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.

Inherent-state melting and the onset of glassy dynamics in two-dimensional supercooled liquids.

Below the onset temperature To, the equilibrium relaxation time of most glass-forming liquids exhibits glassy dynamics characterized by a super-Arrhenius temperature dependence. In this supercooled regime, the relaxation dynamics also proceeds through localized elastic excitations corresponding to hopping events between inherent states, i.e., potential-energy-minimizing configurations of the liquid. Despite its importance in distinguishing the supercooled regime from the high-temperature regime, the microscopic origin of To is not yet known. Here, we construct a theory for the onset temperature in two dimensions and find that an inherent-state melting transition, described by the binding-unbinding transition of dipolar elastic excitations, delineates the supercooled regime from the high-temperature regime. The corresponding melting transition temperature is in good agreement with the onset temperature found in various two-dimensional (2D) atomistic models of glass formers and an experimental binary colloidal system confined to a water-air interface. Additionally, we find the predictions for the renormalized elastic moduli to agree with the experimentally observed values for the latter 2D colloidal system. We further discuss the predictions of our theory on the displacement and density correlations at supercooled conditions, which are consistent with observations of the Mermin-Wagner fluctuations in experiments and molecular simulations.

Electric Fields and Charge Separation for Solid Oxide Fuel Cell Electrodes.

Activation losses at solid oxide fuel cell (SOFC) electrodes have been widely attributed to charge transfer at the electrode surface. The electrostatic nature of electrode-gas interactions allows us to study these phenomena by simulating an electric field across the electrode-gas interface, where we are able to describe the activation overpotential using density functional theory (DFT). The electrostatic responses to the electric field are used to approximate the behavior of an electrode under electrical bias and have found a correlation with experimental data for three different reduction reactions at mixed ionic-electronic conducting (MIEC) electrode surfaces (H2O and CO2 on CeO2; O2 on LaFeO3). In this work, we demonstrate the importance of decoupled ion-electron transfer and charged adsorbates on the performance of electrodes under nonequilibrium conditions. Finally, our findings on MIEC-gas interactions have potential implications in the fields of energy storage and catalysis.

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.

Theory of freezing point depression in charged porous media.

Freezing in charged porous media can induce significant pressure and cause damage to tissues and functional materials. We formulate a thermodynamically consistent theory to model freezing phenomena inside charged heterogeneous porous space. Two regimes are distinguished: free ions in open pore space lead to negligible effects of freezing point depression and pressure. On the other hand, if nanofluidic salt trapping happens, subsequent ice formation is suppressed due to the high concentration of ions in the electrolyte. In this case our theory predicts that freezing starts at a significantly lower temperature compared to pure water. In one dimension, as the temperature goes even lower, ice continuously grows until the salt concentration reaches saturation, all ions precipitate to form salt crystals, and freezing completes. Enormous pressure can be generated if initial salt concentration is high before salt entrapment. We show modifications to the classical nucleation theory due to the trapped salt ions. Interestingly, although the freezing process is enormously changed by trapped salts, our analysis shows that the Gibbs-Thompson equation on confined melting point shift is not affected by the presence of the electrolyte.

Tuning the stability of electrochemical interfaces by electron transfer reactions.

The morphology of interfaces is known to play a fundamental role in the efficiency of energy-related applications, such as light harvesting or ion intercalation. Altering the morphology on demand, however, is a very difficult task. Here, we show ways the morphology of interfaces can be tuned by driven electron transfer reactions. By using non-equilibrium thermodynamic stability theory, we uncover the operating conditions that alter the interfacial morphology. We apply the theory to ion intercalation and surface growth where electrochemical reactions are described using Butler-Volmer or coupled ion-electron transfer kinetics. The latter connects microscopic/quantum mechanical concepts with the morphology of electrochemical interfaces. Finally, we construct non-equilibrium phase diagrams in terms of the applied driving force (current/voltage) and discuss the importance of engineering the density of states of the electron donor in applications related to energy harvesting and storage, electrocatalysis, and photocatalysis.

Lithium-Battery Anode Gains Additional Functionality for Neuromorphic Computing through Metal-Insulator Phase Separation.

Specialized hardware for neural networks requires materials with tunable symmetry, retention, and speed at low power consumption. The study proposes lithium titanates, originally developed as Li-ion battery anode materials, as promising candidates for memristive-based neuromorphic computing hardware. By using ex- and in operando spectroscopy to monitor the lithium filling and emptying of structural positions during electrochemical measurements, the study also investigates the controlled formation of a metallic phase (Li7 Ti5 O12 ) percolating through an insulating medium (Li4 Ti5 O12 ) with no volume changes under voltage bias, thereby controlling the spatially averaged conductivity of the film device. A theoretical model to explain the observed hysteretic switching behavior based on electrochemical nonequilibrium thermodynamics is presented, in which the metal-insulator transition results from electrically driven phase separation of Li4 Ti5 O12 and Li7 Ti5 O12 . Ability of highly lithiated phase of Li7 Ti5 O12 for Deep Neural Network applications is reported, given the large retentions and symmetry, and opportunity for the low lithiated phase of Li4 Ti5 O12 toward Spiking Neural Network applications, due to the shorter retention and large resistance changes. The findings pave the way for lithium oxides to enable thin-film memristive devices with adjustable symmetry and retention.

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.