Structures and diffusion in metal oxides

Another important crystal structure incorporating two ionic species is spinel, which has the composition AB2O4, or AO B2O3. In this phase one-third of the cations occupy tetrahedrally oxygen co-ordinated sites, and two-thirds occupy octahedrally co-ordinated sites. 

In all of these oxide phases it is possible that departures from the simple stoichiometric composition occur through variation of the charges of some of the cationic species. Furthermore, if a cation is raised to a higher oxidation state, by the addition of oxygen to the lattice, a corresponding number of vacant cation sites must be formed to compensate the structure. Thus in nickel oxide NiO, which at stoichiometric composition has only Ni2+ cations, oxidation leads to Ni3+ ion formation to counterbalance the addition of extra oxide ions. At the same time vacant sites must be added to the cation lattice to retain the NaCl structure. This balanced process can be described by a normal chemical equation thus 

This type of point defect formation is summarized by the general notation due to Kroger and Vink in the equivalent form 

Here Oo represents the oxide ion which is incorporated, h represents the Ni3+ ion which is a positive hole, and an extra negative charge being indicated by the superscript dot, thus VNi is the vacant cation site where the double dot represents the absence of two positive charges at that site. 

Another source of departure from stoichiometry occurs when cations are reduced, as for example in the reduction of zinc oxide to yield an oxygen-defective oxide. The zinc atoms which are formed in this process dissolve in the lattice, Zn+ ions entering interstitial sites and the corresponding number of electrons being released from these dissolved atoms in much the same manner as was found when phosphorus was dissolved in the Group IV semiconductors. The Kroger-Vink representation of this reduction is 

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