Ab initio investigation of defect formation at ZrO${}_2$-CeO${}_2$ interfaces

The structural and electronic properties of low index (100) and (111) ZrO${}_2$-CeO${}_2$ interfaces are analyzed on the basis of density functional theory calculations. The formation energy and relative stability of substitutional defects, oxygen vacancies, and vacancy-dopant complexes are investigated for the (100) orientation. By comparing these results with the ones obtained in bulk structures, we provide a possible explanation for the higher experimental ionic conductivity measured at the interface.

Figure 1

(a) Supercell of the (100) ZrO${}_2$-CeO${}_2$ interface. (b) Supercell of the (111) ZrO${}_2$-CeO${}_2$ interface. The large gray and blue spheres and the small red spheres represent Ce, Zr, and O atoms, respectively.

Figure 2

Charge density of the (100) CeO${}_2$-ZrO${}_2$ junction. The red areas indicate charge accumulation, while the blue areas indicate charge depletion. Panel (b) represents one of the two planes at the interface level where oxygen atoms lie. Panels (c) and (d) represent the planes where the oxygen atoms lie in the CeO${}_2$ and ZrO${}_2$ side of the junction, respectively.

Figure 3

Schematic representation of $E_{{\mathrm{V}}_{\mathrm{O}}}$ (in eV) at the interface and in strained CeO${}_2$ and ZrO${}_2$ bulk structures. The values for neutral vacancies are in black, and the ones for positive charged vacancies are in red. The positions of V${}_{\mathrm{O}}$ are indicated by arrows. The cells shown in the picture represent only a small portion of the real simulation cell used for the calculation.

Figure 4

Schematic representation of the defect formation energy difference (in eV) for the V${}_{\mathrm{O}}$-2Y complex in ZrO${}_2$ and for the V${}_{\mathrm{O}}$-2Gd complex in CeO${}_2$. The V${}_{\mathrm{O}}$, Y, and Gd positions are indicated by arrows.

Figure 5

Schematic representation of V${}_{\mathrm{Zr}}$ and V${}_{\mathrm{Ce}}$ formation energies. Both relative and absolute values of formation energies (in eV) are indicated. The energy has been calculated by placing the vacancies at different distances (in number of layers) from the interface. The positions of the vacancies, relative to the interface, are indicated by arrows.