Thermodynamics of proton insertion across the perovskite-brownmillerite transition in La0.5Sr0.5CoO3-δ

La${1-x}$Sr${x}$CoO3-$δ$ is a promising off-stoichiometric metal oxide that undergoes a topotactic perovskite ($δ$ = 0) to brownmillerite ($δ$ = 0.5) transition under electrochemical and thermochemical stimuli, with concomitant variations in its electrical, magnetic, thermal, and optical properties. Recent studies on thin-film cycling in electrochemical devices show incomplete reversibility of this transition, with significant acid-etching serving as a degradation mechanism. While earlier investigations examined the protonation of brownmillerite SrCoO2.5, the thermodynamics of protonation across the perovskite-to-brownmillerite transition remain poorly understood. In this work, we combine density functional theory calculations with predictions from universal machine-learning interatomic potentials to elucidate the energetics and implications of protonation across the transition for La0.5Sr0.5CoO3-$δ$. These calculations reveal negative hydrogen insertion energies and strong competition with oxygen vacancy formation across the transition for a wide range of conditions. The extent of protonation is primarily limited by the availability of Co 3d states to accommodate reduction by inserted hydrogen. Although hydrogen insertion is often thermodynamically favorable within a defect picture, a convex hull analysis of the resulting HyLa0.5Sr0.5CoO3-$δ$ phases reveals them to be unstable against decomposition into hydroxides among other products. This instability increases with hydrogen content and provides a thermodynamic basis for the acid-etching observed during electrochemical cycling. This work advances the fundamental understanding of protonation in La0.5Sr0.5CoO3-$δ$ and contextualizes experimental observations of related materials in the presence of moisture or H2.

💡 Research Summary

This paper investigates the thermodynamics of proton (hydrogen) insertion in La₀.₅Sr₀.₅CoO₃₋δ (LSCO) across its topotactic perovskite‑to‑brownmillerite transition, a process that is central to the operation of electrochemical devices such as electric‑double‑layer transistors (EDLTs) and solid‑oxide fuel cells. The authors combine conventional density‑functional theory (DFT) calculations with a universal machine‑learning interatomic potential (uMLIP) to evaluate the energetics of two key neutral defects: oxygen vacancies (v_O) and hydrogen interstitials (H_i).

Using GGA+U (U_Co = 3 eV) they compute defect formation free energies that explicitly include temperature, oxygen partial pressure, and applied electrochemical potential. Corrections for the overbinding of O₂ in GGA (+0.687 eV) and for the experimental water formation energy (−0.3508 eV) are applied. The resulting formation energies show that both v_O and H_i become thermodynamically favorable under reducing (positive bias) conditions, i.e., when μ_O is low and μ_H is high. This indicates that, during a positive gate voltage, oxygen can leave the lattice while water electrolysis supplies protons that readily occupy interstitial sites.

A key insight is that the availability of Co 3d electronic states limits the amount of hydrogen that can be accommodated. Bader charge analysis reveals that each inserted H forms an OH bond and reduces a neighboring Co³⁺ to Co²⁺. Once the Co 3d manifold is saturated (approximately y ≈ 0.5 hydrogen per formula unit), further proton insertion becomes energetically costly. Interaction energies between co‑existing vacancies and protons are generally positive, demonstrating competition rather than synergistic defect formation at higher concentrations.

To explore the vast configurational space of non‑dilute defect concentrations, the authors employ the UMA‑s‑1 universal machine‑learning potential, which reproduces DFT energies with near‑quantum accuracy but at orders‑of‑magnitude lower computational cost. Hundreds of candidate HyLa₀.₅Sr₀.₅CoO₃₋δ structures (denoted H‑LSCO) are relaxed, and a convex‑hull analysis is performed across the hydrogen‑composition axis. The hull shows that low‑hydrogen phases (y ≤ 0.25) lie close to the LSCO line, whereas higher‑hydrogen phases (y ≥ 0.5) are thermodynamically unstable, preferring decomposition into cobalt hydroxide, strontium hydroxide, and metallic Co. This decomposition pathway provides a clear thermodynamic basis for the acid‑etching (etching by acidic species) observed experimentally during repeated electrochemical cycling.

Structural consequences of proton insertion are also quantified. Hydrogen incorporation expands the lattice anisotropically (≈2–3 % in‑plane, ≈4–5 % out‑of‑plane) and converts the electronic character from metallic to semiconducting, widening the band gap from ~0 eV to 0.6–0.9 eV. Density‑of‑states analysis shows reduced Co‑O hybridization and a shift of Co 3d states toward lower energies, consistent with the observed increase in resistivity and optical band‑gap widening in protonated samples.

The authors discuss practical implications for device engineering. To mitigate acid‑etching, they recommend limiting the maximum gate voltage to avoid excessive proton insertion, reducing water content in the ion‑gel electrolyte to lower μ_H, and applying protective, acid‑resistant overlayers (e.g., TiO₂, Al₂O₃) on metal contacts. Conversely, the brownmillerite phase, being stable under low‑hydrogen conditions, may be advantageous for high‑temperature applications such as solid‑oxide fuel cells, where oxygen vacancy conductivity is desired.

In summary, the study provides a comprehensive thermodynamic framework that explains why proton insertion is energetically allowed yet ultimately self‑limiting in LSCO. The competition between Co electronic capacity and the propensity of highly protonated phases to decompose into hydroxides rationalizes the experimentally observed degradation. These insights guide the design of more robust LSCO‑based electrochemical devices by informing voltage windows, moisture control, and surface protection strategies.