Mayenite Electrides and Their Doped Forms for Oxygen Reduction Reaction in Solid Oxide Fuel Cells

: The oxygen reduction reaction is an important reaction at the cathode in solid oxide fuel cells. Materials that exhibit high chemical and mechanical stability, high ionic and electronic conductivity, and are non-toxic are of great interest as cathodes for the reduction of oxygen. Here, we use density functional theory simulations to examine the e ﬃ cacy of 12CaO · 7Al 2 O 3 and 12SrO · 7Al 2 O 3 electrides and their doped forms for the conversion of O 2 gas to form O 2 − in their nanocages via encapsulation. Calculations show that encapsulation is exoergic in the un-doped electrides, and the formation of O 2 − is conﬁrmed by the charge analysis. A stronger encapsulation is noted for C12A7 electride than the S12A7 electride. The C12A7 electride doped with B or Ga also exhibits exoergic encapsulation, but its encapsulation energy is slightly lower than that calculated for the un-doped C12A7 electride. There is an enhancement in the encapsulation for the S12A7 electride doped with B compared to its un-doped form. Doping of Ga in S12A7 electride exhibits only a very small change in the encapsulation with respect to its un-doped form. The present results can be of interest in the design of cathode material for solid oxide fuel cells.


Introduction
A range of electrochemical energy storage technologies, such as batteries [1][2][3], fuel cells [4][5][6], and supercapacitors [7][8][9], has been investigated so far to cut the emission of the so-called greenhouse gases. In terms of fuel flexibility and high efficiency, solid oxide fuel cells (SOFC) are considered as promising devices to meet the global energy demand [10]. The performance of fuel cells relies on the electrode (anode and cathode) and electrolyte materials that are safe, low-cost, and efficient.
Fast oxygen ion conductivity is one of the essential conditions for an electrolyte in SOFC and has been observed in C12A7:(O 2− ) 2 [39,40]. Furthermore, the insulating nature of C12A7:(O 2− ) 2 makes this material more promising for use as an electrolyte, and its oxygen ion conductivity is only one order magnitude less than that observed in yttria-stabilized zirconia [39]. The electride form of C12A7 is a candidate material for use as a cathode material in SOFC as it is electrically conductive and consists of nanocages where oxygen gas from the air can be encapsulated to form O 2− (via the ORR). Additionally, the encapsulated O 2− ions can diffuse fast as they do in C12A7:(O 2− ) 2 towards electrolyte. The encapsulation capability of C12A7 and S12A7 electrides for ORR has not been explored yet. Furthermore, electrides doped with B and Ga are also worth testing to examine where there is an enhancement in the encapsulation.
In this work, we use spin-polarized density functional theory together with dispersion (DFT+D) to examine the reduction of oxygen gas to form O 2− ions in the nanocages of C12A7 and S12A7 electrides and their doped forms. The current methodology allows us to calculate encapsulation energies, charges on the encapsulated O atoms, densities of states (DOSs), and charge density plots associated with the encapsulated complexes. The results to be presented here can be of interest in the development of cathode materials for SOFC.

Computational Methods
DFT calculations are performed to obtain energy minimized structures and electronic structures of pristine, encapsulated, and doped C12A7:(e − ) 4 and S12A7:(e − ) 4 using the Vienna Ab initio Simulation Program (VASP) code [41,42]. This code uses projected augmented wave (PAW) pseudopotentials [43] and plane-wave basis sets. A plane-wave basis set with the cut-off of 500 eV and a 2 × 2 × 2 Monkhorst-Pack [44] k-point mesh, which generates 8 k-points, are used in all calculations. The exchange-correlation energy is modeled using a generalized gradient approximation (GGA) scheme, as defined by Perdew, Burke, and Ernzerhof (PBE) [45]. Full geometry optimization (both atom positions and lattice constants are relaxed simultaneously) is done with the aid of the conjugate gradient algorithm [46]. In all relaxed configurations, forces on the atoms are less than 0.001 eV/Å. Dispersion forces are modeled using a semi-empirical approach, as described by Grimme et al. [47].
Encapsulation energy for a single O atom in C12A7:(e − ) 4 with respect to 1/2 O 2 as a reference state is calculated using the following equation: 2 ] is the total energy of a single O atom encapsulated in C12A7:(e − ) 4 , E [C12A7:(e − ) 4 ] is the total energy of bulk C12A7:(e − ) 4 , and E ( 1 2 O 2 ) is the half the energy of diatomic oxygen molecule. A similar equation is used for the encapsulation of a single oxygen atom in the doped C12A7 and S12A7 structures.

Structures of C12A7
:(e − ) 4 and S12A7:(e − ) 4 First, the bulk structures of C12A7:(e − ) 4 and S12A7:(e − ) 4 are relaxed under constant pressure. The relaxed structures are shown in Figure 1. The calculated lattice parameters, together with the experimental values, are reported in Table 1. There is a good agreement between the calculated and experimental lattice parameters of C12A7:(e − ) 4 . The S12A7:(e − ) 4 has larger lattice parameters than C12A7:(e − ) 4 , and this is reflected in the cage pole distance of S12A7:(e − ) 4 (refer to Figure 1c).

Structures of C12A7:(e − )4 and S12A7:(e − )4
First, the bulk structures of C12A7:(e − )4 and S12A7:(e − )4 are relaxed under constant pressure. The relaxed structures are shown in Figure 1. The calculated lattice parameters, together with the experimental values, are reported in Table 1. There is a good agreement between the calculated and experimental lattice parameters of C12A7:(e − )4. The S12A7:(e − )4 has larger lattice parameters than C12A7:(e − )4, and this is reflected in the cage pole distance of S12A7:(e − )4 (refer to Figure 1c).
1752. 51 1908.59 In our previous study [27], the electronic structure of C12A7:(e − ) 4 has been discussed. The calculated DOS plot shows that C12A7:(e − ) 4 is a metal (refer to Figure 2a). This is due to the extra-framework electrons occupying nanocages. A similar metallic character is noted for S12A7:(e − ) 4 (refer to Figure 2b). Electron charge densities near the Fermi level are plotted for both C12A7:(e − ) 4 and S12A7:(e − ) 4 . There is a uniform distribution of electrons in twelve cages of both electrides (refer to Figure 2c,d).

Encapsulation of Oxygen Atoms in C12A7:(e − )4 and S12A7:(e − )4
The encapsulation of two oxygen atoms is considered consequently in the empty cages of C12A7:(e − )4 and S12A7:(e − )4. The relaxed cages containing O 2− ions are shown in Figure 3. The encapsulation results in a significant contraction in the cage pole distances. This is due to the strong attraction between Ca 2+ (or Sr 2+ ) and encapsulated O 2− ions. Cage pole distances are shorter in C12A7 than that observed in S12A7. This is because of the higher charge density of Ca 2+ than that of Sr 2+ and shorter lattice constant of C12A7 than that of S12A7.  The encapsulation of two oxygen atoms is considered consequently in the empty cages of C12A7:(e − ) 4 and S12A7:(e − ) 4 . The relaxed cages containing O 2− ions are shown in Figure 3. The encapsulation results in a significant contraction in the cage pole distances. This is due to the strong attraction between Ca 2+ (or Sr 2+ ) and encapsulated O 2− ions. Cage pole distances are shorter in C12A7 than that observed in S12A7. This is because of the higher charge density of Ca 2+ than that of Sr 2+ and shorter lattice constant of C12A7 than that of S12A7.

Encapsulation of Oxygen Atoms in C12A7
:(e − )4 and S12A7:(e − )4 The encapsulation of two oxygen atoms is considered consequently in the empty cages of C12A7:(e − )4 and S12A7:(e − )4. The relaxed cages containing O 2− ions are shown in Figure 3. The encapsulation results in a significant contraction in the cage pole distances. This is due to the strong attraction between Ca 2+ (or Sr 2+ ) and encapsulated O 2− ions. Cage pole distances are shorter in C12A7 than that observed in S12A7. This is because of the higher charge density of Ca 2+ than that of Sr 2+ and shorter lattice constant of C12A7 than that of S12A7.  The calculated lattice constants and volumes of encapsulated structures are reported in Table 2. The contraction in the cage pole distances is further evidenced by the contraction in the lattice constants and volumes with respect to their electride forms. The encapsulation of two oxygen atoms leads to the stoichiometric forms of C12A7 and S12A7. The experimental lattice constants of those structures are in good agreement with the calculated values (refer to Table 2). The encapsulation energies and the Bader charges [50] on the encapsulated oxygen atoms are reported in Table 3. The encapsulation energy calculated for the second oxygen is lower than that calculated for the first encapsulation in both cases. This is due to the less number of electrons available for the second encapsulation. The encapsulation is stronger in C12A7 than S12A7. This is because of the stronger attraction of cage pole Ca 2+ ions to encapsulate O 2− ions than that of Sr 2+ ions. The Bader charge approximation shows that the encapsulated oxygen atom gains~1.40 electrons from the extra-framework electrons in the cages. Notably, the Bader charge on the framework oxygen atom in the cages is~−1.74. This is due to the strong bonding between Al 3+ ions and cage wall O 2− ions, resulting in short Al-O bond distances of~1.75 Å.

Encapsulation of Oxygen Atoms in C12A7:(e − )4 and S12A7:(e − )4 Doped with B and Ga
Next, the electride structures are doped with B and Ga on the Al site. Figure 5 shows the relaxed structures. Calculated lattice parameters and volumes are reported in Table 4. In the case of B-doped eletrides (refer to Figure 5a,b), cage pole distances are slightly contracted with respect to those calculated in their un-doped electrides. This is due to the strong bonding between B and the cage wall oxygen, as evidenced by the shorter B-O bond distances (1.53 Å-1.56 Å) than the Al-O bond distances (1.74 Å-1.79 Å) in the un-doped electrides. The formation of a stronger B-O bond than the Al-O bond is due to the fact that the ionization potential of B (8.2980) [51] is larger than that of Al (5.9858) [51].

Doped with B and Ga
Next, the electride structures are doped with B and Ga on the Al site. Figure 5 shows the relaxed structures. Calculated lattice parameters and volumes are reported in Table 4. In the case of B-doped eletrides (refer to Figure 5a,b), cage pole distances are slightly contracted with respect to those calculated in their un-doped electrides. This is due to the strong bonding between B and the cage wall oxygen, as evidenced by the shorter B-O bond distances (1.53 Å-1.56 Å) than the Al-O bond distances (1.74 Å-1.79 Å) in the un-doped electrides. The formation of a stronger B-O bond than the Al-O bond is due to the fact that the ionization potential of B (8.2980) [51] is larger than that of Al (5.9858) [51]. The reduction in the calculated lattice parameters and volumes is further evidence for the strong B-O bond, as reported in Table 4. Doping of Ga has a very small impact on the cage pole distances, lattice parameters, and volumes with respect to the values calculated for un-doped electrides (refer to Tables 1 and 4). However, there is a very small increase in the cage pole distances, lattice parameters, and volumes compared to those calculated in their un-doped electride forms. This is because the ionization potential of Ga (5.9993) [51] is slightly larger than that of Al (5.9858). The reduction in the calculated lattice parameters and volumes is further evidence for the strong B-O bond, as reported in Table 4. Doping of Ga has a very small impact on the cage pole distances, lattice parameters, and volumes with respect to the values calculated for un-doped electrides (refer to Tables 1 and 4). However, there is a very small increase in the cage pole distances, lattice parameters, and volumes compared to those calculated in their un-doped electride forms. This is because the ionization potential of Ga (5.9993) [51] is slightly larger than that of Al (5.9858).    The calculated DOS plots for all doped configurations are shown in Figure 6. In the case of B·C12A7:(e − ) 4 , the electronic structure is slightly affected. The Fermi energy is increased only by 0.03 eV compared to the value calculated for C12A7:(e − ) 4 . The Fermi energy is unaltered upon B encapsulation in S12A7:(e − ) 4 . The resultant complexes are still metallic. Doping of Ga in C12A7:(e − ) 4 has resulted in a small shift in the Fermi energy level by 0.06 eV. A similar effect is noted for Ga·S12A7:(e − ) 4 . Again, metallic nature is still kept. Atomic DOS plots calculated for B and Ga show that B or Ga states mainly appear in the valence band. Finally, two oxygen atoms are encapsulated, consequently in the doped electrides. Relaxed structures of encapsulated oxygen atom-containing cages are shown in Figure 7. Table 5 reports the lattice parameters and volumes calculated in the relaxed configurations. There is an increase in the volume for oxygen encapsulated B-doped electride structures (refer to Table 5) in comparison with that calculated in the oxygen encapsulated un-doped electrides (refer to Table 2). Lattice constants are also contracted in all B-doped configurations. In the case of Ga, there is an expansion in the lattice constants and the volumes. The explanation for this difference is due to the formation of shorter B-O Finally, two oxygen atoms are encapsulated, consequently in the doped electrides. Relaxed structures of encapsulated oxygen atom-containing cages are shown in Figure 7. Table 5 reports the lattice parameters and volumes calculated in the relaxed configurations. There is an increase in the volume for oxygen encapsulated B-doped electride structures (refer to Table 5) in comparison with that calculated in the oxygen encapsulated un-doped electrides (refer to Table 2). Lattice constants are also contracted in all B-doped configurations. In the case of Ga, there is an expansion in the lattice constants and the volumes. The explanation for this difference is due to the formation of shorter B-O and longer Ga-O bonds than that of Al-O bonds (refer to Figure 7). Cage pole distances in the oxygen-containing cages are shortened upon doping of B compared to that observed in the corresponding un-doped structures. Ga-doped structures exhibit only a very small effect on the cage pole distances.     The calculated encapsulation energies and Bader charges on the B (or Ga) and the encapsulated oxygen atoms are reported in Table 6. In all configurations, B (or Ga) forms a +3 charge, as Al does. The encapsulation is exothermic in all cases, meaning that oxygen is more stable inside the cages as O 2− ion than its gaseous form. Bader charge approximation confirms that the encapsulated oxygen atom gains~1.40 electrons from the extra-framework electrons. The encapsulation energy calculated for the second oxygen atom is slightly lower than that calculated for the first oxygen atoms due to the lower number of electrons available for the second encapsulation. The encapsulation energies are more negative for C12A7 electrides than S12A7 electrides. This is due to the smaller size of the cage in C12A7 than S12A7, as evidenced by the smaller cage pole distance. In the case of B or Ga-doped C12A7 electrides, the encapsulation energies are less exothermic than that calculated for the un-doped C12A7 electrides (refer to Tables 3 and 6). Conversely, there is a small increase in the encapsulation energies for B-doped S12A7 electride in comparison with un-doped S12A7. The encapsulation is not significantly affected by the doping of Ga in S12A7. The calculated DOS plots for the encapsulated configurations are shown in Figure 8. The encapsulation reduces the Fermi energy (refer to Figures 6 and 8). There is a significant change in the Fermi energy level between the first and the second atom encapsulation. This is because the metallic character of the first encapsulated structure disappears upon the second atom encapsulation. As both dopants (B and Ga) are isoelectronic with Al and all three atoms are in the +3 charge state, doping does not increase or decrease the concentration of electrons.

Conclusions
The encapsulation efficacy of C12A7 and S12A7 electrides and their doped forms are examined for the ORR at the cathode in SOFC using spin-polarized DFT simulations. The exothermic encapsulation is observed for both electrides, and the reduction of oxygen is confirmed by the negative Bader charge on the encapsulated oxygen atoms. The encapsulation is stronger in C12A7 electride than the S12A7 electride. The doped C12A7 electrides are also promising as they exhibit exoergic encapsulation, though the encapsulation is slightly lower than that calculated for the undoped C12A7 electride. Conversely, there is an enhancement in the encapsulation for the S12A7 electride doped with B compared to its un-doped form. The Ga-doped S12A7 electride exhibits a negligible change in the encapsulation with respect to its un-doped form. The current simulation

Conclusions
The encapsulation efficacy of C12A7 and S12A7 electrides and their doped forms are examined for the ORR at the cathode in SOFC using spin-polarized DFT simulations. The exothermic encapsulation is observed for both electrides, and the reduction of oxygen is confirmed by the negative Bader charge on the encapsulated oxygen atoms. The encapsulation is stronger in C12A7 electride than the S12A7 electride. The doped C12A7 electrides are also promising as they exhibit exoergic encapsulation, though the encapsulation is slightly lower than that calculated for the un-doped C12A7 electride. Conversely, there is an enhancement in the encapsulation for the S12A7 electride doped with B compared to its un-doped form. The Ga-doped S12A7 electride exhibits a negligible change in the encapsulation with respect to its un-doped form. The current simulation study can stimulate future experimental studies designing of cathode material for SOFC. The performance of electride materials should be tested and compared with traditional cathodes, such as lanthanum strontium manganite (LSM) and lanthanum strontium cobalt ferrite (LSCF).