Mechanisms of oxygen ion diffusion in a nanoporous complex oxide $12\mathrm{Ca}\mathrm{O}\bullet 7{\mathrm{Al}}_2{\mathrm{O}}_3$

We performed a theoretical analysis of ${\mathrm{O}}^{2-}$ diffusion mechanisms in a nanoporous complex oxide $12\mathrm{Ca}\mathrm{O}\bullet 7{\mathrm{Al}}_2{\mathrm{O}}_3$ (C12A7). This material can be viewed as a positively charged framework, arranged in subnanometer sized cages, hosting extra-framework ${\mathrm{O}}^{2-}$ ions occupying one in six cages. Using both classical molecular-dynamics simulations and ab initio calculations we demonstrate that the diffusion of ${\mathrm{O}}^{2-}$ species is dominated by the exchange of framework and extra-framework ${\mathrm{O}}^{2-}$ ions rather than by an interstitial diffusion mechanism. The results allow us to rationalize the origins of the experimentally observed high oxide ion conductivity of C12A7 and the stability of its lattice under positive ion-beam irradiation.

Figure 1

(Color online) Local atomic structure of C12A7. (a) Two adjacent cages connected via intercage opening. Cages A and B are seen from the top and the side, respectively. Symmetry axis $S_4$ for cage B and Ca(I) atoms for A and B are also shown. The $S_4$ axis for cage A is perpendicular to the plane of the figure. (b) Intercage opening formed by Ca-O-Al-O-Al-O ring. The local atomic structures of O(I), O(II), and O(III) oxygen sites are also shown. The framework Al, O, and Ca atoms are shown with small (red), medium (blue), and large (gold) spheres, respectively.

Figure 2

(Color online) Quantum-mechanical clusters used in this work: (a) one-cage cluster comprising the wall of one framework cage; (b) two-halves cluster (shown on the background of two adjacent cages) comprising halves of two framework cages connected via an intercage opening (see also Fig. 1). The framework Al, O, and Ca atoms are shown with small (red), medium (blue), and large (gold) spheres.

Figure 3

(Color online) Displacement of atoms accumulated during heating C12A7 to $1700\mathrm{K}$ for the case of identical interatomic potentials for the framework and extra-framework oxygen atoms. Panels (a) and (b) show displacements of framework Ca (black) and Al (red) atoms, respectively. Panels (c) and (d) show displacements of oxygen atoms: atoms in (c) were originally the framework oxygens (green), while atoms in (d) were originally the extra-framework oxygens (blue).

Figure 4

(Color online) Cartesian coordinates of four ${\mathrm{O}}^{2-}$ ions, denoted as $A$ (black), $B$ (red), $C$ (green), and $D$ (blue), monitored during a $50\text{−}\mathrm{ps}$ MD simulation run at $700\mathrm{K}$. The data demonstrate that all four ions change their lattice sites almost simultaneously (within $750\mathrm{fs}$) and that their diffusion takes place via an exchange mechanism $A\to B\to C\to D$, i.e., ion $A$ moves to the site originally occupied by ion $B$, while $B$ moves to the site of $C$ and $C$ moves to the site of $D$.

Figure 5

(Color online) Displacement of atoms accumulated during heating C12A7 to $1700\mathrm{K}$. Atomic charges of extra-framework oxygens were scaled from $-0.2\mid e\mid$ to $-1.3\mid e\mid$. Panels (a) and (b) show displacements of framework Ca (black) and Al (red) atoms, respectively. Panels (c) and (d) show displacements of oxygen atoms: (c) shows framework oxygens (green), while atoms in (d) are extra-framework oxygens (blue).

Figure 6

(Color online) Arrhenius plot of the diffusion coefficient for ${\mathrm{O}}^{2-}$ self-diffusion $\left(D_{{\mathit{O}}^{2-}}\right)$: (a) experimental data from Ref. 17 (solid blue line); (b) values of $D_{{\mathit{O}}^{2-}}$ calculated using molecular dynamics (black dots), and a linear fit to them (red dashed line).

Figure 7

(Color online) Configuration of an extra-framework ${\mathrm{O}}^{2-}$ ion in C12A7: (a) side view, (b) top view. The framework Al, O, and Ca atoms are shown with tiny (red), small (blue), and medium (gold) spheres, respectively. The large sphere (blue) represents the extra-framework ${\mathrm{O}}^{2-}$ ion.

Figure 8

(Color online) Schematics of transition state configurations for four diffusion pathways near the intercage opening: (a) interstitial pathway; (b)–(d) are exchange pathways via framework oxygen sites O(I), O(II), and O(III), respectively [see also Fig. 1b]. Tiny (red), small (blue), and medium (gold) spheres show framework Al, O, and Ca atoms, respectively. Large spheres (blue) show oxygen species involved in the diffusion.