**2. Formation of local defect complexes**

Whenever charged point defects (*ACe* / ) are incorporated into the crystal structure, to maintain electroneutrality, defects possessing opposite charges must be created. These oppositely charged defects strongly interact with each other because of electrostatic attraction. Further, the elastic interactions also exist to relax the local stresses surrounding these defects. For example, an oversized substitutional impurity cation may attract an open space of vacancy. This leads to the formation of local defect complexes such as (*ACe* / <sup>−</sup> *VO* •• <sup>−</sup> *ACe* / ) and (*ACe* / <sup>−</sup> *VO* •• ) • . These defect complexes trap the oxygen vacancies and effectively reduce the number of mobile oxygen-ions. In most literature, it is commonly accepted that the primary reason for the significant decrease in ionic conductivity of doped ceria at higher dopant content is essentially because of the formation of local defect complexes.

**Figure 5** depicts a case where *VO* •• defect is trapped in a tetrahedral site of the fluorite structure surrounded by oppositely charged dopant cations and neutral host cations. There are several experimental studies which support the formation of local defect structures. Extended X-ray absorption

**Figure 5.** Oxygen vacancy defect trapped inside the tetrahedral void to form local defect complex. Ce4+, A3+ and O2<sup>−</sup> are shown by blue, green, and red spheres, respectively, while oxygen vacancy is shown by red cube.

fine structures (EXAFS) have been extensively utilized to study the local structures around the cations and anions in lower-valent cation-doped ceria [34–36]. In case of Gd*<sup>x</sup>* Ce1-*<sup>x</sup>* O2-*x*/2, the addition of Gd3+ leads to a decrease in the interatomic distance Gd-O which is attributed to the formation of the defect complexes with two Gd3+ and one oxygen vacancy [37]. The formation of local defect structure is also evident in the nuclear magnetic resonance study where the average coordination number is estimated for cations in Y3+- and Sc3+-doped CeO2 [38]. The tendency of oxygen vacancies to preferentially associate with Sc3+ was found to be stronger than with Y3+ in these systems.

Besides the doping amount, the physical properties of dopant cations also influence the bulk conductivity of ceria. Numerous investigations have been performed to understand these correlations in doped ceria systems [1, 15–19]. **Figure 4** depicts the dependence of ionic conductivity in A0.10Ce0.90O1.95 on the ionic size of the trivalent dopant cation (A3+) at 600°C. While the work performed by Omar et al. [15] showed a continuous increase in the bulk conductivity with the increase in ionic size, others [17, 20–22] reported a conductivity maximum around Gd3+ and Sm3+. It is interesting to note that the maximum in conductivity observed around these cations is independent of dopant concentration [6]. In the literature, several empirical, semi-empirical and atomistic models have been reported to clarify this and elucidate the effect of doping amount and the dopant-type on the conductivity. This chapter reviews some of these models to provide insights into the mechanisms underlying the oxygen-ion conduction process in doped ceria.

electroneutrality, defects possessing opposite charges must be created. These oppositely charged defects strongly interact with each other because of electrostatic attraction. Further, the elastic interactions also exist to relax the local stresses surrounding these defects. For example, an oversized substitutional impurity cation may attract an open space of vacancy.

defect complexes trap the oxygen vacancies and effectively reduce the number of mobile oxygen-ions. In most literature, it is commonly accepted that the primary reason for the significant decrease in ionic conductivity of doped ceria at higher dopant content is essentially

rounded by oppositely charged dopant cations and neutral host cations. There are several experimental studies which support the formation of local defect structures. Extended X-ray absorption

**Figure 5.** Oxygen vacancy defect trapped inside the tetrahedral void to form local defect complex. Ce4+, A3+ and O2<sup>−</sup> are

shown by blue, green, and red spheres, respectively, while oxygen vacancy is shown by red cube.

/ ) are incorporated into the crystal structure, to maintain

/ <sup>−</sup> *VO* •• <sup>−</sup> *ACe* /

defect is trapped in a tetrahedral site of the fluorite structure sur-

) and (*ACe*

/ <sup>−</sup> *VO* •• ) • . These

**2. Formation of local defect complexes**

because of the formation of local defect complexes.

This leads to the formation of local defect complexes such as (*ACe*

••

Whenever charged point defects (*ACe*

48 Cerium Oxide - Applications and Attributes

**Figure 5** depicts a case where *VO*

The binding energy associated with the local defect structures is mainly dependent on the electrostatic attraction of the defects caused by the effective charges in the lattice. Further, it also includes terms due to the relaxation of the lattice around the defect which depends on the polarizability and the size of dopant cation. Several groups have found a difference in the magnitudes of *EA* when measured in the high- and low-temperature regimes [14, 39]. Typically, the activation energy value estimated in a low-temperature regime is higher than that in the high-temperature region. In a few investigations, a kink is noticed around 350–600°C in the Arrhenius plot of the measured ionic conductivity [14]. Nevertheless, there are several other studies where instead of a sharp, a gradual change in slope with temperature is reported [8, 40]. It has been argued that in a low-temperature regime, most of the oxygen vacancies are bound to various traps to form local defect complexes [41]. However, at higher temperatures, the thermal vibrations of the local defect structures become dominant. At a certain temperature, the thermal energy overcomes the binding energy of these local defect complexes, and the majority of oxygen vacancy defects are set free to migrate from one site to another. Thus, the oxygen vacancies require only migration (Δ*Hm*) to cross the energy barrier at higher temperatures. As a result, in the low-temperature region, the total *EA* is composed of Δ*Hm* and association enthalpy (Δ*Ha* ), whereas in the hightemperature region, the measured *EA* is only because of migration enthalpy of oxygen-ions.

In the literature, several methods have been used to determine the association enthalpy. Omar et al. [42] have taken a difference in the magnitudes of *EA* obtained in the high- and lowtemperature regimes and reported the association enthalpy in Sm*x*/2Nd*x*/2Ce1-*<sup>x</sup>* O2-*x*/2 in the range

**Figure 6.** Association enthalpy (Δ*Ha* ) is plotted against the Nd3+ doping amount in Ce<sup>1</sup> <sup>−</sup> *<sup>x</sup>* Nd*<sup>x</sup>* O<sup>2</sup> <sup>−</sup> *<sup>x</sup>*/2. For the calculation of Δ*Ha* , the minimum value of the *EA* measured in the low-temperature range (i.e., below 350°C) has been assumed to be equal to the enthalpy of migration [32].

of 0.02–0.05 eV [42]. Nowick et al. [43] obtained the association enthalpy by estimating the migration enthalpy in pure CeO2 to be 0.67 eV. Stephen and Kilner [32] have taken the minimum value of *EA* measured in the low-temperature regime in Nd*<sup>x</sup>* Ce1-*<sup>x</sup>* O2-*x*/2 as a migration enthalpy. The association enthalpy initially decreases and then increases after reaching a minimum value at *x* = 0.03 (shown in **Figure 6**) [32]. The increase in association enthalpy is attributed to the development of deep vacancy association. A similar trend in association enthalpy is also observed for other dopant cations such as Y3+, Gd3+ and Sm3+ and so on [11, 14, 44].
