Oxygen vacancy fluxes

When the oxygen vacancy,, and electron hole, h, are the primary mobile charge carriers, the oxygen vacancy flux may be derived from eqn (18.5) as ... 

We proceed by considering a slab of an oxide crystal AO and assume that a cation vacancy flux is driven across it. In contrast to the single sublattice alloy discussed above, where the vacancies have been introduced into the lattice as an independent component, the vacancy flux j° in AO can be induced by different oxygen activities at the two opposite surfaces. At the oxidizing surface, the defect reaction is y 02 = Oq +V +2-h In semiconducting AO, the flux of ionized A vacancies is compen-... 

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. 

If we identify jy in Eqn. (8.66) with j° in Eqn. (8.3), we can use Eqn. (8.3) to calculate the (steady state) demixing when a stress driven vacancy flux flows across the solid solution (A,B)0. At a fixed oxygen potential, we obtain from the steady state condition... 

Instead of forcing the data to conform to the d-wave picture, we take the approach that the deviations from. v-wave behavior are due to quantifiable phenomena, most notably temperature-dependent fhixon de-pinning. Since the maximum temperature for the data acquired at each held is below the melting curve (see Fig. 4 of Ref. 11), the vortex lattice is subject to pinning, as occurs in very clean crystals where the flux lattice becomes locked-in by weak pinning at oxygen vacancies and/or other defects. 

If, for example, oxygen vacancies Vq, denoting a missing O ) and electrons are present and then also associates such as Vq (one electron trapped by an oxygen vacancy) and Vq (two electrons trapped by an oxygen vacancy), the flux and conductivities in Equation (1.3) address the total oxygen ensemble, G o) = I (Vq does not contribute being effectively neutral). The ensemble... 

At constant temperature, the fluxes of oxygen vacancies and electrons are expressed as... 

The two compositions, SCF and BSCF, have very similar oxygen fluxes at high temperature, but at lower temperature, BSCF has a much higher oxygen flux than SCF. This has been ascribed to the occurrence of a low temperature phase with the brownmillerite (see Fig. 2.9) structure in which the oxygen vacancies are ordered in rows [25]. Such ordered phases tend to have a lower permeability for oxygen [26]. 

Equations (19.13) to (19.15) follow from the condition that steady-state fluxes of cation vacancies, cation interstitials, and oxygen vacancies, are the same at the two interfaces. Finally, it is possible to calculate the values of... 

Since oxygen vacancy defects also tend to decrease the Q-factor, the firing atmosphere and post-firing anneahng must be carefully considered. This is reminiscent of the severe processing problems of high-temperature superconductors (see Section 9.7). In fact, the dielectric loss in ceramics is analogous to the resistance experienced by flux penetration in type 11 superconductors. 

In oxygen-deflcient perovskites (general formula of ABO3 a) the ion flux is carried by oxygen-ion vacancies and we may write the above equation in terms of oxygen vacancy conductivity, ay, and vacancy electrochemical potential, jly,... 

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