Correlations Between Oxygen Diffusion Parameters

Many attempts have been made to rationalize the differences seen in the diffusion of oxygen in the perovskites in terms of a simplified parameter such as the tolerance factor, t = y Hayashi et al. [44] evaluated a large amount of 

A cations and one B cation [48]. Furthermore, it has been observed that correlations exist between measured transport parameters, e.g., the relationship between the self-diffusion coefficient and the surface exchange coefficient [11], 

The expression for the tracer diffusion coefficient (Eq. (5.4)) can be rewritten as follows  

There are several models that attempt to relate the entropy and the enthalpy of thermally activated processes in general and diffusion in particular. Zener [57] proposed that the major part of the free energy of the activated state is associated with elastic distortion of the lattice caused by the diffusing ion. An alternative relationship between the entropy, Sa, and the enthalpy of diffusion, Ea, was used by Almond and West [58] to explain the MNR in AgI-Ag2Mo04 glasses  

Philibert, Atom Movements Diffusion and Mass Transport in Solids. Presses Univer-sitaires de France, Paris (1966) 

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Muehlenbachs and Connolly (1991) and Gautason and Muhlenbachs (1993) demonstrated that oxygen diffusion in dry systems exhibits reasonably good correlations between anion porosity and the activation parameters. Eg and In Do, as shown in Figure... 

The key results for the pressure dependence of the diffusivity of oxygen at 4000 K for the three types of parameter sets are shown in Fig. 11 [55]. The results for silicon are qualitatively very similar to those for oxygen. A common characteristic for the three parameter sets is that the diffusion coefficients show maxima as reported for silicate by Angell et al. [56, 57]. This is exactly the anomalous diffusion property. Moreover, anew finding here is that there exists a conspicuous correlation between the pressures which give the highest diffusivity and the Pc s estimated before. 

This flux will be dependent upon the surface vacancy concentration, the surface electron concentration, and the dissociation rate of the dioxygen molecule however, at present, the rate-limiting step has yet to be identified. Kilner et al. [11] have derived a simple relationship for the surface exchange coefficient in terms of the bulk and surface vacancy concentrations, in an attempt to explain the apparent correlation found between the activation enthalpy for the surface exchange coefficient and the diffusion coefficient, in a number of La-based perovskites. Adler et al. [12] have also arrived at a similar relationship for k, by consideration of the AC electrode behavior of symmetrical cells with a double cathode structure. As already mentioned, the exact mechanisms of oxygen surface exchange remain elusive however, the vacancy concentration is clearly a very important parameter. 

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