed to a step change in mercury concentration at its external surface at t = 0 (corresponding to the injection location). The calculations indicate that with a 10 pm activated carbon particle, the intraparticle diffusion will be important only when the pore diameter is about 3 A, i.e., the atomic diameter of mercury. Because the micropore size of the activated carbon is generally larger than 3 A, it can be concluded that intraparticle diffusion is unlikely to be the controlling step in the carbon injection process. 

It is simplest to consider these factors as they are reflected in the entropy of the solution, because it is easy to subtract from the measured entropy of solution the configurational contribution. For the latter, one may use the ideal entropy of mixing, — In, since the correction arising from usual deviation of a solution (not a superlattice) from randomness is usually less than — 0.1 cal/deg-g atom. (In special cases, where the degree of short-range order is known from x-ray diffuse scattering, one may adequately calculate this correction from quasi-chemical theory.) Consequently, the excess entropy of solution, AS6, is a convenient measure of the sum of the nonconfigurational factors in the solution. 

This approximation was denoted initially by the acronym IQG [34] and later on by IP (Independent Pairs) [35]. It gave satisfactory results in the study of the Beryllium atom and of its isoelectronic series as well as in the BeH system. The drawback of this approximation is that when the eigen-vectors are diffuse, i.e. there is more than one dominant two electron configuration per eigen-vector, the determination of the corresponding nj is ambiguous. In order to avoid this problem the MPS approximation, which does not have this drawback, was proposed. 

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