Oxide-ion conduction in the Dion–Jacobson phase CsBi2Ti2NbO10−δ

Oxide-ion conductors have found applications in various electrochemical devices, such as solid-oxide fuel cells, gas sensors, and separation membranes. Dion–Jacobson phases are known for their rich magnetic and electrical properties; however, there have been no reports on oxide-ion conduction in this family of materials. Here, for the first time to the best of our knowledge, we show the observation of fast oxygen anionic conducting behavior in CsBi2Ti2NbO10−δ. The bulk ionic conductivity of this Dion–Jacobson phase is 8.9 × 10−2 S cm−1 at 1073 K, a level that is higher than that of the conventional yttria-stabilized zirconia. The oxygen ion transport is attributable to the large anisotropic thermal motions of oxygen atoms, the presence of oxygen vacancies, and the formation of oxide-ion conducting layers in the crystal structure. The present finding of high oxide-ion conductivity in rare-earth-free CsBi2Ti2NbO10−δ suggests the potential of Dion–Jacobson phases as a platform to identify superior oxide-ion conductors.

The TECs were estimated using the lattice parameters refined by the Rietveld analyses of the synchrotron X-ray diffraction data (Fig. 1a). Thermal expansion anomalies were observed around the o-t phase transition temperature. TECs are defined as follows.

Supplementary Tables
Supplementary Table 1. Bond-valence-based energy barrier for oxide-ion migration (E b ) No.

Supplementary
U eq 0.0734 (8) Supplementary   The oxide-ion conductivity is lower than  tot , thus, we used the inequality "<" in the table as  Table 8. Average thermal expansion coefficients (TECs) of CsBi 2 Ti 2 NbO 10− in static air, which were estimated using the lattice parameters refined by the Rietveld analyses of the synchrotron X-ray diffraction data (Fig. 1a) The average TECs in the temperature range between T and T 0 are defined as follows.
where T 0 = 298 K and the superscripts o and t denote the orthorhombic and tetragonal, respectively.
where r is the distance between these two points charges q 1 and q 2 , 0 is the permittivity of free space. To estimate the electrostatic force on a Bi 3+ cation around z = 0.13, F 1 , we consider the Coulomb's forces between the Bi 3+ cation and four layers of k = ±2 and ±1 (Supplementary Figure 11a). The F 1 is calculated as follows, where the interatomic distance r 2 is assumed to be r 1 . Thus, the Bi 3+ cation around z = 0.13 can be displaced upward along the c axis (black arrows in Supplementary Figure 11b).
Similarly, the electrostatic force on a Bi 3+ cation around z = 0.13, F 2 is 3 4

(3)
Thus, the Bi 3+ cation around z = 0.13 can be displaced downward along the c axis (arrows in Supplementary Figure 11b). These results indicate that the Bi 3+ cations in

Computations: Screening of 69 candidates for oxide-ion conducting materials and investigation of the oxide-ion diffusion path by the bond-valence method.
We selected the chemical composition CsBi 2 Ti 2 NbO 10 as a candidate for oxide-ion conductors by screening 69 Dion-Jacobson phases using 83 crystallographic data through the bond-valence (BV) method. 1418 Owing to its simple calculation procedure, the BV method is more efficient than the density functional theory (DFT)-based calculations and molecular dynamics (MD) simulations for exploring oxide-ion conductors. The bond-valence-based energy landscapes (BVELs) for a test oxide ion for 83 crystallographic data of 69 Dion-Jacobson phases were examined to search for oxide-ion conductors. The BV-based energy for each oxide was calculated using its crystallographic parameters from the inorganic crystal structure database (ICSD) 19 with the computer programme, softBV. 20 The BV parameters used in the calculations were given by Adams in the software. 21 The spatial resolution was set to 0.1 Å. The BV-based energy barriers, E b , for the oxide-ion migration were estimated using BVELs (Supplementary Figure 1, Supplementary Table   1). The E b of CsBi 2 Ti 2 NbO 10 was relatively low (E b = 0.5 eV). Furthermore, the BV-based energy of CsBi 2 Ti 2 NbO 10 was calculated with the crystallographic parameters refined using in situ high-temperature neutron-diffraction data taken at 973 K to investigate the anisotropic thermal motions and diffusion paths of the oxide ions.