The cubic perovskite unit cell structure is shown. The front face oxygen ion is shown as translucent to allow view of the central zirconium ion. The oxygen ions on the highlighted OZrO body centered line are darker for contrast. In , the packing along the OZrO body centered line and along the diagonal BaOBa face line suggest the same lattice size. If a larger doping ion replaces the central zirconium ion, the resulting larger cube has extra space in the faces allowing the oxygen octahedral corners to tilt.
Doping with at the corner Zr site leads to (−,−,−) distortions. Each − is comprised of octahedral tilting in the dopant layers leading to the distortions seen in (a) with slight octahedral tilting in the opposite direction in the subsequent undoped layer leading to the slightly oppositely distorted layer in (b). The view along the other two axes is similar. From darkest to lightest, the atoms are black oxygen ions in the undoped layer, blue yttrium ions in corners of the top layer, other red oxygen ions, and finally green zirconium ions. The barium ions occupy centers in subcubes and are left out for clarity. The doping level is 12.5%.
Layer 1 unit 1 (L1U1) of Fig. 2(a) is equivalent to the reflection of layer 2 unit 4 (L2U4) of that Fig. 2(b). Here, L1U1 and L2U4 have been rotated to clarify that a reflection of one yields the other. The second layer oxygens from Fig. 2 are colored black to clarify orientation. The same relationship holds for the pairs L1U2/L2U3, L1U3/L2U2, and L1U4/L2U1.
Cube 1 in Fig. 2(a) is shown with proton binding energies written on each binding oxygen ion. Note that the same edge oxygen ion is shown on adjacent faces. However, the binding site energy on this oxygen ion is different on each face since the energy is for bound protons with OH bond directed toward the center of that specific face. Transition state energies are written between binding oxygens ions. All energies are in eV.
Two examples of favorable pathways for proton conduction are shown. These are composed of rotations (R), intraoctahedral transfers (T), and an interoctahedral transfer (I). One is an eight step pathway (RRTTRRTT) and the other is a seven step pathway (RRIRRTT) which takes a short cut I step instead of two T steps. A repeating cycle of either can yield conduction through the system. Pathways with all T steps on the side of the dopant and all T steps on the opposite side of the dopant are also seen. There are also pathways where all rotations happen on the side of the plane.
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