Na-ion batteries are promising alternatives to Li-ion systems for electrochemical energy storage because of the higher natural abundance and widespread distribution of Na compared to Li. High capacity anode materials, such as phosphorus, have been explored to realize Na-ion battery technologies that offer comparable performances to their Li-ion counterparts. While P anodes provide unparalleled capacities, the mechanism of sodiation and desodiation is not well-understood, limiting further optimization. Here, we use a combined experimental and theoretical approach to provide molecular-level insight into the (de)sodiation pathways in black P anodes for sodium-ion batteries. A determination of the P binding in these materials was achieved by comparing to structure models created via species swapping, ab initio random structure searching, and a genetic algorithm. During sodiation, analysis of P chemical shift anisotropies in NMR data reveals P helices and P at the end of chains as the primary structural components in amorphous NaP phases. X-ray diffraction data in conjunction with variable field Na magic-angle spinning NMR support the formation of a new NaP crystal structure (predicted using density-functional theory) on sodiation. During desodiation, P helices are re-formed in the amorphous intermediates, albeit with increased disorder, yet emphasizing the pervasive nature of this motif. The pristine material is not re-formed at the end of desodiation and may be linked to the irreversibility observed in the Na-P system.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification.

Using first-principles structure searching with density-functional theory (DFT), we identify a novel Fm 3̅ m phase of Cu 2 P and two low-lying metastable structures, an I 4̅3 d –Cu 3 P phase and a Cm –Cu 3 P 11 phase. The computed pair distribution function of the novel Cm –Cu 3 P 11 phase shows its structural similarity to the experimentally identified Cm –Cu 2 P 7 phase. The relative stability of all Cu–P phases at finite temperatures is determined by calculating the Gibbs free energy using vibrational effects from phonon modes at 0 K. From this, a finite-temperature convex hull is created, on which Fm 3̅ m –Cu 2 P is dynamically stable and the Cu 3– x P ( x < 1) defect phase Cmc 2 1 –Cu 8 P 3 remains metastable (within 20 meV/atom of the convex hull) across a temperature range from 0 to 600 K. Both CuP 2 and Cu 3 P exhibit theoretical gravimetric capacities higher than contemporary graphite anodes for Li-ion batteries; the predicted Cu 2 P phase has a theoretical gravimetric capacity of 508 mAh/g as a Li-ion battery electrode, greater than both Cu 3 P (363 mAh/g) and graphite (372 mAh/g). Cu 2 P is also predicted to be both nonmagnetic and metallic, which should promote efficient electron transfer in the anode. Cu 2 P’s favorable properties as a metallic, high-capacity material suggest its use as a future conversion anode for Li-ion batteries; with a volume expansion of 99% during complete cycling, Cu 2 P anodes could be more durable than other conversion anodes in the Cu–P system, with volume expansions greater than 150%. The structures and figures presented in this paper, and the code used to generate them, can be interactively explored online using .

The properties of materials depend heavily on their atomistic structure; knowledge of the possible stable atomic configurations that define a material is required to understand the performance of many technologically and ecologically relevant devices, such as those used for energy storage (A. F. Harper et al., 2020; Marbella et al., 2018). First-principles crystal structure prediction (CSP) is the art of finding these stable configurations using only quantum mechanics (A. F. Harper, Evans, et al., 2020). Density-functional theory (DFT) is a ubiquitous theoretical framework for finding approximate solutions to quantum mechanics; calculations using a modern DFT package are sufficiently robust and accurate that insight into real materials can be readily obtained. The computationally intensive work is performed by well-established, low-level software packages, such as CASTEP (Clark et al., 2005) or Quantum Espresso (Giannozzi et al., 2009), which are able to make use of modern highperformance computers. In order to use these codes easily, reliably and reproducibly, many high-level libraries have been developed to create, curate and manipulate the calculations from these low-level workhorses; matador is one such framework. Evans et al., (2020). matador: a Python library for analysing, curating and performing high-throughput density-functional theory calculations.

As the number of novel data-driven approaches to material science continues to grow, it is crucial to perform consistent quality, reliability and applicability assessments of model performance. In this paper, we benchmark the Materials Optimal Descriptor Network (MODNet) method and architecture against the recently released MatBench v0.1, a curated test suite of materials datasets. MODNet is shown to outperform current leaders on 4 of the 13 tasks, whilst closely matching the current leaders on a further 3 tasks; MODNet performs particularly well when the number of samples is below 10,000. Attention is paid to two topics of concern when benchmarking models. First, we encourage the reporting of a more diverse set of metrics as it leads to a more comprehensive and holistic comparison of model performance. Second, an equally important task is the uncertainty assessment of a model towards a target domain. By applying a distance metric in feature space, we found that significant variations in validation errors can be observed, depending on the imbalance and bias in the training set (i.e., similarity between training and application space). Both issues are often overlooked, yet important for successful real-world applications of machine learning in materials science and condensed matter.