Voltage curve during overdischarge

The voltage during overdischarge is shown in Fig. 1(a). The overdischarge profile can be approximately divided into 3 stages according to the characteristics of the voltage variations. In Stage I (−11% < SOC ≤ 0%), the voltage dropped rapidly from 3.4 V to the minimum voltage of approximately −2.19 V, following a clear platform at approximately 1 V. In Stage II (−20% < SOC ≤ −11%), the voltage stopped declining and rebounded gradually with several fluctuations. In Stage III (−100% < SOC ≤ −20%), the voltage underwent a monotonic gradual increase asymptotically to 0 V without fluctuations.

Figure 1 Voltage analysis during overdischarge. (a) voltage profile during overdischarge and terminal conditions of cells 2–16 dotted in the descending order of SOC, (b) incremental capacity analysis of Stage II with peaks and valleys marked, (c) enlarged view of Stage II showing the inflection points with error bars. Full size image

The voltage drop in Stage I is caused by the increasing potential of anode and the decreasing potential of cathode; because overdischarge leads to deintercalation of Li+ from the anode and insertion into the cathode. In Stage II, when the anode potential reaches approximately 3.4~3.5 V15,19, anodic corrosion of the Cu collector is triggered; the anode potential thus enters an electrochemical reaction platform for the Cu dissolution. Copper ions dissolved in the electrolyte can travel through the separator and deposit on the cathode; the cathode potential thus increases due to the reduction of copper ions. The overpotential for Cu dissolution can account for the voltage valley at approximately −11% SOC. In Stage III, the electrochemical reactions of Cu dissolution and deposition continue and the internal short becomes more severe, with a decrease of R ISCr . Therefore, the absolute value of the voltage, which is the product of the overdischarge current and R ISCr , decreases and approaches zero.

The cells under overdischarge that were terminated in Stage I exhibited no discernible changes in properties, whereas in Stage III, the voltage increased slowly asymptotically to 0 V, suggesting the occurrence of severe ISCr. However, in Stage II, the properties of the voltage curve were more complex because the results varied at different terminal conditions. To detail the variations in voltage and its influence on overdischarge, the voltage curve of stage II was analyzed by incremental capacity analysis30, as shown in Fig. 1(b); the peaks and valleys of the incremental capacity curve indicate the inflection points of the voltage curve, denoted as MIN, A, B, C, D and E in Fig. 1(c). The terminal conditions in Stage II were chosen to be near the inflection points according to the voltage curve analysis above. Inflection point B in Fig. 1(b) is located at a significant peak of incremental capacity, representing the electrochemical reaction platform where Cu collector dissolution is inferred. Figure 2 illustrates the process of Cu dissolution during overdischarge and the formation of the ISCr induced by overdischarge. The internal short caused by Cu deposition occurs after the cell is overdischarged to SOC < −12% and becomes more severe during the overdischarge process.

Figure 2 Copper dissolution and deposition during overdischarge and the formation of internal short circuit. Full size image

Recharging after different degrees of overdischarge

Cells were recharged with 8.33 A (1/3C) current after the overdischarge tests terminated under different conditions (see Supplementary Table S1). The recharge experiments were separated into two categories (with and without ISCr) according to the occurrence of ISCr.

Cells 2, 3 and 4 did not exhibit ISCr after being overdischarged to MIN, A and B (Fig. 1(c)), respectively, as they could be fully recharged and cycled without any signs of ISCr or significant capacity loss. The results of the non-ISCr cells suggest that if the overdischarge is terminated before point B at approximately −12% SOC (the first platform after the occurrence of the minimum voltage), the cell can be fully charged back and reused with only minor side effects.

The other samples (with ISCr) overdischarged over point B showed evident characteristics of ISCr with different resistances (R ISCr ). Cells 5 and 6, overdischarged to −13.0% and −13.7% respectively, could be fully recharged with 8.33 A (1/3C) current (Fig. 3(a)). After the recharge, cells 5 and 6 displayed significant self-discharge and the depleting OCV of cells 5 and 6 is shown in Fig. 3(b). It was more difficult to fully charge cell 6 compared to cell 5, as the charging time was longer for cell 6. Moreover, the OCV of cell 6 depletes more rapidly than that of cell 5. This phenomenon suggests that cells 5 and 6 both suffered from ISCr and the R ISCr of cell 6 was lower than that of cell 5.

Figure 3 The recharge process and depleting OCV. (a) recharge process of cells 5 and 6 with ISCr, compared with normal cell 1, (b) the depleting OCV and simulation results of cells 5 and 6. Full size image

Cells that had been overdischarged to SOC < −14.5% could not be fully recharged to 4.2 V with 8.33 A (1/3C) current. During the recharge process, their voltages increased once the recharge began but soon reached a stable value. The stable voltage during the recharge process becomes lower as the overdischarge increased further, suggesting a lower R ISCr .

Estimation of R ISCr using a prognostic/mechanistic model

R ISCr can be quantitatively evaluated by analyzing the depleting OCV after the cell is fully recharged. The R ISCr of cells 5 and 6 are estimated using prognostic/mechanistic model8,27,28 combined with an equivalent circuit model of a battery with ISCr29, as shown in Fig. 4(b). According to the equivalent circuit model, the simulated OCV, denoted as V sim (t) in Eqn. (1), is equal to the voltage caused by R ISCr .

Figure 4 Equivalent circuit model. (a) a normal battery, (b) a battery with ISCr. Full size image

The current I(t) is a constant 0 because the voltage of the battery is observed at an open circuit, as shown in Eqn. (2). Combining Eqn. (2) with Kirchhoff’s current law in Eqn. (3), we obtain Eqn. (4), which indicates that the current through R ISCr and internal resistance R should be the equivalent at any given time.

Eqn. (5) is written according to Kirchhoff’s voltage law, where E(t) denotes the electromotive force given by the prognostic/mechanistic model in Eqn. (6). V p (y(t)) and V n (x(t)) denote the cathode potential and anode potential, respectively. y(t) is defined as a customized variable in the half-cell tests instead of the stoichiometric lithium content in the cathode8. Furthermore, x(t) refers to the value x in Li x C 6 31. Half-cells with Li y Ni 1/3 Co 1/3 Mn 1/3 O 2 (NCM)/Li and graphite/Li were made and cycled at C/20 current at 25 °C to acquire V p (y) and V n (x) (see Supplementary Fig. S1).

Eqn. (7), which is derived from Eqns (4, 5, 6), determines the current during self-discharge. By combining Eqn. (7) with Eqn. (1), we obtain the expression of V sim (t) in Eqn. (8).

The cathode potential V p (y(t)) and anode potential V n (x(t)) change over time during the self-discharge process because y(t) and x(t) are functions of time, as shown in Eqns (9, 10), where y 0 (x 0 ) denotes the initial value of y (x), C p (C n ) represents the capacity of the cathode (anode) and is the integral of the self-discharge current. The cathode potential and anode potential during self-discharge can be determined by combining y(t) and x(t) with the separated half-cell quasi-equilibrium voltage curve, as shown in Supplementary Fig. S1.

Therefore, the OCV during self-discharge can be simulated from Eqns (7, 8, 9, 10) by choosing appropriate settings for [R, R ISCr , y 0 , x 0 , C p , C n ] using an optimization method, such as a genetic algorithm, as in refs 8,28. The root mean squared error (RMSE) between the simulated open circuit voltage V sim (t) and the observed open circuit voltage is calculated to evaluate the degree of coincidence, as shown in Eqn. (11). n is the length of data used for the simulation and represents the time points.

Figure 3(b) compares the simulated OCV with the observed OCV for cells 5 and 6. The simulated voltage curves fit the experimental observations well, indicating that the model and identified parameters approximately reflect the ISCr of the overdischarged cells.

The of the cells that could not be fully recharged with 8.33 A (1/3C) current is estimated simply dividing the stable voltage by the charging current, because all of the charging current is entirely bypassed by R ISCr .

Figure 5 shows the relationship between the estimated R ISCr and the overdischarge SOC. The results suggest that ISCr occurs after the inflection point B at approximately −12% SOC, where the first platform after the minimum voltage is located. The R ISCr declines with a lower overdischarge SOC. This method of inducing ISCr by overdischarge is effective and can be well controlled.

Figure 5 The relationship between R ISCr and terminal SOC. Full size image

SEM and XRD results

The SEM and XRD results reveal the surface morphology and structural characterization of ISCr induced by overdischarge. Digital photographs of the electrodes dissembled from cells 1 and 10, which were dismantled after the overdischarge test, are shown in Fig. 6(g–j). Both the cathode and anode of cell 10 are stained with Cu deposition, which is irregularly observed throughout the entire electrodes.

Figure 6 SEM images and digital photographs of cells 1 (SOC = 0%) and 10 (SOC = −20%). (a) anode of cell 1 (SEM image), (b) anode of cell 10 (SEM image), (c) anode of cell 10 under high-magnification (SEM image), (d) cathode of cell 1 (SEM image), (e) cathode of cell 10 (SEM image), (f) cathode of cell 10 under high-magnification (SEM image), (g) anode of cell 1 (digital photograph), (h) anode of cell 10 (digital photograph), (i) cathode of cell 1 (digital photograph), (j) cathode of cell 10 (digital photograph). Full size image

The SEM morphologies of the materials on the electrodes from cells 1 and 10 are compared in Fig. 6(a–f). Figure 6(a,d) show normal graphite and Li y Ni 1/3 Co 1/3 Mn 1/3 O 2 materials on the anode and cathode, respectively. The surface of the graphite anode of cell 1 is smooth and the cathode is flat with a porous structure. However, after overdischarge to −20% SOC (as in cell 10), the smooth graphite anode is dotted with small spherical depositions, as shown in Fig. 6(b,c), whereas the cathode of cell 10 is also contaminated by larger spherical depositions on the cathode materials, as shown in Fig. 6(e,f).

The XRD results in Fig. 7 suggest that Cu deposition increases gradually on both the anode and cathode during the entire overdischarge process. The emerging peaks of Cu support the previous assumption that Cu foil dissolution and deposition occur on the electrodes during overdischarge.

Figure 7 XRD results of cells 1, 5 and 10. (a) anode (graphite), (b) cathode (NCM). Full size image