Relaxation of Irregular Structure Elements

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. 

In physical and chemical metallurgy, the Kirkendall effect, which is closely related to point defect relaxation during interdiffusion, has been studied extensively. It can be quantitatively defined as the internal rate of production or annihilation of vacan- 

Following these introductory remarks, the next sections are devoted to a detailed discussion of defect relaxation phenomena. 

In order to do so we must first evaluate the chemical diffusion coefficients of the pair of majority defects (e.g., V and h ) in the semiconducting oxide A O. The coupling of the defect fluxes (jh--2jV = 0) to maintain electroneutrality results in a chemical diffusion coefficient Dv. This controls the change in nonstoichiometry, 5( ,/) through defect transport and reads 

Let us assume that the oxide sample exists in the form of a parallelepiped. The solution to Fick s second law under the given boundary conditions gives for the change in time of the integral number of vacancies wv 

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Our neglect of the discreteness of the crystal lattice does not introduce noticeable discrepancies. Continuum theory, based on the original concept by Smoluchowski, is quite acceptable for the description of diffusion controlled relaxation of irregular structure elements in crystals. 

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