A method and system for evaluating anisotropic expansion of silicon particles applied to silicon-based negative electrodes

Abstract

The application discloses a kind of silicon particles anisotropic expansion evaluation method and system applied to silicon-based negative electrode, the method includes: S1, constructs silicon particles anisotropic lithium insertion submodel;S2, constructs silicon particles mechanical property submodel;S3, silicon particles anisotropic lithium insertion submodel and silicon particles mechanical property submodel are coupled into silicon particles anisotropic expansion model;S4, whether silicon particles anisotropic expansion model meets the requirement is verified;S5, based on the silicon particles anisotropic expansion model that is verified to pass, the anisotropic expansion of different types is expanded, and the anisotropic expansion degree is evaluated.The application analyzes the influence of anisotropic expansion on coating stress distribution by model, reduces the number of tests, shortens the development cycle, can multidimensional evaluation coating protects the characteristics of silicon particles, selects reasonable coating, reduces the probability of silicon particles crushing, relieves anisotropic expansion, improves electrode performance.

Description

Technical Field

[0001] This invention relates to the field of electrochemistry, and more specifically to a method and system for evaluating the anisotropic expansion of silicon particles in silicon-based anodes. Background Technology

[0002] Lithium-ion batteries are widely used in new energy vehicles, energy storage, and other fields due to their low self-discharge rate, long cycle life, and high energy density. With the rapid development of technology, the energy density requirements for lithium-ion batteries are becoming increasingly stringent in various fields, leading to extensive research into high-energy-density electrode materials.

[0003] Silicon has a specific capacity more than 10 times that of graphite. Using silicon as the anode material in lithium-ion batteries would significantly improve energy density. However, alloying silicon with lithium results in approximately 300% volume expansion. This massive expansion can cause silicon particles to break, damaging the electrode structure. Furthermore, during the first charge-discharge cycle, crystalline silicon exhibits a distinct lattice orientation. During alloying with lithium, it undergoes significant anisotropic expansion along different lattice orientations, making silicon particles more prone to breakage during the first cycle and impacting battery performance. In the industry, coating layers are commonly used to protect silicon particles. Therefore, it is necessary to study the anisotropic expansion characteristics of coated silicon particles during lithium intercalation. However, current research on silicon particles mainly focuses on the massive volume expansion, analyzing the breakage risk and protective measures after expansion; little attention has been paid to the anisotropic expansion of silicon particles. Anisotropic expansion leads to uneven stress distribution in silicon particles, making them more susceptible to breakage and requiring more stringent protective measures. Moreover, anisotropic expansion affects particle contact within the electrode, and currently, there is a lack of methods to evaluate the degree of anisotropic expansion. Summary of the Invention

[0004] This invention addresses the problems in existing technologies by disclosing a method and system for evaluating the anisotropic expansion of silicon particles in silicon-based anodes. The invention constructs an anisotropic lithium intercalation sub-model for silicon particles to characterize the anisotropy of lithium concentration during lithium intercalation in crystalline silicon; it also constructs a mechanical property sub-model for silicon particles to simulate and analyze the stress and strain characteristics of silicon particles. These two sub-models are coupled to form an anisotropic expansion model for silicon particles. This model is then used to evaluate the anisotropic expansion of silicon particles. By analyzing the impact of anisotropic expansion on the stress distribution of the coating layer, the number of experiments is reduced, the development cycle is shortened, and the protective properties of the coating layer on silicon particles can be evaluated from multiple dimensions. This allows for the selection of a suitable coating layer, reducing the probability of silicon particle breakage, mitigating anisotropic expansion, and improving electrode performance.

[0005] This invention is achieved through the following technical solution:

[0006] This invention first provides a method for evaluating the anisotropic expansion of silicon particles in silicon-based anodes, comprising the following steps:

[0007] S1. Construct an anisotropic lithium intercalation model of silicon particles to characterize the anisotropy of lithium concentration in crystalline silicon during lithium intercalation.

[0008] S2. Construct a sub-model of the mechanical properties of silicon particles to simulate and analyze the stress and strain characteristics of silicon particles;

[0009] S3. Couple the anisotropic lithium intercalation sub-model of silicon particles and the mechanical property sub-model of silicon particles into an anisotropic expansion model of silicon particles;

[0010] S4. Based on the results of the silicon particle expansion test, determine whether the accuracy of the anisotropic expansion model of silicon particles meets the requirements. If it meets the requirements, proceed to step S5. If it does not meet the requirements, adjust the model until it meets the accuracy requirements.

[0011] S5. Based on the validated anisotropic expansion model of silicon particles, perform different types of anisotropic expansion extensions and evaluate the degree of anisotropic expansion.

[0012] As a further solution, the specific method of S1 includes:

[0013] S11. Based on the simulation of the concentration characteristics of silicon-lithium alloys in the research object, the specific formula is as follows:

[0014] (1);

[0015] (2);

[0016] Wherein, equation (1) represents the lithium concentration variation characteristics of the coating layer, C co This indicates the concentration in a specific region of the coating layer, in mol / m³. 3 ;D co The value m represents the lithium diffusion coefficient of the coating layer, describing the diffusion rate of lithium. 2 / s is a specific numerical value; Equation (2) represents the lithium concentration variation characteristics of silicon particles, C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 ;D pa The lithium diffusion coefficient of silicon particles is represented by m. 2 / s, the mechanism of lithium intercalation in silicon particles is an alloying reaction with lithium, that is, lithium-silicon alloy is formed in the lithium-intercalated region, while the unintercalated region is still silicon. Therefore, there is a clear interface, hence D in equation (2) pa It is no longer a specific numerical value, and its expression is shown in equation (3):

[0017] (3);

[0018] Among them, D si The constant lithium diffusion coefficient of silicon particles is expressed in mol / s; C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 C max_si This indicates the lithium concentration after complete lithium intercalation of silicon particles, in mol / m³. 3 ;

[0019] S12. Since silicon particles have different lithium intercalation capabilities along the lattice direction, their lithium intercalation process also exhibits anisotropy. That is, equation (3) needs to add a concentration direction function f(x) to characterize the anisotropy of lithium intercalation, as shown in equation (4):

[0020] (4);

[0021] S13. According to the law of conservation of mass, the lithium flux is the same at the interface between the silicon particles and the coating layer. That is, the lithium flux flowing out from the inside of the coating layer is the same as the lithium flux flowing in from the outside of the silicon particles, as shown in Equation (5):

[0022] (5);

[0023] Among them, J co This represents the lithium flux flowing out from the inside of the coating layer, in mol / (m 2 ·s); J pa This represents the lithium flux flowing into the outer side of the silicon particles, in mol / (m²). 2 ·s); the concentration on the outermost side of the coating layer is the boundary condition for this lithium diffusion model.

[0024] As a further embodiment, the method of S2 includes:

[0025] S21. The anisotropic expansion of silicon particles is related to their degree of lithium intercalation, as shown in the following formula:

[0026] (6);

[0027] (7);

[0028] In the above formula, equation (6) represents the expansion characteristics of the coating layer, where ε co_xx and ε co_yy β represents the strain in the x and y directions of the coating layer, respectively; co_xx and β co_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; co_xx With C co_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m.3 ;

[0029] Equation (7) represents the expansion characteristics of silicon particles, where ε pa_xx and ε pa_yy β represents the strain in the x and y directions of the coating layer, respectively; pa_xx and β pa_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; pa_xx With C pa_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m. 3 Among them, silicon particles have different expansion capabilities along the lattice direction, thus exhibiting anisotropic expansion. Therefore, the expansion coefficient β of silicon particles is... pa We need to add an expansion direction function g(x), namely β. pa ·g(x);

[0030] S22. Whether it is the coating layer or the silicon particles, the expansion of their volume will inevitably bring about changes in stress, as shown in Equation (8).

[0031] (8);

[0032] Where i represents the coating layer (CO) and silicon particles (Pa), respectively, and σ i_xx σ represents the stress in the x-direction of the coating layer and silicon particles. i_yy E represents the stress in the y-direction of the coating layer and silicon particles. i This represents the Young's modulus of the coating layer and silicon particles, in GPa. i ε represents the Poisson's ratio of the coating layer and the silicon particles; i_xx and ε i_yy These represent the strain components in the x and y directions of the coating layer and silicon particles, respectively.

[0033] As a further approach, the anisotropic expansion model of silicon particles in S3 is as follows:

[0034] (9);

[0035] Among them, U r (θ) represents the radial displacement of a silicon particle along the radial direction at any angle; θ high θ represents the angular range of the region with large radial strain. low This indicates the angular range of the region with relatively small radial strain. This represents the average radial strain in the region with large radial strain. α represents the average radial strain in the region with smaller radial strain; α is the anisotropy, which represents the degree of anisotropy in the expansion of silicon particles. The larger the value of α, the higher the degree of anisotropic expansion of silicon particles, and vice versa. This represents the original radius of the silicon particle.

[0036] As a further improvement, in S5, the accuracy of the anisotropic expansion model of silicon particles needs to reach 95%.

[0037] This invention also provides a silicon particle anisotropic expansion assessment system for silicon-based anodes, comprising:

[0038] The sub-model construction module constructs an anisotropic lithium intercalation sub-model for silicon particles and a mechanical property sub-model for silicon particles, respectively.

[0039] The model building module couples the anisotropic lithium intercalation model of silicon particles and the mechanical property model of silicon particles into an anisotropic expansion model of silicon particles.

[0040] The model verification module compares the experimental results with the simulation prediction results of the anisotropic expansion model to determine whether the anisotropic expansion model meets the accuracy requirements.

[0041] The model prediction module extends the anisotropic expansion model that meets the accuracy requirements with different types of anisotropic expansion and evaluates the degree of anisotropic expansion.

[0042] The features and beneficial effects of this invention are as follows:

[0043] (1) This invention constructs an anisotropic lithium intercalation sub-model for silicon particles to characterize the anisotropy of lithium concentration in crystalline silicon during lithium intercalation; constructs a mechanical property sub-model for silicon particles to simulate and analyze the stress and strain characteristics of silicon particles; and couples the above two sub-models to form an anisotropic expansion model for silicon particles. The anisotropic expansion model for silicon particles is verified and its accuracy is determined to be above 95%. Then, the anisotropic expansion model for silicon particles is used to evaluate the anisotropic expansion of silicon particles. This model takes into account the role of the coating layer. By analyzing the influence of anisotropic expansion on the stress distribution of the coating layer through this model, the number of experiments can be reduced, the R&D cycle can be shortened, the cost can be reduced, and a large amount of simulation result data can be obtained. The protective characteristics of the coating layer on silicon particles can be evaluated in multiple dimensions, a reasonable coating layer can be selected, the probability of silicon particle breakage can be reduced, anisotropic expansion can be alleviated, and electrode performance can be improved.

[0044] (2) This invention realizes the simulation of anisotropic expansion of silicon particles, and optimizes the coating structure of silicon particles by predicting data through the model, thereby reducing the risk of silicon particle breakage, slowing down the degree of anisotropic expansion, avoiding the deterioration of contact between particles due to anisotropic expansion, and improving electrode performance in multiple dimensions.

[0045] (3) This invention can easily realize the simulation of anisotropic expansion at the particle scale or even the electrode scale of silicon-based negative electrode, analyze the influence of anisotropic expansion on the electrochemical performance of electrodes and batteries, and also invented an anisotropic degree evaluation method for anisotropic expansion characteristics, providing a basis for how to design coating layers and alleviate anisotropic expansion, avoiding a large number of experiments and tests, greatly improving R&D efficiency, and enabling analysis and optimization of anisotropic expansion of silicon particles from multiple perspectives. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart of the method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes, as described in an embodiment of the present invention.

[0048] Figure 2 This is a silicon particle lithium intercalation expansion result provided in specific embodiment 1 of the present invention;

[0049] Figure 3 This is a schematic diagram of a silicon particle finite element model provided in specific embodiment 1 of the present invention;

[0050] Figure 4 This is a schematic diagram of the direction function of the lithium diffusion coefficient of silicon particles provided in specific embodiment 1 of the present invention;

[0051] Figure 5 This is a schematic diagram of the concentration distribution of an anisotropic lithium intercalation model of silicon particles provided in specific embodiment 1 of the present invention;

[0052] Figure 6 This is a schematic diagram of the anisotropic expansion direction function of silicon particles provided in specific embodiment 1 of the present invention;

[0053] Figure 7 This is a schematic diagram of the Young's modulus function of silicon particles provided in specific embodiment 1 of the present invention;

[0054] Figure 8 This is a schematic diagram of the Poisson's ratio function of silicon particles provided in specific embodiment 1 of the present invention;

[0055] Figure 9 This is a schematic diagram of the expansion state of an anisotropic expansion model of silicon particles provided in a specific embodiment 1 of the present invention;

[0056] Figure 10This is a schematic diagram of a silicon particle finite element model provided in specific embodiment 2 of the present invention;

[0057] Figure 11 This is a schematic diagram of the direction function of the lithium diffusion coefficient of silicon particles provided in specific embodiment 2 of the present invention;

[0058] Figure 12 This is a schematic diagram of the concentration distribution of an anisotropic lithium intercalation model of silicon particles provided in specific embodiment 2 of the present invention;

[0059] Figure 13 This is a schematic diagram of the anisotropic expansion direction function of silicon particles provided in specific embodiment 2 of the present invention;

[0060] Figure 14 This is a schematic diagram of the expansion state of an anisotropic expansion model of silicon particles provided in specific embodiment 2 of the present invention. Detailed Implementation

[0061] To facilitate understanding of the present invention, a more comprehensive description of the present invention will be given below, and embodiments of the present invention will be provided, but this does not limit the scope of the present invention.

[0062] Because silicon particles are easily fractured, they are usually protected by a coating layer. The more severe the anisotropic expansion of the silicon particle, the more irregular its expanded shape, the uneven stress distribution, and the more prone the coating layer is to cracking and breaking. While the silicon particle coating layer provides protection and influences the anisotropic expansion of the silicon particle, it does not possess the ability to actively undergo anisotropic expansion. Therefore, the core of the anisotropic expansion model lies in the silicon particle itself. Therefore, this invention proposes a method for evaluating the anisotropic expansion of silicon particles in silicon-based anodes. An anisotropic lithium intercalation sub-model is constructed to characterize the anisotropy of lithium concentration in crystalline silicon during lithium intercalation. A mechanical property sub-model is also constructed to simulate and analyze the stress and strain characteristics of silicon particles. These two sub-models are coupled to form an anisotropic expansion model of silicon particles. This model is then validated, confirming an accuracy of over 95%. The anisotropic expansion of silicon particles is then averaged using this model, which considers the role of the coating layer. This model analyzes the impact of anisotropic expansion on the stress distribution of the coating layer, reducing the number of experiments, shortening the R&D cycle, lowering costs, and obtaining a large amount of simulation data. It allows for multi-dimensional evaluation of the protective properties of the coating layer on silicon particles, enabling the selection of a suitable coating layer, reducing the probability of silicon particle breakage, mitigating anisotropic expansion, and improving electrode performance.

[0063] like Figures 1 to 14 As shown, a method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes includes the following steps:

[0064] S1. Construct an anisotropic lithium intercalation model for silicon particles to characterize the anisotropy of lithium concentration in crystalline silicon during lithium intercalation.

[0065] S2. Construct a sub-model of the mechanical properties of silicon particles to simulate and analyze the stress and strain characteristics of silicon particles;

[0066] S3. Couple the anisotropic lithium intercalation sub-model of silicon particles and the mechanical property sub-model of silicon particles into an anisotropic expansion model of silicon particles;

[0067] S4. Compare the simulation results of the anisotropic expansion model with the experimental results of silicon particle expansion to verify whether the model accuracy reaches more than 95%. If the requirements are met, proceed to step S5. If the requirements are not met, debug the model until the model meets the accuracy requirements.

[0068] S5. Based on the validated anisotropic expansion model of silicon particles, extend it to different types of anisotropic expansion and evaluate the degree of anisotropic expansion.

[0069] This invention simulates the anisotropic expansion of silicon particles and constructs an anisotropy evaluation method. By comprehensively applying this evaluation method and simulation model, the coating structure of silicon particles is optimized, the risk of silicon particle breakage is reduced, the degree of anisotropic expansion is slowed down, and the deterioration of inter-particle contact caused by anisotropic expansion is avoided, thereby improving electrode performance in multiple dimensions.

[0070] In some embodiments, silicon particle expansion is caused by the lithium intercalation process; therefore, it is necessary to first construct an anisotropic lithium intercalation model of silicon particles. The specific method is as follows:

[0071] S11. Based on the simulation of the concentration characteristics of silicon-lithium alloys in the research object, the specific formula is as follows:

[0072] (1);

[0073] (2);

[0074] In the above formula, equation (1) represents the lithium concentration variation characteristics of the coating layer, C co This indicates the concentration in a specific region of the coating layer, in mol / m³. 3 ;D co The value m represents the lithium diffusion coefficient of the coating layer, describing the diffusion rate of lithium. 2 / s is a specific numerical value. Equation (2) represents the lithium concentration variation characteristics of silicon particles, C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 ;D pa The lithium diffusion coefficient of silicon particles is represented by m. 2 / s. The mechanism of lithium intercalation in silicon particles is an alloying reaction with lithium, that is, lithium-silicon alloy is formed in the lithium-intercalated region, while the unintercalated region is still silicon. Therefore, there is a clear interface, hence D in equation (2) pa It is no longer a specific numerical value, and its expression is shown in equation (3).

[0075] (3);

[0076] Among them, D si The constant lithium diffusion coefficient of silicon particles is expressed in mol / s; C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 C max_si This indicates the lithium concentration after complete lithium intercalation of silicon particles, in mol / m³. 3 .

[0077] S12. Since silicon particles have different lithium intercalation capabilities along the lattice direction, their lithium intercalation process also exhibits anisotropy. That is, Equation (3) needs to add a concentration direction function f(x) to characterize the anisotropy of its lithium intercalation, as shown in Equation (4).

[0078] (4);

[0079] S13. According to the law of conservation of mass, the lithium flux is the same at the interface between the silicon particles and the coating layer. That is, the lithium flux flowing out from the inside of the coating layer is the same as the lithium flux flowing in from the outside of the silicon particles, as shown in Equation (5).

[0080] (5);

[0081] Among them, J co This represents the lithium flux flowing out from the inside of the coating layer, in mol / (m 2 ·s); J pa This represents the lithium flux flowing into the outer side of the silicon particles, in mol / (m²). 2 ·s). The concentration at the outermost edge of the coating layer is the boundary condition for this lithium diffusion model.

[0082] In summary, the anisotropic lithium intercalation model for silicon particles is shown below:

[0083] (1);

[0084] (2);

[0085] (4);

[0086] (5);

[0087] Silicon particle expansion is caused by the lithium intercalation process. The anisotropic lithium intercalation sub-model of silicon particles in this invention includes the lithium concentration variation characteristics of the coating layer and the lithium concentration variation characteristics of the silicon particles. It also considers the lithium intercalation mechanism of silicon particles, the different lithium intercalation capabilities of silicon particles along the lattice direction, and the characteristics of the interface between silicon particles and the coating layer. By fitting the above contents, the anisotropic lithium intercalation state of silicon particles is more comprehensively reflected, so that the anisotropic lithium intercalation sub-model of silicon particles can adapt to the situation of different initial morphologies of silicon particles and improve the accuracy of data processing.

[0088] In some embodiments, based on the lithium diffusion model, a sub-model of the mechanical properties of silicon particles is constructed using finite element software, including the following steps:

[0089] S21. The anisotropic expansion of silicon particles is related to their degree of lithium intercalation, as shown in the following formula:

[0090] (6);

[0091] (7);

[0092] In the above formula, equation (6) represents the expansion characteristics of the coating layer, where ε co_xx and ε co_yy β represents the strain in the x and y directions of the coating layer, respectively; co_xx and β co_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; co_xx With C co_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m. 3 .

[0093] Equation (7) represents the expansion characteristics of silicon particles, where ε pa_xx and ε pa_yy β represents the strain in the x and y directions of the coating layer, respectively; pa_xx and β pa_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; pa_xx With C pa_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m. 3 Among them, silicon particles have different expansion capabilities along the lattice direction, thus exhibiting anisotropic expansion. Therefore, the expansion coefficient β of silicon particles is... pa We need to add an expansion direction function g(x), namely β. pa ·g(x).

[0094] S22. Whether it is the coating layer or the silicon particles, the expansion of their volume will inevitably bring about changes in stress, as shown in Equation (8).

[0095] (8);

[0096] Where i represents the coating layer (CO) and silicon particles (Pa), respectively, and σ i_xx σ represents the stress in the x-direction of the coating layer and silicon particles. i_yy E represents the stress in the y-direction of the coating layer and silicon particles. i This represents the Young's modulus of the coating layer and silicon particles, in GPa. i ε represents the Poisson's ratio of the coating layer and the silicon particles; i_xx and ε i_yy represents the strain components in the x and y directions of the coating layer and the silicon particles, respectively. Equation (8) can be used to analyze the stress characteristics caused by the lithium intercalation expansion of the silicon particles and to evaluate the protective performance of the coating layer.

[0097] In summary, the sub-model of the mechanical properties of silicon particles includes...

[0098] (6);

[0099] (7);

[0100] (8);

[0101] This invention constructs a sub-model of the mechanical properties of silicon particles, incorporating both the expansion characteristics of the coating layer and the expansion characteristics of the silicon particles. It also considers the differences between the lithium-intercalated and non-lithium-intercalated regions of silicon particles, thus simulating anisotropic expansion. This model can be used to analyze the stress characteristics generated by the expansion of silicon particles due to lithium intercalation, evaluate the protective performance of the coating layer, select a reasonable coating layer, and reduce the probability of silicon particle breakage.

[0102] In some embodiments, it is well known that the more severe the anisotropic expansion of silicon particles, the more irregular their expanded shape, the more uneven the stress distribution, and the more prone the coating layer is to cracking and breakage. Therefore, Equation (9) is used to evaluate the degree of anisotropic expansion of silicon particles. The constructed anisotropic expansion model of silicon particles is as follows:

[0103] (9);

[0104] Among them, U r (θ) represents the radial displacement of a silicon particle along the radial direction at any angle; θ high θ represents the angular range of the region with large radial strain. low This indicates the angular range of the region with relatively small radial strain. This represents the average radial strain in the region with large radial strain. α represents the average radial strain in the region with smaller radial strain; α is the anisotropy, representing the degree of anisotropy in the expansion of silicon particles. The larger the value of α, the higher the degree of anisotropic expansion of silicon particles, and vice versa. This represents the original radius of the silicon particle.

[0105] This invention uses an anisotropic expansion model of silicon particles to accurately predict the degree of anisotropy in silicon particle expansion, avoiding the need for extensive experimental testing and data analysis in existing technologies, thus greatly improving R&D efficiency and reducing costs.

[0106] This invention can easily simulate anisotropic expansion at the particle scale or even the electrode scale of silicon-based anodes, analyze the impact of anisotropic expansion on the electrochemical performance of electrodes and batteries, and also invent an anisotropic degree evaluation method for anisotropic expansion characteristics, providing a basis for how to design coating layers and mitigate anisotropic expansion, avoiding a large number of experiments and tests, greatly improving R&D efficiency, and analyzing and optimizing the anisotropic expansion of silicon particles from multiple perspectives.

[0107] Because silicon particles possess symmetry, the anisotropic expansion model for silicon particles is based on a quarter-circle cross-section of the silicon particle, resulting in symmetry. The silicon particle coating acts as a protective layer, influencing the anisotropic expansion but not possessing the ability to actively undergo anisotropic expansion. Therefore, the core of the anisotropic expansion model lies in the silicon particle itself. To improve efficiency and avoid repetitive work, we first simulate and experimentally verify the anisotropic expansion of pure silicon particles. Then, based on this model's theory and parameters, we analyze and evaluate the model with the coating layer.

[0108] Example 1

[0109] The silicon particles used in this embodiment have an elliptical cross-section, with a major axis of 1113 nm and a minor axis of 603 nm.

[0110] The silicon particles have no coating layer; the specific steps are as follows:

[0111] A1. For the lithium intercalation process of pure silicon particles, in-situ TEM technology is used for experiments, such as... Figure 2 As shown, after lithium insertion and expansion, the major axis of the silicon particle becomes 1497 nm and the minor axis becomes 1339 nm. Clearly, the deformation of the minor axis after lithium insertion is greater than that of the major axis, indicating anisotropic expansion.

[0112] A2, such as Figure 3 As shown, the horizontal axis represents Figure 2 The semi-major axis of the initial morphology of the medium silicon particles, and the ordinate represents... Figure 2The semi-minor axis of the initial morphology of the silicon particles, i.e., the semi-major axis of the model is 556.5 nm and the semi-minor axis is 301.5 nm, is consistent with the initial cross-sectional dimensions of the silicon particles in the experiment. The initial data of the particles (major axis of 1113 nm, minor axis of 603 nm) were input into the anisotropic lithium intercalation model of the silicon particles;

[0113] A3. To maintain consistency with experiments, this model does not include a coating layer. Therefore, this anisotropic lithium intercalation model of silicon particles does not need to consider equation (1), and only equation (5) needs to consider... .

[0114] Figure 4 This is a schematic diagram of the concentration direction function f(x) of the lithium diffusivity coefficient of silicon particles, where the horizontal axis represents the angle of the silicon particles. In this embodiment, Figure 3 In the model shown The lithium intercalation capability is worst in the 45° (4 / 4) direction, with the lithium intercalation capability decreasing from... / 4 to both sides (0 and / 4) Gradually increase. Therefore Figure 4 The x-axis represents |θ- / 4|, where θ is Figure 3 The angle in the middle, ranging from 0 to / 2. θ=0 indicates Figure 3 The x-axis direction, θ= / 2 indicates Figure 3 The y-axis direction, θ= / 6 indicates a 6 Figure 3 The x-axis is at a 30° angle to the x-axis; the y-axis represents dimensionless parameters.

[0115] when Figure 4 When the x-coordinate is 0, f(x) is 0.629, i.e., |θ- / 4|=0, θ= / 4, at which point f(x) is at its minimum, and the lithium intercalation capability is at its worst; when x is When θ = 4, f(x) corresponds to 1, i.e., |θ - / 4|= / 4, θ=0 or / 2 represents Figure 3 The x-axis and y-axis of the model, i.e. Figure 3 The silicon particles shown exhibit the strongest lithium intercalation capability at the edges of the model. Therefore,

[0116] (10);

[0117] And the transition region in equation (10) is 0.1.

[0118] Based on the inherent properties of the material, the constant lithium diffusion coefficient D of silicon particles siIt is 1.64 × 10 -16 m 2 / s, lithium concentration C after complete lithium intercalation of silicon particles max_si 268000 mol / m 3 .

[0119] When the model is in its initial stage, i.e., t=0, there is no lithium intercalation in this silicon particle, so the lithium concentration is 0, i.e., C. Pa =0, at this time for equation (4), D Pa The lithium diffusion coefficient of silicon particles is represented by D. si ·f(x), at this time for = Then D Pa =1.64×10 -16 ×0.629=1.03156×10 -16 m 2 / s; for = 2, then D Pa =1.64×10 -16 ×1=1.64×10 -16 m 2 / s, the lithium diffusion coefficient D at other angles of the silicon particle Pa Then, depending on the specific angle And calculate with f(x). Additionally, since it is the initial time, C Pa =0, therefore the lithium flux J in equation (5) is 0. Pa =0, the rate of change of silicon particle concentration with time in equation (2) =0.

[0120] When silicon particles begin to intercalate lithium, a lithium flux J is applied to the outermost layer of the silicon particles. Pa =1.84×10 -4 mol / (m 2 (·s), representing the amount of water flowing into the silicon particle per second per square meter, is 1.84 × 10⁻⁶. -4 mol of lithium. Thus, equation (5) represents the continuous influx of lithium into the silicon particle. Based on the iterations of equations (4), (5), and (1), the lithium concentration throughout the silicon particle region is obtained. For example, for = Furthermore, at the point where the outermost regions of the silicon particles intersect, when the time is 200s, the lithium concentration C at that point is... Pa 257000 mol / m 3 According to equation (4), the lithium diffusion coefficient D at the current moment can be calculated. Pa =2.18×10 - 15 m 2 / s; According to equation (1), the rate of change of lithium concentration with time can be calculated. =166 mol / (m 3 ·s); in = Furthermore, at the point where it intersects with the outermost region of the silicon particle, the lithium concentration C at that point is [value missing] after 200 seconds. Pa 262000 mol / m 3 According to equation (4), the lithium diffusion coefficient D at the current moment can be calculated. Pa =6.68×10 -15 m 2 / s; According to equation (1), the rate of change of lithium concentration with time can be calculated. =131 mol / (m 3 ·s). The above is the concentration data calculation for two points. Figure 3 The entire silicon particle region shown was calculated using the above method, ultimately forming... Figure 5 The silicon particle concentration cloud map shown indicates that the silicon particles have completed the lithium intercalation process.

[0121] Figure 5 The silicon particles exhibit anisotropic lithium intercalation, with the quarter-elliptical cross-section of each particle symmetrically processed to present a complete ellipse. The outer dark area represents the lithium-intercalated region, while the inner light area represents the non-lithium-intercalated region, showing a clear interface and a non-uniform lithium concentration. Figure 5 The horizontal and vertical axes in the graph represent the dimensions of silicon particles in the x and y directions, respectively. The contour plot represents the silicon particle concentration C. Pa With maximum lithium intercalation concentration C max_si The ratio, such as 0.999, indicates the silicon particle concentration C in that region. Pa Approximately 268,000 mol / m 3 0.214 indicates the silicon particle concentration C in this region. Pa 57352 mol / m 3 .

[0122] A4. To maintain consistency with experiments, the silicon particle mechanical property sub-model does not include a coating layer; therefore, equation (6) need not be considered in the silicon particle mechanical property sub-model. The constant expansion coefficient β of silicon particles... pa 5.3×10 -6 m 3 / mol, but due to the different crystal orientations of silicon particles, their coefficient of thermal expansion varies at different angles. Figure 2 The silicon particles shown have unique crystal orientations, so the experimental results show that the long axis and short axis exhibit different expansion states.

[0123] Figure 6 The expansion direction function g(x) for the anisotropic expansion of silicon particles exhibits a linear function, therefore... Figure 6 The x-axis represents θ, where θ is Figure 3 The angle in the middle, ranging from 0 to / 2. θ=0 indicates Figure 3 The x-axis direction, θ= / 2 indicates Figure 3 The y-axis direction, θ= / 6 indicates a 6 Figure 3 The x-axis is at a 30° angle to the x-axis; the y-axis represents dimensionless parameters.

[0124] when Figure 6 When the x-coordinate is 0, g(x) corresponds to 0.00792, that is, when θ=0, it means... Figure 3 In the model, g(x) is minimized along the x-axis, resulting in the worst expansion capacity; when x is... When θ = 2, g(x) corresponds to 1.288, that is, θ = / 2 means Figure 3 In the model, the y-axis is the direction where g(x) is largest and the expansion capacity is strongest. That is, when x is 0, g(x) = 0.00792; when x is 0, g(x) = 0.00792. When x = 2, g(x) = 1.228, and interpolation is performed in the middle interval.

[0125] Will Figure 5 The concentration region shown and Substituting the concentration field distribution into equation (6), the strain at each point within the silicon particle region is obtained. and For example, take Figure 5 At 200s, the point where θ=0 and intersects with the outermost region of the silicon particle, this point = 262000 mol / m 3 , = =β pa =5.3×10 -6 m 3 / kg, g(x)=0.00792, then according to equation (7), the lithium insertion expansion strain at this point is 0.012. Based on this calculation criterion, the lithium insertion expansion deformation state of the entire silicon particle region can be calculated.

[0126] The lithium-intercalated region of a silicon particle differs from the non-lithium-intercalated region; therefore, the Young's modulus E of the lithium-intercalated region is different. Pa Compared to Poisson Pa Young's modulus E of the non-lithium-intercalated region Pa Compared with Poisson Pa They are different; please refer to the following for details. Figure 7 and Figure 8 As shown, this data represents the inherent properties of the material. Figure 7 E represents the Young's modulus of silicon particles. Pa The horizontal axis represents the ratio of the current lithium intercalation concentration to the maximum allowable lithium intercalation concentration, and the vertical axis represents the corresponding Young's modulus E. Pa When the x-axis is 0, the y-axis is 186 GPa; when the x-axis is 0.97, the y-axis is 35 GPa, with intermediate values ​​calculated via interpolation. For example, when the model first starts calculating, the silicon particles are not lithium-intercalated, and the lithium concentration C is... Pa =0, that is, C Pa / C max_si =0, at this time Young's modulus E Pa The value is 186 GPa; for the 200s time point. ， The point where θ=0 and intersects with the outermost region of the silicon particle, this point 262000 mol / m 3 , / C max_si =262000 / 268000=0.977, which is greater than 0.97, therefore Young's modulus E Pa The value is 35 GPa. Figure 8 Poisson's ratio of silicon particles Pa The horizontal axis represents the ratio of the current lithium intercalation concentration to the maximum allowable lithium intercalation concentration, and the vertical axis represents the corresponding Poisson's ratio. Pa When the x-axis is 0, the y-axis is 0.24; when the x-axis is 0.97, the y-axis is 0.22, with intermediate values ​​calculated via interpolation. For example, when the model first starts calculating, the silicon particles are not lithium-intercalated, and the lithium concentration C is... Pa =0, that is, C Pa / C max_si =0, at this point Poisson's ratio Pa It is 0.24; for the 200s time. ， The point where θ=0 and intersects with the outermost region of the silicon particle, this point 262000 mol / m 3 , / C max_si =262000 / 268000=0.977, which is greater than 0.97, therefore Poisson's ratio is... Pa The value is 0.22. Based on this calculation standard, the Young's modulus E of silicon particles in any region at any time can be calculated. Pa Compared to Poisson Pa .

[0127] In equation (8), i represents the silicon particle and the coating layer. In this specific embodiment, the coating layer is not considered. Therefore, it is only necessary to substitute the strain of the silicon particle into equation (8) to complete the simulation of anisotropic expansion. For example, as mentioned above, take Figure 5 At 200s, the point where θ=0 and intersects the outermost region of the silicon particle, according to equation (7), has a lithium intercalation expansion strain of 0.012, i.e. = =0.012, corresponding Young's modulus E Pa 35 GPa, Poisson's ratio Pa The value is 0.22. Substituting this into equation (8) yields... = =0.615 GPa, meaning the stress is 0.615 GPa. The expansion calculation for the entire silicon particle region is performed according to this calculation standard.

[0128] A5 Figure 9 This is a schematic diagram of the expansion state of an anisotropic expansion model of silicon particles. The 1 / 4 ellipse of the cross-section of the silicon particle is symmetrically processed to present a complete ellipse. Figure 9 In the diagram, the horizontal and vertical axes represent the dimensions of silicon particles in the x and y directions, respectively, and the contour plot represents the silicon particle concentration C. Pa With maximum lithium intercalation concentration C max_si The ratio, such as 0.999, indicates the silicon particle concentration C in that region. Pa Approximately 268,000 mol / m 3 0.214 indicates the silicon particle concentration C in this region. Pa 57352 mol / m 3 .contrast Figure 9 and Figure 5 The significant changes in size along the x and y coordinates indicate that the silicon particles underwent anisotropic expansion. Furthermore, Figure 9 The black circular outline in the figure represents the size profile of the silicon particle before expansion, which also shows the expansion state of the silicon particle. Simulation results of the anisotropic expansion model of silicon particles: major axis 1531 nm, minor axis 1291 nm. Compared with experimental results, the error of the major axis is |1531-1497| / 1497=2.3%, and the error of the minor axis is |1291-1339| / 1339=3.6%. The model accuracy is above 95%, proving that the simulation results of this model are accurate and demonstrating the feasibility of the theoretical method.

[0129] Depend on Figure 9 It can be visually observed that the major axis is 1531 nm, the minor axis is 1291 nm, and 0- The deformation between / 2 is relatively smooth, therefore, it can be directly assumed that =1531 nm, =1291 nm. For an ellipse, R0 is represented by the geometric mean radius, i.e. =1405.88 nm. Therefore, the anisotropy degree α is calculated as (1531-1291) / 1405.88 = 0.166. This value represents the degree of anisotropic expansion of the silicon particles in this specific embodiment. The larger the value, the more severe the anisotropic expansion. It should be noted that the specific anisotropic expansion morphology of the silicon particles is related to the initial state of the silicon particles. If the model simulation results deviate significantly from the experimental results, the model parameters need to be adjusted, mainly focusing on the concentration direction function f(x) and the expansion direction function g(x), to ensure that the expansion morphology of the silicon particles after model simulation is consistent with the experimental state, and then the model can be extended.

[0130] The above embodiments have been experimentally verified, proving that the theoretical method of the model is correct. Therefore, based on the theoretical method of this model, the embodiments are extended to further illustrate the evaluation method of anisotropy.

[0131] Example 2

[0132] This embodiment uses spherical silicon particles as the research object. Based on the model framework of Embodiment 1, an anisotropic expansion model of silicon particles is built using any finite element software. The model is a quarter-circle of the silicon particle interface and has a coating layer. The final result exhibits symmetry. The specific steps are as follows:

[0133] B1. Simulate spherical silicon particles by establishing a spherical cross-section model. Considering symmetry, the initial stage of the model is a quarter circle, as shown below. Figure 10 As shown. Figure 10 In this process, the initial radius R0 of the silicon particle is 1.5 μm, and a coating layer is formed on the outside of the silicon particle with a thickness l of 0.01 μm.

[0134] The calculation is performed using expressions (1) to (5) from the previous embodiment.

[0135] B2, Figure 11 This is a schematic diagram of the concentration direction function f(x) of the lithium diffusivity coefficient of silicon particles in this embodiment, where the horizontal axis represents the angle of the silicon particles. In this embodiment, Figure 10 In the model shown The lithium intercalation capability is worst in the 4 / 4 (45°) direction, and then the lithium intercalation capability decreases from... / 4 to both sides (0 and / 4) Gradually increase. Therefore Figure 11 The x-axis represents |θ- / 4|, where θ is the angle in the diagram, ranging from 0 to 4. / 2. θ=0 indicates Figure 10 The x-axis direction, θ= / 2 indicates Figure 10 The y-axis direction, θ= / 6 indicates a 6 Figure 10 The x-axis is at a 30° angle to the x-axis; the y-axis represents dimensionless parameters.

[0136] when Figure 11 When the x-coordinate is 0, f(x) is 0.629, i.e., |θ- / 4|=0, θ= / 4, at which point f(x) is at its minimum, and the lithium intercalation capability is at its worst; when x is When θ = 4, f(x) corresponds to 1, i.e., |θ - / 4|= / 4, θ=0 or / 2 represents Figure 10 The x-axis and y-axis of the model, i.e. Figure 10 The silicon particles shown exhibit the strongest lithium intercalation capability along the x-axis and y-axis of the model. Based on the above calculations, the concentration direction function f(x) in this embodiment is consistent with that in Example 1, therefore formula (1) can be directly used.

[0137] Based on the inherent properties of the material, the lithium diffusion coefficient D of the coating layer in the anisotropic lithium intercalation model of silicon particles is... co 1.0×10 -9 m 2 / s. Constant lithium diffusion coefficient D of silicon particles si It is 1.64 × 10 -16 m 2 / s, maximum lithium intercalation concentration of silicon particles C max_si 268000 mol / m 3 .

[0138] When the model is in its initial stage, i.e., t=0, there is no lithium intercalation in the silicon particle and the coating layer, therefore the lithium concentration is 0, i.e., C. CO =C Pa =0, at this time for equation (4), D Pa The lithium diffusion coefficient of silicon particles is represented by D. si ·f(x), at this time for = Then D Pa =1.64×10 -16 ×0.629=1.03156×10 -16 m 2 / s; for = Then D Pa =1.64×10 -16 ×1=1.64×10 -16 m 2 / s, the lithium diffusion coefficient D at other angles of the silicon particle Pa Then, depending on the specific angle And calculate with f(x). Additionally, since it is the initial time, C CO =C Pa =0, therefore the lithium flux J outside the coating layer in equation (5) is 0. CO =0, flux J of silicon particles Pa =0, the change of silicon particle concentration with time in equation (2) =0, change in coating concentration over time =0.

[0139] When the model begins simulating lithium intercalation, lithium enters the entire model from the outermost layer of the coating, thus assigning a lithium flux J to the edge of the outermost layer of the coating. CO =1.84×10 -4 mol / (m 2 (·s), representing the amount of water flowing into the silicon particle per second per square meter, is 1.84 × 10⁻⁶. -4 mol of lithium. Thus, equation (5) represents the continuous influx of lithium flux into the silicon particle through the coating layer. The lithium concentration throughout the silicon particle region is obtained by iterating through equations (4), (5), and (1). For example, the lithium flux J in the outermost region of the coating layer... CO =1.84×10 -4 mol / (m 2 ·s), the flux inside the coating layer is 'Then the flux inside the coating layer is equal to the flux outside the silicon particle, i.e., at the interface. '= Due to the lithium diffusion coefficient D of the coating layer co Lithium diffusion coefficient D of silicon particles Pa The difference is several orders of magnitude, and the coating layer is very thin, so lithium flows much more inside the coating layer than inside the silicon particles, therefore J CO = '= =1.84×10 -4 mol / (m 2 ·s). = Taking two points where the coating layer intersects with the outer side of the silicon particle as an example, when the time is 1000s, the lithium concentration C at that point in the coating layer is... CO 260,000 mol / m 3 The lithium concentration C at this point on the silicon particle Pa 260,000 mol / m 3 According to equation (4), the lithium diffusion coefficient D at that point on the silicon particle at the current moment can be calculated.Pa =3.06×10 -15 m 2 / s; According to equation (2), the rate of change of lithium concentration in silicon particles with time can be calculated. =4.92×10 -5 mol / (m 3 The value of ·s is relatively small, indicating that the lithium concentration of silicon particles at this point has essentially reached its maximum, and the lithium concentration of silicon particles at this point remains essentially unchanged over time. The rate of change of lithium concentration of the coating layer at the corresponding point over time. Equal to silicon particles, with the same meaning. The above is a calculation of concentration data from two points. Figure 10 The entire silicon particle region shown was calculated using the above method, ultimately forming... Figure 12 The silicon particle concentration cloud map shown indicates that the silicon particles have completed the lithium intercalation process.

[0140] Figure 12 The anisotropic lithium intercalation state of silicon particles when lithium is intercalated to a certain extent is shown by symmetrical processing. The dark outer layer is the lithium intercalation area, and the light inner layer is the non-lithium intercalation area. There is a clear interface, and the lithium concentration is non-uniform. Figure 12 The horizontal and vertical axes in the graph represent the dimensions of silicon particles in the x and y directions, respectively. The contour plot represents the silicon particle concentration C. Pa With maximum lithium intercalation concentration C max_si The ratio, such as 0.97, indicates the silicon particle concentration C in that region. Pa Approximately 268,000 mol / m 3 0.0142 indicates the silicon particle concentration C in this region. Pa 3805.6 mol / m 3 .

[0141] B3. Construct a sub-model of the mechanical properties of silicon particles based on finite element method software, and determine the expansion coefficient β of the coating layer. co A constant coefficient of thermal expansion (β) of 0 indicates that the coating layer does not expand. pa 5.3×10 -6 m 3 / kg, but due to the different crystal orientations of silicon particles, their coefficient of thermal expansion varies at different angles. Figure 10 The silicon particle model shown has a unique crystal orientation. Therefore, an expansion direction function is set. Figure 13 This is a schematic diagram of the expansion function g(x) in this embodiment, where the horizontal axis represents the angle of the silicon particle. In this embodiment, Figure 10 In the model shown The expansion capacity is worst in the 4 / 4 (45°) direction, then the expansion capacity decreases from... / 4 to both sides (0 and / 4) Gradually increase. Therefore Figure 13 The x-axis represents |θ- / 4|, where θ is Figure 10 The angle in the middle, ranging from 0 to / 2. θ=0 indicates Figure 10 The x-axis direction, θ= / 2 indicates Figure 10 The y-axis direction, θ= / 6 indicates a 6 Figure 10 The x-axis is at a 30° angle; the ordinate represents dimensionless parameters. When Figure 13 When the x-coordinate is 0, g(x) is 0.2, i.e., |θ- / 4|=0, θ= / 4, at which point g(x) is at its minimum, and the expansion capacity is the worst; when x is When θ = 4, g(x) corresponds to 1, i.e., |θ - / 4|= / 4, θ=0 or / 2 represents Figure 10 The x-axis and y-axis of the model, i.e. Figure 3 The silicon particles shown exhibit the strongest expansion capacity at the edges of the model. Therefore,

[0142] (11)

[0143] Furthermore, the transition region in equation (1) is 0.1. This expansion direction function g(x) is used for the anisotropic expansion of silicon particles in this embodiment, describing the anisotropic expansion morphology of silicon particles in this embodiment, which is different from the expansion direction function g(x) in embodiment 1.

[0144] Will Figure 12 The concentration region shown , , , Substituting the concentration field distribution into equation (6), however, the coating layer does not have the ability to expand, therefore and Since the value is 0, only the strain at each point within the silicon particle region can be obtained. and For example, take Figure 10 At 1000s, θ= The point that intersects with the outermost region of the silicon particle at / 4, this point = 260000 mol / m 3 , = =β pa =5.3×10 -6 m 3 / kg, g(x)=0.2, then according to equation (7), the lithium intercalation expansion strain at this point is 0.276, that is = 0.276. Based on this calculation criterion, the lithium insertion expansion and deformation state of the entire silicon particle region can be calculated.

[0145] The lithium-intercalated region of a silicon particle differs from the non-lithium-intercalated region; therefore, the Young's modulus E of the lithium-intercalated region is different. Pa Compared to Poisson Pa Young's modulus E of the non-lithium-intercalated region Pa Compared with Poisson Pa They are not the same. This is because the Young's modulus E of silicon particles... Pa Compared with Poisson Pa This is an inherent characteristic of silicon particles; therefore, in this embodiment, the Young's modulus E of the silicon particles is... Pa Compared with Poisson Pa Same as in Example 1, refer to Figure 7 and Figure 8 This will not be elaborated upon here. Similarly, the Young's modulus E of the coating layer... CO Compared with Poisson CO The values ​​are 19.25 GPa and 0.22 GPa, respectively, which are inherent characteristics of the coating layer.

[0146] In equation (8), i represents the coating layer and silicon particles, respectively, but the expansion strain of the coating layer is... = 0, therefore, we only need to substitute the expansion strain of the silicon particles into equation (8) to complete the simulation of anisotropic expansion. For example, Figure 10 At 1000s, θ= The point where / 4 intersects with the outermost region of the silicon particle has an expansion strain of 0.276, i.e. = 0.276, = 260000 mol / m 3 Its maximum lithium intercalation concentration C of silicon particles max_si =268000 mol / m 3 The ratio is 0.97, therefore according to Figure 7 and Figure 8 The corresponding Young's modulus E of the silicon particle at that point Pa 35 GPa, Poisson's ratio Pa The value is 0.22. Substituting this into equation (8) yields... = =14.14 GPa, meaning the stress is 14.14 GPa. The expansion calculation for the entire silicon particle region is performed according to this calculation standard.

[0147] In this specific embodiment, reference is made to Figure 14 The anisotropic expansion state shown is treated symmetrically, therefore it is similar to... Figure 10 In contrast, the cross-section is no longer a quarter circle. The horizontal and vertical axes in the figure represent the x-axis and y-axis dimensions of the silicon particles after anisotropic expansion, respectively, and the contour plot represents the concentration ratio. Figure 14 and Figure 12 In comparison, it exhibits a significant change in shape. Additionally, Figure 14 The black circular outline represents the size profile of the silicon particle before expansion, and can also be used to determine the expansion state of the silicon particle. Centered on zero, the angular range of the region with the largest radial variation is from 0 to... / 8 and 3 / 8 to / 2, therefore θ high = / 4; The angular range of the region with smaller radial variation is / 8 to 3 / 8, therefore θ low = / 4. Radial displacement U r (θ) = ucosθ + vsinθ, where u is the x-direction displacement of the reference point, v is the y-direction displacement of the reference point, and θ is the angle between the reference point and the x-axis. R0 is 1.5 μm. The displacements U of different regions of the silicon particle are then considered. r Substituting (θ) into equation (9), we finally obtain the average radial strain in the region with larger radial strain. The average radial strain in the region with smaller radial strain is 1.2165 μm. The value is 0.72706 μm. (1.2165-0.72706) / 1.5=0.326, so the anisotropy degree α is 0.326. This value represents the degree of anisotropic expansion of silicon particles in this specific embodiment. The larger the value, the more severe the anisotropic expansion.

[0148] An anisotropic expansion assessment system for silicon particles applied to silicon-based anodes, comprising:

[0149] The sub-model construction module constructs an anisotropic lithium intercalation sub-model for silicon particles to characterize the anisotropy of lithium concentration during the lithium intercalation process of crystalline silicon, and a mechanical property sub-model for silicon particles to simulate and analyze the stress and strain characteristics of silicon particles.

[0150] The model building module couples the anisotropic lithium intercalation model of silicon particles and the mechanical property model of silicon particles into an anisotropic expansion model of silicon particles.

[0151] The model verification module compares the experimental results with the simulation prediction results of the anisotropic expansion model to determine whether the anisotropic expansion model meets the accuracy requirements.

[0152] The model prediction module extends the anisotropic expansion model that meets the accuracy requirements with different types of anisotropic expansion and evaluates the degree of anisotropic expansion.

[0153] The judgment requirement in the model verification module is as follows: when the accuracy of the heterogeneous expansion model is greater than 95%, the requirement is met and the model prediction is selected; otherwise, the model is debugged until the accuracy requirement is met.

[0154] The present invention also provides a computer device applicable to a method for evaluating the anisotropic expansion of silicon particles in a silicon-based anode, comprising a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the method for evaluating the anisotropic expansion of silicon particles in a silicon-based anode as proposed in the above embodiments.

[0155] The present invention also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements a method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes as described in the above embodiments.

[0156] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0157] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0158] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0159] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0160] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0161] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes, characterized in that: Includes the following steps: S1. Construct an anisotropic lithium intercalation model of silicon particles to characterize the anisotropy of lithium concentration in crystalline silicon during lithium intercalation. S2. Construct a sub-model of the mechanical properties of silicon particles to simulate and analyze the stress and strain characteristics of silicon particles; S3. Couple the anisotropic lithium intercalation sub-model of silicon particles and the mechanical property sub-model of silicon particles into an anisotropic expansion model of silicon particles; S4. Based on the results of the silicon particle expansion test, determine whether the accuracy of the anisotropic expansion model of silicon particles meets the requirements. If it meets the requirements, proceed to step S5. If it does not meet the requirements, adjust the model until it meets the accuracy requirements. S5. Based on the approved anisotropic expansion model of silicon particles, perform different types of anisotropic expansion extensions and evaluate the degree of anisotropic expansion. The anisotropic expansion model of silicon particles in S3 is as follows: ； Among them, U r (θ) represents the radial displacement of a silicon particle along the radial direction at any angle; θ high θ represents the angular range of the region with large radial strain. low This indicates the angular range of the region with relatively small radial strain. This represents the average radial strain in the region with large radial strain. α represents the average radial strain in the region with smaller radial strain; α is the anisotropy, which represents the degree of anisotropy in the expansion of silicon particles. The larger the value of α, the higher the degree of anisotropic expansion of silicon particles, and vice versa. This represents the original radius of the silicon particle.

2. The method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes according to claim 1, characterized in that: The method of S1 includes: S11. The simulated concentration characteristics of silicon and lithium alloys are as follows: (1)； (2)； Wherein, equation (1) represents the lithium concentration variation characteristics of the coating layer, C co This indicates the concentration in a specific region of the coating layer, in mol / m³. 3 ;D co The value m represents the lithium diffusion coefficient of the coating layer, describing the diffusion rate of lithium. 2 / s is a specific numerical value; Equation (2) represents the lithium concentration variation characteristics of silicon particles, C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 ;D pa The lithium diffusion coefficient of silicon particles is represented by m. 2 / s, represented as: (3)； Among them, D si The constant lithium diffusion coefficient of silicon particles is expressed in mol / s; C pa This indicates the concentration of silicon particles in a specific region, in mol / m³. 3 C max_si This indicates the lithium concentration after complete lithium intercalation of silicon particles, in mol / m³. 3 ; S12. Since the lithium intercalation ability of silicon particles varies along the lattice direction, the lithium intercalation process also exhibits anisotropy. Therefore, a concentration direction function f(x) needs to be added. Equation (3) is used to characterize the anisotropy of lithium intercalation as follows: (4)； S13. According to the law of conservation of mass, the lithium flux is the same at the interface between silicon particles and the coating layer, which can be expressed as: (5)； Among them, J co This represents the lithium flux flowing out from the inside of the coating layer, in mol / (m 2 ·s); J pa This represents the lithium flux flowing into the outer side of the silicon particles, in mol / (m²). 2 ·s); the concentration on the outermost side of the coating layer is the boundary condition for this lithium diffusion model.

3. The method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes according to claim 1, characterized in that: The method of S2 includes: S21. The relationship between the anisotropic expansion of silicon particles and their degree of lithium intercalation is as follows: (6)； (7)； Equation (6) represents the expansion characteristics of the coating layer, ε co_xx and ε co_yy β represents the strain in the x and y directions of the coating layer, respectively; co_xx and β co_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; co_xx With C co_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m. 3 ; Equation (7) represents the expansion characteristics of silicon particles, ε pa_xx and ε pa_yy β represents the strain in the x and y directions of the coating layer, respectively; pa_xx and β pa_yy C represents the expansion coefficients of the coating layer in the x and y directions, respectively; pa_xx With C pa_yy These represent the lithium concentration distributions in the x and y directions of the coating layer, respectively, in mol / m. 3 Among them, silicon particles have different expansion capabilities along the lattice direction, thus exhibiting anisotropic expansion. Therefore, the expansion coefficient β of silicon particles is... pa We need to add an expansion direction function g(x); The volume expansion and stress relationship between the S22 coating layer and silicon particles are as follows: (8)； Where i represents the coating layer (CO) and silicon particles (Pa), respectively, and σ i_xx σ represents the stress in the x-direction of the coating layer and silicon particles. i_yy E represents the stress in the y-direction of the coating layer and silicon particles. i This represents the Young's modulus of the coating layer and silicon particles, in GPa. i ε represents the Poisson's ratio of the coating layer and the silicon particles; i_xx and ε i_yy These represent the strain components in the x and y directions of the coating layer and silicon particles, respectively.

4. The method for evaluating the anisotropic expansion of silicon particles applied to silicon-based anodes according to claim 1, characterized in that: In S5, the accuracy of the anisotropic expansion model of silicon particles is not less than 95%.

Images