Negative Electrode For Lithium-ion Batteries Research Articles

Research on Quantitative Diagnosis of Dendrites Based on Titration Gas Chromatography Technology

Lithium plating can cause capacity fade and thermal runaway safety issues in lithium-ion batteries. Therefore, accurately detecting the amount of lithium plating on the surface of the battery’s negative electrode is crucial for battery safety. This is especially crucial in high-energy-density applications such as battery energy storage systems or in electric vehicles (EVs). Early detection of lithium plating is crucial for evaluation of reliability and longevity. It also serves as a method for early diagnostics in practical industrial applications or infrastructure, such as EV transportation. This can enhance its impact on customers. This study validates the effectiveness of titration gas chromatography (TGC) technology in quantitatively detecting lithium plating on graphite negative electrodes in lithium-ion batteries. The results show that it can detect a minimum of 2.4 μmol of metallic lithium. Compared with the heating direct current resistance and reference electrode methods, which can be used to perform only qualitative dendrite detection, TGC has a wider range of detection. Compared with the nuclear magnetic resonance (NMR) method with higher quantitative detection accuracy, the maximum difference between the detection results of the two methods was only 7.2%, but the TGC method had lower cost and higher implementation convenience. In summary, among various dendrite detection methods, the TGC method can not only realize the effective quantitative detection of lithium plating, but also comprehensively consider its detection range, implementation convenience, cost, and detection accuracy, indicating that it is suitable for engineering applications and has the prospect of realizing large-scale quantitative detection of lithium plating in lithium-ion batteries.

Facilely Fabricating F-Doped Fe3N Nanoellipsoids Grown on 3D N-Doped Porous Carbon Framework as a Preeminent Negative Material.

Transition metal nitride negative electrode materials with a high capacity and electronic conduction are still troubled by the large volume change in the discharging procedure and the low lithium ion diffusion rate. Synthesizing the composite material of F-doped Fe3N and an N-doped porous carbon framework will overcome the foregoing troubles and effectuate a preeminent electrochemical performance. In this study, we created a simple route to obtain the composite of F-doped Fe3N nanoellipsoids and a 3D N-doped porous carbon framework under non-ammonia atmosphere conditions. Integrating the F-doped Fe3N nanoellipsoids with an N-doped porous carbon framework can immensely repress the problem of volume expansion but also substantially elevate the lithium ion diffusion rate. When utilized as a negative electrode for lithium-ion batteries, this composite bespeaks a stellar operational life and rate capability, releasing a tempting capacity of 574 mAh g-1 after 550 cycles at 1.0 A g-1. The results of this study will profoundly promote the evolution and application of transition metal nitrides in batteries.

Application of the Multi-Species, Multi-Reaction Model to Coal-Derived Graphite for Lithium-Ion Batteries

Graphite is a critical material used as the negative electrode in lithium-ion batteries. Both natural and synthetic graphites are utilized, with the latter obtained from a range of carbon raw materials. In this paper, efforts to synthesize graphite from coal as a domestic feedstock for synthetic graphite are reported. Domestic coal-derived graphite could address national security and energy issues by standing up domestic supply chains for battery critical materials. The performance in lithium-ion coin cells of this coal derived graphite is compared to a commercial battery-grade graphite. For the first time, a multi-species, multi-reaction (MSMR) modeling technique is applied to synthetic graphite derived from coal. Key thermodynamic, transport, and kinetic parameters are obtained for the coal derived graphite and compared to the same parameters for commercial battery-grade graphite. Modeling of synthetic graphites will allow for virtual evaluation of these materials toward production of domestically sourced graphite.

A Protocol for Predicting Lithium-Ion Battery Performances Reflecting the Three-Dimensional Structure of Electrodes

As social needs for higher capacity and longer life of lithium-ion batteries increase, shortening the period from research to development and commercialization of batteries has become an extremely important issue. To minimize the above period, a protocol for predicting the performances of (lithium-ion) batteries is highly urged for. Many reports have been published so far regarding the simulation technology of charge-discharge profiles of lithium-ion batteries.1,2 However, in most of simulations, the porous structure of lithium-ion battery electrodes is simplified into a 1D or 2D models. To achieve more accurate battery performance prediction, we adopted the actual 3D structure of the positive and negative electrodes of lithium-ion batteries in simulations.A plasma FIB SEM (Helious5, Thermofisher Scientific Inc.) was used to obtain the 3D structures of the positive and negative electrodes of the lithium-ion battery. The porosity and tortuosity of the electrodes were calculated by reconstructing a 3D image and performing image analysis. Based on this 3D structure, we also calculated the lithium ion conductivity in the electrode. The obtained 3D structural parameters were applied to the simulation of battery characteristics and compared with actual charge/discharge test results. We have also developed a performance prediction protocol that allows to reflect the measured physical properties of battery materials in the simulation.Figure 1 shows cross-sectional images of two different high-nickel-type positive electrodes prepared under different experimental conditions. It can be seen that the active materials are packed densely for both the electrodes, but the level of conductive carbon and binder dispersion is different. The particle size distribution of the active materials was also found to be largely different between the two samples. Structural parameters were obtained from the 3D structure by image analysis, and highly accurate performance prediction was performed. It can be predicted that the rate capability reflects the structural homogeneity. Also, the simulation revealed that the particle size distribution plays an important role for achieving favorable rate capability. Acknowledgement This work was financially supported by the NEXT Center of Innovation Program (COI-NEXT, Grant Number JPMJPF2016) of the Japan Science and Technology Agency. References (1) M Doyle , J. Newman, A. S. Gozdz, C . N. Schmts, and M. Tarascon, J. Electrochem. Soc. 1996, 143, 1890(2) G. Li and C. W. Monroe, Annu. Rev. Chem. Biomol. Eng. 2020, 11 277. Figure 1

Elucidating the Lithium-Ion Storage Mechanism in Insertion-Available Hard Carbon with Abundant Closed Porosity: Toward a Practical Material for Batteries

Traditionally, standard lithium-ion batteries (LIBs) are composed of a positive electrode made of metal oxides and a negative electrode made of highly crystallized graphite materials. Graphite materials, with a theoretical capacity of 372 mAh g-1, are chosen as the negative electrode because lithium-ion storage in graphite materials involves lithium-ion intercalation/de-intercalation between graphitic interlayers, a characteristic of faradaic reactions. During galvanostatic charge/discharge (GCD), long plateau regions at low voltages (e.g., 0-0.1 V (vs. Li+/Li)) resulting from multi-staged ion intercalation/de-intercalation are achieved. The low voltage of this intercalation/de-intercalation reaction contributes to enhancing the nominal voltage of LIBs, leading to a higher energy density of the battery.On the other hand, sodium-ion batteries (SIBs) have been extensively researched over the past 10 years as alternative to LIBs to compensate for the gradual scarcity of lithium metal resources. Hard carbon (HC) materials, also known as amorphous non-graphitizable carbons, were introduced to be the negative electrode material for SIBs, since most HCs exhibit very similar electrochemical responses in sodium-ion storage as lithium-ion storage in graphite materials.However, when examining the application of HC materials in lithium-ion storage, it becomes apparent that the development has been significantly limited over the past 20 years. Recent research primarily focuses on biomass-derived HCs and heteroatom-doping on these carbons. This type of HC is abundant in heteroatoms (e.g., N, P, and S) inherited from the intrinsic properties of biomass precursors. While high capacities and excellent rate capabilities are claimed for these biomass-derived HCs, the electrochemical responses of lithium-ion storage in these HCs often exhibit capacitive reactions with a completely sloping region on their GCD curves. Consequently, the miscalculation of capacities can be induced by assessing reversible capacities beyond excessively high voltages (> 1.5 V), even reaching 3 V. The appropriate working voltage window for HCs should be lower than 1.5 V to match with the positive electrodes. Thus, if reevaluating these HCs in a normal voltage window, the obtained reversible capacities are relatively small, due to the deficiency of faradaic reactions signified by the plateau region at low voltages on GCD curves. Additionally, very low initial coulombic efficiencies are often obtained for these highly defected and heteroatom-doped HCs, attributed to the vigorous consumption of electrolyte during the SEI layer formation on their defective sites. As a result, in this work, we introduce a straightforward method to fabricate hard carbon microbeads with tunable microporous structures by carbonizing cross-linked phenolic-formaldehyde (PF) resin spheres, produced through microwave-assisted suspension polymerization. The ultimate goal is to transform HC into a practical battery material for the negative electrode in LIBs, which must possess several abilities similar to graphite (i.e., reversible faradaic reactions with an obvious plateau region at low voltages on GCD curves, low surface area to suppress SEI formation, and good cycling stability). Additionally, the lithium-ion storage mechanism in HCs with varying open/closed porosity is carefully elucidated. By probing the porosity of HC with multiple gas (N2, O2, and CO2) adsorptions, a solid correlation between porous properties and electrochemical responses has been successfully established. As displayed in Figure 1, the results indicate that carbon porosity can change with carbonization temperature. With increasing temperatures, open pores are initially transformed into closed pores, and ultimately, non-porous properties are detected. The electrochemical behaviors in these HCs with distinct porosity differ significantly as demonstrated by GCD curves in Figure 2.It has been found that ultra-micro closed pores (<0.7 nm) are capable of providing confined spaces for lithium ions to be inserted/extracted, characterized as faradaic reactions. Therefore, a plateau region at low voltages can be acquired, leading to additional reversible capacities. Unlike some reported methods, such as holding at a constant voltage, charging/discharging at a very small current density, or overcharging to negative voltage regions, these faradaic reactions are easily unlocked at a current density of 50 mA g-1 in a safe voltage window of 0-0.12 V. As a result, the optimized HC delivers a total reversible capacity of 550 mAh g-1 at 50 mA g-1 in the voltage range of 0-1.5 V. The excellent rate capability and cycling stability of optimized HC are also confirmed. Furthermore, by the post-treatment with hydrogen-assisted reduction, the performance is further enhanced, achieving a reversible capacity of 574 mAh g-1 and an initial coulombic efficiency of 75%. These breakthrough outcomes provide valuable insights for the rational design of hard carbon materials. The optimized hard carbon could be a promising candidate for replacing traditional graphite materials in next-generation LIBs. Figure 1

Single-Nanometer-Sized Boron and Phosphorus Co-Doped Silicon Nanoparticles for Negative Electrode of Lithium-Ion Batteries

Single-Nanometer-Sized Boron and Phosphorus Co-Doped Silicon Nanoparticles for Negative Electrode of Lithium-Ion Batteries

Principle &amp; application of energy storage based on 2D material: Evidence from graphene

The development of new energy and related industries has raised higher requirements for energy storage devices. Graphene, a 2-D carbon material with a single atomic layer thickness, possesses excellent mechanical properties, thermal conductivity, SSA, optical transparency, and rapid electron migration, among other unique physical and chemical properties. The addition of graphene is predicted to enhance the rate performance, durability and energy density of electrochemical energy storage devices. This study summarizes the recent research in the production and application of graphene in electrochemical energy storage devices, primarily focusing on supercapacitors and the positive and negative electrode of lithium-ion batteries. The main roles of graphene include serving as an ultrathin support and buffering material, an active substance, and a conductive material. In addition, the limitations of graphene due to its production technologies and the potential brought by its super flexibility and lightweight properties are discussed. Finally, a brief outlook in the field of graphene is provided.

Application of Nanomaterials in the Negative Electrode of Lithium-Ion Batteries

Li-ion batteries (LIBs) widely power modern electronics. However, there are certain limitations in the energy density, cycle life, and safety of traditional lithium-ion batteries, which restrict their further application and development. Therefore, new methods and technologies need to be explored to improve the performance stability of LIB. The emergence of nanomaterials provides new ideas and methods for the improvement of lithium-ion batteries. Nanomaterials have special structures and properties, and can improve the performance of LIB by regulating their morphology, size, and surface chemical properties. An overview of the development in research on using nanomaterials in LIB is given in this article. First, the features and benefits of nanomaterials were described, as well as the basic principles and development history of lithium-ion batteries. The use and performance of nanomaterials in lithium-ion batteries were then elaborated from a variety of angles, including nanosilicon, nanocarbon, and nanoiron oxide. Finally, the future applications of nanomaterials in lithium-ion batteries were prospected, and their development trends and challenges were pointed out. This article aims to provide a reference for the application of nanomaterials in lithium-ion batteries and promote further development in this field.

Holistic optimization of lithium-ion battery negative electrode formulation using a combination of theory of mixtures, Box-Behnken matrix, multi-variant analysis and desirability functions of Derringer-Suich

Holistic optimization of lithium-ion battery negative electrode formulation using a combination of theory of mixtures, Box-Behnken matrix, multi-variant analysis and desirability functions of Derringer-Suich

Numerical investigation on the elastoplastic behavior and fatigue life of the current collector of lithium-ion batteries based on the electrochemical-thermal-mechanical coupling model

This paper numerically investigates the elastoplastic behavior and fatigue life of the current collector for the negative electrode of lithium-ion batteries (LIBs) based on the electrochemical-thermal-mechanical (ETM) coupling model. First, we discuss the effects of the thickness and yield stress of the current collector on the elastoplastic behavior. Then, we examine the influence of various current collector thicknesses on the stress in the active layer. Finally, the fatigue life of the current collector under different elastoplastic behaviors is predicted based on the Manson-Coffin-Basquin equation. The results indicate that the current collector will change from plastic shakedown (PS) to cyclic plasticity (CP) with decreasing current collector thickness or yield stress. Meanwhile, with the decrease of the current collector thickness, the peak stress in the current collector increases, while the stress level in the active layer decreases. The investigation of the fatigue life reveals that, the case of CP not only relieves the stress in the active layer but also provides more space (due to a thinner collector) for the active material to improve the energy density of the battery. The aforementioned studies shed light on the fatigue and elastoplastic behaviors of LIBs collectors.

Simple Estimation of Creep Properties of Negative Electrode for Lithium-Ion Battery

The macroscopic creep properties of negative electrodes in lithium-ion batteries and their estimation methods have been investigated based on the microscopic structure of the electrode. Tensile and creep tests were conducted on a negative electrode consisting of carbon powder and polyvinylidene fluoride (PVDF) binder. The stress-strain curve, the time history of the tensile strain, and the creep rupture time were measured in these tests and estimated using the simple model proposed in this study. The proposed model approximates the alignment of carbon particles as body-centered cubic (bcc) or face-centered cubic (fcc). The external load on the model was supported by a PVDF binder located between carbon particles. The test results showed that PVDF binder mechanical properties affect the macroscopic mechanical properties of the negative electrode, including the creep properties. The stress-strain curve and time history of the tensile strain were located between the upper and lower limits of the proposed model. The tensile strength and creep rupture time agree with the lower limit of the proposed model.

Effect of Water-Soluble CMC/SBR Binder Ratios on Si-rGO Composites Using µm- and nm-Sized Silicon as Anode Materials for Lithium-Ion Batteries

Silicon-containing materials are still the most promising alternatives to graphite as the negative electrodes of lithium-ion batteries. However, the different Li+ storage mechanism combined with the high capacity result in new requirements for the passive electrode components, such as the binder. To ensure sufficient cycling stability, silicon must be embedded in a suitable carbonaceous matrix. For this purpose, we used a simple ball milling process with reduced graphene oxide (rGO) to produce Si-rGO composites with µm- and nm-sized silicon particles. The rGO was synthesized previously from a two-step thermal synthesis method developed in-house. Subsequently, electrodes with varying CMC/SBR ratios (3:1, 1:1, and 1:3) were prepared from the composites containing the different Si particle sizes. It was found that the optimal binder ratio depends on the size of the Si particles. For the nm-Si-rGO composite, a CMC/SBR ratio of 3:1 results in a total capacity over 51 cycles of 20.6 Ah g−1, which means an improvement of 20% compared to CMC/SBR = 1:3 (17.1 Ah g−1). In contrast, we demonstrate that for µm-Si-rGO composites with an optimal CMC/SBR ratio of 1:1 (13.0 Ah g−1), compared to nm-Si-rGO, a higher SBR content is beneficial for the cycling behavior. Moreover, a comparison with graphite from the literature indicates that a rGO-matrix reduces the need for SBR.

Modifying nano-silicon with nano-antimony through molten salt electrolysis for superior lithium storage materials

The application of silicon to lithium-ion batteries (LIBs) remains a challenge due to the severe volume expansion effect of silicon. In this work, a nano Si-Sb bimetal is obtained by the molten salt electrolysis of mixture of silicon and antimony sulfide (Sb2S3). The uniform hybrid of antimony nanoparticles not only prevents the agglomeration of silicon but also selectively decomposes the electrolyte additives and alleviates the rupture of SEI effectively, which can mitigate the volume expansion of silicon. When used as a negative electrode for LIBs, the Si-Sb bimetallic electrode delivers a reversible capacity of 1524 mAh/g after 100 cycles at a current density of 1 A/g. Even at 3 A/g, the reversible capacity is as high as 1062 mAh/g after 200 cycles. This work offers a new way for the fabrication of Si-based alloy anodes through using molten salt electrolysis.

PVP-assisted synthesis of hollow Ni0.75Zn0.25Fe2O4 nanospheres for lithium-ion batteries

Hollow Ni0.75Zn0.25Fe2O4 nanospheres with a diameter of about 250–300 nm and thickness of 30–40 nm have been successfully fabricated through a PVP (polyvinylpyrrolidone)-assisted hydrothermal strategy. PVP plays an important role in the formation of hollow structure and a plausible formation mechanism of hollow Ni0.75Zn0.25Fe2O4 nanospheres is also proposed in this paper. The as-fabricated hollow Ni0.75Zn0.25Fe2O4 nanospheres display a good dispersibility and high specific surface area of 34.7 m2 g−1. Hollow Ni0.75Zn0.25Fe2O4 nanospheres also demonstrate satisfactory cycle life and rate performance when evaluated as a lithium ion battery negative electrode. Namely, after 120 cycles, the discharge specific capacity is 1321.3 mAh g−1 at 200 mA g−1, and the capacity retention rate is as high as 99.2%. Furthermore, the average discharge capacities are 1482.5, 1451.5, 1330.9, 1232.3, 1031.2 and 944.8 mAh g−1 under the current densities of 100, 200, 500, 1000, 2000 and 4000 mA g−1, respectively. The promising electrochemical performance of the hollow Ni0.75Zn0.25Fe2O4 nanosphere could be attributed to the unique hollow structure of nanospheres, which offers a higher specific surface area and shorten transmission pathways of electrons and ions, buffering the volume expansion during the Li+ insertion/desorption process.

An insight into lithium-ion transport in germanium-doped lithium titanate anode through NMR spectroscopy and post-carbonization for anode applications in lithium-ion battery

Adapting toward lithium titanate as a negative electrode for lithium-ion batteries led to the safest and long-lasting battery technology, especially for electric vehicle applications. However, the poor conductivity and lithium-ion diffusion of lithium titanate have to be addressed for widespread usage in next-generation E-mobility. The lithium-ion motion inside lithium titanate and germanium-doped lithium titanate was investigated through pulsed-field gradient nuclear magnetic resonance spectroscopy and temperature-dependent ionic conductivity studies. The superior charge carrier mobility of germanium enhanced the lithium-ion diffusion in lithium titanate significantly to 1.48 × 10−8 cm2 s−1 in Li4Ge0.1Ti4.9O12 at 500 °C. While germanium improves the ionic diffusion, an ex situ carbon coating was adapted over the sample for electronic conductivity enhancement. Samples with two different carbon contents (5 and 10 wt. %) were examined for electrochemical analysis. Significant improvements in battery performance were observed on carbon-coated germanium-doped lithium titanate. The carbon-coated sample gave superior initial performance (191 and 178 mAh g−1 for 10 and 5 wt. % carbon at 0.1C) than the pristine lithium titanate and preserved the exceptional capacity retention over a thousand cycles at 1C rate.

Titanium Oxyfluoride as a Material for Negative Electrodes of Lithium-Ion Batteries.

A study of the electrochemical characteristics of titanium oxyfluoride obtained with the direct interaction of titanium with hydrofluoric acid is reported. Two materials T1 and T2 synthesized under different conditions in which some TiF3 is formed in T1 are compared. Both materials exhibit conversion-type anode properties. Based on the analysis of the charge-discharge curves of the half-cell, a model is proposed according to which the first electrochemical introduction of lithium occurs in two stages: the first stage is the irreversible reaction resulting in a reduction in Ti4+/3+, and the second stage is the reversible reaction with a change in the charge state Ti3+/1.5+. The difference in material behavior is quantitative: T1 has a higher reversible capacity but lower cycling stability and a slightly higher operating voltage. The Li diffusion coefficient determined from the CVA data for both materials averages 1.2-3.0 × 10-14 cm2/s. A distinctive feature of titanium oxyfluoride anodes is the asymmetry in kinetic characteristics that revealed themselves during lithium embedding and extraction. In the long cycling regime, the excess of Coulomb efficiency over 100% was found in the present study.

Guest Ion-Dependent Reaction Mechanisms of New Pseudocapacitive Mg3 V4 (PO4 )6 /Carbon Composite as Negative Electrode for Monovalent-Ion Batteries.

Polyanion-type phosphate materials, such as M3 V2 (PO4 )3 (M = Li/Na/K), are promising as insertion-type negative electrodes for monovalent-ion batteries including Li/Na/K-ion batteries (lithium-ion batteries (LIBs), sodium-ion batteries (SIBs), and potassium-ion batteries (PIBs)) with fast charging/discharging and distinct redox peaks. However, it remains a great challenge to understand the reaction mechanism of materials upon monovalent-ion insertion. Here, triclinic Mg3 V4 (PO4 )6 /carbon composite (MgVP/C) with high thermal stability is synthesized via ball-milling and carbon-thermal reduction method and applied as a pseudocapacitive negative electrode in LIBs, SIBs, and PIBs. In operando and ex situ studies demonstrate the guest ion-dependent reaction mechanisms of MgVP/C upon monovalent-ion storage due to different sizes. MgVP/C undergoes an indirect conversion reaction to form Mg0 , V0 , and Li3 PO4 in LIBs, while in SIBs/PIBs the material only experiences a solid solution with the reduction of V3+ to V2+ . Moreover, in LIBs, MgVP/C delivers initial lithiation/delithiation capacities of 961/607 mAh g-1 (30/19 Li+ ions) for the first cycle, despite its low initial Coulombic efficiency, fast capacity decay for the first 200 cycles, and limited reversible insertion/deinsertion of 2 Na+ /K+ ions in SIBs/PIBs. This work reveals a new pseudocapacitive material and provides an advanced understanding of polyanion phosphate negative material for monovalent-ion batteries with guest ion-dependent energy storage mechanisms.

Electron and Ion Transport in Lithium and Lithium-Ion Battery Negative and Positive Composite Electrodes.

Electrochemical energy storage systems, specifically lithium and lithium-ion batteries, are ubiquitous in contemporary society with the widespread deployment of portable electronic devices. Emerging storage applications such as integration of renewable energy generation and expanded adoption of electric vehicles present an array of functional demands. Critical to battery function are electron and ion transport as they determine the energy output of the battery under application conditions and what portion of the total energy contained in the battery can be utilized. This review considers electron and ion transport processes for active materials as well as positive and negative composite electrodes. Length and time scales over many orders of magnitude are relevant ranging from atomic arrangements of materials and short times for electron conduction to large format batteries and many years of operation. Characterization over this diversity of scales demands multiple methods to obtain a complete view of the transport processes involved. In addition, we offer a perspective on strategies for enabling rational design of electrodes, the role of continuum modeling, and the fundamental science needed for continued advancement of electrochemical energy storage systems with improved energy density, power, and lifetime.

Effect of Current Density on Specific Characteristics of Negative Electrodes for Lithium-Ion Batteries Based on Heat-Treated Petroleum Coke

The results of comparative studies of the effect of current density on the average discharge voltage and specific discharge capacity of carbon electrodes based on heat-treated petroleum coke and graphite are presented. The carbon obtained by heat treatment of petroleum coke is shown to have better kinetic characteristics than graphite. The increase in the current density from 0.2 mA/cm2 (36 mA/g) to 2 mA/cm2 (364 mA/g) leads to a decrease in the discharge capacity of heat-treated petroleum coke by 26%; graphite, by 93%. When the current density is restored to 0.2 mA/cm2, the discharge capacity of carbon electrodes is also restored to its initial value. The increase in the current density is also shown to lead to increase in the average discharge voltage of lithium–carbon cells. Thus, with the increase in current density from 0.2 to 2 mA/cm2, the average discharge voltage of the lithium–carbon cells with the electrode active component of the heat-treated petroleum coke increased from 0.39 to 0.62 V; that of graphite, from 0.14 to 0.35 V.

Effect of Current Density on Specific Characteristics of Negative Electrodes for Lithium-Ion Batteries Based on Heat-Treated Petroleum Coke

Effect of Current Density on Specific Characteristics of Negative Electrodes for Lithium-Ion Batteries Based on Heat-Treated Petroleum Coke