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.@en

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 LiMnyFe1-yPO4 (LFMP), LiCoyFe1-yPO4 (LFCP), LiCoxMnyFe1-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 LiMn0.4Fe0.6PO4 as a superior composition that favors a solid solution phase transition, making it ideal for high-power applications.@en

Computational modeling is shaping the fundamental understanding of key thermodynamic and kinetic properties in batteries, the importance of which is undeniable for the implementation of next-generation batteries, mobile and large-scale applications (chapter 1). In the present thesis, we employ density functional theory (DFT) at the nanoscale and phase field modeling at the mesoscale (chapter 2) to study both state-of-the-art and novel battery chemistries...@en

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 Na0.25TiO2 (I2/m) is confirmed. At high Na-ion concentrations the calculated formation energies predict a first-order phase transition toward the layered O′3-Na0.68TiO2 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 N0.25TiO2 phase, rationalizing why experimentally the Na0.5TiO2 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-Na0.75TiO2 phase through a dominating divacancy hopping mechanism.@en

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 Na0.25TiO2 (I2/m) is confirmed. At high Na-ion concentrations the calculated formation energies predict a first-order phase transition toward the layered O′3-Na0.68TiO2 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 N0.25TiO2 phase, rationalizing why experimentally the Na0.5TiO2 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-Na0.75TiO2 phase through a dominating divacancy hopping mechanism.@en

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.@en

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.@en

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.@en

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. @en

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.@en

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. @en

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 Li4+ xTi5O12 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 Li4+ xTi5O12 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.@en

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.@en

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.@en

Solid-state batteries have significant advantages over conventional liquid batteries, providing improved safety, design freedom, and potentially reaching higher power and energy densities. The major obstacle in the commercial realization of solid-state batteries is the high resistance at the interfaces. To overcome this bottleneck, it is essential to achieve an in-depth fundamental understanding of the crucial electro- chemical processes at the interface. Conventional electrochemical stability calculations for solid electrolytes, determining the formation energy toward the energetically favorable decomposition products, often underestimate the stability window because kinetics are not included. In this work, we introduce a computational scheme that takes the redox- activity of the solid electrolytes into account in calculating the electrochemical stability, and it in many cases appears to dictate the electrochemical stability. This methodology is applied to different chemical and structural classes of solid electrolytes, exhibiting excellent agreement with experimentally observed electrochemical stability. In contrast with current perception, the results suggest that the electrochemical stability of solid electrolytes is not always determined by the decomposition products but often originates from the intrinsic stability of the material itself. The processes occurring outside the stability window can lead toward phase separation or solid solution depending on the reaction mechanism of the material. These newly gained insights provide better predictions of the practical voltage ranges and structural stabilities of solid electrolytes, guiding solid-state batteries toward better interfaces and material design.@en