Diffusion mechanism interstitialcy

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

In the case of interstitials, two diffusion mechanisms can be envisaged (Figure 7.9). An interstitial can jump to a neighbouring interstitial position. This is called interstitial diffusion and is the mechanism by which tool steels are hardened by incorporation of nitrogen or carbon. Alternatively, an interstitial can jump to a filled site and knock the occupant into a neighbouring interstitial site. This knock-on process is called interstitialcy diffusion. 

When the lattice is heavily distorted, interstitial diffusion becomes difficult, so that another diffusion mechanism is present, which is known as interstitialcy mechanism. Interstitialcy diffusion is facilitated by exchanging position between an atom at the regular lattice site with a neighboring interstitial atom, as shown schematically in Fig. 5.8. They can be different types of atoms. 

Consider an atom on a normal lattice site of a cation or anion sub-lattice. If this atom is to move by the interstitialcy mechanism, an atom on a nearest neighbour interstitial site has to push the atom on the normal site to a neighbouring interstitial site. Thus for this diffusion mechanism an atom may only diffuse when it has an interstitial atom on a neighbouring site, and as for vacancy diffusion the diffusion coefficient of the atoms is proportional to the fraction (concentration) of interstitial atoms or ions in the sub-lattice. 

In the discussions of diffusion mechanisms in Chapter 5 it was pointed out that successive jumps of tracers atoms in a solid may for some mechanisms not be completely random, but are to some extent correlated. This is, for instance, the case for the vacancy and interstitialcy mechanisms. For a correlated diffusion of a tracer atom in a cubic crystal the tracer diffusion coefficient, Dt, is related to the random diffusion coefficient for the atoms. Dr, through the correlation coefficient f ... 

An alternative mechanism by which interstitial atoms can diffuse involves a jump to a normally occupied site together with simultaneous displacement of the occupant into a neighboring interstitial site. This knock-on process is called interstitialcy diffusion. 

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. 

Growth of oxidation-induced stacking faults proceeds by the absorption of the generated self-interstitials. Oxidation-enhanced diffusion can occur as a result of the presence of the excess interstitials via the Watkins (36) replacement mechanism or by an interstitialcy process. 

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.

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