Complete Diagram Electronic Defects

Although Fig. 7.10e is similar to that for ionic defects (Fig. 7.9e), there are a number of significant differences. In particular, the stoichiometric range is now far 

The high-pressure region is associated with the electroneutrality equation [h ] = 2[V ]. Holes predominate, so that the material is a p-type semiconductor in this regime. In addition, the conductivity will increase as the g power of the partial pressure of the gaseous X2 component increases. The number of metal vacancies (and nonmetal excess) will increase as the partial pressure of the gaseous X2 component increases and the phase will be distinctly nonstoichiometric. There is a high concentration of cation vacancies that would be expected to enhance cation diffusion. 

As in the case of ionic defects, the form of this diagram can easily be modified to smooth out the abmpt changes between the three regions by including intermediate electroneutrality equations. 

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It is important that the complete diagram displays prominently information about the assumptions made. Thus, the assumption that Schottky defect formation was preferred to the formation of electronic defects is explicitly stated in the form Ks > Ke (Fig. 7.9e). As Frenkel defect formation has been ignored altogether, it is also possible to write Ks > Ke > > Kt , where A p represents the equilibrium constant for the formation of Frenkel defects in MX. 

Figure 7.10 Brouwer diagram for a phase MX in which electronic defects are the main point defect type (a) initial points on the diagram, (b) variation of defect concentrations in the near-stoichiometric region, (c) extension to show variation of defect concentrations in the high partial pressure region, (d) extension to show variation of defect concentrations in the low partial pressure region, and (e) the complete diagram.

The conductivities due to each of these defects are determined by their concentrations multiplied by their mobilities. As a result of the electron-hole equilibrium, these defects cannot both be present in high concentration at the same time. Therefore, perovskite proton conductors normally display protonic, oxide ion and one type of electronic conductivity. For an HTPC in oxidizing conditions the main defects are Vo, OHo, and h/. The situation can be visualized in the diagram of Fig. 6, which indicates the domains favorable for applications in fuel cell electrolytes and hydrogen transport membranes. The domain for oxygen transport membranes (i.e., no proton conduction) is included for the sake of completeness. 

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