Defect-diffusion mechanism

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

House, J. E. (1993). Coord. Chem. Rev. 128, 175—191. A review of anation reactions and apphcations of the defect-diffusion mechanism. 

O Brien, P. (1983). Polyhedron 2, 233. A review of racemization reactions of sohd coordination compounds and an extension of the defect-diffusion mechanism to racemization. 

The higher-temperature results were explained in terms of a doubly ionized Cdf-related donor or a Cd defect diffusion mechanism. At lower temperatures, the results were tentatively explained in terms of a Vc j-related mechanism. 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

What we find is that the difference in diffusion mechanisms gives rise to the creation of new sites across the diffusion zone and actually causes a deformation in the solid because the Va defects pile up and finally... 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Figure 5.11 Diffusion mechanisms (a) exchange (e) and ring (r) diffusion (b) kick-out diffusion, leading to (c) a substitutional defect and a self-interstitial.

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

G. Neumann. Diffusion mechanisms in metals. In G.E. Murch and D.J. Fischer, editors, Defect and Diffusion Forum, volume 66-69, pages 43-64, Brookfield, VT, 1990. Sci-Tech Publications. 

In Fig. 9.1, Dd for nondissociated dislocations is practically equal to DB, which indicates that the diffusion processes in nondissociated dislocation cores and large-angle grain boundaries are probably quite similar. Evidence for this conclusion also comes from the observation that dislocations can support a net diffusional transport of atoms due to self-diffusion [15]. As with grain boundaries, this supports a defect-mediated mechanism. 

At more elevated temperatures, the diffusion mechanisms become more complex and jumps to more distant sites occur, as do collective jumps via multiple defects. At still higher temperatures, adatoms apparently become delocalized and spend significant fractions of their time in flight rather than in normal localized states. In many cases, the Arrhenius plot becomes curved at these temperatures (as in Fig. 9.1), due to the onset of these new mechanisms. Also, the diffusion becomes more isotropic and less dependent on the surface orientation. 

Most polymers that have been of interest as membrane materials for gas or vapor separations are amorphous and have a single phase structure. Such polymers are converted into membranes that have a very thin dense layer or skin since pores or defects severely compromise selectivity. Permeation through this dense layer, which ideally is defect free, occurs by a solution-diffusion mechanism, which can lead to useful levels of selectivity. Each component in the gas or vapor feed dissolves in the membrane polymer at its upstream surface, much like gases dissolve in liquids, then diffuse through the polymer layer along a concentration gradient to the opposite surface where they evaporate into the downstream gas phase. In ideal cases, the sorption and diffusion process of one gas component does not alter that of another component, that is, the species permeate independently. 

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