Correction to: Nature Energyhttps://doi.org/10.1038/s41560-023-01414-5, published online 3 January 2024. In the version of this article initially published, lithium (green, “Li”) and sodium (purple, “Na”) color key labels in Fig. 3a,d,e were interchanged and are now amended in the HTML and PDF versions of the article.

Transport electrification and grid storage hinge largely on fast-charging capabilities of Li- and Na-ion batteries, but anodes such as graphite with plating issues drive the scientific focus towards anodes with slopped storage potentials. Here we report fast charging of ampere-hour-level full Na-ion batteries within about 9 minutes for continuous 3,000 cycles based on hard carbon anodes. These anodes, in addition to displaying a sloped storage voltage, provide capacity at a nearly constant voltage just above the plating potential, without observing Na-metal plating under high areal capacity. Comparing the electrochemical behaviour of Li and Na in hard carbon through experimental and computational techniques, a unified storage mechanism relying on the dimensions of wedge nanopores and drawing parallels with underpotential deposition for metals is brought forward, providing a rational guide for achieving fast storage in hard carbon anodes.

Phase separation during the lithiation of redox-active materials is a critical factor affecting battery performance, including energy density, charging rates, and cycle life. Accurate physical descriptions of these materials are necessary for understanding underlying lithiation mechanisms, performance limitations, and optimizing energy storage devices. This work presents an extended regular solution model that captures mutual interactions between sublattices of multi-sublattice battery materials, typically synthesized by metal substitution. We apply the model to phospho-olivine materials and demonstrate its quantitative accuracy in predicting the composition-dependent redox shift of the plateaus of LiMn_yFe_1-yPO₄ (LFMP), LiCo_yFe_1-yPO₄ (LFCP), LiCo_xMn_yFe_1-x-yPO₄ (LFMCP), as well as their phase separation behavior. Furthermore, we develop a phase-field model of LFMP that consistently matches experimental data and identifies LiMn_0.4Fe_0.6PO₄ as a superior composition that favors a solid solution phase transition, making it ideal for high-power applications.

There are several questions and controversies regarding the Na storage mechanism in hard carbon. This springs from the difficulty of probing the vast diversity of possible configurational environments for Na storage, including surface and defect sites, edges, pores, and intercalation morphologies. In the effort to explain the observed voltage profile, typically existing of a voltage slope section and a low-voltage plateau, several experimental and computational studies have provided a variety of contradicting results. This work employs density functional theory to thoroughly examine Na storage in hard carbon in combination with electrochemical experiments. Our calculation scheme disentangles the possible interactions by evaluating the enthalpies of formation, shedding light on the storage mechanisms. Parallel evaluation of the Li and K storage, and comparison with experiments, put forward a unified reaction mechanism for the three alkali metals. The results underline the importance of exposed metal surfaces and metal-carbon interfaces for the stability of the pore-filling mechanism responsible for the low-voltage plateau, in excellent agreement with the experimental voltage profiles. This generalized understanding provides insights into hard carbons as negative electrodes and their optimized properties.

The potential of the metal–organic framework UiO-66 and its functionalized derivatives for their utilization in the ⁹⁹Mo/^99mTc generator was assessed. Molybdenum adsorption experiments, structure characterization, molecular simulations and column experiments with molybdenum-99 were carried out. The results showed that the maximum molybdenum adsorption capacity achieved for UiO-66 was 335 mg g⁻¹. Adsorption on the surface of the UiO-66 occurs via electrostatic interaction and DFT calculations verified the enhanced affinity between the adsorbents and the molybdenum ions by Zr-O-Mo coordination, anion-π as well as hydrogen bonds. In addition, the performance of a ⁹⁹Mo/^99mTc generator fabricated with Form-UiO-66 was evaluated. The results showed that adsorption was comparable with the experiments using non-active molybdenum and that the ^99mTc elution efficiency of around 70% could be achieved without zirconium breakthrough.

Despite the lower gravimetric capacity, Li ₄ Ti ₅ O ₁₂ is an important alternative to graphite anodes, owing to its excellent high temperature stability, high rate capability, and negligible volume change. Although surfaces with lithium compositions exceeding Li ₇ Ti ₅ O ₁₂ were observed previously during the first charge-discharge cycles, no stable reversible capacities were achieved during prolonged cycling. Here, structural engineering has been applied to enhance the electrochemical performance of epitaxial Li ₄ Ti ₅ O ₁₂ thin films as compared to polycrystalline samples. Variation in the crystal orientation of the Li ₄ Ti ₅ O ₁₂ thin films led to distinct differences in surface morphology with pyramidal, rooftop, or flat nanostructures for respectively (100), (110), and (111) orientations. High discharge capacities of 280-310 mAh·g ^-1 were achieved due to significant surface contributions in lithium storage. The lithiation mechanism of bulk Li ₄ Ti ₅ O ₁₂ thin films was analyzed by a phase-field model, which indicated the lithiation wave to be moving faster along the grain boundaries before moving inward to the bulk of the grains. The (100)-oriented Li ₄ Ti ₅ O ₁₂ films exhibited the highest capacities, the best rate performance up to 30C, and good cyclability, demonstrating enhanced cycle life and doubling of reversible capacities in contrast to previous polycrystalline studies.

The original HTML version of this Article omitted to list Zhengcao Li as a corresponding author. Correspondingly, the original PDF version of this Article incorrectly stated that ‘Correspondence and requests for materials should be addressed to M.W. (email: m.wagemaker@tudelft.nl)’, instead of the correct ‘Correspondence and requests for materials should be addressed to Z.L. (email: zcli@tsinghua.edu.cn) or to M.W. (email: m.wagemaker@tudelft.nl)’. This has been corrected in both the PDF and HTML versions of the Article.

Computational modeling is vital for the fundamental understanding of processes in Li-ion batteries. However, capturing nanoscopic to mesoscopic phase thermodynamics and kinetics in the solid electrode particles embedded in realistic electrode morphologies is challenging. In particular for electrode materials displaying a first order phase transition, such as LiFePO₄, graphite, and spinel Li₄Ti₅O₁₂, predicting the macroscopic electrochemical behavior requires an accurate physical model. Herein, a thermodynamic phase field model is presented for Li-ion insertion in spinel Li₄Ti₅O₁₂ which captures the performance limitations presented in literature as a function of all relevant electrode parameters. The phase stability in the model is based on ab initio density functional theory calculations and the Li-ion diffusion parameters on nanoscopic nuclear magnetic resonance (NMR) measurements of Li-ion mobility, resulting in a parameter free model. The direct comparison with prepared electrodes shows good agreement over three orders of magnitude in the discharge current. Overpotentials associated with the various charge transport processes, as well as the active particle fraction relevant for local hotspots in batteries, are analyzed. It is demonstrated which process limits the electrode performance under a variety of realistic conditions, providing comprehensive understanding of the nanoscopic to microscopic properties. These results provide concrete directions toward the design of optimally performing Li₄Ti₅O₁₂ electrodes.

The main challenge of sodium-ion batteries is cycling stability, which is usually compromised due to strain induced by sodium insertion. Reliable high-voltage cathode materials are needed to compensate the generally lower operating voltages of Na-ion batteries compared to Li-ion ones. Herein, density functional theory (DFT) computations were used to evaluate the thermodynamic, structural, and kinetic properties of the high voltage λ-Mn₂O₄ and λ-Mn_1.5Ni_0.5O₄ spinel structures as cathode materials for sodium-ion batteries. Determination of the enthalpies of formation reveal the reaction mechanisms (phase separation vs solid solution) during sodiation, while structural analysis underlines the importance of minimizing strain to retain the metastable sodiated phases. For the λ-Mn_1.5Ni_0.5O₄ spinel, a thorough examination of the Mn/Ni cation distribution (dis/ordered variants) was performed. The exact sodiation mechanism was found to be dependent on the transition metal ordering in a similar fashion to the insertion behavior observed in the Li-ion system. The preferred reaction mechanism for the perfectly ordered spinel is phase separation throughout the sodiation range, while in the disordered spinel, the phase separation terminates in the 0.625 < x < 0.875 concentration range and is followed by a solid solution insertion reaction. Na-ion diffusion in the spinel lattice was studied using DFT as well. Energy barriers of 0.3-0.4 eV were predicted for the pure spinel, comparing extremely well with the ones for the Li-ion and being significantly better than the barriers reported for multivalent ions. Additionally, Na-ion macroscopic diffusion through the 8a-16c-8a 3D network was demonstrated via molecular dynamics (MD) simulations. For the λ-Mn_1.5Ni_0.5O₄, MD simulations at 600 K bring forward a normal to inverse spinel half-transformation, common for spinels at high temperatures, showing the contrast in Na-ion diffusion between the normal and inverse lattice. The observed Ni migration to the tetrahedral sites at room temperature MD simulations explains the kinetic limitations experienced experimentally. Therefore, this work provides a detailed understanding of the (de)sodiation mechanisms of high voltage λ-Mn₂O₄ and λ-Mn_1.5Ni_0.5O₄ spinel structures, which are of potential interest as cathode materials for sodium-ion batteries.

Electrical mobility demands an increase of battery energy density beyond current lithium-ion technology. A crucial bottleneck is the development of safe and reversible lithium-metal anodes, which is challenged by short circuits caused by lithium-metal dendrites and a short cycle life owing to the reactivity with electrolytes. The evolution of the lithium-metal-film morphology is relatively poorly understood because it is difficult to monitor lithium, in particular during battery operation. Here we employ operando neutron depth profiling as a noninvasive and versatile technique, complementary to microscopic techniques, providing the spatial distribution/density of lithium during plating and stripping. The evolution of the lithium-metal-density-profile is shown to depend on the current density, electrolyte composition and cycling history, and allows monitoring the amount and distribution of inactive lithium over cycling. A small amount of reversible lithium uptake in the copper current collector during plating and stripping is revealed, providing insights towards improved lithium-metal anodes.

First principle DFT calculations are used to study the thermodynamic and kinetic properties of Na-ion insertion in TiO₂ hollandite, a potential anode for Na-ion batteries. The experimentally observed phase transformation from tetragonal TiO₂ (I4/m) to monoclinic Na_0.25TiO₂ (I2/m) is confirmed. At high Na-ion concentrations the calculated formation energies predict a first-order phase transition toward the layered O′3-Na_0.68TiO₂ structure. Further sodiation initiates a solid solution reaction toward the layered O3-NaTiO₂ phase, which was recently brought forward as a promising anode for Na-ion batteries. This transformation irreversibly transforms the one-dimensional hollandite tunnel structure into the layered structure and potentially brings forward an alternative route toward the preparation of the hard to prepare O3-NaTiO₂ material. Energy barrier calculations reveal fast Na-ion diffusion at low concentrations and sluggish diffusion upon reaching the N_0.25TiO₂ phase, rationalizing why experimentally the Na_0.5TiO₂ phase is not achieved. Detailed analysis of the kinetic behavior in the hollandite structure via molecular dynamics simulations reveals the importance of correlated atomic motions and dynamic lattice deformations for the Na-ion diffusion. In addition, exceptional Na-ion kinetics were predicted for the layered O′3-Na_0.75TiO₂ phase through a dominating divacancy hopping mechanism.

Phase transitions play a crucial role in Li-ion battery electrodes being decisive for both the power density and cycle life. The kinetic properties of phase transitions are relatively unexplored and the nature of the phase transition in defective spinel Li_{4+ x}Ti₅O₁₂ introduces a controversy as the very constant (dis)charge potential, associated with a first-order phase transition, appears to contradict the exceptionally high rate performance associated with a solid-solution reaction. With the present density functional theory study, a microscopic mechanism is put forward that provides deeper insight in this intriguing and technologically relevant material. The local substitution of Ti with Li in the spinel Li_{4+ x}Ti₅O₁₂ lattice stabilizes the phase boundaries that are introduced upon Li-ion insertion. This facilitates a subnanometer phase coexistence in equilibrium, which although very similar to a solid solution should be considered a true first-order phase transition. The resulting interfaces are predicted to be very mobile due to the high mobility of the Li ions located at the interfaces. This highly mobile, almost liquid-like, subnanometer phase morphology is able to respond very fast to nonequilibrium conditions during battery operation, explaining the excellent rate performance in combination with a first-order phase transition.