Ionic dopants

It has been noted that the conductivity and activation energy can be correlated with the ionic radius of the dopant ions, with a minimum in activation energy occurring for those dopants whose radius most closely matches that of Ce4+. Kilner et al. [83] suggested that it would be more appropriate to evaluate the relative ion mismatch of dopant and host by comparing the cubic lattice parameter of the relevant rare-earth oxide. Kim [84] extended this approach by a systematic analysis of the effect of dopant ionic radius upon the relevant host lattice and gave the following empirical relation between the lattice constant of doped-ceria solid solutions and the ionic radius of the dopants. 

Figure 8.2. Binding energy for the cluster as a function of the dopant ionic size in ceria ...

Cerium oxide, ceria, has a fluorite structure and shows oxide anion conducting behavior differ from other rare earth oxides. However, the O ionic conductivity of pure ceria is low because of a lack of oxide anion vacancies. For ion conduction, especially for anion, it is important to have such an enough vacancy in the crystal lattice for ion conduction. Therefore, the substitution of tetravalent Ce" by a lower valent cation is applied in order to introduce the anion vacancies. For the dopant cation, divalent alkaline earth metal ions and some rare earth ions which stably hold trivalent state are usually selected. Figure 9-28 shows the dopant ionic radius dependencies of the oxide ionic conductivity for the doped ceria at 800°C. In the case of rare earth doped Ce02, the highest O ion conductivity was obtained for... 

Fig. 6.2 Relation between dopant ionic radius, conductivity, and content of dopant, reported by Arachi et al. [35] (Reproduced by permission of Elsevier)...

The mismatch between dopant rare-earth oxide and host ceria gives rise to the static positional disorder, which leads to the higher atomic displacement parameters. The static positional disorder reflects the local distortion or lattice strain due to the mismatch between host CeOs and dopant ROj 5, which prevents fast oxide-ion movement across the crystal lattice (Fig. 1.33(d)). Therefore, oxide-ion conductivity decreases with increasing Uo(R) as shown in Fig. 1.34(b). On the other hand, we would expect that an increase of dynamic disorder and effective index would improve oxide-ion conductivity. Uq R) increases with an increase of effective index from R = Gd to R = La, which indicates the possibility that the bulk oxide-ion conductivity of Ceo8Ro.20i.9 increases with an increase of dopant ionic radius r(R) from R = Gd to R = La. Further careful structural investigation of ceria-based materials is needed to determine both the dynamic and static components of the atomic displacement parameter of oxygen atoms. 

Figure 12.12 Activation energy as a function of acceptor dopant concentration for different rare-earth elements. Inset shows the minimum activation enthalpy as a function of dopant ionic radius. Adapted from Faber et Reprinted with kind permission from Springer Science and Business Media.

Extensive atomistic simulation work " has provided valuable insights into the nature of defect association and migration. It is generally recognized that both attractive coulombic interactions and attractive or repulsive elastic lattice relaxation play a major role in the energetics of ionic transport. The atomistic simulations conclude that for small dopants, the oxide ion vacancies preferentially associate with dopant ions, whereas for large dopants the oxide ion vacancies tend to associate with Ge host cations. The switchover is estimated to occur at a rare-earth dopant ionic radius similar to that of Gd, which offers a rational for the minimum in activation energy and the maximum in ionic conductivity observed for Gd- or Sm-doped Andersson et con-... 

Possibly, the homogeneity region widening with an increase of the dopant ionic radius could be explained by two factors compensating for each other - the large dopant cation and the presence of anion vacancies. The first factor leads to the unit cell expansion and the second one leads to its reduction because the larger the unit cell, the higher its capacity to adopt anion vacancies. 

Fig. 4.1 The maximum dopant content and conductivities at 1273k as a function of dopant ionic radii in doped zirconia...

Figure 4,5 Ion migration enthalpy and association enthalpy versus dopant ionic radius.

Fig. 3.5 Effect of dopant ionic radius on conductivity and dopant content...

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