Vacancy exchange

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

Because of die rigidity and directionality of die covalent bonds die energies of self-diffusion have been found to be higher diaii diose of metals. In die case of silicon, it appears drat a furdier complication is drat an intersti-tialcy mechanism predominates above 1000°C. Below diis teiiiperamre, bodi elements appear to self-diffuse by atom-vacancy exchange as for die metals. 

Correlation diminishes the effectiveness of atomic jumps in diffusional random motion. For example, when an atom has just moved through site exchange with a vacancy, the probability of reversing this jump is much higher than that of making a further vacancy exchange step in one of the other possible jump directions. Indeed, if z is the coordination number of equivalent atoms in the lattice, the fraction of ineffective jumps is approximately 2/z (for sufficiently diluted vacancies as carriers) [C. A. Sholl (1992)]. 

The vacancy exchange mechanism is described in Section 8.1.2. 

Considering Eq. 2.21 in a case in which diffusion occurs in a crystal by the vacancy exchange mechanism, there are four components, Cj., c i, c2, and cy. Because the crystal remains fixed during the diffusion, the C-frame is again used for measuring the flux. The system is chemically homogeneous, so... 

Figure 8.3 Atom-vacancy exchange in f.c.c. crystal. Atom initially at A jumps into a...

Equation 8.19 contains the correlation factor, f, which in this case is not unity since the self-diffusion of tracer atoms by the vacancy mechanism involves correlation. Correlation is present because the jumping sequence of each tracer atom produced by atom-vacancy exchanges is not a random walk. This may be seen by... 

Solution. The diffusion of the atoms will be correlated because of the vacancy exchange mechanism and, therefore, using Eq. 7.52,... 

The frequency w at which an atom and an adjacent neighboring vacancy exchange can be written as... 

Figure 4 A ball-model (top view) of a diffusion event in which the passage of a surface vacancy leads to a multi-lattice-spacing displacement of the indium atom (bright). The arrow indicates the random walk pathway of the vacancy, and the indium-vacancy exchanges are marked with crosses to show the pathway of the indium between its beginning and endpoints.

The same problem has been solved in an alternate way for all dimensions [42]. From this solution one can calculate the number of tracer-vacancy exchanges up to time t. In two dimensions the distribution is geometric, with mean (log t)/tt. The continuum version of this problem has been considered as well in the form of an infinite-order perturbation theory [43] the solution matches the asymptotic form of the lattice model. 

By definition, the rate at which the tracer atom is displaced by a surface vacancy is the product of the vacancy density at the site next to the tracer times the rate at which vacancies exchange with the tracer atom. For the case where the interaction between the tracer atom and the vacancy is negligible, the activation energy obtained from the temperature dependence of the total displacement rate equals the sum of the vacancy formation energy EF and the vacancy diffusion barrier ED. When the measurements are performed with finite temporal resolution and if there is an interaction present between the vacancy and the indium atom, this simple picture changes. 

The tracer atom is displaced if the vacancy returns to any of its 4 neighboring sites 0, 1,2, etc. times, and then exchanges places with it. The possibility that multiple displacements add up to a zero net displacement is ignored.2 The precise value of x, the probability to make a successful exchange, is determined by the energy difference between the modified (E u) and unmodified (ED) vacancy exchange... 

The observed rate of long jumps is equal to the equilibrium rate at which vacancies exchange with the tracer atom, divided by the average number of elementary displacements caused by a single vacancy,... 

Figure 20. Model boundary interphase exchange currents involving lattice vacancy injection at the compound-electrolyte interface and vacancy exchange into the metal releasing an electron and transferring a metal ion into the compound layer (12)...

The following limiting cases should be mentioned 1. If Fa > Fg, then/g — 1, and the particle B diffuses without correlation through A. 2. If Fa Fg, then /g is very small. This means that the particle B exchanges places back and forth with a neighbouring vacancy very many times before the vacancy exchanges with an A particle and the elementary step of the B particle becomes effective. 

Near Resonant Vacancy Exchange between Inner Shells of Colliding... 

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