Dopant interstitial compensation

In the compensation mechanism by the formation of oxygen vacancies, anionic vacancies are created by the balance of charge when two Ce " cations are replaced by two cations. In the dopant interstitial compensation mechanism, three Ce cations are replaced by three cations, and the neutrality is achieved by leasing an additional cation in the interstitial sites of the cubic fluorite structure of Ce02. Finally, in the compensation mechanism by interstitial cerium, Ce or Ce " cations are released in the interstitial sites after insertion of M " cations [1]. 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). Formation of interstitials is also ruled out by measurements of true density and comparison with calculated values . For the smaller cations (i.e. Al ), some compensation via dopant interstitial may occur. The reactions described in Eq. 2.18 and 2.21 (for a divalent cation) therefore summarise the main route to defect formation in solid solutions of the type Ce. jMj02,o.5x and Ce, xMx02.x respectively. 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

Using the same arguments as we used in CaO, one would expect that an increased concentration of lanthanide dopant should introduce a like number of fluoride interstitials into the lattice. If the pairing of the interstitials with the lanthanide is not complete, the number of free interstitials would increase. The larger number of interstitials should lead to an increase in the number of lanthanides that have the fluoride interstitial charge compensation in a nearby position relative to the ones that have the interstitial distant according to the law of mass action. Laser spectroscopy shows the opposite effect though. 

Fig. 1.15. Electron concentration (dashed line) of Sn-doped indium oxide and Al-doped ZnO in dependence on oxygen partial pressure for a dopant concentration of 1 % [117]. With increasing oxygen partial pressure the donors become compensated by oxygen interstitials (In20s) or by zinc vacancies (ZnO). Reprinted with permission from [117]. Copyright (2007) by the American Physical Society...

A variety of defect formation mechanisms (lattice disorder) are known. Classical cases include the - Schottky and -> Frenkel mechanisms. For the Schottky defects, an anion vacancy and a cation vacancy are formed in an ionic crystal due to replacing two atoms at the surface. The Frenkel defect involves one atom displaced from its lattice site into an interstitial position, which is normally empty. The Schottky and Frenkel defects are both stoichiometric, i.e., can be formed without a change in the crystal composition. The structural disorder, characteristic of -> superionics (fast -> ion conductors), relates to crystals where the stoichiometric number of mobile ions is significantly lower than the number of positions available for these ions. Examples of structurally disordered solids are -> f-alumina, -> NASICON, and d-phase of - bismuth oxide. The antistructural disorder, typical for - intermetallic and essentially covalent phases, appears due to mixing of atoms between their regular sites. In many cases important for practice, the defects are formed to compensate charge of dopant ions due to the crystal electroneutrality rule (doping-induced disorder) (see also -> electroneutrality condition). 

The electrical properties of the titanate-based pyrochlores can be described by point defect models in which the acceptor (A) and donor (D) impurities are compensated by oxide ion vacancies, or oxide ion interstitials, respectively. The principal defect reactions inclnde the redox reaction, Equation (5.67), the Frenkel disorder, Equation (5.57), dopant ionization, intrinsic electronic disorder, Equation (5.60), and the electroneutrality relation. For these compounds the total electroneutrality condition given by Equation (5.55) is, on the one hand, reduced, taking Equation (5.57) into account, and is, on the other hand, extended to include acceptor and donor impurities. In addition, defect association is included explicitly. 

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