Effects of cycling on lithium-ion battery hysteresis and overvoltage

Currently, lithium-ion batteries are widely used as energy storage systems for mobile applications. However, a better understanding of their nature is still required to improve battery management systems (BMS). Overvoltages and open-circuit voltage (OCV) hysteresis provide valuable information regarding battery performance, but estimations of these parameters are generally inaccurate, leading to errors in BMS. Studies on hysteresis are commonly avoided because the hysteresis depends on the state of charge and degradation level and requires time-consuming measurements. We have investigated hysteresis and overvoltages in Li(NiMnCo)O2/graphite and LiFePO4/graphite commercial cells. Here we report a direct relationship between an increase in OCV hysteresis and an increase in charge overvoltage when the cells are degraded by cycling. We find that the hysteresis is related to diffusion and increases with the formation of pure phases, being primarily related to the graphite electrode. These findings indicate that the graphite electrode is a determining factor for cell efficiency.

Currently, studies on the effect of hysteresis are commonly avoided in commercial Li-ion applications because hysteresis measurements are time-consuming, with the hysteresis depending on the battery degradation and state of charge (SoC). If the increase in hysteresis could be determined from the increase in overvoltage, which can be obtained from data that are already available in the BMS, the time required for updating the OCV hysteresis in practical applications would be drastically reduced. In this paper, we aim to find a relationship between the variation in overvoltage with ageing, which reflects the transport and transfer characteristics of the cells, and OCV hysteresis.

Results
Overvoltage and OCV hysteresis in NMC cells. The overvoltages generated in NMC cells during charging (η CH ) and discharging (η DCH ) and the OCV hysteresis (V HYS ) are obtained from the difference between the cell voltages and OCVs (Fig. 1), as described in the Methods section. The overvoltages are calculated at low rates (C/50 and C/25) for fresh and aged cells (Fig. 2). In general, we find that the generated overvoltage increases during cycling, except for particular SoC values, such as those near 60%, when discharging at C/25 (Fig. 2d).
We find that the overvoltage depends on the charge and discharge rates, as expected from the literature 20 . However, we note that the overvoltage rate dependence is also SoC dependent. For instance, this dependence can be clearly observed in the discharge overvoltage of an aged cell if we compare the results for an SoC of 64% at C/50 (Fig. 2b) and C/25 (Fig. 2d), in which a large variation is observed compared with neighbouring SoCs.
We find that the OCV hysteresis is larger for the aged cells (Fig. 3), except for SoCs, of approximately 25% and 13%, for which there is no variation with ageing. For both ageing states, various peaks are observed in the curves, which are related to a larger hysteresis at some particular SoCs. We find that these peaks tend to shift to higher SoCs as the cell ages.
In general, the increase in overvoltage is larger during charging than during discharging (Fig. 4), indicating that more energy is lost during charging as the cells age, which reduces their energy efficiency. Interestingly, we find that the larger increase in overvoltage during charging compared with discharging (determined from the difference between the two contributions) shows a direct correspondence with the increase in hysteresis (blue and green open symbols in Fig. 4, respectively). Moreover, some differences are observed between the results for C/25 and C/50 (Fig. 4a,b). The most evident difference is detected at SoCs near 64%, at which the increase in charge overvoltage obtained at the higher rate of C/25 (Fig. 4b) is larger than that obtained at the lower rate of C/50 (Fig. 4a). This difference may be attributed to a kinetic artefact introduced by the larger current for C/25. Smaller differences between the curves (on the order of a few millivolts) are observed outside this SoC range.
Overvoltage and OCV hysteresis in LFP cells. The same analysis was conducted in an LFP/graphite cell in order to generalise the results obtained for the NMC/graphite cells. The results for the LFP cells show that the charge overvoltage increases with ageing, whereas the discharge overvoltage decreases (Fig. 5). In a previous study, we demonstrated that the discharge overvoltage decreases during the first 300 cycles (due to a decrease in impedance) and then increases until the end of the ageing test (cycle 1049) 21 . However, the increase experienced by the cells during the cycling test is not sufficient to exceed the initial discharge overvoltage. Thus, if intermediate cycles are not evaluated, one might wrongly conclude that the discharge overvoltage decreases with cycling, whereas in reality, the overvoltage has been increasing for more than 700 cycles. For this particular chemistry, initial decreases in overvoltage or impedance have been commonly reported in the literature [22][23][24] . The decreased impedance and increased capacity at high rates upon initial stages of cycling have been previously attributed to electrochemical milling or decrepitation of the LFP particles 25,26 . However, the aim of this paper is not to determine the origin of this decrease but whether there is any relation between overvoltage and hysteresis.
If we compare the hysteresis increase during the cycling test (ΔV HYS ) with the difference between the increases in charge and discharge overvoltages (Δη CH-DCH ), we find a correspondence between the two parameters ( Fig. 5), www.nature.com/scientificreports www.nature.com/scientificreports/ as observed for the NMC cells (Fig. 4). Although the increase in discharge overvoltage is negative, the larger increase in charge overvoltage follows the same tendency as the hysteresis increase, and both terms have similar values. Larger differences can be observed at SoC values above 95%.

OCV hysteresis and phase transformations in NMC cells.
The SoCs corresponding to the formation of various phases through which the electrodes pass during the charging process were determined by an incremental capacity analysis (highlighted in yellow and separated by vertical dashed lines in Fig. 6). A correspondence is found between the SoCs at which hysteresis tends to increase and the SoCs at which the phases are formed (Fig. 6). In particular, six peaks (or discontinuities) are detected in the hysteresis for the fresh cell (numerically labelled in Fig. 6a,c), whereas only five peaks can be identified for the aged cell (Fig. 6b,d). The peaks labelled as 2, 3 and 4 coincide with the formation of graphite stages (Fig. 6a). In a previous work, we attributed the phase changes coinciding with peaks 2, 3, 4 and 5 to the negative electrode 8 . In particular, these changes were associated with the formation of 4L, 3L, 2L and 2 stages of graphite 8 . Nevertheless, we find that peak 6 coincides with a phase transformation in the lithium oxide electrode (Fig. 6c). Unfortunately, no information can be provided about the particular phase to which the electrode transforms at these SoCs. Unlike the other peaks, the origin of peak 1 is not clear because it coincides with the formation of phases at both electrodes (Fig. 6a,c), as will be discussed in detail in the following section.  www.nature.com/scientificreports www.nature.com/scientificreports/

Similarities in OCV hysteresis in NMC and LFP cells. Similarities in hysteresis are expected between
the two cells considered in this study (NMC and LFP), as both cells contain graphite as a negative electrode. Therefore, the hysteresis measured for the NMC cells was compared with that for the LFP cells (Fig. 7). The same pattern was observed (Fig. 7a), with an exact match for the peak positions and amplitudes, except for the peak at the lowest SoC (peak 1), was reported by Barai et al. for a cell composed of LFP and graphite 27 . We found that peaks 1-5 appear in both evaluated cells (NMC and LFP), particularly in the fresh cells (Fig. 7a). These results indicate that peaks 1-5 correspond to the graphite electrode. Graphite passes through five different phases during lithiation and delithiation, which correspond to the five peaks identified in our results (Fig. 7a). For the NMC cells, the only peak that could not be associated with a particular electrode in Fig. 6 was peak 1 because single phases were formed in both electrodes. From the comparison with the LFP cell, it is clear that peak 1 corresponds to the graphitic electrode (Fig. 7). Despite a clear identification of the peaks corresponding to graphite, the peaks occur at different SoCs and exhibit different amplitudes depending on the chemistry.  www.nature.com/scientificreports www.nature.com/scientificreports/

Discussion
We found that the increase in overvoltage at very low rates (C/50 and C/25) after the degradation process (Δη CH and Δη DCH ) coincide for both charging and discharging, but an additional term arises during charging. This additional term is directly related to the hysteresis. This affirmation is valid for both chemistries, NMC and LFP, as inferred from Figs 4 and 5. As a physical interpretation, it is assumed that one component of the transport and charge transfer is equally affected by ageing during charging and discharging, whereas another component of the transport and charge transfer (and possible side reactions) is affected only during charging. In general, the increase in overvoltage with cycling can be explained as the transport of ions becoming more inefficient (i.e. dissipating more energy) and/or the charge transfer slowing, which also dissipates more energy. This effect arises from the consumption of additional energy during the charging process, as the cell is cycled. Consequently, the  www.nature.com/scientificreports www.nature.com/scientificreports/ final state of the cell differs depending on the direction of the current, as reflected by the hysteresis. We conclude that the additional energy required for recharging the battery after cycling is due to the increase in hysteresis, as can be inferred from the results (Figs 4 and 5).
The assumption of side reactions may be appropriate because the voltage during charging is larger than that during discharging, resulting in a greater possibility for overcoming the activation energy of secondary reactions. However, the degradation of the transport and transfer characteristics may be produced by changes in the conductive properties of any of the elements comprising the cell or by the reduced rate of the electrochemical reaction. For the SoCs at which the single phases are formed, there is a sharp increase in overvoltage 8 and hysteresis (Fig. 6). The increase in overvoltage towards the end of a phase transformation has been associated with ionic transport, particularly diffusion 8 . Thus, the results indicate that hysteresis and diffusion are closely related. Possible causes of the deterioration of the transport properties of the cells include wearing of the components, loss of contact or defect formation in the electrode structure. In particular, defects in the electrodes have been related to hysteresis 9,19,28 . Irreversible processes associated with hysteresis include mechanical strain 9,29 , particle fractures 29 , the formation of dislocations 9,19,28 , structural disordering 28 , boundary motion and plastic deformation 19,28 and volume changes, dislocations or the presence of impurities 19 . Some factors that contribute to hysteresis and enhance the morphological changes include electrochemical inhomogeneities in phase and composition 29 , the movement of an interface 19 or the strain accommodation energy of phase transformations induced from the volume changes between lithiated and delithiated phases 9,19 . Therefore, the occurrence of morphological changes due to cycling may be responsible for the coincidence in overvoltage and hysteresis increases. In fact, electrode defects produced during cycling (primarily during the charging process) have been reported in the literature 10,29,30 .
Hysteresis is generally not considered in practical applications because it usually accounts for a small portion of the total loss. However, the neglect of hysteresis is a source of error, which accumulates during battery operation. As we have shown in this paper, valuable information can be obtained from the hysteretic behaviour of a system in terms of energy efficiency and mechanical degradation. For greater accuracy in practical applications, we aim to facilitate an online calculation of the OCV hysteresis by defining a relationship between hysteresis and battery performance (from overvoltage measurements). Our results exhibit a direct relationship between the observed hysteresis increase with cycling and the overvoltage increase with ageing. Furthermore, the same behaviour has been observed in two different chemistries, indicating a possible generalisation of this technique. This generalisation would enable updating of the OCV hysteresis as cells are cycled in real applications.

Evaluated cells. We analysed two types of commercial Li-ion cells with LiCoO 2 -Li(NiMnCo)O 2 (LCO-
NMC or simply NMC) and LiFePO 4 (LFP) as the positive electrode and graphite as the negative electrode. The NMC cells had a capacity of 2.8 Ah and were supplied by LG_Chem in the 18650 format. The expected cycle life reported by the manufacturer at which the cell maintains a capacity equal to or higher than 78% of the nominal capacity is 300 cycles when charging and discharging at C/2 at a temperature of 23 °C ± 2 °C. LFP cells were provided by AA Portable Power Corp in the 14430 format with a nominal capacity of 0.4 Ah. The expected cycle life reported by the manufacturer at which the cell maintains a capacity equal to or higher than 70% of the nominal capacity is 1000 cycles when charging and discharging at a symmetric rate of C/5 at a temperature of 20 °C ± 5 °C.
Cycling. To evaluate the cells at various ageing levels, the cells were subjected to a cycle-ageing process. The cells were charged at a constant current and voltage at the recommended C-rate and discharged at the maximum discharge C-rate allowed by the manufacturer. NMC cells were charged at C/2 and discharged at 3C/2 in an HVBT 5560 Arbin Tester capable of measuring current and voltage. The cells were subjected to 350 cycles in a climatic chamber at 25 °C. The capacity fade experienced by the cells during discharging at C/25 and 3 C/2 was 15% and 20%, respectively. LFP cells were charged at C/5 and discharged at 2C. The cells were cycled 1000 times in a climatic chamber at 25 °C. The LFP cells were cycled in two steps with two different instruments. The first cycling step was performed in an HVBT 5560 Arbin Tester, and the second cycling step was conducted with a VSP Bio-logic potentiostat/galvanostat under the same conditions. The temperature was controlled with a laboratory-cooled incubator, ILW53, provided by Pol-Eko Aparatura. The capacity fade experienced by the cells during discharging at C/25 and 2C was 23% and 15%, respectively.
Prior to the cycle-ageing test, the cells underwent six formation cycles at 25 °C to stabilise their capacity and to allow the initial formation of the SEI layer. Thus, we consider the cells as fresh immediately after the formation cycles (fresh cells) and as aged at the end of the cycle-ageing procedure (aged cells). The capacity fade experienced by the NMC cells at a discharging rate of 3 C/2 was 24% with respect to the nominal capacity and 15% in the case of the LFP cells, evaluated at a discharge rate of 2 C. A more detailed description of the ageing process can be found elsewhere 21 . OCV and hysteresis. The OCV measurements were based on the galvanostatic intermittent titration technique (GITT), which is commonly used to measure the OCV of batteries 9,31 . The GITT consists of charging and discharging the cell with pulses followed by relaxation periods. At the end of each relaxation period, the OCV is measured. GITT measurements were carried out during charging and discharging, resulting in two OCV curves: one for charging (OCV CH ) and one for discharging (OCV DCH ). The difference between the charging and discharging OCV curves is termed the OCV hysteresis (V HYS ) 27,32,33 : www.nature.com/scientificreports www.nature.com/scientificreports/ In this study, the GITT was performed with 150-min charge/discharge pulses at C/50 followed by a 16-h resting period. To maintain a constant starting SoC, four charge/discharge cycles at C/50 with a constant current were applied, followed by a remnant capacity procedure at C/50 prior to the GITT analysis. Measurements were acquired with a VSP potentiostat/galvanostat provided by Bio-logic. During the GITT tests, the cells were configured for two electrode measurements at four points, in which voltage measurements were carried out closer to the electrodes than the current injection. The cells were maintained at 25 °C in an IL53 incubator provided by Pol-Eko Aparatura.
Overvoltage calculation. The overvoltage was calculated as the difference between the OCV obtained by the GITT technique and the cell voltage under polarisation (V cell ) during discharging (η DCH ) and charging (η CH ):

CH cell CH CH
OCV hysteresis and overvoltage increases. The increases in hysteresis and overvoltage due to cycling were obtained as the difference between the aged cell values and the fresh cell values. For the hysteresis, the increase was obtained for each SoC value (ΔV HYS ), as the difference between the hysteresis measured for the aged cell (V HYS(aged) ) and that for the fresh cell (V HYS(fresh) ): The increase in overvoltage was obtained for each SoC value during discharging and charging (Δη DCH and Δη CH ) as the difference between the overvoltage produced in the aged cell (η DCH(aged) and η CH(aged) , respectively) and that in the fresh cell (η DCH(fresh) and η CH(fresh) ): In general, we found that the overvoltage increase was larger during charging. Thus, to represent the larger increase in overvoltage experienced by the cells during charging (Δη CH-DCH ), we calculated the difference between the increase during charging (Δη CH ) and the increase during discharging (Δη DCH ):

CH DCH C H D CH
Half-cells fabrication. Cell opening was applied to the NMC cells, as described elsewhere 21 . Cell opening was performed for one fresh cell after the formation cycles (fresh cell) and one aged cell after the cycle-ageing process (aged cell). Round samples with a diameter of 16 mm were harvested from positive and negative electrodes of the fresh and aged cells.
To build half-cells, one side of the active material of the harvested samples was removed by applying N-methyl-2-pyrrolidone (NMP) solvent by hand until the active material detached from the current collector. In particular, half-cells were built in a coin cell format by introducing the harvested positive or negative electrode, fresh separator, 90 μL of fresh electrolyte and metallic lithium as the counter electrode.
Incremental capacity analysis. Incremental capacity analysis was performed for the half-cells at 25 °C during a charging process at C/25. Thus, the injected charge was measured as a function of the measured voltage. At each point, the incremental capacity was obtained as the portion of capacity associated with each voltage step (dQ/dV) and was represented as a function of the SoC.
Peaks in the incremental capacity curves indicate the coexistence of distinct phases (represented as plateaus in thermodynamic voltage curves). Each chemistry has a characteristic peak pattern, and each peak in the incremental capacity curve has a unique shape and intensity. In contrast, changes in slope in the thermodynamic voltage curve (transitions between plateaus) are related to the formation of pure or single phases [34][35][36][37] .

Conclusions
We found that the hysteresis increases towards the end of phase transformations (i.e. the formation of pure phases) as well as the overvoltage, which has been previously associated with diffusion (transport characteristics). After ageing the cells by cycling, we found that the hysteresis increased and that the overvoltage exhibited a larger increase during charging than discharging. The most important finding of this work is a direct correspondence between the additional increase in overvoltage during charging and the increase in hysteresis after the cycle-ageing test. The same trend was detected in both NMC and LFP cells. We found that the increase in hysteresis due to cycle ageing is primarily related to the graphite electrode. In particular, mechanical degradation (i.e. structural modification of the cells) is a possible cause, as it would alter the transport characteristics (diffusion overvoltage) and would also be reflected in the OCV hysteresis.