Method and system for predicting cycle performance of all-solid-state lithium metal battery

Abstract

The invention belongs to the related technical field of all-solid-state lithium metal batteries, and discloses an all-solid-state lithium metal battery cycle performance prediction method and system, and the method comprises the steps: building an electrochemical mechanical coupling polycrystalline phase field model according to the Helmholtz free energy evolution of dendrites; wherein grain boundary phase field parameters and dendritic phase field parameters are introduced into the polycrystalline phase field model to distinguish a three-phase system; deducing a lithium diffusion control equation, an electrostatic potential distribution equation and a stress balance equation; randomly generating a polycrystalline solid electrolyte by adopting a Voronoi algorithm; performing simulation solution on the polycrystalline phase field model by using finite element analysis software; and predicting the cycle performance of the all-solid-state lithium metal battery according to a simulation result. According to the invention, deep systematic research on the growth and stripping mechanism of the lithium dendrites in the solid-state battery can be realized, so that the cycle performance of the battery can be predicted based on the lithium dendrites, and targeted regulation and improvement are facilitated to improve the performance of the battery.

Description

Technical Field

[0001] The present invention belongs to the technical field related to all-solid-state lithium metal batteries, and more specifically, relates to a method and system for predicting the cycling performance of all-solid-state lithium metal batteries. Background Art

[0002] All-solid-state lithium metal batteries (ASSLMBs) have attracted much attention due to their high energy density and good safety. As a negative electrode material, metallic lithium has the potential to break through the energy density limit of traditional lithium-ion batteries. However, it faces many problems in practical applications.

[0003] When used in liquid electrolytes, lithium metal is prone to generate lithium dendrites and may also form a solid electrolyte interface, which will reduce the Coulombic efficiency of the battery, shorten the cycle life, and even cause short circuits, bringing safety risks. In all-solid-state batteries, although solid electrolytes (SEs) can block the propagation of lithium dendrites to a certain extent, there are still problems such as irregular lithium deposition and the generation of inactive lithium due to repeated plating / stripping, resulting in poor actual cycling performance of the battery.

[0004] Early studies found that lithium filaments often appear at microstructural defects, especially at grain boundaries (GBs), indicating that the microstructure has a significant impact on lithium penetration behavior. There are currently two hypotheses about the reason for the preferential penetration of dendrites along grain boundaries: one is that the mechanical and transport properties of grain boundaries are special, resulting in different local electrochemical mechanical responses between dendrites and solid electrolytes, leading to non-uniform lithium deposition; the other is that grain boundaries capture excess electrons in the electroplating electrode, causing lithium ions at grain boundaries to reach the reduction overpotential earlier, and even promoting the nucleation of dendrites inside the electrolyte, and then the propagation and growth of dendrites are dominated by the mechanical properties of SE. However, the fundamental mechanism of various failure modes induced by grain boundaries in inorganic solid electrolytes is currently not well understood.

[0005] To solve these problems, the existing methods are mainly divided into two categories. One category is to change the material properties, such as controlling the grain size, coating a nano-layer on the grain surface, introducing specific substances to construct special grain boundaries, etc., to improve the mechanical and electrochemical properties of the material. The other category is to regulate the operating conditions, such as charging with pulsed current, reasonably regulating the stacking pressure and working temperature, etc., to improve the cycling performance of the battery.

[0006] However, the existing technologies have obvious deficiencies: 1. There is a lack of in-depth understanding of how stacking pressure and working temperature affect the growth and stripping mechanisms of lithium dendrites, especially in polycrystalline solid electrolytes, and the specific reasons for the growth of lithium dendrites along grain boundaries have not been clarified. 2. Most existing studies obtain the complex interactions among factors such as stress, contact, reaction, diffusion, and current density during the electroplating and stripping processes through experimental observation of macroscopic variables or interface morphology changes, lacking systematic research. 3. In terms of theoretical calculations, although the phase field method is used to study the mechanism of lithium metal anodes, most current theoretical calculations focus on the interface evolution and surface flatness during the electroplating process and mainly concentrate on the field of liquid lithium batteries, with less simulation research on the formation mechanism of non-active lithium in solid-state batteries.

[0007] Therefore, there is an urgent need for a method to systematically study the growth and stripping mechanisms of lithium dendrites in all-solid-state lithium metal batteries to improve the performance and safety of the batteries. Summary of the Invention

[0008] In view of the above deficiencies or improvement requirements of the existing technologies, the present invention provides a method and system for predicting the cycling performance of all-solid-state lithium metal batteries, which are used to solve the problem that the existing technologies lack research methods for the growth and stripping mechanisms of lithium dendrites in solid-state batteries, thereby restricting the improvement of battery performance.

[0009] To achieve the above object, according to one aspect of the present invention, a method for predicting the cycling performance of all-solid-state lithium metal batteries is provided, including:

[0010] Constructing an electrochemomechanical coupled polycrystalline phase field model based on the evolution of the Helmholtz free energy of dendrites, wherein grain boundary phase field parameters and dendrite phase field parameters are introduced in the polycrystalline phase field model to distinguish the three-phase system of metallic lithium phase, grain boundary phase, and grain phase;

[0011] Comprehensively deriving a lithium diffusion control equation, an electrostatic potential distribution equation, and a stress balance equation according to the change of the chemical potential energy of the lithium system;

[0012] Randomly generating a polycrystalline solid electrolyte by using the Voronoi algorithm, with a lithium metal block arranged at the bottom of the polycrystalline solid electrolyte, and the polycrystalline solid electrolyte and the lithium metal block form a calculation region, and boundary conditions and working temperature parameters are set for the calculation region;

[0013] Inputting the polycrystalline phase field model, the lithium diffusion control equation, the electrostatic potential distribution equation, and the stress balance equation into finite element analysis software, and using the finite element analysis software to perform simulation and solution on the polycrystalline phase field model of the calculation region; predicting the cycling performance of the all-solid-state lithium metal battery according to the simulation results.

[0014] According to the method for predicting the cycling performance of all-solid-state lithium metal batteries provided by the present invention, the grain boundary phase field parameter is The dendritic phase field parameter is ξ. In the three-phase system, the metallic lithium phase has ξ = 1. The grain boundary phase has ξ = 0. The grain phase has ξ = 0. ξ and The value ranges are from 0 to 1 respectively. The polycrystalline phase field model specifically includes:

[0015]

[0016] where t is time. represents the evolution of the grain boundary with time. is the interface mobility, and Ψ is the total Helmholtz free energy of the system.

[0017]

[0018] L σ = h(ξ)L σ,Li +(1 - g(ξ))L σ,SE ;

[0019] where, represents the evolution of the dendrite with time; L σ represents the interface mobility; h(·) represents the interpolation function; L σ,Li is the interface mobility of lithium; L σ,SE is the interface mobility of the solid electrolyte; h′(ξ) is the derivative of h(ξ); M η is the rate constant; i BV is the current density calculated by the Butler - Volmer formula. is the convection term; u is the velocity field of the deformation. Among them, the stress - corrected Butler - Volmer formula is adopted.

[0020] According to the all - solid - state lithium - metal battery cycle performance prediction method provided by the present invention, the electroplating phase field equation finally obtained by the polycrystalline phase field model is:

[0021]

[0022] where W is the barrier height; g(ξ) is the double - well function; k is the gradient coefficient; is the Hamiltonian operator; is the angle between the reference axis and the surface migration normal, where ξ′ x and ξ′ y are the partial derivatives of the dendrite ξ with respect to the coordinate axes x and y respectively; L η = M η i0 is affected by temperature during the cycle; i0 is the exchange current density; a Li is the lithium metal activity. is the lithium ion activity in the solid electrolyte; F is the Faraday constant, R is the universal gas constant, and T is the temperature; α is the symmetry coefficient of the electrochemical reaction (0 < α < 1); where c Li is the lithium metal concentration; is the bulk concentration of lithium metal; is the lithium ion concentration in the solid electrolyte; is the lithium ion site density in the solid electrolyte;

[0023] The stripping phase field equation is:

[0024]

[0025] where: is a variable that determines the electronic activity state of local metallic lithium; is a variable that determines the ionic activity state of local metallic lithium; f step is a step function from 1 to 0, φ Li is the lithium metal potential, φ bulk is the reference potential; x Li is the interface position of the lithium metal, x bulk is the reference initial position; where, the non-ideality of the electrochemical reaction is introduced into the interfacial reaction kinetics, and the activity coefficient is modified to

[0026] According to the all-solid-state lithium metal battery cycle performance prediction method provided by the present invention, the lithium diffusion control equation is:

[0027]

[0028] where, μ Li is the chemical potential of lithium atoms; D eff is the effective diffusion coefficient of lithium ions; is the bulk concentration of lithium metal; is the lithium ion site density in the solid electrolyte; is the standard chemical potential of lithium; is the standard chemical potential of lithium ions in the solid electrolyte; D Li 、D GB and D G are the diffusion coefficients of lithium ions in metallic lithium, grain boundaries, and grains, respectively;

[0029] The electrostatic potential distribution equation is described by the Poisson equation, specifically:

[0030]

[0031] where, σ eff is the effective conductivity, σ Li, σ GB and σ G are the electrical conductivities of metallic lithium, grain boundaries, and within grains, respectively, and φ is the electric potential distribution in the system;

[0032] The stress balance equation is specifically:

[0033]

[0034] ε el = ε - ε0 - ε th ;

[0035]

[0036] where C eff is the effective elastic stiffness tensor, C Li is the stiffness tensor of lithium metal, C GB is the stiffness tensor of the grain boundaries of the solid electrolyte, C G is the stiffness tensor of the grains of the solid electrolyte, and C0 is the stiffness tensor at the voids to ensure the calculation; ε el is the elastic strain, ε is the total strain; ε0 = λ ii ξ is the inelastic strain generated due to the volume expansion of lithium metal during lithium deposition, and λ ii is a constant diagonal matrix; ε th = α SE (T - T0) is the thermal expansion of the electrolyte caused by the temperature increase, α SE is the thermal expansion coefficient, T is the operating temperature, and T0 = 293K is the reference temperature.

[0037] According to the method for predicting the cycling performance of an all-solid-state lithium metal battery provided by the present invention, in the polycrystalline phase field model, the lithium diffusion control equation, the electrostatic potential distribution equation, and the stress balance equation, the Arrhenius equation is used to quantify the temperature-sensitive parameters.

[0038] According to the method for predicting the cycling performance of an all-solid-state lithium metal battery provided by the present invention, the quantification of the temperature-sensitive parameters using the Arrhenius equation is specifically as follows:

[0039]

[0040] where X T represents the value of the temperature-sensitive parameter at temperature T, X0 represents the value of the temperature-sensitive parameter at the reference temperature T0, E a,X is the activation barrier related to the parameter X T , and k B is the Boltzmann constant.

[0041] According to the method for predicting the cycling performance of an all-solid-state lithium metal battery provided by the present invention, setting boundary conditions for the calculation region specifically includes:

[0042] For the concentration field and the electric potential field, Dirichlet boundary conditions are adopted, specifically setting fixed values on the upper and lower boundaries, and zero flux on the left and right boundaries;

[0043] In the mechanical field, the upper boundary is set to be fixed, the left and right boundaries are supported by rollers, and pressure is applied to the lower boundary.

[0044] According to the method for predicting the cycling performance of an all-solid-state lithium metal battery provided by the present invention, predicting the cycling performance of the all-solid-state lithium metal battery based on the simulation results specifically includes:

[0045] Obtaining the dendrite height and the battery capacity loss from the simulation results, and quantifying the short-circuit risk through the normalized dendrite height;

[0046] Predicting the cycling performance of the battery based on the short-circuit risk and the battery capacity loss;

[0047] Among them, the short-circuit risk is quantified by the normalized dendrite height H, and its formula is as follows:

[0048]

[0049] where h max is the farthest distance from the dendrite tip to the initial cathode surface under the corresponding working conditions, and h0 is the farthest growth distance of the dendrite under the ideal uniform deposition state;

[0050] The battery capacity loss ω l , and its formula is as follows:

[0051]

[0052] where Q loss is the remaining dead lithium capacity after the stripping ends; Q total is the plating capacity.

[0053] According to the method for predicting the cycling performance of an all-solid-state lithium metal battery provided by the present invention, it further includes:

[0054] Establishing an optimization model with the best cycling performance of the battery as the goal; by changing the pressure and working temperature in the boundary conditions, performing multiple simulation solutions to determine the optimal pressure and working temperature control strategies.

[0055] According to another aspect of the present invention, there is provided a system for predicting the cycling performance of an all-solid-state lithium metal battery. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the method for predicting the cycling performance of an all-solid-state lithium metal battery described in any one of the above.

[0056] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the method and system for predicting the cycle performance of an all-solid-state lithium metal battery provided by the present invention are as follows:

[0057] 1. A multi-crystalline phase field model of electrochemomechanical coupling is proposed based on the evolution of Helmholtz free energy, which can establish the evolution process of phase field parameters over time, thereby realizing the simulation of dendrite evolution. The introduction of grain boundary phase field parameters and dendrite phase field parameters in the model can better distinguish the three-phase system of metallic lithium phase, grain boundary phase, and grain phase, improving the simulation accuracy; through the finite element analysis of the multi-crystalline phase field model, an in-depth systematic study of the growth and stripping mechanisms of lithium dendrites in solid-state batteries can be achieved, so that the cycle performance of the battery can be predicted based on lithium dendrites, and it is beneficial to carry out targeted regulation and improvement to enhance the battery performance;

[0058] 2. The constructed electrochemomechanical phase field model comprehensively considers the interaction of multiple factors, can study the growth and stripping mechanisms of lithium dendrites more comprehensively and deeply, and makes up for the deficiencies of the prior art; through this model, the influence of external pressure and working temperature on the lithium deposition morphology is studied, and the coupling relationship between temperature and pressure parameters and electrochemical overpotential is realized, providing a theoretical basis for optimizing the battery stacking pressure and working temperature;

[0059] 3. By introducing the Arrhenius equation of temperature-sensitive parameters, the regulation mechanism of temperature on ion transport and interface kinetics is revealed, providing scientific guidance for formulating the battery working temperature strategy;

[0060] 4. An interface failure criterion based on grain boundary orientation is proposed, which can accurately predict the penetration path of lithium dendrites in polycrystalline electrolytes, providing a new idea for the microstructure design of solid electrolytes;

[0061] 5. The simulation results are highly consistent with the experimental data, verifying the reliability of the model and significantly reducing the trial-and-error cost in the research and development of all-solid-state batteries. Description of the Drawings

[0062] Figure 1 is the flowchart of the method for predicting the cycle performance of an all-solid-state lithium metal battery provided by an embodiment of the present invention;

[0063] Figure 2 is the schematic diagram of the model construction principle in the method for predicting the cycle performance of an all-solid-state lithium metal battery provided by an embodiment of the present invention;

[0064] Figure 3 is the schematic diagram of the geometric structure, boundary conditions, and initial value settings in the method for predicting the cycle performance of an all-solid-state lithium metal battery provided by an embodiment of the present invention;

[0065] Figure 4It is the effect diagram calculated in the full-solid-state lithium-metal battery cycle performance prediction method provided by the embodiments of the present invention;

[0066] Figure 5 It is the contour map of the normalized dendrite height varying with pressure and temperature calculated in the full-solid-state lithium-metal battery cycle performance prediction method provided by the embodiments of the present invention;

[0067] Figure 6 It is the contour map of the battery capacity loss rate varying with pressure and temperature calculated in the full-solid-state lithium-metal battery cycle performance prediction method provided by the embodiments of the present invention. Detailed implementation manners

[0068] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0069] Please refer to Figure 1 and Figure 2 This embodiment provides a full-solid-state lithium-metal battery cycle performance prediction method, and the full-solid-state lithium-metal battery cycle performance prediction method includes:

[0070] Construct an electrochemomechanical coupled polycrystalline phase field model based on the evolution of the Helmholtz free energy of dendrites, wherein grain boundary phase field parameters and dendrite phase field parameters are introduced in the polycrystalline phase field model to distinguish the three-phase system of metallic lithium phase, grain boundary phase and grain phase;

[0071] Comprehensively derive the lithium diffusion control equation, the electrostatic potential distribution equation and the stress balance equation according to the change of the chemical potential energy of the lithium system;

[0072] Randomly generate a polycrystalline solid electrolyte by using the Voronoi algorithm, a lithium metal block is arranged at the bottom of the polycrystalline solid electrolyte, the polycrystalline solid electrolyte and the lithium metal block form a calculation region, and boundary conditions and working temperature parameters are set for the calculation region;

[0073] Input the polycrystalline phase field model, the lithium diffusion control equation, the electrostatic potential distribution equation and the stress balance equation into finite element analysis software, and use the finite element analysis software to perform simulation and solution on the polycrystalline phase field model of the calculation region; predict the cycle performance of the full-solid-state lithium-metal battery according to the simulation results.

[0074] Specifically, since the SE contains microstructures such as grain boundaries, in order to distinguish grain boundaries and bulk-phase grains (GB) in the SE phase, a non-conserved grain boundary phase field parameter It is 1 at the grain boundary and 0 in the bulk phase. At the same time, the dendritic phase field parameter ξ is introduced to distinguish the three-phase system. At this time: the metallic lithium phase (ξ = 1, ), the grain boundary phase (ξ = 0, ), and the grain phase (ξ = 0, ). The value ranges of these two parameters are both from 0 to 1. The calculation formula for the total Helmholtz free energy Ψ of the system is:

[0075] Ψ = ∫ V [f init + f chem + f elec + f els dV;

[0076] Among them, f init , f chem , f elec , f els are the interfacial energy, chemical energy, electric potential energy, and elastic strain energy of the system respectively; V represents the system volume. The specific expressions are as follows:

[0077] is the interfacial energy of the system; where g(ξ) = Wξ 2 (1 - ξ) 2 is the double-well function; where W = h(ξ)W Li + (1 - h(ξ))W SE is the potential barrier height, W Li and W SE are the potential barrier heights of the lithium phase and the solid electrolyte phase respectively; represents the gradient energy at the interface; k = k0[1 + δcos(ωθ)], k0 = h(ξ)k Li + (1 - h(ξ))k SE is the gradient coefficient. k Li and k SE are the gradient coefficients of the lithium phase and the solid electrolyte phase respectively. The current model assumes that the solid electrolyte has isotropic properties. Therefore, k Li and k SE take constant values. This equation describes the relationship between the gradient energy and the gradient of the dendritic phase field parameter ξ. δ is the anisotropy strength, and ω is the crystallographic symmetry mode (ω = 4 for body-centered cubic lithium metal). is the angle between the reference axis and the surface migration normal, where ξ′ x and ξ′ y are the partial derivatives of the dendrite ξ with respect to the coordinate axes x and y respectively.

[0078] is the chemical energy of the system. The concentration set c i summarizes the species in the system (i = Li +, the concentration of Li and the anion). is the reference chemical potential of component i, is the bulk concentration of lithium metal, is the lithium ion site density in the solid electrolyte, R is the universal gas constant, and T is the temperature. This equation reflects the relationship between chemical energy and the concentrations, chemical potentials, and temperature of each component.

[0079] is the electric potential energy of the system, where z i is the chemical valence state of the species, F is the Faraday constant, and c i is the concentration of the substance, (i = Li and e, corresponding to the Li metal electrode and the electrolyte respectively) represents the local electrostatic potential.

[0080] f els (ξ, u) = 0.5σ el ∶ε e is the elastic strain energy of the system, where σ el is the elastic stress tensor, and ε e is the elastic strain tensor. u represents the velocity field.

[0081] The polycrystalline phase field model, that is, the nonlinear phase field models for dendrites and grain boundaries determining the evolution of the electrode - polycrystalline electrolyte interface from the change in Helmholtz free energy are respectively:

[0082]

[0083] where t is time, represents the evolution of the grain boundary over time, is the interface mobility, and Ψ is the total Helmholtz free energy of the system.

[0084]

[0085] L σ = h(ξ)L σ,Li +(1 - h(ξ))L σ,SE ;

[0086] where, represents the evolution of the dendrite over time; L σ represents the interface mobility, reflecting the ease of movement of the interface under external action; h(·) represents the interpolation function; L σ,Li is the interface mobility of lithium; L σ,SE is the interface mobility of the solid electrolyte; h′(ξ) is the derivative of h(ξ), and its function is to limit the electrochemical reaction to the electrode / electrolyte interface; M η is the rate constant, affecting the rate of the electrochemical reaction; i BVis the current density calculated by the Butler-Volmer formula; is the convection term to describe the phase evolution driven by mechanical deformation; u is the velocity field of the deformation; among them, considering the mechanical stress effect, the stress-corrected Butler-Volmer formula is:

[0087]

[0088] Among them, is the exchange current density. k a and k c are the rate constants of the anodic reaction and the cathodic reaction respectively. F is the Faraday constant, R is the universal gas constant, T is the temperature, a Li is the lithium metal activity, is the lithium ion activity in the solid electrolyte. α is the symmetry coefficient of the electrochemical reaction (0 < α < 1). is the overpotential on the deformed surface;

[0089] Among them, η a is the activation overpotential, introducing η m = CP h V m is the mechanical overpotential, where V m is the molar volume of lithium metal, P h is the hydrostatic stress, P h > 0 indicates compression, P h < 0 indicates tension, C is the correction term. Among them, φ L i is the electrode potential, φ e is the solid electrolyte potential, is the standard half-cell potential. When η = 0, the net reaction rate is 0; when η < 0, the cathodic reaction is dominant, and the electroplating process occurs, Li + + e - → Li; when η > 0, the anodic reaction is dominant, and the stripping process occurs, Li - e - → Li + .

[0090] Furthermore, through the scaling of the grain boundary phase field parameter , the properties of the SE smoothly change from the properties of the bulk grains to the properties of the GB at the interface. The above formula can be written as:

[0091]

[0092] Among them, for the sake of simplifying the calculation, the grain boundary phase field parameter only plays a role of identification and does not evolve with time.

[0093] The electroplating phase field equation finally obtained by the polycrystalline phase field model is:

[0094]

[0095] Wherein, W is the barrier height; g(ξ) is the double-well function; k is the gradient coefficient; is the Hamiltonian operator; is the angle between the reference axis and the normal of the surface migration, where ξ′ x and ξ′ y are the partial derivatives of the dendrite ξ with respect to the coordinate axes x and y respectively; L η = M η i0 is affected by temperature during the cycle; i0 is the exchange current density; a Li is the lithium metal activity, is the lithium ion activity in the solid electrolyte; F is the Faraday constant, R is the universal gas constant, T is the temperature; α is the symmetry coefficient of the electrochemical reaction (0 < α < 1); wherein c Li is the lithium metal concentration; is the bulk concentration of the lithium metal; is the lithium ion concentration in the solid electrolyte; is the lithium ion site density in the solid electrolyte;

[0096] The stripping phase field equation is:

[0097]

[0098] Wherein: is a variable for determining the electronic active state of local metallic lithium; f Li+ = f step (x Li - x bulk ) is a variable for determining the ionic active state of local metallic lithium; f step is a step function from 1 to 0, φ Li is the lithium metal potential, φ bulk is the reference potential; x Li is the interface position of the lithium metal, x bulk is the reference initial position;

[0099] When the local lithium metal is separated from the lithium block, the electronic path is disconnected, and the local lithium metal no longer participates in subsequent reactions, φ Li decreases, will change from 1 to 0, that is, dead lithium is formed. Otherwise, it remains 1, indicating the active Li state. Different from the liquid battery, when the solid battery is stripped, holes separated from the electrolyte will be formed at the interface. At this time, the ionic path is disconnected, and the local lithium metal no longer undergoes an electrochemical reaction, x Li decreases, will change from 1 to 0, and the electrochemical reaction term will disappear. In addition, due to the dissolution of lithium metal, a high local concentration will form at the interface, especially at high stripping rates. Therefore, the non-ideality of the electrochemical reaction is introduced into the interfacial reaction kinetics, and the activity coefficient is modified to

[0100] Referring to Figure 2 , the polycrystalline phase field model proposed in this embodiment introduces grain boundary and dendrite phase field parameters to distinguish the three-phase system, and at the same time uses the interpolation function h(x) to consider the mobility L of the lithium electrode and solid electrolyte interface σ , the difference in the energy barrier height W and the gradient coefficient k, establish the electrode-polycrystalline electrolyte interface evolution equation and the related equation considering mechanical stress, and by introducing and two step functions are used to judge the formation of dead lithium due to the disconnection of the electronic path and ion path during the stripping process. By modifying the situation where the concentration at the interface does not satisfy the infinite dilution solution assumption during the stripping process is comprehensively considered.

[0101] In some specific embodiments, the specific derivation process of the lithium diffusion control equation is as follows:

[0102] According to the concentration c of lithium atoms in the sediment Li , and the concentration of lithium ions in the solid electrolyte the concentration c of lithium species at the interface Li can be regarded as an interpolation of c Li and :

[0103]

[0104] Following the KKS model, assuming that the chemical potentials of lithium atoms and lithium ions are equal, that is μ Li is the chemical potential of lithium atoms, and the expressions of c Li and can be obtained:

[0105]

[0106] Among them, is the site density of lithium metal, is the bulk concentration of lithium ions in LLZO. is the standard chemical potential of lithium, is the standard chemical potential of lithium ions in the solid electrolyte.

[0107] Since the electrochemical reaction consumes lithium ions and generates lithium atoms at the lithium-solid electrolyte interface, resulting in the conservation of lithium species (ions and atoms), the diffusion equation of lithium species is obtained:

[0108]

[0109] Substituting the above relevant formulas, the lithium diffusion control equation in the system is obtained as follows:

[0110]

[0111] where μ Li is the chemical potential of lithium atoms; D eff is the effective diffusion coefficient of lithium ions; is the bulk concentration of lithium metal; is the lithium ion site density in the solid electrolyte; is the standard chemical potential of lithium; is the standard chemical potential of lithium ions in the solid electrolyte; D Li 、D GB and D G are the diffusion coefficients of lithium ions in metallic lithium, grain boundaries, and grains, respectively.

[0112] The electrostatic potential distribution equation is described by the Poisson equation, and the electrostatic potential is controlled by the Poisson equation. Its distribution is described by the Poisson equation with a source term:

[0113]

[0114] where σ eff is the effective conductivity, and σ Li 、σ GB and σ G are the conductivities of metallic lithium, grain boundaries, and grains, respectively, is the potential distribution in the system.

[0115] The stress balance equation is specifically as follows: During lithium deposition, mechanical stress is generated due to the volume change of the lithium metal negative electrode. For simplicity in calculation, the following assumptions are made: Plastic deformation is not considered; Contact mechanics is not considered, and it is assumed that the lithium electrolyte interface is a perfect contact; It is considered that the inelastic strain caused by the volume expansion of lithium metal is the only source of the evolution of internal stress.

[0116] By solving the stress balance, the Li stress distribution at the interface is obtained, and its expression is:

[0117]

[0118] ε el =ε - ε0 - ε th ;

[0119]

[0120] where C effis the effective elastic stiffness tensor, C Li is the stiffness tensor of lithium metal, C GB is the stiffness tensor of the solid electrolyte grain boundary, C G is the stiffness tensor of the solid electrolyte grain, and C0 is the stiffness tensor at the void to ensure the operation; ε el is the elastic strain, ε is the total strain (assuming small deformation theory); ε0 = λ ii ξ is the inelastic strain generated due to the volume expansion of lithium metal during lithium deposition, λ ii is a constant diagonal matrix; ε th = α SE (T - T0) is the thermal expansion of the electrolyte caused by the temperature rise (neglecting the thermal expansion of lithium metal because the stress is released due to the creep of lithium metal during heating), α SE is the coefficient of thermal expansion, T is the operating temperature, and T0 = 293K is the reference temperature. The elastic strain includes the volume expansion and thermal expansion effects.

[0121] Furthermore, it is proposed to couple the temperature with the ion diffusion coefficient and the reaction constant, quantify the temperature-sensitive parameters using the Arrhenius equation, and consider the thermal expansion, which can better simulate the influence of temperature on the growth and stripping of lithium dendrites. The temperature distribution inside the battery is affected by the external environment and its heat generation and heat dissipation conditions. Since the volume of the simulated geometric region is small, it is assumed that the operating temperature is uniformly distributed within the simulation range, and the influence of the temperature gradient is neglected.

[0122] Temperature significantly affects the formation and growth of lithium dendrites by influencing ion transport and reaction kinetics. To couple the thermal effect, while considering the thermal expansion, in the polycrystalline phase field model, lithium diffusion control equation, electrostatic potential distribution equation, and stress balance equation, the Arrhenius equation is used to quantify the temperature-sensitive parameters.

[0123] Quantifying the temperature-sensitive parameters using the Arrhenius equation is specifically as follows:

[0124]

[0125] where, X T represents the value of the temperature-sensitive parameter (such as the lithium ion diffusion coefficient D, reaction constant L η ) at temperature T, X0 represents the value of the temperature-sensitive parameter at the reference temperature T0, E a,X is the activation barrier related to the parameter X T , k B is the Boltzmann constant. By coupling the temperature with the ion diffusion coefficient and the reaction constant in the above way, and considering the thermal expansion at the same time, the influence of temperature on the growth and stripping of lithium dendrites is simulated.

[0126] Further, setting boundary conditions for the calculation region specifically includes:

[0127] The concentration field and the electric potential field adopt Dirichlet boundary conditions, specifically setting fixed values on the upper and lower boundaries and zero flux on the left and right boundaries; in the mechanical field, the upper boundary is fixed, the left and right boundaries are supported by rollers, and pressure is applied to the lower boundary. When using finite element analysis software to solve the model, it is also necessary to set the initial values of the model, determine the size of the calculation region, the initial values of the phase field parameters, the type of boundary conditions, and input the physical property parameters and each physical field, perform mesh division, and then solve. First, simulate the electroplating process, and then enter the stripping module to simulate the stripping process.

[0128] In some specific embodiments, finite element analysis software is used to solve the electro-chemical-mechanical phase field simulation. The Voronoi algorithm is used to randomly generate a polycrystalline model, which is used to simulate the real polycrystalline structure to make the simulation results closer to the actual situation. As Figure 3 shown, set the initial values and boundary conditions of the model:

[0129] Size of the calculation region: The size of the calculation region is set to 28μm × 28μm;

[0130] Initial values of the phase field parameters: Determine the initial values of the phase field parameters ξ and φ according to the actual physical meaning and simulation requirements. In the initial state, set the values of ξ and φ in different regions according to the initial state of the system. For example, ξ = 1 in the lithium metal region and ξ = 0 in the solid electrolyte region, etc.

[0131] Type of boundary conditions: The concentration field and the electric potential field adopt Dirichlet boundary conditions, that is, fixed values are set on the upper and lower boundaries and zero flux on the left and right boundaries. In the mechanical field, the upper boundary is fixed, the left and right boundaries are supported by rollers, and pressure is applied to the lower boundary.

[0132] Operating temperature: Set a constant operating temperature T.

[0133] The initial conditions for stripping in the stripping process can be inherited from the end conditions of electroplating or can be carried out according to the set initial conditions.

[0134] Input the phase field equation, concentration equation, electric potential equation, and stress equation into the finite element simulation software, and collect the physical property parameters involved in the research system; obtain the kinetic parameters such as reaction constants, current density, overpotential, etc. during the electroplating / stripping process of the lithium metal electrode measured in the experiment, and input the control equations, variables, and parameters into the finite element simulation software. Select triangular meshes to discretize the geometric calculation domain. Select a segregated solver to study the transient problem of lithium metal evolution, and set the time step and total calculation time. The calculation results are as Figure 4As shown. It is optimized and regulated by setting the boundary stacking pressure and working temperature to inhibit dendritic growth and slow down the capacity loss of lithium metal batteries.

[0135] Furthermore, predicting the cycling performance of all-solid-state lithium metal batteries based on the simulation results specifically includes:

[0136] Obtaining the dendritic height and battery capacity loss according to the simulation results, and quantifying the short-circuit risk through the normalized dendritic height;

[0137] Predicting the cycling performance of the battery based on the short-circuit risk and battery capacity loss;

[0138] Among them, the short-circuit risk is quantified by the normalized dendritic height H, and its formula is as follows:

[0139]

[0140] Among them, h max is the farthest distance from the tip of the dendrite to the initial cathode surface under the corresponding working conditions, and h0 is the farthest growth distance of the dendrite in the ideal uniform deposition state.

[0141] In some specific embodiments, a cloud map of the relationship between the short-circuit risk coefficient and pressure and temperature is constructed, as Figure 5 shown. Subsequently, enter the stripping module. With the help of the function and obtain the battery capacity loss, and its formula is as follows:

[0142]

[0143] Among them, Q loss is the capacity of dead lithium remaining after the stripping ends; Q total is the plating capacity.

[0144] Furthermore, the method further includes:

[0145] Establish an optimization model with the best cycling performance of the battery as the goal; by changing the pressure and working temperature in the boundary conditions, perform multiple simulation solutions to determine the optimal pressure and working temperature control strategy.

[0146] An optimization model can be established with the minimum short-circuit risk and the least capacity loss as the goals to determine the optimal pressure and temperature control strategy. In some specific embodiments, the battery capacity loss at different pressures and temperatures is obtained through multiple simulations, and a cloud map of the capacity loss rate versus pressure and temperature is further constructed, as Figure 6 shown. Finally, with the goal of minimizing the short-circuit risk coefficient and the least capacity loss of the lithium metal battery, determine the optimal pressure and temperature control strategy. The pressure range and temperature range where the short-circuit risk coefficient and the battery capacity loss are respectively less than the preset thresholds can be selected as the actual control strategy.

[0147] Furthermore, this embodiment also provides a system for predicting the cycling performance of an all-solid-state lithium-metal battery. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the method for predicting the cycling performance of an all-solid-state lithium-metal battery described in any one of the above.

[0148] In view of the problems in the prior art of insufficient understanding of the lithium dendrite growth and stripping mechanisms in all-solid-state lithium-metal batteries and the lack of systematic research methods, this embodiment provides a method for regulating the electroplating and stripping behaviors of polycrystalline all-solid-state lithium-metal batteries based on an electrochemical-mechanical phase-field model, aiming to reveal the influence mechanisms of external pressure and operating temperature on the electroplating and stripping behaviors of the battery, and further optimize the battery performance.

[0149] This embodiment relates to a technology and method based on an electrochemical-mechanical phase-field model to improve the electroplating and stripping behaviors of polycrystalline all-solid-state lithium-metal batteries by regulating pressure and temperature. This technology can be applied to the R & D and production processes of various all-solid-state lithium-metal batteries. By optimizing the electroplating and stripping performances of the battery under different pressure and temperature conditions, the cycling stability of the battery can be improved, the short-circuit risk can be reduced, and thus the overall performance of the battery can be enhanced. In practical applications, it can be used in fields with high requirements for battery performance such as electric vehicles and mobile electronic devices, providing a more reliable and efficient power solution for them.

[0150] It is easy for those skilled in the art to understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the cycling performance of an all-solid-state lithium metal battery, characterized in that, Including: Constructing a multi - crystal phase - field model of electrochemical - mechanical coupling based on the evolution of the Helmholtz free energy of dendrites, where grain - boundary phase - field parameters and dendrite phase - field parameters are introduced in the multi - crystal phase - field model to distinguish the three - phase system of metallic lithium phase, grain - boundary phase, and grain phase; Comprehensively deriving the lithium diffusion control equation, electrostatic potential distribution equation, and stress balance equation according to the change of the chemical potential energy of the lithium system; Randomly generating a polycrystalline solid electrolyte by using the Voronoi algorithm, setting a lithium metal block at the bottom of the polycrystalline solid electrolyte, and the polycrystalline solid electrolyte and the lithium metal block form a calculation region, and setting boundary conditions and working temperature parameters for the calculation region; Inputting the multi - crystal phase - field model, lithium diffusion control equation, electrostatic potential distribution equation, and stress balance equation into finite - element analysis software, and using the finite - element analysis software to simulate and solve the multi - crystal phase - field model of the calculation region; predicting the cycle performance of the all - solid - state lithium - metal battery according to the simulation results.

2. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to claim 1, wherein The grain boundary phase field parameter is The dendrite phase field parameter is ξ. In the three-phase system, the metallic lithium phase is ξ = 1. The grain boundary phase is ξ = 0. The grain phase is ξ = 0. ξ and The value ranges are from 0 to 1 respectively. The multi - crystal phase - field model specifically includes: where t is time, represents the evolution of the grain boundary with time, is the interface mobility, and Ψ is the total Helmholtz free energy of the system; L σ = h(ξ)L σ,Li + (1 - h(ξ))L σ,SE ; Among them, represents the evolution of dendrites over time; L σ represents the interface mobility; h(·) represents the interpolation function; L σ,Li is the interface mobility of lithium; L σ,SE is the interface mobility of the solid electrolyte; h′(ξ) is the derivative of h(ξ); M η is the rate constant; i BV is the current density calculated by the Butler-Volmer formula; is the convection term; u is the velocity field of deformation; among them, the stress-corrected Butler-Volmer formula is adopted.

3. The method for predicting the cycle performance of the all-solid-state lithium metal battery according to claim 2, wherein The electroplating phase - field equation finally obtained by the multi - crystal phase - field model is: where W is the barrier height; g(ξ) is the double-well function; k is the gradient coefficient; is the Hamiltonian operator; is the angle between the reference axis and the surface migration normal, where ξ x ′ and ξ ′ y are the partial derivatives of the dendrite ξ with respect to the coordinate axes x and y, respectively; L η = M η i0 is affected by temperature during the cycle; i0 is the exchange current density; a Li is the lithium metal activity, is the lithium ion activity in the solid electrolyte; F is the Faraday constant, R is the universal gas constant, T is the temperature; α is the symmetry coefficient of the electrochemical reaction (0 < α < 1); where c Li is the lithium metal concentration; is the bulk concentration of the lithium metal; is the lithium ion concentration in the solid electrolyte; is the lithium ion site density in the solid electrolyte; The stripping phase - field equation is: f Li+ = f step (x Li - x bulk ) is a variable for determining the ionic active state of local metallic lithium; f step is a step function from 1 to 0, φ Li is the lithium metal potential, φ bulk is the reference potential; x Li is the interfacial position of the lithium metal, x bulk is the reference initial position; wherein, the non-ideality of the electrochemical reaction is introduced into the interfacial reaction kinetics, and the activity coefficient is modified to 4. The method for predicting the cycle performance of the all-solid-state lithium metal battery according to claim 2, wherein, The lithium diffusion control equation is: Among them, μ Li is the chemical potential of lithium atoms; D eff is the effective diffusion coefficient of lithium ions; is the bulk concentration of lithium metal; is the lithium ion site density in the solid electrolyte; is the standard chemical potential of lithium; is the standard chemical potential of lithium ions in the solid electrolyte; D Li 、D GB and D G are the diffusion coefficients of lithium ions in metallic lithium, grain boundaries, and grains, respectively; The electrostatic potential distribution equation is described by the Poisson equation, specifically: Among them, σ eff is the effective conductivity, and σ Li , σ GB and σ G are the conductivities of metallic lithium, grain boundaries, and within grains, respectively, is the electric potential distribution in the system; The stress balance equation is specifically: ε el = ε - ε0 - ε th ; Among them, C eff is the effective elastic stiffness tensor, C Li is the stiffness tensor of lithium metal, C GB is the stiffness tensor of the solid electrolyte grain boundary, C G is the stiffness tensor of the solid electrolyte grain, and C0 is the stiffness tensor at the void to ensure the operation; ε el is the elastic strain, and ε is the total strain; ε0 = λ ii ξ is the inelastic strain generated due to the volume expansion of lithium metal during lithium deposition, and λ ii is a constant diagonal matrix. ε th = α SE (T - T0) is the thermal expansion of the electrolyte caused by the temperature rise, α SE is the coefficient of thermal expansion, T is the operating temperature, and T0 = 293K is the reference temperature.

5. The method for predicting the cycling performance of an all-solid-state lithium metal battery according to any one of claims 1-4, characterized in that, In the multi - crystal phase - field model, lithium diffusion control equation, electrostatic potential distribution equation, and stress balance equation, the Arrhenius equation is used to quantify temperature - sensitive parameters.

6. The method for predicting the cycle performance of the all-solid-state lithium metal battery according to claim 5, characterized in that, Quantifying the temperature - sensitive parameters by using the Arrhenius equation is specifically as follows: where X T represents the value of the temperature-sensitive parameter at temperature T, X0 represents the value of the temperature-sensitive parameter at the reference temperature T0, E a,X is the activation barrier associated with the parameter X T and k B is the Boltzmann constant.

7. The cycle performance prediction method for all-solid-state lithium metal batteries according to any one of claims 1-4, characterized in that Setting boundary conditions for the calculation region specifically includes: The concentration field and the electric potential field adopt Dirichlet boundary conditions, specifically setting fixed values on the upper and lower boundaries, and zero flux on the left and right boundaries; In the mechanical field, the upper boundary is set to be fixed, the left and right boundaries are supported by rollers, and pressure is applied to the lower boundary.

8. The method for predicting the cycling performance of an all-solid-state lithium metal battery according to any one of claims 1-4, characterized in that, Predicting the cycle performance of the all - solid - state lithium - metal battery according to the simulation results specifically includes: Obtaining the dendrite height and battery capacity loss according to the simulation results, and quantifying the short - circuit risk through the normalized dendrite height; Predicting the cycle performance of the battery according to the short - circuit risk and battery capacity loss; Among them, the short - circuit risk is quantified by the normalized dendrite height H, and its formula is as follows: Among them, h max is the farthest distance from the dendrite tip to the initial cathode surface under the corresponding working conditions, and h0 is the farthest growth distance of the dendrite under the ideal uniform deposition state; Battery capacity loss ω l , and its formula is as follows: Among them, Q loss is the residual dead lithium capacity after stripping; Q total is the plating capacity.

9. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1-4, characterized in that Also including: Establishing an optimization model with the best cycle performance of the battery as the goal; By changing the pressure and working temperature in the boundary conditions, performing multiple simulation solutions to determine the optimal pressure and working temperature control strategy.

10. A cycle performance prediction system for all-solid-state lithium metal batteries, characterized in that, The system includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it executes the method for predicting the cycle performance of an all - solid - state lithium - metal battery based on a dendrite phase - field model according to any one of claims 1 - 9 above.

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