Vacancy drift

Assuming that the anion vacancies drift to the CS defect as a result of the point defect-extended defect interaction, an estimate can be made of the activation energy for the migration of anion vacancies. 

In concluding, let us comment on the time needed to attain the steady state after establishing the surface activities. Two transient processes having different relaxation times occur I) the steady state vacancy concentration profile builds up and 2) the component demixing profile builds up until eventually the system becomes truly stationary. Even if the vacancies have attained a (quasi-) steady state, their drift flux is not stationary until the demixing profile has also reached its steady state. This time dependence of the vacancy drift is responsible for the difficulties that arise when the transient transport problem must be solved explicitly, see, for example, [G. Petot-Er-vas, et al. (1992)]. 

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

The oxygen vacancies then diffuse to the gas interface where they are annihilated by reaction with adsorbed oxygen. The important point, however, is that metal is consumed and oxide formed in the same reaction zone. The oxide drift has thus only to accommodate the net volume difference between the metal and its equivalent amount of oxide. In theory this net volume change could represent an increase or a decrease in the volume of the system, but in practice all metal oxides in which anionic diffusion predominates have a lower metal density than that of the original metal. There is thus a net expansion and the oxide drift is away from the metal. 

In cases where the antisite defects are balanced, such as a Ga atom on an As site balanced by an As atom on a Ga site, the composition of the compound is unaltered. In cases where this is not so, the composition of the material will drift away from the stoichiometric formula unless a population of compensating defects is also present. For example, the alloy FeAl contains antisite defects consisting of iron atoms on aluminum sites without a balancing population of aluminum atoms on iron sites. The composition will be iron rich unless compensating defects such as A1 interstitials or Fe vacancies are also present in numbers sufficient to restore the stoichiometry. Experiments show that iron vacancies (VFe) are the compensating defects when the composition is maintained at FeAl. 

Equation (8.14) demonstrates once more that the cation flux caused by the oxygen potential gradient consists of two terms 1) the well known diffusional term, and 2) a drift term which is induced by the vacancy flux and weighted by the cation transference number. We note the equivalence of the formulations which led to Eqns. (8.2) and (8.14). Since vb = jv - Vm, we may express the drift term by the shift velocity vb of the crystal. Let us finally point out that this segregation and demixing effect is purely kinetic. Its magnitude depends on ft = bB/bA, the cation mobility ratio. It is in no way related to the thermodynamic stability (AC 0, AG go) of the component oxides AO and BO. This will become even clearer in the next section when we discuss the kinetic decomposition of stoichiometric compounds. 

The vacancy current is therefore due solely to the cross term arising from the current of conduction electrons (which is proportional to E). The coupling coefficient for the vacancies is the off-diagonal coefficient Lvq which can be evaluated using the same procedure as that which led to Eq. 3.54 for the electromigration of interstitial atoms in a metal. Therefore, if (5V) is the average drift velocity of the vacancies induced by the current and Mv is the vacancy mobility,... 

Figure 1 is a schematic representation of Frenkel s notion an atom or ion can get dislodged from its normal site to form etn interstitial-vacancy pair. He further proposed that they do not always recombine but instead may dissociate and thus contribute to diffusional transport and electrical conduction. They were free to Wcuider about in a "random walk" mcuiner essentially equivalent to that of Brownian motion. . . this meant they should exhibit a net drift in an applied field. 

Let us modify the scheme described in the previous paragraph for the case of phase formation at a direct current imposed onto the diffusion zone, from A to B or in the reverse direction (the pattern of phase formation at direct current is reviewed in detail in Chapters, alternative approach discussed in [19]). Current-induced electron wind results in drift components in component and vacancy fluxes described by... 

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