Defects in Ceramic Oxides
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shes for minus. Alternative intrinsic defects are the cation Frenkel, V|i + Mj, or the anion Frenkel, V 0 + O", where M[ and O," refer, respectively, to cation and oxygen-ion interstitials. Similarly, introduction of an aliovalent (heterovalent) dopant also requires charge compensation. For example, in MO, doping with a cation R3+ (effective charge +1, or RM requires compensation, which may take the form 2RM + VM, representing compensation by one cation vacancy for every two dopant ions. Because of this requirement, aliovalent impurities that are unintentionally présent (typically in amounts ~100 ppm) may give rise to defect concentrations that far exceed the intrinsic defect concentration. Thus, unintentional and uncontrolled defects may dominate the transport behavior! 3. Because oppositely charged defects are présent, Coulombic interactions play an important rôle and may lead to the formation of associated pairs or higher clusters, especially when the température is not too high. However, even unassociated defects may interact through electrical forces, giving rise to "Debye-Hûckel" interactions.2 4. The existence of charge-compensating defects on opposite sublattices and the corresponding equilibrium conditions through mass-action type équations means that the defect concentrations on the two sublattices are coupled, Le., the introduction of defects on one sublattice can profoundly affect the defect structure on the other. Because of the potential problem of impurities controlling the defect structure (item 2 above), it is désirable to deliberately control the introduction of defects. The two best ways to accomplish this are: (1) to introduce aliovalent impurities, and (2) to take the material off stoichiometry through appropriate P(0 2 ) anneals. If we use a figure of 100 ppm as typical of the uncontrolled impurity content in "pure" oxides, then we clearly wish to introduce defects in a concentration >0.01 mol%. On the other hand, for defect concentrations >1%, defect interactions became too complex to permit the application of mass-
action équations, which are our principal quantitative tool. Clearly, then, thèse considérations limit us to defect concentrations in the range from 0.01 to 1 mol%. The remainder of this article will illustrate thèse basic principles by using some well-studied oxide Systems as examples. For convenience, they are separated into families belonging to the same crystal structure. Oxides of the Rocksalt Structure Two families of rocksalt-structured oxides are to be considered. The most ionic, and therefore the closest in behavior to the (rocksalt-structured) alkali halides are the alkaline earth oxides: MgO, CaO, and SrO. They generally remain very close to stoichiometry and so their defect behavior can be considered without the complication of electronic defects. The second rocksalt structured family is that of the transition-metal oxides: NiO, CoO, MnO, and FeO. Thèse oxides ail tend to become nonstoichiometric, in the direction M,_ s O, with 5 taking on higher values the higher the P
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