Phase field simulation method, device and electronic equipment for three-dimensional dendrite

Abstract

The application discloses a phase field simulation method and device of three-dimensional dendrite and electronic equipment, and relates to the technical field of three-dimensional dendrite simulation. The method comprises the following steps: obtaining free energy density; obtaining an initial phase field variable equation, an initial ion concentration equation and an initial electric potential equation; constructing an initial anisotropy parameter function, fitting anisotropy parameters in the anisotropy parameter function to obtain a target anisotropy parameter function; inputting initial conditions and boundary conditions; discretizing the initial phase field variable equation, the initial ion concentration equation and the initial electric potential equation to obtain target phase field variable equations, target ion concentration equations and target electric potential equations in several directions; obtaining target phase field variable distributions, target ion concentration distributions and target electric potential distributions; drawing an isosurface to obtain the morphology of a negative electrode surface or dendrite. The application can reflect the anisotropy of crystal growth from the perspective of three-dimensional space, and can be widely applied in the technical field of rechargeable ion batteries.

Description

Technical Field

[0001] The present invention relates to the technical field of rechargeable ion batteries, and in particular to a phase field simulation method, device and electronic equipment for three-dimensional dendrites. Background Art

[0002] The phase-field model is a computational research model based on thermodynamics that describes the microstructural evolution of material systems, employing order parameters to describe the phase state of matter. Currently, the phase-field model is used to study dendrite growth at the negative electrode of lithium metal batteries. Through this model, images of the negative electrode dendrite growth morphology, target ion concentration distribution, and target potential distribution can be calculated on a continuum scale. However, the anisotropy parameter has only one normal direction related to the angle of the coordinate axis, so the phase-field model can only be implemented in two dimensions and cannot reproduce the three-dimensional anisotropy of crystal growth. Summary of the Invention

[0003] In view of this, the main purpose of the embodiments of the present invention is to provide a phase-field simulation method, device and electronic equipment for three-dimensional dendrites, so as to realize the anisotropy of crystal growth from a three-dimensional spatial perspective.

[0004] To achieve the above objectives, an embodiment of the present invention provides a three-dimensional dendrite phase field simulation method, the method comprising:

[0005] Based on Gibbs free energy, obtain the free energy density;

[0006] According to the free energy density, an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation are obtained;

[0007] constructing an initial anisotropic parameter function, and fitting anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function;

[0008] Enter initial conditions and boundary conditions;

[0009] Discretizing the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions;

[0010] According to the target anisotropy parameter function, the initial conditions, and the boundary conditions, a transient solution of the target phase field variable equation, the target ion concentration equation, and the target potential equation is obtained to obtain a target phase field variable distribution, a target ion concentration distribution, and a target potential distribution;

[0011] According to the target phase field variable distribution, the target ion concentration distribution and the target potential distribution, an isosurface is drawn to obtain the morphology of the negative electrode surface or dendrite.

[0012] In some embodiments, the free energy density includes chemical free energy density, gradient energy density, and electrostatic energy density, and the expression of the Gibbs free energy is:

[0013]

[0014] Where G represents Gibbs free energy; V represents volume; f ch (u,c i ) represents the chemical free energy density; f grad (u) represents the gradient energy density; f elec (u,c i ,φ) represents the electrostatic energy density; u represents the phase field variable; c i represents the ion concentration of component i; φ represents the electric potential.

[0015] In some embodiments, the expression for the chemical free energy density is:

[0016]

[0017] The expression of the gradient energy density is:

[0018]

[0019] The expression of the electrostatic energy density is:

[0020]

[0021] Among them, f ch (u,c i ) represents the chemical free energy density; f grad (u) represents the gradient energy density; f elec (u,c i ,φ) represents the electrostatic energy density; u represents the phase field variable; c i represents the ion concentration of component i; φ represents the potential; W represents the energy barrier parameter; c0 represents the initial electrolyte concentration; R represents the gas constant; T represents the thermodynamic temperature; c + represents the cation concentration; c - represents the anion concentration; represents the free energy density under standard conditions; represents the reference chemical potential of component i under standard conditions; is the Del operator; k represents the anisotropy parameter; ρ e represents charge density; φ represents electric potential; F represents Faraday constant; Z i represents the number of ion charges; i represents the component.

[0022] In some embodiments, obtaining an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation based on the free energy density includes:

[0023] Based on the Allen-Cahn equation, an initial phase field variable equation is obtained according to the phase field variable of the free energy density;

[0024] Based on the Nernst-Planck equation, an initial ion concentration equation is obtained according to the ion concentration of the free energy density;

[0025] Based on the Poisson equation and the potential of the free energy density, an initial potential equation is obtained.

[0026] In some embodiments, the expression of the initial anisotropy parameter function is:

[0027]

[0028] Where k represents the anisotropy parameter; k0 represents the average gradient energy coefficient; δ1 and δ2 represent the corresponding anisotropy strength; ω1 and ω2 represent the corresponding anisotropic mode number; θ represents the angle between the projection of the normal on the plane and the x-axis; Represents the angle between the normal and the projection of the normal on the plane.

[0029] In some embodiments, constructing an initial anisotropy parameter function and fitting anisotropy parameters in the initial anisotropy parameter function to obtain a target anisotropy parameter function includes:

[0030] Get crystal plane index;

[0031] Place the crystal plane corresponding to the crystal plane index in spherical coordinates to obtain the initial crystal surface energy function;

[0032] Fitting the initial crystal surface energy function to obtain a target crystal surface energy function;

[0033] An initial anisotropic parameter function is constructed, and anisotropic parameters in the initial anisotropic parameter function are fitted to obtain a target anisotropic parameter function.

[0034] To achieve the above objectives, another aspect of the present invention provides a phase-field simulation device for three-dimensional dendrites, the device comprising:

[0035] The first module is used to obtain the free energy density based on Gibbs free energy;

[0036] The second module is used to obtain an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation according to the free energy density;

[0037] The third module is used to construct an initial anisotropic parameter function, and fit the anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function;

[0038] The fourth module is used to input initial conditions and boundary conditions;

[0039] A fifth module is used to discretize the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions;

[0040] A sixth module is used to obtain the transient solution of the target phase field variable equation, the target ion concentration equation and the target potential equation according to the target anisotropy parameter function, the initial condition and the boundary condition, and obtain the target phase field variable distribution, the target ion concentration distribution and the target potential distribution;

[0041] The seventh module is used to draw an isosurface according to the target phase field variable distribution, the target ion concentration distribution and the target potential distribution to obtain the morphology of the negative electrode surface or dendrite.

[0042] To achieve the above-mentioned purpose, an embodiment of the present invention further provides an electronic device, which includes a processor and a memory; the memory stores a program; the processor executes the program to perform the aforementioned phase field simulation method of a three-dimensional dendrite.

[0043] To achieve the above objectives, an embodiment of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the aforementioned phase-field simulation method of a three-dimensional dendrite.

[0044] To achieve the above objectives, embodiments of the present invention further provide a computer program product or computer program, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned three-dimensional dendrite phase-field simulation method.

[0045] The embodiments of the present invention include at least the following beneficial effects: the present invention provides a phase field simulation method, device and electronic device for three-dimensional dendrites, wherein the method obtains free energy density based on Gibbs free energy; obtains an initial phase field variable equation, an initial ion concentration equation and an initial potential equation based on the free energy density; constructs an initial anisotropy parameter function, fits the anisotropy parameters in the initial anisotropy parameter function to obtain a target anisotropy parameter function; inputs initial conditions and boundary conditions; discretizes the initial phase field variable equation, the initial ion concentration equation and the initial potential equation, Obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions; obtain transient solutions of the target phase field variable equations, target ion concentration equations, and target potential equations based on the target anisotropy parameter function, the initial conditions, and the boundary conditions, and obtain target phase field variable distributions, target ion concentration distributions, and target potential distributions; draw isosurfaces based on the target phase field variable distributions, the target ion concentration distributions, and the target potential distributions to obtain the morphology of the negative electrode surface or dendrites, thereby realizing the anisotropy of crystal growth from a three-dimensional spatial perspective. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0047] Figure 1 This is a flow chart of a phase-field simulation method for three-dimensional dendrites provided by an embodiment of the present invention;

[0048] Figure 2 yes Figure 1 Flowchart of step S200 in FIG.

[0049] Figure 3 yes Figure 1 Flowchart of step S300 in FIG.

[0050] Figure 4 is a schematic diagram of two introduced angles provided by an embodiment of the present invention in a three-dimensional rectangular coordinate system;

[0051] Figure 5 is a schematic diagram of a lithium metal deposition model in a three-dimensional space provided by an embodiment of the present invention;

[0052] Figure 6 is a schematic diagram of a target anisotropy parameter function provided by an embodiment of the present invention;

[0053] Figure 7 Schematic diagram of the morphology of the negative electrode surface and dendrites in three-dimensional space provided by an embodiment of the present invention;

[0054] Figure 8 Schematic diagram of the structure of a three-dimensional dendrite phase field simulation device provided in an embodiment of the present application;

[0055] Figure 9 This is a schematic diagram of the hardware structure of the electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0057] Before explaining the embodiments of the present application in detail, some of the nouns and terms involved in the embodiments of the present application are first explained. The nouns and terms involved in the embodiments of the present application are subject to the following explanations.

[0058] Dendrites are branched crystals that remain at a certain stage of their growth process. In the field of rechargeable ion batteries, dendrites typically refer to branch-like structures that form on electrode surfaces or within the battery. These dendrites may be deposited from substances such as metals or lithium in the electrode material. Dendrite formation can negatively impact battery performance and safety.

[0059] The phase field model, based on thermodynamics, considers the combined effects of ordering potential and thermodynamic driving forces to establish phase field equations to describe the evolutionary dynamics of a system. Its core concept is to introduce one or more continuously varying order parameters, using a diffusion interface model instead of the traditional sharp interface to describe the interface. The order parameter is used to describe the phase state of matter. For example, when the order parameter is 0, it represents a liquid state, when it is 1, it represents a solid state, and when the order parameter is between 0 and 1, it represents a diffusion interface.

[0060] At present, the mainstream secondary battery in the market is mainly a rocking chair type lithium ion battery, that is, a rechargeable battery with both positive and negative electrodes made of ion intercalation materials. Compared with lithium batteries with metal lithium as the negative electrode, rocking chair type lithium ion batteries have better safety and cycle performance. However, theoretical calculations show that lithium metal batteries have a higher theoretical specific capacity (3860mAh g) than traditional graphite-based negative electrode lithium ion batteries. -1). However, the irregular deposition and dendrite growth problems of lithium ions during the electroplating process limit the specific capacity and cycle life of lithium metal batteries. The appearance and uncontrollable growth of dendrites may cause the dendrites to pierce the diaphragm and cause short circuit, resulting in battery failure. It may also cause side reactions and the shedding of lithium metal, thereby reducing the cycle efficiency, safety and stability of the battery. Through the phase field model, images such as the negative electrode dendrite growth morphology, target ion concentration distribution and target potential distribution at the continuum scale can be calculated. However, most of the existing phase fields are based on two-dimensional models, that is, the research object is simplified in two dimensions. In fact, phase field variables and variables such as concentration and potential are field variables in three-dimensional space. If these variables are placed on a two-dimensional model, one of the spatial dimensions will collapse. If handled improperly, it is easy to cause inconsistencies in the physical dimensions of the model, and the real situation cannot be restored well.

[0061] In view of this, an embodiment of the present invention provides a phase field simulation method, device and electronic device for three-dimensional dendrites. The scheme constructs an initial anisotropy parameter function, fits the parameters in the anisotropy parameter function, obtains the target anisotropy parameter function, and combines the target anisotropy parameter function to obtain the transient solution of the phase field variable equation, the transient solution of the target ion concentration equation and the transient solution of the target potential equation. Each equation is corrected so that the model can simulate dendrite growth or electrochemical deposition in three dimensions.

[0062] Figure 1 This is an optional flow chart of a three-dimensional dendrite phase field simulation method provided in an embodiment of the present application. Figure 1 The method may include but is not limited to steps S100 to S700.

[0063] Step S100, obtaining free energy density according to Gibbs free energy;

[0064] Step S200, obtaining an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation according to the free energy density;

[0065] Step S300, constructing an initial anisotropic parameter function, fitting the anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function;

[0066] Step S400, input initial conditions and boundary conditions;

[0067] Step S500, discretizing the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions;

[0068] Step S600, according to the target anisotropy parameter function, the initial condition and the boundary condition, obtaining the transient solution of the target phase field variable equation, the target ion concentration equation and the target potential equation, obtaining the target phase field variable distribution, the target ion concentration distribution and the target potential distribution;

[0069] Step S700, according to the target phase field variable distribution, the target ion concentration distribution and the target potential distribution, drawing an isosurface to obtain the morphology of the negative electrode surface or dendrite.

[0070] In step S100 of some embodiments, the volume integral of the free energy of each micro volume element in the system can obtain the Gibbs free energy of the system, and the Gibbs free energy can be used to well investigate the contribution of each part of energy to the free energy of the system. Then the Gibbs free energy formula is:

[0071] G = ∫ V fdV

[0072] Wherein, G represents the Gibbs free energy; f represents the free energy density of the system, corresponding to the free energy of each micro volume element; V represents the volume.

[0073] Specifically, the main variables studied in the phase field model include phase field variable, ion concentration and potential, etc., and other physical fields are added if there are other physical fields. Exemplarily, there are only two phases in the system, which contain negative electrode and electrolyte, and a order parameter is used to describe the distinction between solid phase (u=1) and liquid phase (u=0) and diffusion interface (0

[0074]

[0075] Wherein, the free energy density includes chemical free energy density, gradient energy density and electrostatic energy density. In the chemical free energy density, the double potential well function is used to ensure that the chemical free energy is minimum when the phase field variable is 1 and the phase field variable is 0, i.e. the chemical free energy is minimum when u=1 and u=0, and the expression of the double potential well function is: Wu 2 (1-u) 2 , wherein, u 2 (1-u) 2It describes the interface energy barrier. The energy barrier parameter is used to adjust the height of the energy barrier when the phase field variable is 0.5. When u = 0.5, W / 16 is the height of the energy barrier. In addition, the initial electrolyte concentration, cation concentration, and anion concentration are obtained to obtain the dilute solution mixing free energy density at the diffusion interface. The expression of the dilute solution mixing free energy density is: c0RT(c + lnc + +c - lnc - ). Then the expression of chemical free energy density is:

[0076]

[0077] The expression of gradient energy density is:

[0078]

[0079] The expression of electrostatic energy density is:

[0080]

[0081] Where G represents Gibbs free energy; V represents volume; f ch (u,c i ) represents the chemical free energy density; f grad (u) represents the gradient energy density; f elec (u,c i ,φ) represents the electrostatic energy density; u represents the phase field variable; c i represents the ion concentration of component i; φ represents the potential; W represents the energy barrier parameter; c0 represents the initial electrolyte concentration; R represents the gas constant; T represents the thermodynamic temperature; c + represents the cation concentration; c - represents the anion concentration; represents the free energy density under standard conditions; represents the reference chemical potential of component i under standard conditions; is the Del operator, k represents the anisotropy parameter, which characterizes the anisotropy of crystal growth; ρ e represents charge density; φ represents electric potential; F represents Faraday constant; Z i represents the number of ion charges; i represents the component.

[0082] refer to Figure 2 In some embodiments, step S200 may include but is not limited to steps S210 to S230:

[0083] Step S210, obtaining an initial phase field variable equation based on the phase field variable of the free energy density based on the Allen-Cahn equation;

[0084] Step S220, based on the Nernst-Planck equation, obtain an initial ion concentration equation according to the ion concentration of the free energy density;

[0085] Step S230, based on the Poisson equation, an initial potential equation is obtained according to the potential of the free energy density;

[0086] Specifically, for the order parameter, the Allen-Cahn equation of the two-phase system is introduced:

[0087]

[0088] According to the variational principle:

[0089]

[0090] The following expression is obtained:

[0091]

[0092] Therefore, the initial phase field variable equation in the two-phase system can be obtained as:

[0093]

[0094] Where u represents the phase field variable; t represents time; L represents the mobility of the two-phase interface, which is a phenomenological parameter; f represents the free energy density of the system; Represents the divergence symbol; stands for Laplace operator; L σ Parameter representing interfacial fluidity; L η Parameter representing the reaction rate; g′(u) is the derivative function of g(u), g(u)=Wu 2 (1-u) 2 , g(u) represents the double-well function; h′(u) is the derivative function of h(u), h(u) is the intermediate function; k represents the anisotropy parameter; α represents the charge transfer coefficient in the electrochemical reaction; n represents the number of exchange electrons in the electrochemical reaction; F represents the Faraday constant; η represents the overpotential; R represents the gas constant; T represents the thermodynamic temperature; c + represents the cation concentration.

[0095] The proportions of different phases are adjusted by the parameters of interface fluidity and reaction rate, and the mobility of the two-phase interface is a phenomenological parameter. In a system, the phenomenological parameters can be adjusted according to the results to make the model and simulation results consistent with the actual situation.

[0096] For the cation concentration in a two-phase system, the following Nernst-Planck equation is given:

[0097]

[0098] In the amphoteric system, the initial ion concentration equation is:

[0099]

[0100] Where M is the mobility parameter determined according to thermodynamics and diffusion kinetics; represents the Del operator; D eff represents the effective diffusion coefficient; φ represents the electric potential; c s represents the molar density of the negative electrode metal; c0 represents the initial electrolyte concentration, that is, the initial ion concentration.

[0101] For the electric potential, according to Poisson's equation, the initial electric potential equation is as follows:

[0102]

[0103] Where, σ eff represents the effective conductivity.

[0104] refer to Figure 3 In some embodiments, step S300 includes but is not limited to steps S310 to S340:

[0105] Step S310, obtaining crystal plane indices;

[0106] Step S320, placing the crystal plane corresponding to the crystal plane index in spherical coordinates to obtain an initial crystal surface energy function;

[0107] Step S330, fitting the initial crystal surface energy function to obtain a target crystal surface energy function;

[0108] Step S340, constructing an initial anisotropic parameter function, fitting the anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function;

[0109] Specifically, if Figure 4 As shown, two angles are introduced in the three-dimensional rectangular coordinate system These two angles are used to describe the normal direction at a certain point on the crystal interface, that is, the gradient Where θ represents the angle between the projection of the normal on the xOy plane and the x-axis. Represents the angle between the normal and the projection of the normal on the xOy plane. Then the initial anisotropy parameter function in the gradient energy can be constructed, and the expression of the initial anisotropy parameter function is:

[0110]

[0111] In the formula, k represents an anisotropy parameter; k0 represents an average gradient energy coefficient, which is related to the surface energy of the crystal; δ1 and δ2 represent corresponding anisotropy strengths; and ω1 and ω2 represent corresponding anisotropy mode numbers. In the gradient energy density, the anisotropy parameter adjusts the size of the gradient energy density as a coefficient, thereby adjusting the proportion of the gradient energy density in the free energy density of the system. The minimization of the gradient energy density is related to the surface energy of the crystal, while the chemical free energy density and the electrostatic energy density are related to the degree of electrochemical reaction.

[0112] It should be noted that the growth of dendrites has anisotropy, for example, lithium metal is a BCC structure, due to the difference in surface energy of each surface in the crystal structure, the binding energy of lithium ions on the crystal surface is different, and lithium ions are more likely to deposit on the surface with lower surface energy. In the phase field model of the negative electrode as lithium metal, ω1 and ω2 in k are both set to 4, that is, the tetrametric symmetry of lithium metal deposition can be investigated. Similarly, in the phase field model of metal cations in other types of batteries, ω1 and ω2 in k are both set to 4, which can investigate the tetrametric symmetry of the deposition of the metal cations. Exemplarily, as shown in Figure 5 , Figure 5 a lithium metal deposition model is illustrated, in which the anisotropy mode numbers ω1 = 4 and ω2 = 4 in a three-dimensional model are set. In this model, it is assumed that the crystal is deposited with lithium ions from a small circular protrusion at the bottom for a certain time. Since there is a smaller surface energy in the direction of the six corners of the octahedron, lithium ions in the electrolyte are more likely to deposit there, thereby simulating the anisotropy of metal deposition.

[0113] In addition, the parameters in the initial anisotropy parameter function are fitted according to the data of the crystal surface energy. Specifically, due to the difference in the crystal surface energy γ(h, k, l), the anisotropy parameter k in the gradient energy density affects the gradient energy size in each direction. According to the first-principle calculation, only the surface energy value of a specific crystal plane index can be obtained. According to the crystal surface energy corresponding to the crystal plane index, a table containing the crystal plane index and the corresponding crystal surface energy can be obtained. However, the surface energy data of different crystal planes in the table are discrete data points. Therefore, it is very difficult to calculate the crystal surface energy γ(h, k, l) in large quantities, where (h, k, l) represents the crystal plane index. Therefore, the crystal surface energy γ(h, k, l) is converted to By placing the crystal plane represented by the crystal plane index in the spherical coordinates, the normal of the crystal plane is obtained. At the same time, the initial crystal surface energy function about the normal is obtained. Exemplarily, the form of the initial crystal surface energy function also conforms to the form of the initial anisotropy parameter function. Therefore, the expression of the initial crystal surface energy function is:

[0114]

[0115] According to the crystal structure, ω1 and ω2 are determined, and then the discrete data points are substituted into the initial crystal surface energy function to fit the target crystal surface energy function According to the target crystal surface energy function, the anisotropy parameters in the phase field model are fitted in combination with δ1, δ2, ω1 and ω2 in the target crystal surface energy function, and the target anisotropy parameter function is constructed by comparison And adjust the gradient energy density f grad The parameters in (u) make the gradient energy density have a similar trend to the initial crystal surface energy function. As shown in Figure 6 , the image of the target anisotropy parameter function is shown. Figure 6

[0116] In step S400 of some embodiments, the input initial conditions include an initial phase field variable distribution, an initial ion concentration distribution and an initial electric potential distribution; the input boundary conditions include an ion source and a boundary voltage or an ion source and a current density.

[0117] In step S500 of some embodiments, the expressions of two angles are constructed:

[0118]

[0119]

[0120] Discretize the initial phase field variable equation to obtain the expansion form of the gradient operator in the initial phase field variable equation, and obtain the target phase field variable equations in the x-axis direction, the y-axis direction and the z-axis direction, wherein the target phase field variable equation in the x-axis direction is:

[0121]

[0122] The target phase field variable equation in the y-axis direction is:

[0123]

[0124] The target phase field variable equation in the z-axis direction is:

[0125]

[0126] In the formula, u x represents the partial derivative of the initial phase field variable in the x-axis direction, u y represents the partial derivative of the initial phase field variable in the y-axis direction, u z ​​represents the partial derivative of the initial phase field variable in the z-axis direction, Γ represents the subsequent term and the constant term.

[0127] In addition, the initial ion concentration equation is discretized to obtain the expanded form of the gradient operator in the initial ion concentration equation, and the target ion concentration equations in the x-axis direction, the y-axis direction, and the z-axis direction are obtained, wherein the target ion concentration equation in the x-axis direction is:

[0128]

[0129] The target ion concentration equation in the y-axis direction is:

[0130]

[0131] The target ion concentration equation in the z-axis direction is:

[0132]

[0133] The initial potential equation is discretized to obtain the expanded form of the gradient operator in the initial potential equation, and the target potential equations in the x-axis direction, the y-axis direction, and the z-axis direction are obtained. The target potential equation in the x-axis direction is:

[0134]

[0135] The target potential equation in the y-axis direction is:

[0136]

[0137] The target potential equation in the z-axis direction is:

[0138]

[0139] refer to Figure 7 After obtaining the initial state for a period of time, the transient solutions of the target phase field variable equation, the target ion concentration equation and the target potential equation can obtain the target phase field variable distribution, target ion concentration distribution and target potential distribution, and draw the isosurface to obtain the following: Figure 7 The morphology of the negative electrode surface and dendrites shown realizes the anisotropy of crystal growth from a three-dimensional perspective.

[0140] refer to Figure 8 The embodiment of the present invention further provides a three-dimensional dendrite phase field simulation device 800, which can implement the above-mentioned three-dimensional dendrite phase field simulation method, and the device includes:

[0141] The first module 801 is used to obtain free energy density based on Gibbs free energy;

[0142] The second module 802 is used to obtain an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation according to the free energy density;

[0143] The third module 803 is used to construct an initial anisotropic parameter function, and fit the anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function;

[0144] The fourth module 804 is used to input initial conditions and boundary conditions;

[0145] The fifth module 805 is used to discretize the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in multiple directions;

[0146] A sixth module 806 is configured to obtain a transient solution of the target phase field variable equation, the target ion concentration equation, and the target potential equation based on the target anisotropy parameter function, the initial condition, and the boundary condition, and obtain a target phase field variable distribution, a target ion concentration distribution, and a target potential distribution;

[0147] The seventh module 807 is used to draw an isosurface according to the target phase field variable distribution, the target ion concentration distribution and the target potential distribution to obtain the morphology of the negative electrode surface or dendrite.

[0148] An embodiment of the present invention also provides an electronic device, which includes a processor and a memory; the memory stores a program; the processor executes the program to execute the aforementioned phase field simulation method of a three-dimensional dendrite; the electronic device has the function of carrying and running the business data processing software system provided by an embodiment of the present invention, such as a personal computer (PC), a mobile phone, a smart phone, a personal digital assistant (PDA), a wearable device, a handheld computer PPC (Pocket PC), a tablet computer, a vehicle-mounted terminal, etc.

[0149] It can be understood that the contents of the above method embodiments are applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0150] refer to Figure 9 , Figure 9 The hardware structure of an electronic device according to another embodiment is shown. The electronic device includes:

[0151] The processor 901 can be implemented as a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application;

[0152] The memory 902 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 902 can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 902 and is called by the processor 901 to execute a three-dimensional dendrite phase field simulation method according to the embodiments of this application.

[0153] Input / output interface 903, used to implement information input and output;

[0154] Communication interface 904, used to implement communication interaction between this device and other devices, which can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WiFi, Bluetooth, etc.);

[0155] Bus 905 , which transmits information between various components of the device (e.g., processor 901 , memory 902 , input / output interface 903 , and communication interface 904 );

[0156] The processor 901 , the memory 902 , the input / output interface 903 and the communication interface 904 are connected to each other in communication within the device via a bus 905 .

[0157] An embodiment of the present invention further provides a computer-readable storage medium, wherein the storage medium stores a program, and the program is executed by a processor to implement the aforementioned phase-field simulation method of a three-dimensional dendrite.

[0158] It can be understood that the contents of the above method embodiments are all applicable to the present storage medium embodiment, the functions specifically implemented by the present storage medium embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0159] The embodiment of the present application further provides a computer program product or computer program, which comprises computer instructions stored in a computer readable storage medium. A processor of a computer device can read the computer instructions from the computer readable storage medium, and the processor executes the computer instructions to enable the computer device to perform the three-dimensional dendrite phase field simulation method.

[0160] In summary, the three-dimensional dendrite phase field simulation method, device and electronic equipment provided by the embodiment of the present application have the following advantages:

[0161] 1. The three-dimensional dendrite phase field simulation method, device and electronic equipment provided by the embodiment of the present application can reflect the anisotropy of crystal growth from the three-dimensional space, and avoid the problem that the dimensions may not be consistent.

[0162] 2. In the embodiment of the present application, the anisotropy parameter of the gradient energy is fitted with reference to the crystal surface energy, the normal of the negative surface is represented by a pair of angles, and the angle is easy to calculate, which facilitates the simplification and solution of the phase field model.

[0163] In some alternative embodiments, the functions / operations mentioned in the block diagram can not occur in the order mentioned in the operation diagram. For example, depending on the functions / operations involved, two blocks shown in succession can actually be executed substantially simultaneously or the blocks can sometimes be executed in reverse order. In addition, the embodiments presented and described in the flowcharts of the present application are provided by way of example, and the purpose is to provide a more comprehensive understanding of the technology. The disclosed method is not limited to the operations and logical flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and in which sub-operations described as part of larger operations are independently executed.

[0164] In addition, although the present application is described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the functions and / or features described can be integrated in a single physical device and / or software module, or one or more functions and / or features can be implemented in separate physical devices or software modules. It can also be understood that a detailed discussion of the actual implementation of each module is unnecessary for an understanding of the present application. Rather, given the properties, functions and internal relationships of the various functional modules in the devices disclosed herein, the actual implementation of the module will be within the routine skill of the engineer, given the present disclosure. Therefore, those skilled in the art can implement the present application as set forth in the claims using ordinary skill and without undue experimentation. It can also be understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present application, which is defined by the full scope of the appended claims and their equivalents.

[0165] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0166] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0167] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0168] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0169] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0170] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

[0171] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A phase field simulation method for three-dimensional dendrites, characterized in that: include: Based on Gibbs free energy, obtain the free energy density; According to the free energy density, an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation are obtained; constructing an initial anisotropic parameter function, and fitting anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function; Enter initial conditions and boundary conditions; Discretizing the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions; According to the target anisotropy parameter function, the initial conditions, and the boundary conditions, a transient solution of the target phase field variable equation, the target ion concentration equation, and the target potential equation is obtained to obtain a target phase field variable distribution, a target ion concentration distribution, and a target potential distribution; Drawing isosurfaces according to the target phase field variable distribution, the target ion concentration distribution, and the target potential distribution to obtain the morphology of the negative electrode surface or dendrite; Wherein, obtaining the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation according to the free energy density includes: Based on the Allen-Cahn equation, an initial phase field variable equation is obtained according to the phase field variable of the free energy density; Based on the Nernst-Planck equation, an initial ion concentration equation is obtained according to the ion concentration of the free energy density; Based on the Poisson equation, an initial potential equation is obtained according to the potential of the free energy density; The expression of the initial anisotropy parameter function is: ； in, represents the anisotropy parameter; represents the average gradient energy coefficient; 、 represents the corresponding anisotropy strength; 、 represents the corresponding anisotropic mode number; Represents the projection of the normal on the plane and The angle between the axes; Represents the angle between the normal and the projection of the normal on the plane; The constructing of the initial anisotropic parameter function and fitting the anisotropic parameters in the initial anisotropic parameter function to obtain the target anisotropic parameter function includes: Get crystal plane index; Place the crystal plane corresponding to the crystal plane index in spherical coordinates to obtain the initial crystal surface energy function; Fitting the initial crystal surface energy function to obtain a target crystal surface energy function; According to the target crystal surface energy function, the anisotropy parameters in the initial anisotropy parameter function are fitted to construct a target anisotropy parameter function.

2. The phase field simulation method of three-dimensional dendrite according to claim 1, characterized in that: The free energy density includes chemical free energy density, gradient energy density and electrostatic energy density. The expression of Gibbs free energy is: ； in, represents Gibbs free energy; Represents volume; represents the chemical free energy density; represents the gradient energy density; represents the electrostatic energy density; represents the phase field variable; Representative groups are ion concentration; Represents electric potential.

3. The phase field simulation method of three-dimensional dendrite according to claim 2, characterized in that: The expression of the chemical free energy density is: ； The expression of the gradient energy density is: ； The expression of the electrostatic energy density is: ； in, represents the chemical free energy density; represents the gradient energy density; represents the electrostatic energy density; represents the phase field variable; Representative groups are ion concentration; represents electric potential; represents the energy barrier parameter; represents the initial electrolyte concentration; represents the gas constant; represents thermodynamic temperature; represents the cation concentration; represents the anion concentration; represents the free energy density under standard conditions; Representative standard conditions The reference chemical potential of is the Del operator; represents the anisotropy parameter; represents the charge density; represents the Faraday constant; Represents the amount of ion charge; Representative components.

4. A three-dimensional dendrite phase field simulation device, characterized in that: include: The first module is used to obtain the free energy density based on Gibbs free energy; The second module is used to obtain an initial phase field variable equation, an initial ion concentration equation, and an initial potential equation according to the free energy density; The third module is used to construct an initial anisotropic parameter function, and fit the anisotropic parameters in the initial anisotropic parameter function to obtain a target anisotropic parameter function; The fourth module is used to input initial conditions and boundary conditions; A fifth module is used to discretize the initial phase field variable equation, the initial ion concentration equation, and the initial potential equation to obtain target phase field variable equations, target ion concentration equations, and target potential equations in several directions; A sixth module is used to obtain the transient solution of the target phase field variable equation, the target ion concentration equation and the target potential equation according to the target anisotropy parameter function, the initial condition and the boundary condition, and obtain the target phase field variable distribution, the target ion concentration distribution and the target potential distribution; A seventh module is used to draw an isosurface based on the target phase field variable distribution, the target ion concentration distribution, and the target potential distribution to obtain the morphology of the negative electrode surface or dendrite; The second module is specifically used for: Based on the Allen-Cahn equation, an initial phase field variable equation is obtained according to the phase field variable of the free energy density; Based on the Nernst-Planck equation, an initial ion concentration equation is obtained according to the ion concentration of the free energy density; Based on the Poisson equation, an initial potential equation is obtained according to the potential of the free energy density; The expression of the initial anisotropy parameter function is: ； in, represents the anisotropy parameter; represents the average gradient energy coefficient; 、 represents the corresponding anisotropy strength; 、 represents the corresponding anisotropic mode number; Represents the projection of the normal on the plane and The angle between the axes; Represents the angle between the normal and the projection of the normal on the plane; The third module is specifically used for: Get crystal plane index; Place the crystal plane corresponding to the crystal plane index in spherical coordinates to obtain the initial crystal surface energy function; Fitting the initial crystal surface energy function to obtain a target crystal surface energy function; According to the target crystal surface energy function, the anisotropy parameters in the initial anisotropy parameter function are fitted to construct a target anisotropy parameter function.

5. An electronic device, characterized in that: including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that The storage medium stores a program, and the program is executed by a processor to implement the method according to any one of claims 1 to 3.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 3 is implemented.

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