Jump mechanism vacancy, interstitial

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

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.

Frenkel defects and impurity ions can diffuse through the silver halide lattice by a number of mechanisms. Silver ions can diffuse by a vacancy mechanism or by replacement processes such as collinear or noncollinear interstitialcy jump mechanisms [18]. The collinear interstitial mechanism is one in which an interstitial silver ion moves in a [111] direction, forcing an adjacent lattice silver ion into an interstitial position and replacing it The enthalpies and entropies derived from temperature-dependent ionic conductivity measurements for these processes are included in Table 4. The collinear interstitial mechanism is the most facile process at room temperature, but the other mechanisms are thought to contribute at higher temperatures. 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

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. 

In the case of interstitials—self-interstitials, impurities, or dopants—two diffusion mechanisms can be envisaged. In the simplest case, an interstitial can jump to a neighboring interstitial position (Fig. 5.8a). This is called interstitial diffusion and is sometimes referred to as direct diffusion to distinguish it from vacancy diffusion (indirect diffusion). 

In the case of interstitial diffusion in which we have only a few diffusing interstitial atoms and many available empty interstitial sites, random-walk equations would be accurate, and a correlation factor of 1.0 would be expected. This will be so whether the interstitial is a native atom or a tracer atom. When tracer diffusion by a colinear intersticialcy mechanism is considered, this will not be true and the situation is analogous to that of vacancy diffusion. Consider a tracer atom in an interstitial position (Fig. 5.18a). An initial jump can be in any random direction in the structure. Suppose that the jump shown in Figure 5.18b occurs, leading to the situation in Figure 5.18c. The most likely next jump of the tracer, which must be back to an interstitial site, will be a return jump (Fig. 5.18c/). Once again the diffusion of the interstitial is different from that of a completely random walk, and once again a correlation factor, / is needed to compare the two situations. 

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). 

The jump vector. A, wUl obviously depend on the mechanism and the structure. For example, an atom diffusing through the octahedral interstitial sublattice in an FCC metal, with lattice spacing a (Fig. 6.6), must jump the distance between interstitial sites, A = fl/V2. This is, of course, the same distance an atom diffusing by the vacancy mechanism must jump. It will be recalled that for every atom in a close-packed stmcture, there are two tetrahedral interstitial sites and one octahedral interstitial site. The reader might ask if the distances between the tetrahedral sites ate the same. 

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. 

This is an important result because it implies that the mobility of a charged species is directly related to its defect diffusivity, a not-too-surprising result since the mobility of an ion must reflect the ease by which the defects jump around in a lattice. Note that if diffusion is occurring by a vacancy mechanism, A Cdef/cion 10, whereas if diffusion is occurring by an interstitial mechanism, then A 1.0 and = z, e/Djnt/(/f7 ). 

The atomic mechanism of diffusion was, for many years, controversial, although for interstitial solutes (e.g., hydrogen, helium, carbon, nitrogen, and oxygen [and possibly boron] in iron), there has never been any doubt that diffusion is by migration from one interstice to another. In fee metals, at least, it seems fairly certain that substitutional alloy atoms diffuse by activated jumps into vacant lattice sites, that is, by the vacancy mechanism. In solid solutions in which one component is interstitial, two noncompeting processes occur, and two independent diffusion coefficients are obtained. 

The interstitial mechanism is generally favored for small atoms (e.g., impurity cations such as Na in Si or C in Fe) that can fit into the interstitial sites in a crystal lattice. Interstitial diffusion is generally faster than vacancy diffusion because bonding of interstitials to the surrounding atoms is normally weaker and there are generally many more available interstitial sites than vacancy sites to jump to. Larger atoms, for example the oxygen anions in most oxide ceramics, must diffuse via a vacancy... 

The mechanism of diffusion varies greatly depending on the crystalline structure and the nature of the solute. For crystals with lattices of cubic symmetry, the dif-fusivity is isotropic, but not so for noncubic crystals. In interstitial mechanisms of diffusion, small diffusing solute atoms pass through from one interstitial site to the next. The matrix atoms of the crystal lattice move apart temporarily to provide the necessary space. When there are vacancies where lattice sites are unoccupied, an atom in an adjacent site may jump into such a vacancy. This is called the vacancy mechanism. 

As defects in oxides with large deviations from stoichiometry constitute complex defects, there has been considerable discussion and speculation about the diffusion mechanism in such oxides. It has, for instance, been suggested that complex defects coexist in a dynamic equilibrium with single defects, and that the diffusion processes also under these conditions really involve diffusion of single defects. In the case of defect clusters it has alternatively been proposed that the smaller clusters may move as a unit. A translational mechanism that has been proposed for a 4 1 cluster in wustite is illustrated in Fig.5.10. The jump processes in the motion of a 4 1 complex is quite complex, and the mechanism requires two distinct, sequential jumps. Atom 1 jumps to fill a vacancy in the complex defect and thereby creates a new vacancy. In the process the interstitial ion in the cluster... 

The diffusivity of a constituent such as the host metal or oxygen ions by an interstitial mechanism is not only proportional to the probability that the interstitial defect jumps, but also to the probabiUty that a constituent ion is interstitial, i.e., the fractional concentration of interstitials. Thus the diffusion coefficient of the constituent contains the temperature and oxygen pressure dependencies of the concentration of interstitials in addition to the temperature dependency of the mobility of these defects. As in the case of vacancy diffusion, the fixation of the defect concentration by doping or freezing as well as association and trapping of defects apply also to interstitial diffusion. 

---