Macro-micro combination-based method for quantitatively evaluating battery electrode charging strategy

Abstract

Disclosed in the present invention is a macro-micro combination-based method for quantitatively evaluating a battery electrode charging strategy, comprising: constructing an electrochemical-stress mod

Description

The present disclosure relates to a method for macro-microscopic joint quantitative evaluation of battery electrode charging strategies, and belongs to the field of power battery technologies. BACKGROUND As a critical energy storage device for electric vehicles, power batteries have a significant impact on the performance and promotion of electric vehicles. The negative electrode, as an important component of the power battery, plays a crucial role in the performance and rapid charging capability of the battery. In the past few decades, traditional negative electrode materials have mainly focused on graphite-based materials, which have been widely used in many applications due to their high energy storage density and long cycle life. However, graphite anodes have some limitations in high-power discharge and rapid charging. To overcome these limitations, researchers have begun to introduce a series of new negative electrode materials, such as silicon-based materials, silicon nitride, siliconcarbon composites, etc. These new materials have been extensively studied to improve the charge transfer rate of the negative electrode and enhance rapid charging performance. In terms of charging strategies, the traditional constant current-constant voltage (CC-CV) charging strategy is widely adopted in commercial applications. However, with the introduction of new negative electrode materials, traditional charging strategies cannot fully exploit the performance potential of the negative electrode. Therefore, researchers have proposed a series of improved charging strategies, such as pulse charging and discharging strategies, progressive charging strategies, etc., aiming to optimize the negative electrode charging process and improve battery performance and lifespan. However, for the current electrode charging strategy evaluation methods, some researchers evaluate the impact of charging strategies on battery performance through performance tests or cycle tests. However, these methods are mostly indirect evaluations and cannot intuitively achieve quantitative analysis of charging strategies. Although researchers have conducted extensive studies on electrode charging strategies and established relevant evaluation methods, there is a lack of a comprehensive macro-microscopic joint assessment method that considers the relationship between microstructure and macroscopic performance to achieve a comprehensive evaluation of electrode charging strategies. SUMMARY Objective: Addressing the shortcomings in the prior art, the present disclosure provides a method for quantitatively evaluating battery electrode charging strategies based on macro-microscopic joint assessment. By constructing an electrochemical-stress model, designing rate optimization strategies, quantitatively verifying the rate optimization strategies through macro-microscopic joint assessment, and conducting macro-microscopic joint analysis and evaluation. Technical Solution: A method for macro-microscopic joint quantitative evaluation of battery electrode charging strategies, characterized by comprising the following steps: SI: constructing an electrochemical-stress model to determine the distribution and evolution of electrode diffusion stress; S2: based on the law of stress evolution during lithiation obtained in SI, using a multi-stage constant current optimization strategy to optimize the lithiation process, designing rate optimization strategies according to the material's yield strength stress; S3: quantitatively verifying the rate optimization strategies designed in S2 through long-cycle testing, EIS electrochemical impedance spectroscopy testing, scanning electron microscopy testing, and selected area electron diffraction testing for macroscopic and microscopic validation, respectively; and S4: performing a macro-microscopic joint analysis on the quantitative validation results from S3: where by jointly comparing the volume expansion rate of negative electrode particles and the long-cycle performance associated with different optimization strategies, a macro-microscopic joint quantitative evaluation of the optimization strategies is conducted. The present disclosure constructs an electrochemical-stress model to determine the distribution and evolution of electrode diffusion stress. Based on the law of stress evolution during lithiation, a multi-stage constant current optimization strategy is adopted to optimize the lithiation process, and rate optimization strategies are designed according to the material's yield strength stress. The rate optimization strategies are quantitatively validated through long-cycle testing, electrochemical impedance spectroscopy testing, scanning electron microscopy testing, and selected area electron diffraction testing, enabling macroscopic and microscopic joint quantitative evaluation. Preferably, step SI specifically includes the following steps: S101: using a half-cell and a simplified two-dimensional plane model, the distribution and evolution of electrode diffusion stress are converted into a plane strain problem to obtain the electrochemical reaction equation; SI02: calculating the normalised equivalent stress of the battery to obtain the stress relationship equation; SI03: based on the electrochemical reaction equation and stress relationship equation obtained in SI01 and SI02, establishing the electrochemical-stress model and determining the distribution and evolution law of electrode diffusion stress. Preferably, the specific steps of SI01 are as follows: using a half-cell and a simplified two-dimensional plane model, the distribution and evolution of electrode diffusion stress are converted into a plane strain problem, where the electrolyte control equations consist of charge conservation and mass conservation equations: loRT <^ln / —--- Id--— ^IncJ (^-l)Vlnce+4 =0 (1) r\C ( 7 t i ^ + ^-\^seD^ce+^\=Re (2) where, oe is the electrolyte conductivity; (pe is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is Faraday's constant; / is the activity coefficient of the salt; ce is the concentration of the electrolyte salt; t+ is the migration number of lithium ions; ie is the electrolyte current density; £e is the volume fraction of the electrolyte; De is the diffusion coefficient of the electrolyte salt; Re is the total sum of lithium ion sources in the electrolyte; t is time. The control equation for the electrode is defined by Ohm's law: V-4 =° (3) where, is represents the electrode current density. The electrochemical reactions at the interface between the electrode and electrolyte are described by the Butler-Volmer equation: / -aFt] c, \Co,ref J (4) (5) where, jr represents the local current density; 10 is the exchange current density; aa is the anodic transfer coefficient, with a value of 0.5; ac is the cathodic transfer coefficient, with a value of 0.5; is the overpotential; io,,e / is the reference exchange current density; ce, / e / is the reference electrolyte concentration. The conservation of lithium ions in the active material under the influence of the electric field can be defined by Fick's law. The diffusion-based transport of lithium ions is given by the mass conservation equation of Equation (6): where, c is the concentration of lithium ions in the solid phase; J is the diffusion flux; t is time. According to kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of active particles: J = -McX / / (7) where, M is the migration rate of lithium in the solid phase; / / is the chemical potential. To reflect the effect of stress on the diffusion process, the static stress term is added to the chemical potential: / / = / / 0 + RT In X - Qcrh ' _ (8) . h 3 where, / / o is a constant representing the chemical potential under stress-free conditions; X is the molar fraction of lithium ions; Q is the partial molar volume; ch is the hydrostatic stress; on is the normal stress in the x-axis direction; 022 is the normal stress in the y-axis direction; 033 is the normal stress in the z-axis direction. Preferably, the specific steps of SI02 are as follows: - assuming that the active particles are not subjected to any external forces; - assuming isotropic volume changes; - consider the elastic behaviour of the active material; - neglecting the influence of particle morphology and its related spatial arrangement on the transport of lithium in the electrode; and - not considering failure criteria of particles, only calculating the generated stress. The expression of solid mechanics in the initial configuration is: , V (9) Fd =I + ^u where, u represents displacement; Fa is the elastic deformation gradient; 5 is the elastic stress tensor; and I is the identity tensor. The thermal strain eth caused by thermal expansion is given by Equation (10): {S = C-.sel £el Fh FFt -I (10) where, C is the elastic tensor; is the elastic strain tensor; 8tot is the total strain tensor; a is the thermal expansion coefficient; Tre / is the reference temperature; I is the velocity gradient tensor; F is the deformation gradient. For isotropic spherical particles, the strain components are related to the radial displacement u. Based on the theory of large deformation continuum mechanics, the strain-displacement relationship can be expressed as: 1 f du, du du, du. dxt dxj dxj (11) where, ey is the strain component, uh uj, Uk are displacement components, x,, x} are position components. The constitutive relationship for diffusion stress-strain of lithium ions can be expressed as: (12) where, Ey is the strain component; E is Young's modulus; v is the Poisson's ratio; 0¾ is the stress component; 5y is the Dirac delta function, which equals 1 when i =J and 0 when i j. cO is the initial concentration of lithium ions in the solid phase. For the assumed spherical particles, stress can also be divided into radial stress and tangential stress. Equation (12) can be written as: / \ lp / X / / \ / \ X “I ( £ — c-a ) fl \r) v ) -1¼ lr) + ^)) J+--- Lj 3 t \ 1 r / \ / (c-c^Q. s0[r)= — \a0[r)^2var[r) +1-- E 3 ' (13) where er(r) and ee(r) are the radial and tangential strain components respectively; (Tr(r) and oe(r) are the radial and tangential stress components respectively. For the spherical particles under no external forces, the stress equilibrium equation for the sphere is: Jcr 2 --+ dr r (14) where, r is the radius of the sphere, oyand oe are the stress components in the axis coordinates. For the elastic deformation of a sphere, the relationship between strain and displacement of the particle is: du dr u r (15) where, er and eg are the strain components in the axis coordinates, u is displacement. During lithiation, when spherical electrode particles are unconstrained externally, the surfaces of the spherical electrode particles are in a state of stress boundary freedom. Therefore, the following boundary conditions apply: U=° I .. =0 By combining equations (13) to (15) and equation (16), we can obtain the relationship between lithium-ion concentration and diffusion stress: where cav(r) is the average lithium concentration inside the active particle. When r approaches 0, cm(r) approaches c(0), then the stress at the centre of the particle is: 2FO lima, (r) = lima,(r) = —----(cOT(Rs) c(0)) y_' y_9 1-v ' (18) The above equation indicates that the stress at the center of the spherical particle is hydrostatic pressure. In the stress tensor of the spherical particle, or(r) =0^(1). Therefore, the average hydrostatic stress is: -c(r)) (19) after elastic deformation, if the stress exceeds the yield strength of the material, the material will undergo corresponding plastic deformation. The value of the yield criterion is equivalent to the Von Mises stress of the battery, which is calculated by the formula: a = ' 2 (20). Preferably, the specific steps of SI03 are as follows: based on the Nernst-Einstein relationship, relating the migration rate M of lithium in the solid phase to the solid-phase diffusion coefficient D as follows: D=MRT, and combining equations (7) and (8) to obtain: 1 1 N(RT\nX) = RT—NX = RT-Nc X c (21) substituting Equation (8) and Equation (21) into Equation (7) to simplifyEquation (8) to: Qc - RT substituting Equation (21) back into Equation (6) to obtain: de ( . Q. Qc , — = D\ --Vc-V<t,--V2cr dt { RT RT ‘ (23) at the initial moment, the concentration of solid-phase lithium ions is 0, and the flux of lithium ions at the interface between the solid phase and the liquid phase is determined by the surface current density jr of the particles. Therefore, the initial and boundary conditions are as follows: 4..=° 4½ p in summary, the relationship between diffusion stress and lithium-ion concentration is obtained de ~dt J = -D c — a Fn ) ( -a Fn —-- -exp —2-- RT ) I RT Preferably, the specific steps of S2 are as follows: S201: determining the stress range of material yield strength; S202: designing the rate optimization scheme: using a smaller rate to suppress deformation and stress in the negative electrode particles during the peak stress generation stage; then, using a larger rate to accelerate lithium insertion or extraction to design an optimization scheme; when the stress exceeds the stress range of the yield strength determined in S201, continuing to optimize the stress within the exceeded range; and for the stresses that do not exceed the range, continuing to maintain the original charging or discharging rate. Preferably, the specific steps of S201 are as follows: From the mechanism of the influence of rate on stress, it can be seen that the magnitude of the rate has a significant impact on stress. Lower rates can greatly reduce stress. From the discussion of stress changes during the charging and discharging processes, it can be observed that during the lithium insertion process, the stress reaches its peak at the initial charging stage and then gradually decreases, while during the lithium extraction process, the stress behaves in the opposite manner. Therefore, a smaller rate can be used during the peak stress generation stage to suppress deformation and stress in the negative electrode particles. Then, a larger rate can be used to accelerate lithium insertion / extraction. Assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium-ion concentration, we obtain the following equation: ar = ^ro '1 0-53 ■............................... | (25) I c max / where, oyo is the yield stress of the negative electrode before lithiation; c is the lithium-ion concentration; cmax is the saturation lithium-ion concentration. Preferably, the specific steps of S3 are as follows: S301: Macroscopic quantitative validation and evaluation of the rate optimization scheme through long-cycle tests and EIS (Electrochemical Impedance Spectroscopy) tests. S302: Microscopic quantitative validation and evaluation of electrode slices by disassembling the battery after the cycle test in S301 and conducting scanning electron microscopy (SEM) tests and selected area electron diffraction (SAED) tests on the electrode slices. Preferably, the specific steps of S301 are as follows: S3011: optimization verification through long-cycle tests for the rate optimization scheme: Long-cycle tests are conducted to evaluate the long-term performance of the battery under different optimization strategies. By comparing the charge-discharge capacity, charge-discharge efficiency, and capacity retention rate of the battery under different optimization strategies during cycling, the influence of the rate optimization scheme on the long-term cycling performance of the battery can be comprehensively evaluated. The method to obtain Coulombic Efficiency (CE) is as follows: C£ = ^3^ X100% (26) where Cdtscharge is the discharge capacity and Charge is the charge capacity. The method to obtain specific discharge capacity C is as follows: XT । _ ^discharge (27) m where, Cdischarge represents the discharge capacity of the battery, and m represents the mass of the electrode active material. S3012: optimization verification of the rate optimization scheme using EIS (Electrochemical Impedance Spectroscopy) tests: Conduct EIS tests on batteries cycled under different optimization strategies to obtain the electronic transfer impedance of batteries cycled under different optimization strategies for comparison. The electrode processes in the battery are treated as equivalent to a simple circuit composed of resistors and capacitors in series and parallel. By applying a perturbation signal and observing the corresponding output signal, the equivalent circuit model of EIS is determined based on the EIS spectrum measured. Preferably, the specific steps of S302 are as follows: S3021: optimization verification of the rate optimization scheme using scanning electron microscopy (SEM) tests: Observing the pulverisation phenomenon of negative electrode particles and changes in the thickness of the active material layer. Scanning electron microscopy utilises the differences in characteristics of micro-regions on the material surface. Under the action of an electron beam, different brightness differences are generated in different regions of the sample, thereby obtaining images with a certain contrast. The imaging signals are secondary electrons, backscattered electrons, or absorbed electrons, among which secondary electrons are the main imaging signals. The high-energy electron beam bombards the sample surface, exciting various physical signals on the sample surface, and then different signal detectors are used to receive the physical signals and convert them mto image information. S3022: optimization verification of the rate optimization scheme using selected area electron diffraction (SAED) tests: microscopic testing of irreversible volume expansion generated by electrode material particles after long cycling. The lattice spacing d after cycling is calculated from the electron diffraction pattern, and then the lattice constant a and the unit cell volume are calculated using Equation (28) based on the formula for the lattice spacing of cubic crystals. The formula for calculating the lattice spacing of cubic crystals is: d= . a (28) where, d denotes the lattice spacing, a denotes the lattice constant, and h, k, I denote the Miller indices of crystal planes. Selected area electron diffraction utilises the correspondence between selected area morphology observation and electron diffraction structure analysis to achieve in-situ analysis of the morphology characteristics and crystallographic properties of crystal samples. By setting a selected area aperture on the objective lens imaging plane, the diffraction region is selected and confined. Only the sample micro area where the internal viewpoint of the aperture hole is located can be penetrated by the imaging electron beam, thereby achieving the purpose of matching microscopic observation with electron diffraction. Advantages: By adopting a macro-microscopic joint assessment approach, the present disclosure investigates the effects of charging strategies on the microstructure of electrode materials and the cycling performance of batteries, and quantitatively reveals the optimization effects of different strategies. By establishing an electrochemical-stress model, the micro-reaction kinetics and stress response of the electrode during charging are determined, providing a more accurate basis for optimizing charging strategies. Through macroscopic performance evaluation based on long-cycle testing and EIS electrochemical impedance spectroscopy testing, the feasibility of optimized charging strategies in dynamic battery applications is validated. The microscopic evaluation results from SEM scanning electron microscopy analysis and SAED selected area electron diffraction analysis are combined with macroscopic evaluation results to achieve a joint quantitative evaluation of cycle-induced stress and volume expansion rate for different optimization strategies. By considering both the microscopic properties of electrode materials and the macroscopic performance of charging strategies, a more comprehensive and accurate assessment of the impact of different charging strategies on battery performance is achieved, thus optimizing charging strategies to enhance battery performance and cycle life. BRIEF DESCRIPTION OF THE DRAWINGS In order to more clearly illustrate the technical solutions in the embodiments or prior art of the present disclosure, the accompanying drawings to be used in the description of the embodiments or prior art will be briefly introduced below, and it will be obvious that the accompanying drawings in the following description are only embodiments of the present disclosure, and that for a person of ordinary skill in the field, other attachments can be obtained in accordance with the accompanying drawings provided, without putting in any creative labour. FIG. 1 shows a flow chart of the method of the present disclosure. FIG. 2 shows a schematic diagram of two-dimensional single-particle porous silicon. FIG. 3 shows a lithiation diagram of single-particle silicon. FIG. 4 shows a comparison of test and simulated discharge curves. FIG. 5 shows a stress interval diagram of the yield strength of the negative electrode material during IC charging and discharging. FIG. 6 shows the evolution of the stress on the surface of the silicon active particles under different optimization strategies: (a) Scheme 1 (b) Scheme 2 (c) Scheme 3 (d) Scheme 4. FIG. 7 shows the evolution of the stress in the centre of the silica-active particles under different optimization strategies: (a) Scheme 1 (b) Scheme 2 (c) Scheme 3 (d) Scheme 4. FIG. 8 shows the comparison of (a) long cycling, (b) EIS fitting and (c) charge transfer resistance for different optimization strategies at 5°C. FIG. 9 shows the comparison of (a) long cycle, (b) EIS fitting and (c) charge transfer resistance for different optimization strategies at 25°C. FIG. 10 shows the comparison of (a) long cycle, (b) EIS fitting and (c) charge transfer resistance for different optimization strategies at 55°C. FIG. 11 shows the surface and cross-section comparisons of SEM of electrode sheets after cycling with different optimization strategies at 5 °C: (a, f) - 1 C; (b, g) - Scheme 1; (c, h) - Scheme 2; (d, i) - Scheme 3; (e, j) - Scheme 4. FIG. 12 shows the surface and cross-section comparisons of SEM of electrode sheets after cycling with different optimization strategies at 25°C: (a, f) -1 C; (b, g) - Scheme 1; (c, h) - Scheme 2; (d, i) - scheme 3; (e, j) - Scheme 4. FIG. 13 shows the surface and cross-section comparisons of SEM of electrode sheets after cycling with different optimization strategies at 55°C (a, f) -1 C; (b, g) - Scheme 1; (c, h) - Scheme 2; (d, i) - Scheme 3; (e, j) - Scheme 4. FIG. 14 shows the electron diffraction test of the SAED selected area for (a) Scheme 1 and (b) Scheme 3 at room temperature 5°C. FIG. 15 shows the SAED selected area electron diffraction test plot of (a) Scheme 1 versus (b) Scheme 4 at room temperature 25°C. FIG. 16 shows the SAED selected area electron diffraction test plot of (a) Scheme 2 versus (b) Scheme 3 at a high temperature of 55°C. DETAILED DESCRIPTION OF THE EMBODIMENTS The technical solutions in the embodiments of the present disclosure will be described clearly and completely in the following in conjunction with the accompanying drawings in the embodiments of the present disclosure, and it is obvious that the described embodiments are only a part of the embodiments of the present disclosure and not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by a person of ordinary skill in the art without making creative labour fall within the scope of protection of the present disclosure. In the description of the present disclosure, it is to be understood that the terms "top", "bottom", "front", "back", "left", "right", "vertical", "horizontal", "top ", "bottom", "inside", "outside", etc. indicate orientation or positional relationships based on those shown in the accompanying drawings, and are intended only to facilitate the describe the present disclosure and to simplify the description, and are not intended to indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore are not to be construed as limitations of the present disclosure. In the present disclosure, unless otherwise expressly provided and limited, "over" or "under" the first feature of the second feature may include the first and second features being in direct contact or the first and second features being in contact not directly but by means of additional features between them. The first feature is in contact with the second feature. Furthermore, the first feature being "above", "above" and "above" the second feature includes the first feature being directly above and diagonally above the second feature, or simply indicating that the first feature is horizontally higher than the second feature, above the second feature. The first feature being "below", "under", and "beneath" the second feature includes the first feature being directly below and diagonally below the second feature, or simply indicating that the first feature is less than the second feature in horizontal height, second feature. As shown in FIG. 1, A method for macro-microscopic joint quantitative evaluation of battery electrode charging strategies, is characterized by comprising the following steps: SI: constructing an electrochemical-stress model to determine the distribution and evolution of electrode diffusion stress. SI01: using a half-cell and a simplified two-dimensional plane model, the distribution and evolution of electrode diffusion stress are converted into a plane strain problem to obtain the electrochemical reaction equation: As shown in FIG. 2, using a half-cell and a simplified two-dimensional plane model, the distribution and evolution of electrode diffusion stress are converted into a plane strain problem. The electrolyte control equations consist of charge conservation and mass conservation equations: <^+^^fl + |^V-l)Vhi^^ (1) F 4 emce de ( it} s —— + V ■ —c 1 )\ c +.......-.......-..... = R (2) e I e e e p I e \ / Where, <7e is the electrolyte conductivity; is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is Faraday's constant; / is the activity coefficient of the salt; ce is the concentration of the electrolyte salt; t+ is the migration number of lithium ions; ie is the electrolyte current density; ee is the volume fraction of the electrolyte; De is the diffusion coefficient of the electrolyte salt; Re is the total sum of lithium-ion sources in the electrolyte; t is time. The control equation for the electrode is defined by Ohm's law: V-4=0 (3) Where, is represents the electrode current density. The electrochemical reactions at the interface between the electrode and electrolyte are described by the Butler-Volmer equation: . । f a„FrT\ ( -a Fri i=in \ exp —2— -exp —-— r 0 \ RT ) I RT zo zo.< (4) (5) Where. / / • represents the local current density; iO is the exchange current density; aa is the anodic transfer coefficient, with a value of 0.5; ac is the cathodic transfer coefficient, with a value of 0.5; is the overpotential; io.refis the reference exchange current density; ce,refis the reference electrolyte concentration. The conservation of lithium ions in the active material under the influence of the electric field can be defined by Fick's law. The diffusion-based transport of lithium ions is given by the mass conservation equation of Equation (6): ^+V.j = o (6) dt Where, c is the concentration of lithium ions in the solid phase; J is the diffusion flux; t is time. According to kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of active particles: J = -McX ju. (7) Where, M is the migration rate of lithium in the solid phase; Li is the chemical potential. To reflect the effect of stress on the diffusion process, the static stress term is added to the chemical potential: fi = / uRT]nX Qa ' .^11+^22+^33 (8) h 3 Where, / / 0 is a constant representing the chemical potential under stress-free conditions; X is the molar fraction of lithium ions; Q is the partial molar volume; Oh is the hydrostatic stress; on is the normal stress in the x-axis direction; 022 is the normal stress in the y-axis direction; 033 is the normal stress in the z-axis direction. S102: Calculating the normalised equivalent stress of the battery to obtain the stress relationship equation: - Assuming that the active particles are not subjected to any external forces. - Assuming isotropic volume changes. - Considering the elastic behaviour of the active material. - Neglecting the influence of particle morphology and its related spatial arrangement on the transport of lithium in the electrode. - Not considering failure criteria of particles, only calculating the generated stress. The expression of solid mechanics in the initial configuration is: d2u _ , ' V dk> ) Fd = I + U Where, u represents displacement; Fa is the elastic deformation gradient; 5 is the elastic stress tensor; I is the identity tensor. The thermal strain eth caused by thermal expansion is given by Equation (10): 's = C:eel Ft — Stot “ Sth Fh=^(T-Tref) (10) Where, C is the elastic tensor; etot is the elastic strain tensor; etot is the total strain tensor; a is the thermal expansion coefficient; Zre / is the reference temperature; I is the velocity gradient tensor; F is the deformation gradient. For isotropic spherical particles, the strain components are related to the radial displacement u. Based on the theory of large deformation continuum mechanics, the strain-displacement relationship can be expressed as: du du, du, J । K A dxt dxj dxj (11) Where, £y is the strain component, Ui, uj, Uk are displacement components, x,, Xj are position components. The constitutive relationship for diffusion stress-strain of lithium ions can be expressed as: (12) Where, is the strain component; E is Young's modulus; v is the Poisson's ratio; 0¾ is the stress component; is the Dirac delta function, which equals 1 when i =j and 0 when i j; cO is the initial concentration of lithium ions in the solid phase. For the assumed spherical particles, stress can also be divided into radial stress and tangential stress. Equation (12) can be written as: (13) Where er(r) and se(r) are the radial and tangential strain components respectively; odr) and oe(r) are the radial and tangential stress components respectively. For spherical particles under no external forces, the stress equilibrium equation for the sphere dar 2 z , , + dr r (14) Where, r is the radius of the sphere, a. and co are the stress components in the axis coordinates. For the elastic deformation of a sphere, the relationship between strain and displacement of the particle is: du dr u r (15) Where, er and ee are the strain components in the axis coordinates, u is displacement. During lithiation, when spherical electrode particles are unconstrained externally, the surfaces of the spherical electrode particles are in a state of stress boundary freedom. Therefore, the following boundary conditions apply: u I =0 I n                                      (16) =0 I r Irfe By combining equations (13) to (15) and equation (16), we can obtain the relationship between lithium-ion concentration and diffusion stress: (17) Where cav(r) is the average lithium concentration inside the active particle. When r approaches 0, ca (r) approaches c(0), then the stress at the centre of the particle is: lim cr ( r) = lim crrt ( r r^O v ’ r^O ' (is) The above equation indicates that the stress at the centre of the spherical particle is hydrostatic pressure. In the stress tensor of the spherical particle, or(r) =o<t>(r). Therefore, the average hydrostatic stress is: (19) After elastic deformation, if the stress exceeds the yield strength of the material, the material will undergo corresponding plastic deformation. The value of the yield criterion is equivalent to the Von Mises stress of the battery, which is calculated by the formula: z x v 2 (20). SI03: establishing an electrochemical-stress model based on the electrochemical reaction equation and stress relationship equation obtained in SI01 and SI02, and deriving the distribution and evolution law of electrode diffusion stress. Based on the Nernst-Einstein relationship, the migration rate M of lithium in the solid phase is related to the solid-phase diffusion coefficient D as follows: D=MRT. Therefore, combining equations (7) and (8), we can obtain: T(RT\n X} = RT= RT-^c (21) By substituting Equation (8) and Equation (21) into Equation (7), we can simplify it to: Qc - RT Therefore, by substituting Equation (21) back into Equation (6), we obtain: — = D\ V2c--Vc • Vcr.--V2^ ar I RT h RT (22) (23) At the initial moment, the concentration of solid-phase lithium ions is 0, and the flux of lithium ions at the interface between the solid phase and the liquid phase is determined by the surface current density jr of the particles. Therefore, the initial and boundary conditions are as follows: (24) In summary, the relationship between diffusion stress and lithium-ion concentration is obtained as follows: de _ --r V ‘J — U di J = -D\ c--Ver, RT h J = f(c,ah) . [ [ a Fi]\ (-aFri exp ——- Hexp —-—- A ( RT J A RT As shown in FIG. 4, considering the difficulty in actual stress testing, the validity of the theoretical model is verified solely from the perspective of voltage response. Here, using the electrochemical-stress model verification of porous silicon anode material as an example, the verification is conducted under 0.IC and 0.5C discharge conditions. The verification results indicate that the experimental and simulation results are relatively consistent. However, some deviations still exist between the theoretical and experimental results due to the model's neglect of the formation of the SEI (Solid Electrolyte Interphase) film. The good fit between the simulation and experimental results validates the applicability and feasibility of the model for theoretical predictions of silicon electrodes. The parameters for constructing the electrochemical-stress model of the nano silicon in this embodiment are shown in Table 1: Table 1. Parameters for Constructing the Electrochemical-Stress Model Symbol Parameter Name Unit Value Tref Reference temperature K 293.15 CO Initial solid-phase lithium concentration mol / m3 0 Cmax Maximum solid phase concentration mol / m3 278000 Rs Spherical particle radius nm 80 a Coefficient of thennal expansion K'1 3 / Cmax p Material density g / cm3 1.6 E Young's modulus GPa 80 V Poisson's ratio 1 0.29 D Solid phase diffusion coefficient m2 / s 2.36X10'17 to, ref pi Reference exchange current density A / m2 51.48 i o, refLi Reference exchange current density A / m2 12.6 S2: Based on the law of stress evolution during lithiation obtained in SI, using a multi-stage constant current optimization strategy to optimize the lithiation process, designing rate optimization strategies according to the material's yield strength stress. S201: determine the stress range of material yield strength. From the mechanism of the influence of rate on stress, it can be seen that the magnitude of the rate has a significant impact on stress. Lower rates can greatly reduce stress. From the discussion of stress changes during the charging and discharging processes, it can be observed that during the lithium insertion process, the stress reaches a peak at the initial charging stage and then gradually decreases, while during the lithium extraction process, stress exhibits the opposite behaviour. Therefore, a smaller rate can be used during the peak stress generation stage to suppress deformation and stress in the negative electrode particles. Then, a larger rate can be used to accelerate lithium insertion / extraction. Assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium-ion concentration, we obtain the following equation: ar =crr0' 11-0.53--^-I (25) I C I Where, aro is the yield stress of the negative electrode before lithiation; c is the lithium-ion concentration; cmax is the saturation lithium-ion concentration. As shown in FIG. 5, using porous silicon material as an example, the stress range of the anode material's yield strength during IC charge-discharge can be obtained from Equation (25), which is 0 to 60% SOC (State of Charge). Within this range, the material is indicated to not fracture, while exceeding this range indicates that the material has yielded. S202: design Rate Optimization Scheme: From the yield strength stress range of the anode material during IC charge-discharge, it can be observed that under IC stress, the stress exceeds the material's yield strength in the 0 to 60% SOC range. Therefore, it is decided to perform rate optimization within this range. Beyond this range, the stress remains within the yield strength, allowing the IC charge / discharge rate to be maintained. In this embodiment, four optimization strategies have been designed, as shown in Table 2: Table 2. Specific parameters of the four optimization strategies Optimization Scheme Lithiation Process (0 to 60% SOC) Delithiation Process (60 to 100% SOC) scheme 1 0.3C[0-60%] 1.0C[60-100%] 1.0C[100-0%] scheme 2 0.3C[0-60%] 1.0C [60-100%] 1.0C[100-60%] 0.3C[60-0%] scheme 3 0.3C[0-30%] 0.74C[30-60%] 1.0C [60-100%] 1.0C[100-0%] scheme 4 0.3C[0-30%] 0.74C [30-60%] 1.0C[60-100%] 1.0C[l 00-60%] 0.74C[60-30%] 0.3C[30-0%] In Scheme 1 and Scheme 2, single-rate optimization is performed in the 0-60% range with the goal of reducing stress. In Scheme 3 and Scheme 4, dual-rate optimization is performed in the 0-60% range with the goals of reducing stress and shortening the charge-discharge time, using 30% SOC as the segmentation point. Additionally, the stress distribution of IC cycling is used as a reference for comparison. As shown in FIG. 6, the evolution of stress on the surface of silicon active particles under different optimization strategies is illustrated, with the red dashed lines indicating the yield strength range. For multi-step constant current strategies, the stress within the silicon particles is minimal when the rate is 0.3 C. Changing the rate from 0.3 C to a higher rate causes a sharp increase in stress, but keeping the rate within the yield strength range can still reduce the risk of silicon particle fracture. When optimizing the rate to 0.3 C, the peak stress decreases from 0.94 GPa to 0.29 GPa. In the 30-60% SOC range, optimizing the rate to 0.74 C reduces the initial stress from 0.45 GPa to 0.32 GPa. Scheme 1 and Scheme 3 can reduce stress during the lithiation process, while Scheme 2 and Scheme 4 are suitable for the entire charge-discharge cycle. Although these strategies can suppress the initial peak stress, these strategies may also introduce additional peaks or stress fluctuations, which could lead to cyclic damage or fatigue of the active particles. Therefore, experiments are needed to validate the optimization strategies to balance the reduction of stress and the potential for cyclic fatigue damage. As shown in FIG. 7, the evolution of stress at the centre of silicon active particles under different optimization strategies is illustrated. From FIG. 7, it can be seen that due to the distribution of pores, the stress level at the particle centre is generally lower than that at the particle surface, so the four optimization strategies are also applicable for reducing the stress at the particle centre. The initial rate optimization scheme effectively suppresses the stress at the centre of the silicon particles, showing a trend similar to the surface stress distribution of silicon particles shown in FIG. 6. Specifically, Scheme 1 and Scheme 3 reduce the tensile stress during the lithiation process, while Scheme 2 and Scheme 4 can suppress stress throughout the entire charge-discharge cycle. The above results demonstrate the feasibility of using multi-step constant current strategies to control the stress evolution of electrode materials. S3: quantitatively verifying the rate optimization strategies designed in S2 through long-cycle testing, EIS electrochemical impedance spectroscopy testing, scanning electron microscopy testing, and selected area electron diffraction testing for macroscopic and microscopic validation, respectively. S301: macroscopic quantitative validation and evaluation of the rate optimization scheme through long-cycle tests and EIS (Electrochemical Impedance Spectroscopy) tests. S3011: optimization verification through long-cycle tests for the rate optimization scheme: Long-cycle tests are conducted to evaluate the long-term performance of the battery under different optimization strategies. By comparing the charge-discharge capacity, charge-discharge efficiency, and capacity retention rate of the battery under different optimization strategies during cycling, the influence of the rate optimization scheme on the long-term cycling performance of the battery can be comprehensively evaluated. The method to obtain Coulombic Efficiency (CE) is as follows: C£ = ^3^ X100% (26) Where Catscharge is the discharge capacity and Ccharge is the charge capacity. The method to obtain specific discharge capacity C is as follows: Q , _ discharge (27) m S3012: optimization verification of the rate optimization scheme using EIS (Electrochemical Impedance Spectroscopy) tests: Conduct EIS tests on batteries cycled under different optimization strategies to obtain the electronic transfer impedance of batteries cycled under different optimization strategies for comparison. The electrode processes in the battery are treated as equivalent to a simple circuit composed of resistors and capacitors in series and parallel. By applying a perturbation signal and observing the corresponding output signal, the equivalent circuit model of EIS is determined based on the EIS spectrum measured. In this example, long-cycle tests based on multi-step constant current charging optimization strategies were performed at 5°C, 25°C, and 55°C: As shown in FIG. 8a, the variation in discharge-specific capacity and Coulombic efficiency with the number of cycles under different optimization strategies at 5°C indicates that the discharge capacity for all four strategies is superior to that at a rate of 1 C. However, all strategies exhibit varying degrees of capacity decay as cycling progresses. It can be observed that for approximately the first 75 cycles, Scheme 2 has the highest discharge capacity, with Scheme 1 showing a slight increase in capacity. After 75 cycles, Scheme 1 maintains the highest capacity retention, with a discharge-specific capacity of 145 mAh g'1 even after 200 cycles. In contrast, Scheme 2 experiences capacity decline over long-term cycling; as stress accumulates within the particles and battery impedance gradually increases, the capacity of the porous silicon-lithium half-cell using Scheme 2 falls below that of Scheme 1 after a certain number of cycles. A similar phenomenon is observed when comparing Scheme 3 and Scheme 4, but due to significant early-cycle capacity decline in Scheme 3, the overall impedance is slightly higher than in Scheme 4. Despite the use of stress control optimization strategies, battery capacity still declines significantly at lower temperatures, indicating that ambient temperature also significantly affects battery performance. As shown in FIG. 9a, the variation in discharge-specific capacity and Coulombic efficiency with the number of cycles under different optimization strategies at 25°C clearly shows that the discharge-specific capacity under all four strategies is far superior to that at a rate of 1 C. However, Scheme 3 experiences rapid capacity decay towards the end of the cycle, resulting in only 16 mAh g’1 after 200 cycles due to the loss of electrical contact in the electrode. Strategies 1 and 2 exhibit the best cycling performance, with discharge-specific capacities of 856 mAh gA-l and 666 mAh gA-l, respectively, after cycling. Compared to the results at 5 °C, as the temperature increases, the advantages of the four strategies become more apparent; the trend in capacity distribution during cycling is similar to that at 5°C. As shown in FIG. 10a, the variation in discharge-specific capacity and Coulombic efficiency with the number of cycles under different optimization strategies at 55°C indicates that all four optimization strategies exhibit good cycling performance. After 200 cycles, Strategies 1 and 2 provide discharge-specific capacities of 850 and 1478 mAh g'1, respectively. Even the higher rate strategies, Strategies 3 and 4, provide discharge-specific capacities of 511 and 690 mAh gA-l, respectively. This demonstrates that elevated temperatures not only reduce the high-stress levels in silicon but also accelerate lithium-ion diffusion, reducing the concentration gradient of lithium ions in the solid-liquid phase, thereby decreasing diffusion polarisation and impedance, and ultimately improving the electrochemical performance of the battery. S3012: Optimization verification of the rate optimization scheme using EIS tests. In this example, electrochemical impedance spectroscopy (EIS) tests based on multi-step constant current charging optimization strategies were performed at 5°C, 25°C, and 55°C: As shown in FIG. 8c, from the charge transfer resistance (Ret) after cycling at 5°C under each strategy, it can be seen that Scheme 1 has the smallest charge transfer resistance at 607 Q, followed by Scheme 2 at 731.2 Q. The charge transfer resistances for Scheme 3 and Scheme 4 are 840.3 Q and 792.6 Q, respectively. The impedance results correspond well with the long-cycle performance results under different strategies. As shown in FIG. 9c, from the charge transfer resistance (Ret) after cycling at 25 °C under each strategy, it can be seen that thanks to the relatively low rate during the early stages of chargedischarge, Scheme 1 has the smallest charge transfer resistance at 77.9 Q, followed by Scheme 2 at 293.4 Q. The charge transfer resistances for Scheme 3 and Scheme 4 are 385 Q and 344.3 Q, respectively. The increase in temperature also reduces the impedance during the electrode cycling process, which can accelerate the electrochemical reactions of the electrode. As shown in FIG. 10c, from the charge transfer resistance (Ret) after cycling at 5 5 °C under each strategy, it can be seen that the charge transfer resistances for Scheme 1 and Scheme 2 are 41.37 Q and 9.2 Q, respectively. The charge transfer resistances for Scheme 3 and Scheme 4 are 259.8 Q and 173 Q, respectively. The increase in temperature also reduces the impedance during the electrode cycling process, which can accelerate the electrochemical reactions of the electrode. S302: Microscopic quantitative validation and evaluation of electrode slices by disassembling the battery after the cycle test in S301 and conducting scanning electron microscopy (SEM) tests and selected area electron diffraction (SAED) tests on the electrode slices. S3021: Optimization verification of the rate optimization scheme using scanning electron microscopy (SEM) tests. In this example, scanning electron microscopy (SEM) tests based on multi-step constant current charging optimization strategies were conducted at 5°C, 25°C, and 55°C: As shown in FIGS. Ila and f, comparing the SEM surface and cross-sectional images of the electrode slices after cycling under different optimization strategies at 5°C, it can be observed that the extent of surface cracking on the electrode slices is more severe after cycling with Scheme 3 and Scheme 4. Partial pulverisation can also be seen in the cross-sectional images of Scheme 3 and Scheme 4, which is one of the reasons for the rapid capacity decline m the middle and later stages of these two strategies. The electrode surfaces of Scheme 1 and Scheme 2 remain relatively intact overall, with the initial thickness of the active material layer for both being 9.2 pm, which increases to 25.8 pm and 22.2 pm, respectively, after cycling. The silicon electrode cycled with Scheme 1 exhibits better surface integrity, smaller cracks, and fewer pores, consistent with the previously measured cycling performance. The influence of charge-discharge rates on silicon volume expansion is more pronounced at low temperatures. As shown in FIGS. 12b and g, comparing the SEM surface and cross-sectional images of the electrode slices after cycling under different optimization strategies at 25°C, it can be observed that under Scheme 1, there are fine and long surface cracks, but the electrode slices still maintain a relatively complete morphology, with the thickness of the active material layer increasing from the original 9.2 pm to 20.8 pm. For Scheme 2, there are fewer and smaller cracks on the electrode slices, with the surface being the most intact and the thickness increasing to 23.7 pm. Both Scheme 1 and Scheme 2 alleviate the phenomenon of electrode cracking caused by silicon particle volume expansion and reduce the probability of particle pulverisation. However, for Scheme 3 and Scheme 4, due to the multi-stage and high-rate cycling, there are many wide cracks on the electrode surface, and particle pulverisation can be observed in the cross-section of the electrode slices, leading to rapid capacity decay of the battery in a short period of time. After cycling, the thickness of the active material layer for Scheme 3 and Scheme 4 increases to 26.7 pm and 17.4 pm, respectively. As shown in FIG. 13, at a high temperature of 55°C, although the pulverisation of silicon particles at 1 C rate is somewhat alleviated, the pulverisation of silicon particles is still severe, with the thickness of the active material layer increasing to 15.2 pm and detaching from the current collector. Thanks to the higher temperature, the surfaces of the electrode slices under all four strategies are relatively intact with fewer cracks after cycling, and Scheme 2 even shows no obvious cracks. The thickness of the active layer for all four strategies increases from the original 9.2 pm to 16.9 gm, 15.8 gm, 21.7 gm, and 19.1 gm, respectively. According to the stress evolution law obtained from the negative electrode model, reducing the charge-discharge rate while increasing the ambient temperature can effectively reduce surface cracks and damage, with mechanical effects becoming more apparent and resulting in smaller capacity losses. In this example, selective area electron diffraction (SAED) testing based on multi-step constant current charging optimization strategies was conducted at 5°C, 25°C, and 55°C. The lattice spacing d values after cycling were calculated from the electron diffraction patterns, and then the lattice constant a and unit cell volume were determined using Equation (28) for calculating the interplanar spacing in cubic lattices. The formula for calculating the interplanar spacing of cubic crystals is: d = . a (28) dlr ■ k ■ I where d represents the interplanar spacing, a denotes the lattice constant, and h, k, and 1 are the Miller indices of the crystal planes. As shown in FIG. 14, at room temperature (5°C), the lattice constants and unit cell volumes after cycling, obtained from the selective area electron diffraction (SAED) testing of the worstperforming and best-performing strategies, namely Scheme 3 and Scheme 1, are presented in Table 3: Table 3. Calculation Results of Lattice Constant a for Scheme 1 and Scheme 3 Scheme Crystal Pitch d / nm Crystal surface (hkl) Lattice constant al A Cycled cell volume u3 / A3 Scheme 1 0.2179 0.2192 0.2162 (220) 6.15938 233.67 Scheme 3 0.2423 (220) 6.82028 317.25 0.2401 0.2410 As shown in FIG. 15, at room temperature (25°C), the lattice constants and unit cell volumes after cycling, obtained from the selective area electron diffraction (SAED) testing of the worstperforming and best-performing strategies, namely Scheme 4 and Scheme 1, are presented in Table 4: Table 4. Calculation Results of Lattice Constant a for Scheme 1 and Scheme 4 Scheme Crystal Pitch d / nm Crystal surface (hkl) Lattice constant a / A Cycled cell volume a' / k' Scheme 1 0.2031 0.2028 0.2041 (220) 5.75113 190.22 Scheme 4 0.2125 0.2094 0.2109 (220) 5.96609 212.36 As depicted in FIG. 16, at a high temperature of 55°C, the lattice constants and unit cell volumes after cycling, obtained from the selective area electron diffraction (SAED) testing of the worstperforming and best-performing strategies, namely Scheme 3 and Scheme 2, are presented in Table 5: Table 5. Calculation Results of Lattice Constant a for Scheme 2 and Scheme 3 Scheme Crystal Pitch d / nm Crystal surface (hkl) Lattice constant a / k Cycled cell volume o3 / A3 Scheme 2 0.1977 0.2020 0.1985 (220) 5.63988 179.39 Scheme 3 0.2040 0.2073 0.2012 (220) 5.77565 192.66 S4: performing a macro-microscopic joint analysis of the quantitative validation results in S3: By jointly comparing the volume expansion rate of negative electrode particles and the long-cycle performance associated with different optimization strategies, a macro-microscopic joint quantitative evaluation of the optimization strategies is conducted. Based on the macroscopic quantitative validation results and microscopic quantitative validation results, a combined macro-microscopic quantitative evaluation was conducted. This evaluation utilised the results of long-term cycling tests, electrochemical impedance spectroscopy (EIS) testing, scanning electron microscopy (SEM) testing, and selective area electron diffraction (SAED) testing. As shown in Table 6, at a temperature of 5 °C, the changes m unit cell volume for the worstperforming and best-performing strategies, namely Scheme 3 and Scheme 1, are presented. Generally, solid silicon exhibits a volume expansion rate of up to 280% under the Li 15 Si4 alloy phase. However, with the use of Scheme 1 and Scheme 3 strategies, the volume expansion rates after long-term cycling at low temperatures remain lower than solid silicon, measuring 45.88% and 98.06%, respectively. This consistency with the distribution pattern of long-term cycling performance indicates that the combined optimization of porous structure design for silicon anodes and charging strategies significantly reduces the large volume expansion of silicon particles, thereby minimising diffusion stress. Table 6. Calculation Results of Unit Cell Volume a3 for Scheme 1 and Scheme 3 Scheme Initial cell volume ao3 / ^ Cycled cell volume a3 / A3 Volume expansion rate % Scheme 1 160.18 233.67 45.88 Scheme 3 160.18 317.25 98.06 As shown in Table 7, the changes in unit cell volume for the worst-performing and bestperforming strategies, namely Scheme 4 and Scheme 1, at 25°C are presented. At this temperature, the volume expansion rates after long-term cycling for Scheme 1 and Scheme 4 strategies are 18.75% and 32.58%, respectively. The microscopic particle expansion rates after cycling with Scheme 1 and Scheme 4 strategies at 25°C align with the distribution pattern of long-term cycling performance. Additionally, compared to the low temperature of 5°C, the volume expansion of silicon particles is reduced by up to 79.31% at 25°C, indicating that higher temperatures can decrease the diffusion stress of silicon particles, leading to improved capacity performance of the optimized silicon electrode batteries. Table 7. Calculation Results of Unit Cell Volume a3 for Scheme 1 and Scheme 4 Scheme Initial cell volume ao3 / A3 Cycled cell volume a3 / k3 Volume expansion rate % Scheme 1 160.18 190.22 18.75 Scheme 4 160.18 212.36 32.58 As shown in Table 8, at a high temperature of 55°C, the changes in lattice constants and unit cell volumes after long-term cycling, obtained from the selective area electron diffraction (SAED) testing of the worst-performing and best-performing strategies, namely Scheme 3 and Scheme 2, are presented. The volume expansion rates after long-term cycling for Scheme 2 and Scheme 3 strategies are 11.99% and 20.28%, respectively. The microscopic particle expansion rates after cycling with Scheme 2 and Scheme 3 strategies align with the distribution pattern of long-term cycling performance. Additionally, at high temperatures, the internal electrochemical reactions of the silicon anode accelerate, leading to a decrease in impedance and diffusion stress, resulting in smaller volume expansion. Silicon particles can thus maintain a more intact structure under these conditions. Table 8. Changes in Lattice Constants and Unit Cell Volumes after Long-term Cycling at 55°C for Scheme 2 and Scheme 3 Table 8. Calculation Results of Unit Cell Volume a3 for Scheme 2 and Scheme 3 Scheme Initial cell volume ao3lk3 Cycled cell volume a3lk3 Volume expansion rate % Scheme 2 160.18 179.39 11.99 Scheme 3 160.18 192.66 20.28 The combined macro-microscopic analysis results demonstrate the effectiveness of optimizing both internal parameters, such as porous structure, and external parameters, such as rate optimization, at the microscopic level. Each embodiment described in this specification follows a progressive approach, highlighting the differences from other embodiments. The similarities between different embodiments can be cross-referenced accordingly. The description of the disclosed devices in the embodiments is relatively straightforward, as the devices correspond to the methods disclosed in the embodiments. Relevant aspects can be referred to in the method section for explanation. The above description of the disclosed embodiments enables those skilled in the art to implement or use the disclosure. It will be apparent to those skilled in the art that various modifications to these embodiments are readily achievable. General principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the disclosure. Therefore, the disclosure is not limited to the embodiments disclosed herein but encompasses the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for macro-microscopic joint quantitative evaluation of battery electrode charging strategies, characterized by comprising the following steps:S1: constructing an electrochemical-stress model to determine a distribution and evolution law of electrode diffusion stress;S2: based on a law of stress evolution during a lithiation process obtained in the SI, using a multistage constant current optimization strategy to optimize the lithiation process, and designing rate optimization strategies according to a yield strength stress of a material;S3: quantitatively verifying the rate optimization strategies designed in the S2 through long-cycle testing, EIS electrochemical impedance spectroscopy testing, scanning electron microscopy testing, and selected area electron diffraction testing for macroscopic and microscopic validation, respectively; andS4: performing a macro-microscopic joint analysis on quantitative validation results from the S3: wherein by jointly comparing a negative electrode particle volume expansion rate and long-cycle performance for different optimization strategies, the macro-microscopic joint quantitative evaluation of the different optimization strategies is conducted.

2. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 1, characterized in that, the SI specifically comprises the following steps:SI01: using a half-cell and a simplified two-dimensional plane model to convert the distribution and evolution of electrode diffusion stress into a plane strain problem to obtain the electrochemical reaction equation.SI02: calculating a normalised equivalent stress of a battery to obtain a stress relationship equation; andSI03: establishing the electrochemical-stress model based on the electrochemical reaction equationand the stress relationship equation obtained in the SI01 and the SI02, and deriving the distribution and evolution law of the electrode diffusion stress.

3. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 2, characterized in that, the SI01 specifically comprises the following steps:using a half-cell and a simplified two-dimensional plane model, the distribution and evolution of electrode diffusion stress are converted into a plane strain problem, the electrolyte control equations consist of charge conservation and mass conservation equations:F I (1)cr ( i t ।s —- + V- -sDVc +— = / 1 (2) dt F )wherein, <7e is the electrolyte conductivity; (pe is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is Faraday's constant; / is the activity coefficient of the salt; ce is the concentration of the electrolyte salt; t+ is the migration number of lithium ions; ie is the electrolyte current density; se is the volume fraction of the electrolyte; De is the diffusion coefficient of the electrolyte salt; Re is the total sum of lithium-ion sources in the electrolyte; t is time;the control equation for the electrode is defined by Ohm's law:V- / ,=0 (3)wherein, is represents the electrode current density;the electrochemical reactions at the interface between the electrode and electrolyte are described bythe Butler-Volmer equation:(4)(5)wherein, jr represents the local current density; io is the exchange current density; aa is the anodic transfer coefficient, with a value of 0.5; ac is the cathodic transfer coefficient, with a value of 0.5; / / is the overpotential; io.refis the reference exchange current density; ce.re / is the reference electrolyte concentration;the conservation of lithium ions in the active material under the influence of the electric field can be defined by Fick's law; the diffusion-based transport of lithium ions is given by the mass conservation equation of Equation (6):— + V-J = 0 (6)St v 7wherein, c is the concentration of lithium ions in the solid phase; J is the diffusion flux; t is time; according to kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of active particles:J = MeV ii (7)wherein, M is the migration rate of lithium in the solid phase; / / is the chemical potential;to reflect the effect of stress on the diffusion process, the static stress term is added to the chemical potential:> = / / 0+7?nnX^QcrA' ^11+^22+^33 (8). h 3wherein, / / 0 is a constant representing the chemical potential under stress-free conditions; X is the molar fraction of lithium ions; Q is the partial molar volume; <5h is the hydrostatic stress; on is the normal stress in the x-axis direction; 022 is the normal stress in the y-axis direction; 033 is the normal stress in the z-axis direction.

4. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 3, characterized in that, the SI02 specifically comprises the following steps:- assuming that the active particles are not subjected to any external forces;- assuming isotropic volume changes;- considering the elastic behaviour of the active material;- neglecting the influence of particle morphology and its related spatial arrangement on the transport of lithium in the electrode; and- not considering failure criteria of particles, only calculating the generated stress, wherein the expression of solid mechanics in the initial configuration is:d2u / . x?■a7' ’ (?)Fd = I + uwherein, u represents displacement; Fa is the elastic deformation gradient; S is the elastic stress tensor; and I is the identity tensor;the thermal strain eth caused by thermal expansion is given by Equation (10):'S = C:selSel — Stot “ Sth(10)lot \sth=a(r-Tr^wherein, C is the elastic tensor; sM is the elastic strain tensor; is the total strain tensor; a is the thermal expansion coefficient; 7 / w is the reference temperature; / is the velocity gradient tensor; F is the deformation gradient;for isotropic spherical particles, the strain components are related to the radial displacement m; based on the theory of large deformation continuum mechanics, the strain-displacement relationship can be expressed as:wherein, ey is the strain component, Ui, uj, and Uk are displacement components, and Xi, Xj areposition components;the constitutive relationship for diffusion stress-strain of lithium ions can be expressed as:(12)wherein, is the strain component; E is Young's modulus; v is the Poisson's ratio; g,; is the stress component; dy is the Dirac delta function, which equals 1 when i =j and 0 when i j; co is the initial concentration of lithium ions in the solid phase;for the assumed spherical particles, stress can also be divided into radial stress and tangential stress. Equation (12) can be written as:wherein zr(r) and ee(r) are the radial and tangential strain components respectively; or(r) and oe(r) are the radial and tangential stress components respectively;for spherical particles under no external forces, the stress equilibrium equation for the sphere is:(14)wherein, r is the radius of the sphere, or and oe are the stress components in the axis coordinates;for the elastic deformation of a sphere, the relationship between strain and displacement of the particle is:(15)wherein, sr and eg are the strain components in the axis coordinates, and u is displacement;during lithiation, when spherical electrode particles are unconstrained externally, the surfaces of the spherical electrode particles are in a state of stress boundary freedom, therefore the followingboundary conditions apply:(16)by combining equations (13) to (15) and equation (16), we can obtain the relationship between lithium-ion concentration and diffusion stress:(17)wherein cav(r) is the average lithium concentration inside the active particle; when r approaches 0, Cav(r) approaches c(0), then the stress at the centre of the particle is:2FO(18);the above equation indicates that the stress at the centre of the spherical particle is hydrostatic pressure; in the stress tensor of the spherical particle, therefore the average hydrostaticstress is:2EQ(19);after elastic deformation, if the stress exceeds the yield strength of the material, the material will undergo corresponding plastic deformation; the value of the yield criterion is equivalent to the VonMises stress of the battery, which is calculated by the formula:(20);5. The method for the macro-microscopic joint quantitative evaluation of the battery electrodecharging strategies according to claim 4, characterized in that, the SI03 specifically comprises thefollowing steps: based on the Nernst-Einstein relationship, relating the migration rate M of lithiumin the solid phase to the solid-phase diffusion coefficient D as follows: D=MRT, and combiningequations (7) and (8) to obtain:V(RTlnX) = RT-VX = RT-Vc X c(21)substituting Equation (8) and Equation (21) into Equation (7) to simplify to:Qc -RTsubstituting Equation (21) back into Equation (6) to obtain:zx c") A— = D\ V2c--Vc-Vcr,--VX dt RT RT Jat the initial moment, the concentration of solid-phase lithium ions is 0, and the flux of lithium ionsat the interface between the solid phase and the liquid phase is determined by the surface currentdensity jr of the particles, therefore, the initial and boundary conditions are as follows:(24)in summary, the relationship between diffusion stress and lithium-ion concentration is obtained asfollows:c)c— _ QdtT _ nl z- V7•J — jLz L V O / .t ( RT h2EQ r X / .-( -a Fi]-exp —-—I RTEQ 9(l-v) 2EQ 9(l-v)6. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 5, characterized in that, the S2 specifically comprises the following steps:S201: determining the stress range of material yield strength; andS202: designing the rate optimization scheme: using a smaller rate to suppress deformation and stress in the negative electrode particles during the peak stress generation stage; then, using a larger rate to accelerate lithium insertion or extraction to design an optimization scheme; when the stress exceeds the stress range of the yield strength determined in S201, continuing to optimize the stress within the exceeded range; and for the stresses that do not exceed the range, continuing to maintain the original charging or discharging rate.

7. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 6, characterized in that, the S201 specifically comprises the following steps:from the mechanism of the influence of rate on stress, it can be seen that the magnitude of the rate has a significant impact on stress; lower rates can greatly reduce stress; from the discussion of stress changes during the charging and discharging processes, it can be observed that during the lithium insertion process, the stress reaches a peak at the initial charging stage and then gradually decreases, while during the lithium extraction process, stress exhibits the opposite behaviour; therefore, a smaller rate can be used during the peak stress generation stage to suppress deformation and stress in the negative electrode particles; then, a larger rate can be used to accelerate lithium insertion / extraction; assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium-ion concentration, we obtain the following equation:= ^ro’J °-53—“I (25)wherein, vyo is the yield stress of the negative electrode before lithiation; c is the lithium-ion concentration; cmax is the saturation lithium-ion concentration.

8. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 7, characterized in that, the S3 specifically comprises the following steps:S301: macroscopic quantitative validation and evaluation of the rate optimization scheme through long-cycle tests and EIS (Electrochemical Impedance Spectroscopy) tests;S302: microscopic quantitative validation and evaluation of electrode slices by disassembling the battery after the cycle test in S301 and conducting scanning electron microscopy (SEM) tests and selected area electron diffraction (SAED) tests on the electrode slices.

9. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 8, characterized in that, the S3 01 specifically comprises the following steps:S3011: optimization verification through long-cycle tests for the rate optimization scheme: long-cycle tests are conducted to evaluate the long-term performance of the battery under different optimization strategies; by comparing the charge-discharge capacity, charge-discharge efficiency, and capacity retention rate of the battery under different optimization strategies during cycling, the influence of the rate optimization scheme on the long-term cycling performance of the battery can be comprehensively evaluated;the method to obtain Coulombic Efficiency (CE) is as follows:CE = Cd,seharge x j 0()0 / o (26)wherein C^charge is the discharge capacity and Ccharge is the charge capacity;the method to obtain specific discharge capacity C is as follows:CQ I _ discharge (27)mS3012: optimization verification of the rate optimization scheme using EIS (Electrochemical Impedance Spectroscopy) tests: conduct EIS tests on batteries cycled under different optimization strategies to obtain the electronic transfer impedance of batteries cycled under different optimization strategies for comparison; the electrode processes in the battery are treated as equivalent to a simple circuit composed of resistors and capacitors in series and parallel; by applying a perturbation signaland observing the corresponding output signal, the equivalent circuit model of EIS is determined based on the EIS spectrum measured.

10. The method for the macro-microscopic joint quantitative evaluation of the battery electrode charging strategies according to claim 9, characterized in that, the S302 specifically comprises the following steps:S3021: optimization verification of the rate optimization scheme using scanning electron microscopy (SEM) tests: observing the pulverisation phenomenon of negative electrode particles and changes in the thickness of the active material layer;scanning electron microscopy utilises the differences in characteristics of micro-regions on the material surface; under the action of an electron beam, different brightness differences are generated in different regions of the sample, thereby obtaining images with a certain contrast; the imaging signals are secondary electrons, backscattered electrons, or absorbed electrons, among which secondary electrons are the main imaging signals; the high-energy electron beam bombards the sample surface, exciting various physical signals on the sample surface, and then different signal detectors are used to receive the physical signals and convert them into image information;S3022: optimization verification of the rate optimization scheme using selected area electron diffraction (SAED) tests: microscopic testing of irreversible volume expansion generated by electrode material particles after long cycling; the lattice spacing d after cycling is calculated from the electron diffraction pattern, and then the lattice constant a and the unit cell volume are calculated using Equation (28) based on the formula for the lattice spacing of cubic crystals;the formula for calculating the lattice spacing of cubic crystals is:d = . a (28)d^+ld+l2the formula denotes d as the lattice spacing, a as the lattice constant, and h, k, I as the Miller indices of crystal planes;selected area electron diffraction utilises the correspondence between selected area morphology observation and electron diffraction structure analysis to achieve in-situ analysis of the morphologycharacteristics and crystallographic properties of crystal samples; by setting a selected area aperture on the objective lens imaging plane, the diffraction region is selected and confined; only the sample micro area where the internal viewpoint of the aperture hole is located can be penetrated by the imaging electron beam, thereby achieving the purpose of matching microscopic observation with electron diffraction.

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