Vacancy sinks

The vacancy relaxation time, r, depends on the (average) distance, A/, between the vacancy sinks as... 

By modeling r in this way, we have tacitly assumed that the atomic oxygen has free access to the vacancy sinks which are the internal sites of repeatable growth for the lattice molecules. Properly spaced dislocations with fast oxygen diffusion could be a prototype of those sinks. 

AGbo > [ AGa0, almost pure metal A is precipitated in the internal reduction zone. The reaction at the front is induced by a point defect flux which stems from the difference in oxygen potentials (point defect concentration) between the internal reaction front and the external surface. The reaction front and surface act as source and sink for the point defect flux. For example, when we assume that (A,B)0 contains transition-metal ions (e.g., (Ni,Mg)0), the defects are cation vacancies and compensating electron holes. The (reducing) external surface acts as a vacancy sink according to the reaction... 

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

K.C. Jain and R.W. Siegel. Temperature dependence of the vacancy sink efficiency of stacking-fault tetrahedra in quenched gold. Phil. Mag., 25(1) 105—115, 1972. 

The vacancies are annihilated at the grain boundaries i.e., the grain boundaries act as vacancy sinks. It is also assumed that where the vacancies are annihilated, their concentration is given by Q [Eq. (10.7)]. i.e.. under a stress-free planar interface. 

In the simplest model for representing the elimination of porosity in a solid. Fig. 3.11, volume diffusion takes place by means of lattice defects, in particular, vacancies. Pores play the role of vacancy sources, and grain boundaries act as vacancy sinks. The key point in this mechanism is that a... 

Fig. 9 Schematic view of high, medium, and iow excess vacancy concentrations as a function of distance from a grain boundary serving as a vacancy sink. The equilibrium vacancy concentration at the given temperature is given by the dotted line. (Ref. [25], from Physical Metallurgy Principles, 3rd edition by Reed-Hill/Abbaschian, 1992. Reprinted with permission of Brooks/Cole, a division of Thomson Learning www.thomsonrights.com, Fax 800 730-2215.)...

In the latter reaction, additional lattice sites are created, so that the vacancies must be annihilated at vacancy sinks, or voids and cavities are created. In the case of prevailing anion diffusion, growth of oxide lattice and consumption of metal lattice occur at the interface... 

Hence, the question arises as to how the system can implement the law of conservation of matter if lattice motion and vacancy sinks/sources functioning encounter difliculties or become impossible. The answer is simple - internal forces will appear in the system that will level the fluxes without displacement of lattice. If one excludes ionic crystals, there are two, known to us, types of such balancing forces - stress gradient and nonequilibrium vacancy concentration gradient For the result to be obtained, the type of such unclear force is of secondary importance, while the result is significant. 

Apparently, in the absence of any acting vacancy sinks/sources, the flux of vacancies toward a more mobile component will lead to their accumulation on this component s side and depletion on the side of a less active component. As a result, a nonuniform distribution of nonequilibrium vacancies will evolve. Correspondingly, a vacancy concentration gradient will appear, and it must influence both vacancies and atoms fluxes. 

The principal result of the Nazarov-Gurov (NG) theory, developed in the 1970s, is that owing to high mobility of vacancies, their distribution can be considered as to be of quasi-steady state type, and so (if vacancy sinks/sources are not functioning) 9jV/9x 0 and, moreover, jv 0. This means that Ja + Jb =... 

The Model for Regular Chains of Ideal Vacancies Sinks/Sources 17... 

From the viewpoint of diffusion conductance, the NG and Darken equations describe extreme, marginal cases. Darken s equation corresponds to parallel connection when the interdiffusion rate is usually determined by the more mobile component. The NG equation conforms to series (consecutive) connection at which the interdiffusion rate is mainly determined by the less mobile component - the more mobile one has to wait until slower atoms accomplish their migration. The discrepancy between equations becomes most apparent whenever the components mobility ratio is much larger or much less than one. In the general case, we may expect the correct description of interdiffusion to correspond to a certain combination of parallel and series (consecutive) connection, depending on vacancies sinks/sources effectiveness. We will see that the NG and Darken equations conform to different spatial and time scales. 

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