Yolk-Shell P3-Type K0.5[Mn0.85Ni0.1Co0.05]O2:A Low-Cost Cathode for Potassium-Ion Batteries

Jiaxin Hao,Ke Xiong,Jiang Zhou ,Apparao M.Rao,Xianyou Wang,Huan Liu,and Bingan Lu*

Low-cost preparation methods for cathodes with high capacity and long cycle life are crucial for commercializing potassium-ion batteries(PIBs).Presently,the charging/discharging strain that develops in the active cathode material of PIBs causes cracks in the particles,leading to a sharp capacity fade.Here,to abate the strain release and the need for an industrially relevant process,a simple low-cost co-precipitation method for synthesizing yolk-shell P3-type K0.5[Mn0.85Ni0.1Co0.05]O2(YS-KMNC)was reported.As cathode material for PIBs,the YS-KMNC delivers a high reversible capacity(96 mAh g-1at 20 mA g-1)and excellent cycle stability(80.5% retention over 400 cycles at a high current density of 200 mA g-1).More importantly,a full battery assembled with the YS-KMNC cathode and a commercial graphite anode exhibits a high operating voltage(0.5-3.4 V)and an excellent cycling performance(84.2% retention for 100 cycles at 100 mA g-1).Considering the low-cost,simple production process and high performance of YS-KMNC cathode,this work could pave the way for the commercial development of PIBs.

Keywords

cathode materials,K0.5[Mn0.85Ni0.1Co0.05]O2,strain release,volume expansion,yolk-shell structure

1.Introduction

Potassium-ion batteries(PIBs)are cost-effective for large-scale energy storage due to the natural abundance and low cost of potassium;[1,2]and the high capacity of graphite(270 mAh g-1)that can be used as the anode.[3]Recently,we demonstrated that graphite anodes coated with a robust passivation layer could cycle for over 2000 cycles with a negligible capacity decay.[4]Notwithstanding such progress,practical applications of PIBs remain hampered due to the lack of structure stable cathode materials.Because of the large size of K+ions,a significant volume change is inevitable upon K+ions extraction and insertion into the cathode materials.[5-8]With repeated cycling,the non-uniform volume change creates internal strain that causes the particles to crack,which is one of the wellknown degradation mechanisms leading to a sharp capacity fade in PIBs.[9-12]

Previous studies have demonstrated that layered transition metal oxides can reversibly insert K+ions,and are therefore regarded as promising cathode materials for PIBs.[13,14]In addition,transition metal oxides also have a high theoretical capacity,and simple synthesis methods that are amenable for large-scale production.[15,16]From an industrial application standpoint,it is desirable to have primary particles intentionally aggregate and form microscale secondary particles so that the packing density can be improved along with a reduction in side reactions between the active material and the electrolyte.As mentioned above,to release the internal strain developed during charging/discharging,such secondary particles develop intergranular cracks.To alleviate the strain-induced particle cracking and to obtain high packing density,a rational structural design for layered transition metal oxides is needed for PIB cathodes.[17-22]In the case of this,we draw inspiration from the lithium-ion batteries(LIBs).For examples,Amine et al.demonstrated that if a thick shell completely encapsulates the core,the structural deterioration during electrochemical cycling can be suppressed,which consequently enhances the LIB’s cycle performance;[23]likewise,Yang et al.also showed that the multilayered shells around the core improve the structural stability of LIBs due to the presence of void space between the layers that act as buffer zones to accommodate charge/discharge-induced changes in volume.[24]However,no core-shell or similar structures have been investigated for PIB cathodes to date,and yet,it is worth exploring them for commercializing PIBs.

Here,for the first time,using a low-cost co-precipitation method,we synthesis a microscale yolk-shell P3-K0.5[Mn0.85Ni0.1Co0.05]O2(YS-KMNC)as cathodes for PIBs.In situ XRD profiles were collected and compared with density functional theory calculations to monitor the lattice parameters and volume changes during the charging/discharging process of PIBs with YS-KMNC cathodes.Upon K+ion deintercalation,a significant change in the lattice parameters(～4.6% expansion along c-axis and a contraction of～2.4% in the ab plane)was observed,which consequently generates a huge internal strain between the secondary particles.The finite element simulation was used to explore the influence of strain in the YS-KMNC compared with that in conventional KMNC.Compared to the solid spherical structure of conventional KMNC,the YS-KMNC structure could effectively alleviate the internal strain caused by volume change.As a result,the YS-KMNC delivered a high capacity(96 mAh g-1at 20 mA g-1)and superior cycling stability(80.5% capacity retention after 400 cycles at 200 mA g-1).Moreover,the practical utility of YS-KMNC cathodes is also demonstrated by constructing the full battery with a graphite anode.This study demonstrates that the unique yolk-shell structure may provide fresh insights and directions for developing the next-generation low-cost stable cathodes for PIBs.

2.Results and Discussion

Figure 1a is a SEM image of the YS-KMNC oxide precursor in which the uniform spherical structures(diameter ～ 8-12 μm)represent the MNC oxides.The inset is a high magnification image,from which the yolk-shell structure with a shell thickness about 2 μm is evident.The uniformly distributed pores in the yolk-shell structures are mainly caused by the release of CO2during the high-temperature decomposition of the carbonate precursor.After mixing with K2CO3and followed with annealing at 850°C,the macroscopic structures of the YS-KMNC are shown in Figure 1b,c and Figure S1.It is evident that the pores vanish,and the structure becomes more compact due to recrystallization and crystal growth of the oxide at high temperatures.Importantly,the distinct yolk-shell structure is preserved and the thickness of the shell is about 2 μm,consistent with that in the oxide precursor.We discuss later in this study that the preserved yolk-shell structure is beneficial for releasing strain that develops during volume changes.To further explore the crystal structure of YS-KMNC,transmission electron microscopy(TEM)was employed and the results are shown in Figure 1d-g.The long-range ordered lattice fringes can be seen in Figure 1e-g,which suggests high crystallinity and a highly preferred orientation.Figure 1e and f shows the presence of a regular lattice fringe with a d-spacing of 0.636nm,which corresponds to the(003)planes of the YS-KMNC.Compared with the polycrystalline particles,the long-range lattice orientation is beneficial for decreasing the potassium diffusion energy barrier and is also conducive for ensuring a superior capacity retention during cycling.[25]Figure 1h depicts the original XRD data and the Rietveld-refined profile for the YS-KMNCs.All major diffraction peaks can be indexed to a rhombohedral crystal structure with a R-3m space group.The Rietveld refinement shows that the YS-KMNC has a well-ordered layered structure(as illustrated in Figure 1i,P3-K0.5Mn0.85Ni0.1Co0.05O2) with the lattice parameters a=2.868?A and c=21.113?A,consistent with previous reports.[26,27]The XRD pattern of the conventional KMNC is shown in Figure S2,which is identical to that of the YS-KMNC,thus confirming identical crystal structures for both.Figure 1j depicts the typical yolk-shell structure and the corresponding element maps.All elements(K,Co,Ni,Mn)are uniformly distributed in the YS-KMNC due to the directional migration of the metal elements during the high-temperature calcination.[28]The two cylindrical structures in Figure 1k represent the silver electrodes that were used in the current-voltage(I-V)measurements(Figure 1l)of an isolated YS-KMNC(represented by the black spot present in between the electrodes in Figure 1k).The I-V data revealed the semiconducting nature of the YS-KMNC.

Figure 1.a)SEM image of yolk-shell MNC oxide(YS-MNC),inset:the high magnification image;b)SEM image for YS-KMNC;c)high magnification SEM image of a YS-KMNC,and the inset is a schematic of the YS-KMNC;d-g)TEM and HRTEM images of a YS-KMNC;h)XRD patterns and the Rietveld refinement plot of YS-KMNCs;i)schematic illustration of the layered structure,red:O atoms;purple:K atoms;jasper:transition metal atoms(Mn,Co,and Ni);j)elemental mapping of a typical YS-KMNC;k)an optical image of the I-V measurement setup;and l)I-V profile of a YS-KMNC.

To study the role of structure on potassium storage and the performance of YS-KMNC,cyclic voltammetry and galvanostatic measurements were performed using metal K as the counter electrode.Figure 2a shows the first three CV curves in the range of 1.5-3.9 V at a scan rate of 0.1 mV s-1.The distinct redox peaks connote reversible redox reaction between K+ions and transition metal during charge storage.The two pairs of redox peaks present below 2.7 V can be assigned to the Mn4+/Mn3+redox pair.[29]At potentials higher than 2.7 V,the reversible oxidation/reduction peaks present at～3.1 V are due to the Ni2+/Ni3+redox couple,while the peaks at～3.8 V are due to the sequential oxidation of Co3+to Co4+.[30-32]Figure S3 depicts the first three galvanostatic charging/discharging curves at a current density of 20 mA g-1.The initial voltage(vs.K/K+)of the battery is about 2.75 V,and the first charge/discharge capacity is 49/106 mAh g-1,suggesting about 0.2 mol K extraction and 0.43 mol K insertion in per formula unit in the cathode,respectively.The slight capacitance decrease in the first and second discharge can be ascribed to the irreversible reaction between the electrolyte and the cathode material.The galvanostatic curves at different current densities are shown in Figure 2b.Even at a high current density of 300 mA g-1,clear charging and discharging platforms are evident in the curves,indicating that the electrode material could withstand the rapid insertion and extraction of K+ions.As displayed in Figure 2c,the discharge capacity is 96,77,67,63,56,52,and 45 mAh g-1for YS-KMNC at a current density of 20,50,80,100,150,200,and 300 mA g-1,respectively.In comparison,the conventional KMNC delivered a capacity of only 24 mAh g-1at a current density of 300 mA g-1.As for the structural stability of the cathode,when cycled at a current density of 20 mA g-1for 55 cycles(Figure 2d),the capacity retention is 94% for the YS-KMNC with respect to the capacity of the second discharge cycle,while the conventional KMNC retains only 75% under similar conditions.When cycled at a high current density of 200 mA g-1(Figure 2g)for 400 cycles,the YS-KMNC still exhibits a high-capacity retention of 80.5% ,which is much higher than that exhibited by the conventional KMNC(64.2% after 90 cycles).

Figure 2.Electrochemical performance of YS-KMNC and conventional KMNC cathodes.CV curves a)at a scan rate of 0.1 mV s-1and galvanostatic charging/discharging curves b)at different current densities for YS-KMNC;c)rate capability at different current densities;d)cycling performance at a current density of 20 mA g-1;e)comparison of the discharge capacity,average voltage,and energy density for YS-KMNC and other reported cathode materials for PIBs;f)comparison of the cycle performance between the YS-KMNC and the reported cathode materials;and g)cycle stability at a high current density of 200 mA g-1.

Moreover,in order to evaluate the advantages of the KMNC with the yolk-shell structure for potassium storage,we compared its specific capacity,average voltage,and energy density with those of many cathode materials reported in the literature(Figure 2e and Table S2).[6,9,13,26,27,31,33-47]Apparently,although some properties of YSKMNC are inferior to those of other types of cathode materials(vanadium-based oxide,organic and Prussian blue and its derivatives),the YS-KMNC exhibits a more balance performance with remarkable capacity,high average voltage,and outstanding energy density.Generally speaking,the vanadium-based cathodes support a much higher operating voltage,but their strong toxicity greatly limits their application.The organic cathode materials exhibit a higher specific capacity but poor stability,while the Prussian blue and its derivatives,despite their high operating voltage and capacity,suffer from difficulty in controlling defects and water,which makes it challenging for a large-scale preparation.[11,48-52]On the other hand,the layered transition metal oxides have a high theoretical capacity and are easy to synthesize for cost-effective mass production.Figure 2f and Table S2 also present the comparison of cycle stability,average voltage,and electrolyte between YSKMNC and other layered cathode materials for PIBs.[13,14,27,30,31,41,42,44-47]It is obvious that YS-KMNC has a higher capacity retention and an excellent cycling stability,which confirms the superiority of the yolk-shell structure design.From the above discussion,it is clear that the YS-KMNC delivers an outstanding energy storage performance not only in cycle stability but also in capacity and energy density.

To further explore the structural evolution during K+ion intercalation and deintercalation,in situ XRD measurements were performed for two complete charging/discharging cycles and the results are displayed in Figure 3 and Figure S4.It is noteworthy that the in situ spectra of the YS-KMNC and conventional KMNC show no difference,suggesting that the unit cell changes are consistent during charging and discharging for both types of cathodes.As observed in Figure 3a and 3b,upon discharging,an obvious shift to higher angle is observed for(003)and(006)peaks.The shift in the(003)and(006)peak positions indicates a contraction along the c-axis,because the insertion of positive charge K+ions can decrease the electrostatic repulsion between the adjacent oxygen layers.[43,44]At the same time,the(101)and(102)peaks shift toward lower angles,which connote expansion in the ab plane during the insertion of K+ions,which is caused by an increase in the metal ionic radii when transition metal ions gain electrons during the discharge process.[23,31]When recharged to 3.9 V,the K+ions are extracted from the lattice,and the(003),(006),(101),and(102)peaks all shift back to their original peak positions,indicating a reversible insertion/extraction process of K+ions in the cathode materials.As reported in previous research, for P3-K0.5MnO2and P3-K0.5Mn0.9Ni0.1O2,both exhibit an obvious peak splitting in their(101)and(012)peaks when charged to a higher voltage due to the appearance of distorted P3 phase(P’3 phase,C2/m space group).[30]For the YS-KMNC and conventional KMNC,however,no splitting in the(101)and(012)peaks was observed at high voltage,indicating a higher structural stability owing to the addition of cobalt element that stabilizes the structure.[32]Overall,the in situ XRD study suggests that no additional diffraction peaks are present,and the change in the peak positions is due to a change in the lattice spacing.In other words,the entire electrochemical process is a single-phase reaction and consistent with that reported previously for K0.75Mn0.8Ni0.1Fe0.1O2,P3-K0.45Ni0.1Co0.1Mn0.8O2,and P3-K0.54Mn0.5Co0.5O2.[31,43,46]Obviously,such simple single-phase electrochemistry is beneficial for the cycle stability.

Figure 3.Panels a)and b)depict in situ XRD patterns of YS-KMNC cathode and the corresponding charge/discharge processes at 20 mA g-1in the voltage range of 1.5-3.9 V;and c)predicted lattice parameters for KxMn0.85Ni0.1Co0.05O2as a function of K+ions present in the structure.

We further investigate the crystal structure as a function of different K+ion concentration using the density functional theory calculation(Figure 3c).By comparing the K content in the original material with the change in K content at the first charge and discharge,we selected P3-KxMn0.85Ni0.1Co0.05O2(x=0.25,0.5,and 0.75)as our model compounds to calculate the change in lattice parameters.As displayed in Figure 3c and Table S1,when K+ions are inserted,the c-lattice parameter gradually decreased from～19.39?A to～18.52?A,and the ab plane or in-plane parameter increased from 2.72?A to 2.79?A.The results of the simulation are in agreement with the in situ XRD data. Comparing P3-K0.75Mn0.85Ni0.1Co0.05O2with P3-K0.25Mn0.85Ni0.1Co0.05O2,its c-lattice expands by～4.6% along with a contraction of～2.4% in the ab plane,which are all almost twice that of LIBs.[53]As reported for LIBs,the non-uniform changes along the c-axis,and in the ab plane,during the charging and discharging process creates a huge internal strain,which consequently cracks electrode materials.[54]In PIBs,the huge lattice change can result in severe internal strain,which will lead to more serious material cracking.For our YS-KMNC cathode,however,it delivers an outstanding cycling stability,implying that its structural design is meritorious in that it can accommodate much more strain generated in PIBs,but further research is necessary.

Figure 4b and c shows the models and results for finite element simulations through which strain in different parts for the YS-KMNC and the conventional KMNC during volume expansion was deduced.To ensure the accuracy of the analysis,the mechanical properties of all unit cells were kept consistent except for the differences in the internal structure.Clearly,the internal strain at the center of the spherical particle is much higher than at the surface.This result is consistent with the observed phenomenon,that is,the layer transition metal oxide begins to crack from the inside under high voltage in LIBs.[54]Figure 4b depicts the strain profile for the yolk-shell structure.As can be seen,the center of the double-layer structure is also subjected to a large strain,but relatively this strain is less than that experienced by the solid spherical structure.In addition,the dark blue area in the strain profile of the yolk-shell structure is much larger than that of the conventional spherical structure,which suggests that the yolk-shell structure experiences a lower internal strain throughout the sphere with volume changes.Figures 4d,e,and Figure S5 show the structural morphology of the cathode materials after cycling.Clearly,the structure of YS-KMNC is relatively intact,but the conventional KMNC suffers a greater structural damage,indicating that the yolk-shell structure has better mechanical stability.Thus,compared with the solid spherical structure,the yolk--shell structure can better alleviate the internal strain generated by the insertion or extraction of K+ions(Figure 4a),which mitigates particle cracking and leads to the observed improvements in the electrochemical properties.[55]Moreover,in the absence of cracks in the particles,(i)a deeper penetration of electrolyte into the particle is circumvented,which otherwise could accelerate the growth of cracks;and(ii)the side reaction between electrolyte and cathode materials is reduced,which further improves the cycle stability of the cathode material.[56,57]

Figure 4.a)Illustration depicting the mechanisms that lead to particle cracking and stable particle in conventional and YS-KMNC,respectively;b,c)the finite element model for strain variation during volume expansion;and d)and e)SEM images of conventional KMNC and YS-KMNC after 100 cycles.

To assess the feasibility of using YS-KMNC in practical applications,a full battery using YS-KMNC as cathode and graphite as anode was assembled.Figure 5a schematically depicts the working principle of the full battery.Before assembling the full battery,the graphite anode is discharged to 0.01V as a half battery to remove the large irreversible capacity,as well as to form a stable SEI film on the surface,which is beneficial for improving the coulombic efficiency of the full battery.The string of lighted LEDs(held by the thumb)indicates that the full battery is well suited for practical applications(Figure 5b).Figure 5c suggests that the full battery can be operated in the voltage range of 0.5-3.4 V,and exhibits a considerable discharge capacity of 57 mAh g-1(Figure 5d)at a high current density of 100 mA g-1(based on the mass of the cathode).After 100 cycles,the slight change in the charge-discharge curves indicates a nearly consistent energy storage mechanism in the full battery.Additionally,the full battery delivers a high coulombic efficiency of＞99% and a high-capacity retention of 84.2% after 100 cycles(Figure 5e).The outstanding cycle stability is ascribed to the novel structure of YS-KMNC that mitigates particle cracking due to the strain created during cycling.

Figure 5.a)Schematic illustration of the YS-KMNC/graphite full battery;b)a string of lighted LEDs powered by two full batteries,inset:an optical image of the batteries;c)charge-discharge profiles of the half battery and full battery;d)charge-discharge profiles of the full battery cycled at a voltage range of 0.5-3.4 V with a current density of 100 mA g-1;and e)cycling performance at a constant current density of 100 mA g-1.

3.Conclusion

In summary,YS-KMNC has been synthesized by a low-cost,commercially viable co-precipitation method,and its electrochemical properties are compared with those of conventional KMNC.The analysis of in situ XRD revealed that the layered KMNC undergoes a huge lattice change(expands～4.6% along c-axis and shrinks～2.4% in the ab plane)upon cycling,which creates internal strain among secondary particles leading to severe particle cracking.However,such strain-induced particle cracking can be effectively alleviated by using yolk-shell KMNC cathodes as demonstrated experimentally,and ratified by the finite element simulations in this study.When used as cathode for PIBs,the YS-KMNC yielded a high capacity of 96 mAh g-1at 20 mA g-1and an excellent cycle stability (80.5% retention over 400 cycles at 200 mA g-1).Moreover,potassium-ion full batteries(based on YSKMNC cathode/graphite anode)were also assembled,which delivered a high operating voltage(0.5-3.5V)and high-capacity retention of 84.5% over 100 cycles.Due to the low-cost and commercially viable synthesis method,the stable YS-KMNC is posited to promote the largescale applications of PIBs.

4.Experimental Section

Synthesis of yolk-shell K0.5[Mn0.85Ni0.1Co0.05]O2:All the chemicals were analytical grade and used without further purification.As a first step,the yolk-shell[Mn0.85Ni0.1Co0.05]CO3precursor was synthesized using the co-precipitation method.Firstly,MnSO4and NiSO4were dissolved in water to obtain a mixed solution with a concentration of 1.6 M(Mn:Ni=0.85:0.15),which is hereafter referred as solution A.Next,a mixed solution B(concentration of 1.6 M)is also prepared by dissolving the MnSO4and CoSO4in water(Mn:Co=0.85:0.15).Then,solution A(70 ml)and solution B(30 ml)were mixed and pumped into a stirred tank reactor.At the same time,the Na2CO3solution(1.6 M)and NH3·H2O solution(0.32 M)were also pumped into the tank reactor to react with sulfate solution.The pumping rate,pH,temperature,and stirring speed must be carefully controlled(pumping rate:0.9 ml min-1;pH:7.5;temperature:45°C;stirring speed:1500 r min-1).After pumping the above solution,further pumping must be stopped for an hour for aging the reaction.Next,pump another 150 ml mixed solution(100 ml solution A and 50 ml solution B).The conventional spherical[Mn0.85Ni0.1Co0.05]CO3was obtained by directly pumping a mixture of 170 ml solution A and 80ml solution B without intermediate aging process.To obtain oxide precursors,the carbonate precursors were calcined in a muffle furnace for 5h at 500°C.Finally,the oxide powder was mixed with appropriate amount of K2CO3and calcined at 850°C for 12 h in air to get yolk-shell K0.5[Mn0.85Ni0.1Co0.05]O2(or YS-KMNC)and conventional K0.5[Mn0.85Ni0.1Co0.05]O2(or conventional KMNC).

Material characterization:The Bruker D8 ADVANCE(Cu Kα)was used to obtain the XRD data.For in situ XRD tests,the operando experiments were run at a current density of 20 mA g-1with a potassium as the counter electrode and the electrolyte is 0.8 M KPF6.The morphology was observed by scanning electron microscope(FESEM,Hitachi S-4800,15 kV).The elemental mapping was performed using an inductively coupled plasma series mass spectrometer(Agilent 7900 ICP-MS).The I-V curves were measured by transferring the YS-KMNC onto an ITO pre-patterned substrate to prepare the two-electrode device.

Electrochemical measurements:The cathode materials were mixed with acetylene black,polyvinylidene fluoride(mass ration:6:3:1)in N-methylpyrrolidinone(NMP)to obtained a mixed slurry.Then,the slurry was coated onto Al foil and dried at 120°C in vacuum oven for 12 h.All batteries were assembled inside a glove box(both oxygen and water content are below 0.5 ppm).For half batteries,the K metal was used as the anode.For electrolyte selection,it is worth mentioning that although KFSI-based electrolytes exhibit better performance for most PIB anode materials,they are expensive and will corrode aluminum foil under high voltages.[57]Therefore,we use 0.8 M KPF6as electrolyte for our cathode materials.The average mass loading of active material on the cathode is 1.5-2 mg cm-2.The charge/discharge tests were performed using the Neware BTS-53 system in the voltage range of 1.5-3.9 V.The CV curves were recorded using the electrochemical workstation(CHI660E)at a scan rate of 0.1 mV s-1(1.5-3.9 V vs K/K+). All electrochemical testing was performed at room temperature.

For full battery,commercial graphite was used as anode.The anode was prepared as follows:Graphite,acetylene black,and polyvinylidene fluoride with a mass ratio of 8:1:1 were mixed in NMP to obtain a uniform slurry.Next,the slurry was coated onto Al foils and dried at 80°C in a vacuum oven for 12 h.Before assembling the full battery,the anode was first assembled as a half battery and discharged to 0.01 V to remove the irreversible capacity at the first discharge.For the full battery,the capacity ratio of the cathode and anode was about 1:1.05.

Density functional theory calculation(DFT):The electronic structures were computed by the Vienna ab initio simulation package(VASP)of density functional theory(DFT).The projector-augmented wave(PAW)model with the Perdew-Burke-Ernzerhof(PBE)function was employed to describe the interactions between core and electrons.An energy cut-off of 450 eV was used for the planewave expansion of the electronic wave function.The Brillouin zones of all systems were sampled with the gamma-point centered Monkhorst-Pack grids.A 2×4×1 Monkhorst-Pack k-point setup was used for bulk geometry optimization.The force and energy convergence criteria were set to 0.02 eV?A-1and 10-5eV,respectively.

Finite element simulation analysis:The internal strain caused by the volume expansion due to the insertion of K+ions was analyzed using finite element method with the simulation software of ANSYS Workbench.To simplify the model,all cells were assumed uniform and with the same mechanical parameters.For expansion coefficients(βij),we set β11= β22=-2.5% ,β33=4.5% ,and others βij=0,consistent with the DFT calculation.[58]The strain and strain caused by the insertion of K+ions was described by the following constitutive equations:[18]

where ?ijis the stretch tensor, σijis the strain tensor,v is Poisson’s ratio,and E is Young’s modulus.All mechanical parameters are obtained by the DFT calculation.

Acknowledgments

This work was financially supported by the National Nature Science Foundation of China(Nos.51922038,51672078,51932011,51972346,51802356,and 51872334),the Hunan Outstanding Youth Talents(No.2019JJ20005),and the Innovation-Driven Project of Central South University(No.2020CX024),and AMR acknowledges the financial support from NASA-EPSCoR under Award#NNH17ZHA002C and South Carolina EPSCoR/IDeA Program under Award #18-SR03.

Conflict of Interest

The authors declare no conflict of interest.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.