Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel.

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3-6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Correlative operando microscopy of oxygen evolution electrocatalysts.

Transition metal (oxy)hydroxides are promising electrocatalysts for the oxygen evolution reaction1-3. The properties of these materials evolve dynamically and heterogeneously4 with applied voltage through ion insertion redox reactions, converting materials that are inactive under open circuit conditions into active electrocatalysts during operation5. The catalytic state is thus inherently far from equilibrium, which complicates its direct observation. Here, using a suite of correlative operando scanning probe and X-ray microscopy techniques, we establish a link between the oxygen evolution activity and the local operational chemical, physical and electronic nanoscale structure of single-crystalline ß-Co(OH)2 platelet particles. At pre-catalytic voltages, the particles swell to form an α-CoO2H1.5·0.5H2O-like structure-produced through hydroxide intercalation-in which the oxidation state of cobalt is +2.5. Upon increasing the voltage to drive oxygen evolution, interlayer water and protons de-intercalate to form contracted ß-CoOOH particles that contain Co3+ species. Although these transformations manifest heterogeneously through the bulk of the particles, the electrochemical current is primarily restricted to their edge facets. The observed Tafel behaviour is correlated with the local concentration of Co3+ at these reactive edge sites, demonstrating the link between bulk ion-insertion and surface catalytic activity.

Closed-loop optimization of fast-charging protocols for batteries with machine learning.

Simultaneously optimizing many design parameters in time-consuming experiments causes bottlenecks in a broad range of scientific and engineering disciplines1,2. One such example is process and control optimization for lithium-ion batteries during materials selection, cell manufacturing and operation. A typical objective is to maximize battery lifetime; however, conducting even a single experiment to evaluate lifetime can take months to years3-5. Furthermore, both large parameter spaces and high sampling variability3,6,7 necessitate a large number of experiments. Hence, the key challenge is to reduce both the number and the duration of the experiments required. Here we develop and demonstrate a machine learning methodology  to efficiently optimize a parameter space specifying the current and voltage profiles of six-step, ten-minute fast-charging protocols for maximizing battery cycle life, which can alleviate range anxiety for electric-vehicle users8,9. We combine two key elements to reduce the optimization cost: an early-prediction model5, which reduces the time per experiment by predicting the final cycle life using data from the first few cycles, and a Bayesian optimization algorithm10,11, which reduces the number of experiments by balancing exploration and exploitation to efficiently probe the parameter space of charging protocols. Using this methodology, we rapidly identify high-cycle-life charging protocols among 224 candidates in 16 days (compared with over 500 days using exhaustive search without early prediction), and subsequently validate the accuracy and efficiency of our optimization approach. Our closed-loop methodology automatically incorporates feedback from past experiments to inform future decisions and can be generalized to other applications in battery design and, more broadly, other scientific domains that involve time-intensive experiments and multi-dimensional design spaces.

Correlative image learning of chemo-mechanics in phase-transforming solids.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on LiXFePO4, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Fictitious phase separation in Li layered oxides driven by electro-autocatalysis.

Layered oxides widely used as lithium-ion battery electrodes are designed to be cycled under conditions that avoid phase transitions. Although the desired single-phase composition ranges are well established near equilibrium, operando diffraction studies on many-particle porous electrodes have suggested phase separation during delithiation. Notably, the separation is not always observed, and never during lithiation. These anomalies have been attributed to irreversible processes during the first delithiation or reversible concentration-dependent diffusion. However, these explanations are not consistent with all experimental observations such as rate and path dependencies and particle-by-particle lithium concentration changes. Here, we show that the apparent phase separation is a dynamical artefact occurring in a many-particle system driven by autocatalytic electrochemical reactions, that is, an interfacial exchange current that increases with the extent of delithiation. We experimentally validate this population-dynamics model using the single-phase material Lix(Ni1/3Mn1/3Co1/3)O2 (0.5 < x < 1) and demonstrate generality with other transition-metal compositions. Operando diffraction and nanoscale oxidation-state mapping unambiguously prove that this fictitious phase separation is a repeatable non-equilibrium effect. We quantitatively confirm the theory with multiple-datastream-driven model extraction. More generally, our study experimentally demonstrates the control of ensemble stability by electro-autocatalysis, highlighting the importance of population dynamics in battery electrodes (even non-phase-separating ones).

Tuning electrochemically driven surface transformation in atomically flat LaNiO3 thin films for enhanced water electrolysis.

Structure-activity relationships built on descriptors of bulk and bulk-terminated surfaces are the basis for the rational design of electrocatalysts. However, electrochemically driven surface transformations complicate the identification of such descriptors. Here we demonstrate how the as-prepared surface composition of (001)-terminated LaNiO3 epitaxial thin films dictates the surface transformation and the electrocatalytic activity for the oxygen evolution reaction. Specifically, the Ni termination (in the as-prepared state) is considerably more active than the La termination, with overpotential differences of up to 150 mV. A combined electrochemical, spectroscopic and density-functional theory investigation suggests that this activity trend originates from a thermodynamically stable, disordered NiO2 surface layer that forms during the operation of Ni-terminated surfaces, which is kinetically inaccessible when starting with a La termination. Our work thus demonstrates the tunability of surface transformation pathways by modifying a single atomic layer at the surface and that active surface phases only develop for select as-synthesized surface terminations.

Electro-chemo-mechanical charge carrier equilibrium at interfaces.

Electrochemical interfaces involving solids enable charge transfer, electrical transport, and mass storage in energy devices. One central concept that determines the interfacial charge carrier concentration is the space-charge field. The classical theory accounts for electrochemical equilibrium in the absence of mechanical effects; such effects have recently been found critical in many solids, such as materials for lithium-ion and solid-state batteries, perovskite solar cells, and fuel cells. Towards elucidating the interplay between charge carriers and mechanics, we establish a generalized electro-chemo-mechanical space-charge model and categorize the carriers into physically-meaningful four types, based on the signs of the charge number (i.e., polarity) and the partial molar volume (i.e., expansion coefficient). Beyond the electrostatic effects discussed in the literature, our work reveals the importance of elastic effects, as demonstrated by simulations of a composite beam bending experiment. The analysis highlights opportunities to systematically tune the interfacial electrical conductivity and the reaction kinetics of solids through mechanics. Our treatment provides a rational basis for understanding stress-driven phenomena at interfaces in a wide range of solids.

The Role of Metal Substitution in Tuning Anion Redox in Sodium Metal Layered Oxides Revealed by X-Ray Spectroscopy and Theory.

We investigate high-valent oxygen redox in the positive Na-ion electrode P2-Na0.67-x [Fe0.5 Mn0.5 ]O2 (NMF) where Fe is partially substituted with Cu (P2-Na0.67-x [Mn0.66 Fe0.20 Cu0.14 ]O2 , NMFC) or Ni (P2-Na0.67-x [Mn0.65 Fe0.20 Ni0.15 ]O2 , NMFN). From combined analysis of resonant inelastic X-ray scattering and X-ray near-edge structure with electrochemical voltage hysteresis and X-ray pair distribution function profiles, we correlate structural disorder with high-valent oxygen redox and its improvement by Ni or Cu substitution. Density of states calculations elaborate considerable anionic redox in NMF and NMFC without the widely accepted requirement of an A-O-A' local configuration in the pristine materials (where A=Na and A'=Li, Mg, vacancy, etc.). We also show that the Jahn-Teller nature of Fe4+ and the stabilization mechanism of anionic redox could determine the extent of structural disorder in the materials. These findings shed light on the design principles in TM and anion redox for positive electrodes to improve the performance of Na-ion batteries.

Metal-oxygen decoordination stabilizes anion redox in Li-rich oxides.

Reversible high-voltage redox chemistry is an essential component of many electrochemical technologies, from (electro)catalysts to lithium-ion batteries. Oxygen-anion redox has garnered intense interest for such applications, particularly lithium-ion batteries, as it offers substantial redox capacity at more than 4 V versus Li/Li+ in a variety of oxide materials. However, oxidation of oxygen is almost universally correlated with irreversible local structural transformations, voltage hysteresis and voltage fade, which currently preclude its widespread use. By comprehensively studying the Li2-xIr1-ySnyO3 model system, which exhibits tunable oxidation state and structural evolution with y upon cycling, we reveal that this structure-redox coupling arises from the local stabilization of short approximately 1.8 Å metal-oxygen π bonds and approximately 1.4 Å O-O dimers during oxygen redox, which occurs in Li2-xIr1-ySnyO3 through ligand-to-metal charge transfer. Crucially, formation of these oxidized oxygen species necessitates the decoordination of oxygen to a single covalent bonding partner through formation of vacancies at neighbouring cation sites, driving cation disorder. These insights establish a point-defect explanation for why anion redox often occurs alongside local structural disordering and voltage hysteresis during cycling. Our findings offer an explanation for the unique electrochemical properties of lithium-rich layered oxides, with implications generally for the design of materials employing oxygen redox chemistry.

Evolution of the Solid-Electrolyte Interphase on Carbonaceous Anodes Visualized by Atomic-Resolution Cryogenic Electron Microscopy.

The stability of modern lithium-ion batteries depends critically on an effective solid-electrolyte interphase (SEI), a passivation layer that forms on the carbonaceous negative electrode as a result of electrolyte reduction. However, a nanoscopic understanding of how the SEI evolves with battery aging remains limited due to the difficulty in characterizing the structural and chemical properties of this sensitive interphase. In this work, we image the SEI on carbon black negative electrodes using cryogenic transmission electron microscopy (cryo-TEM) and track its evolution during cycling. We find that a thin, primarily amorphous SEI nucleates on the first cycle, which further evolves into one of two distinct SEI morphologies upon further cycling: (1) a compact SEI, with a high concentration of inorganic components that effectively passivates the negative electrode; and (2) an extended SEI spanning hundreds of nanometers. This extended SEI grows on particles that lack a compact SEI and consists primarily of alkyl carbonates. The diversity in observed SEI morphologies suggests that SEI growth is a highly heterogeneous process. The simultaneous emergence of these distinct SEI morphologies highlights the necessity of effective passivation by the SEI, as large-scale extended SEI growths negatively impact lithium-ion transport, contribute to capacity loss, and may accelerate battery failure.

Fluid-enhanced surface diffusion controls intraparticle phase transformations.

Phase transformations driven by compositional change require mass flux across a phase boundary. In some anisotropic solids, however, the phase boundary moves along a non-conductive crystallographic direction. One such material is LiXFePO4, an electrode for lithium-ion batteries. With poor bulk ionic transport along the direction of phase separation, it is unclear how lithium migrates during phase transformations. Here, we show that lithium migrates along the solid/liquid interface without leaving the particle, whereby charge carriers do not cross the double layer. X-ray diffraction and microscopy experiments as well as ab initio molecular dynamics simulations show that organic solvent and water molecules promote this surface ion diffusion, effectively rendering LiXFePO4 a three-dimensional lithium-ion conductor. Phase-field simulations capture the effects of surface diffusion on phase transformation. Lowering surface diffusivity is crucial towards supressing phase separation. This work establishes fluid-enhanced surface diffusion as a key dial for tuning phase transformation in anisotropic solids.

Quantifying and Elucidating Thermally Enhanced Minority Carrier Diffusion Length Using Radius-Controlled Rutile Nanowires.

The minority carrier diffusion length (LD) is a crucial property that determines the performance of light absorbers in photoelectrochemical (PEC) cells. Many transition-metal oxides are stable photoanodes for solar water splitting but exhibit a small to moderate LD, ranging from a few nanometers (such as α-Fe2O3 and TiO2) to a few tens of nanometers (such as BiVO4). Under operating conditions, the temperature of PEC cells can deviate substantially from ambient, yet the temperature dependence of LD has not been quantified. In this work, we show that measuring the photocurrent as a function of both temperature and absorber dimensions provides a quantitative method for evaluating the temperature-dependent minority carrier transport. By measuring photocurrents of nonstoichiometric rutile TiO2-x nanowires as a function of wire radius (19-75 nm) and temperature (10-70 °C), we extract the minority carrier diffusion length along with its activation energy. The minority carrier diffusion length in TiO2-x increases from 5 nm at 25 °C to 10 nm at 70 °C, implying that enhanced carrier mobility outweighs the increase in the recombination rate with temperature. Additionally, by comparing the temperature-dependent photocurrent in BiVO4, TiO2, and α-Fe2O3, we conclude that the ratio of the minority carrier diffusion length to the depletion layer width determines the extent of temperature enhancement, and reconcile the widespread temperature coefficients, which ranged from 0.6 to 1.7% K-1. This insight provides a general design rule to select light absorbers for large thermally activated photocurrents and to predict PEC cell characteristics at a range of temperatures encountered during realistic device operation.

Analyzing the dependence of oxygen incorporation current density on overpotential and oxygen partial pressure in mixed conducting oxide electrodes.

The oxygen incorporation reaction, which involves the transformation of an oxygen gas molecule to two lattice oxygen ions in a mixed ionic and electronic conducting solid, is a ubiquitous and fundamental reaction in solid-state electrochemistry. To understand the reaction pathway and to identify the rate-determining step, near-equilibrium measurements have been employed to quantify the exchange coefficients as a function of oxygen partial pressure and temperature. However, because the exchange coefficient contains contributions from both forward and reverse reaction rate constants and depends on both oxygen partial pressure and oxygen fugacity in the solid, unique and definitive mechanistic assessment has been challenging. In this work, we derive a current density equation as a function of both oxygen partial pressure and overpotential, and consider both near and far from equilibrium limits. Rather than considering specific reaction pathways, we generalize the multi-step oxygen incorporation reaction into the rate-determining step, preceding and following quasi-equilibrium steps, and consider the number of oxygen ions and electrons involved in each. By evaluating the dependence of current density on oxygen partial pressure and overpotential separately, one obtains the reaction orders for oxygen gas molecules and for solid-state species in the electrode. We simulated the oxygen incorporation current density-overpotential curves for praseodymium-doped ceria for various candidate rate-determining steps. This work highlights a promising method for studying the exchange kinetics far away from equilibrium.

Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes.

Many battery electrodes contain ensembles of nanoparticles that phase-separate on (de)intercalation. In such electrodes, the fraction of actively intercalating particles directly impacts cycle life: a vanishing population concentrates the current in a small number of particles, leading to current hotspots. Reports of the active particle population in the phase-separating electrode lithium iron phosphate (LiFePO4; LFP) vary widely, ranging from near 0% (particle-by-particle) to 100% (concurrent intercalation). Using synchrotron-based X-ray microscopy, we probed the individual state-of-charge for over 3,000 LFP particles. We observed that the active population depends strongly on the cycling current, exhibiting particle-by-particle-like behaviour at low rates and increasingly concurrent behaviour at high rates, consistent with our phase-field porous electrode simulations. Contrary to intuition, the current density, or current per active internal surface area, is nearly invariant with the global electrode cycling rate. Rather, the electrode accommodates higher current by increasing the active particle population. This behaviour results from thermodynamic transformation barriers in LFP, and such a phenomenon probably extends to other phase-separating battery materials. We propose that modifying the transformation barrier and exchange current density can increase the active population and thus the current homogeneity. This could introduce new paradigms to enhance the cycle life of phase-separating battery electrodes.

Surface electrochemistry of CO2 reduction and CO oxidation on Sm-doped CeO(2-x): coupling between Ce(3+) and carbonate adsorbates.

The efficient electro-reduction of CO2 to chemical fuels and the electro-oxidation of hydrocarbons for generating electricity are critical toward a carbon-neutral energy cycle. The simplest reactions involving carbon species in solid-oxide fuel cells and electrolyzer cells are CO oxidation and CO2 reduction, respectively. In catalyzing these reactions, doped ceria exhibits a mixed valence of Ce(3+) and Ce(4+), and has been employed as a highly active and coking-resistant electrode. Here we report an operando investigation of the surface reaction mechanism on a ceria-based electrochemical cell using ambient pressure X-ray photoelectron spectroscopy. We show that the reaction proceeds via a stable carbonate intermediate, the coverage of which is coupled to the surface Ce(3+) concentration. Under CO oxidation polarization, both the carbonate and surface Ce(3+) concentration decrease with overpotential. Under CO2 reduction polarization, on the other hand, the carbonate coverage saturates whereas the surface Ce(3+) concentration increases with overpotential. The evolution of these reaction intermediates was analyzed using a simplified two-electron reaction scheme. We propose that the strong adsorbate-adsorbate interaction explains the coverage-dependent reaction mechanism. These new insights into the surface electrochemistry of ceria shed light on the optimization strategies for better fuel cell electrocatalysts.

Modeling the impedance response of mixed-conducting thin film electrodes.

In this paper a novel numerical impedance model is developed for mixed-conducting thin films working as electrodes for solid oxide fuel cells. The relative importance of interfaces is considered by incorporating double layer contributions at the film/gas boundary. Simulations are performed on a model system, namely doped ceria, in a symmetric cell configuration using geometrically well-defined patterned metal current collectors. Results reveal that experimentally consistent bulk impedances and surface capacitances can be extracted using the model. The impedance response depends strongly on the pattern spacing of the current collector, and is attributed to the electronic in-plane drift-diffusion as well as to the interplay between the surface reaction resistance and the electronic/ionic bulk drift-diffusion resistance.

Intercalation pathway in many-particle LiFePO4 electrode revealed by nanoscale state-of-charge mapping.

The intercalation pathway of lithium iron phosphate (LFP) in the positive electrode of a lithium-ion battery was probed at the ∼40 nm length scale using oxidation-state-sensitive X-ray microscopy. Combined with morphological observations of the same exact locations using transmission electron microscopy, we quantified the local state-of-charge of approximately 450 individual LFP particles over nearly the entire thickness of the porous electrode. With the electrode charged to 50% state-of-charge in 0.5 h, we observed that the overwhelming majority of particles were either almost completely delithiated or lithiated. Specifically, only ∼2% of individual particles were at an intermediate state-of-charge. From this small fraction of particles that were actively undergoing delithiation, we conclude that the time needed to charge a particle is ∼1/50 the time needed to charge the entire particle ensemble. Surprisingly, we observed a very weak correlation between the sequence of delithiation and the particle size, contrary to the common expectation that smaller particles delithiate before larger ones. Our quantitative results unambiguously confirm the mosaic (particle-by-particle) pathway of intercalation and suggest that the rate-limiting process of charging is initiating the phase transformation by, for example, a nucleation-like event. Therefore, strategies for further enhancing the performance of LFP electrodes should not focus on increasing the phase-boundary velocity but on the rate of phase-transformation initiation.

Beyond Constant Current: Origin of Pulse-Induced Activation in Phase-Transforming Battery Electrodes.

Mechanistic understanding of phase transformation dynamics during battery charging and discharging is crucial toward rationally improving intercalation electrodes. Most studies focus on constant-current conditions. However, in real battery operation, such as in electric vehicles during discharge, the current is rarely constant. In this work we study current pulsing in LiXFePO4 (LFP), a model and technologically important phase-transforming electrode. A current-pulse activation effect has been observed in LFP, which decreases the overpotential by up to ∼70% after a short, high-rate pulse. This effect persists for hours or even days. Using scanning transmission X-ray microscopy and operando X-ray diffraction, we link this long-lived activation effect to a pulse-induced electrode homogenization on both the intra- and interparticle length scales, i.e., within and between particles. Many-particle phase-field simulations explain how such pulse-induced homogeneity contributes to the decreased electrode overpotential. Specifically, we correlate the extent and duration of this activation to lithium surface diffusivity and the magnitude of the current pulse. This work directly links the transient electrode-level electrochemistry to the underlying phase transformation and explains the critical effect of current pulses on phase separation, with significant implication on both battery round-trip efficiency and cycle life. More broadly, the mechanisms revealed here likely extend to other phase-separating electrodes, such as graphite.