Transport in Binary Ionic Crystals AX

Conceptually it is often convenient to formulate transport only in terms of point defect fluxes since point defects are the primary mobile species. Regular SE s in ionic crystals are then rendered mobile by point defect jumps. We assume (in accordance with many systems of practical importance) that the X anions are (almost) immobile and refer the fluxes to the X sublattice. At sufficiently low concentrations of point defects, their individual elementary jumps are independent. Thus 

Boundary condition l). In the absence of an external electrical circuit, current cannot flow, that is, X Zjji = 0. Inserting ionic and electronic fluxes (Eqns. (4.99) and (4.100)) into this condition, one obtains 

Equation (4.102) follows from Eqn. (4.101) since A = A+ +e etc and by definition tej= 1 -(/A + tx). Ba and px are (neutral) component potentials. If one eliminates the electrical potential gradient from the flux equations, it is found that 

Although the parabolic rate law has the same form as the mean square displacement (see Section 4.3.1), its physical background is quite different. Parabolic growth is always observed in a one dimensional experiment when due to a gradient-driven flux and where the boundaries are kept at constant potentials. 

Boundary condition 2). Let us now fix two inert electrodes with a voltage difference, A U, across AX (Fig. 4-3 b). Since inert electrodes are reversible for electrons (electron holes) only, 

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