Development of new energy becomes popular due to the energy shortages and environmental pollution. The existing commercial secondary batteries are primarily lithium-ion batteries, which use organic solvents and lithium salts as electrolytes. These batteries have two significant drawbacks, i.e., global lithium resources are insufficient and unevenly distributed, and organic solvents are flammable, having safety risks. These drawbacks severely affect the further development of lithium-ion batteries. Sodium solid-state electrolytes (SSEs) are emerged as an ideal material for future battery electrolytes due to the high energy density, good thermal stability, strong mechanical rigidity, low cost and improved safety. This paper was to explore a potential sodium SSEs by a high-throughput screening method based on machine learning (ML) and first-principles calculations. The potential sodium SSEs were predicted by machine learning models and were validated through Ab initio molecular dynamics (AIMD) simulations. In addition, the conduction mechanism of sodium ions was also analyzed based on the results of the first-principles calculations.

The dataset of inorganic sodium-containing compounds was established before building ML models. All the data in this dataset were from the Materials Project database. Solid-state electrolytes have good thermodynamic stability and insulation. The materials with a band gap less than 1.5 eV or energy above hull greater than 0.03 eV/atom were excluded, resulting in a final dataset of 3631 sodium-containing inorganic compounds.

To achieve the optimal performance of the regression model, we tried four ML algorithms, i.e., Random Forest (RF), eXtreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and K-Nearest Neighbors (KNN). Magpie (Materials Agnostic Platform for Informatics and Exploration) was used to obtain the crystal structure information into 145 attributes as the input of ML models. To validate the performance of the screened sodium solid-state electrolytes and further analyze the migration mechanism of sodium ions, AIMD simulations and CI-NEB (Climbing Image Nudged Elastic Band) calculations were conducted to calculate their ionic conductivity, activation energy, probability density distribution, van Hove correlation functions and energy barriers along specific diffusion paths.

In the four machine learning regression models, XGBoost has the optimum performance on both training and testing sets with R² = 0.999 and 0.994, respectively, indicating its high accuracy and strong generalization ability. The XGBoost model is used to predict 3631 of sodium-containing inorganic compounds, discovering that 126 of them have a potential to be superior SSEs. We further screen these and select 14 compounds for AIMD simulations, among which four materials (i.e., Na₃HfTiSi₂PO₁₂, Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈) show a high ionic conductivity and a low activation energy. Since the difference between the machine learning prediction and AIMD calculated value is within an order of magnitude, the high-throughput screening method used is reliable. Among the four candidate SSE materials, Na₃HfTiSi₂PO₁₂ belongs to the NASICON family. A previous study indicates that Na₃HfZrSi₂PO₁₂ is a promising sodium SSE material, which is similar to Na₃HfTiSi₂PO₁₂, except that Ti is replaced by Zr, indirectly proving the reliability of the machine learning model prediction.

To clarify the sodium ion migration mechanism, the motion trajectories of various particles in each compound are investigated. The results show that at all simulation temperatures, the diffusion of sodium ions is evident, while other ions remain relatively stable, forming reliable channels for sodium ion migration. From the distinct parts, the four materials exhibit migration correlation, indicating that sodium ions do not move independently but rather diffuse cooperatively, which contributes significantly to the ionic conductivity. The migration pathways of Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈ are discussed according to the probability density distributions. Moreover, the energy barrier of migration in Na₂LuPCO₇ shows that the maximum obstacle is to bypass the triangular plane formed by CO₃ within the diffusion channel.

We used the best-performing XGBoost model to search the established dataset of 3631 inorganic sodium-containing compounds, identifying 126 compounds with a high ionic conductivity. Also, we selected 14 of the 126 compounds for AIMD simulations to calculate their ionic conductivity and activation energy, ultimately identifying four inorganic sodium-containing compounds (i.e., Na₃HfTiSi₂PO₁₂, Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈) with a high ionic conductivity. We derived the van Hove correlation functions and probability density distributions based on the AIMD simulation results. It was indicated that the common characteristic of the four high ionic conductivity materials could be the presence of stable sodium ion diffusion channels with sodium ions migrating in a coordinated manner. Finally, the migration mechanism of sodium ions was analyzed based on the results of AIMD and CI-NEB.

Understanding electron behavior is crucial in secondary battery research, as electrons directly participate in electrochemical reactions. Over the past few decades, Goodenough and his co-workers developed an electron theory for secondary batteries, introducing the splitting of d-orbital energy levels in transition metals, which reconstructs the local crystal field. This theory has provided valuable insights for optimizing the structure and performance of battery materials. However, the theory is not easy to be handled and difficult to intuitively understand due to its reliance on complex atomic and molecular orbitals, as well as orbital hybridization theories. With the advancement of material science, particularly density functional theory (DFT) and first-principles high-throughput calculations in quantum crystallography, researchers can obtain more precise insights into electronic structures and key parameters, such as the Fermi energy levels, band structures near the Fermi level, electron state, and density of states (DOS). These electronic characteristics are vital for understanding the electrochemical performance of electrode materials in secondary battery. This study was to investigate the band structures of phosphate cathodes for sodium-ion batteries via the first-principles calculations in order to establish a qualitative and semi-quantitative correlation between electronic properties and electrochemical behavior.

Three typical phosphate compounds, i.e., β-NaVP₂O₇, Na₃V₂(PO₄)₂F₃ and Na₃V₂(PO₄)₃, were selected as model materials. Their crystal structures were obtained from the Inorganic Crystal Structure Database (ICSD) and optimized by the Vienna Ab initio Simulation Package (VASP) with the Perdew-Burke-Ernzerhof (PBE) functional and projector-augmented wave (PAW) pseudopotentials. The key computational parameters included a plane-wave cutoff energy of 520 eV and Monkhorst-Pack k-point grids of 4×3×3 for β-NaVP₂O₇, 3×3×2 for Na₃V₂(PO₄)₂F₃ and 2×3×3 for Na₃V₂(PO₄)₃. The convergence criteria were set at 10^-5 eV for energy and -0.01 eV/Å for forces. The band structures and density of states (DOS) were initially calculated using optimized structures for theoretically perfect crystals. However, since the actual sodium ion content in some phosphate cathodes deviates from the perfect crystal, the structural modifications were implemented. For Na₃V₂(PO₄)₃, the unit cell was doubled, and the number of sodium ions was adjusted according to symmetry rules to align with practical requirements. For Na₃V₂(PO₄)₂F₃, no unit cell expansion needed, but the number of sodium ions reduced based on symmetry considerations. For β-NaVP₂O₇, no sodium ion adjustments required. After these corrections, the band structures and DOS were recalculated. The electrochemical performance was further validated through galvanostatic charge/discharge tests at 0.2 C, with the specific capacities and cycling stability evaluated for 50 cycles.

High-throughput calculations can yield the more precise Fermi energies for the selected phosphate cathodes, with β-NaVP₂O₇ at 2.06 eV, Na₃V₂(PO₄)₂F₃ at 1.70 eV, and Na₃V₂(PO₄)₃ at 2.91 eV. Correspondingly, the bandgaps are determined to be 2.53 eV for β-NaVP₂O₇, 2.74 eV for Na₃V₂(PO₄)₂F₃, and 1.93 eV for Na₃V₂(PO₄)₃. These electronic parameters have a direct impact on the discharge voltages and conductivity of the materials. Note that β-NaVP₂O₇ with the minimum Fermi energy, achieves the maximum discharge voltage of 4.2 V, aligning with theoretical predictions that lower Fermi levels correspond to higher working voltages. Despite its relatively high Fermi level, Na₃V₂(PO₄)₃ maintains a stable 3.4 V platform due to its uniform energy band distribution near the Fermi level along the entire recommended band path, minimizing electron behavior changes and transition barriers. This uniform distribution facilitates consistent electron transport, resulting in an exceptional cycling stability with 99.4% capacity retention after 50 cycles. In contrast, β-NaVP₂O₇ and Na₃V₂(PO₄)₂F₃ exhibit non-uniform energy band distributions near the Fermi level, indicating multiple electron transition pathways that contribute to instable voltage plotforms. The discharge specific capacities of these materials are measured as 92.7 mA·h·g^-1 for β-NaVP₂O₇, 124 mA·h·g^-1 for Na₃V₂(PO₄)₂F₃ and 115.2 mA·h·g^-1 for Na₃V₂(PO₄)₃. A correlation between the integral of DOS near the Fermi level band and the discharge specific capacity of electrode materials occurs. Higher integrals of DOS for conductive electrons near the Fermi level correspond to greater discharge capacities, as demonstrated in the comparative analysis of these electrode materials.

This study established a correlation between high-throughput quantum crystallography calculations and electrochemical performance in sodium-ion battery cathodes. The Fermi levels directly affected discharge voltages, with lower Fermi levels corresponding to higher working voltages. A uniform band structure near the Fermi level over the whole recommended band path improved a cycling stability. The integral of the DOS near the Fermi level could be a critical factor determining the specific capacity of electrode materials. In addition, high-throughput calculations also revealed that structural imperfections, such as uncertain atomic occupancy in Na₃V₂(PO₄)₂F₃ and Na₃V₂(PO₄)₃, significantly could affect computational accuracy. The more precise Fermi energy values, band configurations, and DOS parameters were obtained via refining ion-occupancy corrections and implementing supercell expansions, providing deeper insights into fundamental electrochemical properties of these materials. These findings established a theoretical framework for designing next-generation battery materials via optimizing band structures for optimizing energy density and stability. This study could highlight a potential of high-throughput quantum crystallography calculations in predicting and improving electrochemical performance, thus offering a roadmap for the development of next-generation battery materials.

Aqueous electrolytes have potential applications in electrochemical energy storage devices due to their intrinsic non-flammable properties. Though its electrochemical stability window is narrow and normally it is hard to form effective solid electrolyte interphase, some researchers conduct in-depth research and propose several related solutions. Water-in-salt (WiS) electrolytes, as one of super-concentrated aqueous electrolytes, become one of the most promising systems. Some studies indicate that they can maintain a good electrochemical performance in a wide temperature range. However, its microscopic mechanism is still unclear. Therefore, in this paper, the microscopic structure and dynamic properties of LiTFSI-based aqueous electrolytes were investigated via molecular dynamics simulations.

All-atom classical molecular dynamics simulations were performed by using a software package named LAMMPS. The calculated system was composed of Li cation, TFSI anion and water molecules. The 20 mol/kg salt concentration system was selected as a main research object, and the component ratio was LiTFS∶H₂O of 128∶355. In addition, a system with a salt concentration of 3.5 mol/kg (LiTFSI∶H₂O of 32∶507) was also used as a comparison for simultaneous study. The selection principle of the two systems was to be consistent with that of the previous work. The force field parameters also followed the previous selection, where the simulation results were verified via the experimental data. Each system was simulated at different temperatures (i.e., 253, 273, 298, 323 K, and 343 K). For each salt concentration system, a relatively large simulation box was established and randomly put the corresponding number of particles into the box. Afterwards, the equilibrium system at each temperature was obtained through the initial structure optimization, and the heating or cooling procedure under the NPT ensemble. Finally, the production runs of 100-200 ns was carried out under the NVT ensemble, and the results of this step were used for post-analysis. In the whole production runs, the simulation timestep was 1 fs, and the data output interval was 50 fs for stress tensors, 1 ps for unwrapped coordinates, and 10 ps for trajectory-based analysis.

The RDF calculations indicate that in the super-concentrated system (20 mol/kg), it is hardly affected by temperature, and at a lower concentration (3.5 mol/kg), the peak value is slightly affected by temperature. This indicates that the microscopic solvation structure between Li and water molecules in the high concentration system is more thermodynamically stable. To further explain this phenomenon, we calculate the potential of mean force (PMF). The results show that the solvation binding energy and activation energy of Li-Ow in the high concentration system both are almost temperature-independent, while the low concentration system shows a certain temperature dependence for the activation energy differences of 1-2 k_BT in the temperature range.

Furthermore, the connection matrix analysis (where the red region represents a closer contact distance between the two atoms and a higher binding strength) show that this part is mainly from Li-Ow, Li-O, Hw-O, Hw-O four pairs. The first two pairs represent O atom from the first solvation shell of Li, and the latter two groups represent the hydrogen bonds. In addition, the yellow region represents that although the contact distance between atoms is relatively far (i.e., still within 3 Å), the binding strength is still high, such as Li-Hw, Li-S, Hw-S, Ow-O, Ow-Ow, O-O pairs. The connection matrix also gives important information that the Li-Li pair is formed at a distance of about 3 Å, which is an interesting phenomenon.

The properties of Li-Li dimers in high concentration systems are investigated. Through the RDF, the first peak appears at 3 Å, and the peak gradually increases as the temperature decreases, implying a more intense binding or a longer binding time. From the auto-correlation function (ACF) and the lifetime of the dimer existence, the ACF decreases rapidly with the increase of temperature, and the lifetime decreases significantly from 8500 ps to 160 ps, which is consistent with the Brownian motion and can also be confirmed via the analysis of dynamic properties.

Also, the relationship among the viscosity, diffusion coefficient, ionic conductivity and their temperature dependence of the two studied systems is analyzed. In general, the dynamic properties are obviously affected by temperature, both in high concentration system and low concentration system. In the analysis of the ionic conductivity, the Haven ratio is calculated to characterize the effect of collective diffusion in the system. The results show that the collective diffusion behavior in the high concentration system significantly affects the ionic conductivity, and is independent of temperature. At a low concentration, the effect of collective diffusion on ionic conductivity changes with temperature, and the effect gradually disappears at high temperatures.

In this work, molecular dynamics simulations were used to investigate the microscopic structure and dynamic properties of a typical aqueous electrolyte at two concentrations and their performance in a wide temperature range. The thermal stability of the micro-solvation structure of the high concentration system was analyzed via the RDF and PMF, providing a microscopic explanation for the excellent performance of super-concentrated aqueous electrolyte at extreme temperatures. The analysis of the connection matrix could further clarify the microscopic picture of the studied system. The analysis of the properties of Li-Li dimers could be related to the structure and dynamic behavior. The study of dynamic properties such as viscosity, diffusivity and conductivity showed the intrinsic coupling between them and their relationship with structural properties. In particular, the coupling relationship between collective dynamics and conductivity in two different concentration electrolyte systems was proposed and compared.

Solid-state lithium batteries are regarded as a promising alternative to traditional lithium-ion batteries due to their high energy density and safety. The development of solid electrolytes with high ionic conductivity is key to their application. The lithium-ion transport mechanisms in solid electrolytes can be categorized into single-ion migration and multi-ion correlated migration. Generally, multi-ion correlated migration can significantly reduce energy barriers compared to single-ion migration, making the promotion of correlated migration a crucial principle in designing solid electrolyte materials with high ionic conductivity. Titanite-type LiTaSiO₅ is a new oxide solid electrolyte, in which Zr⁴⁺ doping at Ta⁵⁺ site introduces excess lithium ions, facilitating correlated migration and significantly improving ionic conductivity. However, the relationship between lithium-ion distribution, correlated migration, and ionic transport properties still require in-depth investigation. In this study, ab initio molecular dynamics (AIMD) simulations were employed to investigate the possible Li sites and migration channels in the monoclinic titanite-type Li_1+xTa_1-xZr_xSiO₅(x = 0, 0.125) systems. The relationships between lithium-ion distribution, the degree of correlated migration, and ionic transport properties were also elucidated.

AIMD simulations were performed using the Vienna ab initio simulation package (VASP) with the plane wave projector augmented (PAW) method and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. For the pristine LiTaSiO₅ (ICSD No. 39648, space group P2₁/c), a 2×2×2 supercell was constructed, containing 32 formula units (256 atoms total). For the Zr-doped system, four Ta⁵⁺ were substituted with Zr⁴⁺, with four additional Li⁺ ions incorporated to maintain charge neutrality. AIMD simulations were carried out for the canonical (NVT) ensemble using a Nosé-Hoover thermostat at four elevated temperatures (800, 1000, 1200, and 1400 K) with a time step of 2 fs. To enhance computational efficiency, the plane-wave basis set was determined with a cutoff energy of 400 eV and integration in reciprocal space was performed at the Γ-point only. All the structures were heated from 100 K to targeted temperatures by velocity scaling over 2 ps, and then equilibrated at the desired temperature for 20 ps. The analysis of possible Li sites, jump events, and diffusion properties based on AIMD data was performed using our in-house developed code, which is integrated into our group's computational platform for electrochemical energy storage materials design (bmaterials.cn).

The framework structure of the monoclinic titanite-type LiTaSiO₅ consists of SiO₄ tetrahedra and TaO₆ octahedra. Through crystal structure analysis, we identified 11 distinct interstitial sites (It1-Itl1), where the It1 site corresponds to the Li1 lattice site while It2 and It3 sites align with two previously reported potential interstitial sites. Lithium ion migration exhibits strong preference for specific channels. At 800 K, 81.8% of jumps occur along the It2-Li1/It4-It7-It3-It7-Li1/It4-It2 channel ([101] direction) through elementary channels (Li1-It2, Li1-It7, It2-It4, It3-It7 and It4-It7), clearly identifying this as the optimal long-range migration channel. The non-unity occupation probabilities at all sites indicate Li⁺ disorder, with primary Li⁺ distribution at Li1, It2, It3, It4, and It7 sites. Previous studies confirm that Li1 is the lowest-energy stable site, while It2 and It3 serve as saddle points in the energy landscape. Zr doping significantly alters the Li⁺ distribution by increasing the Li⁺ concentration and promoting occupation of higher-energy sites. At 800 K, Li1 occupancy decreases from 41.8% to 33.1%, while It2 and It3 occupancies increase dramatically from 7.2% to 27.9% and from 7.4% to 24.3%, respectively. This redistribution, accompanied by increased configurational entropy, enhanced Li⁺ disorder and promotes low-energy-barrier correlated migration. As a result, the correlated migration percentage increases, the overall activation energy decreases, and the Li⁺ diffusion coefficient improves significantly.

The main conclusions of this study are summarized as following. The LiTaSiO₅ unit cell contains 11 distinct types of interstitial sites and shows anisotropic lithium-ion transport along the [101] direction through the It2-Li1/It4-It7-It3-It7-Li1/It4-It2 channel. After Zr doping, the lithium-ion concentration increases, leading to higher occupancy of lithium ions at high-energy sites (It2/It3), more disordered lithium-ion distribution, and an increase configurational entropy. This Li distribution enhances the probability of low-energy-barrier correlated migration, resulting in a higher correlated migration percentage, reduced overall activation energy, and significantly improved ionic transport performance.

The methodologies employed in this study are applicable to inorganic crystalline solid electrolytes with stable framework structures, which have been successfully applied in previous studies to several representative lithium/sodium solid electrolytes, such as LiTa₂PO₈ and Na₃Zr₂Si₂PO₁₂. However, these methods rely on the framework ions to identify the positions of lithium ions during the migration processes, making them unsuitable for certain specific solid electrolyte systems, such as amorphous solid electrolytes or those exhibiting the polyanion rotation effect.

Compared with organic lithium-ion batteries, all-solid-state batteries are expected to improve battery safety and energy density simultaneously. They have attracted extensive attention. The ideal solid electrolyte material should have the basic properties of electronic insulation, wide electrochemical window, good interface compatibility and high ionic conductivity. Many types of solid electrolyte materials are reported, including oxides, sulfides, halides, borohydrides and phosphates, each of which has advantages and disadvantages. For instance, lithium-based halide and sulfide solid electrolytes have a high ionic conductivity but a narrow electrochemical window, and they are unstable to lithium metal negatives. The interface compatibility between oxide solid electrolyte and electrode is poor, and lithium dendrites grow rapidly along the grain boundary in oxide solid electrolyte. To further develop all-solid-state batteries with a higher energy density, a longer cycle life and a higher safety, solid electrolyte materials with excellent comprehensive performance must be designed. Anti-perovskite superionic conductors based on cluster anions have attracted much attention due to their potential applications in solid electrolytes for rechargeable batteries. However, little theoretical studies on the phase stability, electrochemical stability and interface compatibility of anti-perovskite X₃OBH₄(X=Li, Na) materials have been reported yet. In this work, the electronic structure, phase stability, electrochemical stability, interface compatibility, mechanical properties and ion transport properties of anti-perovskite X₃OBH₄(X=Li, Na) materials were systematically investigated via first-principles calculation.

All the calculations were performed based on density functional theory (DFT) by a projector augmented wave method, as implemented in the Vienna ab initio Simulation Package (VASP). The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) was applied to treat the electronic exchange-correlation interactions. The cutoff energy was set to 520 eV. The crystal structure was fully relaxed until the convergence criteria for each atomic force and energy were less than 0.02 eV/Å and 10^-5 eV, respectively. Based on electrochemical energy storage materials design platform (bmaterials.cn), the phase stability and interfacial stability (including electrochemical and chemical stability) of X₃OBH₄(X=Li, Na) were evaluated.

The results show that X₃OBH₄(X=Li, Na) is a thermodynamically metastable and wide-band insulator at 0 K, which is unstable at a high pressure. Based on the energy calculated by DFT, the phase diagrams of Na-NaBH₄-O₂ and Li-LiBH₄-O₂ are constructed, respectively, and the calculated E_hull of Li₃OBH₄ and Na₃OBH₄ is 52.4 meV/atom and 110.7 meV/atom, respectively. X₃OBH₄(X=Li, Na) is thermodynamically unstable at 0 K. Since the E_hull value is relatively small, it is possible to stabilize the compound through the regulation of external conditions such as high temperature, high pressure and high entropy. Based on the lithium (sodium) giant potential phase diagram of the constructed X-O-B-H quaternary system, the voltage distribution and phase equilibrium of X₃OBH₄(X=Li, Na) in the process of lithiation/delithiation are calculated by DFT. The electrochemical window range of X₃OBH₄(X=Li, Na) is 0.53-0.93 V and 0-0.41 V, respectively. The corresponding decomposition product XBH₄(X=Li, Na) has a wide electrochemical stability window, which can protect the solid electrolyte. The calculated moduli of B, E and G of X₃OBH₄ (X=Li, Na) are greater than those of lithium (sodium) metal or even Li₃PS₄ electrolyte, indicating that X₃OBH₄ (X=Li, Na) can effectively block the growth of lithium (sodium) dendrites and has a good mechanical contact at the electrode/solid electrolyte interface. In addition, the low migration barriers of X₃OBH₄(X=Li, Na) are 0.34 eV and 0.35 eV, respectively, and the ionic conductivity at room temperature can reach 10^-4 S/cm. The rotation of the superhalogen promotes the movement of the lithium/sodium ions, thereby increasing their ionic conductivity.

The electronic properties, phase stability, electrochemical stability, chemical stability, mechanical properties and ion transport mechanism of the anti-perovskite type X₃OBH₄(X=Li, Na) were systematically investigated via first-principles calculation. The results showed that the crystal structure of X₃OBH₄(X=Li, Na) could be a metastable electronic insulator with a wide band gap. Under electrochemical oxidation conditions, X₃OBH₄(X=Li, Na) could be thermodynamically unstable and easily oxidized at relatively high voltages. However, the decomposition products could form a protective layer at the interface, preventing the electrolyte from further reacting and providing an improved electrochemical stability. In addition, X₃OBH₄(X=Li, Na) also had a good interface compatibility with typical cathode materials. The calculated mechanical properties indicated that X₃OBH₄(X=Li, Na) was brittle. However, their relatively large shear modulus indicated that they could be stable for lithium/sodium metal dendrites growth. By CI-NEB calculation, X₃OBH₄(X=Li, Na) showed a low migration barrier. In summary, these theoretical results could favor to better understand the thermodynamic and kinetic processes of X₃OBH₄(X=Li, Na), and provide a theoretical guidance for the development of high-performance solid electrolytes.

All-solid-state batteries (ASSBs), which replace flammable organic-based liquid electrolytes into ion-conducting solids, are expected to address the safety challenges for conventional lithium-ion batteries. Solid-state electrolyte materials as the most important constituent in ASSBs can be classified as oxide, sulfide, and halide solid-state electrolytes according to the anion type in the structural framework. To improve the efficiency of solid-state electrolytes in ion transport, some research efforts focus on the structural features suitable for cation migration events. Zeolite is a type of inorganic crystalline material made up of vertex-connected TO₄ tetrahedra (i.e., T = Si, Al, P, etc.) with ordered microporous structures. They have one-, two-, or three-dimensional channel systems and cation exchange capabilities, which make them ideal for use as fast ion conductors. Zeolite membranes with a close-packed structure have a low electronic conductivity (i.e., 1.5 × 10^-10 S/cm), making them an ideal option for solid-state batteries due to the high stability to air components and ability to reduce dendrite growth. In this paper, the molecular dynamics (MD) simulations of zeolite structures of relatively large sizes were accelerated via training a machine learning interatomic potential function (MLIP) with a good generalization ability, in turn screening zeolite structural frameworks suitable for Na⁺ transport as promising solid-state electrolytes for sodium ions in ASSBs.

The zeolite structure was characterized using the Smooth Overlap of Atomic Positions (SOAP) descriptor method provided by a software package named DScribe. Ab initio arithmetic molecular dynamics (AIMD) data used to construct the training dataset were computed by the Vienna Ab initio Simulation Package (VASP). The projector-augmented-wave (PAW) pseudopotential method and the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) function were used for the first-principles calculations, and the centre of the Γ-point in the Brillouin zone was chosen as the k-point, the NVT systematic and the Nosé-Hoover thermostat were used for the simulations, and a Nosé-mass corresponding to a period of 40 time steps was chosen (SMASS = 0, a simulation time-step of 1 fs, and a simulation temperature of 1000 K). The MLIP model was based on the Nosé-Hoover model.

The MLIP was fine-tuned based on a pretrained model of the Crystal Hamiltonian Graph Neural Network (CHGNet) with the energy and force calculated by AIMD as target values, and the model was trained with a learning rate of 10^-3. The trained CHGNet potential function was embedded into the Atomic Simulation Environment (ASE) library to carry out the MD simulations under the NVT regime with a simulation step of 1 fs and a total simulation duration of 100 ps.

The CHGNet pretrained model is based on the first-principles computational data of more than 1.5 million inorganic structures in the Materials program database, and it needs to be fine-tuned via adding the relevant data to achieve the better results when used for the computation of specific systems. To ensure that the data in the training set are applicable to all zeolite structures in the Na-Si-Al-O quaternary, the SOAP descriptors are used to select the ten structures with the differences in structural frameworks for the construction of the dataset, and the model obtained by training is capable of achieving a superior generalization in terms of simulated temperatures and systems. The model is used to select 18 representative structures from 124 zeolite structures for MD simulations at 1200 K. In most of the structures, Na⁺ is moved slightly and adsorbed to the edge of the pore channel, and only Na⁺ in ACO framework (ICSD 027717) is able to achieve a high enough mean-square displacement (MSD) of more than 800 Ų, which is extrapolated to obtain a potential barrier of 0.25 eV and an extrapolated room temperature ionic conductivity of 2.66 mS/cm after supplementing the multi-temperature simulation data. This is promising to be investigated as an important zeolite-structured solid-state electrolyte.

In this work, different structures selected by SOAP descriptors were used to fine-tune the CHGNet potential function model to obtain MLIP with a better generalization ability in the Na-Si-Al-O quaternary system. Using this MLIP for MD simulations indicated that in most of the zeolite structures Na ions could be adsorbed far away from the cavity centre and could not form a continuous transport channel, but the ACO framework (ICSD 027717) with a migration barrier of 0.25 eV and an extrapolated room-temperature ionic conductivity of 2.66 mS/cm occurred. Na⁺ ions could be transported rapidly with the help of a pore structure, and it could be considered as a solid-state sodium battery electrolyte material for further studies.

In lithium-ion batteries, electrode active particles are used to store and release lithium ions. The insertion and extraction of lithium ions are accompanied by a local deformation of the electrode active material, which can lead to mechanical degradation. Studies on the chemo-mechanical behavior of electrode particles can favor to improve the capacity and cycle life of batteries. Silicon has a super high capacity as an anode and is considered as a promising electrode material. However, its excessively high volume change rate hinders the further development of silicon electrodes. Two main reasons lead to mechanical failure of silicon electrode particles, i.e., the non-uniform volume change due to Li-ion concentration gradient, and the contact between particles upon lithium insertion induced volume expansion. Contacts between elastic deformable parts with simple morphologies are investigated based on the Hertz theory, which mainly analyzes contacts via calculating the contact area and indentation depth. Simulations of solids are mainly based on the Lagrangian description, which requires to create multiple systems and inter-system connections that are computationally complex. A phase-field model is developed with Eulerian description that can conveniently identify and distinguish the inside and outside of an object by the value of a variable "order parameter". In addition, some examples for calculation the contact between electrode particles with different morphologies are also calculated to explore the ability of the proposed method.

The calculation model is based on 3 equations, i.e., the equilibrium equation, Cahn-Hilliard equation and the reference map equation. After splitting the Cahn-Hilliard equation into two parts, 4 variables v, Ф, μ, ξ need to be calculated. The constitutive law is calculated through ξ and contact force is calculated through the Ф of the contact bodies. Deformation gradient is decomposed into elastic part and lithium-intercalation-induced part. The elastic part is constructed on neo-Hookean theory, and lithium-intercalation-induced part is calculated through the concentration of Li. Elastic constants are also functions of the concentration as Si and Li both contribute to it. 4 PDEs are generated, including the Cahn-Hilliard equation, the equilibrium equation and the evolution equation of ξ. After applying boundary conditions, the PDEs are transformed to weak forms. The simulations are performed by the finite element method.

A simple elastic contact problem is simulated to verify the feasibility and accuracy of the method. The result is compared with the Hertz theory. The lithiation of electrode particles is then simulated. The electrode particles are initialized as cylinders with regular and irregular profiles. The figure of von Mises stress shows that the contact between particles with regular profile is equivalent to the contact between a nanowire and rigid plane. And particles show different behaviors when they start lithiation at different durations. Particles with irregular circle profile shows a higher stress when the contact with rigid plane while the stress is lower when contacting with other particles. That is because particles rotate when the irregular profiles contact, which releases part of the stress and expands the contact area. To exclude the effects of rotation, considering that friction and binder can impede rotation, an example of 1/4 electrode particles is simulated. Particle rotation has a significant effect on stress relief, especially in the final stages of expansion, where the maximum stress can be reduced by approximately 1/3. Finally, simulations are performed with a reference to the actual electrode particle morphology. The internal stress in the particles becomes stable at a certain point and no longer increases significantly with deeper lithiation.

The simulation modeling of the contact between solids was implemented based on the phase-field method, and its feasibility and accuracy were verified through a simple example. Subsequently, the simulations of the contact problem of the lithiation of electrode particles were carried out to investigate the deformation and stress state of electrode particles with different shapes when the contact occurs to show the region where mechanical degradation might occur. The simulation of electrode particles' lithiation showed different behaviors when the profile changed. This was because particles with irregular profile rotate when contacts occured so that concave surface and convex surface coupled. However, smaller contact area resulted in higher stress when concave surface contacted with rigid plane. The final simulations were performed with a reference to the morphology of the electrode particles in the real situation. These simulations could provide a reference for the study of the lithiation behavior of electrode particles in Li-ion batteries, showing the possible sites of mechanical damage or fracture of the electrode particles when they squeezed against each other, which in turn could be expected to contribute to the optimal design of Li-ion batteries in the future.

Lithium-ion batteries are currently the most widely used secondary batteries, extensively applied in electric vehicles, laptops, and smartphones. However, commercial lithium-ion batteries generally use flammable organic solvents, which pose safety issues such as leakage and self-ignition. As the demand for higher energy density grows in fields like aerospace and electric vehicles, the existing commercial lithium-ion batteries cannot available. All-solid-state lithium-ion batteries (ASSLBs) with a high energy density and a good safety become one of the ideal alternatives to address the issues of the existing lithium-ion batteries. However, the bottleneck for ASSLB applications is the lack of solid electrolyte (SE) materials with a high ionic conductivity and a good stability simultaneously. Recently, a novel class of revived ternary halide SEs represented by Li₃InCl₆ (LInC) has attracted much attention due to their high room temperature ionic conductivity, high oxidative stability, compatibility with high voltage cathodes, and particularly high humidity stability. However, there are still some application-related issues regarding LIC that remain unclear, such as mechanical and thermal properties, especially the Li-ion migration mechanisms. First-principles calculations can reveal the underlying mechanisms in an atomic scale, compared to experimental methods. This paper was to evaluate the fundamental physical properties required for LInC as a SE material and reveal the main factors for high ionic conductivity, thus providing methods for the improvement and application of LIC SE. The geometric and electric structure, mechanical and thermal properties, defect chemistry, and Li-ion migration mechanism of LIC were investigated, and the findings indicated that LIC could be used as a promising SE material for ASSLBs.

In this work, all the calculations were performed by first-principles methods based on density functional theory (DFT) implementing in a software named VASP (Vienna Ab initio Simulation Package). The interaction between ion cores and valence electrons was described by Projector-Augmented Wave (PAW) with a plane wave cutoff energy of 640 eV. The exchange-correlation functional was described by the Perdew-Burke-Ernzerhof (PBE) functional within the Generalized Gradient Approximation (GGA). During geometry relaxation, the numerical integration over the Brillouin zone was performed by the Monkhorst-Pack method with a k-point grid of 3×2×3; for electronic structure calculations, the grid is 5×3×5, and a Gaussian smearing was applied to the Fermi level with a width of 0.2 eV. The electronic structure and band structure of the system were calculated by hybrid density functionals based on the Heyd-Scuseria-Ernzerhof (HSE06) method. All atoms within the unit cell were fully relaxed with a convergence criterion of 10^-5 eV/atom, and the interatomic forces were less than 0.01 eV/Å. In addition, for the calculation of defects and Li ion migration barriers, a supercell of 2×1×2 was also constructed, containing 24 Li, 8 In, and 48 Cl atoms. The Climb Image Nudged Elastic Band (CI-NEB) method was used to search for the migration path of Li⁺ and to calculate the migration barrier.

We modeled LInC crystal based on the XRD experimental data. LInC unit cell with C2/m space group exhibits the lattice constants (i.e., a = 6.63 Å, b = 11.34 Å, c = 6.46 Å, α = γ = 90°, and β = 112.0°), which are in good agreement with the experimental data. All Cl atoms fully occupy the 4i and 8j Wyckoff sites, In atoms partially occupy the 4g site within the plane (001), and Li atoms fully occupy the 4h and 2d sites within the plane (002). The band structure illustrates LIC with a bandgap of 4.71 eV, indicating a great theoretical electrochemical window. Furthermore, DFT calculations demonstrate that LInC possesses low elastic moduli with B=14.71 GPa, G=7.05 GPa, and E=18.24 GPa, which is smaller than those of Li₁₀GeP₂S₁₂ (LGPS) and Li₃YCl₆ (LYC), and exhibits a high Pugh ratio (i.e., B/G=2.09), indicating its favorable mechanical properties and ductility. LInC can be suitable as a solid electrolyte for all-solid-state batteries. The defect chemistry and Li-ion migration of LInC show that although isolated with a formation energy of -1.43 eV can form spontaneously, migration barriers as high as 0.48 eV indicates that the contribution of to the conductivity of LInC is negligible. Similarly, despite presenting a low migration barrier of 0.17 eV in ab plane, isolated has a high formation energy of 4.75 eV, indicating a negligible contribution to conductivity of bulk LInC. For four considered neutral defect pairs, the defect formation energies and Li-ion migration barriers follow an order of and , respectively. The results indicate that Frenkel defect pair is the dominant defect type, playing a critical role in the high ionic conductivity of LInC. The contribution of and defect pairs to the ionic conductivity of LInC bulk is also not negligible. This work provides valuable insights for evaluating LInC as SE material, and elucidates some dominant factors for a high ionic conductivity of LInC.

This work systematically investigated the basic properties and Li-ion migration mechanisms of LInC by first-principles calculation methods. The results showed that LInC had high theoretical electrochemical window as well as good mechanical property and ductility. Furthermore, the Frenkel defect pair with the low formation energy of 0.24 eV presented a low migration barrier of 0.26 eV, confirming that it could be the dominant defect type in LInC, and Li vacancies were the predominant carriers in LInC bulk. The findings of this work could provide a theoretical basis for the modification and application of LInC materials.

Selective catalytic reduction (SCR) technology is widely used due to the advantages of high denitrification efficiency and low operating cost. The existing commercial SCR catalysts are mainly vanadium-based catalysts with V₂O₅ as an active component, metal oxides WO₃ and MoO₃ as additives, and anatase TiO₂ as a carrier. They have a good denitrification activity at 320-420 ℃, but have a poor activity at a low temperature. The denitrification activity of vanadium-based catalysts is mainly related to their redox capacity, acidic sites, and chemisorbed oxygen. In order to improve their denitrification activity, in this work, V-Mo-P/TiO₂ catalysts were prepared by an impregnation-roasting method. The effect of roasting atmospheres (i.e., air, hydrogen, and nitrogen) on the active components and denitrification performance of vanadium-molybdenum-titanium catalysts (V-Mo-P/TiO₂) was investigated.

A certain amount of oxalic acid was added into deionized water and dissolved under stirring., Ammonium metavanadate was then added into the solution, heated at 100 ℃ and stirred until the solution became dark blue. Afterwards, ammonium molybdate and diammonium hydrogen phosphate were added into the solution. TiO₂ was added and impregnated into the solution under stirring for 2 h, and then dried in an oven at 108 ℃ for 12 h to obtain a precursor of V-Mo-P/TiO₂ catalysts. The precursor was ground, pressed, and sieved to 40-60 mesh and placed in a fixed-bed reactor, and then roasted in different gases (i.e., air, nitrogen, and hydrogen) at 450 ℃ for 4 h to obtain different catalyst samples, which were named Air-450 ℃, N₂-450 ℃, and H₂-450 ℃, respectively.

The structure of the catalysts was analyzed by a model PANalytical X-Pert PRO MPD X-ray diffractometer (XRD, PANALYTEC Co., the Netherlands). The pore structure of the catalysts was determined by a model NOVA2200e specific surface area analyzer (Kantar Instruments Co., USA). The surface elemental valence of the catalysts was characterized by a model ESCALAB250Xi Instrument (Thermo Co., USA). The elemental valence states on the catalyst surface were determined by an X-ray photoelectron spectroscope (XPS). The redox capacity and surface acidity of the catalysts were characterized with H₂-TPR and NH₃-TPD, respectively, and the NO adsorption on the catalyst surface was determined with NO-TPDe. Pyridine adsorption test (Py-FT IR) was performed using a model PE Spectrum II infrared spectrometer (PerkinElmer Co., USA) to characterize the types and strengths of the acidic sites on the catalyst surface.

The catalyst activity was tested in a fixed-bed reactor at a gas flow rate of 1400 mL/min, a NO concentration of 500 mg-Nm³, an O₂ concentration of 8%, and an NH₃∶NO volume ratio of 1∶1 at 80-300 ℃. The catalysts were used in a fixed-bed reactor with a gas flow rate of 1400 mL/min, a NO concentration of 500 mg-Nm³, an O₂ concentration of 8%, and an NH₃∶NO volume ratio of 1∶1. The denitrification tail gas was examined by a model OPTIMA7 flue gas analyzer (MRU Co., Germany) to calculate the denitrification efficiency of the catalyst.

At 100-250 ℃, the NO conversion of Air, N₂, and H₂ catalysts increases with the increase of temperature. Clearly, the denitrification performance of the catalysts obtained by roasting in three atmospheres is different, and the denitrification activity in different gases follows an order of Air > N₂ > H₂, in which the catalysts roasted in air have the optimum low-temperature catalytic activity.

The ratios of V⁴⁺/(V⁴⁺+V⁵⁺) in the catalysts roasted in air, nitrogen, and hydrogen are 0.440, 0.482, and 0.538, respectively, indicating that more V⁴⁺ is produced in a reducing atmosphere. Roasting in air can oxidize V⁴⁺ to V⁵⁺ to a certain extent, thus increasing the percentage of V⁵⁺ on the catalyst surface and the amount of chemisorbed oxygen O_α. From the results of H₂-TPR reduction, the corresponding integral area sizes are Air-450 ℃> N₂-450 ℃> H₂-450 ℃, indicating that polymerized vanadium is more easily formed in air. From the results of the NH₃-TPD desorption, the NH₃ desorption of the Air-450 ℃ catalyst is more than that of other two catalysts, and the number of acidic sites is in the following order of Air-450 ℃> N₂-450 ℃> H₂-450 ℃. The results of Py-FT IR further show that the acidic sites on the surfaces of the three catalysts are mainly of B-acid and L-acid. Roasting in air can increase the number of B- and L-acidic sites of the catalysts simultaneously, in which the B-acidic sites increased integrated areas of the catalysts roasted in air, nitrogen, and hydrogen are 1695, 1254 and 481, respectively, which are also basically consistent with the results of the NH₃-TPD characterization. The results of NO-TPD desorption indicate that the catalyst surface at Air-450 ℃ is more prone to forming highly active bridged or double-toothed nitrates. The V—O bond and B acidic sites in polymerized vanadium make it easier for the catalyst to adsorb and activate NH₃ species, which then reacts rapidly with the bridged or double-dentate nitrates to generate N₂ and H₂O. The reaction process mainly follows the L-H mechanism. The abundant O_α on its surface accelerates the formation of NO oxidized to NO₂, promoting a rapid SCR reaction. The V-Mo-P/TiO₂ catalysts roasted in air are superior to those roasted in nitrogen and hydrogen in terms of NO removal in the low-temperature section.

V-Mo-P/TiO₂ catalysts for low-temperature denitrification were prepared by an impregnation method, and the denitrification activities of V-Mo-P/TiO₂ catalysts roasted in air, nitrogen, and hydrogen atmospheres were investigated. The order of their catalytic activities was as follows: air > nitrogen > hydrogen. The results of H₂-TPR and XPS revealed that the catalysts roasted in air had a larger proportion of exposed V⁵⁺ on their surfaces, and contained abundant chemisorbed oxygen O_α, which further accelerated the oxidation of NO to NO₂, and participated in the "fast SCR" reaction of denitrification. Moreover, the catalysts roasted in air at 450 ℃ were characterized by NH₃-TPD, Py-FT IR and NO-TPD, and the results indicated that the catalysts possessed more abundant B acid sites, and the B acid and polymerized vanadium were more prone to adsorption of activated NH₃ species, which further reacted with the bridged and double-toothed nitrate formed on the surface of the catalysts to generate N₂ and H₂O, thus promoting the SCR denitrification reaction by L-H mechanism.

Formaldehyde, as an indoor pollutant and carcinogen, exists commonly in building materials and furniture products, posing a serious threat to human health. To address this issue, cellulose aerogel materials with their porous network structure can effectively remove pollutants. Cellulose aerogels exhibit a great potential in the field of adsorption due to their advantages of abundant raw material sources and environmental friendliness. Chitosan, due to the presence of amino groups, is widely studied for various applications, particularly for formaldehyde adsorption. Its adsorption performance is especially remarkable, as it can form specific interactions with formaldehyde, enabling an efficient removal. In this paper, a commonly available poplar wood powder was used to directly extract cellulose from plant-based raw materials. Cellulose-chitosan composite aerogels were prepared by a sol-gel method for the adsorption of formaldehyde gas. The structure, morphology, and adsorption conditions of the composite aerogels were investigated to evaluate their performance.

The round-bottom flask containing formaldehyde aqueous solutions of different concentrations was placed in a heater of the gas device to vaporize the solution, allowing formaldehyde gas to fill the apparatus. After 2 h, the formaldehyde adsorption tests were initiated when the formaldehyde gas concentration in the device reached a stable level. Adsorption tests were conducted separately on chitosan, cellulose aerogel, and cellulose-chitosan composite aerogel. The adsorption experiment for chitosan lasted for 12 h, with samples collected every hour to measure the formaldehyde concentration. For cellulose aerogel and cellulose-chitosan composite aerogel, the adsorption experiments lasted for 2 h, with samples taken every 15 minutes to monitor the formaldehyde concentration.

At a formaldehyde concentration of 8 mg/m³, the formaldehyde adsorption capacities at equilibrium for CS, CA, and CCA were 0.412, 2.336 mg/g, and 15.681 mg/g, respectively. CS exhibits the minimum adsorption performance, while CCA shows the most significant adsorption effect, outperforming CA. The removal efficiencies are 53.85%, 74.06%, and 98.00%, respectively when using 1 mg, 3 mg, and 5 mg of CCA at an initial formaldehyde concentration of 8 mg/m³. The 5 mg dosage of CCA achieves a removal efficiency of close to 100%, making it the most economical option for formaldehyde removal. Formaldehyde adsorption tests are conducted on 5 mg of CCA at different formaldehyde concentrations ranging from 2 mg/m³ to 16 mg/m³. The adsorption capacity increases significantly as the concentration increases from 2 mg/m³ to 8 mg/m³, indicating that formaldehyde concentration affects the adsorption performance. The maximum formaldehyde adsorption capacities at equilibrium for CCA-1, CCA-2, and CCA-4, with chitosan proportions of 0.05%, 0.10%, and 0.20% (in mass), are 13.264, 15.681 mg/g, and 15.877 mg/g, respectively. The difference in maximum adsorption capacities between CCA-2 and CCA-4 is relatively small, indicating that the optimal chitosan proportion is 0.1% to avoid resource wastage.

The results showed that the cellulose-chitosan composite aerogel exhibited a superior formaldehyde adsorption performance, compared to cellulose aerogel and pure chitosan. A significant advantage of introducing chitosan was its ability to specifically bind with formaldehyde, effectively enhancing the adsorption performance and broadening the application scope of cellulose aerogels, thereby achieving a high-value utilization of plant-based raw materials. Moreover, the composite aerogel demonstrated an effective adsorption at different formaldehyde concentrations, further expanding its applicability under varying conditions. In summary, the cellulose-chitosan composite aerogel exhibited excellent formaldehyde removal capabilities, showing a great potential for applications, particularly in household environments.