**4. Dopant cation-oxygen vacancy interaction energetic**

In the past, multiple atomistic computer simulation techniques have been used to study the interaction energetic involved between the cations and oxygen vacancies in acceptor cation-doped CeO2 . Butler et al. [48] reported that the ionic radius of dopant has a major influence on the stability of defect complexes. Minervini et al. [49] studied the binding energy of an oxygen vacancy with dopant cation using the energy minimization techniques. It was found that the oxygen vacancies prefer to reside in the first neighboring sites of small dopant cations and in the second neighboring sites of large dopant cations. For Gd3+ dopant cation, the oxygen vacancy shows similar preference to reside in first and second neighboring sites. Moreover, the binding energy was also estimated to be lowest in Gd3+-doped CeO2 . Although these theoretical studies show a close match with the experimental results, they are based on empirical atomistic models.

which leads to minimal deep traps inside the doped ceria lattice. Thus, Pm3+-doped CeO2 was predicted to exhibit higher oxygen-ion conductivity than any other acceptor-doped ceria

**Figure 9.** Total interaction energy between dopant cation and oxygen vacancy sitting in nearest neighbor (NN) and next to nearest neighbor (NNN) site (of dopant cations) for rare- earth dopant cations. The negative numbers imply attractive

*Effective* is the weighted average ionic radius of Sm3+/Nd3+. The figure is modified after Andersson et al. [16].

Unfortunately, Pm is a radioactive element and cannot be used as a dopant in ceria. The best dopant should be having an effective atomic number around Pm3+ (61) with an ionic radius of 1.093 Å. According to Andersson et al. [16], a co-doping approach, with Sm3+ and Nd3+ as co-dopants, provides an experimental scenario for examining the validity of this hypothesis. Omar et al. [8, 42] have studied the influence of co-doping Sm3+ and Nd3+ on the oxygen-ion

number of Pm3+, that is, 61. By doing so, similar total interactions between the dopant cations and oxygen vacancies sitting in NN and NNN sites (of dopant cations) are expected, which may lead to enhancement in the oxygen-ion conductivity. It was reported that for compositions containing 10 mol.% of dopant, Sm3+ and Nd3+-doped ceria exhibits 14% higher grain ionic conductivity than that of Gd0.10Ce0.90O2.95 at 550°C, in air (shown in **Figure 3**). The obtained high conductivity of co-doped samples validates the density functional theory prediction about

Pm3+ to be the best dopant cation for achieving high oxygen-ion conductivity in CeO<sup>2</sup>

. Sm3+ and Nd3+ were added in an equal ratio to obtain the effective atomic

.

Doped Ceria for Solid Oxide Fuel Cells http://dx.doi.org/10.5772/intechopen.79170 53

materials.

interactions. The *rSm*/*Nd*

conductivity of CeO2

Andersson et al. [16] performed the quantum mechanical calculations within the density functional theory (DFT) formalism in trivalent cation-doped CeO<sup>2</sup> . Both electrostatic and elastic interaction energies between the dopant cation and oxygen vacancy located in nearest neighbor (NN) site and in the next to nearest neighbor (NNN) site (of dopant cation) were predicted using the *ab*-*initio* calculations. It was found that for Pm3+ dopant cation, the total interaction energy values are similar for both the configurations (shown in **Figure 9**). As a result, the Pm3+-doped CeO2 system contains the maximum number of oxygen sites with equiinteraction energy inside the host lattice. There will be no site preference for oxygen vacancies

**Figure 9.** Total interaction energy between dopant cation and oxygen vacancy sitting in nearest neighbor (NN) and next to nearest neighbor (NNN) site (of dopant cations) for rare- earth dopant cations. The negative numbers imply attractive interactions. The *rSm*/*Nd Effective* is the weighted average ionic radius of Sm3+/Nd3+. The figure is modified after Andersson et al. [16].

**4. Dopant cation-oxygen vacancy interaction energetic**

functional theory (DFT) formalism in trivalent cation-doped CeO<sup>2</sup>

was also estimated to be lowest in Gd3+-doped CeO2

**Figure 8.** Lattice parameter mismatch between A0.10Ce0.90O2-*<sup>δ</sup>*

52 Cerium Oxide - Applications and Attributes

(A3+) at 500°C. The grain (bulk) oxygen-ion conductivity of A0.10Ce0.90O2-*<sup>δ</sup>*

result, the Pm3+-doped CeO2

CeO2

In the past, multiple atomistic computer simulation techniques have been used to study the interaction energetic involved between the cations and oxygen vacancies in acceptor cation-doped

close match with the experimental results, they are based on empirical atomistic models.

Andersson et al. [16] performed the quantum mechanical calculations within the density

elastic interaction energies between the dopant cation and oxygen vacancy located in nearest neighbor (NN) site and in the next to nearest neighbor (NNN) site (of dopant cation) were predicted using the *ab*-*initio* calculations. It was found that for Pm3+ dopant cation, the total interaction energy values are similar for both the configurations (shown in **Figure 9**). As a

interaction energy inside the host lattice. There will be no site preference for oxygen vacancies

system contains the maximum number of oxygen sites with equi-

. Butler et al. [48] reported that the ionic radius of dopant has a major influence on the stability of defect complexes. Minervini et al. [49] studied the binding energy of an oxygen vacancy with dopant cation using the energy minimization techniques. It was found that the oxygen vacancies prefer to reside in the first neighboring sites of small dopant cations and in the second neighboring sites of large dopant cations. For Gd3+ dopant cation, the oxygen vacancy shows similar preference to reside in first and second neighboring sites. Moreover, the binding energy

and CeO2

. Although these theoretical studies show a

is plotted against the ionic radius of dopant cation

at 500°C is also shown [15].

. Both electrostatic and

which leads to minimal deep traps inside the doped ceria lattice. Thus, Pm3+-doped CeO2 was predicted to exhibit higher oxygen-ion conductivity than any other acceptor-doped ceria materials.

Unfortunately, Pm is a radioactive element and cannot be used as a dopant in ceria. The best dopant should be having an effective atomic number around Pm3+ (61) with an ionic radius of 1.093 Å. According to Andersson et al. [16], a co-doping approach, with Sm3+ and Nd3+ as co-dopants, provides an experimental scenario for examining the validity of this hypothesis. Omar et al. [8, 42] have studied the influence of co-doping Sm3+ and Nd3+ on the oxygen-ion conductivity of CeO2 . Sm3+ and Nd3+ were added in an equal ratio to obtain the effective atomic number of Pm3+, that is, 61. By doing so, similar total interactions between the dopant cations and oxygen vacancies sitting in NN and NNN sites (of dopant cations) are expected, which may lead to enhancement in the oxygen-ion conductivity. It was reported that for compositions containing 10 mol.% of dopant, Sm3+ and Nd3+-doped ceria exhibits 14% higher grain ionic conductivity than that of Gd0.10Ce0.90O2.95 at 550°C, in air (shown in **Figure 3**). The obtained high conductivity of co-doped samples validates the density functional theory prediction about Pm3+ to be the best dopant cation for achieving high oxygen-ion conductivity in CeO<sup>2</sup> .
