The reorientation of protonic defects in barium zirconate: Low-temperature tunneling regime and transition to the adiabatic regime

Abstract

In most proton-conducting oxides, proton conductivity is mediated by a Grotthuss-like mechanism, i.e. the succession of transfers, in which the proton jumps from an oxygen onto another (breaking, and then reforming an ionocovalent hydroxyl bond OH), and reorientations, in which the OH bond simply rotates without breaking. We focus in this work on this second step, i.e. the reorientation of the protonic defect, in barium zirconate, one of the most promising proton-conducting oxides. Considered alone, the rotations of a proton are responsible for a rotational diffusion of this proton around a given oxygen atom. The reorientation of the protonic defect, like transfer, is strongly affected by the quantum effects associated with the protonic motions, and can only take place thanks to two specific lattice vibrations: (i) a reorganization, that symmetrizes the proton potential and puts the proton levels in the initial and final wells in coincidence, and (ii) the increase of the separation between the protonated oxygen and the nearest neighbor barium atom (that forms an obstacle to the reorientation of the protonic defect). The former (necessary step) mostly consists in rotations of the two oxygen octahedra sharing the protonated oxygen, while the latter (facilitating step) helps to overcome the proton‑barium electrostatic repulsion and lowers the proton barrier. We show that the reorientation of the protonic defect in barium zirconate undergoes a transition at about 220 K between a low-temperature and a high-temperature regime. Below ∼ 220 K, it is governed by tunneling, with a reorientation rate having an activation energy of 0.09 eV and a prefactor of ∼ 0.4 THz, due to quasi-non-adiabatic transitions between coincident protonic ground states (GS → GS), and involving an effective proton coupling of 5.7 meV. Above 220 K, two additional contributions, corresponding to transitions between the first excited protonic state (1st) in one of the two wells, and the protonic ground state (GS) in the other well, become dominant. These asymmetric transitions (1st → GS and GS → 1st) are quasi-adiabatic, and their rates are associated with an activation energy of 0.14 eV and a prefactor of 1.7 THz. The contribution due to adiabatic symmetric transitions between first excited protonic states (1st → 1st) should become equivalent to each of the asymmetric ones only at high temperature (above 900 K).