Internal Oxidation in Nonmetallic Solid Solutions

The arrows denote ingoing (- ) and outgoing ( -) (Fig. 9-4). It is implicit in Eqn. (9.8) that the B ions of the wiistite (W) are oxidized to B when they form the spinel (Sp) lattice. If we neglect any lattice mismatch, V = - - Let us designate the volume fraction of the spinel product in the (internal) reaction zone as A. The rate of advance of the front ( K) can then be written as 

This equation says that if the advance corresponds to 1 mole of oxygen, (2/4) moles of vacancies arrived at the reaction front (4 - (A, B) O - (A, B)304). As long as k attains a constant (= steady state) value, the balance of B cations yields (with respect to the local reaction A1 NoB O = (1 —A)-A, BnO+(A/4)-AB204 + A2+ions) 

For the last part of Eqn. (9.10), we have assumed that N i 1, corresponding to a high thermodynamic stability of the (spinel) product phase. A semi-quantitative, and by no means strict, discussion of the internal reaction kinetics is as follows. As long as div/v = 0 in the region S F, we can formulate the cation vacancy flux as 

From Eqn. (9.11), we can eventually evaluate Af (= (fF+ s ) as the width of the internal (spinel) precipitate region, as a function of time. s is the coordinate of the surface (Fig. 9-4). It moves towards the oxidizing gas at a velocity of Vm jv, where / v corresponds to the Az+ cation counterflux arriving at the surface ( s) and being oxidized by 02(g) to AO (and the compensating electron holes which flow with the vacancies to the reaction front). We thus obtain 

We note that (Dy v) is proportional to the self-diffusion coefficient of the cations in AO near the surface. 

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