The rate performance of any electrode or solid electrolyte material used in a battery is critically dependent on the migration barrier (Em) governing the motion of the intercalant ion, which is a difficult-to-estimate quantity both experimentally and computationally. The foundation for constructing and validating accurate machine learning (ML) models that are capable of predicting Em, and hence accelerating the discovery of novel electrodes and solid electrolytes, lies in the availability of high-quality dataset(s) containing Em. Addressing this critical requirement, we present a comprehensive dataset comprising 621 distinct literature-reported Em values calculated using density functional theory based nudged elastic band computations, across 443 compositions and 27 structural groups consisting of various compounds that have been explored as electrodes or solid electrolytes in batteries. Our dataset includes compositions corresponding to fully charged and/or discharged states of electrodes, with intermediate compositions incorporated in select instances. Crucially, for each compound, our dataset provides structural information, including the initial and final positions of the migrating ion, along with its corresponding Em in easy-to-use .xlsx and JSON formats. We envision our dataset to be highly useful for the scientific community, facilitating the development of advanced ML models that can predict Em precisely and accelerate materials discovery.
Ionic conductivity (σ) is one of the most important properties that is used to characterize materials used for electrochemical applications, such as a battery electrode or an electrolyte. Typically, ionic conduction is a thermally activated process defined by the Nernst-Einstein equation as,
where q and x are the charge and concentration of the intercalant (or the electroactive ion), respectively. D(x) is the diffusion coefficient of the intercalant that varies with x, T is the temperature and k is the Boltzmann constant. D(x) relates the diffusive flux (J) and the concentration gradient (∇ x of the intercalating species via the Fick's first law (J = -D(x) ∇ x). Further, D(x) can be written as,
D is the jump diffusion coefficient, which captures all the cross correlations among the individual atomic migrations and θ is the thermodynamic factor that captures the non-ideality of the solid solution (i.e., the interactions between the migrating ions and the host framework). θ is defined as , where μ is the chemical potential of the migrating ion. In solid electrodes and electrolytes, x is typically the site fraction of the migrating ion. For an ideal solid solution where each ionic hop has an identical hop frequency that is independent of the local concentration/configuration, D(x) becomes,
g is the geometric factor that determines how the diffusion channels are connected, f is the correlation factor, a and ν, are the hop distance and vibrational prefactor, respectively, and E is the activation energy of migration. Ion transport within a crystalline lattice occurs through ionic migration events, where an ion moves from its original or interstitial site in a lattice to a neighboring vacant site, via a transition state. The migration process is influenced by the energy landscape encountered by the ion during its movement, with the E playing a crucial role in determining the ease of ionic mobility and, consequently, the material's σ.
Extensive research has focused on enhancing ionic conductivity by minimizing E, as this directly improves the rate capabilities of battery systems. Previous studies have shown the underlying host structure to play a vital role in influencing D, such as the presence of interconnected prismatic sites leading to improved Na mobility in P2-type layered structures. In compositions like LiNiO, Li off-stoichiometry leading to Ni ions in the Li layers obstructing diffusion pathway can effect the Li-ion conductivity significantly. Indeed, dopants that stabilize the layered structure, such as Ti have been used to improve Na mobility. In the case of phosphates, nuclear magnetic resonance (NMR) studies reveal that intercalant diffusivity is not governed by a single, uniform barrier but by a distribution of local energy barriers that are dictated by the arrangement of neighboring transition metal cations. Additionally, subtle electrostatic distortions that screen electrostatic interactions between the intercalant and the anion framework have been shown to improve intercalant mobility in polyanionic structures.
Galvanostatic intermittent titration technique (GITT) measurements in Mn and Fe rich disordered rocksalt structures have revealed the importance of Li-exccess compositions, particle size, and the underlying redox process as some of the important factors that affect the intercalant diffusivity. Bonnick et al. illustrated the influence of poor electronic conductivity resulting in strong electrostatic interactions within thiospinel lattices (e.g., MgZrS) resulting in a reduction of ionic diffusivity. In summary, various structural and chemical modifications have been explored across different types of intercalation compounds, including layered, spinel, olivine, polyanionic, and other frameworks, to enhance ionic conductivity, with some approaches using targeted machine learning (ML) techniques as well. However, developing universal optimization strategies across a wide range of intercalation systems remains challenging due to the interplay between structure, composition, and other factors besides the lack of a robust E dataset that spans a diverse range of materials.
In general, estimating diffusivities or E using experimental techniques like variable temperature NMR, GITT, and electrochemical impedance spectroscopy (EIS), are either experimentally challenging or resource intensive. This is due to the extremely short time scales (10 s) or small length scales ( ~ few Å) of the elementary process of ionic hopping, influence of surface and structural chemistry of electrodes/electrolytes on the measurement, variations in sample preparation and measurement conditions resulting in differences in interfacial formation, bulk stoichiometry and defects, and specific equipment requirements (e.g., the need for inert ion-blocking electrodes in EIS). Thus, experimental NMR/GITT/EIS data documenting E is unavailable for a wide range of materials.
Computational methodologies to estimate E have gained prominence, since calculated E can be used as a screening metric within high-throughput workflows before experimental validation. Computational techniques include empirical approaches such as bond valence sum (BVS) analysis and nudged elastic band (NEB) calculations (usually based on first principles simulations) or molecular dynamics (MD). BVS analysis, though computationally swift, has accuracy limitations as it relies on an ionic bond model, making it more suitable for close-packed lattices with highly electronegative anions. NEB calculations strive to estimate the migration barrier within a potential energy surface (PES) constructed by either density functional theory (DFT) or interatomic potentials by modeling the ionic migration path using intermediate images that are connected by fictitious spring forces and subsequently relaxing the images to identify the saddle point that corresponds to the transition state. NEB calculations when performed in conjunction with DFT typically provide accurate E. However, the DFT-NEB approach is computationally intensive for large systems (>100 atoms), and its accuracy/convergence can depend on the chosen exchange-correlation (XC) functional within DFT. Classical MD (based on interatomic potentials) and ab-initio MD techniques can directly estimate D(x) at multiple T, thus yielding E from Equation (3), but are computationally demanding due to the time and length scales that need to be captured. Note that ab-initio MD calculations are generally more accurate in estimating E or D(x) compared to classical MD due to the more accurate PES constructed by first principles.
Some strategies have been explored to reduce the computational costs and constraints, while retaining the accuracy, of both the DFT-NEB and ab-initio MD approaches. For example, the 'pathfinder' approach in conjunction with the 'ApproxNEB' scheme aims to reduce the computational constraints of DFT-NEB by mitigating convergence issues via selection of a 'better' initial migration path for calculation. However, the scheme still requires performing a full DFT-NEB calculation and is prone to the underlying constraints of the DFT-NEB approach. Another pathway is integrating ab-initio MD simulations with machine learned interatomic potentials (MLIPs), where the MLIPs can theoretically provide higher computational speeds with the accuracy comparable to DFT. While several MLIP frameworks that are accurate remain chemistry-specific (i.e., there are high computational costs associated with training the MLIPs), the foundational or universal MLIPs have not been tested rigorously on D(x) or E predictions, yet. More importantly, we need datasets of E that are available over a wide-range of chemistries and structures to be able to test universal MLIPs in their utility in predicting E and/or build ML models that are tailored to accurately predict E that can be used for screening through materials.
In this work, we present a literature-based curated dataset of 621 DFT-NEB-derived E values across various compounds that have been studied as electrodes or solid electrolytes in lithium, sodium, potassium, and multivalent ion based battery systems. Our dataset includes fully charged and discharged states of electrode materials, with intermediate (non-stoichiometric) compositions considered in 30 cases. Additionally, we provide structural information for each compound, including the initial and final positions of the migrating ion, along with its corresponding energy barrier, which can be used in the construction of ML models that require structural inputs, such as graph-based models leveraging transfer learning. Our dataset includes a total of 275 distinct entries contributed by 99 systems exhibiting multiple migration pathways. We envision our dataset to be a powerful resource for the scientific research and industrial communities, enabling the development of robust ML models and MLIPs that can eventually accelerate materials discovery for batteries and other applications.