Diffusion mechanisms interstitialcy mechanism

Figure 5.10 (a) Colinear (ciy) and noncolinear interstitialcy (nciy) diffusion, schematic and (b) simulation indicating that a noncolinear diffusion mechanism is responsible for F diffusion in RbBiF4. [Redrawn after C. R. A. Catlow, J. Chem. Soc. Faraday Trans., 86, 1167-1176 (1990).]... 

Figure 8.4 Substitutional diffusion by the interstitialcy mechanism, (a) The interstitial defect corresponding to the interstitial atom (3) is separated from a particular substitutional atom B (shaded), (b) The interstitial defect moved adjacent to B when the previously interstitial atom (3) replaced the substitutional atom (2). (2) then became the interstitial atom, (c) Atom (2) has replaced B, and B has become the interstitial atom, (d) B has replaced atom (4). which has become the interstitial atom, (e) The interstitial defect has migrated away from B. As a result. B has completed one nearest-neighbor jump and the interstitial defect has moved at least four times.

Diffusion by the interstitial mechanism and by the interstitialcy mechanism are quite different processes and should not be confused. Diffusion by the vacancy and interstitialcy mechanisms requires the presence of point defects in the system, whereas diffusion by the ring and interstitial mechanisms does not. 

Diffusion of Self-Interstitial Imperfections by the Interstitialcy Mechanism in the F.C.C. Structure. For f.c.c. copper, self-interstitials have the (100) split-dumbbell configuration shown in Fig. 8.5d and migrate by the interstitialcy mechanism illustrated in Fig. 8.6. The jumping is uncorrelated,8 (f = 1), and a/ /2 is the nearest-neighbor distance, so... 

Self-Diffusion by the Interstitialcy Mechanism. If their formation energy is not too large, the equilibrium population of self-interstitials may be large enough to contribute to the self-diffusivity. In this case, the self-diffusivity is similar to that for self-diffusion via the vacancy mechanism (Eq. 8.19) with the vacancy formation and migration energies replaced by corresponding self-interstitial quantities. The... 

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

The activation energy for self-diffusivity of the Ag cations by the interstitialcy mechanisms is the sum of one-half the Frenkel defect formation enthalpy and the activation enthalpy for migration,... 

It has sometimes been claimed that the observation of a Kirkendall effect implies that the diffusion occurred by a vacancy mechanism. However, a Kirkendall effect can be produced just as well by the interstitialcy mechanism. Explain why this is so. 

Solution. Substitutional atoms of type 1 may diffuse more rapidly than atoms of type 2 if they diffuse independently by the interstitialcy mechanism in Fig. 8.4. To sustain the unequal fluxes, interstitial-atom defects can be created at climbing dislocations acting... 

A mechanism related to interstitial diffusion is the interstitialcy mechanism. In this process, an interstitial atom moves into a lattice site by dis-... 

For diffusion models based on self-interstitials, C° Cv°. Dopant diffusion and self-diffusion are assumed to occur via an interstitialcy mechanism (32). Mobile complexes consisting of self-interstitials in various charge states and impurities are assumed to exist. 

Point Defect Generation During Phosphorus Diffusion. At Concentrations above the Solid Solubility Limit. The mechanism for the diffusion of phosphorus in silicon is still a subject of interest. Hu et al. (46) reviewed the models of phosphorus diffusion in silicon and proposed a dual va-cancy-interstitialcy mechanism. This mechanism was previously applied by Hu (38) to explain oxidation-enhanced diffusion. Harris and Antoniadis (47) studied silicon self-interstitial supersaturation during phosphorus diffusion and observed an enhanced diffusion of the arsenic buried layer under the phosphorus diffusion layer and a retarded diffusion of the antimony buried layer. From these results they concluded that during the diffusion of predeposited phosphorus, the concentration of silicon self-interstitials was enhanced and the vacancy concentration was reduced. They ruled out the possibility that the increase in the concentration of silicon self-interstitials was due to the oxidation of silicon, which was concurrent with the phosphorus predeposition process. 

The interstitial solute diffuses by jumping from one interstitial site to the other (see Figure 5.10). This mechanism is also called the direct interstitial mechanism in order to differentiate it from the interstitialcy mechanism. 

Self-diffusion in materials occurs by repeated occupation of defects. Depending on the defects involved one can distinguish between (1) vacancy, (2) interstial, and (3) interstitialcy mechanisms [107], As an example, different diffusion paths for oxygen interstitials are illustrated in Fig. 1.16 [129]. For a detailed description of diffusion paths for oxygen vacancies, zinc vacancies and zinc interstitials the reader is also referred to literature [129,130]. 

Fig. 1.17. Oxygen diffusion in ZnO [129]. Top Dependence of diffusivity on chemical potential and Fermi level at a temperature of 1 300 K illustrating the competition between vacancy and interstitialcy mechanisms. The dark grey areas indicate the experimental data range around 1 300 K. Bottom Comparison between calculation and experiment. Experimental data from Moore and Williams [131], Hofmann and Lauder [132], Robin et al. [133], Tomlins et al. [134], Haneda et al. [135], and Sabioni et al. [136]. Solid and dashed lines correspond to regions I (interstitialcy mechanism dominant) and II (vacancy mechanism dominant) in the top graph, respectively. Copyright (2006) by the American Physical Society...

Atoms larger than this would produce excessively large structural distortions if they were to diffuse by the direct interstitial mechanism. Hence, in these cases diffusion tends to occur by what is known as the interstitialcy mechanism. In this process, the large atom that initially moves into an interstitial position displaces one of its nearest neighbors into an interstitial position and takes the displaced... 

Solid-state diffusion, which is involved in the release of oxygen, proceeds generally through the movement of point defects. The vacancy mechanism, the interstitial mechanism, and the interstitialcy mechanism can occur depending on the distortion of the solid lattice and the nature of the diffusing species. When one of the steps 1-5 is the slowest step representing the major resistance, that step is the rate-controlling one, which is not necessarily the chemical reaction (step 3). 

Figure 6.5. Schematic illustrating the different mechanisms for atomic diffusion in a BCC lattice. In the vacancy mechanism, an atom in a lattice site jumps to an adjacent vacant lattice site. In the interstitial mechanism, an interstitial atom jumps into an adjacent vacant interstitial site. In the interstitialcy mechanism, an interstitial atom pushes an atom residing in a lattice site into an adjacent vacant interstitial site and occupies the displaced atom s site.

Elliott (1987, 1988 and 1989) approached the relaxation problem differently. In his diffusion controlled relaxation (DCR) model, Elliott, like Charles (1961) considers ionic motion to occur by an interstitialcy mechanism. There is a local motion of cations (for example Li ion in a silicate glass) among equivalent positions located around a NBO ion. Motions of cations among these positions causes the primary relaxational event and it occurs with a characteristic microscopic relaxation time t. The process gives rise to a polarization current. However, when another Li ion hops into one of the nearby equivalent positions with a probability P(/), a double occupancy results around the anion and this makes the relaxation instantaneous. Since the latter process involves the diffusion of a Li ion, the process as a whole involves both polarization and diffusion currents. Thus the relaxation function can be written as [l-P(/)]exp(-t/r). [1-P(0] is a function of the jump distance and the diffusion constant. Making use of the Glarum-Bordewijk relation (Glarum, 1960 Bordewijk, 1975) for [1-/ (/)] Elliott (1987) has shown that... 

When the diffusing interstitial atoms have a size comparable to that of the lattice atoms, the interstitialcy mechanism for diffusion may take place. In this case the interstitial impurity atom moves into a host lattice site by pushing a neighboring normal atom into the adjacent interstitial site. This process repeats itself when a self-interstitial atom pushes the substitutionally located impurity atom into an interstitial site. 

The kick-out mechanism is rather similar to the interstitialcy mechanism. In this case, a host self-interstitial atom diffuses around the lattice. When it reaches a substitutional impurity atom, the self-interstitial pushes the impurity atom into an adjacent interstitial site. The interstitial impurity then diffuses interstitially until it reverts back to a host lattice site by displacing a host atom. It is experimentally difficult to distinguish the kick-out mechanism from the interstitialcy mechanism. The generally accepted view is that the interstitial impurity atoms may tend to diffuse longer distances before returning to the normal lattice sites for the kick-out mechanism, whereas the impurity atoms tend to diffuse interstitially for a relatively short distance before going into the normal lattice sites for the interstitialcy mechanism. 

There are essentially three mechanisms by which atoms will diffuse, as shown schematically in Fig. 7. In to c. The first, the vacancy mechanism, involves the jump of an atom or ion from a regular site into an adjacent vacant site (Fig. 7.In). The second, interstitial diffusion, occurs as shown schematically in Fig. l. b and requires the presence of interstitial atoms or ions. The third, less common mechanism is the interstitialcy mechanism, shown in Fig. 7.1c, where an interstitial atom pushes an atom from a regular site into an interstitial site. 

Figure 7.9 Self-diffusion mechanisms. Note v, vacancy i, interstitial iy, interstitialcy...

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