Interstitialcy mechanism

Interstitialcy migration depends on the geometry of the interstitial defect. However, an a priori prediction of interstitial defect geometry is not straightforward in real materials. For an f.c.c. crystal, a variety of conceivable interstitial defect candidates are illustrated in Fig. 8.5. The lowest-energy defect will be stable and predominant. For example, in the f.c.c. metal Cu, the stable configuration is the (100) split-dumbbell configuration in Fig. 8.5d [3]. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The 

2Interstitial point defects involving normally substitutional atoms will always exist (although typically at very low concentration) at equilibrium in a crystal at finite temperatures because, as in the case of vacancies described above, their enthalpy of formation can always be compensated by a configurational entropy increase. 

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The above two mechanisms may be regarded as isolated ion hops. Sometimes, especially in solid electrolytes, cooperative ion migration occurs. An example is shown in Fig. 2.1(c) for the so-called interstitialcy or knock-on mechanism. A Na" ion. A, in an interstitial site in the conduction plane of j -alumina (see later) cannot move unless it persuades one of the three surrounding Na ions, B, C or D, to move first. Ion A is shown moving in direction 1 and, at the same time, ion B hops out of its lattice site in either of the directions, 2 or 2. It is believed that interstitial Ag" ions in AgCl also migrate by an interstitialcy mechanism, rather than by a direct interstitial hop. 

In jS-alumina, Na ions appear to move by means of a knock-on or interstitialcy mechanism in which it is convenient to regard the excess Na ions as occupying interstitial sites. When these sites are nearly empty, as in crystals of composition close to the NaAlnOi, stoichiometry, then the conductivity is much reduced. In /S"-alumina, by contrast, it is more appropriate to regard conduction as a vacancy process in which the limiting composition without vacancies would correspond to NaAljOg. 

An interesting feature of the conduction mechanism in these materials and the LISICONS is that it is, at least partially, an interstitialcy mechanism. Both structure types contain examples of face-sharing tetrahedral sites. Fig. 2.13. Such sites are much too close together for both to be occupied simultaneously. Crystal structure refinements show that often, on average, one site of each pair contains a Li ion but the occupancy appears to be random. This means that, during conduction, one site of each pair may contain a Li ion but this is ejected when an incoming... 

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 activation energy for enhanced diffiision due to an interstitialcy mechanism is determined from equation 39... 

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 42. Elementary jump mechanisms in crystals a) vacancy mechanism, b) direct interstitial mechanism, c) (collinear or non-collinear), indirect interstitial mechanism (interstitialcy mechanism).

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.

Compare/contrast the vacancy, direct interstitial, and interstitialcy mechanisms of mass transport. 

In this structure there are perovskite layers of ABO3 separated by AO rock salt layers. It is this layered structure that allows great flexibility in the oxygen stoichiometry of these materials. It is possible to incorporate excess oxygen (5 > 0) in the unusual form of interstitial oxygens, which provide an alternative to the vacancy-based conduction mechanism present in the perovskite and fluorite oxides, where the dopant-vacancy interactions can limit the observed conductivity. The mobility of the oxide ions in these materials occurs mainly through an interstitialcy mechanism in the aZ)-plane, although evidence of low Ea for the conduction in the c-direction via a Frenkel mechanism has also been reported. ... 

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