A method and system for predicting the cycle performance of an all-solid-state lithium metal battery

Abstract

The application belongs to the technical field of all-solid-state lithium metal batteries, and discloses an all-solid-state lithium metal battery cycle performance prediction method and system, which comprises the following steps: taking the Helmholtz free energy evolution of dendrites as the basis to construct an electrochemical-mechanical coupling polycrystalline phase field model, wherein the polycrystalline phase field model introduces grain boundary phase field parameters and dendrite phase field parameters to distinguish a three-phase system; deriving lithium diffusion control equations, electrostatic potential distribution equations and stress balance equations; randomly generating a polycrystalline solid-state electrolyte by using a Voronoi algorithm; simulating and solving 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 the simulation result. The application can realize in-depth and systematic research on the lithium dendrite growth and stripping mechanism in the solid-state battery, thereby enabling the cycle performance of the battery to be predicted based on the lithium dendrites, and being conducive to targeted regulation and improvement to improve the battery performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of all-solid-state lithium metal batteries, and more particularly relates to a method and system for predicting the cycle performance of an all-solid-state lithium metal battery. BACKGROUND

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

[0003] When used in liquid electrolytes, lithium metal is prone to lithium dendrites and may form a solid electrolyte interface, which reduces the battery's coulombic efficiency, shortens the cycle life, and even causes short circuits, posing a safety risk. In all-solid-state batteries, although solid electrolytes (SEs) can block the propagation of lithium dendrites to some extent, there are still problems of irregular lithium deposition and the formation of non-active lithium due to repeated plating / detaching, resulting in poor actual cycle performance of the battery.

[0004] Early studies have 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 two hypotheses about the reasons for dendrite preferential penetration along grain boundaries: one is that the mechanical and transport properties of grain boundaries are special, leading to different local electrochemical mechanical responses of dendrites and solid-state electrolytes, causing uneven lithium deposition; the other is that grain boundaries capture excess electrons in the plated electrode, causing lithium ions at the grain boundaries to reach the reduction overpotential earlier, and even prompting dendrites to nucleate inside the electrolyte, and then the propagation and growth of dendrites are dominated by the mechanical properties of SE. However, the fundamental mechanisms of the various failure modes induced by grain boundaries in inorganic solid-state electrolytes are not well understood.

[0005] To solve these problems, existing methods mainly fall into two categories. One is to change the material properties, such as controlling the grain size, coating a nanolayer 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 is to regulate the operating conditions, such as using pulse current charging, reasonably regulating the stacking pressure and working temperature, etc., to improve the cycle performance of the battery.

[0006] However, the prior art has obvious deficiencies: 1. There is a lack of in-depth understanding of how stacking pressure and working temperature affect the growth and stripping mechanism of lithium dendrites, especially the specific reasons for the growth of lithium dendrites along the grain boundary in polycrystalline solid electrolyte. 2. Existing researches mostly observe macroscopic variables or interface morphology changes through experiments to learn about the complex interaction between stress, contact, reaction, diffusion and current density during plating and stripping, lacking systematic research. 3. In terms of theoretical calculation, although the phase field method is used to study the mechanism of lithium metal negative electrode, current theoretical calculation mostly focuses on the interface evolution and surface flatness during plating, and mainly concentrates in the field of liquid lithium battery, with less simulation research on the formation mechanism of non-active lithium in solid-state battery.

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

[0008] In view of the above defects or improvement needs of the prior art, the present application provides a full-solid-state lithium metal battery cycle performance prediction method and system for solving the problem that the prior art lacks a research method for the growth and stripping mechanism of lithium dendrites in solid-state batteries, thereby limiting the improvement of battery performance.

[0009] To achieve the above-mentioned purpose, according to one aspect of the present application, a full-solid-state lithium metal battery cycle performance prediction method is provided, comprising:

[0010] A polycrystalline phase field model of electrochemical mechanical coupling is constructed based on the Helmholtz free energy evolution of dendrites, wherein grain boundary phase field parameters and dendrite phase field parameters are introduced in the polycrystalline phase field model to distinguish three-phase systems of metal lithium phase, grain boundary phase and grain phase;

[0011] Lithium diffusion control equation, electrostatic potential distribution equation and stress balance equation are comprehensively derived according to the chemical potential energy change of lithium system;

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

[0013] The polycrystalline phase field model, lithium diffusion control equation, electrostatic potential distribution equation and stress balance equation are input into a finite element analysis software, and the polycrystalline phase field model of the calculation region is simulated and solved by using the finite element analysis software; the cycle performance of the full-solid-state lithium metal battery is predicted according to the simulation result.

[0014] According to the full-solid-state lithium metal battery cycle performance prediction method provided by the present application, the grain boundary phase field parameters are The dendrite phase field parameter is ξ, the lithium metal phase in the three-phase system is ξ=1, The grain boundary phase is ξ=0, The grain phase is ξ=0, ξ and The value ranges are 0 to 1 respectively; the polycrystal phase field model specifically comprises:

[0015]

[0016] Wherein 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] Wherein, represents the evolution of the dendrite with time; L σ represents the interface mobility; h(·) represents an 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; wherein the stress-corrected Butler-Volmer formula is adopted.

[0020] According to the full solid-state lithium metal battery cycle performance prediction method provided by the application, the electrodeposition phase field equation finally derived by the polycrystal phase field model is:

[0021]

[0022] Wherein W is the potential barrier height; g(ξ) is a double potential well function; k is the gradient coefficient; is the Hamiltonian operator; is the angle between the reference axis and the surface migration normal, wherein 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, for the lithium ion activity in the solid-state electrolyte; F is the Faraday constant, R is the universal gas constant, and T is the temperature; a is the symmetry coefficient of the electrochemical reaction (0 < a < 1); wherein c Li for the lithium metal concentration; for the bulk concentration of lithium metal; for the lithium ion concentration in the solid-state electrolyte; for the lithium ion site density in the solid-state electrolyte;

[0023] The phase-field equation for the stripping is:

[0024]

[0025] wherein: is a variable to determine the electronic activity state of the local metal lithium; is a variable to determine the ionic activity state of the local metal 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 initial position of the reference; wherein the non-ideality of the electrochemical reaction is introduced into the interface reaction kinetics, the activity coefficient is modified to

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

[0027]

[0028] wherein, 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-state electrolyte; is the standard chemical potential of lithium; is the standard chemical potential of lithium ions in the solid-state electrolyte; D Li , D GB and D G are the diffusion coefficients of lithium ions in the metal lithium, the grain boundary and the grain, respectively;

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

[0030]

[0031] wherein, 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. is the potential distribution in the system;

[0032] The stress balance equation is specifically:

[0033]

[0034] ε el =ε-ε0-ε th ;

[0035]

[0036] 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 grains, and C0 is the stiffness tensor of 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 caused by 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 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 cycle performance of an all-solid-state lithium metal battery provided by the present invention, the Arrhenius equation is used to quantify temperature-sensitive parameters in the polycrystalline phase field model, lithium diffusion control equation, electrostatic potential distribution equation, and stress balance equation.

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

[0039]

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

[0041] The method for predicting the cycle performance of the all-solid-state lithium metal battery according to the application sets a boundary condition for the calculation region, specifically including:

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

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

[0044] The method for predicting the cycle performance of the all-solid-state lithium metal battery according to the application predicts the cycle performance of the all-solid-state lithium metal battery according to the simulation results, specifically including:

[0045] The dendrite height and the battery capacity loss are obtained according to the simulation results, and the short circuit risk is quantified by the normalized dendrite height;

[0046] The cycle performance of the battery is predicted according to the short circuit risk and the battery capacity loss;

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

[0048]

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

[0050] The battery capacity loss ω l is calculated according to the formula as follows:

[0051]

[0052] Wherein, Q loss is the residual dead lithium capacity after stripping; and Q total is the plating capacity.

[0053] The method for predicting the cycle performance of the all-solid-state lithium metal battery according to the application further includes:

[0054] An optimization model is established to optimize the cycle performance of the battery; the pressure and the working temperature in the boundary condition are changed to perform multiple simulation solutions to determine the optimal pressure and working temperature control strategy.

[0055] According to another aspect of the application, a system for predicting the cycle performance of an all-solid-state lithium metal battery is provided, which includes a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method for predicting the cycle performance of the all-solid-state lithium metal battery according to any one of the above.

[0056] Overall, compared with the prior art, the full-solid-state lithium metal battery cycle performance prediction method and system provided by the present application:

[0057] 1. A multi-crystal phase field model based on Helmholtz free energy evolution is proposed to establish an electrochemical-mechanical coupling model, which can establish the evolution process of phase field parameters with time, thereby realizing the evolution simulation of dendrites. The introduction of grain boundary phase field parameters and dendrite phase field parameters in the model can better distinguish the three-phase system of metal lithium phase, grain boundary phase and grain phase, and improve the simulation accuracy. Through finite element analysis of the multi-crystal phase field model, the growth and stripping mechanism of lithium dendrites in solid-state batteries can be systematically studied, thereby the cycle performance of the battery can be predicted based on lithium dendrites, and targeted regulation and improvement can be facilitated to improve the battery performance;

[0058] 2. The electrochemical-mechanical phase field model constructed comprehensively considers the interaction of multiple factors, can more comprehensively and deeply study the growth and stripping mechanism of lithium dendrites, and makes up for the shortcomings of the prior art; through the model, the influence of external pressure and working temperature on the morphology of lithium deposition is studied, the coupling relationship between temperature and pressure parameters and electrochemical overpotential is realized, and a theoretical basis is provided 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 dynamics is revealed, which provides scientific guidance for formulating battery working temperature strategy;

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

[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 development of full-solid-state batteries. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is a flowchart of the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the present application;

[0063] Figure 2 is a model construction principle diagram in the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the present application;

[0064] Figure 3 is a schematic diagram of the geometric structure, boundary condition and initial value setting in the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the present application;

[0065] Figure 4is an effect picture calculated in the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the application;

[0066] Figure 5 is a cloud picture of normalized dendrite height changing with pressure and temperature calculated in the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the application;

[0067] Figure 6 is a cloud picture of battery capacity loss rate changing with pressure and temperature calculated in the full-solid-state lithium metal battery cycle performance prediction method provided by the embodiment of the application. DETAILED DESCRIPTION

[0068] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in each embodiment of the present application 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 The embodiment provides a full-solid-state lithium metal battery cycle performance prediction method, which comprises the following steps:

[0070] The Helmholtz free energy evolution of dendrites is taken as the basis to construct an electrochemical-mechanical coupling polycrystalline phase field model, wherein a grain boundary phase field parameter and a dendrite phase field parameter are introduced in the polycrystalline phase field model to distinguish a three-phase system of a metal lithium phase, a grain boundary phase and a grain phase;

[0071] Lithium diffusion control equations, electrostatic potential distribution equations and stress balance equations are comprehensively derived according to the chemical potential energy changes of the lithium system;

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

[0073] The polycrystalline phase field model, the lithium diffusion control equations, the electrostatic potential distribution equations and the stress balance equations are input into a finite element analysis software, and the polycrystalline phase field model of the calculation region is simulated and solved by using the finite element analysis software; the cycle performance of the full-solid-state lithium metal battery is predicted according to the simulation results.

[0074] Specifically, since the SE contains microstructure structures such as grain boundaries, in order to distinguish the grain boundaries and the bulk grain (GB) in the SE phase, a non-conservative grain boundary phase field parameter is introduced It is 1 at the grain boundary and 0 in the bulk phase. Meanwhile, a dendritic phase field parameter ξ is introduced to distinguish the three-phase system, in which: lithium metal phase (ξ = 1, ), grain boundary phase (ξ = 0, ) and grain phase (ξ = 0, ). The value of these two parameters ranges from 0 to 1. The formula of the total Helmholtz free energy Ψ of the system is:

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

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

[0077] is the interfacial energy of the system; where g(ξ) = Wξ 2 (1-ξ) 2 is a double-well function; where W = h(ξ)W Li +(1-h(ξ))W SE is the height of the potential barrier, W Li and W SE are the heights of the potential barrier of lithium phase and solid-state 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 lithium phase and solid-state electrolyte phase, respectively. The current model assumes that the solid-state electrolyte has isotropic properties, so k Li and k SE take constant values. This formula describes the relationship between the gradient energy and the gradient of the dendritic phase field parameter ξ. δ is the strength of anisotropy, 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 dendritic 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 +concentration of species i. is the reference chemical potential of component i, is the bulk concentration of lithium metal, is the lithium ion site density in the solid-state electrolyte, R is the universal gas constant, and T is the temperature. This equation embodies the relationship between chemical energy and the concentration, chemical potential, and temperature of each component.

[0079] is the electrical potential energy of the system, where z i is the chemical valence of the species, F is the Faraday constant, and c i is the concentration of the species, (i = Li and e, corresponding to the Li metal electrode and 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, i.e., the nonlinear phase field model of dendrites and grain boundaries that determines the evolution of the electrode-polycrystalline electrolyte interface from the Helmholtz free energy change, is as follows:

[0082]

[0083] where t is time, represents the evolution of the grain boundary over time, is the interfacial 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 interfacial mobility, reflecting the ease with which the interface moves under external action; h(·) represents the interpolation function; L σ,Li is the interfacial mobility of lithium; L σ,SE is the interfacial mobility of the solid electrolyte; h'(ξ) is the derivative of h(ξ), which serves to limit the electrochemical reaction to the electrode / electrolyte interface; M η is the rate constant, affecting the rate of the electrochemical reaction; i BVcurrent density calculated for the Butler-Volmer equation; is the convection term to describe the phase evolution driven by mechanical deformation; u is the velocity field of deformation; where the stress correction Butler-Volmer equation is adopted to consider the mechanical stress effect:

[0087]

[0088] where, is the exchange current density. k a and k c are the rate constants for the anodic and cathodic reactions, 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-state electrolyte. a is the symmetry factor of the electrochemical reaction (0 < a < 1). is the overpotential on the deformed surface;

[0089] where, η a is the activation overpotential, which is introduced 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 represents compression, P h < 0 represents tension, and C is a correction term. where φ L i is the electrode potential, φ e is the solid-state electrolyte potential, is the standard half-cell potential. When η = 0, the net reaction rate is 0; when η < 0, the cathodic reaction dominates, and the plating process occurs, Li + + e - → Li; when η > 0, the anodic reaction dominates, and the stripping process occurs, Li-e - → Li + .

[0090] Further, through the scaling of the grain boundary phase field parameter , the property of SE smoothly transforms from that of the bulk particle to that of the GB at the interface. The above equation can be written as:

[0091]

[0092] where, for simplicity of calculation, the grain boundary phase field parameter only serves as an identifier and does not evolve with time.

[0093] The plating phase field equation ultimately derived by the polycrystalline phase field model is:

[0094]

[0095] 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, y; L η = M η i0 is affected by temperature in the cycle process; i0 is the exchange current density; a Li is the lithium metal activity, is the lithium ion activity in the solid-state electrolyte; F is the Faraday constant, R is the universal gas constant, T is the temperature; a is the symmetry coefficient of the electrochemical reaction (0 < a < 1); where c Li is the lithium metal concentration; is the bulk concentration of lithium metal; is the lithium ion concentration in the solid-state electrolyte; is the lithium ion site density in the solid-state electrolyte;

[0096] The peeling phase field equation is:

[0097]

[0098] where: is a variable that determines the electronic activity state of the local metal lithium; f Li+ = f step (x Li -x bulk ) is a variable that determines the ionic activity state of the local metal 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 lithium metal, x bulk is the initial position of the reference;

[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 the subsequent reaction, φ Li decreases, will change from 1 to 0, i.e., dead lithium is formed. Otherwise, it remains 1, indicating an active Li state. Unlike liquid batteries, when peeling occurs in solid-state batteries, a hole is formed at the interface that is disconnected from the electrolyte, at which time the ionic path is disconnected and the local lithium metal no longer undergoes an electrochemical reaction, x Li decreases, The electrochemical reaction term will disappear as 1 becomes 0. Moreover, 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 interface reaction kinetics, the activity coefficient is modified to

[0100] Referring to Figure 2 , the polycrystalline phase field model proposed in this embodiment distinguishes the grain boundary and dendritic phase field parameters in the three-phase system, and uses an interpolation function h(x) to consider the different migration rates L σ , energy barrier height W, and gradient coefficient k of the lithium electrode and solid-state electrolyte interface, establishes the electrode-polycrystalline electrolyte interface evolution equation and related equations considering mechanical stress, and introduces and two step functions to determine the formation of dead lithium due to the disconnection of the electronic and ionic paths during the stripping process, and modify to comprehensively consider the case where the concentration at the interface does not satisfy the infinite dilution solution assumption during the stripping process.

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

[0102] According to the concentration c Li of lithium atoms in the deposit and the concentration of lithium ions in the solid-state electrolyte Li The concentration of lithium species c Li at the interface can be seen as the interpolation of c Li and c Li :

[0103]

[0104] Following the KKS model, it is assumed that the chemical potentials of lithium atoms and lithium ions are equal, i.e. μ Li is the chemical potential of lithium atoms, and the expressions of c Li and c are obtained:

[0105]

[0106] where is the site density of lithium metal, is the body concentration of lithium ions in LLZO. is the standard chemical potential of lithium, is the standard chemical potential of lithium ions in the solid-state electrolyte.

[0107] Due to the consumption of lithium ions and the generation of lithium atoms at the lithium-solid-state electrolyte interface by the electrochemical reaction, the lithium species (ions and atoms) are conserved, and the diffusion equation of lithium species is obtained:

[0108]

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

[0110]

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

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

[0113]

[0114] where σ eff is the effective conductivity, σ Li , σ GB and σ G are the conductivities in lithium metal, grain boundary and grain, respectively, is the potential distribution in the system.

[0115] The stress balance equation is specifically: during lithium deposition, mechanical stress is generated due to the volume change of lithium metal anode. To simplify the 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 perfect contact; the non-elastic strain caused by the volume expansion of lithium metal is considered as the only source of internal stress evolution.

[0116] The Li stress distribution at the interface is obtained by solving the stress balance, 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 solid electrolyte grain boundary, C G is the stiffness tensor of solid electrolyte grain, C0is the stiffness tensor at void to ensure operation; ε el is the elastic strain, ε is the total strain (adopting small deformation theory assumption); ε0= λ ii is the inelastic strain due to 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 electrolyte caused by temperature rise (ignoring the thermal expansion of lithium metal because the stress is released when lithium metal creeps during temperature rise), α SE is the thermal expansion coefficient, T is the working temperature, T0= 293 K is the reference temperature. The elastic strain contains the effects of volume expansion and thermal expansion.

[0121] Further, the temperature is coupled with the ion diffusion coefficient and the reaction constant, the Arrhenius equation is used to quantify the temperature sensitive parameter, and the thermal expansion is considered, so that the influence of temperature on lithium dendrite growth and stripping can be better simulated. The temperature distribution in 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 working temperature is uniformly distributed in the simulation range, and the influence of temperature gradient is ignored.

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

[0123] The Arrhenius equation is used to quantify the temperature sensitive parameter as follows:

[0124]

[0125] Wherein, X T represents the value of the temperature sensitive parameter (such as lithium ion diffusion coefficient D, reaction constant L η ) at temperature T, X0represents the value of the temperature sensitive parameter at reference temperature T0, E a,X is the activation barrier related to the parameter X T , k B is the Boltzmann constant. By the above manner, the temperature is coupled with the ion diffusion coefficient and the reaction constant, and the thermal expansion is considered, so that the influence of temperature on lithium dendrite growth and stripping is simulated.

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

[0127] The concentration field and the 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 the lower boundary is subjected to pressure. When solving the model using finite element analysis software, the initial value of the model also needs to be set, the size of the calculation region, the initial value of the phase field parameters, the type of boundary conditions, and the physical property parameters and various physical fields are input, the mesh is divided, and then the solution is performed. First, the electroplating process is simulated, and then the stripping process is simulated in the stripping module.

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

[0129] The size of the calculation region is set to 28 pm x 28 pm.

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

[0131] The type of boundary conditions: The concentration field and the potential field adopt Dirichlet boundary conditions, i.e., 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 the lower boundary is subjected to pressure.

[0132] Working temperature: Set a constant working temperature T.

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

[0134] The phase field equation, concentration equation, potential equation, and stress equation are input into the finite element simulation software, and the physical property parameters involved in the research system are collected; the reaction constants, current density, overpotential, and other kinetic parameters measured in the experiment during the lithium metal electrode electroplating / stripping process are obtained, and the control equation, variables, and parameters are input into the finite element simulation software. Triangular mesh is selected to discretize the geometric calculation domain. The separation solver is selected to study the transient problem of lithium metal evolution, and the time step and total calculation time are set. The calculation results are as shown in Figure 4The boundary stack pressure and working temperature are set to optimize and regulate to inhibit dendrite growth and slow down the capacity loss of lithium metal batteries.

[0135] Further, the cycle performance of the all-solid-state lithium metal battery is predicted according to the simulation results, specifically including:

[0136] According to the simulation results, the dendrite height and the capacity loss of the battery are obtained, and the short circuit risk is quantified by the normalized dendrite height;

[0137] The cycle performance of the battery is predicted according to the short circuit risk and the capacity loss of the battery;

[0138] Wherein, the short circuit risk is quantified by the normalized dendrite height H, and the formula is as follows:

[0139]

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

[0141] In some specific embodiments, a cloud chart of the short circuit risk coefficient with respect to the pressure and temperature relationship is constructed, as shown in Figure 5 Subsequently, the peeling module is entered. With the functions and the capacity loss of the battery is obtained, and the formula is as follows:

[0142]

[0143] Wherein, Q loss is the residual dead lithium capacity after peeling; Q total is the plating capacity.

[0144] Further, the method further includes:

[0145] An optimization model is established to optimize the cycle performance of the battery. By changing the pressure and working temperature in the boundary conditions, multiple simulations are performed to determine the optimal pressure and working temperature control strategy.

[0146] An optimization model can be established to minimize the short circuit risk and the capacity loss, and the optimal pressure and temperature control strategy is determined. In some specific embodiments, the capacity loss of the battery under different pressures and temperatures is obtained by multiple simulations, and a cloud chart of the capacity loss rate with respect to the pressure and temperature is further constructed, as shown in Figure 6 Finally, the optimal pressure and temperature control strategy is determined to minimize the short circuit risk coefficient and the capacity loss of the lithium metal battery. The pressure range and temperature range with the short circuit risk coefficient and the capacity loss less than the preset threshold value can be selected as the actual control strategy.

[0147] Further, the embodiment also provides a full-solid-state lithium metal battery cycle performance prediction system, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program to execute the full-solid-state lithium metal battery cycle performance prediction method of any one of the above.

[0148] The embodiment aims at the problems of insufficient understanding of lithium dendrite growth and stripping mechanism of full-solid-state lithium metal batteries in the prior art and lack of systematic research methods, and provides a method for regulating plating and stripping behavior of polycrystalline full-solid-state lithium metal batteries based on an electrochemical mechanical phase field model, which aims to reveal the influence mechanism of external pressure and working temperature on the plating and stripping behavior of the battery, and then optimize the battery performance.

[0149] The embodiment relates to a technology and method for improving plating and stripping behavior of polycrystalline full-solid-state lithium metal batteries by regulating pressure and temperature based on an electrochemical mechanical phase field model. The technology can be applied to the research and development and production process of various full-solid-state lithium metal batteries. By optimizing the plating and stripping performance of the battery under different pressure and temperature conditions, the cycle stability of the battery is improved, the short circuit risk is reduced, and the overall performance of the battery is improved. In practical applications, it can be used in fields with high requirements for battery performance such as electric vehicles and mobile electronic devices to provide more reliable and efficient power supply solutions.

[0150] Those skilled in the art will readily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for predicting the cycle performance of an all-solid-state lithium metal battery, characterized in that: include: An electrochemical-mechanically coupled polycrystalline phase-field model is constructed based on the evolution of the Helmholtz free energy of dendrites, wherein the polycrystalline phase-field model introduces grain boundary phase-field parameters and dendrite phase-field parameters to distinguish the three-phase system of metallic lithium phase, grain boundary phase and grain phase; According to the change of chemical potential energy of lithium system, the lithium diffusion control equation, electrostatic potential distribution equation and stress balance equation are comprehensively derived; A polycrystalline solid electrolyte is randomly generated using a Voronoi algorithm, a lithium metal block is set at the bottom of the polycrystalline solid electrolyte, the polycrystalline solid electrolyte and the lithium metal block form a calculation area, and boundary conditions and operating temperature parameters are set for the calculation area; Inputting the polycrystalline phase field model, lithium diffusion governing 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 polycrystalline phase field model in the calculation area; and predicting the cycle performance of the all-solid-state lithium metal battery based on the simulation results; The grain boundary phase field parameters are , the dendrite phase field parameter is , the metallic lithium phase in the three-phase system is , ; Grain boundary phase is , ; Grain phase is , , and The value ranges are arrive ; The polycrystalline phase field model specifically includes: ； in t For time, represents the evolution of grain boundaries over time, is the interface mobility, is the total Helmholtz free energy of the system; ； ； in, represents the evolution of dendrite over time; represents the interface mobility; represents the interpolation function; is the interfacial mobility of lithium; is the interfacial mobility of the solid electrolyte; yes The derivative of is the rate constant; is the current density calculated by the Butler-Volmer formula; is the convection term; is the deformed velocity field; where the stress-corrected Butler-Volmer formula is used.

2. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to claim 1, wherein: The electroplating phase field equation finally obtained by the polycrystalline phase field model is: ； in, is the barrier height; is the double-well function; is the gradient coefficient; is a Hamiltonian operator; is the angle between the reference axis and the surface migration normal, where and Dendrites Partial derivatives about the coordinate axes x and y; Because it is affected by temperature during the cycle; is the exchange current density; is the lithium metal activity, is the lithium ion activity in the solid electrolyte; is the Faraday constant, is the universal gas constant, It is the temperature; is the symmetry coefficient of the electrochemical reaction, ;in , ; 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; The exfoliation phase field equation is: ； in: Variables that determine the electronically active state of local metallic lithium; Variables that determine the ionic activity state of local metallic lithium; is a step function from 1 to 0, is the lithium metal potential, is the reference potential; is the interface position of lithium metal, is the initial position of the reference; the non-ideality of the electrochemical reaction is introduced into the interface reaction kinetics, and the activity coefficient Modified to .

3. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to claim 1, wherein: The governing equation for lithium diffusion is: ； ； ； in, is the chemical potential of lithium atoms; 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 solid electrolyte; 、 and are the diffusion coefficients of lithium ions in metallic lithium, grain boundaries, and grains, respectively; The electrostatic potential distribution equation is described by Poisson's equation, specifically: ； ； in, is the effective conductivity, 、 and are the electrical conductivities of metallic lithium, grain boundaries, and within grains, respectively. is the potential distribution in the system; The stress balance equation is specifically: ； ； ； ； in, is the effective elastic stiffness tensor, is the stiffness tensor of lithium metal, is the stiffness tensor of the solid electrolyte grain boundary, is the stiffness tensor of the solid electrolyte grain, is the stiffness tensor at the cavity to ensure the operation; is the elastic strain, is the total strain; is the inelastic strain caused by the volume expansion of lithium metal during lithium deposition. is a constant diagonal matrix; is the thermal expansion of the electrolyte caused by the temperature increase, is the coefficient of thermal expansion, is the operating temperature, is the reference temperature.

4. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1 to 3, wherein: 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 temperature sensitive parameters.

5. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to claim 4, wherein: The Arrhenius equation is used to quantify the temperature sensitive parameters as follows: ； in, Indicates temperature The value of the temperature sensitive parameter under Indicates reference temperature The value of the temperature sensitive parameter, Is with parameters The associated activation barrier, is the Boltzmann constant.

6. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1 to 3, wherein: Setting boundary conditions for the calculation area specifically includes: The concentration field and electric potential field adopt Dirichlet boundary conditions, specifically setting fixed values ​​at the upper and lower boundaries and zero flux at the left and right boundaries; The upper boundary is fixed in the mechanical field, the left and right boundaries are supported by rollers, and pressure is applied to the lower boundary.

7. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1 to 3, wherein: The cycle performance of all-solid-state lithium metal batteries is predicted based on simulation results, including: Obtain dendrite height and battery capacity loss based on simulation results, and quantify short-circuit risk by normalizing dendrite height; Predict battery cycle performance based on short circuit risk and battery capacity loss; Among them, the normalized dendrite height To quantify the short circuit risk, the formula is as follows: ； in, is the maximum distance between the dendrite tip and the initial cathode surface under the corresponding working conditions, is the maximum growth distance of dendrite under ideal uniform deposition conditions; Battery capacity loss , the formula is as follows: ； in, It is the dead lithium capacity remaining after stripping; is the electroplating capacity.

8. The method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1 to 3, wherein: Also includes: Establish an optimization model with the goal of optimizing battery cycle performance; By changing the pressure and operating temperature in the boundary conditions, multiple simulations are performed to determine the optimal pressure and operating temperature control strategy.

9. A system for predicting the cycle performance of an all-solid-state lithium metal battery, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for predicting the cycle performance of an all-solid-state lithium metal battery according to any one of claims 1 to 8 is executed.

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