Magnesium vacancy concentration

In this expression of the eleetrie neutrality, we can consider two Brouwer cases following the relative values of C compared with the aluminum vacancy concentration. We will consider the case in which C is sufficiently large indeed, on the contrary, we can easily check that the defect concentrations are the same as those for pure (without dopant) alumina, that is, independent of the magnesium concentration. We wiU thus write ... 

The occurrence of vacancies requires the adoption of two definitions of the degree of inversion, depending on the hypothesis made about the vacancies. Tetrahedral hypothesis . ft measures the concentration of indium in tetrahedral positions with respect to the maximum possible concentration. Octahedral hypothesis /3 measures the concentration of magnesium in octahedral positions with respect to the maximum possible concentration. 

Fig. 3 Iso-density surfaces (about 15% of maximum density) for the two gap states per (2v X 2y/i) 2D unit cellassociated with a 25% concentration of vacancies in a close packed configuration, (a) on the left bonding combination of the two localized states trapped at the vacancy sites (b) on the right, antibonding combination. A top view of the surface is presented with oxygen atoms as black dots and magnesiums as light spheres. The location of the vacancies is indicated by black boxes, (from Ref. 69)...

We will discuss the concrete case of a-alumina (AI2O3), which can, at first approximation, be considered as the Schottky solid, that is, it contains aluminum vacancies and oxygen vacancies. Let us consider the effect of introduction of magnesium cations in substitution (valence 2) at the concentration C. We assume that the solid is closed compared with magnesium and thus C is a constant. 

These relations show that the concentration of oxygen vacancies increases with the introduction of magnesium, whereas that of aluminum vacancies decreases. 

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