Graphite is the most widely used anode material in lithium-ion batteries with over 98% market share. However, despite its first application over 30 years ago, the lithium insertion processes and associated dynamics in graphite remain poorly understood, especially for the dilute stages. A fundamental understanding of how the symmetry-breaking phase transitions occur pseudo-continuously under operating conditions is still lacking. Here, we provide a unified picture of ion intercalation dynamics during the dilute stages of graphite intercalation, using operando optical microscopy combined with random field Ising modelling. We show that during the dilute stages, single graphite particle undergoes rapid, localised avalanche-like (de)intercalation, leading to micron-sized regions (de)intercalating within seconds. These avalanches are reminiscent of phase transition behaviour seen in disordered materials such as martensitic transformations, Barkhausen noise and ferroelectric/elastic materials - associated with step changes in the order parameter, where the system changes from one phase to another under an applied driving force by jumping from one metastable state to another. Here, using a modified random field Ising model, we relate these avalanches to static disorder in graphite, which disrupts ion filling dynamics, leading to pseudo-continuous transitions between stages, accounting for the experimental electrochemistry profile as well as the temperature dependent avalanche dynamics. Finally, we develop a methodology to spatio-temporally analyse avalanches between intraparticle regions, revealing spatially heterogeneous connectivity and temporal patterns between regions during the dilute stages. Our work highlights the role of local and static disorder in eliciting unexpected phase transition behaviour, and provides new tools and concepts for studying layered battery materials.

Core-shell electrode particles are a promising morphology control strategy for high-performance lithium-ion batteries. However, experimental observations reveal that these structures remain prone to mechanical failure, with shell fractures and core-shell debonding occurring after a single charge. In this work, we present a novel, comprehensive computational framework to predict and gain insight into the failure of core-shell morphologies and the associated degradation in battery performance. The fully coupled chemo-mechano-damage model presented captures the interplay between mechanical damage and electrochemical behaviours, enabling the quantification of particle cracking and capacity fade. Both bulk material fracture and interface debonding are captured by utilising the phase field method. We quantify the severity of particle cracking and capacity loss through case studies on a representative core-shell system (NMC811@NMC532). The results bring valuable insights into cracking patterns, underlying mechanisms, and their impact on capacity loss. Surface cracks are found to initiate when a significantly higher lithium concentration accumulates in the core compared to the shell. Interfacial debonding is shown to arise from localised hoop stresses near the core-shell interface, due to greater shell expansion. This debonding develops rapidly, impedes lithium-ion transport, and can lead to more than 10\% capacity loss after a single discharge. Furthermore, larger particles may experience crack branching driven by extensive tensile zones, potentially fragmenting the entire particle. The framework developed can not only bring new insight into the degradation mechanisms of core-shell particles but also be used to design electrode materials with improved performance and extended lifetime.

Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated particle cracking behaviour. However, only the beginning of life has been considered and effects such as damage accumulation have been neglected. Here, a multi-physics phase field fatigue model has been developed to study crack propagation in battery electrode particles undergoing hundreds of cycles. In addition, we couple our electrochemo-mechanical formulation with X-ray CT imaging to simulate fatigue cracking of realistic particle microstructures. Using this modelling framework, non-linear crack propagation behaviour is predicted, leading to the observation of an exponential increase in cracked area with cycle number. Three stages of crack growth (slow, accelerating and unstable) are observed, with phenomena such as crack initialisation at concave regions and crack coalescence having a significant contribution to the resulting fatigue crack growth rates. The critical values of C-rate, particle size and initial crack length are determined, and found to be lower than those reported in the literature using static fracture models. Therefore, this work demonstrates the importance of considering fatigue damage in battery degradation models and provides insights on the control of fatigue crack propagation to alleviate battery capacity degradation.

Reliable digital twins of lithium-ion batteries must achieve high physical fidelity with sub-millisecond speed. In this work, we benchmark three operator-learning surrogates for the Single Particle Model (SPM): Deep Operator Networks (DeepONets), Fourier Neural Operators (FNOs) and a newly proposed parameter-embedded Fourier Neural Operator (PE-FNO), which conditions each spectral layer on particle radius and solid-phase diffusivity. Models are trained on simulated trajectories spanning four current families (constant, triangular, pulse-train, and Gaussian-random-field) and a full range of State-of-Charge (SOC) (0 % to 100 %). DeepONet accurately replicates constant-current behaviour but struggles with more dynamic loads. The basic FNO maintains mesh invariance and keeps concentration errors below 1 %, with voltage mean-absolute errors under 1.7 mV across all load types. Introducing parameter embedding marginally increases error, but enables generalisation to varying radii and diffusivities. PE-FNO executes approximately 200 times faster than a 16-thread SPM solver. Consequently, PE-FNO's capabilities in inverse tasks are explored in a parameter estimation task with Bayesian optimisation, recovering anode and cathode diffusivities with 1.14 % and 8.4 % mean absolute percentage error, respectively, and 0.5918 percentage points higher error in comparison with classical methods. These results pave the way for neural operators to meet the accuracy, speed and parametric flexibility demands of real-time battery management, design-of-experiments and large-scale inference. PE-FNO outperforms conventional neural surrogates, offering a practical path towards high-speed and high-fidelity electrochemical digital twins.

Non-invasive parametrisation of physics-based battery models can be performed by fitting the model to electrochemical impedance spectroscopy (EIS) data containing features related to the different physical processes. However, this requires an impedance model to be derived, which may be complex to obtain analytically. We have developed the open-source software PyBaMM-EIS that provides a fast method to compute the impedance of any PyBaMM model at any operating point using automatic differentiation. Using PyBaMM-EIS, we investigate the impedance of the single particle model, single particle model with electrolyte (SPMe), and Doyle-Fuller-Newman model, and identify the SPMe as a parsimonious option that shows the typical features of measured lithium-ion cell impedance data. We provide a grouped parameter SPMe and analyse the features in the impedance related to each parameter. Using the open-source software PyBOP, we estimate 18 grouped parameters both from simulated impedance data and from measured impedance data from a LG M50LT lithium-ion battery. The parameters that directly affect the response of the SPMe can be accurately determined and assigned to the correct electrode. Crucially, parameter fitting must be done simultaneously to data across a wide range of states-of-charge. Overall, this work presents a practical way to find the parameters of physics-based models.

Predicting lithium-ion battery lifetime is one of the greatest unsolved problems in battery research right now. Recent years have witnessed a surge in lifetime prediction papers using physics-based, empirical, or data-driven models, most of which have been validated against the remaining capacity (capacity fade) and sometimes resistance (power fade). However, there are many different combinations of degradation mechanisms in lithium-ion batteries that can result in the same patterns of capacity and power fade, making it impossible to find a unique validated solution. Experimentally, degradation mode analysis involving measuring the loss of lithium inventory, loss of active material at both electrodes, and electrode drift/slippage has emerged as a state-of-the-art requirement for cell degradation studies. In this paper we coupled five degradation mechanisms together for the first time. We also showed how three models with different levels of complexity can all fit the remaining capacity and resistance well, but only the model with five coupled degradation mechanisms could also fit the degradation modes at all temperatures. This work proves that validating only against capacity and power fade is no longer sufficient, and state-of-the-art experimental and modelling degradation studies should include degradation mode analysis for validation in the future.

Robotic cutting, or milling, plays a significant role in applications such as disassembly, decommissioning, and demolition. Planning and control of cutting in real-world scenarios in uncertain environments is a complex task, with the potential to benefit from simulated training environments. This letter focuses on sim-to-real transfer for robotic cutting policies, addressing the need for effective policy transfer from simulation to practical implementation. We extend our previous domain generalisation approach to learning cutting tasks based on a mechanistic model-based simulation framework, by proposing a hybrid approach for sim-to-real transfer based on a milling process force model and residual Gaussian process (GP) force model, learned from either single or multiple real-world cutting force examples. We demonstrate successful sim-to-real transfer of a robotic cutting policy without the need for fine-tuning on the real robot setup. The proposed approach autonomously adapts to materials with differing structural and mechanical properties. Furthermore, we demonstrate the proposed method outperforms fine-tuning or re-training alone.

High-throughput computing (HTC) is a pivotal asset in many scientific fields, such as biology, material science and machine learning. Applying HTC to the complex physics-based degradation models of lithium-ion batteries enables efficient parameter identification and sensitivity analysis, which further leads to optimal battery design and operating conditions. However, running physics-based degradation models comes with pitfalls, as solvers can crash or get stuck in infinite loops due to numerical errors. Also, how to pipeline HTC for degradation models has seldom been discussed. To fill these gaps, we have created ParaSweeper, a Python script tailored for HTC, designed to streamline parameter sweeping by running as many ageing simulations as computational resources allow, each with different parameters. We have demonstrated the capability of ParaSweeper based on the open-source platform PyBaMM, and the approach can also apply to other numerical models which solve partial differential equations. ParaSweeper not only manages common solver errors, but also integrates various methods to accelerate the simulation. Using a high-performance computing platform, ParaSweeper can run millions of charge/discharge cycles within one day. ParaSweeper stands to benefit both academic researchers, through expedited model exploration, and industry professionals, by enabling rapid lifetime design, ultimately contributing to the prolonged lifetime of batteries.

Challenges associated with in-service mechanical degradation of Li-ion battery cathodes has prompted a transition from polycrystalline to single crystal cathode materials. Whilst for single crystal materials, dislocation-assisted crack formation is assumed to be the dominating failure mechanism throughout battery life, there is little direct information about their mechanical behaviour, and mechanistic understanding remains elusive. Here, we demonstrated, using in situ micromechanical testing, direct measurement of local mechanical properties within LiNi0.8Mn0.1Co0.1O2 single crystalline domains. We elucidated the dislocation slip systems, their critical stresses, and how slip facilitate cracking. We then compared single crystal and polycrystal deformation behaviour. Our findings answer two fundamental questions critical to understanding cathode degradation: What dislocation slip systems operate in Ni-rich cathode materials? And how does slip cause fracture? This knowledge unlocks our ability to develop tools for lifetime prediction and failure risk assessment, as well as in designing novel cathode materials with increased toughness in-service.

Heterogeneities in lithium ion batteries can be significant factors in electrode under utilisation and degradation while charging. Bilayer electrodes have been proposed as a convenient and scalable way to homogenise the electrode response. In this paper, the design of a bilayer cathode for Li-ion batteries composed of separate layers of lithium nickel manganese cobalt oxide (NMC622) and lithium iron phosphate (LFP) is optimised using the multilayer Doyle-Fuller-Newman (M-DFN) model. Changes to the carbon binder domain, electrolyte volume fraction, and tortuosity provided the greatest control for improving Li-ion charge mobility. The optimised bilayer design was able to charge at 3C between 0-90% SOC in 18.6 minutes, achieving 4.4 mAh/cm2. Comparing the optimal bilayer to the LFP-only electrode, the bilayer achieved 41% higher capacity. Through mechanistic physics-based modelling, it was shown that the 3C charging improvement of the optimised bilayer was achieved by enabling a more homogeneous current density distribution through the thickness of the electrode and electrolyte depletion prevention. The findings were confirmed on a high-fidelity X-ray computed tomography (CT) based microstructural model. The results illustrate how modelling can be used to rapidly search novel electrode designs

Battery models generally fall into two categories: physics-based models and ECM models. Physics-based Doyle-Fuller-Newman (DFN) models can accurately simulate the battery internal electrochemical processes, but to properly account for thermal effects requires a strong coupling between a DFN model and a 3D thermal model, which is computationally unaffordable. Distributed Equivalent Circuit Network (ECN) models can perform simulations with high speed and reasonable accuracy. However, these models rely heavily on the characterisation experiments for ECN parameter identification, which is resource-intensive and can lead to inaccurate parametrisation outcomes due to internal thermal inhomogeneity. To harness the strengths of both models, we propose a computational framework to integrate electrochemical DFN model and 3D distributed ECN model together. Using this framework, we simulate constant current discharge experiments of Kokam 7.5 Ah pouch cell (Model SLPB75106100) and compare the simulations with the commonly-used lumped DFN-thermal model. The computational model outperforms the lumped DFN model at low-temperature and/or high C-rate scenarios significantly. The largest predicting error of the framework at 3 C-rate &Tam = 25oC and at 1 C-rate &Tam = 0 oC is approximately 1/3 of that for DFN model. At 3 C-rate &Tam = 5oC, the difference between these two can rise to 377 mV. By integrating DFN and 3D-distributed ECN together, the computational framework can simulate the complicated interplay between electrochemistry, thermal process, and electricity within a cell fast and accurately. We anticipate this computational framework to be a valuable toolset to assist researchers and engineers in the design and control of Li-ion batteries.

We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the isothermal Stefan--Maxwell equations, separating the thermodynamic forces that drive diffusion from the force that drives heat flow. The Onsager--Stefan--Maxwell transport-coefficient matrix is symmetric, and the second law of thermodynamics imbues it with simple spectral characteristics. This new approach allows for heat to be considered as a pseudo-species and proves equivalent to both the intuitive extension of Fick's law and the generalized Stefan--Maxwell equations popularized by Bird, Stewart, and Lightfoot. A general inversion process facilitates the unique formulation of flux-explicit transport equations relative to any choice of convective reference velocity. Stefan--Maxwell diffusivities and thermal diffusion factors are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and xenon. The framework is deployed to perform numerical simulations of steady three-dimensional thermodiffusion in a ternary gas.

Physics-based electrochemical battery models derived from porous electrode theory are a very powerful tool for understanding lithium-ion batteries, as well as for improving their design and management. Different model fidelity, and thus model complexity, is needed for different applications. For example, in battery design we can afford longer computational times and the use of powerful computers, while for real-time battery control (e.g. in electric vehicles) we need to perform very fast calculations using simple devices. For this reason, simplified models that retain most of the features at a lower computational cost are widely used. Even though in the literature we often find these simplified models posed independently, leading to inconsistencies between models, they can actually be derived from more complicated models using a unified and systematic framework. In this review, we showcase this reductive framework, starting from a high-fidelity microscale model and reducing it all the way down to the Single Particle Model (SPM), deriving in the process other common models, such as the Doyle-Fuller-Newman (DFN) model. We also provide a critical discussion on the advantages and shortcomings of each of the models, which can aid model selection for a particular application. Finally, we provide an overview of possible extensions to the models, with a special focus on thermal models. Any of these extensions could be incorporated into the microscale model and the reductive framework re-applied to lead to a new generation of simplified, multi-physics models.

Predicting lithium-ion battery degradation is worth billions to the global automotive, aviation and energy storage industries, to improve performance and safety and reduce warranty liabilities. However, very few published models of battery degradation explicitly consider the interactions between more than two degradation mechanisms, and none do so within a single electrode. In this paper, the first published attempt to directly couple more than two degradation mechanisms in the negative electrode is reported. The results are used to map different pathways through the complicated path dependent and non-linear degradation space. Four degradation mechanisms are coupled in PyBaMM, an open source modelling environment uniquely developed to allow new physics to be implemented and explored quickly and easily. Crucially it is possible to see 'inside' the model and observe the consequences of the different patterns of degradation, such as loss of lithium inventory and loss of active material. For the same cell, five different pathways that can result in end-of-life have already been found, depending on how the cell is used. Such information would enable a product designer to either extend life or predict life based upon the usage pattern. However, parameterization of the degradation models remains as a major challenge, and requires the attention of the international battery community.

For many practical applications, fully coupled three-dimensional models describing the behaviour of lithium-ion pouch cells are too computationally expensive. However, owing to the small aspect ratio of typical pouch cell designs, such models are well approximated by splitting the problem into a model for through-cell behaviour and a model for the transverse behaviour. In this paper, we combine different simplifications to through-cell and transverse models to develop a hierarchy of reduced-order pouch cell models. We give a critical numerical comparison of each of these models in both isothermal and thermal settings, and also study their performance on realistic drive cycle data. Finally, we make recommendations regarding model selection, taking into account the available computational resource and the quantities of interest in a particular study.

A model of a lithium-ion battery containing a cosolvent electrolyte is developed and implemented within the open-source PyBaMM platform. Lithium-ion electrolytes are essential to battery operation and normally contain at least two solvents to satisfy performance requirements. The widely used Doyle-Fuller-Newman battery model assumes that the electrolyte comprises a salt dissolved in a single effective solvent, however. This single-solvent approximation has been disproved experimentally and may hinder accurate battery modelling. Here, we present a two-solvent model that resolves the transport of ethylene carbonate (EC) and lithium salt in a background linear carbonate. EC concentration polarization opposes that of Li+ during cycling, affecting local electrolyte properties and cell-level overpotentials. Concentration gradients of Li+ can be affected by cross-diffusion, whereby EC gradients enhance or impede salt flux. A rationally parametrized model that includes EC transport predicts 6% more power loss at 4.5C discharge and ~0.32% more capacity loss after a thousand 1C cycles than its single-solvent equivalent. This work provides a tool to model more transport behaviour in the electrolyte that may affect degradation and enables the transfer of microscopic knowledge about solvation structure-dependent performance to the macroscale.

Lithium-ion battery manufacturing is a highly complicated process with strongly coupled feature interdependencies, a feasible solution that can analyse feature variables within manufacturing chain and achieve reliable classification is thus urgently needed. This article proposes a random forest (RF)-based classification framework, through using the out of bag (OOB) predictions, Gini changes as well as predictive measure of association (PMOA), for effectively quantifying the importance and correlations of battery manufacturing features and their effects on the classification of electrode properties. Battery manufacturing data containing three intermediate product features from the mixing stage and one product parameter from the coating stage are analysed by the designed RF framework to investigate their effects on both the battery electrode active material mass load and porosity. Illustrative results demonstrate that the proposed RF framework not only achieves the reliable classification of electrode properties but also leads to the effective quantification of both manufacturing feature importance and correlations. This is the first time to design a systematic RF framework for simultaneously quantifying battery production feature importance and correlations by three various quantitative indicators including the unbiased feature importance (FI), gain improvement FI and PMOA, paving a promising solution to reduce model dimension and conduct efficient sensitivity analysis of battery manufacturing.

Electrochemical impedance spectroscopy (EIS) is a widely used experimental technique for characterising materials and electrode reactions by observing their frequency-dependent impedance. Classical EIS measurements require the electrochemical process to behave as a linear time-invariant system. However, electrochemical processes do not naturally satisfy this assumption: the relation between voltage and current is inherently nonlinear and evolves over time. Examples include the corrosion of metal substrates and the cycling of Li-ion batteries. As such, classical EIS only offers models linearised at specific operating points. During the last decade, solutions were developed for estimating nonlinear and time-varying impedances, contributing to more general models. In this paper, we review the concept of impedance beyond linearity and stationarity, and detail different methods to estimate this from measured current and voltage data, with emphasis on frequency domain approaches using multisine excitation. In addition to a mathematical discussion, we measure and provide examples demonstrating impedance estimation for a Li-ion battery, beyond linearity and stationarity, both while resting and while charging.

The Python Battery Optimisation and Parameterisation (PyBOP) package provides methods for estimating and optimising battery model parameters, offering both deterministic and stochastic approaches with example workflows to assist users. PyBOP enables parameter identification from data for various battery models, including the electrochemical and equivalent circuit models provided by the popular open-source PyBaMM package. Using the same approaches, PyBOP can also be used for design optimisation under user-defined operating conditions across a variety of model structures and design goals. PyBOP facilitates optimisation with a range of methods, with diagnostics for examining optimiser performance and convergence of the cost and corresponding parameters. Identified parameters can be used for prediction, on-line estimation and control, and design optimisation, accelerating battery research and development.