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Two low-expansion Li-ion cathode materials with promising multi-property performance


We have identified CrOF4 and NbFe3(PO4)6 as candidate cathodes with density functional theory (DFT) calculations which suggest a useful balance of low chemical expansion and gravimetric energy density. Low chemical expansion is a likely requirement for high cycle batteries and the employment of solid electrolytes. CrOF4 and NbFe3(PO4)6 have predicted average voltages of 5.1 and 4.0 V and chemical expansion less than 3% and 1% within the stoichiometric range of 0 to 1 Li per formula unit, respectively, significantly outperforming commonly used cathode materials. While practical energy densities can be challenging to estimate with DFT calculations, DFT suggests that these exhibit gravimetric capacity densities in excess of 200 and 100 Ah/kg and gravimetric energy density in excess of 1020 and 400 Wh/kg, respectively, depending on irreversible processes during cycling. These were identified by screening approximately 38,000 compounds using statistical models trained on available data and physically motivated descriptors.

Imapct statement

Renewable power sources such as solar and wind energy require stable, long lasting grid energy-storage systems that can hold and distribute energy when the sun is set. Battery cathodes with high mechanical durability are required for high cycle applications approaching 1000 or more cycles, including grid and electric vehicle applications. However, useful battery cathodes must also satisfy a number of other constraints, including high energy density, high rate capability, and electrolyte compatibility in addition to sustainability requirements such as elimination of cobalt and other elements that are expensive or are acquired at the expense of ethical issues. Historical approaches to the identification of new cathodes have focused largely on the optimization of a single of these properties rather than a holistic optimization. Here we identify two new cathode candidates that satisfy a useful balance of the spectrum of required cathode properties, including minimal chemical expansion for maximization of cycle life, smaller than commonly employed cathodes. These new cathodes were identified using a data driven approach that identifies promising multi-property materials through statistical models. This approach represents a new paradigm for materials search that directly addresses the largest bottleneck for materials deployment: multi-property optimization.

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Data availability

Data were gathered from the Materials Project Database, through the associated API and are freely available to other researchers. In-house code was written to compute and consolidate the features used to describe the set of materials in the article. It is not published, but can be requested by contacting the corresponding author.


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This work was supported by Toyota Research Institute, the Stanford TomKat center, the Stanford StorageX program, the Knight-Hennessy Scholar program at Stanford, and NSF GRFP Grant No. DGE-1656518. Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.


We acknowledge funding from Toyota Research Institute, the Stanford TomKat center, the Stanford StorageX program, the Knight-Hennessy Scholar program at Stanford, and NSF GRFP Grant No. DGE-1656518.

Author information




All authors contributed to the study design. Data preparation and statistical processing were performed by N.Z. Computational data collection and analysis were performed by B.R. The drafts of the manuscript were written by B.R., N.Z., and E.R. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Brandi Ransom.

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The authors have no conflicts of interest to declare that are relevant to the content of this article.



DFT calculations

DFT training data values for all metrics in the “Discussion of top candidates” section were taken from the Battery Explorer portion of Materials Project in July, 2017. The DFT data contained in the Battery Explorer are computed using lithiated versions of the material at varying amounts of lithiation. Capacity and energy density in this training set for most compounds are computed assuming one lithium per transition-metal atom (e.g., FePO\(_4\) is lithiated to LiFePO\(_4\)). However, some other compounds, including CoO\(_2\) are lithiated to Li\(_0.5\)CoO\(_2\) due to the knowledge of a phase transition at this state of charge, setting the limit of reversible capacity.

DFT calculations were performed using the Projector-Augmented Wave pseudopotential implementation of the Vienna Ab Initio Simulation Package, version 5.4.1. In the DFT calculations, electron exchange and correlation effects are described by the generalized gradient approximation (GGA+U) functional of PBE. Wave functions are expanded in a plane-wave basis set with a kinetic energy cutoff of 520 eV using tetrahedron smearing of 200 meV. For each material, the k-point grid (either Monkhorst–Pack or Gamma centered), electronic relaxation convergence thresholds, valence electrons considered by the potential, cell volume, and number of atoms are provided in Table VII. Ionic relaxation convergence thresholds are 10× the value of the electronic convergence thresholds.

The +U adjustment was also added to d orbitals for transition metals in all calculations except for TiO\(_2\), and these values can be found in Table VII. Values of U here were chosen to reproduce the redox reaction energy measured experimentally.63,64 These choices of U were made in part to facilitate comparison with calculations in the Materials Project, which utilizes the same U parameters. More details on the method of mixing GGA and GGA+U energies can be found at Materials Project documentation

To add lithium to crystal structures that do not contain lithium, beginning with one unit cell of the unlithiated structure (ranging in size from 20 to 102 atoms), lithium atoms were added one by one and electronically and structurally relaxed between each added atom. Approximate configurations for Li atoms were obtained by placing them in locations coordinated by anions and within void spaces in the crystal structure. Any errors associated with these configurations are expected to lead to smaller cell energies, making the computed voltage a lower bound on the actual voltage.

Role of structural features

A feature of our statistical model is that it can resolve stoichiometrically identical compositions with differing crystal structures due to the incorporation of some structural features. These features include functions of ionic radii to describe the free space within the unit cell. Figure 8 shows the range of model confidences in materials with different structures but the same composition (stoichiometry). For example, in the compositional family of CoPO\(_4\) compounds, the compounds are generally ranked with a positive probability, but we see more than a \(30\%\) change between the lowest ranked and the top ranked compound in the compositional family. Our DFT calculations are compared to the Materials Project DFT calculations and experimental measurements for common cathodes in Table IV to assess accuracy of the predictions. Chemical expansion is among the more challenging quantities to predict, with deviations between DFT and experimental measurements of several percent. These may be due to a combination of DFT issues (treatment of van der Waals interactions, choice of +U parameter), structural ambiguity of the Li atom positions in large low symmetry unit cells, and potentially experimental issues, phase transformations, and kinetic effects. We have performed structural annealing calculations on CrOF\(_4\) and NbFe\(_3\)(PO\(_4\))\(_6\) that suggest variations of several percents in predicted strain can occur throughout the lithium concentrations studied here.

Table VII The relevant parameters for the DFT relaxations discussed in this work are presented.
Figure 7

Comparison of low-dimensional t-distributed stochastic neighbor embedding (t-SNE) projections of training data distribution (left) to the distribution of candidate materials predicted to be promising (right). The gray background in both images depicts the space of more than 38,000 screened materials. On the right is a color-coded t-SNE plot of the top compounds screened by different models, specifically the combined label, energy density, voltage, and strain. The proximity of the prediction points to our training points suggests a higher degree of confidence in those predictions (right). Additionally, we find that there are large regions of materials space where little training data exist (left), suggesting opportunities for targeted data collection.

Figure 8

Distributions for different compositional families sorted by least probable (gray) and most probable (green) for the combined label classifier. These particular compositions are chosen because they exhibit a variety of crystal structures, depicted as variations within each composition. This suggests that structural features can play a role in distinguishing between different structural candidates, beyond features that capture only the composition.

Figure 9

Distribution of feature-label correlation coefficients for each label: (a) average voltage, (b) energy density, (c) capacity, (d) strain, and (e) the combined label. This shows that the features are not correlated with any of the properties, which reinforces the necessity of multi-feature optimization.

Degree of extrapolation in the predictions

Most machine learning approaches are aimed at interpolating between training data and would not be expected to perform well in regions where there is sparse training data. However, the incorporation of physically motivated features here brings some possibility for extrapolation. Figure 7 in the Appendix shows a 2D t-SNE projection of the data, indicating that some predictions lie within the entire training data set and some do not. This plot indicates that enhanced data collection in the unexplored spaces may yield fruitful cathodes.

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Ransom, B., Zhao, N., Sendek, A.D. et al. Two low-expansion Li-ion cathode materials with promising multi-property performance. MRS Bulletin (2021).

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