Simulation method for the change in roundness during the grain growth of ternary cathode materials

Abstract

This invention discloses a simulation method for the change in grain roundness during the growth of ternary cathode materials, belonging to the technical field of ternary cathode materials. The simulation method includes: S1, acquiring SEM images at different initial moments of isothermal temperatures and using them as the initial state of a cellular automaton; S2, calculating the grain growth rate and determining the grain growth distance at each moment, and determining the cell orientation transition moment by comparing it with the cell edge length; S3, calculating the grain boundary energy difference before and after the cell orientation transition to determine the cell orientation transition; S4, further transformation for convex and concave cells; S5, designing cell state transition rules based on grain growth rate, local grain boundary curvature, and the minimum energy principle to establish a two-dimensional cellular automaton model to simulate the change in grain roundness during grain growth. The simulation method proposed in this invention successfully and comprehensively simulates the roundness change during grain growth.

Description

Technical Field

[0001] This invention relates to the field of ternary cathode material technology, specifically to a method for simulating the change in grain roundness during the grain growth process of ternary cathode materials. Background Technology

[0002] Ternary cathode materials are next-generation high-performance lithium-ion battery raw materials, and grain growth is one of the most crucial processes occurring during the sintering and preparation of ternary cathode materials. The electrochemical performance and densification degree of ternary cathode materials are determined by their microstructure, and grain growth is a significant factor influencing this microstructure. However, due to the limitations of the high-temperature production environment, the growth state of primary grains inside the furnace has been difficult to detect and control, posing a significant challenge to the production of high-quality ternary cathode materials. Therefore, obtaining information on the morphological evolution of primary grains during sintering and understanding the changes in grain roundness are of great importance for improving the performance of ternary cathode materials.

[0003] Traditional research on ternary cathode materials is typically based on extensive sintering experiments. Researchers have found that increasing sintering time promotes crystal growth, with primary grain size increasing with sintering time. However, conducting sintering experiments is usually time-consuming and labor-intensive, and it's impossible to cover all sintering regimes and times. Therefore, researchers have also conducted simulation studies of the grain growth process, establishing grain growth models using phase-field methods and cellular automata to dynamically simulate the evolution of the grain growth process. However, most analyses of the grain growth process focus on grain size, with little attention paid to changes in grain morphology during growth. Yet, the microstructure of the grains significantly impacts their electrochemical performance, making the study and simulation of roundness changes during grain growth crucial. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned technical deficiencies and provide a method for simulating the change in grain roundness during the grain growth process of ternary cathode materials, thereby solving the technical problem of how to simulate the change in roundness during grain growth in the prior art.

[0005] To achieve the above-mentioned technical objectives, the present invention provides a method for simulating the change in grain roundness during the grain growth process of ternary cathode materials, comprising the following steps:

[0006] S1. Obtain SEM images at different initial moments of constant temperature and use them as the initial state of the cellular automata.

[0007] S2. Calculate the grain growth rate and obtain the grain growth distance at each moment. Determine the cell orientation transition time by comparing it with the cell side length.

[0008] S3. Transform the boundary cells into neighbor orientations in sequence, and calculate the grain boundary energy difference before and after the cell orientation transformation to determine the transformation of the cell orientation.

[0009] S4. Calculate the local grain boundary curvature of each boundary cell, determine the concavity and convexity, and make further transformations for convex and concave cells.

[0010] S5. Based on the grain growth rate, local grain boundary curvature and the minimum energy principle, design cell state transition rules to establish a two-dimensional cellular automaton model to simulate the grain roundness change during grain growth.

[0011] In step S2, the growth rate of the grains is calculated using the following formula:

[0012]

[0013] Where t is the sintering time, dR / dt is the rate of change of grain size, i.e., the growth rate; M is the grain boundary mobility, which conforms to Arrhenius's law and is related to the isothermal temperature; σ is the surface energy; α is a dimensionless constant; the equivalent radius R of the grain is the radius of the equivalent circle with the same area as the grain; and the critical radius R of the grain is... cr The average radius of all grains in the cell space; parameter

[0014] The growth rate at each moment is accumulated to obtain the grain growth distance. An orientation change can only occur when the growth distance is greater than or equal to the cell edge length. The grain growth distance is calculated using the following formula:

[0015] D t =D t-Δt +vΔt≥a

[0016] Among them, D t and D t-Δt Let t and t-Δt represent the growth distances at times t and t-Δt, respectively; a represents the cell side length; the time step of the cellular automaton is Δt = a / v. max ; where v max This represents the maximum grain growth rate.

[0017] In any embodiment, in step S3, the grain boundary energy difference before and after the cell orientation transformation is calculated by the following formula:

[0018] ΔE i→j < indicates the grain boundary energy difference after cell i is transformed into neighboring cell j;

[0019] The grain boundary energy of the central cell i can be expressed as follows:

[0020]

[0021] In the formula, E(θ) is a function related to the orientation angle, given by the Read-Shockley relation; δ is the Kronecher notation; k is the k-th neighbor of the cell; n is the total number of neighboring cells of the cell; q i q is the orientation number of cell i; k Let be the orientation number of the k-th neighbor of the cell;

[0022] E(θ)=E m sinθ[1-ln(sinθ)], where, E m =μbθ m / 4π(1-ν) is the grain boundary energy of a large-angle grain boundary, which is related to the material's shear modulus μ, Poisson's ratio ν, and Burger vector b; θ m It is the orientation difference of large-angle grain boundaries; grain orientation difference angle Δq is the difference in orientation number between adjacent grains, q max This represents the maximum value of grain orientation. The Kronecher notation is defined as follows:

[0023]

[0024] In any implementation, step S4, determining the concavity / convexity of the cell and making a corresponding transformation, includes:

[0025] Calculate the local curvature of the boundary cell. If the local curvature κ > 0, it means the boundary curves outward at that point, and the boundary cell is convex. If the local curvature κ < 0, it means the boundary curves inward at that point, and the boundary cell is concave. The formula for calculating the local curvature is:

[0026] Where A is the shape factor; a is the cell size; kink is the total number of cells belonging to grain i in the neighborhood when the grain boundary is straight; Ni is the total number of neighbors belonging to grain i in the neighborhood; and N is the total number of grains in the neighborhood.

[0027] When a boundary cell convexes outward, it is transformed into the orientation of its surrounding neighbors, thus achieving inward contraction of the current grain boundary; when a boundary cell is concave inward, the surrounding neighboring cells are oriented to the same orientation, thus achieving outward expansion of the grain boundary.

[0028] In any implementation, step S6 is included after step S5:

[0029] The boundary coordinates of each grain are obtained in the cellular automaton, the least square circle of the grain boundary is fitted, the roundness of each grain is calculated by Hausdorff distance, and the probability density corresponding to the roundness value is calculated by kernel density estimation.

[0030] The calculation of the roundness of each grain using the Hausdorff distance includes:

[0031] Fit a least-squares circle to the grain boundary; for each point in the grain boundary point set B, calculate the minimum distance d(B, C) from it to all points in the least-squares circle boundary point set C, and find the maximum value of all d(B, C), denoted as max d(B, C); similarly, for each point in the least-squares circle boundary point set C, calculate the minimum distance d(C, B) from it to all points in the grain boundary point set B, and find the maximum value of d(C, B), denoted as max d(C, B); finally, the Hausdorff distance is defined as the maximum distance between two point sets, expressed as follows:

[0032] d H (A,B)=max(maxd(B,C),maxd(C,B)).

[0033] In any implementation, prior to step S1, the method further includes:

[0034] Analyze the variation pattern of roundness during grain growth.

[0035] In any implementation, the analysis of the roundness variation during grain growth includes: using the Canny edge detection algorithm to extract the primary grain boundaries in the SEM image, and using Hausdorff distance as a roundness index to obtain the probability density distribution of grain roundness at different isothermal times.

[0036] In any embodiment, the ternary cathode material is LiNi. 0.83 Co 0.11 Mn 0.06 O2.

[0037] Compared with the prior art, the beneficial effects of the present invention include: the simulation method for the change of grain roundness during the grain growth process of ternary cathode material proposed in the present invention, based on the physical mechanism of grain growth and the evolution characteristics of cellular automata, realizes the dynamic simulation of grain growth, and the change of its roundness also conforms to the actual sintering situation, thus more comprehensively simulating the change of grain roundness during grain growth. Attached Figure Description

[0038] Figure 1 This is the probability density distribution curve of grain boundary extraction and grain roundness from a single grain SEM image in Embodiment 1 of the present invention; wherein, Figure 1 (a) shows a single grain boundary extraction image; Figure 1 (b) represents the roundness probability density curve of a single image.

[0039] Figure 2 This is the synthesis of LiNi in Example 1 of the present invention.0.83 Co 0.11 Mn 0.06 SEM images of grains under different isothermal times of O2; in the figure, (a) represents the SEM image at 0h of isothermal time; (b) represents the SEM image at 6h of isothermal time; and (c) represents the SEM image at 12h of isothermal time.

[0040] Figure 3 This is the synthesis of LiNi in Example 1 of the present invention. 0.83 Co 0.11 Mn 0.06 The grain roundness probability density distribution curves of O2 at different isothermal times; in the figure, (a) represents the grain roundness probability density curve at 0h of isothermal time; (b) represents the grain roundness probability density curve at 6h of isothermal time; and (c) represents the grain roundness probability density curve at 12h of isothermal time.

[0041] Figure 4 These are the grain morphology evolution diagrams and grain roundness probability density distribution curves during the cellular automata simulation process in Example 1; where (a), (c) and (e) represent grain morphology evolution diagrams at different times; and (b), (d) and (f) represent grain roundness probability density distribution curves at different times.

[0042] Figure 5 These are the curves showing the changes in average roundness and average size of the grains during the simulation process in Example 1; where (a) represents the curve showing the relationship between the average roundness of the grains and the simulation time; and (b) represents the curve showing the relationship between the average size of the grains (lnD) and the simulation time (lnt). Detailed Implementation

[0043] The "range" disclosed in this application is defined by a lower limit and an upper limit. A given range is defined by selecting a lower limit and an upper limit, which define the boundaries of a particular range. Ranges defined in this way can include or exclude endpoints and can be arbitrarily combined; that is, any lower limit can be combined with any upper limit to form a range. For example, if ranges of 60–120 and 80–110 are listed for a specific parameter, it is understood that ranges of 60–110 and 80–120 are also expected. Furthermore, if minimum range values ​​of 1 and 2 are listed, and if maximum range values ​​of 3, 4, and 5 are listed, then the following ranges are all expected: 1–3, 1–4, 1–5, 2–3, 2–4, and 2–5. In this application, unless otherwise stated, the numerical range "a–b" represents a shortened representation of any combination of real numbers between a and b, where a and b are real numbers. For example, the numerical range "0~5" indicates that all real numbers between "0~5" have been listed in this article; "0~5" is simply a shortened representation of these numerical combinations. Furthermore, when a parameter is stated as an integer ≥2, it is equivalent to disclosing that the parameter is, for example, an integer such as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, etc.

[0044] Unless otherwise specified, the terms "comprising" and "including" as used in this application can be open-ended or closed-ended. For example, "comprising" and "including" can mean that other components not listed may also be included, or that only the listed components may be included.

[0045] Unless otherwise specified, the term "or" is inclusive in this application. For example, the phrase "A or B" means "A, B, or both A and B". More specifically, the condition "A or B" is satisfied by any of the following conditions: A is true (or exists) and B is false (or does not exist); A is false (or does not exist) and B is true (or exists); or both A and B are true (or exist).

[0046] This specific embodiment provides a method for simulating the change in grain roundness during the grain growth process of ternary cathode materials, including the following steps:

[0047] S1. Obtain SEM images at different initial moments of constant temperature and use them as the initial state of the cellular automata.

[0048] S2. Calculate the grain growth rate and determine the grain growth distance at each moment. Determine the cell orientation transition time by comparing it with the cell edge length. The grain growth rate is calculated using the following formula:

[0049]

[0050] Where t is the sintering time, dR / dt is the rate of change of grain size, i.e., the growth rate; M is the grain boundary mobility, which conforms to Arrhenius's law and is related to the isothermal temperature; σ is the surface energy; α is a dimensionless constant; the equivalent radius R of the grain is the radius of the equivalent circle with the same area as the grain; and the critical radius R of the grain is... cr The average radius of all grains in the cell space; parameter

[0051] The growth rate at each moment is accumulated to obtain the grain growth distance. An orientation change can only occur when the growth distance is greater than or equal to the cell edge length. The grain growth distance is calculated using the following formula:

[0052] D t =D t-Δt +vΔt≥a

[0053] Among them, D t and D t-Δt Let t and t-Δt represent the growth distances at time t and t-Δt respectively; a represents the cell side length, and the time step Δt of the cellular automaton is Δt = a / v. max ; where v max This represents the maximum grain growth rate.

[0054] S3. The boundary cells are sequentially converted to neighbor orientations, and the grain boundary energy difference before and after the cell orientation transformation determines the cell orientation change; the grain boundary energy difference before and after the cell orientation transformation is calculated by the following formula:

[0055] ΔE i→j < indicates the grain boundary energy difference after cell i is transformed into neighboring cell j;

[0056] The grain boundary energy of the central cell i can be expressed as follows:

[0057]

[0058] In the formula, E(θ) is a function related to the orientation angle, given by the Read-Shockley relation; δ is the Kronecher notation; k is the k-th neighbor of the cell; n is the total number of neighboring cells of the cell; q i q is the orientation number of cell i; k Let be the orientation number of the k-th neighbor of the cell;

[0059] E(θ)=E m sinθ[1-ln(sinθ)], where, E m =μbθ m / 4π(1-ν) is the grain boundary energy of a large-angle grain boundary, which is related to the material's shear modulus μ, Poisson's ratio ν, and Burger vector b; θm It is the orientation difference of large-angle grain boundaries; grain orientation difference angle Δq is the difference in orientation number between adjacent grains, q max This represents the maximum value of grain orientation. The Kronecher notation is defined as follows:

[0060]

[0061] S4. Calculate the local grain boundary curvature of each boundary cell, determine the concavity and convexity, and make further transformations for convex and concave cells.

[0062] S5. Based on the grain growth rate, local grain boundary curvature and minimum energy principle, design cell state transition rules to establish a two-dimensional cellular automaton model to simulate the grain roundness change during grain growth.

[0063] In some embodiments, after converting the boundary cells to neighbor orientations sequentially, the method further includes determining the concavity / convexity of the boundary cells:

[0064] Calculate the local curvature of the boundary cell. If the local curvature κ > 0, it means the boundary curves outward at that point, and the boundary cell is convex. If the local curvature κ < 0, it means the boundary curves inward at that point, and the boundary cell is concave. The formula for calculating the local curvature is:

[0065] Where A is the shape factor; a is the cell size; kink is the total number of cells belonging to grain i in the neighborhood when the grain boundary is straight; Ni is the total number of neighbors belonging to grain i in the neighborhood; and N is the total number of grains in the neighborhood.

[0066] When a boundary cell convexes outward, it is transformed into the orientation of its surrounding neighbors, thus achieving inward contraction of the current grain boundary; when a boundary cell is concave inward, the surrounding neighboring cells are oriented to the same orientation, thus achieving outward expansion of the grain boundary.

[0067] In some embodiments, after step S5, step S6 is further included:

[0068] The boundary coordinates of each grain are obtained in a cellular automaton, a least-squares circle of the grain boundary is fitted, the roundness of each grain is calculated using Hausdorff distance, and the probability density corresponding to the roundness value is calculated using kernel density estimation; the calculation of the roundness of each grain using Hausdorff distance includes:

[0069] Fit a least-squares circle to the grain boundary; for each point in the grain boundary point set B, calculate the minimum distance d(B, C) from it to all points in the least-squares circle boundary point set C, and find the maximum value of all d(B, C), denoted as max d(B, C); similarly, for each point in the least-squares circle boundary point set C, calculate the minimum distance d(C, B) from it to all points in the grain boundary point set B, and find the maximum value of d(C, B), denoted as max d(C, B); finally, the Hausdorff distance is defined as the maximum distance between two point sets, expressed as follows:

[0070] d H (A,B)=max(maxd(B,C),maxd(C,B)).

[0071] In some embodiments, prior to step S1, the method further includes:

[0072] The analysis of the roundness variation during grain growth specifically includes: using the Canny edge detection algorithm to extract the primary grain boundaries in the SEM image, and using Hausdorff distance as a roundness index to obtain the probability density distribution of grain roundness at different isothermal times.

[0073] The boundaries of each primary particle are extracted from the preprocessed image using the Canny edge detection algorithm; the preprocessing of the image includes the following steps:

[0074] T1. Remove noise from SEM images during the sintering process of ternary cathode materials;

[0075] T2. Use histogram equalization to improve the contrast of SEM images;

[0076] T3. Use threshold segmentation to convert the SEM image into a binary image;

[0077] T4. Perform morphological processing on the binary image using morphological opening operations.

[0078] In some embodiments, the ternary cathode material is LiNi. 0.83 Co 0.11 Mn 0.06 O2.

[0079] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0080] In this invention, the terms "some embodiments," "this embodiment," and examples are used to describe a subset of all possible embodiments. However, it is understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0081] If the application documents contain similar descriptions such as "first / second", the following explanation shall be added: In the following description, the terms "first / second / third" are used only to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first / second / third" may be interchanged in a specific order or sequence where permitted, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein.

[0082] In this embodiment, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, object A and / or object B can represent three situations: object A exists alone, object A and object B exist simultaneously, and object B exists alone.

[0083] The following describes embodiments of this application. The embodiments described below are exemplary and are only used to explain this application, and should not be construed as limiting this application. Where specific techniques or conditions are not specified in the embodiments, they shall be performed in accordance with the techniques or conditions described in the literature in the art or in accordance with the product manual.

[0084] Example 1

[0085] This embodiment proposes a modeling method for grain roundness variation during the growth of ternary cathode materials. By analyzing the roundness variation law during grain growth using experimental data and existing knowledge, a grain growth evolution model is established based on a two-dimensional cellular automata, which can effectively reflect the roundness variation of grains during growth and provide guidance for the preparation of high-performance cathode materials.

[0086] The method for calculating the roundness of primary grain SEM images of ternary cathode materials involved in this embodiment is as follows:

[0087] T1. Mean filtering is applied to the SEM image I(i,j) acquired during the sintering process of the ternary cathode material to remove noise from the image, resulting in image I. a (i, j);

[0088] T2. Improving Image I using Histogram Equalization a The contrast of (i, j) is used to obtain image I. b (i, j);

[0089] T3. Apply threshold segmentation to image I b (i, j) is converted into a binary image I.c (i, j), distinguishing between foreground and background;

[0090] T4. Applying morphological opening operations to binary images I c Morphological processing is performed on (i, j) to obtain the preprocessed image I. d (i, j);

[0091] T5. Use the Canny edge detection algorithm to process the preprocessed image I. d (i, j) extracts the boundaries of each primary particle. See attached examples. Figure 1 As shown, where, Figure 1 (a) represents the image of a single grain boundary extraction; for each extracted grain boundary coordinate, its roundness is measured by Hausdorff distance, and the probability density curve of roundness is shown in the figure. Figure 1 As shown in (b).

[0092] Measuring roundness using Hausdorff distance involves: fitting a least-squares circle to the grain boundary; calculating the minimum distance d(B,C) from each point in the grain boundary point set B to all points in the least-squares circle boundary point set C, and finding the maximum value of all d(B,C), denoted as max d(B,C); similarly, calculating the minimum distance d(C,B) from each point in the least-squares circle boundary point set C to all points in the grain boundary point set B, and finding the maximum value of d(C,B), denoted as max d(C,B); finally, Hausdorff distance is defined as the maximum distance between two point sets, which is used as a measure of roundness.

[0093] d H (A,B)=max(maxd(B,C),maxd(C,B)) (1)

[0094] At high temperatures, polycrystalline materials undergo grain growth, a process essentially characterized by the continuous migration of grain boundaries, with larger grains engulfing smaller ones. The driving force behind grain growth stems from the energy difference between grain boundaries before and after growth. Initially, there are more fine grains with numerous grain boundaries and correspondingly higher grain boundary energies. As the grains grow, they coarsen, resulting in fewer grain boundaries and lower grain boundary energies. Therefore, the transformation of fine grains into coarse grains is a spontaneous process. During grain growth, the principle of minimum energy for gradually decreasing grain boundary energies is followed. Ideally, the grain shape with the lowest energy should be spherical, leading to a tendency towards spherical growth and a continuous increase in sphericity. Under the influence of the driving force, grain boundaries migrate, causing larger grains to gradually grow. Smaller grains are "engulfed" by neighboring larger grains and gradually disappear. Therefore, as sintering progresses, the average grain size increases, while the number of grains continuously decreases.

[0095] To further analyze the changes in grain roundness during grain growth, sintering experiments of ternary cathode materials at different isothermal temperatures and times were designed, and the grain morphology of the sintered samples was observed using scanning electron microscopy (SEM). Ni 0.83 Co 0.11 Mn 0.06 The (OH)₂ precursor and LiOH·H₂O were mixed in a ratio of 1:1.05 and ground uniformly. Then, the mixture was heated in a tube furnace from room temperature to 750℃, 800℃, and 850℃, respectively, and held at these temperatures for 3h, 6h, 9h, and 12h to synthesize LiNi. 0.83 Co 0.11 Mn 0.06 O2 sample. Figure 2 This paper presents SEM images of grains taken at various isothermal times. It shows that with increasing isothermal time, the grain size significantly increases, the morphology changes from elongated to polyhedral, and the grain boundaries gradually become smoother and more defined. Simultaneously, the probability density distribution curves of grain roundness at different isothermal times are statistically analyzed. Figure 3 It is evident that the peak and average values ​​of grain roundness decrease with the extension of sintering time, and the curves generally show a leftward shift, indicating that the roundness of the grains gradually improves.

[0096] The simulation method for simulating grain growth using cellular automata proposed in this invention is as follows: A cellular automaton is a dynamic model composed of several unit cells in a specific cellular space. The evolution of each cell through interaction with other cells according to certain cellular rules is determined by the neighbor type. Cellular automata can flexibly compile cell transformation rules and has been widely used in the field of grain growth simulation. The components of a cellular automaton can be mainly divided into the following parts: cell, cellular space, neighbor type, and cell transformation rules. A cell is the basic unit of a cellular automaton model. Common two-dimensional cell shapes include hexagons, squares, and triangles, etc. Cell space is a collection of spatial regions composed of countless discrete cells. Common cell neighbor types are Von Neumann and Moore. The state transition rule is the core of the cellular automaton. The transition rule determines the state transition function of the cell at the next moment by considering the current state of the cell and the states of its surrounding neighbors, as shown in Equation (2):

[0097]

[0098] Where ζ represents cell C i The state at time t, C k Let f be the k-th neighbor cell of a given cell, and f be the mapping relationship of the cellular automaton.

[0099] When constructing a cellular automaton model to simulate the grain growth process of ternary cathode materials, square cells and molar neighbor types are used.

[0100] Considering the growth rate and energy-driven mechanism during grain growth, the cellular automata transition rules are as follows:

[0101] During grain growth, the growth of grains is essentially the migration of grain boundaries. The velocity of grain boundary migration is proportional to the pressure difference caused by the curvature on both sides of the grain boundary, while the grain growth rate is proportional to the grain boundary migration rate. Therefore, the average grain growth rate can be established as follows, which is related to factors such as mobility, initial grain radius, and critical radius.

[0102]

[0103] Where t is the sintering time, dR / dt is the rate of change of grain size, i.e., the growth rate; M is the grain boundary mobility, which conforms to Arrhenius's law and is related to the isothermal temperature; σ is the surface energy; α is a dimensionless constant; the equivalent radius R of the grain is the radius of the equivalent circle with the same area as the grain; and the critical radius R of the grain is... cr It is usually equal to the average radius of all grains in the cell space. From the above formula, it can be seen that if the grain size is greater than the critical radius R... cr It will absorb other grains and grow; smaller than R cr The grain will shrink and integrate into other grains. The parameter Mσα can be identified as a whole according to the following formula:

[0104]

[0105] However, in the evolution of cellular automata, the orientation of each cell is unique. Therefore, when a grain grows at a growth rate v, the orientation of the cell can only change when its growth distance reaches the cell length.

[0106] D t =D t-Δt +vΔt≥a (5)

[0107] Among them, D t and D t-Δt represents the growth distance at times t and t-Δt, respectively; a represents the cell side length, which can be determined by the ratio between the SEM image and the cell space; in this embodiment, a = 4.5 nm; the time step of the cellular automaton Δt = a / v max ; where v max This represents the maximum grain growth rate.

[0108] In this embodiment, if D tIf ≥a, then the boundary cells are successively converted to neighbor orientations, and the grain boundary energy difference before and after the cell orientation transformation is calculated.

[0109] Initially, grains are mostly elongated, while at the final sintering state, they tend to exhibit smooth grain boundaries and larger polygonal shapes. During this process, the driving force for grain growth is the difference in interfacial energy before and after growth. According to the principle of minimum energy, grain boundaries always move from the side with higher interfacial energy to the side with lower interfacial energy, thus achieving grain growth. In cellular automata, the more orientations around a grain and the greater the difference, the more disordered its distribution, and consequently, the greater its grain boundary energy. Based on the grain boundary energy calculation model proposed by J. Geiger, grain boundary energy can be flexibly linked to the number of orientations. The grain boundary energy of the central cell i is expressed as follows:

[0110]

[0111] In the formula, E(θ) is a function related to the orientation angle, given by the Read-Shockley relation; δ is the Kronecher notation; k is the k-th neighbor of the cell; n is the total number of neighboring cells of the cell, which is taken as 8 in this embodiment; q i q is the orientation number of cell i; k Let be the orientation number of the k-th neighbor of the cell.

[0112] E(θ)=E m sinθ[1-ln(sinθ)] (7)

[0113] Where E m =μbθ m / 4π(1-ν) is the grain boundary energy of a large-angle grain boundary, which is related to the material's shear modulus μ, Poisson's ratio ν, and Burger vector b; θ m This refers to the orientation difference at large-angle grain boundaries, typically taken as 15°; the grain orientation difference angle... Δq is the difference in orientation number between adjacent grains, q max This represents the maximum value of grain orientation. The Kronecher notation is defined as follows:

[0114]

[0115] According to the principle of minimum energy, the orientation of the central cell is successively transformed into the orientation of its surrounding neighbors. If the transformed ΔE i→j If the value is less than 0, then the transformation can occur. The change in grain boundary energy after cell i transforms into its neighboring cell j can be calculated using the following formula:

[0116]

[0117] During growth, the size and morphology of the grains change simultaneously. In cellular automata, the process of large grains engulfing small grains can be realized by changing the orientation of the cells, thereby causing changes in grain size and boundary shape, which in turn causes changes in grain morphology. To improve the smoothness of grain boundaries and gradually optimize grain roundness, the orientation conversion of convex and concave boundary cells is further considered. Curvature is an indicator that measures the degree of curvature at a point on a curve. In cellular automata, the curvature of boundary cells can be calculated using the local grain boundary curvature calculation model proposed by Kremeyer. In this model, the first and second nearest neighbors are taken as the neighborhood. If the local curvature κ > 0, that is, there is positive curvature at the point, it means that the boundary bends outward at the point and the boundary cell is convex; if the local curvature κ < 0, that is, there is negative curvature at the point, it means that the boundary bends inward at the point and the boundary cell is concave. The formula for calculating local curvature is as shown in equation (10):

[0118]

[0119] Where A is the shape factor, which is usually 1.28 for a regular quadrilateral cell; a is the cell size; kink is the total number of cells belonging to grain i in the neighborhood when the grain boundary is straight; Ni is the total number of neighbors belonging to grain i in the neighborhood; and N is the total number of grains in the neighborhood, N = 24.

[0120] After determining the concavity or convexity of the boundary cells, different transformation strategies are adopted to gradually smooth the grain growth boundary and improve the roundness of the grain shape. When the boundary cell is convex, it should be transformed into the orientation of its surrounding neighbors to achieve inward contraction of the current grain boundary; while when the boundary cell is concave, the surrounding neighbor cells should be oriented to the same orientation to achieve outward expansion of the grain boundary.

[0121] After each evolution step, the roundness of each grain is calculated, and the probability density distribution of roundness in the cellular space is statistically analyzed. The boundary coordinates of each grain can be obtained in the cellular automaton, a least-squares circle of the grain boundary is fitted, and the roundness of each grain is calculated using Hausdorff distance. Then, the probability density of the roundness value is calculated using kernel density estimation, and finally, the probability density distribution curve of roundness is plotted.

[0122] Based on the relevant properties of ternary cathode materials, the parameters in the model were identified. Simultaneously, relevant literature was consulted to obtain LiNi... 0.83 Co 0.11 Mn 0.06 The shear modulus μ of O2 is 66.88 GPa and the Poisson's ratio ν is 0.254. The initial state of grain growth is input into the cellular automata model, and the evolution of grain morphology is carried out according to the transformation rules to obtain the cellular automata simulation results of the grain growth process of ternary cathode material. Figure 4 This illustrates the morphological changes and the changes in the probability density distribution curve of grain roundness during grain growth. From... Figure 4 In (a), 4(c), and 4(e), it is evident that the grains gradually grow from their initial elongated shape to more rounded polygons. Small grains gradually shrink or are even engulfed, the grain size gradually becomes more uniform, the average grain size increases while the number of grains decreases. Meanwhile, in Figure 4 (b) The probability density distribution curve of grain roundness is widely distributed and relatively right-skewed at the initial time, indicating that the grain roundness values ​​are large and dispersed, and the grain roundness is poor with large differences between each other. Figure 4 As shown in (d) and 4(f), the grain morphology changes as the simulation progresses, and its roundness probability density curve gradually shifts to the left and narrows, indicating that the roundness of the grains is gradually improving. Figure 4 In (f), the simulated grain roundness probability density distribution curve is almost identical to the real roundness probability density distribution curve extracted from the SEM image after 12 hours of sintering, indicating that it accurately simulates the grain roundness change during grain growth.

[0123] The average roundness variation of each grain during the statistical simulation is as follows: Figure 5 As shown in (a), the average roundness of the grains gradually decreases as the simulation progresses, indicating that the roundness gradually improves during grain growth. In this embodiment, the error between the simulated average roundness and the actual average roundness is less than 0.1, meeting the error requirement and completing the simulation. Simultaneously, the average grain size during grain growth is consistent with the simulation time. Therefore, lnD and lnt should exhibit a linear relationship. The change in average grain size during the statistical simulation process, such as... Figure 5 (b) shows that the two are basically in a linear relationship.

[0124] Other beneficial effects:

[0125] 1) This invention proposes a method for calculating the roundness of primary particles of ternary cathode materials using SEM images, and analyzes the variation law of grain roundness during grain growth based on experimental data and growth mechanism.

[0126] 2) A simulation method for the grain roundness change during the grain growth process of ternary cathode materials is proposed. A two-dimensional cellular automaton model is established based on the grain growth rate, local grain boundary curvature and minimum energy principle to simulate the morphological changes during grain growth, which fully reflects the changes in grain roundness and size.

[0127] 3) A method is proposed to identify grain boundaries and calculate the roundness of each grain in SEM images of primary particles. The SEM images are preprocessed by mean filtering, histogram equalization, binarization and morphological opening operation. Then, the grain boundaries are extracted by Canny edge detection and the roundness of the grains is measured by Hausdorff distance.

[0128] 4) The proposed cellular automata modeling strategy for grain growth process, based on the physical mechanism of grain growth and the evolution characteristics of cellular automata, realizes dynamic simulation of grain growth. Not only does the change in grain size conform to growth kinetics, but the change in its roundness also conforms to the actual sintering situation, thus simulating grain growth more comprehensively.

[0129] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for simulating the change in grain roundness during the grain growth process of a ternary cathode material, characterized in that, Includes the following steps: S1. Obtain SEM images at different initial moments of constant temperature and use them as the initial state of the cellular automata. S2. Calculate the grain growth rate and obtain the grain growth distance at each moment. Determine the cell orientation transition time by comparing it with the cell side length. S3. Transform the boundary cells into neighbor orientations in sequence, and calculate the grain boundary energy difference before and after the cell orientation transformation to determine the transformation of the cell orientation. S4. Calculate the local grain boundary curvature of each boundary cell, determine the concavity and convexity, and make further transformations for convex and concave cells. S5. Based on the grain growth rate, local grain boundary curvature and the minimum energy principle, design cell state transition rules to establish a two-dimensional cellular automaton model to simulate the grain roundness change during grain growth. In step S2, the growth rate of the grains is calculated using the following formula: Where t is the sintering time, dR / dt is the rate of change of grain size, i.e., the growth rate; M is the grain boundary mobility, which conforms to Arrhenius's law and is related to the isothermal temperature; σ is the surface energy; α is a dimensionless constant; the equivalent radius R of the grain is the radius of the equivalent circle with the same area as the grain; and the critical radius R of the grain is... cr The average radius of all grains in the cell space; parameter The growth rate at each moment is accumulated to obtain the grain growth distance. An orientation change can only occur when the growth distance is greater than or equal to the cell edge length. The grain growth distance is calculated using the following formula: D t =D t-Δt +vΔt≥a Among them, D t and D t-Δt Let t and t-Δt represent the growth distances at time t and t-Δt respectively; a represents the cell side length, and the time step Δt of the cellular automaton is Δt = a / v. max ; where v max This represents the maximum grain growth rate.

2. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 1, characterized in that, In step S3, the grain boundary energy difference before and after the cell orientation transformation is calculated using the following formula: ΔE i→j < indicates a meta-element The grain boundary energy difference after cell i transforms into neighboring cell j; The grain boundary energy of the central cell i can be expressed as follows: In the formula, E(θ) is a function related to the orientation angle, given by the Read-Shockley relation; δ is the Kronecher notation; k is the k-th neighbor of the cell; n is the total number of neighboring cells of the cell; q i q is the orientation number of cell i; k Let E(θ) be the orientation number of the k-th neighbor of the cell; E(θ) = E m sinθ[1-ln(sinθ)], where, E m =μbθ m / 4π(1-ν) is the grain boundary energy of a large-angle grain boundary, which is related to the material's shear modulus μ, Poisson's ratio ν, and Burger vector b; θ m It is the orientation difference of large-angle grain boundaries; grain orientation difference angle Δq is the difference in orientation number between adjacent grains, q max This represents the maximum value of grain orientation; the Kronecher notation is defined as follows:

3. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 1, characterized in that, In step S4, determining the convexity / concavity of the cell and making a corresponding orientation change includes: Calculate the local curvature of the boundary cell. If the local curvature κ > 0, it means the boundary curves outward at that point, and the boundary cell is convex. If the local curvature κ < 0, it means the boundary curves inward at that point, and the boundary cell is concave. The formula for calculating the local curvature is: Where A is the shape factor; a is the cell size; kink is the total number of cells belonging to the current cell's grain i in the neighborhood when the grain boundary is straight; N i is the total number of neighbors belonging to grain i within the neighborhood; N is the total number of grains in this neighborhood; When a boundary cell convexes outward, it is transformed into the orientation of its surrounding neighbors, thus achieving inward contraction of the current grain boundary; when a boundary cell is concave inward, the surrounding neighboring cells are oriented to the same orientation, thus achieving outward expansion of the grain boundary.

4. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 1, characterized in that, Following step S5, step S6 is also included: The boundary coordinates of each grain are obtained in the cellular automaton, the least square circle of the grain boundary is fitted, the roundness of each grain is calculated by Hausdorff distance, and the probability density corresponding to the roundness value is calculated by kernel density estimation.

5. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 4, characterized in that, The calculation of the roundness of each grain using the Hausdorff distance includes: Fit a least-squares circle to the grain boundary; for each point in the grain boundary point set B, calculate the minimum distance d(B, C) from it to all points in the least-squares circle boundary point set C, and find the maximum value of all d(B, C), denoted as maxd(B, C); similarly, for each point in the least-squares circle boundary point set C, calculate the minimum distance d(C, B) from it to all points in the grain boundary point set B, and find the maximum value of d(C, B), denoted as max d(C, B); finally, the Hausdorff distance is defined as the maximum distance between two point sets, expressed as follows: d H (A,B)=max(max d(B,C),max d(C,B))。 6. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 1, characterized in that, Before step S1, the following is also included: Analyze the variation pattern of roundness during grain growth.

7. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 6, characterized in that, The analysis of the roundness variation during grain growth includes: using the Canny edge detection algorithm to extract the primary grain boundaries in the SEM image, and using Hausdorff distance as a roundness index to obtain the probability density distribution of grain roundness at different isothermal times.

8. The method for simulating the grain roundness change during the grain growth process of ternary cathode materials according to claim 1, characterized in that, The ternary cathode material is LiNi. 0.83 Co 0.11 Mn 0.06 O2.

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