A method for calculating the cycle capacity of solid-state batteries based on a temperature-pressure coupled calculation model.

Abstract

This invention provides a method for calculating the cycle capacity of solid-state batteries based on a temperature-pressure coupled calculation model. The temperature-pressure coupled calculation model established in this invention provides a method for calculating the charge-discharge cycle capacity of solid-state batteries under different temperatures and pressures. This calculation method can calculate the optimal cycle temperature range and optimal external pressure range for any solid-state battery, which can help researchers design lithium solid-state batteries with higher energy density and longer cycle life.

Description

Technical fields:

[0001] This invention relates to a method for calculating the cycle capacity of solid-state batteries based on a temperature and pressure coupled calculation model. Background technology:

[0002] With the rapid advancement of lithium-ion battery research, there are higher expectations for lithium batteries in terms of energy density, cycle life, and safety. However, the current energy density of commercially available lithium batteries at 300Wh / kg is almost at the material limit, and the volatile and flammable nature of traditional organic liquid electrolytes makes batteries highly susceptible to explosion in the event of a short circuit or thermal runaway. In recent years, solid-state batteries, with their advantages of high mechanical strength, high energy density, and long cycle life, have received extensive research attention. Compared to traditional organic liquid electrolytes, solid-state electrolytes with high mechanical strength can effectively suppress the growth of lithium dendrites, which can not only effectively solve the problem of frequent battery thermal runaway, but also has higher energy density and better temperature adaptability.

[0003] Ambient temperature and external pressure during solid-state battery cycling have a significant impact on the charge-discharge cycle capacity of solid-state batteries. Before reaching the battery's self-heating temperature, an increase in ambient temperature is undoubtedly beneficial to the cycle performance of solid-state batteries; in addition, the mechanical integrity of solid-state batteries is largely constrained by their mechanical properties, and external pressure has a crucial impact on their capacity.

[0004] Although a great deal of research has been conducted on the cycle performance of solid-state batteries under different ambient temperatures and external pressures, the relationship between the coupling effect of ambient temperature and external pressure on the cycle capacity of solid-state batteries has not yet been systematically elucidated. Summary of the Invention:

[0005] This invention provides a method for calculating the cycle capacity of solid-state batteries based on a temperature and pressure coupling calculation model in order to solve the problems existing in the prior art.

[0006] The technical solutions adopted in this invention are as follows:

[0007] The method for calculating the cycle capacity of solid-state batteries based on a temperature-pressure coupled calculation model includes the following steps:

[0008] 1) Establish a local current density model on the electrode surface:

[0009] Establishing the solid-state battery cathode in the electrochemical reaction process of solid-state batteries or Local current density model on the negative electrode surface j loc :

[0010]

[0011] Where j0 is the exchange current density provided by the solid-state battery;

[0012]

[0013] η is the local overpotential, defined as follows:

[0014]

[0015] Where k0 is the reaction rate constant; F is the Faraday constant; α a and α c c represents the charge transfer coefficients of the anode and cathode of the solid-state battery, respectively. s,max and c s,suff These are the maximum concentration and surface concentration of solid-phase lithium, respectively; U oc It is the open-circuit voltage of a solid-state battery; This represents the potential of the solid electrode. is the potential of the solid-state electrolyte; R is the molar gas constant, with a value of 8.341 J / (mol·K); T is the temperature of the solid-state battery; C e This refers to the concentration of active lithium ions in the solid electrolyte.

[0016] 2) Establish a mechanical model for solid-state batteries:

[0017] Before establishing the mechanical model of the solid-state battery, it is assumed that both the solid electrodes and the solid electrolyte of the solid-state battery are isotropic, homogeneous, and linearly elastic. Then, a mechanical model is established to simulate and calculate the total strain of the solid-state battery; the mechanical model ε ij for:

[0018] ε ij =ε ij me +ε ij ei_T +ε ij ei_c

[0019] ε ij me The strain of a solid-state battery caused by external pressure is calculated using the following formula:

[0020]

[0021] Where, σ ij ν is the stress component; E is Young's modulus; ν is Poisson's ratio; δ ij σ is the Dirac delta function; kk It is normal stress;

[0022] ε ij ei_TThe characteristic strain of a solid electrode caused by temperature is calculated using the following formula:

[0023] ε ij ei_T =αΔTε ij

[0024] Where: α and ΔT are the thermal expansion coefficient and temperature change of the solid-state battery, respectively;

[0025] ε ij ei_c The characteristic strain of a solid-state battery caused by particle diffusion is determined by the diffusion coefficient, and the calculation formula is as follows:

[0026]

[0027] Where: Δc is the change in the concentration of diffusing particles, and Ω is the molar volume of the active material in the solid-state battery;

[0028] 3) Establish a coupled temperature-pressure-electrochemistry model for solid-state batteries:

[0029] The established coupling model χ0(T) is:

[0030]

[0031] Where: E a,i χ is the activation energy. 0,ref T is used as the reference temperature ref =Parameter of 25℃;

[0032] 4) Establish a capacity decay model for solid-state batteries:

[0033] Many factors influence the capacity decay of solid-state batteries. The solid electrode-solid electrolyte interphase (SEI) continues to grow with cycling, and this is the most significant factor contributing to capacity decay. To date, the growth mechanism of SEI has been extensively studied, and kinetic-driven SEI film growth models are widely used to simulate battery capacity decay. The formula is as follows:

[0034] S+2Li + +2e - →p

[0035] Wherein: S is the reactive substance that undergoes the reaction; Li + Lithium ions are represented by e-, electrons by e-, and P is the product formed during the reaction on the negative electrode side, i.e., the SEI film. The generation of P leads to the loss of cyclic lithium, which in turn causes a decrease in the capacity of solid-state batteries.

[0036] Therefore, the capacity decay model of solid-state batteries is established by increasing the thickness of the SEI film (solid electrode-solid electrolyte interphase) on the negative electrode side of the solid-state battery. The process is as follows:

[0037] Local current density j on the surface of the negative electrode particles in a solid-state battery side It is expressed as follows:

[0038]

[0039] Where: j side,0 Defined as exchange current density; F is Faraday constant; R is molar gas constant; T is solid-state battery temperature;

[0040] η s The overpotential for the side reaction in a solid-state battery is represented as follows:

[0041]

[0042] Among them, R sei It is the SEI film resistance on the negative electrode side, which increases with the increase of the thickness of the SEI film on the negative electrode side;

[0043] j is the total reaction current on the negative electrode of the solid-state battery, which includes the aforementioned j. side and the local current density model on the negative electrode surface j loc ;

[0044] SEI film thickness δ on the negative electrode side sei The rate of increase is determined by Faraday's law:

[0045]

[0046] Where M sei and ρ sei These represent the molar mass and density of the SEI film on the negative electrode side, respectively.

[0047] Resistance R of the SEI film on the negative electrode side sei With δ sei Related to R sei The calculation formula is as follows:

[0048]

[0049] Among them, κ sei The conductivity of the SEI film on the negative electrode side;

[0050] 5) Input the local current density model, mechanical model, coupling model and capacity decay model of the electrode surface established in steps 1) to 4) into the multiphysics interface pre-built in COMSOL Multiphysics finite element software. Then, input the characteristic parameters of the solid-state battery according to the characteristic parameters required by COMSOL Multiphysics finite element software. Calculate the cycle capacity of the solid-state battery by combining the model established in steps 1) to 4) with the built-in formulas of COMSOL Multiphysics finite element software.

[0051] Furthermore, in the mechanical model, the Young's modulus E and Poisson's ratio ν of the solid-state battery composite electrode are calculated using fitting equations from the COMSOL finite element software. The equations are expressed as follows:

[0052]

[0053]

[0054] Among them, E p ε is the Young's modulus of the active particle; e υ is the volume fraction of the solid electrolyte; p ε0, ε1, υ0, m, and n are all fitting parameters.

[0055] The present invention has the following beneficial effects:

[0056] Currently, existing technologies have developed numerous calculation models and methods for solid-state batteries under different temperatures and external pressures. However, the coupling effect of ambient temperature and external pressure on the cycle capacity of solid-state batteries has not been systematically elucidated, and the calculation method for the coupling effect of ambient temperature and external pressure on the cycle capacity of solid-state batteries is still unclear.

[0057] The temperature-pressure coupled calculation model established in this invention provides a method for calculating the charge-discharge cycle capacity of solid-state batteries under different temperatures and pressures. This calculation method can calculate the optimal cycle temperature range and optimal external pressure range for any solid-state battery, which can help researchers design lithium solid-state batteries with higher energy density and longer cycle life. Attached image description:

[0058] Figure 1 The geometric model of the NMC811-Li6PS5Cl-Li / In all-solid-state battery.

[0059] Figure 2 for Figure 1 The all-solid-state battery's capacity and coulombic efficiency after 10 cycles under the aforementioned different external pressures.

[0060] Figure 3 for Figure 1 Specific capacity and cycle retention of all-solid-state batteries under 1-10 cycles of charge-discharge at 0℃, 20℃, 40℃, and 60℃.

[0061] Figure 4 for Figure 1 The temperature distribution of the all-solid-state battery during cycling at 0.1C at an ambient temperature of 60°C.

[0062] Figure 5 for Figure 1 The changes in specific capacity and cycle retention of all-solid-state batteries over 10 charge-discharge cycles at different cycling temperatures.

[0063] Figure 6 and Figure 7 Corresponding to Figure 1 Temperature and stress distribution of an all-solid-state battery during the first charge process when subjected to 15KN at 60°C.

[0064] Figure 8 for Figure 1 The graph shows the experimental data of applying an external force of 15KN to an all-solid-state battery and performing 10 charge-discharge cycles at 0.1C in a constant temperature environment of 60℃. Detailed implementation method:

[0065] The invention will now be further described with reference to the accompanying drawings.

[0066] Based on the temperature and pressure coupled calculation model of this invention, taking the NMC811-Li6PS5Cl-Li / In all-solid-state battery as an example, the ambient temperature range is 0℃-60℃, the external pressure range is 0KN-20KN, the battery geometry is 10mm*7.85mm*2mm, the charging cut-off voltage is 3.8V, the discharging cut-off voltage is 2.4V, and the charging / discharging current is ±0.14mA. The 10-cycle charge-discharge capacity at a 0.1C cycle rate was calculated. The geometric model of this solid-state battery is as follows. Figure 1 As shown.

[0067] 1) Calculation of the cycle capacity of solid-state batteries under different external pressures;

[0068] Different external pressures were applied to the NMC811-Li6PS5Cl-Li / In all-solid-state battery, and the cycle capacity and coulombic efficiency were calculated after 10 cycles under each of these different external pressures. The calculation results are as follows: Figure 2 .

[0069] Figure 2In this context, Capacity represents specific capacity, Number of cycles represents the number of cycles, charge represents the charging process, discharge represents the discharging process, and Coulomb efficiency represents the coulomb efficiency.

[0070] 2) Calculation of solid-state battery cycle capacity under different ambient temperatures

[0071] In the temperature-pressure coupled calculation model, the external pressure F is set to 0. A parametric scan of the ambient temperature T is performed (T = range(0, 20, 60) to calculate the specific capacity and cycle retention of the battery during 1-10 charge-discharge cycles at 0℃, 20℃, 40℃, and 60℃. The calculation results are as follows: Figure 3 As shown.

[0072] Figure 3 In this context, Capacity represents specific capacity, Number of cycles represents the number of cycles, charge represents the charging process, discharge represents the discharging process, and Cycle retention rate represents the cycle retention rate.

[0073] The temperature distribution of the NMC811-Li6PS5Cl-Li / In all-solid-state battery during cycling at 0.1C at an ambient temperature of 60°C is as follows. Figure 4 As shown:

[0074] 3) Calculation of solid-state battery cycle capacity under temperature-pressure coupling effect

[0075] The optimal external pressure range for the NMC811-Li6PS5Cl-Li / In all-solid-state battery is 10KN-20KN. Within this optimal range, 15KN was selected as the external pressure applied to the battery in the coupling calculations. The changes in the specific capacity and cycle retention rate of the battery over 10 charge-discharge cycles at different cycling temperatures were calculated. The calculation results are as follows. Figure 5 :

[0076] Figure 5 In this context, Capacity represents specific capacity, Number of cycles represents the number of cycles, charge represents the charging process, discharge represents the discharging process, and Cycle retention rate represents the cycle retention rate.

[0077] The temperature and stress distribution of a 15kN NMC811-Li6PS5Cl-Li / In solid-state battery during the first charge cycle at 60°C are as follows: Figure 6 , Figure 7 As shown.

[0078] 4) Experimental verification

[0079] An ambient temperature of 60℃ and an external pressure of 15KN were selected for relevant experimental verification to demonstrate the accuracy of the calculation model established in this invention.

[0080] The experimental subject was a button-type NMC811-Li6PS5Cl-Li / In solid-state battery with a diameter of 10 mm and a thickness of 2 mm. The preparation and testing of the NMC-Li / In battery are described below. First, a positive electrode composite material was prepared by hand-grinding LiNbO3-coated NMC and Li6PS5Cl powders at a weight ratio of 7:3. An electrolyte layer was prepared by pressing 80 mg of electrolyte powder into a polyetheretherketone (PEEK) mold (10 mm diameter) at 200 MPa. Then, 10 mg of the positive electrode composite material was dispersed on the surface of the prepared electrolyte particles and pressed at 350 MPa. Finally, a lithium / indium foil (0.1 mm thick, 8 mm diameter) was attached to the other side of the electrolyte particles and pressed at 100 MPa. The density of the NMC battery was 8.92 mg / cm³. 2 The battery was subjected to constant current cycling using the Land CT2001A battery testing system (Wuhan Land Electronics Co., Ltd., China).

[0081] A 15 kN external force was applied to the button battery. The battery under this force was then subjected to 10 charge-discharge cycles at 0.1 C in a constant temperature environment of 60°C. The experimental data are as follows: Figure 8 As shown.

[0082] Calculations show that the optimal external stress range for the NMC811-Li6PS5Cl-Li / In solid-state battery is 10KN-20KN. When subjected to an external force of 15KN and cycled at 0.1C in a constant temperature environment of 60℃, the battery exhibits an initial stable discharge capacity of 140.91mAh / g and a capacity retention rate of 97.78% after ten cycles. Experimental data shows that under the same conditions, its initial stable discharge capacity is 142.17mAh / g, and its capacity retention rate after ten cycles is 97.49%.

[0083] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the cycle capacity of a solid-state battery based on a temperature and pressure coupled computational model, characterized in that: Comprising the following steps: 1) Establishing a local current density model of the electrode surface: Establishing a solid-state battery positive electrode in a solid-state battery electrochemical reaction process or Negative electrode surface local current density model j loc : ， where j0 is the exchange current density provided by the solid-state battery; ， η is the local overpotential, defined as follows: ， wherein k0 is the reaction rate constant; F is the Faraday constant; a a and a c are the charge transfer coefficients of the anode and cathode of the solid-state battery, respectively; c s,max and c s,surf are the maximum concentration and surface concentration of solid lithium, respectively; U oc is the open-circuit voltage of the solid-state battery; φ s is the solid electrode potential; φ e is the solid-state electrolyte potential; R is the molar gas constant, which has a value of 8.341 J / (mol·k); T is the temperature of the solid-state battery; is the active lithium ion concentration in the solid-state electrolyte; 2) Establishing a mechanical model of the solid-state battery: Before the mechanical model of the solid-state battery is established, it is assumed that the solid electrode and the solid-state electrolyte of the solid-state battery are isotropic, homogeneous and linearly elastic, and then the total strain condition of the solid-state battery is simulated and calculated by establishing the mechanical model; the mechanical model ε ij is: ， ε ij me For the strain of the solid-state battery caused by external pressure, the calculation formula is: ， where σ ij are stress components; E is Young's modulus; v is Poisson's ratio; δ ij is the Dirac delta function; σ kk is the normal stress; ε ij ei_T The characteristic strain of the solid-state electrode caused by temperature is calculated by the formula: ， where: α and ΔT are the thermal expansion coefficient and temperature change of the solid-state battery, respectively; ε ij ei_c For the characteristic strain of solid-state batteries due to particle diffusion, it is determined by the diffusion coefficient, and the calculation formula is: ， where: Δc is the change of diffusion particle concentration, and Ω is the molar volume of the active material of the solid-state battery; 3) Establishing a temperature-pressure-electrochemical coupling model of the solid-state battery: The established coupling model χ0(T) is: ， wherein: E a,i is the activation energy, χ 0,ref is the reference temperature using the parameter T ref = 25°C; 4) Establishing a capacity attenuation model of the solid-state battery: The capacity attenuation model of the solid-state battery is established by the increase of the SEI film thickness on the negative side of the solid-state battery, and the process is: Local current density j on the surface of a solid-state battery anode particle side is represented as follows: ， wherein: j side,0 defined as exchange current density; F is Faraday's constant; R is molar gas constant; T is solid-state battery temperature; η s The overpotential for the side reaction of the solid-state battery is expressed as follows: ， wherein R sei is the negative-side SEI film resistance, which increases with the increase in the thickness of the negative-side SEI film; U side is the thermodynamic equilibrium potential of the side reaction occurring on the negative side of the solid-state battery, i.e., the standard electrode potential of the side reaction; j is the total reaction current on the solid-state battery anode, which includes the j side and the anode surface local current density model j loc ; Negative electrode side SEI film thickness δ sei The rate of increase of δ is determined by Faraday's law: ， where M sei and p sei are the molar mass and density of the negative electrode-side SEI film, respectively; The resistance Rsei of the SEI film on the negative side is related to δsei, and the calculation formula of Rsei is as follows: ， wherein, κ sei is the conductivity of the negative electrode side SEI film; 5) Inputting the local current density model, mechanical model, coupling model and capacity attenuation model of the electrode surface established in steps 1) to 4) into the multi-physics interface of the COMSOL Multiphysics finite element software, and then inputting the characteristic parameters of the solid-state battery according to the required characteristic parameters of the COMSOL Multiphysics finite element software, combining the models established in steps 1) to 4) with the built-in formulas of the COMSOL Multiphysics finite element software to calculate the cycle capacity of the solid-state battery. 2.The solid-state battery cycle capacity calculation method based on a temperature and pressure coupling calculation model of claim 1, wherein: In the mechanical model, the Young's modulus E and Poisson's ratio v of the composite electrode of the solid-state battery are calculated by using the fitting equation from the COMSOL finite element software, and the equation is represented as follows: ， where E p is the Young's modulus of the active particles; ε e is the volume fraction of the solid-state electrolyte; υ p is the Poisson's ratio of the active particles; ε0, ε1, υ0, m, n are fitting parameters.

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