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 model to obtain distribution and evolution rules of an electrode diffusion stress; according to the stress evolution rule in a lithiation process, using a multi-stage constant-current optimization strategy to perform rate optimization on the lithiation process, and on the basis of the stress of material yield strength, designing a rate optimization solution; separately performing macroscopic and microscopic quantitative verification on the rate optimization solution by means of a long-cycle test, an electrochemical impedance spectroscopy test, a scanning electron microscope test and a selected area electron diffraction test; and performing macro-micro combined analysis on macroscopic and microscopic quantitative verification results. By using macro-micro combined evaluation, the impact of charging strategies on microstructures of electrode materials and the cycle performance of batteries is studied, thus quantitatively revealing the optimization effects of different optimization strategies. By combining the microscopic characteristics of electrode materials and the macroscopic performance of charging strategies, the impact of different charging strategies on the performance of batteries is studied so as to optimize the charging strategies, thus improving the performance and prolonging the cycle life of batteries.

Description

A method for quantitative evaluation of battery electrode charging strategies based on macro-micro joint Technical Field

[0001] The present invention relates to a method for quantitatively evaluating battery electrode charging strategies based on macro-micro combined evaluation, and belongs to the technical field of power batteries. Background Art

[0002] As a key energy storage device for electric vehicles, power batteries have a significant impact on the performance and promotion of electric vehicles. The negative electrode, as a key component of power batteries, plays a vital role in the battery's performance and fast charging capabilities.

[0003] Over the past few decades, traditional negative electrode materials have primarily 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 negative electrodes have some limitations in terms of high-power discharge and fast charging. To overcome these limitations, researchers have begun to introduce a series of new negative electrode materials, such as silicon-based materials, silicon nitride, and silicon-carbon composites. These new materials are being widely studied with the aim of increasing the charge transfer rate of the negative electrode and improving fast charging performance.

[0004] In terms of charging strategies, the traditional constant current-constant voltage (CC-CV) charging strategy is widely used in commercial applications. However, with the introduction of new negative electrode materials, the traditional charging strategy cannot maximize the performance potential of the negative electrode. Therefore, researchers have proposed a series of improved charging strategies, such as pulse charge and discharge strategies and progressive charging strategies, aiming to optimize the negative electrode charging process and improve battery performance and life.

[0005] However, for the current evaluation methods of electrode charging strategies, some researchers evaluate the impact of charging strategies on battery performance through performance tests or cycle tests. However, these methods are more indirect evaluations and cannot intuitively achieve quantitative analysis of charging strategies. Although researchers have conducted extensive research on electrode charging strategies and established relevant evaluation methods, there is a lack of a macro-micro combined evaluation method that comprehensively considers the relationship between microstructure and macroscopic performance to achieve a comprehensive assessment of electrode charging strategies.

[0006] Summary of the Invention

[0007] Purpose of the invention: In response to the deficiencies in the prior art, the present invention provides a method for evaluating battery electrode charging strategies based on macro-micro joint quantitative evaluation. The present invention constructs an electrochemical-stress model, designs a rate optimization scheme, conducts macro-micro joint quantitative verification of the rate optimization scheme, and then conducts macro-micro joint analysis and evaluation.

[0008] Technical solution: A method for quantitatively evaluating battery electrode charging strategies based on macro-micro combined evaluation, comprising the following steps:

[0009] S1: Construct an electrochemical-stress model to derive the distribution and evolution of electrode diffusion stress;

[0010] S2: Based on the stress evolution law during the lithiation process obtained in S1, a multi-stage constant current optimization strategy is used to optimize the rate of the lithiation process, and a rate optimization scheme is designed based on the material yield strength stress;

[0011] S3: The rate optimization scheme designed in S2 was quantitatively verified at the macro and micro levels through long cycle testing, electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM), and selected area electron diffraction (SAD).

[0012] S4: Conduct a macro-micro joint analysis of the macro and micro quantitative verification results in S3:

[0013] By jointly comparing the volume expansion rate of the negative electrode particles of different optimization schemes and their long-cycle performance, a macro-micro joint quantitative evaluation of different optimization schemes can be made.

[0014] The present invention constructs an electrochemical-stress model to derive the distribution and evolution law of electrode diffusion stress. Based on the law of stress evolution during the lithiation process, a multi-stage constant current optimization strategy is adopted to optimize the rate of the lithiation process. A rate optimization scheme is designed according to the material yield strength stress. The rate optimization scheme is then quantitatively evaluated at both the macro and micro levels through verification using long cycle tests, electrochemical impedance spectroscopy tests, scanning electron microscopy tests, and selected area electron diffraction tests.

[0015] Preferably, the S1 specifically includes the following steps:

[0016] S101: Using a half-cell and a simplified two-dimensional plane model, transform it into a plane strain problem and obtain the electrochemical reaction equation;

[0017] S102: Calculate the normal equivalent stress of the battery and obtain the stress relationship equation;

[0018] S103: Based on the electrochemical reaction equations and stress relationship equations obtained in S101 and S102, an electrochemical-stress model is established, and the electrode diffusion stress distribution and evolution law are obtained.

[0019] Preferably, the specific steps of S101 are as follows:

[0020] Using a half-cell and a simplified two-dimensional plane model, it is transformed into a plane strain problem. The electrolyte governing equations are the charge conservation and material conservation equations:

[0021] Where σ e is the electrolyte conductivity; φ e is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is the Faraday constant; f is the activity coefficient of the salt; c e is the electrolyte salt concentration; t + is the migration number of lithium ions; i e is the electrolyte current density; ε e is the electrolyte volume fraction; D e is the diffusion coefficient of electrolyte salt; R e is the total amount of lithium ion sources in the electrolyte; t is time;

[0022] The governing equation for the electrodes is defined by Ohm's law:

[0023] Where i s is the electrode current density,

[0024] The electrochemical reactions at the interface between the electrode and the electrolyte are described by the Butler-Volmer equation:

[0025] Where, j r is the local current density; i0 is the exchange current density; α a is the anode transfer coefficient, which is 0.5; α c is the cathode transfer coefficient, which is 0.5; η is the overpotential; i 0,ref is the reference exchange current density; c e,ref is the electrolyte reference concentration;

[0026] The conservation of lithium ions in active materials under the action of an electric field can be defined by Fick's law; the diffusion-based lithium ion transport is given by the mass conservation equation of formula (6):

[0027] Where c is the solid phase lithium ion concentration; J is the diffusion flux; t is the time;

[0028] From kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of the active particles:

[0029] Where M is the mobility of lithium in the solid phase; μ is the chemical potential;

[0030] The hydrostatic stress term is added to the chemical potential to reflect the effect of stress on the diffusion process:

[0031] Where μ0 is a constant representing the chemical potential in the stress-free state; X is the molar fraction of lithium ions; Ω is the partial molar volume; σ his the hydrostatic stress; σ 11 is the normal stress in the x-axis direction; σ 22 is the normal stress in the y-axis direction; σ 33 is the normal stress in the z-axis direction.

[0032] Preferably, the specific steps of S102 are as follows:

[0033] Assume that the active particles are not subject to any external forces; the volume changes are isotropic; the active material behaves like an elastic material; ignore the effect of particle morphology and its related spatial arrangement on lithium transport in the electrode; do not consider the failure criterion of the particles, and only calculate the generated stress;

[0034] The expression of solid mechanics in the initial configuration is:

[0035] Where u is the displacement; F d is the elastic deformation gradient; S is the elastic stress tensor; I is the equivalent tensor;

[0036] Thermal strain ε caused by thermal expansion th Given by formula (10):

[0037] Where C is the elastic tensor; ε el is the elastic strain tensor; ε tot is the total strain tensor; α is the thermal expansion coefficient; T ref is the reference temperature; l is the velocity gradient tensor; F is the deformation gradient;

[0038] For isotropic spherical particles, the strain component is related to the radial displacement u. Based on the large deformation theory of continuum mechanics, the strain-displacement relationship can be expressed as:

[0039] Where, ε ij is the strain component, u i 、u j 、u k is the displacement component, x i 、x j is the position component;

[0040] The constitutive relationship of lithium ion diffusion stress-strain can be expressed as:

[0041] Where, ε ij is the strain component; E is Young's modulus; v is Poisson's ratio; σ ij is the stress component; δ ij is the Dirac delta function, which is 1 when i = j and 0 when i ≠ j; c0 is the initial solid phase lithium ion concentration;

[0042] For the assumed spherical particles, the stress can also be divided into radial stress and tangential stress, and Equation (12) can be written as:

[0043] Among them, ε r (r) and ε θ (r) are the radial strain component and the tangential strain component respectively; σ r (r) and σ θ (r) are the radial stress component and the tangential stress component respectively;

[0044] For spherical particles, when there is no external force, the stress equilibrium equation of the sphere is:

[0045] Where r is the radius of the sphere, σ r , σ θ is the stress component in the axial coordinate;

[0046] For the elastic deformation of a sphere, the relationship between the strain and displacement of the particle is:

[0047] Where, ε r , ε θ is the stress component in the axis coordinate, and u is the displacement;

[0048] During the lithiation process, when the spherical electrode particles are unconstrained externally, their surfaces are in a stress-free state, and the following boundary conditions exist:

[0049] Combining equations (13) to (15) and formula (16) yields the relationship between lithium ion concentration and diffusion stress:

[0050] Among them, c av (r) is the average lithium concentration in the active particles. When r approaches 0, c av (r) tends to c(0), then the stress at the center of the particle is:

[0051] The above formula shows that the stress at the center of the spherical particle is the hydrostatic pressure. In the stress tensor of the spherical particle, Then the average hydrostatic stress is:

[0052] 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, and its calculation formula is:

[0053] Preferably, the specific steps of S103 are as follows:

[0054] According to the Nernst-Einstein relationship, the mobility 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:

[0055] According to formula (8) and formula (21), formula (7) can be simplified as:

[0056] Therefore, substituting equation (21) back into equation (6) yields:

[0057] At the initial moment, the solid phase lithium ion concentration is 0, and the lithium flux at the interface between the solid phase and the liquid phase is determined by the particle surface current density j r Therefore, the initial and boundary conditions are as follows:

[0058] In summary, the relationship between diffusion stress and lithium ion concentration is obtained:

[0059] Preferably, the specific steps of S2 are as follows:

[0060] S201: Determine the material yield strength stress range;

[0061] S202: Design rate optimization plan: Design an optimization plan by using a smaller rate to suppress the deformation and stress in the negative electrode particles during the peak stress generation stage, and then using a larger rate to accelerate lithium insertion or removal. When the stress exceeds the yield strength stress range determined in S201, continue to optimize the stress within the range, and continue to maintain the original charge or discharge rate for the remaining stresses that do not exceed the range.

[0062] Preferably, the specific steps of S201 are as follows:

[0063] From the mechanism of the influence of rate on stress, it can be seen that the rate has a greater impact on stress, and a low rate can greatly reduce stress. From the discussion of stress changes during the charge and discharge process, it can be seen that during the lithium insertion process, the stress will reach a peak in the initial state of charge and then gradually decrease. The lithium removal process is the opposite. Therefore, a smaller rate can be used in the peak stress generation stage to suppress the deformation and stress in the negative electrode particles, and then a larger rate can be used to accelerate lithium insertion / delithiation. Assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium ion concentration, the following formula is obtained:

[0064] Where σ Y0 is the yield stress of the negative electrode before lithiation; c is the lithium ion concentration; c max is the saturated lithium ion concentration.

[0065] Preferably, the specific steps of S3 are as follows:

[0066] S301: Macroscopic quantitative verification and evaluation of the rate optimization scheme through long cycle testing and EIS electrochemical impedance spectroscopy testing;

[0067] S302: Disassemble the battery after the S301 cycle, remove the electrode sheet, and perform microscopic quantitative verification and evaluation of the electrode sheet through scanning electron microscopy and selected area electron diffraction testing.

[0068] Preferably, the specific steps of S301 are as follows:

[0069] S3011: Optimize and verify the rate optimization scheme using long-cycle testing: By testing the long-cycle performance under different optimization schemes, the charge and discharge capacity, charge and discharge efficiency, and capacity retention rate of the battery during cycling under different optimization schemes are compared; the long-cycle test is a long-term, multi-cycle charge and discharge test of the battery based on the existing rate optimization scheme. By observing the changes in the charge and discharge capacity, charge and discharge efficiency, that is, the coulombic efficiency and capacity retention rate parameters during the long cycle of the battery, the impact of the rate optimization scheme on the long-term cycle performance of the battery can be comprehensively evaluated;

[0070] Coulomb efficiency C E The method of obtaining it is as follows:

[0071] Where C discharge is the discharge capacity, C charge is the charging capacity;

[0072] The discharge specific capacity C' is obtained as follows:

[0073] Where C discharge is the battery discharge capacity, m is the mass of the electrode active material;

[0074] S3012: Use EIS electrochemical impedance spectroscopy testing to optimize and verify the rate optimization scheme: By performing EIS tests on batteries after cycling with different optimization schemes, the electron transfer impedance of the batteries after cycling with different optimization schemes is obtained, so that different optimization schemes can be compared; the electrode process in the battery is equated to a simple circuit consisting of resistors and capacitors in series and parallel, and the corresponding output signal is obtained by inputting a disturbance signal. The equivalent circuit model of EIS is determined based on the measured electrochemical impedance spectroscopy (EIS) spectrum.

[0075] Preferably, the specific steps of S302 are as follows:

[0076] S3021: The rate optimization scheme was optimized and verified using scanning electron microscopy testing: by observing the pulverization of negative electrode particles and the change in the thickness of the active material layer:

[0077] Scanning electron microscopy utilizes the differences in the characteristics of micro-regions on the surface of materials. Under the action of the electron beam, different brightness differences are generated in different areas 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 most important imaging signals. The high-energy electron beam bombards the sample surface, stimulating various physical signals on the sample surface. Different signal detectors are then used to receive the physical signals and convert them into image information.

[0078] S3022: Optimize and verify the rate optimization scheme using selected area electron diffraction testing: Microscopic testing of the irreversible volume expansion of electrode material particles after long cycles:

[0079] The lattice spacing d after the cycle is calculated from the electron diffraction pattern, and then the lattice constant a and the unit cell volume are calculated according to the cubic lattice interplanar spacing calculation formula (28); the interplanar spacing calculation formula for cubic crystals is:

[0080] Where d is the interplanar spacing; a is the lattice constant; h, k, and l are the Miller indices of the crystal plane;

[0081] Selected area electron diffraction utilizes the micro-area correspondence between selected area morphology observation and electron diffraction structure analysis to achieve in-situ analysis of the morphological characteristics and crystallographic properties of crystal samples. By setting a selected area grating on the objective lens plane, the diffraction area is selected and limited. Only the sample micro-area where the viewpoint inside the aperture is located can be passed by the imaging electron beam, thereby achieving the purpose of matching microscopic observation with electron diffraction.

[0082] Beneficial effects: The present invention studies the influence of charging strategies on the microstructure of electrode materials and battery cycle performance by adopting a macro-micro joint evaluation method, and quantitatively reveals the optimization effects of different optimization strategies. By establishing an electrochemical-stress model, the microscopic reaction kinetics and stress response of the electrode during the charging process are obtained, thereby providing a more accurate basis for the optimization of the charging strategy; through macroscopic performance evaluation based on long cycle testing and EIS electrochemical impedance spectroscopy testing, the feasibility of the optimized charging strategy in power battery applications is verified. By combining the microscopic evaluation results of SEM scanning electron microscopy analysis and SAED selected area electron diffraction analysis with the macroscopic evaluation results, the purpose of conducting a micro-macro joint quantitative evaluation of the cycle-induced stress and volume expansion rate of different optimization strategies is achieved. By jointly considering the microscopic characteristics of the electrode material and the macroscopic performance of the charging strategy, the influence of different charging strategies on battery performance can be more comprehensively and accurately evaluated, and the charging strategy can be optimized to improve battery performance and cycle life. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0084] FIG1 is a flow chart of the method of the present invention;

[0085] FIG2 is a schematic diagram of a two-dimensional single-particle porous silicon;

[0086] Figure 3 is a diagram of the lithiation of a single silicon particle;

[0087] Figure 4 is a comparison of test and simulation discharge curves;

[0088] FIG5 is a stress interval diagram of the yield strength of the negative electrode material during 1C charge and discharge;

[0089] Figure 6 shows the evolution of stress on the surface of silicon active particles under different optimization schemes: (a) Scheme 1 (b) Scheme 2 (c) Scheme 3 (d) Scheme 4;

[0090] Figure 7 shows the evolution of stress at the center of silicon active particles under different optimization schemes: (a) Scheme 1 (b) Scheme 2 (c) Scheme 3 (d) Scheme 4;

[0091] Figure 8 shows the comparison of (a) long cycle, (b) EIS fitting, and (c) charge transfer resistance of different optimization strategies at 5°C;

[0092] Figure 9 shows the comparison of (a) long cycle, (b) EIS fitting, and (c) charge transfer resistance of different optimization strategies at 25°C;

[0093] Figure 10 shows the comparison of (a) long cycle, (b) EIS fitting, and (c) charge transfer resistance of different optimization strategies at 55°C;

[0094] Figure 11 is a comparison of the surface and cross-sectional SEM images of the electrode sheets after cycling with different optimization strategies at 5°C: (a, f) - 1C; (b, g) - Scheme 1; (c, h) - Scheme 2; (d, i) - Scheme 3; (e, j) - Scheme 4;

[0095] Figure 12 is a comparison of the surface and cross-sectional SEM images of the electrode sheets after cycling with different optimization strategies at 25°C: (a, f) - 1C; (b, g) - Scheme 1; (c, h) - Scheme 2; (d, i) - Scheme 3; (e, j) - Scheme 4;

[0096] Figure 13 is a comparison of the surface and cross-sectional SEM images of the electrode sheets after cycling with different optimization strategies at 55°C (a, f)-1C; (b, g)-Scheme 1; (c, h)-Scheme 2; (d, i)-Scheme 3; (e, j)-Scheme 4;

[0097] Figure 14 shows the SAED selected area electron diffraction test patterns of (a) Scheme 1 and (b) Scheme 3 at room temperature of 5°C;

[0098] Figure 15 is the SAED selected area electron diffraction test pattern of (a) Scheme 1 and (b) Scheme 4 at room temperature of 25°C;

[0099] FIG16 is the SAED selected area electron diffraction test pattern of (a) Scheme 2 and (b) Scheme 3 at a high temperature of 55°C. DETAILED DESCRIPTION

[0100] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0101] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention.

[0102] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0103] As shown in FIG1 , a method for quantitatively evaluating battery electrode charging strategies based on macro-micro combined evaluation includes the following steps:

[0104] S1: Construct an electrochemical-stress model to derive the distribution and evolution of electrode diffusion stress:

[0105] S101: Using a half-cell and a simplified two-dimensional plane model, we transform it into a plane strain problem and obtain the electrochemical reaction equation:

[0106] As shown in Figure 2, a half-cell and a simplified two-dimensional plane model are used to transform it into a plane strain problem. The electrolyte control equations are the charge conservation and material conservation equations:

[0107] Where σ e is the electrolyte conductivity; φ e is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is the Faraday constant; f is the activity coefficient of the salt; c e is the electrolyte salt concentration; t + is the migration number of lithium ions; i e is the electrolyte current density; ε e is the electrolyte volume fraction; D e is the diffusion coefficient of electrolyte salt; R e is the total amount of lithium ion sources in the electrolyte; t is time;

[0108] The governing equation for the electrodes is defined by Ohm's law:

[0109] Where i s is the electrode current density,

[0110] The electrochemical reactions at the interface between the electrode and the electrolyte are described by the Butler-Volmer equation:

[0111] Where, j r is the local current density; i0 is the exchange current density; α a is the anode transfer coefficient, which is 0.5; α c is the cathode transfer coefficient, which is 0.5; η is the overpotential; i 0,ref is the reference exchange current density; c e,ref is the electrolyte reference concentration;

[0112] The conservation of lithium ions in active materials under the action of an electric field can be defined by Fick's law; the diffusion-based lithium ion transport is given by the mass conservation equation of formula (6):

[0113] Where c is the solid phase lithium ion concentration; J is the diffusion flux; t is the time;

[0114] From kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of the active particles:

[0115] Where M is the mobility of lithium in the solid phase; μ is the chemical potential;

[0116] The hydrostatic stress term is added to the chemical potential to reflect the effect of stress on the diffusion process:

[0117] Where μ0 is a constant representing the chemical potential in the stress-free state; X is the molar fraction of lithium ions; Ω is the partial molar volume; σ h is the hydrostatic stress; σ 11 is the normal stress in the x-axis direction; σ 22 is the normal stress in the y-axis direction; σ 33 is the normal stress in the z-axis direction.

[0118] S102: Calculate the battery's equivalent stress and obtain the stress relationship:

[0119] Assume that the active particles are not subject to any external forces; that the volume changes are isotropic; that the active material behaves as an elastic material; that the effects of particle morphology and its associated spatial arrangement on lithium transport in the electrode are neglected; and that the particle failure criterion is not considered, with only the generated stress calculated. Figure 3 shows the evolution of a spherical particle from its initial configuration to its current configuration. Initially, the spherical particle has a radius of Rs, and there are no lithium ions or stress within the particle. When lithium ions are embedded in the anode particle, the particle begins to deform, expanding its radius from Rs to Rs(t), generating stress within the particle structure.

[0120] The expression of solid mechanics in the initial configuration is:

[0121] Where u is the displacement; F d is the elastic deformation gradient; S is the elastic stress tensor; I is the equivalent tensor;

[0122] Thermal strain ε caused by thermal expansion th Given by formula (10):

[0123] Where C is the elastic tensor; ε el is the elastic strain tensor; ε tot is the total strain tensor; α is the thermal expansion coefficient; T ref is the reference temperature; l is the velocity gradient tensor; F is the deformation gradient;

[0124] For isotropic spherical particles, the strain component is related to the radial displacement u. Based on the large deformation theory of continuum mechanics, the strain-displacement relationship can be expressed as:

[0125] Where, ε ij is the strain component, u i 、u j 、u k is the displacement component, x i 、x j is the position component;

[0126] The constitutive relationship of lithium ion diffusion stress-strain can be expressed as:

[0127] Where, ε ij is the strain component; E is Young's modulus; v is Poisson's ratio; σ ij is the stress component; δ ij is the Dirac delta function, which is 1 when i = j and 0 when i ≠ j; c0 is the initial solid phase lithium ion concentration;

[0128] For the assumed spherical particles, the stress can also be divided into radial stress and tangential stress, and Equation (12) can be written as:

[0129] Among them, ε r (r) and ε θ (r) are the radial strain component and the tangential strain component respectively; σ r (r) and σ θ (r) are the radial stress component and the tangential stress component respectively;

[0130] For spherical particles, when there is no external force, the stress equilibrium equation of the sphere is:

[0131] Where r is the radius of the sphere, σ r , σ θ is the stress component in the axial coordinate;

[0132] For the elastic deformation of a sphere, the relationship between the strain and displacement of the particle is:

[0133] Where, ε r , ε θ is the stress component in the axis coordinate, and u is the displacement;

[0134] During the lithiation process, when the spherical electrode particles are unconstrained externally, their surfaces are in a stress-free state, and the following boundary conditions exist:

[0135] Combining equations (13) to (15) and formula (16) yields the relationship between lithium ion concentration and diffusion stress:

[0136] Among them, c av (r) is the average lithium concentration in the active particles. When r approaches 0, c av (r) tends to c(0), then the stress at the center of the particle is:

[0137] The above formula shows that the stress at the center of the spherical particle is the hydrostatic pressure. In the stress tensor of the spherical particle, Then the average hydrostatic stress is:

[0138] 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, and its calculation formula is:

[0139] S103: Based on the electrochemical reaction equations and stress relationship equations obtained in S101 and S102, an electrochemical-stress model is established, and the electrode diffusion stress distribution and evolution law are obtained:

[0140] According to the Nernst-Einstein relationship, the mobility 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:

[0141] According to formula (8) and formula (21), formula (7) can be simplified as:

[0142] Therefore, substituting equation (21) back into equation (6) yields:

[0143] At the initial moment, the solid phase lithium ion concentration is 0, and the lithium flux at the interface between the solid phase and the liquid phase is determined by the particle surface current density j r Therefore, the initial and boundary conditions are as follows:

[0144] In summary, the relationship between diffusion stress and lithium ion concentration is obtained:

[0145] As shown in Figure 4, given the difficulty of actual stress testing, the theoretical model's validity was verified solely from the perspective of voltage response. Taking the electrochemical-stress model of porous silicon anode materials as an example, verification was performed using 0.1C and 0.5C discharge conditions. The results show a relatively consistent relationship between the experimental and simulation results. However, since the model ignores the formation of the SEI solid electrolyte interface, some discrepancies still exist between theory and experiment. The good fit between simulation and experimental results confirms the model's applicability and feasibility for theoretical predictions of silicon electrodes.

[0146] The parameters for the nano-silicon model constructed in this embodiment, namely the electrochemical-stress model, are shown in Table 1:

[0147] Table 1. Parameters for building the electrochemical-stress model

[0148] S2: Based on the stress evolution law during the lithiation process obtained in S1, a multi-stage constant current optimization strategy is used to optimize the rate of the lithiation process. The rate optimization scheme is designed according to the material yield strength stress:

[0149] S201: Determine the material yield strength stress range:

[0150] From the mechanism of the influence of rate on stress, it can be seen that the rate has a greater impact on stress, and a low rate can greatly reduce stress. From the discussion of stress changes during the charge and discharge process, it can be seen that during the lithium insertion process, the stress will reach a peak in the initial state of charge and then gradually decrease. The lithium removal process is the opposite. Therefore, a smaller rate can be used in the peak stress generation stage to suppress the deformation and stress in the negative electrode particles, and then a larger rate can be used to accelerate lithium insertion / delithiation. Assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium ion concentration, the following formula is obtained:

[0151] Where σ Y0 is the yield stress of the negative electrode before lithiation; c is the lithium ion concentration; c max is the saturated lithium ion concentration.

[0152] As shown in FIG5 , taking porous silicon material as an example, the stress range of the yield strength of the negative electrode material during 1C charge and discharge can be obtained from formula (25) from 0 to 60% SOC. Within this range, it means that the material will not break, while outside this range, it means that the material has yielded.

[0153] S202: Designing a rate optimization scheme: Based on the yield strength stress range of the negative electrode material during 1C charge and discharge, it can be seen that under 1C stress, within the 0-60% SOC range, the stress exceeds the yield strength of the material. Therefore, it is decided to perform rate optimization within this range. After that, the stress is within the yield strength, and the 1C charge / discharge rate can be maintained. Four optimization schemes are designed in this embodiment, as shown in Table 2:

[0154] Table 2. Specific parameters of the four optimization schemes

[0155] Schemes 1 and 2 perform single-rate optimization in the range of 0 to 60% with the goal of reducing stress. Schemes 3 and 4 perform double-rate optimization in the range of 0 to 60% with 30% SOC as the segment with the goal of reducing stress and shortening charge and discharge time. At the same time, the comparison is based on the 1C cycle stress distribution.

[0156] Figure 6 shows the stress evolution on the surface of silicon active particles under different optimization schemes. The red dashed lines represent the yield strength range. For the multi-stage constant current strategy, stress in the silicon particles is minimal at a rate of 0.3C. Increasing the rate from 0.3C to a higher rate causes a sharp increase in stress, but controlling the rate within the yield strength range still reduces the risk of silicon particle fracture. At the optimized rate of 0.3C, the peak stress decreases from 0.94 GPa to 0.29 GPa. At the optimized rate of 0.74C within the 30-60% SOC range, the stress decreases from 0.45 GPa to 0.32 GPa during the initial stage. Schemes 1 and 3 can reduce stress during lithiation, while Schemes 2 and 4 are applicable throughout the entire charge-discharge cycle. While these schemes can suppress the initial peak stress, they may also introduce additional peaks or sudden stress changes, which could lead to cycling damage or fatigue of the active particles. Therefore, experimental verification of the optimization schemes is necessary to balance the trade-offs between stress reduction and cyclic fatigue damage.

[0157] Figure 7 shows the stress evolution at the center of the silicon active particles under different optimization schemes. As can be seen from Figure 7, due to the distribution of pores, the stress level at the center of the particle is generally lower than that at the particle surface. Therefore, the four optimization schemes are equally applicable to reducing the stress at the particle center. The initial rate optimization scheme also effectively suppresses the stress at the center of the silicon particle, similar to the stress distribution trend on the silicon particle surface shown in Figure 6. Specifically, Schemes 1 and 3 reduce the tensile stress during the lithiation process, while Schemes 2 and 4 can suppress stress throughout the entire charge and discharge cycle.

[0158] The above results demonstrate the feasibility of using a multi-stage constant current strategy to control the stress evolution of electrode materials.

[0159] S3: The rate optimization scheme designed in S2 was quantitatively verified at the macro and micro levels through long cycle testing, electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM), and selected area electron diffraction (SAD).

[0160] S301: Macroscopic quantitative verification and evaluation of the rate optimization scheme through long cycle testing and EIS electrochemical impedance spectroscopy testing:

[0161] S3011: Use long cycle testing to optimize and verify the rate optimization scheme:

[0162] By testing the long-cycle performance under different optimization schemes, the charge and discharge capacity, charge and discharge efficiency, and capacity retention rate of the battery during cycling under different optimization schemes are compared; the long-cycle test is a long-term, multi-cycle charge and discharge test of the battery based on the existing rate optimization scheme. By observing the changes in the charge and discharge capacity, charge and discharge efficiency, that is, the coulombic efficiency and capacity retention rate parameters during the long cycle of the battery, the impact of the rate optimization scheme on the long-term cycle performance of the battery can be comprehensively evaluated;

[0163] Coulomb efficiency C E The method of obtaining it is as follows:

[0164] Where C discharge is the discharge capacity, C charge is the charging capacity;

[0165] The discharge specific capacity C' is obtained as follows:

[0166] Where C discharge is the battery discharge capacity, m is the mass of the electrode active material;

[0167] In this embodiment, a long cycle test based on a multi-stage constant current charging optimization strategy is taken as an example at 5°C, 25°C, and 55°C:

[0168] As shown in Figure 8a, the changes in discharge capacity and coulombic efficiency of different optimized strategies at 5°C with the number of cycles show that the discharge capacity of the four strategies is better than 1C rate, and there is a different degree of capacity decay as the cycle progresses. It can be seen that in the first 75 cycles, the discharge capacity of scheme 2 is the highest, and scheme 1 has a slight increase in capacity. After 75 cycles, scheme 1 has the highest capacity retention rate, and after 200 cycles, the discharge capacity is still 145mAh g -1 . Scheme 2 leads to a decrease in capacity after long-term cycling; as the cycling progresses, stress accumulates inside the particles, and the battery impedance gradually increases, making the capacity of the porous silicon-lithium half-battery using Scheme 2 lower than that of Scheme 1 after a certain period of cycling. A similar phenomenon also occurs in the comparison of Scheme 3 and Scheme 4 strategies, but because the capacity of Scheme 3 drops severely in the early stage of the cycle, the overall impedance is slightly higher than that of Scheme 4. Despite the use of a stress control optimization strategy, the battery capacity still drops severely as the cycling progresses at lower temperatures, indicating that the ambient temperature also significantly affects the performance of the battery.

[0169] As shown in Figure 9a, the changes in discharge capacity and coulombic efficiency of different optimization strategies with the number of cycles at 25 °C clearly show that the discharge capacity under the four strategies is much better than the 1C rate. However, the capacity of scheme 3 decays rapidly due to the loss of electrical contact between the electrodes at the end of the cycle, with only 16 mAh g after 200 cycles. -1Scheme 1 and Scheme 2 have the best cycle performance, with discharge capacity of 856 mAh g after cycle. -1 and 666mAh g -1 Compared with the temperature of 5℃, it was found that as the temperature increased, the advantages of the four strategies began to emerge; and the cycle capacity distribution trend was similar to that at 5℃.

[0170] As shown in Figure 10a, the changes in discharge capacity and coulombic efficiency of different optimization strategies at 55 °C with the number of cycles show that all four optimization strategies show good cycling performance. After 200 cycles, scheme 1 and scheme 2 provide 850 and 1478 mAh g, respectively. -1 Even the higher rate strategies of Scheme 3 and Scheme 4 provide 511 and 690 mAh g -1 This shows that increasing the temperature can not only reduce the strong stress level of silicon, but also accelerate the diffusion of lithium ions, reduce the concentration difference of lithium ions in the solid and liquid phases, and reduce the diffusion polarization between the solid and liquid phases, thereby reducing the impedance and improving the electrochemical performance of the battery.

[0171] S3012: Use EIS electrochemical impedance spectroscopy to verify the rate optimization scheme:

[0172] In this embodiment, the EIS electrochemical impedance spectroscopy test based on the multi-stage constant current charging optimization strategy at 5°C, 25°C and 55°C is taken as an example:

[0173] As shown in Figure 8c, the charge transfer resistance R after each strategy cycle at 5°C ct It can be seen that Scheme 1 has the smallest charge transfer resistance of 607Ω, followed by Scheme 2 at 731.2Ω; the charge transfer resistances of Schemes 3 and 4 are 840.3Ω and 792.6Ω respectively; the impedance results correspond well to the long-cycle performance results under different strategies.

[0174] As shown in Figure 9c, the charge transfer resistance R after each strategy cycle at 25°C ct As can be seen, thanks to the lower charge and discharge rates in the early stages, Scheme 1 has the lowest charge transfer resistance, at 77.9Ω, followed by Scheme 2 at 293.4Ω. Schemes 3 and 4 have charge transfer resistances of 385Ω and 344.3Ω, respectively. Increasing temperature also reduces the impedance of the electrode cycle, which can accelerate the electrochemical reaction at the electrode.

[0175] As shown in Figure 10c, the charge transfer resistance R after each strategy cycle at 55°C ctIt can be seen that the charge transfer resistance of F@1 and F@2 is 41.37Ω and 9.2Ω, respectively, and that of F@3 and F@4 is 259.8Ω and 173Ω. The increase in temperature also reduces the impedance of the electrode cycle process, which can accelerate the electrochemical reaction of the electrode.

[0176] S302: Disassemble the battery after the S301 cycle, remove the electrode sheet, and conduct microscopic quantitative verification and evaluation of the electrode sheet through scanning electron microscopy and selected area electron diffraction test:

[0177] S3021: Use scanning electron microscope testing to optimize and verify the magnification optimization plan:

[0178] In this embodiment, the SEM scanning electron microscope test based on the multi-stage constant current charging optimization strategy at 5°C, 25°C and 55°C is taken as an example:

[0179] As shown in Figures 11a and 11f, by comparing the SEM surface images and cross-sectional images of the electrode sheets after cycling with different optimization strategies at 5°C, it can be seen that the surface cracking of the electrode sheets after cycling with Scheme 3 and Scheme 4 is more serious. Partial pulverization can also be seen from the cross-sectional images of the electrode sheets of Scheme 3 and Scheme 4, which is one of the reasons for the rapid decline in capacity of the two strategies in the middle and late stages. The electrode surfaces of Scheme 1 and Scheme 2 are relatively complete as a whole. The thickness of the active material layer of both is initially 9.2μm, which expands to 25.8μm and 22.2μm respectively after cycling. The silicon electrode cycled with Scheme 1 has better surface integrity, smaller cracks, and fewer holes, which is consistent with the previously measured cycling performance. The effect of charge and discharge rate on the volume expansion of silicon is more obvious at low temperatures.

[0180] As shown in Figures 12b and 12g, a comparison of SEM surface and cross-sectional images of the electrode sheets after cycling at 25°C using different optimized strategies reveals that while Scheme 1 exhibits fine and long surface cracks, the electrode sheet maintains a relatively intact morphology, and the active material layer thickness increases from 9.2μm to 20.8μm. Scheme 2 exhibits fewer and smaller cracks, a more intact surface, and an increased thickness of 23.7μm. Strategies 1 and 2 not only mitigate the cracking of the electrode sheet caused by silicon particle volume expansion but also reduce the probability of particle pulverization. However, due to the multiple stages and high rate characteristics of Schemes 3 and 4, the electrode sheet exhibits numerous and wide surface cracks, and particle pulverization can be seen in the cross-section of the electrode sheet. This, in turn, leads to rapid capacity degradation within a short period of time. After cycling, the active material layer thicknesses of Schemes 3 and 4 increased to 26.7μm and 17.4μm, respectively.

[0181] As shown in Figure 13, at a high temperature of 55°C, the pulverization of silicon particles at the 1C rate was alleviated, but it remained severe. The active material layer thickness increased to 15.2μm and had already fallen off the current collector. Thanks to the increased temperature, the electrode surfaces of all four strategies were relatively intact after the cycle, with few cracks. Strategy 2 even had no visible cracks. The active layer thickness of the four strategies increased from the original 9.2μm to 16.9, 15.8, 21.7, and 19.1μm, respectively.

[0182] The stress evolution law obtained from the negative electrode model can effectively reduce surface cracks and damage by reducing the charge and discharge rate while increasing the ambient temperature. The more obvious the mechanical effect, the smaller the capacity loss.

[0183] S3022: Optimize and verify the magnification optimization scheme using selected area electron diffraction testing:

[0184] In this embodiment, the selected area electron diffraction test based on the multi-stage constant current charging optimization strategy is taken as an example:

[0185] The lattice spacing d after the cycle is calculated from the electron diffraction pattern, and then the lattice constant a and the unit cell volume are calculated according to the cubic lattice interplanar spacing calculation formula (28); the interplanar spacing calculation formula for cubic crystals is:

[0186] Where d is the interplanar spacing; a is the lattice constant; h, k, and l are the Miller indices of the crystal plane;

[0187] As shown in Figure 14, at room temperature of 5°C, the lattice constants and unit cell volumes after cycling were obtained from SAED selected area electron diffraction tests of the worst and best long cycle performance solutions, namely Solution 3 and Solution 1, as shown in Table 3:

[0188] Table 3. Calculation results of lattice constant a values ​​for Scheme 1 and Scheme 3

[0189] As shown in Figure 15, at room temperature of 25°C, the lattice constants and unit cell volumes after cycling were obtained from SAED selected area electron diffraction tests of the worst and best long cycle performance solutions, namely Solution 4 and Solution 1, as shown in Table 4:

[0190] Table 4. Calculation results of lattice constant a values ​​for Scheme 1 and Scheme 4

[0191] As shown in Figure 16, at a high temperature of 55°C, the lattice constants and unit cell volumes after cycling were obtained from SAED selected area electron diffraction tests of the worst and best long cycle performance solutions, namely Solution 3 and Solution 2, as shown in Table 5:

[0192] Table 5. Calculation results of lattice constant a values ​​for Scheme 2 and Scheme 3

[0193] S4: Conduct a macro-micro joint analysis of the macro and micro quantitative verification results in S3:

[0194] By jointly comparing the volume expansion rate of the negative electrode particles of different optimization schemes and their long-cycle performance, a macro-micro joint quantitative evaluation of the different optimization schemes is made. The macro-micro joint quantitative evaluation is performed based on the macro-quantitative verification results and the micro-quantitative verification results, that is, the macro-micro joint quantitative evaluation is performed based on the verification results of the long-cycle test and the EIS electrochemical impedance spectroscopy test and the scanning electron microscopy test and the selected area electron diffraction test:

[0195] Table 6 shows the unit cell volume changes for the worst and best long-cycle performance scenarios, namely, Scheme 3 and Scheme 1, at room temperature (5°C). While solid silicon typically expands by 280% in the Li15Si4 alloy phase, the unit cell volume expansion rates for Schemes 1 and 3 remain lower than those for solid silicon after long-cycle cycles at low temperatures, at 45.88% and 98.06%, respectively. This is consistent with the long-cycle performance distribution. This suggests that the combined optimization of the porous silicon anode structure design and the charge-discharge strategy significantly reduces the large volume expansion of silicon particles, thereby reducing diffusion stress.

[0196] Table 6. Unit cell volume a of Scheme 1 and Scheme 3 3 Value calculation results

[0197] Table 7 shows the unit cell volume changes for Scheme 4 and Scheme 1, the worst and best long-cycle performance options at room temperature (25°C). At 25°C, the volume expansion rates of Scheme 1 and Scheme 4 strategies after long-cycle testing were 18.75% and 32.58%, respectively. The microscopic particle expansion rates after cycling using Scheme 1 and Scheme 4 strategies are consistent with the long-cycle performance distribution pattern. In addition, compared to the low temperature of 5°C, the volume expansion of silicon particles was reduced by up to 79.31%, indicating that increasing temperature can reduce the diffusion stress of silicon particles, allowing the optimized silicon electrode battery to exhibit good capacity performance.

[0198] Table 7. Unit cell volume a of Scheme 1 and Scheme 4 3 Value calculation results

[0199] Table 8 shows the changes in lattice constants and unit cell volumes after cycling, as determined by SAED selected area electron diffraction (SAED) measurements for Schemes 3 and 2, respectively, at a high temperature of 55°C for the worst and best long-cycle performance. The volume expansion rates for Schemes 2 and 3 after long cycling were 11.99% and 20.28%, respectively. The microscopic particle expansion rates after cycling using Schemes 2 and 3 are consistent with the long-cycle performance distribution. Furthermore, at high temperatures, the internal electrochemical reactions of the silicon anode accelerate, reducing impedance and diffusion stress, resulting in less volume expansion and allowing the silicon particles to maintain a relatively intact structure.

[0200] Table 8. Unit cell volume a of Scheme 2 and Scheme 3 3 Value calculation results

[0201] Based on the results of macro-micro joint analysis, the effectiveness of the joint optimization of internal and external parameters of silicon electrodes, namely porous structure and rate optimization, was demonstrated from a microscopic perspective.

[0202] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0203] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation, characterized in that: The following steps are involved: S1: Construct an electrochemical-stress model to obtain the distribution and evolution of electrode diffusion stress; S2: According to the stress evolution law during the lithiation process obtained in S1, a multi-stage constant current optimization strategy is used to optimize the rate of the lithiation process, and a rate optimization scheme is designed according to the material yield strength stress; S3: The rate optimization scheme designed in S2 was quantitatively verified at the macro and micro levels through long cycle test, EIS electrochemical impedance spectroscopy test, scanning electron microscope test and selected area electron diffraction test; S4: Conduct a macro-micro joint analysis of the macro and micro quantitative verification results in S3: By jointly comparing the volume expansion rate of the negative electrode particles of different optimization schemes and their long cycle performance, a macro-micro joint quantitative evaluation of different optimization schemes can be made.

2. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint according to claim 1 is characterized in that: The S1 specifically includes the following steps: S101: Use a half-cell and a simplified two-dimensional plane model to transform it into a plane strain problem and obtain the electrochemical reaction equation; S102: Calculate the normal equivalent stress of the battery and obtain the stress relationship; S103: An electrochemical-stress model is established based on the electrochemical reaction equations and stress relationship equations obtained in S101 and S102, and the distribution and evolution law of electrode diffusion stress are obtained.

3. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint according to claim 2 is characterized in that: The specific steps of S101 are as follows: Using a half-cell and a simplified two-dimensional plane model, it is transformed into a plane strain problem, and the electrolyte control equations are charge conservation and material conservation equations: In the formula, σ e is the electrolyte conductivity; φ e is the electrolyte potential energy; R is the ideal gas constant; T is the temperature; F is the Faraday constant; f is the activity coefficient of the salt; c e is the electrolyte salt concentration; t + is the migration number of lithium ions; i e is the electrolyte current density; ε e is the electrolyte volume fraction; D e is the diffusion coefficient of electrolyte salt; R e is the sum of lithium ion sources in the electrolyte; t is time; The governing equation for the electrodes is defined by Ohm's law: In the formula, i s is the electrode current density, The electrochemical reaction at the interface between the electrode and the electrolyte is described by the Butler-Volmer equation: In the formula, j r is the local current density; i0 is the exchange current density; α a is the anode transfer coefficient, the value is 0.5; α c is the cathode transfer coefficient, which is 0.5; η is the overpotential; i 0,ref is the reference exchange current density; c e,ref is the electrolyte reference concentration; The mass conservation of lithium ions in active materials under the action of electric field can be defined by Fick's law; the diffusion-based lithium ion transport is given by the mass conservation equation of formula (6): Where c is the solid phase lithium ion concentration; J is the diffusion flux; t is time; From the kinetic theory, it is known that there is a linear relationship between the diffusion flux and the chemical potential gradient of the active particles: Where M is the mobility of lithium in the solid phase; μ is the chemical potential; The hydrostatic stress term is added to the chemical potential to reflect the effect of stress on the diffusion process: Where μ0 is a constant representing the chemical potential in the stress-free state; X is the molar fraction of lithium ions; Ω is the partial molar volume; σ h is the hydrostatic stress; σ 11 is the normal stress in the x-axis direction; σ 22 is the normal stress in the y-axis direction; σ 33 is the normal stress in the z-axis direction.

4. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 3 is characterized in that: The specific steps of S102 are as follows: Assume that the active particles are not subject to any external forces; the volume changes are isotropic; the active materials behave like elastic materials; ignore the effects of particle morphology and its related spatial arrangement on lithium transport in the electrode; do not consider the failure criteria of the particles, and only calculate the generated stress; The expression of solid mechanics in the initial configuration is: Where u is displacement; F d is the elastic deformation gradient; S is the elastic stress tensor; I is the identity tensor; Thermal strain ε caused by thermal expansion th Given by formula (10): Where C is the elastic tensor; ε el is the elastic strain tensor; ε tot is the total strain tensor; α is the thermal expansion coefficient; T ref is the reference temperature; l is the velocity gradient tensor; F is the deformation gradient; For isotropic spherical particles, the strain component is related to the radial displacement u. Based on the large deformation theory of continuum mechanics, the strain-displacement relationship can be expressed as: In the formula, ε ij is the strain component, u i 、u j 、u k is the displacement component, x i 、x j is the position component; The constitutive relation of lithium ion diffusion stress-strain can be expressed as: In the formula, ε ij is the strain component; E is Young's modulus; v is Poisson's ratio; σ ij is the stress component; δ ij is the Dirac delta function, which is 1 when i=j and 0 when i≠j; c0 is the initial solid phase lithium ion concentration; For the assumed spherical particles, the stress can also be divided into radial stress and tangential stress, and equation (12) can be written as: Among them, ε r (r) and ε θ (r) are the radial strain component and the tangential strain component respectively; σ r (r) and σ θ (r) are the radial stress component and the tangential stress component respectively; For spherical particles, when there is no external force, the stress equilibrium equation of the sphere is: In the formula, r is the radius of the sphere, σ r , σ θ is the stress component in the axial coordinate; For the elastic deformation of a sphere, the relationship between the strain and displacement of the particle is: In the formula, ε r , ε θ is the stress component in the axis coordinate, and u is the displacement; During the lithiation process, when the spherical electrode particles are unconstrained externally, their surfaces are in a stress-free boundary state, and the following boundary conditions apply: Combining equations (13) to (15) and formula (16) can give the relationship between lithium ion concentration and diffusion stress: Among them, c av (r) is the average lithium concentration in the active particles. When r approaches 0, c av (r) tends to c(0), then the stress at the center of the particle is: The above formula shows that the stress at the center of the spherical particle is the hydrostatic pressure. In the stress tensor of the spherical particle, Then the average hydrostatic stress is: After the material undergoes 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, and its calculation formula is:

5. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint according to claim 4 is characterized in that: The specific steps of S103 are as follows: According to the Nernst-Einstein relationship, the mobility M of lithium in the solid phase and the solid phase diffusion coefficient D have the following relationship: D = MRT; therefore, combining equations (7) and (8), it can be obtained that: According to formula (8) and formula (21), formula (7) can be simplified as: Therefore, substituting equation (21) back into equation (6) yields: At the initial moment, the solid phase lithium ion concentration is 0, and the lithium flux at the interface between the solid phase and the liquid phase is determined by the particle surface current density j r Therefore, the initial and boundary conditions are as follows: In summary, the relationship between diffusion stress and lithium ion concentration is obtained:

6. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 5 is characterized in that: The specific steps of S2 are as follows: S201: Determine the material yield strength stress range; S202: Design rate optimization plan: Design an optimization plan by using a smaller rate to suppress the deformation and stress in the negative electrode particles during the peak stress generation stage, and then using a larger rate to accelerate lithium insertion or removal. When the stress exceeds the yield strength stress range determined in S201, continue to optimize the stress within the range, and continue to maintain the original charge or discharge rate for the remaining stresses that do not exceed the range.

7. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 6 is characterized in that: The specific steps of S201 are as follows: From the mechanism of the influence of rate on stress, it can be seen that the rate has a greater impact on stress, and a low rate can reduce stress to a large extent. From the discussion of stress changes during the charge and discharge process, it can be seen that during the lithium insertion process, the stress will reach a peak value at the initial charge state stage and then gradually decrease. The lithium removal process is the opposite. Therefore, a smaller rate can be used in the peak stress generation stage to suppress the deformation and stress in the negative electrode particles, and then a larger rate can be used to accelerate lithium insertion / delithiation. Assuming that the yield strength of the negative electrode during lithiation is linearly related to the lithium ion concentration, the following formula is obtained: In the formula, σ Y0 is the yield stress of the negative electrode when not lithiated; c is the lithium ion concentration; c max is the saturated lithium ion concentration.

8. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 7 is characterized in that: The specific steps of S3 are as follows: S301: Macroscopic quantitative verification and evaluation of the rate optimization scheme through long cycle test and EIS electrochemical impedance spectroscopy test; S302: Disassemble the battery after the S301 cycle, take out the electrode sheet, and conduct microscopic quantitative verification and evaluation of the electrode sheet through scanning electron microscopy test and selected area electron diffraction test.

9. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 8 is characterized in that: The specific steps of S301 are as follows: S3011: Use long cycle test to optimize and verify the rate optimization scheme: By testing the long cycle performance under different optimization schemes, compare the charge and discharge capacity, charge and discharge efficiency, and capacity retention rate of the battery during cycling under different optimization schemes; the long cycle test is a long-term, multi-cycle charge and discharge test of the battery based on the existing rate optimization scheme. By observing the changes in the charge and discharge capacity, charge and discharge efficiency, i.e., coulomb efficiency, and capacity retention rate parameters during the long cycle of the battery, the impact of the rate optimization scheme on the long-term cycle performance of the battery can be comprehensively evaluated; Coulomb efficiency C E The acquisition method is as follows: In the formula, C discharge is the discharge capacity, C charge is the charging capacity; The discharge specific capacity C' is obtained as follows: In the formula, C discharge is the battery discharge capacity, m is the mass of the electrode active material; S3012: Use EIS electrochemical impedance spectroscopy test to optimize and verify the rate optimization scheme: By performing EIS test on the batteries after cycling with different optimization schemes, the electron transfer impedance of the batteries after cycling with different optimization schemes is obtained, so as to compare different optimization schemes; the electrode process in the battery is equated to a simple circuit composed of resistors and capacitors in series and parallel, and the corresponding output signal is obtained by inputting a disturbance signal, and the equivalent circuit model of EIS is determined based on the measured electrochemical impedance EIS spectrum.

10. The method for quantitatively evaluating battery electrode charging strategy based on macro-micro joint evaluation according to claim 9 is characterized in that: The specific steps of S302 are as follows: S3021: Use scanning electron microscope test to optimize and verify the rate optimization scheme: By observing the pulverization of negative electrode particles and the change in thickness of the active material layer: Scanning electron microscope uses the difference of characteristics of micro-areas on the surface of materials to produce different brightness differences in different areas of the sample under the action of electron beam, so as to obtain images with certain contrast. The imaging signal is secondary electrons, backscattered electrons or absorbed electrons, among which secondary electrons are the most important imaging signals. High-energy electron beam bombards the sample surface, stimulates various physical signals on the sample surface, and then uses different signal detectors to receive the physical signals and convert them into image information. S3022: Optimize and verify the rate optimization scheme using selected area electron diffraction testing: Microscopic testing of the irreversible volume expansion of electrode material particles after long cycles: The lattice spacing d after the cycle is calculated from the electron diffraction pattern, and then the lattice constant a and the unit cell volume are calculated according to the cubic lattice interplanar spacing calculation formula (28); the interplanar spacing calculation formula of the cubic crystal is: In the formula, d is the interplanar spacing; a is the lattice constant; h, k, l are the Miller indices of the crystal plane; Selected area electron diffraction utilizes the micro-area correspondence between selected area morphological observation and electron diffraction structure analysis to achieve in-situ analysis of the morphological features and crystallographic properties of crystal samples. By setting a selected area grating on the objective lens plane, the diffraction area is selected and limited. Only the sample micro-area where the viewpoint inside the aperture is located can be passed through by the imaging electron beam, thereby achieving the purpose of matching microscopic observation with electron diffraction.

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