Acceptor-Doped Case

we will consider BaTiOs doped with a fixed amount (x) of acceptor impurities A on, for example, cation sites (generically denoted as Ac). Specifically, these are assumed to be trivalent substituting Ti or Aji, for example, Al i. The lattice molecule may then be written as  

As one more defect species A i is added, there is a need for one more constraint, in addition to those for the pure case that is, mass conservation or 

The charge neutrality condition [Eq. (7)] and the site conservation conditions [Eq. (9)] should be accordingly modified, respectively, as  

444 I 70 D ect Structure, Nonstoichiometry, and Nonstoichiometry Relaxation of Complex Oxides log o. 

In addition, while the nonmolecularity is still the same as Eq. (14), the nonstoichiometry should be modified due to Eq. (1) as  

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Obviously sensitivity is highest in the acceptor doped case. Here, however, the temperature dependence is also highest, namely... 

TaUe 10.1 Matrix of majority disorder types in the systems of BaTi03- The top left rectangle demarcated by thick solid lines is for the pure case this rectangle plus the rightmost column for the acceptor-doped case and the rectangle plus the bottom-most row for the donor-doped case. 

As one more unknown [Dg ] is added similarly to the acceptor-doped case, one mass-conservation equation for the dopant is added to Eqs. (3)-(6) as ... 

Figure 10.4a, where it is noted that [V""] —Pt) is flat against log For the acceptor-doped case (Figure 10.3c), the majority disorder regime of p = 4[Vj"] is impossible because [ "] w —Pt] is fixed. Consequently, the transformed plot should... 

Figure 10.5 Defect structure for the acceptor-doped case (corresponding to Figure 10.3c or Figure 10.4b), with holes trapped fully > 1).

However, in the onefold kinetics region of Xo in the reducing atmospheres, the surface reaction step must be taken into appropriate account, as in the undoped or acceptor-doped cases [12, 13, 26], for a sufficient precision of the fitting. The relaxations are, thus, fitted (solid lines in Figures 10.18a-e) to the conventional solution similar to Eq. (63), but in one dimension to evaluate Do and the surface reaction rate constant k simultaneously. 

In the case of acceptor doping, a similar change in the electroneutrality equation is required. Consider acceptor doping by a monovalent ion A+ due to reaction with A2X to introduce Am defects, once again assuming that Frenkel defects are not important. The original electroneutrality Eq. (7.12) ... 

Donor-doped PZTs have higher permittivities and d coefficients than acceptor-doped materials and are therefore more suitable for converting mechanical into electrical vibrations. They have higher dissipation factors than acceptor-doped materials and are therefore not as suitable for wave filters. If this were not the case, their low ageing coefficients would be an advantage. 

Note that the presence of a hole suggests p-type conductivity in Fe203. In many cases, however, metal oxides remain n-type when acceptor-doped. If this is the case, it is more appropriate to replace the hole with an electron on the left-hand side of (2.14). 

For the system of BaTi03, the equilibrium conductivity has been the most extensively documented (see, e.g.. Refs. [8, 10, 11]) over the experimentally viable range of —20 < log < 0 at elevated temperatures, although the remaining variable, OxiOj or t] has not been explicitly specified. Figure 10.6a-c shotvs the typical results for the pure [10, 12], acceptor (AlTi)-doped [13], and donor (LaBa)-doped cases [11], respectively. 

Do/bji lO, thus, is observable [30]. If To txi, the twofold kinetics should be observed in principle, although no matter what the value of R, it would take too long to observe or there would be minimal symptoms of the cation sublattice relaxation in the experimentally viable time. If 1 < 1, on the other hand, the cation sublattice relaxation can hardly be detected experimentally, even if the relaxation does occur. This may be the case of undoped or acceptor-doped BaTi03 where the kinetics only appears onefold and very fast. 

If the foreign atom, for instance boron, gallium or indium, has one valence electron less, it can accept one electron from the VB (acceptor doping) (Fig. 6.5b). In the first case an energetic level close to the CB is introduced ... 

Transition metal acceptor doping of A-site deficient Sro.85Yo.iTio.95Mo.o503 8 (M = V, Mn, Fe, Co, Ni, Cu, Zn, Mo, Mg, Zr, Al, Ga) leads to a decrease in total conductivity compared to the undoped composition. This is due to the acceptor dopant off-setting the influence of the donor dopant (Y " in this case). The ionic conductivity of these materials increases upon acceptor doping but it is still 6 orders of magnitude lower than the electronic conductivity [111],... 

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