Point defect reactions

35 The grooving angle of the grain boundary is a function of the grain boundary inter cial tension and of 

after this excursion, let us focus on point defects, which are the heart of the text. We will return in Section 5.8 to higher-dimensional defects in the form of boundary conditions for the distribution of point defects. 

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Equation (4.145) represents a first order relaxation. We found the same result in Section 1.3.1 by linearizing the kinetic equations of the bimolecular point defect reaction (Eqn. (1.7)). 

In Section 4.7, we discussed the relaxation process of SE s in a closed system where the number of lattice sites is conserved (see Eqn. (4.137)). A set of coupled differential equations was established, the kinetic parameters (v(x,iq,x )) of which describe the rate at which particles (iq) change from sublattice x to x. We will discuss rate parameters in closed systems in Section 5.3.3 where we deal with diffusion controlled homogeneous point defect reactions, a type of reaction which is well known in chemical kinetics. 

We start with a bimolecular diffusion controlled point defect reaction of the form A + B = C and assume that the immobile B s are (unsaturated) sinks for A. If we then project each B with its surrounding A s onto the coordinate origin at r = 0, and define the individual reaction volume as (4-7t/3)-/-ab the time dependence of the (projected) A-concentration in space is given by the solution to Fick s second law with the following boundary conditions (setting u = cA(r, t)/cA r,0)) u(r,0) = 1 for r>rABl m(°°,0 = 1 (normalized) u(rAB,t) = 0. The solution reads (Fig.5-8)... 

We saw in our discussion of phase diagrams that FeO never exists. Consider wiistite with composition Fco.gsO. To compensate the charge of Vpe (i.e., for electrical neutrality), we need to replace 3Fe " ions by 2Fe ions. This is the important point the Fe ions change their valence from 2 to 3. This point defect reaction happens automatically. You can imagine it occurring by dissolving Fe203(s) in FeO(s). 

To exhibit nonstoichiometry, the cation must be able to exist in two different valence states (so this is not the same as nonequimolarity that we saw for spinel). The ions Fe, Co, and, to a lesser extent, Ni can do this Mg cannot. An alternative way of writing this point defect reaction is to bring oxygen from the gas state into FeO. 

Write down a point defect reaction for ZnO in which you produce twice as many singly charged defects as doubly charged ones. 

Radiation can also be modified using electrochromism. Electrochromism is the production of color by applying an electrical field. Electrochromic compounds such as WO3 are coated on the glass using a variety of thin film techniques. The point defect reaction is reversible. 

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