Defect equilibration, local

The Kirkendall effect in metals shows that during interdiffusion, the relaxation time for local defect equilibration is often sufficiently short (compared to the characteristic time of macroscopic component transport) to justify the assumption of local point defect equilibrium. In those cases, the (isothermal, isobaric) transport coefficients (e.g., Dh bj) are functions only of composition. Those quantitative methods introduced in Section 4.3.3 which have been worked out for multicomponent diffusion can then be applied. 

In order to clarify the meaning of D in the case of incomplete (local) defect equilibration, let us consider a linear diffusion geometry and assume that the equilibration of the defects with the external oxygen buffer occurs only at one end of the sample. The fluxes of the components can then be expressed as... 

The last two examples show that inter diffusion processes and chemical diffusion coefficients can vary widely, depending upon the transport numbers of the ionic and electronic defects. A theoretical calculation is only possible if it is assumed that defect equilibrium is maintained. Whether the assumption of local defect equilibrium is applicable to an individual case will depend upon the relaxation time for the defect equilibration process. That is, it will depend upon the density of defect sources and sinks. In most cases, therefore, it will depend upon the density of dislocations and of low- and high-angle grain boundaries. 

Since the state of a crystal in equilibrium is uniquely defined, the kind and number of its SE s are fully determined. It is therefore the aim of crystal thermodynamics, and particularly of point defect thermodynamics, to calculate the kind and number of all SE s as a function of the chosen independent thermodynamic variables. Several questions arise. Since SE s are not equivalent to the chemical components of a crystalline system, is it expedient to introduce virtual chemical potentials, and how are they related to the component potentials If immobile SE s exist (e.g., the oxygen ions in dense packed oxides), can their virtual chemical potentials be defined only on the basis of local equilibration of the other mobile SE s Since mobile SE s can move in a crystal, what are the internal forces that act upon them to make them drift if thermodynamic potential differences are applied externally Can one use the gradients of the virtual chemical potentials of the SE s for this purpose ... 

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