Defect Diffusivities

Again according to Wagner [28], the chemical diffusivities in Eq. (72) may be written for an electronic conductor system (t i w 1) as  

The author thanks C.E. Lee for producing the illustrations. These studies were supported financially by the Center for Advanced Materials Processing, under the 21C Frontier Program of the Ministry of Commerce, Industry and Energy, Korea. 

Schmaizried, H. (1964) Point defect in ternary ionic crystals, in Progress in Solid State Chemistry.vcA. 2 (ed. H. Reiss), North-Holland Publishing Co., Amsterdam, pp. 265-303. 

Abelard, P. and Baumard, J.F. (1981) Nonstoichiometry in ternary oxides a new graphical representation of the defect configurations, in Science of Ceramics, voL 11, Swedish Ceramic Society, Gdteborg, pp. 143-148. 

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Several different types of species, including various solid state defects, diffuse and form a phase boimdaty of reaction, which may further react to form specific compositions. 

Figure 5 Schematic illustration of defect diffusion-controlled polymerization.45 Reprinted with permission from McLeish, T. C. B. Jones, R. G. Holder, S. J. Macromolecules 2002, 35, 548-554. 2002 American Chemical Society.

A possible step in this direction can be made through use of earlier relaxation studies on other systems. Hunt and Powles,— when studying the proton relaxation in liquids and glasses, found the relaxation best described by a "defect-diffusion" model, in which a non-exponential correlation function corresponding to diffusion is Included together with the usual exponential function corresponding to rotational motion. The correlation function is taken as the product of the two independent reorientation pro-... 

The De Gennes method can be applied directly to Bueche s model without the defect diffusion formalism. Consider a chain with n main chain atoms, mean square end-to-end distance , and a large number of entanglement obstacles along its contour. For simplicity, suppose the number of main chain atoms between successive obstacles and the scalar distance between obstacles are... 

The second term on the right hand side of Eqn. (13.5) describes the rate of recombination. In the case of diffusion controlled recombination, fc and k may be calculated in terms of defect diffusivities and steady state concentrations. Without radiation, cd = 0, and the Frenkel equilibrium, requires that cv -cA = K/k. If a steady state is attained under irradiation, the rate of radiation produced defects (cp) add to the thermal production rate, and the sum is equal to the recombination rate. Therefore,... 

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. 

T.Y. Tan and U. Gosele. Point-defects, diffusion processes, and swirl defect formation in silicon. Appl. Phys. A, 37(1) 1—17, 1985. 

Fig. 3.3. Schematic classification of processes in solid with defects, (a) Defect diffusion ...

Defect diffusion traditionally is treated as a process in continuum medium. However, discreteness of the crystalline lattice becomes important in particular situations, e.g., when defect recombination occurs in several hops (nearest neighbour recombination) [3, 4] or even for nearest-site hops of defects if their recombination is controlled by the tunnelling whose probability greatly changes on a scale of lattice constant [45, 46],... 

Up to now we have been considering defect diffusion in continuous approximation, despite the fact that crystalline lattice discreteness was explicitly taken into account defining the initial distribution for geminate pairs. Note, however, that such continuous diffusion approximation is valid only asymptotically when defects (particles) before recombination made large number of hops (see Kotomin and Doktorov [50]). This condition could be violated for recombination of very close defects which can happen in several hops. The lattice statement of the annihilation kinetics has been discussed in detail by Schroder et al. [3, 4, 83], Dederichs and Deutz [34]. Let us consider here just the most important points of this problem. 

The end of the present Section aims both to summarize the just mentioned peculiarities of the non-steady-state transient kinetics of the tunnelling luminescence due to step-wise temperature changes, and to develop the theoretical basis for distinguishing two alternative reasons for the tunnelling luminescence temperature dependence thermally activated defect diffusion or rotation. 

Therefore, the method of partial lightsums illustrates once more effects of the defect diffusion a number of close pairs increases, whereas that of distant pairs decreases, unlike the case of defect rotation. 

To conclude this Section, we would like to stress that both experimental and theoretical analyses of the non-steady-state kinetics of the tunnelling luminescence of defects in insulators after the step-like stimulation allow us to distinguish the anisotropic defect rotation and diffusion. For the defect rotation, sharp increases of the I(t) and its smooth decrease are observed for the temperature stimulation cycle, whereas an opposite effect occurs for the defect diffusion. 

I. Reiche, C. Vignaud, L. Favre-Quattropani, L. Chariet, M. Menu, Diffusion in archaeological bone, Defect Diffus. Forum 194-199 (2001) 953-960. 

S. Dabritz, V. Hoffmann, G. Sadowski, D. Bergner. Investigations of phase growth in the copper-tin system //Defect Diffusion Forum - 2001 - V.194-199 - P.1575-1580. 

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