Oxygen spreads through oxides by vacancy migration, and the best source of vacancies of oxygen in oxides are dissolved impurities. In this case, the concentration of vacancies is not dependent on temperature. If a divalent oxide (RO) or trivalent (R2O3) were dissolved as an impurity in a network of tetravalent oxides (RO2), the positions of the cations will be all occupied and some positions of the anions will be free. Therefore, very pure oxides can present very low values of diffusivity for oxygen. Cations can also spread by oxides through vacancy migration or, due to their small size, by interstitial movement.
As was already observed, most of the vacancies and interstitial atoms are a function of the conditions while obtaining atoms: there can be an excess or deficit of cations because the atmosphere in which the oxide forms was quite oxidative or reductive. Figure 2.2.13 presents a variation with the temperature of diffusion coefficients in crystalline oxides.
In purely ionic crystals, there are so many Frenkel (cation vacancies and interstitial cations) and Schottky defects (cation and anion vacancies), that they maintain local electroneutrality. Also, a divalent cation (R2O), dissolved in a network of monovalent cations (RO), requires, for electrical neutrality, a defect with a single negative charge close by. The electrical conductivity of ionic crystals \( \sigma _ {\imath} \) that, at high temperatures, is almost always due to ion diffusion – relating to the diffusion coefficient of the defect D in question:
\[ \sigma _ {\imath} = B [\frac{c _ {d} q_d^2}{kT}] D _ {d} \tag{2.24} \]
where cq and qd are, respectively, the concentration, and the charge of the defect that is conducive to diffusion; k is the Boltzmann constant; B is a constant that depends on the type of defect that produces the diffusion, B=1 for interstitial ions and B>1 for vacancies.
