A phase-field modeling method for lithium dendrite growth at composite solid electrolyte interphase

Abstract

The application relates to the technical field of electrochemical energy storage, and discloses a composite solid electrolyte interface lithium dendrite growth phase field modeling method.The method comprises the following steps: obtaining a microstructure image of a composite solid electrolyte and performing pretreatment to obtain a normalized gray matrix; based on the gray matrix, a heterogeneous material performance field is constructed to make physical parameters continuously change with spatial coordinates, and boundary conditions and initial conditions are set; based on the heterogeneous material performance field, a multi-field dynamic coupling is performed on a phase field, a concentration field, an electric potential field and a mechanical field, and a reversible phase change and dead lithium phase model is established to construct a diffuse interface phase field equation; a non-structured grid finite volume method is used to perform spatial discretization on the diffuse interface phase field equation, and a nonlinear solver is used for iterative solving to obtain a phase field simulation result of lithium dendrite growth.The above scheme can realize high-precision dendrite growth simulation.

Description

Technical Field

[0001] This invention relates to the field of electrochemical energy storage technology, specifically to a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte. Background Technology

[0002] Interface failures in solid-state batteries severely restrict their development, and accurately simulating the growth behavior of lithium dendrites in organic-inorganic composite solid electrolytes is key to optimizing interface design. However, how to non-destructively map experimental characterization images containing complex topological morphologies into simulation models to realistically reflect microscopic heterogeneous characteristics and avoid computational instability is an urgent problem to be solved.

[0003] In related technologies, the phase-field method is mainly used for simulation. When constructing the model, manual parameterization is used to transform electron microscope images into simplified geometric models, and the volume fraction averaging method is used to treat the composite system as a homogeneous material. For interface treatment, a clear interface model is generally used. In the simulation of the evolution process, the phase-field equations in related technologies only consider the lithium ion deposition process in one direction.

[0004] However, the artificially simplified geometric model directly loses key random morphological features such as the edges of inorganic particles, leading to prediction distortion. Simultaneously, the clear interface model causes abrupt changes in physical parameters at the phase interface, directly inducing numerical singularities such as local stress divergence, resulting in computational interruptions. Furthermore, the unidirectional deposition equation lacks the ability to model the exfoliation process and cannot quantify the formation of dead lithium and the evolution of interface porosity. Therefore, the above schemes deviate significantly from the true physical mechanism, resulting in extremely large simulation errors in dendrite growth. Summary of the Invention

[0005] This invention provides a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte, in order to solve the problem of low accuracy in dendrite growth simulation in related technologies.

[0006] In a first aspect, the present invention provides a method for modeling the phase field of lithium dendrite growth at a composite solid electrolyte interface, the method comprising: The microstructure image of the composite solid electrolyte was acquired and preprocessed to obtain a normalized grayscale matrix. Based on the grayscale matrix, a heterogeneous material performance field is constructed that allows physical parameters to change continuously with spatial coordinates, and boundaries and initial conditions are set. Based on the performance field of the heterogeneous material, the phase field, concentration field, potential field and mechanical field are dynamically coupled in multiple fields, and a reversible phase transition and dead lithium phase model is established to construct the phase field equation of the dispersion interface. The phase-field equations of the diffuse interface were spatially discretized using the unstructured mesh finite volume method, and iteratively solved using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

[0007] In one optional implementation, the step of acquiring and preprocessing the microstructure image of the composite solid electrolyte to obtain a normalized grayscale matrix includes: The microstructure image is processed by Gaussian kernel convolution to form an intermediate grayscale matrix with gradient transition; The gray values ​​of the intermediate gray matrix are normalized and mapped to the [0,1] interval, where the mapping value of the pure organic phase region approaches 1 and the mapping value of the pure inorganic phase region approaches 0. The abnormal pixels in the normalized intermediate grayscale matrix are corrected by morphological closing operation to obtain the corrected grayscale matrix.

[0008] In one optional implementation, constructing a spatially resolved heterogeneous material property field based on the grayscale matrix includes: Based on the calibration coefficients, the grayscale matrix Transform pixel coordinates to spatial position coordinates; Based on the material property interpolation equation, the gray-level matrix is... Related to intrinsic material properties; among which, spatial coordinates Material property parameters at the location satisfy:

[0009] in, These are intrinsic performance parameters for pure organic phases. The intrinsic property parameters are those of a pure inorganic phase; the material property parameters include at least ionic conductivity, elastic modulus, interfacial energy density, and diffusion coefficient.

[0010] In an optional implementation, the method further includes: Calculate the grayscale matrix grayscale gradient ; Based on the gray-level gradient Construct the anisotropic gradient energy coefficient tensor, as shown in the following formula:

[0011] in, The matrix gradient coefficient is... For anisotropic strengthening coefficients, For the Kronecker tensor, and These are the components of the grayscale gradient vector, used to indicate the directional constraint of the inorganic particle shape on the lithium-ion diffusion path; The performance field of the heterogeneous material is corrected based on the anisotropic gradient energy coefficient tensor.

[0012] In an optional implementation, the method further includes: A volume expansion stress gradient driving term is added to the phase transition driving force of the phase field equation of the dispersed interface; the volume expansion stress gradient driving term is related to the hydrostatic pressure gradient, the expansion stress coupling coefficient, and the phase field variables; After each time step iteration, a dynamic modulus update algorithm is executed to update the elastic modulus field based on phase field variables and the modulus degradation coefficient caused by lithium deposition.

[0013] In one optional implementation, establishing the reversible phase transition and dead lithium phase model includes: A direction-sensitive polarization factor is introduced to automatically switch the direction of the electrochemical potential gradient by applying the positive or negative sign of the current density, so as to distinguish the kinetic parameters of the deposition process and the stripping process. A dead lithium phase labeling equation is constructed, and the volume fraction of dead lithium corresponding to ion deintercalation failures during the stripping process is calculated and accumulated based on the Herveside step function and the divergence of lithium ion flux.

[0014] In a second aspect, the present invention provides a composite solid electrolyte interface lithium dendrite growth phase field modeling device, the device comprising: The acquisition module is used to acquire microstructure images of the composite solid electrolyte and perform preprocessing to obtain a normalized grayscale matrix. A construction module is used to construct a non-homogeneous material performance field based on the gray-scale matrix, which makes the physical parameters change continuously with spatial coordinates, and to set the boundaries and initial conditions; The model building module is used to dynamically couple the phase field, concentration field, potential field and mechanical field based on the performance field of the heterogeneous material, and to establish a reversible phase transition and dead lithium phase model in order to construct the phase field equation of the dispersion interface. The simulation module is used to spatially discretize the phase-field equation of the diffuse interface using the unstructured mesh finite volume method, and to perform iterative solution using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

[0015] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the composite solid electrolyte interface lithium dendrite growth phase field modeling method described in the first aspect or any corresponding embodiment.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute the composite solid electrolyte interface lithium dendrite growth phase field modeling method described in the first aspect or any corresponding embodiment.

[0017] Fifthly, the present invention provides a computer program product, including computer instructions for causing a computer to execute the composite solid electrolyte interface lithium dendrite growth phase field modeling method described in the first aspect or any corresponding embodiment.

[0018] The technical solution provided by this invention may include the following beneficial effects: The present invention provides a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte. This method acquires a microstructure image of the composite solid electrolyte and converts it into a normalized grayscale matrix. Based on this grayscale matrix, a heterogeneous material performance field is constructed. This overcomes the shortcomings of related technologies that rely on artificial parameterization to simplify geometric models, restores the complex topological morphology in the image, and solves the prediction distortion problem caused by simplifying the composite system as a homogeneous material. By constructing a heterogeneous material performance field that allows physical parameters to continuously change with spatial coordinates, and based on this, a dispersed interface phase field equation is constructed, enabling physical parameters to be realized at different material phase interfaces. A smooth transition eliminates numerical singularities such as local stress divergence induced by abrupt parameter changes. Combining the unstructured mesh finite volume method with a nonlinear solver effectively ensures numerical stability in computational domains containing complex morphologies, preventing computational interruptions. When constructing the phase-field equations for the diffuse interface, a reversible phase transition and dead lithium phase model are established, overcoming the deficiency in related technologies where the phase-field equations only consider the deposition process unidirectionally. This achieves a unified mathematical description of the bidirectional reversible evolution process of lithium metal deposition and stripping, compensating for the lack of modeling capabilities for the stripping process and accurately quantifying the generation of dead lithium and the evolution of interface porosity during stripping. Therefore, the above scheme solves the problem of significant simulation errors caused by serious deviations from the actual physical mechanisms in related technologies, achieving high-precision simulation from lossless mapping of microstructural images to charge-discharge cycle failure processes. Attached Figure Description

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of an application scenario according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the first process of a composite solid electrolyte interface lithium dendrite growth phase field modeling method according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the second process of the composite solid electrolyte interface lithium dendrite growth phase field modeling method according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the third process of the composite solid electrolyte interface lithium dendrite growth phase field modeling method according to an embodiment of the present invention. Figure 5 This is a structural block diagram of a composite solid electrolyte interface lithium dendrite growth phase field modeling device according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0023] In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0024] As an optional application scenario of this invention, such as Figure 1 As shown, the composite solid electrolyte interface lithium dendrite growth phase field modeling system may include at least one front-end terminal device and at least one back-end computing device. Figure 1 The example shows that the system includes an experimental data acquisition terminal 101, an engineering analysis workstation 102, and a high-performance computing cluster 103, and the aforementioned terminal devices are connected to the back-end high-performance computing cluster 103 via a network 110.

[0025] The front-end terminal equipment may include, but is not limited to: a data acquisition control terminal (i.e., experimental data acquisition terminal 101) that communicates with a scanning electron microscope (SEM) or a transmission electron microscope (TEM) to directly export microstructure images in 16-bit grayscale TIFF format (Tag Image File Format); and an engineering analysis workstation 102 equipped with a professional-grade graphics processing unit (GPU) and a high-resolution display to run simulation preprocessing modules and post-processing visualization modules to perform Gaussian blur preprocessing of microstructure images, abnormal pixel correction, grayscale matrix visualization verification, and finally, three-dimensional rendering display of the spatial correlation between lithium dendrite growth morphology and dead lithium distribution.

[0026] The backend computing device (i.e., the high-performance computing cluster 103) can be an independent high-performance computing node or a server cluster composed of multiple parallel computing nodes. Since the embodiments of this invention involve unstructured mesh finite volume discretization and strongly nonlinear multiphysics coupling solutions, the requirements for processor concurrent computing power and memory throughput are extremely high. Therefore, the backend computing device is usually deployed in a laboratory computer room or cloud computing center, specifically for receiving the non-homogeneous material performance field parameters and boundary conditions sent by the front end, and performing time-consuming dynamic coupling iterative solutions of phase field, concentration field, electric potential field and mechanical field.

[0027] Network 110 can be a high-speed wired network or a dedicated computing network, examples of which include, but are not limited to, a laboratory gigabit LAN, an enterprise intranet 10 gigabit Ethernet, or a lossless wireless broadband (infiniband, IB) network for high-performance computing, to ensure low-latency transmission of large-scale microstructure image matrices and massive field variable data during the solution process.

[0028] In this application scenario, the workflow is as follows: After acquiring the microstructure image of the composite solid electrolyte through the experimental data acquisition terminal 101, it is imported into the engineering analysis workstation 102; the engineering analysis workstation 102 completes image preprocessing and grayscale-property analysis mapping, generates the performance field of the heterogeneous material, and submits the calculation task; the high-performance computing cluster 103 in the backend calls the phase field modeling method provided in this embodiment of the invention to complete the numerical solution, and sends the phase field simulation results including the dead lithium volume fraction back to the engineering analysis workstation 102 for interface failure risk assessment and quantitative analysis.

[0029] Interface failures in solid-state batteries severely restrict their development, and accurately simulating the growth behavior of lithium dendrites in organic-inorganic composite solid electrolytes is key to optimizing interface design. However, how to non-destructively map experimental characterization images containing complex topological morphologies into simulation models to realistically reflect microscopic heterogeneous characteristics and avoid computational instability is an urgent problem to be solved.

[0030] In related technologies, the phase-field method is mainly used for simulation, simplifying the composite electrolyte into a homogeneous material. The volume fraction averaging method is used to calculate parameters such as ionic conductivity and elastic modulus. A mixing law model is also employed. In the formula, For various material properties, and The material properties of the inorganic and organic phases are represented respectively. This represents the volume fraction of the inorganic phase. This approach ignores the geometry and spatial distribution of inorganic particles, as well as the regulatory effect of the organic-inorganic interface diffusion layer on local ion transport. This results in the model failing to reflect the heterogeneous characteristics of the real microstructure, such as local aggregation of inorganic fillers and abrupt changes in interface curvature, leading to a large prediction error regarding the preferential growth of dendrites along the edges of inorganic particles. Regarding interface treatment, related techniques generally employ sharp interface models or dynamic mesh methods based on ALE (Arbitrary Lagrangian-Eulerian). The former, when dealing with organic / inorganic phase interfaces, induces numerical singularities due to abrupt changes in material property parameters (such as elastic modulus and ionic conductivity), leading to stress gradient terms in the phase field governing equations. and the second derivative of the concentration field The discontinuity manifests itself in the fact that the stress calculation results of local mesh nodes exceed the material yield strength by 3-5 orders of magnitude (numerical divergence), forcing the simulation to terminate. The latter is due to the need for frequent mesh reconstruction operations, which greatly increases the time required for a single charge-discharge cycle simulation, resulting in reduced computational efficiency. Furthermore, it is difficult to handle the complex geometric topology of randomly distributed inorganic particles, making it difficult to handle the bidirectional evolution of the interface during the cyclic charge-discharge process.

[0031] Furthermore, during lithium metal deposition, the volume expansion caused by dendrite growth generates compressive stress at the interface, which can reach hundreds of megapascals. This stress field significantly modulates the subsequent lithium-ion deposition path by changing the local electrochemical barrier. However, the related technologies have not fully coupled the feedback effect of the mechanical field on the deposition kinetics and have ignored the influence of the local compressive stress gradient caused by the volume expansion of lithium deposition on the redistribution of the ion migration barrier. This results in a large prediction deviation of the dendrite tip growth rate under high current density conditions and a serious underestimation of the risk of dendrites penetrating the electrolyte.

[0032] In addition, the relevant technologies lack direct compatibility with experimental characterization data. It is necessary to convert the microstructure images obtained by scanning electron microscope and transmission electron microscope into geometric models through manual parameterization (such as extracting boundaries by CAD drawing and approximating irregular particles as spheres or polygons). This process introduces subjective errors and cannot retain the random characteristics of the original micromorphology (such as the serrated edges of inorganic particles and the pore topology of organic phases), resulting in a significant deviation between the simulation results and the experimentally observed micro-dendritic bifurcation mode.

[0033] Therefore, the above scheme deviates significantly from the actual physical mechanism, resulting in extremely large errors in the dendrite growth simulation.

[0034] According to an embodiment of the present invention, an embodiment of a method for modeling the phase field of lithium dendrite growth at a composite solid electrolyte interface is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0035] This embodiment provides a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte, which can be used in the aforementioned modeling system for lithium dendrite growth at the interface of a composite solid electrolyte. Figure 2 This is a flowchart of a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte according to an embodiment of the present invention, such as... Figure 2 As shown, the process includes the following steps: Step S201: Obtain the microstructure image of the composite solid electrolyte and perform preprocessing to obtain a normalized grayscale matrix.

[0036] Optionally, a microstructure image of the composite solid electrolyte cross-section is first acquired using a scanning electron microscope or a transmission electron microscope to accurately reflect the spatial distribution of the inorganic filler and the organic phase. Next, the microstructure image is preprocessed. The specific processing scheme can be set according to actual needs. For example, grayscale normalization can be performed to continuously map discrete image grayscale values ​​to the [0,1] interval, establishing a quantitative numerical correspondence between the pure organic phase and the pure inorganic phase. Abnormal pixel correction can also be performed to filter out and correct abnormal pixels in the microstructure image. Finally, after preprocessing, the original microstructure image is transformed into a normalized grayscale matrix.

[0037] Step S202: Based on the grayscale matrix, construct a non-homogeneous material performance field that allows physical parameters to change continuously with spatial coordinates, and set the boundaries and initial conditions.

[0038] The grayscale value of each pixel in the grayscale matrix is ​​directly mapped to the intrinsic physical parameters of the material at the corresponding spatial coordinates (such as ionic conductivity, elastic modulus, interfacial energy, etc.). This allows the physical parameters within the computational domain to undergo continuous spatial changes following the microscopic morphology of the image grayscale, thus preserving the true geometric characteristics of the inorganic filler without loss in the mathematical model and obtaining the performance field of the heterogeneous material. Based on this performance field, boundary conditions and initial conditions are applied, such as setting the initial phase field state of the lithium metal anode interface, the initial ion concentration distribution inside the electrolyte, or periodic or symmetric constraints at the edge of the computational domain, thereby providing the necessary physical starting point and spatial constraint benchmark for subsequent steps.

[0039] Step S203: Based on the performance field of the heterogeneous material, multi-field dynamic coupling is performed on the phase field, concentration field, electric potential field and mechanical field, and a reversible phase transition and dead lithium phase model is established to construct the phase field equation of the dispersion interface.

[0040] First, based on the performance field of this heterogeneous material, the phase field characterizing the transformation of material states, the concentration field characterizing ion transport, the potential field characterizing the internal charge distribution, and the mechanical field characterizing deformation under stress are combined to achieve multi-field dynamic coupling. This allows the various physical parameter variables to influence each other and update in real time within the same time step, thus fully reflecting the complex dynamic interaction mechanism of the intertwined electrochemical and mechanical processes. Simultaneously, for battery charge-discharge cycle conditions, a reversible phase transition and dead lithium phase model is established to characterize the bidirectional reversible phase transition process of lithium metal deposition and stripping, and the inactive lithium phase (dead lithium phase) formed during the stripping process is mathematically characterized. Finally, combining the continuous distribution characteristics of the above-mentioned heterogeneous material performance field, the smooth transformation between different material phase states is described through the form of a diffuse interface. The multi-field coupling mechanism and the reversible phase transition and dead lithium phase model are unified and integrated, thus constructing a complete diffuse interface phase field equation.

[0041] In step S204, the phase-field equation of the dispersed interface is spatially discretized using the unstructured mesh finite volume method, and iteratively solved using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

[0042] First, the unstructured mesh finite volume method is used to spatially discretize the phase-field equations of the dispersed interface, rationally dividing the continuous computational domain into discrete mesh spaces for subsequent numerical calculations. Then, due to the introduction of bidirectional reversible phase transition dynamics and multi-field (especially mechanics and phase-field) coupling mechanisms, the phase-field equations of the dispersed interface contain complex nonlinear cross terms and variable coefficients, making it impossible to directly obtain an accurate analytical solution. Therefore, an iterative solution using a nonlinear solver is necessary. This nonlinear solver repeatedly updates variables during the calculation process and gradually approximates the actual state, ultimately completing the numerical calculation and obtaining the phase-field simulation results of lithium dendrite growth.

[0043] The lithium dendrite growth phase field modeling method at the interface of composite solid electrolytes provided in this embodiment acquires the microstructure image of the composite solid electrolyte and converts it into a normalized grayscale matrix. Based on this grayscale matrix, a heterogeneous material performance field is constructed. This overcomes the shortcomings of related technologies that rely on artificial parameterization to simplify geometric models, restores the complex topological morphology in the image, and solves the prediction distortion problem caused by simplifying the composite system as a homogeneous material. By constructing a heterogeneous material performance field that allows physical parameters to continuously change with spatial coordinates, and based on this, constructing a dispersed interface phase field equation, the physical parameters at different material phase interfaces are realized. The proposed method achieves a smooth transition, eliminating numerical singularities such as local stress divergence induced by abrupt parameter changes. By combining the unstructured mesh finite volume method with a nonlinear solver, it effectively ensures numerical stability in computational domains containing complex morphologies, preventing computational interruptions. In constructing the phase-field equations for the diffuse interface, a reversible phase transition and dead lithium phase model are established, overcoming the limitation of related technologies where the phase-field equations only consider the deposition process unidirectionally. This achieves a unified mathematical description of the bidirectional reversible evolution of lithium metal deposition and stripping, compensating for the lack of modeling capabilities for the stripping process and accurately quantifying the generation of dead lithium and the evolution of interface porosity during stripping. Therefore, this approach solves the problem of significant simulation errors caused by serious deviations from the actual physical mechanisms in related technologies, achieving high-precision simulation from lossless mapping of microstructural images to charge-discharge cycle failure processes.

[0044] This embodiment provides a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte, which can be used in the aforementioned modeling system for lithium dendrite growth at the interface of a composite solid electrolyte. Figure 3 This is a flowchart of a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte according to an embodiment of the present invention, such as... Figure 3 As shown, the process includes the following steps: Step S301: Obtain the microstructure image of the composite solid electrolyte and perform preprocessing to obtain a normalized grayscale matrix.

[0045] The composite solid electrolyte can be an organic-inorganic composite solid electrolyte, such as a polymer-based composite electrolyte doped with inorganic ceramic fillers (e.g., lithium lanthanum zirconium oxide (LLZO) or lithium aluminum titanium phosphorus oxide (LATP)). Due to the significant differences in physical parameters between the inorganic filler and the polymer matrix, its microstructure exhibits high heterogeneity and complex topological morphology, thus requiring the construction of a heterogeneous material performance field. It should be noted that the lithium dendrite growth phase field modeling method at the composite solid electrolyte interface provided in this embodiment is applicable to simulating dendrite growth behavior at the interface between the lithium metal anode and the composite solid electrolyte.

[0046] Optionally, a field emission scanning electron microscope (FE-SEM) or transmission electron microscope can be used to acquire cross-sectional morphology images of the organic-inorganic composite solid electrolyte to obtain the microstructure image. For example, the specific parameters required for this microstructure image are: resolution ≥300 dpi to ensure clear and distinguishable inorganic particle boundaries; imaging area size 10 μm × 10 μm (typical inorganic particle size 0.5-3 μm, μm is micrometer) to cover sufficiently statistically significant microstructural features; grayscale depth in 16-bit grayscale TIFF format to preserve nonlinear brightness variation information; and calibration coefficients for physical size calibration. k scale =d pixel / d real (For example: 1 pixel = 5nm, error < ±2%, nm is nanometer). d pixel In pixels d real The actual size is used to achieve a precise mapping between pixel size and actual size. During acquisition, a cross-sectional sample perpendicular to the electrode / electrolyte interface is selected and ion-polished to expose clear grain boundaries. An example calculation for the calibration coefficients is as follows: when a 1μm scale mark in the microstructure image corresponds to 200 pixels, k scale = 5nm / pixel, where pixel stands for pixel.

[0047] Optionally, a multiphysics parameter mapping library can be constructed, pre-set with electrochemical and mechanical constitutive parameter matrices of mainstream solid electrolyte materials such as lithium lanthanum zirconium oxide (LLZO), polyethylene oxide (PEO), and polyvinylidene fluoride (PVDF), and open user-defined interfaces to achieve modular and plug-and-play configuration of model parameters.

[0048] In one optional implementation, when preprocessing the microstructure image, the microstructure image is first subjected to Gaussian kernel convolution to form an intermediate grayscale matrix with gradient transition; then, the grayscale values ​​of the intermediate grayscale matrix are normalized and mapped to the [0,1] interval, where the mapping value of the pure organic phase region approaches 1 and the mapping value of the pure inorganic phase region approaches 0; finally, morphological closing operation is used to correct abnormal pixels in the normalized intermediate grayscale matrix to obtain the corrected grayscale matrix.

[0049] For example, when performing Gaussian kernel convolution, select... σA Gaussian kernel of 5 pixels is convolved onto the original image, resulting in an organic / inorganic boundary transition region width of approximately 30nm (corresponding to 6 pixels). Image grayscale smoothing is performed using a two-dimensional Gaussian kernel convolution.

[0050] in, The standard deviation of the Gaussian kernel is used to control the degree of blurring, and the unit is pixels. A typical value is [value missing]. ; x , y This is the pixel coordinate offset, in pixels, with a typical value of... , .

[0051] For example, when normalizing the gray values ​​of the intermediate gray matrix, the 16-bit original gray values ​​are mapped to the [0,1] interval. The pure organic phase region z→1 (the brighter parts of the image, where z represents the normalized pixel gray value), and the pure inorganic phase region z→0 (the darker parts of the image). 0 < z < 1 represents the transition region between the two phases. The Gaussian blurred image is then converted into a gray matrix. :

[0052] in, coordinates The pixel grayscale value at that location typically depends on the imaging conditions and ranges from 0 to 65535 (16 bits). This is the maximum grayscale value of the image (white point calibration value). ;set up coordinates Normalized gray value at, 0≤ z ≤1, Continuous distribution.

[0053] This Gaussian kernel convolution process (kernel size) ), forming a grayscale matrix with gradient transition. By adjusting the core size, precise equivalent control of the diffusion layer width at the dispersion interface can be achieved.

[0054] For example, during abnormal pixel correction, for black dots (z<0.1) or white dots (z>0.9) covering less than 0.1% of the area, a closing operation is used to fill holes and smooth burrs. Abnormal pixel correction employs a closing operation:

[0055] in, For structural elements, the unit is pixels, and a typical value is... B =disk(3), which is a disk with a radius of 3 pixels; The original grayscale matrix (including noise / damage) typically has values ​​of 0 ≤ z ≤ 1; The restored grayscale matrix typically has values ​​of 0 ≤ z ≤ 1; Erosion represents the etching process, used to eliminate isolated bright spots and small areas (high grayscale values), suppress noise, and shrink bright areas. The formula for etching is:

[0056] in, p This indicates that the coordinates of the structure element B relative to the center pixel are in the horizontal direction. x Pixel offset (direction), q This indicates that the coordinates of the structure element B are in the vertical direction relative to the center pixel. y (Direction) pixel offset.

[0057] Dilation, or expansion processing, is used to fill holes and cracks (areas with low grayscale values), expand bright areas, and smooth edges. The formula for dilation is:

[0058] The closing operation is used to sequentially close the original image (original grayscale matrix). The corrosion and expansion processes are performed sequentially to close the small holes inside the object, connect adjacent objects, and maintain the stability of the large-scale structure.

[0059] Step S302: Based on the grayscale matrix, construct a heterogeneous material performance field that allows physical parameters to change continuously with spatial coordinates, and set the boundaries and initial conditions.

[0060] Specifically, step S302 includes: Step S3021: Based on the calibration coefficient, the pixel coordinates of the grayscale matrix are transformed into spatial position coordinates, and the grayscale matrix is ​​associated with the intrinsic performance parameters of the material.

[0061] Specifically, firstly, based on the calibration coefficients, the grayscale matrix is... The pixel coordinates are transformed into spatial position coordinates; then, the grayscale matrix is ​​transformed based on the material property interpolation equation. Related to intrinsic material properties; among which, spatial coordinates Material property parameters at the location satisfy:

[0062] in, These are intrinsic performance parameters for pure organic phases. The intrinsic properties of the material are those of a pure inorganic phase; these properties include at least ionic conductivity, elastic modulus, interfacial energy density, and diffusion coefficient.

[0063] By defining arbitrary spatial coordinates Material property parameters at the location The material's performance parameters include ionic conductivity, elastic modulus, interfacial energy density, and diffusion coefficient. It can non-destructively map the intrinsic morphological features of inorganic particles in the original image (such as sharp edges and true particle size distribution) to the computational grid through a linear interpolation mechanism, laying the data foundation for subsequent steps.

[0064] For example, a calibration coefficient can be used to transform the image coordinate system (pixel coordinates) to the physical coordinate system (spatial position coordinates):

[0065]

[0066] in, The horizontal coordinate of the spatial location is represented by the unit m (meter). The vertical coordinate represents the spatial location, and the unit is meters (m). This represents the x-coordinate of a pixel coordinate, in pixels. This represents the ordinate of the pixel coordinate, in pixels. This represents the physical size of a single pixel, expressed in meters per pixel (m / pixel).

[0067] By introducing calibration coefficients to establish a linear mapping relationship between pixel dimension and actual physical dimension, the model has the ability to generalize inputs compatible with microscopic images at different magnification levels.

[0068] Step S3022: Construct the performance field of the heterogeneous material.

[0069] Optionally, an anisotropic gradient correction is also introduced when constructing the spatially resolved property field of the heterogeneous material. First, the gray-level matrix is ​​calculated. grayscale gradient Next, based on this grayscale gradient Construct the anisotropic gradient energy coefficient tensor, as shown in the following formula:

[0070] in, The matrix gradient coefficient is... For anisotropic strengthening coefficients, For the Kronecker tensor, and These are the components of the grayscale gradient vector, used to indicate the directional constraint of the inorganic particle shape on the lithium-ion diffusion path; finally, based on this anisotropic gradient energy coefficient tensor, the performance field of the heterogeneous material is corrected. It should be noted that... i and j This is merely a count for ease of description, and is in contrast to the substances mentioned later. i They are not the same concept.

[0071] By modifying the performance field of heterogeneous materials based on the anisotropic gradient energy coefficient tensor, the traditional scalar gradient coefficient is transformed into a second-order tensor form that depends on the local gray-level gradient. The local structure tensor is constructed using the gray-level gradient, so that the interface energy can exhibit direction dependence, accurately characterizing the directional constraint of the geometric boundary of inorganic particles on the lithium-ion diffusion path.

[0072] For example, anisotropic diffusion in the phase-field equation is controlled by introducing a gray-level gradient. The formula for calculating the anisotropic gradient energy coefficient tensor K is:

[0073] Where K is the anisotropic gradient energy coefficient tensor, with units of J / m (joules per meter). It should be noted that... Coordinates in K Anisotropic gradient energy coefficient tensor at a given location; I represents the matrix gradient coefficient (isotropic part), in J / m; I is the Kronecker tensor. Matrix form; The anisotropic strengthening coefficient; The gradient (vector) of the grayscale matrix is ​​in units of m. -1 ; This is a tensor outer product operation. The physical meaning of this formula is: to set the gradient direction dependency, i.e., along the edge of the inorganic particle (…). The direction forms a higher energy barrier, guiding dendrite growth around the grain; and a curvature response is set, i.e., at the sharp corners of the grain ( The maximum value generates a local energy dissipation point, suppressing dendrite tip breakthrough. This involves calculating the grayscale matrix. grayscale matrix gradient The formula is:

[0074] Next, construct the outer product matrix:

[0075] Finally, the anisotropic gradient energy coefficient tensor K is synthesized and substituted into the dispersed interface phase field equation to correct the performance field of the heterogeneous material.

[0076] In real microstructures, a narrow enhancement region exists at the interface between the organic and nonpolar phases (i.e., In larger regions, influenced by factors such as space charge layer effects and interface defects, the ion diffusion coefficient is higher than the simple average of the organic and inorganic phases. In other regions, the ion diffusion coefficient reflects the properties of the matrix material. To describe this phenomenon, optionally, interface diffusion layer modeling is introduced when constructing the spatially resolved performance field of the heterogeneous material. Specifically, at the organic / inorganic phase interface (based on...), (Identification) Introduces dynamic diffusion related to the grayscale gradient, as shown in the following formula:

[0077] in, The dynamic diffusion coefficient is expressed in m³. 2 / s (square meters per second); This is the matrix diffusion coefficient, in m. 2 / s; The diffusion enhancement coefficient can be dynamically adjusted. The value of is negatively correlated with the local stress level, ensuring the elimination of interface singularities while avoiding excessive smoothing; This is a parameter controlling the width of the interface diffusion layer, in meters (m). -1 ; This represents the grayscale gradient magnitude, in meters (m). -1 This formula defines a spatially continuous, centrally concave, laterally bulging, stress-sensitive interface diffusion enhancement field. Using the image grayscale gradient mode as a spatial positioning scale, it embeds the nanoscale rapid ion transport phenomenon at the solid electrolyte interface, induced by the space charge layer and polymer conformational perturbations, into a macroscopic continuous medium phase-field model in a numerically stable and physically calibrable manner. The physical meaning of this formula is: in the high gradient region, i.e., when... When the value is large (interface diffusion layer), the diffusion coefficient increases to Simulates rapid ion transport at the interface; in the low gradient region, i.e., inside the phase ( ), to maintain the diffusion properties of the matrix.

[0078] Step S3023: Set the boundary and initial conditions.

[0079] For example, when setting the boundary and initial conditions, the initial condition set is: the initial thickness of the lithium metal anode. This means that the computational domain initially consists entirely of composite solid electrolytes, providing observation space for subsequent dendrite growth; the phase field variable ξ=1 at the interface, indicating that the interface between the negative electrode and the electrolyte is considered to be pure lithium metal, providing the initial driving force for dendrite nucleation and outward growth; the electrolyte lithium ion concentration... Furthermore, the lithium ions are uniformly distributed, meaning that initially, the lithium ions inside the electrolyte are stationary and uniform, eliminating interference from initial concentration gradients and ensuring that subsequent observed ion migration is entirely induced by the electric field and dendrite growth. The set periodic boundary conditions include lateral and longitudinal boundaries, with the lateral boundary (…) x (Direction) is:

[0080]

[0081] The longitudinal boundary (y-direction) is: (Symmetrical boundary) in, Indicates the computational domain in the horizontal direction ( x The total physical length (direction), H Indicates the computational domain in the vertical direction ( y Total physical height (direction).

[0082] The horizontal boundary flattens the microscopic domain, enabling the calculation of multiple particle distributions of the equivalent macroscopic interface at a small scale and eliminating the side-truncation effect; the symmetrical vertical boundary suppresses non-physical distortions of the physical field at the top, avoiding interference from artificial boundaries with the core reaction region. Together, these two elements ensure high fidelity of the simulation results under limited computing power.

[0083] Step S303: Based on the performance field of the heterogeneous material, multi-field dynamic coupling is performed on the phase field, concentration field, electric potential field and mechanical field, and a reversible phase transition and dead lithium phase model is established to construct the phase field equation of the dispersion interface.

[0084] Specifically, the phase-field equation of the diffuse interface is taken as the core objective equation. It uniformly receives driving forces (chemical potential, electric potential, stress) or environmental parameters (concentration, modulus) from the dynamic coupling equations of the concentration field, electric potential field, and mechanical field, and then calculates the phase-field variables, which are used to indicate the lithium dendrite growth. At the same time, the evolution of the phase-field variables serves as the source term and geometric constraint, respectively reshaping the concentration distribution, charge distribution, and stress field. The reversible phase transition and dead lithium phase model serve as a post-observer to record irreversible decay, while the dynamic modulus update algorithm serves as a pre-regulator to correct mechanical properties. Each equation achieves nonlinear closed-loop convergence through the solver within a single time step, without unidirectional causal dependence, but rather constitutes a fully coupled synchronous evolution system. Among them, the dynamic coupling equation of concentration field and the phase field equation of diffuse interface form a material conservation closed loop (mainly lithium ions), the dynamic equation of electric potential field and the phase field equation of diffuse interface form a charge conservation closed loop, the dynamic coupling equation of mechanical field and the phase field equation of diffuse interface form a mechanical-phase transition two-way closed loop, and the dynamic coupling equation of mechanical field and the dynamic coupling equation of concentration field form a stress-diffusion closed loop.

[0085] In one alternative implementation, a volume expansion stress gradient driving term is added to the phase transition driving force of the phase field equation of the dispersed interface; the volume expansion stress gradient driving term is related to the hydrostatic pressure gradient, the expansion stress coupling coefficient, and the phase field variables.

[0086] For example, the phase-field equation of the dispersed interface is:

[0087] in, For phase field variables (0 = electrolyte, 1 = lithium metal), , The gradient of the phase field variables; t represents the time step; The phase-field mobility coefficient is expressed in m. 3 / (J·s), determined experimentally; K is the anisotropic gradient energy coefficient tensor; Representing gradient, for example express The gradient; Chemical free energy density, in units of J / m 3 The calculation formula is:

[0088] in, It is matter i The reference chemical potential is in V (volts). R It is the ideal gas constant, with units of J / (mol·K); T It is temperature, and the unit is K (Kelvin). It is the barrier height of any double-well function, in units of J / m. 3 ; Lithium ion concentration, in mol / m³ 3 , This represents the anion concentration, in mol / m³. 3 , Initial lithium-ion concentration, in mol / m³ 3 , For matter i The concentration, in mol / m³ 3 ; Electrostatic energy density, in J / m³ 3 The calculation formula is:

[0089] in, It is the number of electrons transferred. Representative concentration ( i Represents matter i,substance i (Can be lithium ions, lithium atoms, or anions), unit is mol / m 3 , Represents electrostatic potential ( (representing lithium metal electrodes and electrolytes), unit: V; It is Faraday's constant; Elastic energy density, in units of J / m 3 The calculation formula is:

[0090] in, It is the elastic strain tensor, and the calculation formula is as follows:

[0091] in, This represents the total strain tensor. The strain representing the characteristic expansion of lithium deposition is exemplified below. It should be noted that, and Similarly, this will not be elaborated upon here; This is the stiffness tensor, measured in Pa (Pascal), and is calculated using the following formula:

[0092] Where E is Young's modulus, with the unit being Pa; v It is Poisson's ratio; It's Dirac Function (a generalized function that describes the density of point distribution); This is the volumetric expansion stress gradient driving term, with units of J / (m). 3 ·s), the calculation formula is:

[0093] in, The expansion stress coupling coefficient is expressed in meters (m). 2 / (N·s) (square meters per Newton-second), is the experimental calibration value; This is the hydrostatic pressure (mechanical field output), measured in Pa, and is calculated.

[0094] It should be noted that this diffuse interface phase-field equation achieves high-fidelity and stable simulation of dendrite growth by coupling multiple physical constraint mechanisms. Specifically, it introduces gradient tensor anisotropy and uses the anisotropic gradient energy coefficient tensor... The gray-level gradient direction is incorporated into the diffusion characteristic calculation, and the topological barrier effect of the real microstructure is utilized to suppress the irrational penetration of dendrites along the edges of inorganic particles. A concentration-driven term is introduced based on the non-equilibrium lithium-ion concentration. The chemical potential gradient drives the phase field evolution, simulating the concentration polarization effect and accurately reproducing the concentration polarization phenomenon at the reaction interface; a two-way mechanical feedback and stabilization mechanism is established, on the one hand introducing an elastic energy feedback term (elastic energy density). The strain energy (elastic strain tensor) generated by volume expansion This reflects the mechanical resistance of volume expansion to phase transition. On the other hand, it introduces a volume expansion stress gradient driving term, showing a causal relationship between volume expansion stress and hydrostatic pressure: the volume expansion during lithium deposition generates stress on the lithium metal and electrolyte, which in turn acts on the lithium dendrites, generating hydrostatic pressure. The volume expansion stress includes the stress on both the lithium dendrites and the solid electrolyte as a whole, while the hydrostatic pressure only applies to the lithium dendrites. Hydrostatic pressure also drives lithium-ion migration and affects lithium dendrite growth. Indicates the magnitude of pressure, pressure gradient This indicates the direction of pressure application; the stress gradient is the "extra force" experienced by lithium ions in a stress field, which can "push" or "pull" lithium ions towards or away from the growth front. When a large [pressure gradient] exists at the dendrite growth front... (Pointing to the interior of the electrolyte) If at that point there is also an effect caused by volume expansion. (Pointing to the dendrite root), the dot product of the two will enhance or inhibit the phase transition rate. In related techniques (containing only elastic energy feedback), a common problem is that when the dendrite tip approaches the inorganic particle, the elastic energy rises rapidly, causing the simulation results to show that the dendrite "stops." While this avoids penetration, it contradicts the experimental observation of "dendrites creeping laterally along the particle surface." The volume expansion stress gradient driving term decomposes the driving force, originally perpendicular to the particle surface, into a tangential component. Elastic energy feedback term. Working in conjunction with the volume expansion stress gradient driving term, the elastic energy feedback term determines where dendrites cannot grow, while the volume expansion stress gradient driving term determines where dendrites can only grow around. The specific implementation process is as follows: First, the strain and stress are calculated using the mechanical field; then, the elastic energy density and hydrostatic pressure are calculated separately; finally, the elastic energy feedback term and the volume expansion stress gradient driving term are calculated separately. The hydrostatic pressure is generated by the volume expansion caused by lithium deposition. pressure gradient It enhances the driving force of local phase transition, and the volumetric expansion stress gradient driving term has a built-in suppression factor. With the phase field variable When (i.e., completely converted to the lithium metal phase), this inhibition factor This eliminates the excessive evolution of phase variables from the underlying algorithm, avoiding numerical divergence caused by excessive deposition.

[0095] For example, the dynamic coupling equation of the concentration field (the Nernst-Planck equation for heterogeneous environments) is as follows:

[0096] in, Lithium ion concentration, The lithium-ion concentration gradient; The heterogeneous diffusion coefficient, with units of m² / s, is calculated using the following formula:

[0097] in, is the diffusion coefficient of the pure organic phase, with units of m² / s, and is obtained experimentally. is the diffusion coefficient of the pure inorganic phase, with units of m² / s, and is obtained experimentally. It is the Faraday constant, with units of C / mol (charge carried by each mole of electrons); is the ideal gas constant, with units of J / (mol·K); This is the temperature, expressed in Kelvin (K), and can take a value of 298.15 K. This represents the lithium-ion charge number, which can take a value of +1; Electric potential distribution, in V. The potential distribution gradient; This is the partial molar volume, expressed in m³ / mol, and can be taken as 1.3 × 10⁻⁶. -6 m³ / mol; The hydrostatic pressure is expressed in Pa, and is obtained by solving for the mechanical field. The hydrostatic pressure gradient; The lithium metal saturation concentration, expressed in mol / m³, can take values ​​of [value missing]. .

[0098] It should be noted that this concentration field dynamic coupling equation constructs a deep fusion of multiple physical mechanisms. Specifically, according to the diffusion-mechanical coupling theory, the driving force of the stress field on mass transport and phase transition is not only reflected in strain energy storage, but also more directly in the modification of the chemical potential: high local stress will increase the lithium-ion chemical potential, thereby driving lithium-ion diffusion. Therefore, a pressure driving term incorporating the stress gradient is introduced. ( This can reflect the stress gradient caused by volume expansion. The stress gradient affects lithium-ion migration through electrochemical potential, demonstrating stress-diffusion coupling. In real experiments, the interface between organic and inorganic phases is not an ideal interface, but contains a large number of interface defects and space charges. These factors increase the diffusion coefficient at the interface, much higher than the average of the organic and inorganic components. Therefore, an interface diffusion enhancement (heterogeneous diffusion coefficient) is introduced. ), in the interface area ( ), Enhanced simulation of fast ion transport caused by high defect density.

[0099] For example, the dynamic equation for the electric potential field (the improved Poisson equation) is as follows:

[0100] in, The potential distribution is expressed in V and is obtained through calculation. This refers to the heterogeneous conductivity, measured in S / m (Siemens per meter), calculated using the following formula:

[0101] in, The conductivity of the organic phase, The conductivity of the inorganic phase.

[0102] It should be noted that this dynamic equation for the potential field is used to describe charge conservation and electric field distribution, integrating the transient characteristics of electrochemical interfacial reactions with the microscopic heterogeneity of materials. This dynamic equation introduces a dynamic source term. The source term on the right-hand side represents the local charge generation or annihilation caused by phase transitions during lithium metal deposition or stripping. This allows the equation to accurately capture the local potential abrupt changes and overpotential accumulation at the reaction front caused by ion consumption or enrichment. The source term on the right-hand side is determined by the phase transition rate. Driven by the real-time effect of lithium deposition / stripping on charge distribution, the equation introduces anisotropic effective conductivity (organic phase relative to inorganic phase) based on gray-scale mapping on the left side. With the help of the smooth transition of gray-scale gradient, a diffuse conductivity transition layer of a certain width is naturally formed, which realistically simulates the electric field distortion effect caused by space charge layer or defect enrichment at the organic-inorganic interface, and the inorganic particle region ( ) S / m, organic phase The difference in S / m is as much as 10 times.

[0103] For example, the equilibrium equation of dynamic elasticity is:

[0104]

[0105] in, Let be the stress tensor, in Pa, which is solved using Hooke's law; This is the stiffness tensor, in Pa, derived from the elastic modulus. E Compared to Poisson ν Construction (assuming the material is isotropic); E This is the elastic modulus, measured in Pa, and obtained experimentally. ν Poisson's ratio, determined experimentally; The total strain tensor is calculated using the following formula: , for transpose; The displacement is expressed in meters (m) and is obtained through calculation. For displacement gradient; The characteristic strain of lithium deposition expansion was measured experimentally. This is a volume force, measured in N / m³, originating from the binding force of the battery casing on its internal materials, and is determined experimentally.

[0106] It should be noted that the lithium deposition process causes the lithium anode to expand in volume, resulting in expansion strain and thus volume expansion. Therefore, the dynamic elasticity equilibrium equation introduces an expansion strain term. Characterizing the volume expansion caused by lithium deposition, this volume expansion only occurs when... The effect will only become apparent in specific regions; dynamic stiffness updates are introduced, and the elastic modulus... E With phase field variables And changes over time (see step S305 for details, which will not be repeated here).

[0107] In one alternative implementation, when establishing the reversible phase transition and dead lithium phase model, a direction-sensitive polarization factor is introduced by applying a current density. The positive and negative signs of the electrochemical potential gradient are automatically switched to distinguish the kinetic parameters of the deposition and stripping processes. A dead lithium phase labeling equation is constructed, and the volume fraction of dead lithium corresponding to ion insertion / extraction failures during the stripping process is calculated and accumulated based on the Heaviside step function and the divergence of lithium ion flux.

[0108] For example, the reversible phase transition and dead lithium phase model (reversible phase transition kinetic equation) is as follows:

[0109] in, This is the reaction rate constant, with units of m / s; Activation energy, expressed in J / mol; ν represents the chemical potential of lithium metal, expressed in J / mol. The equilibrium chemical potential is expressed in J / mol.

[0110] It should be noted that lithium dendrites are formed during the deposition process, and subsequently, during the stripping stage, they gradually dissolve, which is a reversible path. However, in some cases, such as during the stripping stage, the lithium dendrites dissolve intermittently, breaking the original dendrites into two segments. The segment not connected to the negative electrode is called dead lithium, and this path is irreversible. In this embodiment, direction-sensitive kinetics are introduced into the reversible phase transition and dead lithium phase model to simulate not only the deposition process but also the stripping process, and to consider the generation of dead lithium during stripping. Dead lithium indicates that this portion of lithium cannot participate in subsequent electrochemical reactions; that is, the lithium ions are irreversibly lost, leading to battery capacity loss and aging. The reaction direction is switched by sign to simulate the irreversible path difference between deposition and stripping; the accumulation of dead lithium phase is introduced, and if during stripping... dead lithium volume fraction Increase:

[0111] in, coordinates The volume fraction of dead lithium (the percentage of irreversible lithium metal deposition) at the point; H(·) is the Heaviside step function; For time Phase field variables at time (characterizing the proportion of lithium metal). Lithium-ion flux The divergence (characterizing the lithium-ion inflow / outflow rate) is expressed in mol / (m³·s). The initial time, This represents the time step, in seconds (s). If If this condition is not met, it means that the lithium dendrites successfully dissolved into lithium ions, without forming dead lithium, but instead participated in the electrochemical reaction. The above formula allows for the quantification of dead lithium accumulation caused by failed ion insertion / extraction during the stripping process.

[0112] In step S304, the phase-field equation of the dispersed interface is spatially discretized using the unstructured mesh finite volume method, and iteratively solved using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

[0113] Specifically, the unstructured mesh finite volume method is first used to spatially discretize the phase-field equations of the dispersed interface. This unstructured mesh finite volume method can flexibly fit the serrated edges and complex phase boundaries of inorganic particles directly mapped from the microscopic image, avoiding the step approximation error caused by the structured mesh at curved boundaries. Based on the principle of integral conservation, the finite volume method strictly balances the ion flux and current at each control volume interface, ensuring the absolute conservation of lithium mass and charge throughout the simulation process, which is crucial for the accurate prediction of dead lithium accumulation. This unstructured mesh finite volume method transforms the second derivative into the summation of boundary fluxes, naturally adapting to the drastic but continuous changes in material parameters at the organic-inorganic interface, effectively suppressing numerical oscillations caused by steep parameters, and providing a stable and faithful discretization environment for subsequent nonlinear iterative solutions. Next, the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver is used to process the strongly nonlinear terms in the discretized phase-field equations of the dispersed interface, such as chemical free energy density, elastic energy density, volume expansion stress gradient driving terms, and electromigration terms in the concentration field dynamic coupling equations. and pressure-driven items wait.

[0114] Step S305: Update the elastic modulus field and return to the step of acquiring the microstructure image of the composite solid electrolyte and performing preprocessing.

[0115] In one alternative implementation, a dynamic modulus update algorithm is executed after each time step iteration to update the elastic modulus field based on the phase field variables and the modulus degradation coefficient caused by lithium deposition.

[0116] Optionally, a dynamic modulus update algorithm is constructed to update the elastic modulus field after each time step iteration. The formula for the dynamic modulus update algorithm is as follows:

[0117] in, η The modulus degradation coefficient caused by lithium deposition; For phase field variables (0 = electrolyte, 1 = lithium metal), t represents the time step.

[0118] After executing the dynamic modulus update algorithm, return to step S301 to execute the next round of lithium dendrite growth phase field modeling at the composite solid electrolyte interface, forming an iterative loop.

[0119] This dynamic modulus update algorithm is used to achieve dynamic bidirectional coupling between the mechanical field and the phase field evolution. Physically, there is a significant stiffness difference between the solid electrolyte and the deposited lithium metal (especially porous dendrites containing dead lithium). Based on this, a deep bidirectional feedback closed loop of phase field and mechanical field is constructed using this dynamic modulus update algorithm. Within each time step, as the dendrites grow and evolve (phase field variables...), the dynamic modulus update algorithm... The algorithm continuously reduces the elastic modulus E of the newly formed lithium phase region to reflect its mechanical softening characteristics. This real-time update of the elastic modulus E causes a redistribution of the stress field, which in turn acts as an input condition, inversely controlling the lithium-ion deposition rate and dendrite growth direction in the next time step. Therefore, by implementing this dynamic modulus update algorithm, the limitation of using the mechanical field only as a static background in related technologies is overcome. This effectively addresses the dendrite prediction distortion caused by insufficient coupling of mechanical feedback, significantly improving simulation accuracy.

[0120] The lithium dendrite growth phase field modeling method at the composite solid electrolyte interface provided in this embodiment has the following beneficial effects: (1) By transforming the pixel coordinates of the grayscale matrix to spatial position coordinates and associating the grayscale matrix with the intrinsic performance parameters of the material based on the material property interpolation equation, a heterogeneous material field can be constructed based on the image grayscale, directly mapping the microstructure image to the spatial distribution function of parameters such as ionic conductivity and elastic modulus, while preserving the geometric features of the inorganic particle morphology (such as sharp edges and size distribution); by introducing This method allows dendrites to grow along the high-curvature region of the inorganic particle surface, avoiding penetration into the high-modulus inorganic phase. Based on this, this embodiment achieves localized electric field concentration (increasing the electric field strength by 2-3 times) at the edge of the inorganic particles to drive dendrites to circumvent the surface, which is fundamentally different from the straight-line penetration behavior under a uniform electric field in the homogeneous model of related technologies, thereby reducing the prediction error of dendrite growth path.

[0121] (2) Perform diffusion boundary processing, using Gaussian kernel convolution (Gaussian blur preprocessing) to ensure a continuous transition of the interface grayscale gradient, avoiding discontinuities in derivatives caused by abrupt changes in material parameters; perform artificial diffusion suppression, introducing interface diffusion enhancement (heterogeneous diffusion coefficient) ),exist‖ The larger z‖ region (interface region) simulates fast ion transport caused by high defect density, activates the adaptive diffusion term, and suppresses numerical oscillations. Based on this, this embodiment can solve the problem of discontinuity introduced by the second derivative term of the phase field variable in related technologies. By using continuous gray-scale mapping, the order of the derivative is reduced, divergence is avoided, the occurrence rate of interface stress singularities is reduced, and the simulation time is shortened.

[0122] (3) A direction-sensitive polarization factor is introduced to automatically switch the direction of the electrochemical potential gradient by applying the positive or negative sign of the current density, thus distinguishing the kinetic parameters of the deposition and stripping processes; dead lithium phase accumulation is introduced to quantify the irreversible lithium loss caused by ion insertion / extraction failure during the stripping process. Based on this, this embodiment can overcome the unidirectional model in related technologies that ignores the blocking effect of stripping pores on subsequent deposition, dynamically mark the dead lithium region by the dead lithium volume fraction, and update the effective transport channels in real time, thereby reducing the prediction error of the cycle capacity decay rate and improving the spatial correlation of dead lithium distribution.

[0123] (4) A volume expansion stress gradient driving term is introduced to couple local hydrostatic pressure with phase transition driving force; a dynamic modulus update algorithm is constructed to make the elastic modulus dynamically degrade with phase field variables, characterizing the material softening caused by lithium deposition. Based on this, this embodiment can overcome the problem in related technologies where high current density causes local large deformation (strain > 5%) leading to the failure of linear mechanical models. By capturing the strong correlation between stress and deposition rate through the nonlinear elastic energy density term, the prediction error of dendrite tip growth rate under high current density is reduced.

[0124] (5) A gray-scale-property mapping protocol is established, and the image coordinate system (pixel coordinates) is transformed to the physical coordinate system (spatial position coordinates) through calibration coefficients. This allows for the segmentation of organic / inorganic phases through gray-scale thresholding, preserving the nanoscale surface roughness in the microstructure image. Abnormal pixel correction is performed, and damaged pixels are repaired through morphological closing operations, thereby reducing the area error of inorganic particles. Based on this, this embodiment can overcome the problem of smoothing particle edges required for manual parameterization in related technologies. It avoids geometric distortion through pixel-level lossless mapping, reduces the import error of microstructure parameters (such as inorganic particle spacing and volume fraction), and improves the similarity between simulation and experimental dendrite morphology.

[0125] As one or more specific application embodiments of the present invention, the optimal implementation scheme or the scheme that the inventors most want to embody is described in combination with the specific application scenario.

[0126] Figure 4 This is a flowchart of a method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte according to an embodiment of the present invention, such as... Figure 4As shown, the microstructure of the composite electrolyte is first characterized using scanning electron microscopy to acquire image data. Then, image preprocessing, including Gaussian blurring and morphological closing operations, is performed to generate a gradient transition grayscale matrix. Next, the following steps are performed: constructing the heterogeneous material field (heterogeneous material performance field), mapping multiphysics parameters (multi-field dynamic coupling), constructing the phase field equations of the diffuse interface, and establishing a multi-field coupled dynamic model (reversible phase transition and dead lithium phase model). A numerical solver is then configured, using adaptive mesh generation for high-precision stress field calculation, while GPU acceleration is used for efficient concentration field solving. A bidirectional phase transition process analysis is then performed, followed by dead lithium phase accumulation modeling, and finally, multiphysics visualization output is provided.

[0127] This embodiment also provides a composite solid-state electrolyte interface lithium dendrite growth phase field modeling device, which is used to implement the above embodiments and preferred embodiments, and will not be repeated as already described. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0128] This embodiment provides a composite solid electrolyte interface lithium dendrite growth phase field modeling device, such as... Figure 5 As shown, it includes: The acquisition module 501 is used to acquire the microstructure image of the composite solid electrolyte and perform preprocessing to obtain a normalized grayscale matrix. Module 502 is used to construct a non-homogeneous material performance field based on the grayscale matrix, which makes the physical parameters change continuously with spatial coordinates, and to set the boundaries and initial conditions; The model building module 503 is used to perform multi-field dynamic coupling of phase field, concentration field, electric potential field and mechanical field based on the performance field of the heterogeneous material, and to establish a reversible phase transition and dead lithium phase model in order to construct the phase field equation of the dispersion interface. Simulation module 504 is used to spatially discretize the phase-field equation of the dispersed interface using the unstructured mesh finite volume method, and then iteratively solve it using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

[0129] The composite solid electrolyte interface lithium dendrite growth phase field modeling device provided in this embodiment of the invention can execute the composite solid electrolyte interface lithium dendrite growth phase field modeling method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method. Further functional descriptions of the above modules and units are the same as in the corresponding embodiments above, and will not be repeated here.

[0130] Figure 6This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0131] The following is a detailed reference. Figure 6 This diagram illustrates a suitable structural schematic for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor 601 (e.g., a central processing unit, a graphics processor, etc.), which can perform various appropriate actions and processes based on a program stored in ROM 602 (read-only memory) or a program loaded from memory 608 into RAM 603 (random access memory). RAM 603 also stores various programs and data required for the operation of the electronic device. The processor 601, ROM 602, and RAM 603 are interconnected via bus 604. An I / O interface 605 (input / output interface) is also connected to bus 604.

[0132] Typically, the following devices can be connected to I / O interface 605: input devices 606 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 607 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 608 including, for example, magnetic tapes, hard disks, etc.; and communication devices 609. Communication device 609 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 6 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0133] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 609, or installed from a memory 608, or installed from a ROM 602. When the computer program is executed by the processor 601, it performs the functions defined in the composite solid-state electrolyte interface lithium dendrite growth phase field modeling method of the present invention.

[0134] Figure 6 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0135] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the composite solid-state electrolyte interface lithium dendrite growth phase field modeling method shown in the above embodiments is implemented.

[0136] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0137] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the invention.

Claims

1. A method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte, characterized in that, The method includes: The microstructure image of the composite solid electrolyte was acquired and preprocessed to obtain a normalized grayscale matrix. Based on the grayscale matrix, a heterogeneous material performance field is constructed that allows physical parameters to change continuously with spatial coordinates, and boundaries and initial conditions are set. Based on the performance field of the heterogeneous material, the phase field, concentration field, potential field and mechanical field are dynamically coupled in multiple fields, and a reversible phase transition and dead lithium phase model is established to construct the phase field equation of the dispersion interface. The phase-field equations of the diffuse interface were spatially discretized using the unstructured mesh finite volume method, and iteratively solved using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth. The construction of a heterogeneous material performance field based on the grayscale matrix, which causes physical parameters to vary continuously with spatial coordinates, includes: Based on the calibration coefficients, the grayscale matrix Pixel coordinates are transformed into spatial position coordinates; Based on the material property interpolation equation, the gray-level matrix is... Related to intrinsic material properties; among which, spatial coordinates Material property parameters at the location satisfy: in, These are intrinsic performance parameters for pure organic phases. The intrinsic property parameters are those of a pure inorganic phase; the material property parameters include at least ionic conductivity, elastic modulus, interfacial energy density, and diffusion coefficient. The method further includes: Calculate the grayscale matrix grayscale gradient ; Based on the gray-level gradient Construct the anisotropic gradient energy coefficient tensor, as shown in the following formula: in, The matrix gradient coefficient is... For anisotropic strengthening coefficients, For the Kronecker tensor, and These are the components of the grayscale gradient vector, used to indicate the directional constraint of the inorganic particle shape on the lithium-ion diffusion path; The performance field of the heterogeneous material is corrected based on the anisotropic gradient energy coefficient tensor. The establishment of the reversible phase transition and dead lithium phase model includes: A direction-sensitive polarization factor is introduced to automatically switch the direction of the electrochemical potential gradient by applying the positive or negative sign of the current density, so as to distinguish the kinetic parameters of the deposition process and the stripping process. A dead lithium phase labeling equation was constructed, and the volume fraction of dead lithium corresponding to ion insertion / extraction failures during the stripping process was calculated and accumulated based on the Herveside step function and the divergence of lithium-ion flux. The volume fraction of dead lithium was calculated according to the following formula. : in, coordinates The volume fraction of dead lithium at a given point is used to characterize the proportion of irreversible lithium metal deposition; H(·) is the Herveside step function; For time The phase field variable at time is used to characterize the proportion of lithium metal; Lithium-ion flux The divergence is used to characterize the lithium-ion inflow / outflow rate; The initial time, Indicates a time step.

2. The method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte according to claim 1, characterized in that, The process of acquiring and preprocessing the microstructure image of the composite solid electrolyte to obtain a normalized grayscale matrix includes: The microstructure image is processed by Gaussian kernel convolution to form an intermediate grayscale matrix with gradient transition; The gray values ​​of the intermediate gray matrix are normalized and mapped to the [0,1] interval, where the mapping value of the pure organic phase region approaches 1 and the mapping value of the pure inorganic phase region approaches 0. Morphological closing operations are used to correct abnormal pixels in the normalized intermediate grayscale matrix, resulting in the corrected grayscale matrix.

3. The method for modeling the phase field of lithium dendrite growth at the interface of a composite solid electrolyte according to claim 1, characterized in that, The method further includes: A volume expansion stress gradient driving term is added to the phase transition driving force of the phase field equation of the dispersed interface; the volume expansion stress gradient driving term is related to the hydrostatic pressure gradient, the expansion stress coupling coefficient, and the phase field variables; After each time step iteration, a dynamic modulus update algorithm is executed to update the elastic modulus field based on phase field variables and the modulus degradation coefficient caused by lithium deposition.

4. A device for modeling the phase field of lithium dendrite growth at a composite solid electrolyte interface, characterized in that, The apparatus for performing the lithium dendrite growth phase field modeling method at the composite solid electrolyte interface as described in any one of claims 1 to 3, the apparatus comprising: The acquisition module is used to acquire microstructure images of the composite solid electrolyte and perform preprocessing to obtain a normalized grayscale matrix. A construction module is used to construct a non-homogeneous material performance field based on the gray-scale matrix, which makes the physical parameters change continuously with spatial coordinates, and to set the boundaries and initial conditions; The model building module is used to dynamically couple the phase field, concentration field, electric potential field and mechanical field based on the performance field of the heterogeneous material, and to establish a reversible phase transition and dead lithium phase model in order to construct the phase field equation of the dispersion interface. The simulation module is used to spatially discretize the phase-field equation of the diffuse interface using the unstructured mesh finite volume method, and to perform iterative solution using a nonlinear solver to obtain the phase-field simulation results of lithium dendrite growth.

5. An electronic device, characterized in that, include: A memory and a processor are interconnected, the memory stores computer instructions, and the processor executes the computer instructions to perform the composite solid electrolyte interface lithium dendrite growth phase field modeling method according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the composite solid electrolyte interface lithium dendrite growth phase field modeling method according to any one of claims 1 to 3.

7. A computer program product, characterized in that, The method includes computer instructions for causing a computer to execute the composite solid electrolyte interface lithium dendrite growth phase field modeling method according to any one of claims 1 to 3.

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