I am totally confused about this concept? anybody help me how many types of o2 vacancies can be formed in ceramics samples after doping? i mean what happen if we replace high valent cation by low valent cation(Bi3+ by Sr2+) or (Ti4+ by Nb5+)
There are a number of ways that oxygen vacancies can be created.
By spontaneous intrinsic defects. Such defects are thermally activated: their concentration raises exponentially when temperature is increased. Examples are Frenkel, Schottky and partial Schottky (also called pseudo-Schottky) defects. All of them are charge-neutral, since charged defects cannot be created independently, because the crystal must be neutral. A Frenkel defect is 1 vacancy + 1 interstitial. It can be thought as if O2- ions leave their regular positions in the lattice (resulting in the creation of 1 O2- vacancy) and migrate to interstitial positions. Notice that an oxygen vacancy has charge 2e, while an interstitial oxygen has charge -2e. A Schottky defect can be thought as if all ions of a single molecule leave their regular positions and go to crystal's surface (or the region between grains in a ceramic), forming a new molecule there. In the process, vacancies of all ions constituting the molecule are left behind (including oxygen vacancies). A partial Schottky defect is similar to Schottky defect, but instead of a whole molecule going to the surface, only a neutral fraction does. For example, in SrTiO3, the possibilities are Sr2+ and O2- vacancies (leading to formation of a SrO secondary phase on surface of between grains) or Ti4+ and O2- vacancies (and a TiO2 secondary phase would be formed). As you can see, the secondary phase is usually one of the "reactants".
By non-stoichiometry. If you reduce the amount of one reactant in relation to the stoichiometric amount required to synthesize a stoichiometric material, this may lead to creation of vacancies in your material (but not necessarily...). For example, if you are synthesizing SrTiO3 using the synthesis reaction SrO + TiO2 --> SrTiO3, you can do this by two forms. One is (1-x)SrO + TiO2 --> Sr1-xTiO3-x and the other is SrO + (1-x)TiO2 --> SrTi1-xO3-2x.
By doping. If you replace a cation by another one with lower valence, a negative charge is introduced and must be compensated by a positively charged defect (an oxygen vacancy, for example). If you replace Ti4+ by Zn2+ in SrTiO3, for example, this may (but not necessarily will) be compensated by a O2- vacancy (charge 2e).
By reduction. Oxygen may leave the system as O2(g) during calcination. As each oxygen in O2 is neutral, the two extra electrons in O2- are left in the system, causing reduction of one of the cations. In La3+Mn3+O3, for example, this can be schematically written as La3+Mn3+O3 --> La3+Mn3+1-2xMn2+2xO3-x + (x/2)O2(g). As oxygen leaves the system, oxygen vacancies are created.