The thermodynamics of alkali metal ion intercalation into hard carbon is explained using free energy decomposition:

Here, ΔG _desolvis the free energy required for an ion to escape from its solvation shell, and its variation primarily governs the reaction rate and initial energy barrier of alkali metal ion intercalation; ΔG _bindis the free energy associated with ion binding to the carbon matrix (interlayer/defects on pore walls), which determines the magnitude and stability of the platform voltage—alkali metal ions in hard carbon achieve a low-potential platform only because of structural matching; ΔG _strainreflects the free energy associated with interlayer spacing expansion and structural reorganization, which is related to ionic radius and determines whether the material structure can withstand ion insertion, directly affecting cycling stability and platform capacity. The intercalation behavior of Li⁺, Na⁺, and K⁺in hard carbon differs due to variations in ionic radius, solvation energy, and ionization energy. The platform voltage and intercalation stability are the result of a trade-off among ΔG _desolv, ΔG _bind, and ΔG _strain. Li⁺has the smallest radius (≈0.76 Å) and can stably intercalate between graphite layers, resulting in a low-potential platform; Na⁺has a larger radius (≈1.02 Å), making it thermodynamically unfavorable in graphite, but in hard carbon, it benefits from the larger 002 interlayer spacing (d ₀₀₂≈0.37–0.39 nm) and the synergistic effect of closed micropores, enabling a stable low-potential platform (≈0.08–0.12 V vs Na/Na⁺). Compared to Na⁺, K⁺has an even larger ionic radius (≈1.38 Å), leading to differences in its storage mechanism in hard carbon materials relative to sodium ions. In hard carbon, K⁺typically exhibits a higher intercalation potential (≈0.2–0.3 V vs. K/K⁺), which is closely related to its larger ionic radius and lower ΔG _desolv. Its larger size may cause greater deformation of the hard carbon structure, thereby affecting its cycling stability. Such theoretical analyses provide a solid theoretical foundation for understanding the binding behavior of alkali metal atoms in various substrate systems.

Fortunately, this limitation is effectively mitigated in non-graphitizable HC materials. In electrochemical energy storage research, hard carbon materials are primarily synthesized from organic compounds or biomass-derived precursors through thermal treatment or chemical conversion processes (Figure 2). During carbonization, various reactions occur concurrently, including dehydrogenation and isomerization^[15]. Moreover, because the macromolecular structure of non-graphitizable carbon precursors does not undergo fluidization during thermal treatment, certain structural features are preserved. As a result, some derived hard carbon materials retain the microstructural and morphological characteristics of the original precursors, although their overall packing density remains relatively low. HC is a disordered carbon material composed of randomly oriented graphite layers, with an interlayer spacing of approximately 0.36–0.40 nm. The curved graphite layers and abundant nanopores in its structure together confer advantages such as high specific capacity, good electrochemical stability, and low cost, making it a highly promising anode material for SIBs.

Overall, the sodium storage behavior in hard carbon materials mainly comprises: (1) adsorption on surfaces, defect sites, and functional groups; (2) micropore filling; and (3) intercalation into graphitized carbon layers. In addition, the electrochemical charge–discharge curves of conventional hard carbons are generally divided into two regions: a plateau region below 0.1 V and a sloping region above 0.1 V. However, due to the inherent complexity of the HC structure, its microstructure is highly diverse, the relationship between interlayer spacing and nanoscale pores remains unclear, and the coupling between capacity magnitude and sodium storage mechanisms is not well understood. As a result, significant uncertainty persists regarding the intercalation mechanism, which hinders further optimization and design of carbon-based anode materials^[17-18]. The “insertion–adsorption” model initially proposed for sodium ion storage mechanisms^[19]describes a structure in which aromatic fragments are randomly stacked like a house of cards, forming parallel graphite-like nanodomains and nanoscale pore regions. As research has progressed, this model has evolved into an “adsorption–insertion” mechanism: when HC materials discharge from 0.1 V to 0.001 V, the interlayer spacing expands from 3.96 Å to 4.16 Å, indicating that the plateau region corresponds to an intercalation mechanism^[20]. For example, Qiu et al.^[21]conducted systematic electrochemical analyses of undoped heteroatom-free nanostructured materials, combined with in situ/ex situ experimental techniques, and found that in the early stage of sodium ion intercalation, Na⁺first adsorbs onto defect sites in hard carbon, resulting in a sloping voltage curve. Subsequently, Na⁺is inserted into the interlayers of graphite crystallites at appropriate spacings, forming NaC _xcompounds, analogous to lithium ion insertion in graphite, thereby exhibiting a typical low-voltage plateau feature. When the interlayer spacing exceeds 0.4 nm, such ultra-large interlayer-spaced graphitized carbon layers, together with conventional “defects” (such as pores, edges, and heteroatoms), can contribute to the capacity in the sloping region above 0.1 V. At an interlayer spacing of 0.36–0.40 nm, pseudo-graphitized carbon stores sodium via an “interlayer insertion” mechanism, and the resulting NaC₈can provide a theoretical plateau capacity of 279 mAh·g^-1. Carbon materials with an interlayer spacing of less than 0.36 nm, resembling graphitized carbon, are unable to store sodium. Subsequently, studies have proposed a three-stage synergistic sodium storage mechanism of “adsorption–insertion–filling”^[22]: throughout the sodiation process, no insertion of Na⁺between carbon layers occurs, and the sloping capacity can be attributed to the adsorption of Na⁺on defect sites (>1 V) and on disordered, isolated graphene sheets (1–0.1 V), while the plateau capacity arises from mesopore filling (<0.1 V). Even when the battery discharges to 0 V, the d ₀₀₂peak does not shift. The continuous evolution of these mechanisms provides a new theoretical basis and research perspective for the structural regulation and design of carbon-based materials (Figure 3). However, constrained by experimental conditions and the resolution limitations of various characterization techniques, carbon materials from different sources generally exhibit structural heterogeneity and widespread defect distributions, leading to certain specialized sodium storage mechanisms that remain insufficiently revealed and confirmed. At the same time, traditional theoretical computational methods are limited by temporal and spatial scales, making it difficult to perform comprehensive and effective modeling and validation of the aforementioned mechanisms. The rise of ML methods, however, offers new research pathways and tools for overcoming the limitations of traditional computational approaches and exploring complex sodium storage behaviors.

In materials science, the key to applying ML lies in constructing an appropriate model that relies on a dataset capable of accurately characterizing the relationship between features (such as binding energy or physicochemical properties) and material performance. Next, an appropriate ML algorithm is selected to train this dataset, and the model’s predictive capability is typically evaluated by comparing its output with the true values of data not used in training. In contrast, traditional materials computation methods usually focus solely on obtaining numerical values, while neglecting the potentially hidden important information and underlying relationships within vast but underexplored “redundant data,” which researchers find difficult to uncover based on experience alone. By contrast, ML algorithms offer a more efficient cognitive pathway, enabling optimized solutions to complex problems through the construction of suitable models. As shown in Figure 5,common ML algorithms can be broadly categorized into three types: supervised learning, unsupervised learning, and reinforcement learning. Supervised learning can be further subdivided into regression and classification. Regression is used to analyze the relationship between continuous variables in a dataset and target properties, while classification assigns samples to different categories based on relationships among the data. The hallmark of unsupervised learning is that no explicit input or output variables are predefined in the dataset; its primary task is to identify latent structures, key variables, or data clustering patterns within the dataset. As traditional computational methods continue to advance, the scale of generated data has grown exponentially, often accompanied by issues such as complex structures and information clutter, which has increasingly driven the widespread application of unsupervised ML algorithms in materials data processing. Unlike the two aforementioned approaches, reinforcement learning continuously acquires environmental feedback to dynamically optimize model parameters, exhibiting strong adaptive capabilities and gradually emerging as a key research focus in intelligent materials manufacturing and complex systems modeling.

Due to the complex microstructure of carbon-based anode materials, current research still lacks a systematic analysis and elucidation of the relationship between hard carbon structure and its sodium storage performance. Data-driven ML methods are gradually emerging as crucial tools for analyzing experimental and theoretical data, and for uncovering key relationships between the structure and performance of battery materials. As machine learning applications in electrode material research deepen, prediction results are used to provide confidence intervals and construct calibration curves, thereby assessing the consistency between model outputs and the true distribution. Predicted values from neural network models, random forest models, binary logistic regression models, and others are employed as key metrics. Meanwhile, by integrating methods such as Monte Carlo sampling to account for experimental characterization errors (e.g., deviations in interlayer spacing measurements, uncertainties in pore volume fractions), uncertainty propagation analysis can be performed, helping to understand how input perturbations are transmitted to predictions of capacity and cycling stability. Through SHapley Additive exPlanations (SHAP value analysis) and Permutation Importance (a feature importance method), it is possible to quantitatively identify the structural parameters that contribute most significantly to model outputs. For example, Liu et al.^[33]Using ML methods, key structural parameters are jointly analyzed with thermodynamic and kinetic properties, systematically summarizing and comparing the structure and performance of different types of carbon materials, and evaluating the key factors influencing sodium storage performance (Figure 6). At the same time, attempts are made to construct performance prediction models based on key structural parameters, exploring the pathways through which structural regulation affects sodium storage performance. The research results indicate that the sodium storage mechanism of the target carbon material is dominated by intercalation behavior, supplemented by a certain degree of adsorption and pore-filling behavior. A moderate degree of crystallinity helps achieve high specific capacity and a low voltage platform; meanwhile, a medium level of defect content facilitates rapid (de)intercalation of sodium ions and maintains the structural stability of the material during cycling. k-fold cross-validation (such as repeated stratified k-fold cross-validation, k=10) is employed, and validation is conducted using independent external datasets covering different precursors and carbonization process conditions. In addition, the F1-score (the weighted harmonic mean of precision and recall) is introduced to provide a comprehensive evaluation of classifier performance (with a range from 0 to 1, where values closer to 1 indicate better performance). The Receiver Operating Characteristic–Area Under Curve (ROC-AUC) is used to evaluate a composite metric that reflects both sensitivity and specificity for continuous variables; the AUC value ranges from 0 to 1, with higher values indicating better model performance. By applying two types of classification models separately to classify high-capacity and low-capacity samples, the model’s performance can be assessed more comprehensively, avoiding evaluation bias arising from class imbalance. Experimental results show that by regulating structural parameters such as carbon layer size, interlayer spacing, and defect distribution, it is promising to optimize and enhance the sodium storage performance of carbon materials. This study demonstrates the great potential of ML in battery material research, providing a practical and viable research approach for the development of high-performance carbon materials, and also indicates that the combination of experimental databases and ML methods will play an important role in advancing scientific research and industrializing new energy materials.

Due to the complex spatial distribution and diverse composition of the internal structure of graphite anodes, the embedding process of AM ions within them also exhibits diversity and complexity. To reveal the chemical nature of sodium ion aggregation, Li et al.^[34]conducted a systematic study on the aggregation behavior of Na⁺in graphite anodes. First, they used DFT simulations to model the entire process of Na⁺gradually embedding into graphite and forming dynamic sodium clusters. Subsequently, they combined ML methods to perform an in-depth analysis of the energy data generated during this formation process (Fig. 7a–c). The study found that the clustering behavior of sodium ions is closely related to the different interactions they exhibit in carbon materials, and the analytical results are highly consistent with previous experimental observations. The combined use of ML and DFT not only enables in-depth modeling of the intercalation behavior of AM atoms in carbon materials but also establishes a direct correspondence with experimental results. The synergistic effect of these two approaches provides new insights for DFT-based research, effectively advancing the understanding of Na⁺storage mechanisms and demonstrating the potential to become a general research strategy. By leveraging data-driven methods, this approach reveals the intrinsic relationship between sodium storage performance and material structural parameters, providing theoretical support for constructing a universal structure–performance mapping for carbon materials. This, in turn, facilitates the design optimization and performance enhancement of disordered carbon anode materials in battery technologies.

Chen et al.^[35]constructed a hard carbon structure–performance database comprising 503 data sets, based on previously reported experimental data. The study employed various machine learning models, including random forests, gradient boosting decision trees (GBDT), and extreme gradient boosting (XGB), combined with cross-validation and data augmentation techniques, to predict and analyze the discharge performance of hard carbon materials. By comparing and fitting multiple data sets, the aim was to more accurately quantify the cycling stability of hard carbon materials. Through feature importance analysis, key structural features influencing discharge performance were effectively identified, allowing for adjustments to hard carbon anode parameters. Violin plots and scatter plots were constructed as output feature datasets (Figure 8a),and, in combination with unique ML models, it was concluded that SIBs achieve optimal multi-performance of hard carbon materials during discharge. The optimal structural parameters for SIBs to attain the best electrochemical performance during discharge—such as capacity performance and cycle retention—are derived from the Catboost model (Figures 8b and c).From the Catboost model, it was found that the structural parameters associated with high multi-performance partially overlap with those associated with high capacity, suggesting that high reversible capacity can be achieved under high multi-performance conditions; however, the underlying theoretical connections between these parameters still require further exploration. Chen et al.^[36]used small-angle X-ray scattering (SAXS) to reveal the fractal dimension (D), which was identified as a descriptor of disorder in hard carbon structures under data-driven approaches and was correlated with electrochemical and structural characteristics. As Dincreases, the pseudo-graphite domains decrease, and the carbon layers become more curved, leading to an increase in closed pores. With the increase in D, the diffusion coefficient decreases, resulting in a lower slope capacity percentage in SIBs and narrowing the gap between structural characterization and actual performance. It was demonstrated that, above 0.1 V vs. Na⁺/Na, sodium ion transport is primarily controlled by surface-driven processes, such as the adsorption of Na⁺at edge sites and structural defects. These sites provide fast and stable channels for ion migration, thereby enhancing rate performance in the sloped voltage region. Conversely, in the low-voltage plateau region, reversible capacity and charge-transfer kinetics are influenced by pore filling and interlayer insertion, both of which are diffusion-controlled processes.