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

Abstract: 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.

• The paper demonstrates that proton insertion is thermodynamically favored up to the Co reduction limit, elucidating defect dynamics through DFT and ML methods.
• Methodology integrates first-principles DFT with machine-learned potentials to analyze defect energetics across varying oxygen stoichiometries and protonation levels.
• Key implications include irreversible device degradation and tunable electronic properties via lattice expansion and band gap modulation.

Thermodynamics of Proton Insertion across the Perovskite–Brownmillerite Transition in La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$

Introduction

The study offers a comprehensive evaluation of the thermodynamics of proton insertion (hydrogen interstitial formation) in La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$ (LSCO) as it traverses the topotactic perovskite (P, $\delta = 0$) to brownmillerite (BM, $\delta = 0.5$) phase transition. The inquiry is motivated by empirical evidence highlighting incomplete reversibility in thin-film EDLT devices, attributed to acid-etching, with protons generated by electrolyte gating being strongly implicated. While prior work has revealed the possibility and implications of protonating pure BM SrCoO$_{2.5}$, the present study uniquely focuses on the broader stoichiometry relevant to LSCO and rigorously integrates first-principles DFT with universal machine-learned interatomic potentials.

Methodological Framework

Defective energetics are explored via DFT (PBE+U, $U_\mathrm{eff} = 3.0$ eV on Co) and the UMA ML potential framework, enabling tractable exploration of thousands of non-dilute defect and host configurations. The study centers on dilute and non-dilute defect formation energies (oxygen vacancies, $v_O$, and hydrogen interstitials, $H_i$), convex hull analyses for metastability benchmarking, and electronic structure consequences. Multiple host compositions ($\delta = 0, 0.25, 0.5$) and protonation levels ($y$ in H$_y$La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$) are considered, spanning the relevant reduction domain for Co valence and accommodating critical A-site disorder via SQS construction.

Formation Energies and Defect Thermodynamics

DFT calculations establish that dilute $v_O$ formation energies increase significantly with increasing $\delta$, from 1.08 eV (P) to 3.04 eV (BM), confirming the strong intrinsic resistance of BM to further oxygen removal. In sharp contrast, $H_i$ formation energies are consistently negative (even in BM), validating facile thermodynamics for proton insertion under ambient conditions (300 K, 1 bar H$_2$), and providing a robust underpinning for experimental observations of protonation in LSCO and SrCoO$_{2.5}$ derivatives. Defect competition maps indicate that, at lower temperatures and finite H/O chemical potentials encountered in device operation or ambient synthesis, $H_i$ formation is statistically favored over $v_O$ across the P–BM transition. However, decreasing H/O partial pressures or raising temperature reverses this thermodynamic landscape, validating the synthetic accessibility of highly oxygen-deficient LSCO at elevated T without interference from protonation.

Limits and Mechanisms of Proton Insertion

A critical finding is that the protonation limit in LSCO is fundamentally set by the Co reduction limit: as long as Co can be reduced from 3.5+ towards 2+, proton insertion is both thermodynamically and kinetically accessible. Non-dilute ML-relaxed energetics show negative interaction energies for $H_i$ up to $y$ corresponding to full Co(II), beyond which further proton insertion becomes unfavorable unless compensated by alternative charge accommodation mechanisms (e.g., H$_2$ dimerization, observed at the highest protonation levels).

Moreover, increasing proton content correlates with significant lattice expansion and structural distortion. The magnitude of unit cell expansion due to protonation (e.g., $y = 0.5$ in P-LSCO) is comparable to the structural transformation from P to BM, suggesting that conventional means of tracking oxygen stoichiometry (by lattice parameter) may conflate O vacancy and proton effects.

Impact of Protonation on Oxygen Vacancy Formation

The energetics of $v_O$ formation become lower (by up to ∼1 eV) in the presence of pre-inserted protons (for $y <$ Co(II) limit), introducing a defect-defect interaction that can render oxygen loss more competitive. Beyond the Co(II) reduction threshold, however, this trend reverses and oxygen vacancy formation becomes less favorable, effectively demarcating a "window" where the material is maximally susceptible to simultaneous proton/O vacancy presence.

Thermodynamic (Meta)stability and Decomposition

Despite the universally negative formation energies for proton insertion, convex hull analysis against competing hydrous/oxide phases demonstrates that all protonated LSCO phases ($0<y\leq 2$, $\delta = 0, 0.25, 0.5$) are unstable (energy above hull increases with $y$) to decomposition into mixtures comprising hydroxides and binary phases (e.g., CoO, Sr(OH)$_2$, LaOOH). This behavior is similarly reproduced for SrCoO$_{2.5}$ derivatives. The finding directly rationalizes the acid-etching and irreversible degradation observed during EDLT cycling: proton insertion is facile but thermodynamically drives decomposition, notably in humid environments or under strong gating, consistent with empirical reports of film thinning and irreversible property evolution during device operation.

Electronic Structure Modification

DFT calculations of the electronic structure reveal that both oxygen vacancy formation and protonation induce strong band gap opening and localization of electronic states. Upon reaching the Co(II) reduction threshold ($y$ limit), the band gap approaches ~1.5 eV from originally metallic or weakly insulating unprotonated hosts, consistent with experiment. This coincides with formation of localized -OH bonds and reduced Co, fundamentally altering transport and magnetic properties relevant to gating, switching, and ionic conduction.

Additionally, Bader charge analysis across configurations confirms that protonic electrons localize predominantly on Co, and that the principal limit to further insertion is availability of low-valence Co.

Implications and Future Directions

From an application perspective, both the facile nature of proton insertion and the inherent thermodynamic instability of the resulting phases are double-edged. In NE devices (EDLTs), proton-driven phase evolution is an inevitable source of irreversibility and degradation, especially under ambient or hydrated operation. Conversely, the ability to access metastable protonated states, enabled by kinetic bottlenecks for phase separation, allows exploitation of tunable properties (conductivity, magnetism, structural expansion) in a dynamic and device-relevant regime. The potential for tuning protonation propensity by A-site (La/Sr) manipulation is suggested by the differing stability with respect to decomposition, opening avenues for engineering compositions with enhanced resilience.

Crucially, the study underscores the intrinsic difficulty in disentangling protonation and oxygen vacancy signatures experimentally, given their similar structural, transport, and optical manifestations. Direct hydrogen tracking (e.g., SIMS) remains essential for unambiguous assignments.

Prospective theoretical developments include extension to operando, time-resolved phase evolution, explicit DFT/ML-coupled modeling of proton diffusion pathways, and inclusion of epitaxial strain and interface effects.

Conclusion

This work delivers a rigorous thermodynamic and mechanistic framework for proton insertion in LSCO across the topotactic P–BM transition. Key technical findings include: (1) proton insertion is universally thermodynamically favored up to the Co reduction limit across the phase space; (2) all protonated LSCO phases are unstable with respect to phase separation, offering a direct basis for observed acid-etching/device degradation; (3) both protonation and oxygen vacancies induce pronounced lattice and electronic structure modulation; and (4) at the highest insertion levels, H$_2$ dimerization and complex phase evolution are observed. These insights have direct consequences for the interpretation, design, and lifetime prediction of LSCO-based energy and electronic devices, and provide a technical blueprint for future work in mixed-anion defect engineering and dynamic ionic control in complex oxides.

Reference: "Thermodynamics of proton insertion across the perovskite-brownmillerite transition in La0.5Sr0.5CoO3-δ" (2510.05323)