Conservative ensemble

Both the flux equation (Eq. (34)) as well as the voltage equation (Eq. (35)) are more complicated if the ions can change their valence states. As shown in Ref.3 58 59 the transport parameters then have to refer to conservative ensembles in particular in Eq. (35), instead of /ion, now / ioM. appears. If we take the example of a copper conductor with a Cu21 and a Cu+ mobility, between which electronic equilibrium is established, the ratio between E and the Nernst-value is then... 

The -terms refer to differential defect fractions defined via the corresponding conservative ensembles according to... 

Figure 52 illustrates the situation. The more general case in which different defects contribute will be tackled below in the framework of Conservative Ensembles (Section VI.4.ii.) which also explains the displayed depression ofD by trapping effects (see Fig. 52). 

It can now be shown that as far as the diffusion of certain ensembles, namely of the conservative ensembles , is concerned, the source terms disappear. The resulting chemical diffusion coefficients then have to refer to this ensemble. 

Figure 57. Conservative ensembles in the case of complex defect chemistry for various examples discussed in the text.233 234 (Reprinted from J. Claus, I. Denk, M. Leonhardt, and J. Maier, Influence of Internal Reactions on Chemical Diffusion Application to Fe-doped SrTiCV , Ber. Bunsenges. Phys. Chem. 101, 1386-1392. Copyright 1997 with permission from WILEY-VCH Verlag GmbH.)...

J. Maier, Mass transport in the presence of internal defect reactions-concept of conservative ensembles I, Chemical diffusion in pure compounds. /. Am. Ceram. Soc., 76(5) (1993) 1212-1217 II, Evaluation of electrochemical transport measurements, ibid., 1218-1222 III, Trapping effect of dopants on chemical diffusion, ibid., 1223-1227 IV, Tracer diffusion and intercorrelation with chemical diffusion and ion conductivity, ibid., 1228-1232. 

Maier, J. Mass transport in the presence of internal defect reactions— Concept of conservative ensembles 1, Trapping effect of dopants on chemical diffusion./. Am. Ceram. Soc., 76,1223-1227 [1993). 

In this sense (cq - Cy-) and (Ce - Ch ) refer to conservative ensembles . This is self-evident since all changes take place within these ensembles. Because... 

In the case of ion blockage the stationary current is i e = ie- — io- + 2Fjoo. This corresponds to the fluxes of the corresponding conservative ensembles , as introduced in Section 6.6.1. The basic current and voltage equations are now given in... 

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