Interstitial mechanism

The interstitial sites of a diamond or zinc blend lattice are usually vacant. The probability of an interstitial atom finding an available site to jump into is very high. As it jumps from one site to another, it faces a constriction due to the host atoms (see Fig. 9.11a) the jumping atom needs a little push to squeeze by. This situation is described as having an activation or energy barrier. In this case the barrier is also periodic in the lattice. 

The interstitial mechanism is fundamentally seen in solute atoms which, as was previously stated, are smaller than the solvent atoms in binary interstitial alloys. Then, in the present mechanism 

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An interstitial atom can simply migrate between interstitial sites as in Fig. 8.7. The interstitial atom must attain enough energy to distort the host crystal as it migrates between substitutional sites. This mechanism is expected for small solute atoms that normally occupy interstitial sites in a host crystal of larger atoms. 

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. 

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In some materials, semiconductors in particular, interstitial atoms play a crucial role in diffusion. Thus, Frank and Turnbull (1956) proposed that copper atoms dissolved in germanium are present both substitutionally (together with vacancies) and interstitially, and that the vacancies and interstitial copper atoms diffuse independently. Such diffusion can be very rapid, and this was exploited in preparing the famous micrograph of Figure 3.14 in the preceding chapter. Similarly, it is now recognised that transition metal atoms dissolved in silicon diffuse by a very fast, predominantly interstitial, mechanism (Weber 1988). 

FIGURE 25.3 Schematic representation of ionic motion by (a) a vacancy mechanism and (b) an interstitial mechanism. (From Smart and Moore, 1996, Fig. 5.4, with permission from Routledge/Taylor Francis Group.)... 

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

One type of diffusion mechanism is known as the interstitial mechanism because it involves movement of a lattice member from one interstitial position to another. When diffusion involves the motion of a particle from a regular lattice site into a vacancy, the vacancy then is located where the site was vacated by the moving species. Therefore, the vacancy moves in the opposite direction to that of the moving lattice member. This type of diffusion is referred to as the vacancy mechanism. In some instances, it is possible for a lattice member to vacate a lattice site and for that site to be filled simultaneously by another unit. In effect, there is a "rotation" of two lattice members, so this mechanism is referred to as the rotation mechanism of diffusion. 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

An example of a material (Li3Sb) with a very large Wagner factor is shown in Fig. 8.3. The effective chemical diffusion coefficient is compared with the diffusivity as a function of non-stoichiometry. These data were determined by electrochemical techniques (see Section 8.5). An increase of the diffusion coefficient is observed at about the ideal stoichiometry which corresponds to a change in the mechanism from a predominantly vacancy to interstitial mechanism. The Wagner factor W is as large as 70 000 at the ideal stoichiometry. This gives an effective diffusion coefficient which is more typical of liquids than solids. It is a common... 

FIGURE 5.4 Schematic representation of ionic motion by (a) a vacancy mechanism and (b) an interstitial mechanism. 

Interstitial mechanism As we have seen with regard to Frenkel defects, if an ion is small enough (again, usualy a cation), it can occupy an interstitial site, such as a tetrahedral hole in an octahedral lattice. It may then move to other interstitial sites. 

Consider small interstitial atoms jumping by the interstitial mechanism in b.c.c. Fe with the diffusivity D for a time r. 

Figure 8.7 Interstitial mechanism for diffusion of interstitial atoms. The smaller...

Diffusion of relatively small atoms that normally occupy interstitial sites in the solvent crystal generally occurs by the interstitial mechanism. For example, hydrogen atoms are small and migrate interstitially through most crystalline materials. Carbon is small compared to Fe and occupies the interstitial sites in b.c.c. Fe illustrated in Fig. 8.8 and migrates between neighboring interstitial sites. 

Diffusion of Solute Atoms by the Interstitial Mechanism in the B.C.C. Structure. The... 

Small solute atoms in the interstices between the larger host atoms in a relaxed metallic glass diffuse by the direct interstitial mechanism (see Section 8.1.4). The host atoms can be regarded as immobile. A classic example is the diffusion of H solute atoms in glassy Pd8oSi2o- For this system, a simplified model that retains the essential physics of a thermally activated diffusion process in disordered systems is used to interpret experimental measurements [20-22]. 

Figure 10.6 plots the tracer diffusivity data for a number of solute species in glassy NisoZrso as a function of their metallic radius. The diffusivity increases rapidly as the metallic radius decreases. The relatively rapid diffusion of the small atoms in this case may result from the fact that they diffuse by the interstitial mechanism [10, 18]. 

We do not discuss all these mechanisms here. However, the most important mechanisms, the vacancy mechanism and the interstitial mechanism, are described. 

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. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

Fig. 1.18. Zinc diffusion in ZnO [130]. Top Dependence of diffusivity on chemical potential and Fermi level at a temperature of 1 300 K illustrating the competition between vacancy and interstitial mechanisms. The shaded grey areas indicate the ranges selected for comparison with experimental data. Bottom Comparison between calculation and experiment. Experimental data from Lindner [137], Secco and Moore [138,139], Moore and Williams [131], Wuensch and Tuller [143], Tomlins et al. [62], and Nogueira et al. [144,145]. Solid and dashed lines correspond to regions I (vacancy mechanism) and II (interstitial(cy) mechanism) in the top graph, respectively. Reprinted with permission from [130]. Copyright (2006), American Institute of Physics...

Diffusion of atoms or ions in crystalline solids can occur by at least three possible mechanisms, as shown schematically in Figure 2.7. In some solids, transport proceeds primarily by the vacancy mechanism, in which an atom jumps into an adjacent, energetically equivalent vacant lattice site. The vacancy mechanism is generally much slower than the interstitial mechanism (discussed below). Nonetheless, it is thought to be responsible for self-diffusion in all pure metals and for most substitutional alloys (Shewmon, 1989). 

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... 

Figure 2.7 Diffusion of atoms or ions in crystalline solids can occur by at least three possible mechanisms illustrated here. In the vacancy mechanism (bottom arrow), an atom in a lattice site jumps to an adjacent vacant lattice site. In the interstitial mechanism (middle arrow), an interstitial atom jumps to an adjacent vacant interstitial site. In the intersitialcy mechanism (top two arrows), an interstitial atom pushes an atom residing in a lattice site into an adjacent vacant interstitial site and occupies the displaced atom s former site. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)...

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).

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