Proton-conducting oxides can be utilized in numerous sustainable devices, such as protonic fuel cells [1] and low-power electronics [2]. In order to optimize materials and meet specifications for commercial viability, better understanding of transport mechanisms is required. While electronic and structural descriptors have been found for predicting proton conductivity [3], there are knowledge gaps in the field on the effects of lattice dynamics.

For ternary oxides in particular, protons stay localized to oxide-ions and obey the Grotthuss mechanism [4], where the energy barrier of proton-hopping is believed to correlate with donor-acceptor spacing [5]. Within this class of proton conductors, lattice dynamical studies have been largely limited to perovskites. For example, shrinking donor-acceptor spacing via bond-angle-bending [6] and octahedral tilting [7] were found to be important for proton-transport in a handful of undoped perovskites. Another study found correlations among doped perovskites between energy barrier and phonon-related quantities such as averaged atomic mass [8]. However, further work is required to elaborate on the specific phonon modes facilitating proton-hopping and to formulate descriptors generalizable across different crystal structures.

Here, we developed a featurization of phonon spectra called thermal O...O fluctuation, which quantifies the flexibility of the oxygen sublattice and correlates with energy barriers of proton-hopping for a variety of ternary oxides. Analysis of this featurization can highlight which modes contribute most to thermal O...O fluctuation, while capturing frequency-dependence with higher weighting for low-energy modes. Therefore, we anticipate that this analysis will identify modes which assist proton-hopping. Applying this to the well-studied perovskite BaZrO₃, we extracted the phonon modes dominating thermal fluctuations of nearest-neighbor O...O pairs and found that they align well with the bending and rotational modes identified in literature [6,7]. Applying this featurization further to 77 O...O pairs found in 10 ternary oxides with varied crystal structures, we likewise observed correlations between thermal O…O fluctuation, equilibrium O…O spacing, and calculated energy barriers. These results imply that both static O…O spacing and dynamic fluctuations must be considered to predict proton conductivity in ternary oxides.