A Unified Theory Quantifying How Lattice Dynamics Facilitate Proton Transport in Various Ternary-Oxide Phases

Understanding the lattice dynamics of proton-conducting metal oxides is important for many applications, from optimizing hydrogen production to designing low-power neuromorphic-computing devices. Transport mechanisms in metal oxides are well-studied [1], so we know that protons stay localized to oxygens and hop between neighboring O…O pairs; the energy barrier of hopping is lower for pairs separated by shorter distances.<br/><br/>However, studies considering lattice dynamics are usually limited to simple perovskites, and phonons are only used to estimate attempt frequencies [2]. Others only treat phonons implicitly by correlating energy barrier with coarse quantities like unit-cell volume [3]. Recent work from our research groups has found phonon-based descriptors for proton-conduction in solid acids, which contain hydrogen in their nominal structures [4]. However, studying metal oxides requires a different approach, since the conduction pathways and proton sites within the lattice differ from those in solid acids.<br/><br/>Here, we developed a more general theory describing how lattice dynamics affect proton-transport energy-barriers in a variety of ternary oxides. In particular, we focused on phonon modes which bring neighboring O…O pairs closer together, thereby lowering the associated energy barrier. Lower-frequency modes, which are more accessible at lower temperatures, are more suitable for assisting proton transport. Following this principle, we formulated descriptors like thermal relative displacement between O…O pairs. We interpreted these descriptors by extracting the dominant phonon modes, and we found that they align well with the literature for systems like the perovskite, BaZrO₃. In order to validate this principle more broadly, we aim to correlate phonon-based descriptors with calculated energy barriers for emerging phases like brownmillerite and Ruddlesden-Popper. Although energy barriers are most commonly estimated using nudged-elastic-band, we are evaluating whether these static calculations sufficiently capture lattice flexibility, or whether dynamic simulations are required.<br/><br/>Developing these descriptors and analyzing the dominant modes will enhance our understanding of proton transport. This will enable various downstream applications, such as physically interpretable, high-throughput virtual screening and data generation. Building on prior high-throughput studies [4, 5], we can first pull oxides from a database, then expand the pool of candidates using elemental substitution and doping. Phonon-based descriptors can then be included in a suite of filters which help identify the most promising proton conductors. Given a large enough design space, active learning can also be employed to intelligently select candidates for more thorough calculations.<br/><br/>[1] Kreuer K-D. <i>Chemistry of Materials</i>. 8 (<b>1996</b>) 610-641<br/>[2] Bork N., Bonanos N., Rossmeisl J., Vegge T. <i>Physical Review B</i>. 82 (<b>2010</b>) 014103<br/>[3] Wakamura K. <i>Solid State Ionics</i>. 180 (<b>2009</b>) 1343–1349<br/>[4] Klyukin K., Zguns P., Li J., Yildiz B. <i>In Preparation</i> (<b>2023</b>)<br/>[5] Islam M. S., Wang S., Hall A. T., Mo Y. <i>Chemistry of Materials</i>. 34 (<b>2022</b>) 5938−5948<br/><br/>This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. INC0546071. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.