The diffusion of Li+ in the active material is an important reaction process and is also a limiting part of the internal chemical reaction of the lithium ion battery. Therefore, the Li+ diffusion coefficient is an important parameter for the active material of the lithium ion battery. The diffusion coefficient is important for the rate performance of the lithium ion battery. 4. The meaning of constant current intermittent titration ( GITT ) is an important method for determining the diffusion coefficient.
The GITT method assumes that the diffusion process mainly occurs in the surface layer of the solid phase material. The GITT method mainly consists of two parts. The first part is a small current constant current pulse discharge. In order to satisfy the assumption that the diffusion process only occurs in the surface layer, the constant current pulse discharge Time t is shorter, need to meet t< 2/D , 其中L 为材料的特征长度 , D 为材料的扩散系数; 第二部分为长时间的静置, 以让Li + 在活性物质内部充分扩散达到平衡状态.
The following figure shows a typical GITT process for measuring the diffusion coefficient. The battery is a 1.2 mAh button cell and the positive electrode material is NCM. The battery is first charged to 100% SoC before the test, then discharged at 0.1 C for 15 min, then allowed to stand. At 30min, each discharge is equivalent to about 2.5% SoC, so a total of 40 cycles can be performed. Since the metal Li negative electrode has a very small influence on the battery voltage change, the voltage change during the test mainly comes from the NCM material, that is to say The diffusion coefficient obtained by this method mainly reflects the diffusion coefficient of the positive electrode material NCM.
After the test is completed, we need to use the data obtained above to calculate the diffusion coefficient of the NCM material. Among them, we mainly care about the four voltage data, one is the voltage V0 before the pulse discharge; the other is the constant current discharge transient voltage V1, V0 The difference between V1 and V1 mainly reflects the influence of the ohmic impedance and charge transfer impedance inside the battery on the voltage change; one is the voltage V2 at the end of the constant current discharge, mainly due to the diffusion of Li+ into the NCM material. Voltage change; one is the voltage V3 in the late stage of standing, which is mainly the re-diffusion of Li+ inside the active material, and finally reaches the steady-state voltage change of the active substance. According to the data obtained above, and the second law of Fick The diffusion coefficient of Li+ in a lithium ion battery can be calculated using the formula shown below.
In the above formula, nM is the molar amount, VM is the molar volume, S is the interface area, and t is the discharge pulse duration. If we assume that the NCM particles are rigid pellets, the radius is Rs, then the above formula can be converted into the following formula 2. We can also notice some problems. For example, for materials with very flat voltage platforms such as LTO, LFP and graphite, the variation of Vs is very small in the voltage platform range, close to 0, so the value of the final Ds is also Close to 0, this is obviously inaccurate. To solve this problem, Zheng Shen (first author) and Chao-Yang Wang (corresponding author) of Pennsylvania State University optimize the GITT test results by least squares method. This greatly improves the accuracy of the GITT test.
The following figure shows the model of the button half-cell. The positive electrode is a spherical NCM material and the negative electrode is a metal Li. The impedance model in the half-cell is shown in the following equation. The meaning of the parameters in the formula is shown in the following table.
The figure below shows the solid diffusion coefficient (bottom a) and error of the lithium ion material obtained by the LS-GITT method using the least squares method and the ordinary GITT method according to the test data shown in the first picture at the beginning of this paper. b), wherein the particle radius of the NCM material is Rs=5.3um, from the following figure a, it can be seen that the Ds obtained by the two analytical methods are basically between 10-10-10-11cm2/s (SoC>10%). This is basically consistent with the literature report, but it can be seen that the data volatility obtained by the LS-GITT (solid data point) method is much smaller. The LS-GITT method (solid data can be seen from the error analysis in the following figure b) The error of the point is significantly smaller than the normal GITT method (hollow data point). In most SoC ranges (60%-100%), the accuracy of LS-GITT is an order of magnitude higher than that of GITT. The traditional GITT method is in SoC. The range of 20-60% is more accurate. Once it exceeds this range, the accuracy is significantly reduced, and the optimized LS-GITT method has a very high accuracy in the range of 15%-100%.
The reason why the accuracy of GITT is lower than that of LS-GITT is mainly because the GITT method considers that the active material is mainly surface diffusion and ignores the internal capacity of the active material particles. Let us take NCM material as an example, L2/D is about 5000s, and the discharge pulse The time is 900s, although it is less than 5000s, but it does not satisfy the condition of far less than the condition. Therefore, the voltage change value actually obtained not only includes the value of surface diffusion, but also includes the voltage change caused by the change of SoC, thus leading to the traditional GITT method. The obtained diffusion constant is too large. Although theoretically we can improve the accuracy of GITT by reducing the pulse discharge time, it is unfortunate that as the pulse time becomes smaller, the change of Vs will become smaller, which will lead to lower measurement accuracy. , the increase in noise will also cause the resulting diffusion constant D error to increase.
In view of some problems and shortcomings of the traditional GITT method, ZhengShen overcomes the problem that the GITT method is not accurate enough in some SoC ranges by introducing the least squares method, which significantly improves the constant current intermittent titration in most SoC ranges. The accuracy of calculation is of great significance for the determination of Li+ diffusion coefficient in active materials (see the original content for interested interested partners).
