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Understanding the dilation and dilation relaxation behavior of graphite-based lithium-ion cells
Journal of Power Sources 317 (2016) 93e102
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Understanding the dilation and dilation relaxation behavior of graphite-based lithium-ion cells € we, Jon V. Persson, Michael A. Danzer Marius Bauer*, Mario Wachtler, Hendrik Sto Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW), 89081 Ulm, Germany
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
At high rates, dilation is affected by formation of >2 graphite staging compounds. There can be either positive or negative dilation relaxation after current pulses. A model explaining staging-related relaxation phenomena is presented. Staging relaxation and lithium plating are detectable in dilation data. A compensation procedure for thermal expansion in dilation data is presented.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2016 Received in revised form 19 March 2016 Accepted 22 March 2016
The dilation of lithium-ion cells is sensitive towards swelling phenomena caused by both graphite staging processes and lithium plating on graphite anodes. In this work, the dilation behavior of graphite/ NMC pouch cells is studied with a focus on relaxation phenomena occurring after current pulses. In order to prevent misleading interpretations due to thermal effects, thermal expansion is quantified and a method for the thermal compensation of dilation data is developed. Dilation data are recorded for quasiequilibrium cycling as well as for current pulses at high rates. In the quasi-equilibrium case, the staging behavior is characterized based on dilation and voltage data. By comparison with a graphite half-cell measurement, the major effects in full cell dilation are confirmed to be anode related. In the high rate case, the dilation responses to the actual pulse and the subsequent relaxation phases are recorded systematically. Positive and negative relaxation phenomena are observed depending on the SOC. They are ascribed to both graphite staging and lithium plating processes. A model is presented explaining the unexpected relaxation effects by a temporary coexistence of three or more staging compounds during high rate lithiation and delithiation. Our data thereby confirm the shrinking annuli model introduced by k. Heb and Nova © 2016 Elsevier B.V. All rights reserved.
Keywords: Lithium-ion cell Dilation Relaxation of thickness Lithium plating Graphite staging Swelling
1. Introduction
* Corresponding author. E-mail address: [email protected] (M. Bauer). http://dx.doi.org/10.1016/j.jpowsour.2016.03.078 0378-7753/© 2016 Elsevier B.V. All rights reserved.
Over the last years, dilatometry has proven useful for characterizing lithium-ion cells and individual electrodes. Regarding individual electrodes, electrochemical in-situ dilatometry is a convenient tool to measure expansion/contraction
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during charge and discharge. In contrast to X-ray or neutron diffraction methods, dilatometry monitors the overall expansion of the whole composite electrode. Therefore, dilation data also include the influence of porosity within and between the active material particles, anisotropic expansion effects due to preferential particle orientation, swelling phenomena due to electrolyte uptake by the electrode and electrode binder, and the like. To our knowledge, the first dilatometric investigations of graphite were performed by J.O. Besenhard et al. [1,2], who studied the intercalation of HSO 4 /H2SO4. Furthermore, they investigated the intercalation of lithium ions [3,4] and demonstrated that the intercalation of solvated lithium ions is involved in the early stages of the formation of the solid electrolyte interphase (SEI) [3]. Similar investigations were performed by T. Ohzuku et al. [5]. More recently M. Hahn et al. developed dilatometers with improved resolution, and used it to study charge storage phenomena in supercapacitor electrodes [6,7] as well as to revisit the lithium ion intercalation into graphite for a more indepth analysis [8]. Lately, in-situ dilatometry has been used to study the intercalation of anions into graphite, viz. PF 6 anions from organic carbonate solutions at potentials >4.6 V vs. Li/Liþ, in view of using graphite as a cathode material, e.g. in dual carbon batteries [9]. Regarding the characterization of full-cell behavior, dilatometry is particularly interesting because of its non-destructive character and ability to provide information at low and high current rates. In contrast, many measurement techniques based on cell voltage require a quasi-equilibrium cell state in order to work. Electrochemical impedance spectroscopy, for instance, is only applicable to linear, time-invariant systems and therefore not valid for characterizing battery cells under high current loads [10]. Similar restrictions apply for methods based on a differential evaluation of the voltage response in quasi-equilibrium cycling (differential voltage analysis, incremental capacity analysis [11,12]). Obtaining valuable diagnostic information from voltage measurements at arbitrary current loads is obviously challenging. Dilatometry on full-cells, however, can fill this gap. It can be realized by measuring the external cell dilation using dial gauges, strain gauges, laser scanners, or, in a wider sense, pressure sensors fitted into battery packs. In this work, a dial gauge is used for the investigation of individual lithium-ion pouch cells. It has been shown already that dilation data allow for the online detection of lithium plating [13] and that also thermal expansion and lithium intercalation contribute to the swelling of the cell [14,15]. In this work, we present both half-cell and full-cell dilation experiments at low rates allowing us to identify the origin of dilation features observed for full-cells (graphite-anode-related or not). Based on the low rate results, the dilation behavior is then investigated for charge pulses at higher rates. For the first time, the relaxation phenomena after such high rate current pulses are analyzed, explained and modeled in detail.
2. Fundamentals During cycling, the cell thickness of lithium-ion pouch cells varies in the range of a few percent of the total cell thickness depending on the thickness shares and types of active material. For the cells investigated here, the relative dilation is in a range of 1 e 2 % during cycling. Both reversible and irreversible thickness changes can be observed and assigned to different effects in the cell. Contributions from the electrodes and thermal expansion can be distinguished.
2.1. Anode dilation 2.1.1. Dilation caused by intercalation of lithium ions (graphite staging) Graphite is well known for its ability to intercalate a large variety of guest species such as lithium and to form so-called graphite intercalation compounds (GICs), also known as staging compounds. The guest species are normally not uniformly distributed within the graphite lattice, but rather structures with periodically arranged intercalate layers are formed. This phenomenon is called staging. The GICs are usually labelled according to their stage index, which describes the number of graphene layers between two intercalant layers. Table 1 gives an overview of the lithium GICs formed during electrochemical charge and discharge, along with the approximate compositions x in LixC6, as proposed in Ref. [5], and with the average spacings d between the graphene layers, based on Refs. [5] and [16,17]. It should be noted that the stoichiometry of the staging compounds 3L and 4L is not well defined, and that also different compositions with less lithium have been reported [16e18]. The variations of average layer spacings d for the individual GICs explain why staging leads to reversible dilation during the lithiation and delithiation of the anode. At the beginning of the electrochemical lithiation of graphite a small amount of lithium is randomly distributed within the graphite lattice, forming a solid solution-type compound (1L). After exceeding a critical amount of lithium, an ordering of the lithium atoms takes place within the graphite lattice, and subsequently the stage 4L, 3L, 2L, 2, and 1 compounds are formed. In the dense stage 1 compound every gallery between two graphene layers is occupied by lithium. Within each gallery the lithium atoms are located at the centers of the hexagonal prisms formed by the carbon hexagons of the two adjacent graphene layers, and only every nextnearest site is occupied. This is the maximum amount of lithium which can be accommodated at room temperature and ambient pressure, yielding a lithiation of x ¼ 1 (LiC6) with a theoretical capacity of 372 mAh g1. In the dense stage 2 compound only every second gallery is filled, and all positions within a lithium gallery are occupied (as in the stage 1 compound), yielding a stoichiometry of x ¼ 0.5 (LiC12). For the dilute, liquid-like stage compounds 2L, 3L, and 4L, every 2nd, 3rd, or 4th gallery is filled with lithium. Unlike in the dense stage 1 and 2 compounds, however, the lithium layers are not completely filled, resulting in lower amounts of lithium stored than in the corresponding (hypothetical) dense stage compounds. The phase transitions 1L 4 4L, 3L 4 2L, 2L 4 2, and 2 4 1 are classical 2-phase reactions, giving rise to the typical potential plateaux in the charge/discharge curves, which are characteristic of graphite. The situation is less clear for the 4L 4 3L transition, and a sloping potential decrease is observed with a gradual shift of the Xray diffraction peaks, which points to a single-phase transition [18,5]. Also the transition from empty graphite (2H) to 1L is a single-phase transition. The stage 2L compound is given with values x z 0.25 [18] up to x ¼ 1/3 [16] in the literature. The formation of 2L may be suppressed depending on temperature [18]. (Note that the nomenclature of the stage 1L, 4L, and 3L comk [19] to pounds follows a recent proposal by M. Heb and P. Nova indicate their similarity with the 2L compound, with incompletely filled lithium layers. The same compounds are usually denoted as 10, 4, and 3, respectively.) 2.1.2. Dilation caused by lithium plating As already reported in the literature for a 20 Ah pouch cell [13], one can observe an additional thickness increase for high charge rates at low temperatures. This increase can be attributed to the
M. Bauer et al. / Journal of Power Sources 317 (2016) 93e102
deposition of lithium metal on the negative electrode (lithium plating) which occurs if the local potential drops below 0 V vs. Li/ Liþ [20]. After the charge current is switched off, there is a partial relaxation of this additional cell dilation, which can be explained by intercalation of a fraction of the plated lithium into the graphite electrode (compare [13]). Consequently there are both reversible and irreversible effects of lithium plating on cell thickness. 2.2. Cathode dilation Just like on the negative electrode (denoted as anode), lithium insertion into the positive electrode (cathode) will also have an effect on cell thickness. In our work, cells with an NMC (lithium nickel-manganese-cobalt oxide) chemistry for the positive electrode are investigated. Structural analyses of this material show monotonously decreasing unit cell volumes as the lithiation degree of NMC decreases (as the cell gets charged). The effect is slightly enhanced for low lithiation degrees y < 0.5 in LiyCo1/3Ni1/3Mn1/3O2 [21,22]. In a dilatometric study conducted by Nagayama et al. [23] with an LTO/NMC chemistry, NMC-related dilation was evaluated in a full-cell configuration (LTO is a zero strain material). The cell was shown to be dimensionally highly stable as long as the NMC electrode was operated at voltages up to 4.15 V vs. Li/Liþ. Only at high potentials, some cell shrinkage was detected. In summary, dimensional changes of the NMC cathode are always negative during delithiation (charge). In a wide range of SOC they can be neglected compared to anode-related effects. 2.3. Thermal expansion and its compensation in dilatometry data In addition to the dilation effects caused by lithium insertion or plating, dilatometry data always include contributions from thermal expansion or contraction of both the cell and the measurement set-up. It turns out that in the measurements carried out in this paper, where the ambient temperature is kept constant during each individual test, thermal expansion is negligible compared to the gauge resolution. From the thermal characterization presented in Appendix A, it is clear, however, that in an application of dilatometry for diagnostic purposes on commercial battery modules, where temperature is varying in a range of more than a few degree Celsius, the compensation of thermal expansion in the dilation data is essential to avoid misinterpretation of the data. Please refer to Appendix A for detailed results regarding thermal expansion and for an algorithm to compensate for it. 3. Experimental 3.1. Low-rate dilatometry of a graphite half-cell The half-cell dilatometry measurement of graphite has been performed with an ECD-1 dilatometer cell from El-Cell GmbH (Germany). The dilatometer cell employs a porous glass frit as separator, which serves as a rigid base on which the working electrode can expand. Therefore, only the expansion of the working electrode is measured. (It thus differs from the dilatometer described in Ref. [5] and from the measurement set-up used for the dilation measurements of the pouch-cells in the present work, where the expansion of the whole working electrode/separator/ counter electrode assembly is measured.) The electrode expansion is transmitted via a titanium membrane and a piston onto a linear variable differential transformer (LVDT), which produces a voltage output which varies linearly with the electrode expansion. The graphite electrode under investigation has the composition 92 wt.% graphite (SFG 6, Timcal) and 8 wt.% poly(vinylidene fluoride) (PVdF,
95
Solef 6020, Solvay Solexis), and is prepared by a doctor-blade coating process as described before [24]. The electrode has a diameter of 9 mm and contains ~3 mg of active material. It is used without previous pressing or calendering. Lithium metal is used as counter electrode (placed on the opposite side of the glass frit), and 1 M LiPF6/ethylene carbonate: dimethyl carbonate (1:1 by wt.) (battery grade, UBE Industries) as the electrolyte. Note, that the graphite electrode is charged to x z 0.75 only. This corresponds to the typical maximum lithiation state of graphite in a full-cell, where the anode capacity is over-dimensioned relative to the cathode capacity. 3.2. Low-rate dilatometry of a graphite/NMC commercial cell A quasi-equilibrium full-cell dilatometry experiment is conducted using pouch cells with a nominal capacity CN ¼ 16 Ah (Kokam SLPB 75106205). From a post-mortem analysis of the cell type [25], it is known to contain 16 anode sheets coated on both sides with graphite, 15 cathode sheets coated on both sides with NMC plus two single-sided cathode sheets. The nominal cell thickness is 8 mm. Before the actual test, five cycles are applied to the cell at Ich ¼ Idc ¼ 0.5 C, T ¼ 22.5 C in order to exclude formation effects. During the measurement, charge/discharge currents I ¼ 0.4 A ¼: C/40 are applied and the ambient temperature is set to T ¼ 27.5 C. The voltage range is limited to the boundaries given by the cell specification (2.7 V < V < 4.2 V). Due to the low current value and high temperature, overpotentials are expected to be very low, i.e. the measurements can be regarded as quasi-equilibrium (compare [12]). Dilation data are recorded using a dial gauge with a resolution of 1 mm (0.125‰ in terms of relative dilation of the cell). The measurement set-up (see Fig. 1) is similar to the one described by Bitzer and Gruhle [13] with two solid aluminum plates connected by four threaded metal rods. The cell is mounted on the lower plate and the measuring tip of the dial indicator is located in the middle of the cell surface. The upper plate serves as a mount for the dial indicator. By having a spring located between the point of measurement and the upper plate, a well defined pressure is applied to the small surface area around the measurement point on the cell. Therefore, the dilation data are not biased by gas generation in the pouch cell bag (compare ref. [13]). 3.3. High-rate dilatometry In addition, the dilation behavior is also investigated for high rate current pulses using the same set-up and cell type. For this purpose, a procedure of subsequent GITT (galvanostatic intermittent titration technique) pulses [26,27] is applied. An individual GITT step, comprising a charge pulse and a subsequent relaxation phase, is displayed in Fig. 2(a). GITT steps with discharge pulses are performed in an analogous manner. Our analysis of such GITT steps is focused on the dilation components Dsdil and Dsrel which represent the relative dilation during the current pulse and during the subsequent relaxation phase, respectively. Note that there can be either positive or negative relaxation Dsrel. Table 1 Relevant GICs and corresponding characteristics: x denotes the lithiation in LixC6 [5], d is the layer spacing as published in the referenced publications. Stage
2H
1L
4L
3L
2L
2
1
x d/Å [5] d/Å [16,17]
0 3.36 3.35
<0.04 N/A N/A
~1/6 3.44 N/A
~2/9 3.47 3.47
~1/3 N/A 3.53
1/2 3.52 3.51
1 3.70 3.71
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GITT steps of that kind are repeated from a discharged stage until the cell is fully charged (charge pulses) and vice versa (discharge pulses) as depicted in Fig. 2(b). A charge amount of DQpulse ¼ 1.6 Ah at I ¼ 1.5 C is chosen for the pulses, yielding individual state of charge steps equivalent to 10% of the nominal capacity. Throughout this work, state of charge (SOC) is defined zero at the discharged state (end of a constant current/ constant voltage cycle with Idc ¼ 1 C and Iend ¼ C/20 at Vend ¼ 2.7 V, T ¼ 22.5 C) and one for an amount of charge Q ¼ 16 Ah equal to the nominal capacity CN. The current-free relaxation time Dtrel after each current pulse is 1.5 h. Such GITT procedures (Fig. 2(b)) are applied to initially discharged cells at temperatures T 2 {27.5 C, 22.5 C, 17.5 C, 12.5 C, 5 C, 5 C}. If the upper or lower voltage limit is reached during one of the pulses, the current is reduced during the pulse (CV phase) in order to meet the cell specifications. Consequently, current reduction occurs at high SOCs for charge and low SOCs for discharge pulses. Despite this, the charge amount during the pulse is not varied. The last charge step is terminated according to a CV criterion (Iend ¼ C/ 20 at Vend ¼ 4.2 V) and the charge amount of the first discharge step is chosen equally to the last charge step. For later analyses, these two steps are excluded and not displayed in Fig. 5. Additionally, another cell of the same 16 Ah type is subjected to charge pulses with DSOC ¼ 0.25 from the discharged state to SOC ¼ 0.25 at T 2 {27.5 C, 22.5 C, 17.5 C, 12.5 C, 5 C, 5 C}. 4. Results and discussion 4.1. Quasi-equilibrium dilatometry of the graphite half-cell Fig. 3 shows the first one and a half cycles of an electrochemical in-situ dilatometric measurement of synthetic graphite. The results are in very good agreement with previously published data [8]. The intercalation of graphite starts with an initial strong expansion of about 1.5% between 800 and 200 mV vs. Li/Liþ (regions f þ e in Fig. 3) which can be ascribed to SEI formation via initial solvent cointercalation [3] as well as to an initial particle rearrangement during the first particle expansion upon charge/lithium intercalation. Also the initial lithium intercalation with the formation of the solid solution 1L is supposed to take place in this region. Between 200 and 100 mV vs. Li/Liþ the electrode expands for a further 1.5% which is ascribed to the transitions 1L / 4L / 3L (d þ c). Based on mere voltage and dilation data, we cannot clearly resolve data features indicating the formation of the 2L compound, although it might be there. Therefore, we continue with the simplified assumption of a 3L / 2 transition during the potential plateau at around 100 mV vs. Li/Liþ (b). This is in line with a previous suggestion by Hahn et al. [8]. At the final potential plateau at around 70 mV vs. Li/Liþ, again a strong expansion is observed which corresponds to the phase transition 2 / 1 (a). The overall expansion for the first charge cycle is 4.5% up to SOC ¼ 0.75 (which corresponds to a mixture of the phases 2 and 1). During the first discharge (lithium de-intercalation), the phase transitions occur in the reversed order, and the second charge is similar to the first charge except for the absence of SEI formation (f). The dilation curve can be roughly divided into four parts A to D, corresponding to the potential regions a (A), b (B), c þ d (C) and e (D). The slopes change in the order C > A > D [ B during charge and D > C > A [ B during discharge. The slopes A, B, and C are slightly higher for the second charge than for the first discharge, which might be an indication of further particle rearrangement (after all, we are still in the initial formation cycles). The slope D is an exception to this trend, being higher for the first discharge than for the second charge. The reason for this is not clear, yet. The slope ds/dQ of dilation during a two phase transition is
(ideally) expected to be proportional to the difference quotient of layer spacings over degrees of lithiation, i.e.
ds dðSi Þ d Sj ¼: DSi ;Sj ; ∝ dQ xðSi Þ x Sj
(1)
where Si and Sj symbolically denote the coexisting stages, d(Si/j) denote the corresponding layer spacings and x(Si/j) denote the degrees of lithiation (see Table 1). Using the values from Table 1, the flat dilation characteristic in region B (3L / 2) is explained by calculating the values of DS i ;S j :
9 D4L;3L z0:54 A > = ≪D4L;3L D 0 3L;2 D3L;2 z0:14 A D3L;2 ≪D2;1 > ; D2;1 z0:40 A
(2)
As discussed before, stage 2L is neglected, here. 4.2. Low-rate dilatometry of the graphite/NMC commercial cell The relative dilation of the cell during cycling is nonlinear with a hysteresis as shown in Fig. 4 for the quasi-equilibrium charge/ discharge at I ¼ C/40. At first sight, one recognizes a central region spanning from about 5.3 to 11.5 Ah with a low slope of relative dilation for charge and discharge. For lower and higher values on the charge axis the slope of dilation is significantly higher. In accordance with the half-cell data, we assume the transition 3L 4 2 (again neglecting 2L) in this central region. Consequently, we have 2 4 1 above 11.5 Ah and lower-order stage transitions for Q below 5.3 Ah. Comparing the peaks in differential voltage and the second derivative of dilation, we find perfect accordance at Q ¼ 11.5 Ah. This is the point of the stage 2 single phase configuration (neglecting inhomogeneous lithiation). After repeating similar tests for aged and unaged cells, we are convinced that dilatometry and its second derivative provide a very robust tool for detecting this feature and thus identifying the charge corresponding to an anode lithiation degree x equal to 0.5. Additionally, there is a strong, negative peak in d2/dQ2 at Q z 5.3Ah. In accordance with the half-cell data, we assume that it is related to the stage 3L single phase configuration. Assuming x z 0 at Q ¼ 0 Ah and x ¼ 0.5 at Q ¼ 11.5 Ah, one can calculate a lithiation degree of x z 0.23 at Q ¼ 5.3Ah, which is in good agreement with literature data (x z 0.22) for stage 3L (see Table 1). Obviously, dilatometry on full-cells can provide very useful information for algorithms requiring a reliable identification of graphite-staging-related data features. This is certainly the case regarding aging analyses based on the identification of active material loss vs. loss of cyclable lithium as introduced by Dubarry et al. [28e30]. 4.3. High-rate dilatometry 4.3.1. GITT pulses Fig. 5 shows the resulting dilation components Dsdil (during the current pulse) and Dsrel (during the subsequent relaxation) for the GITT procedure of step width DSOC ¼ 0.1 as introduced in Fig. 2. The data points where a current decay occurred (CV phase during the pulse) are marked by an asterix. In Fig. 5(a) (charge pulses), for higher temperatures, we see a minimum of Dsdil at mid-range SOCs, which is in accordance with the shape of the low-rate dilation curve (flat central region in Fig. 4). Only at T 2 {5 C,5 C}, Dsdil is significantly higher which is explained by lithium plating. Regarding Dsrel, there is a tendency
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4.3.2. Charge pulse 0 < SOC < 0.25 As shown in Fig. 6, it is even possible to observe negative or positive relaxation (depending on ambient temperature) for charge pulses starting at a discharged state and ending at SOC ¼ 0.25. Obviously, there are two distinct underlying processes. In the case of positive relaxation at temperatures T 5 C, we assume stagingrelated relaxation phenomena to be dominant (as explained in the following section). Please note that the time constant of this relaxation phenomenon decreases with increasing temperature (compare Fig. 6). After the pulse at T ¼ 5 C, negative relaxation occurs which indicates that the re-intercalation of plated lithium is the dominant phenomenon here. Fig. 1. Measurement set-up for recording dilatometry data during cycling e (1) Alplate (2) threaded rod (3) cell (4) dial gauge (5) tip with spring and metallic plate (1 cm2) (6) electric contact pads (gold plated). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
5. Modeling 5.1. Annuli model
towards positive relaxation (cell continues dilation after current stops) for low SOCs, towards negative relaxation for mid-range SOCs and negligible relaxation at high SOCs. At T 2 {5 C, 5 C} quite significant values of negative relaxation are observed at midrange and higher SOCs, which we ascribe to the re-intercalation of plated lithium. Due to the current decay for charge pulses at high SOCs, plating effects are reduced at very high SOCs. In the discharge case (Fig. 5(b)), there is a minimum of the absolute value of Dsdil at mid-range SOCs as expected from the lowrate dilation curve (low dilation in 3L 4 2). Regarding Dsrel, significant negative relaxation (i.e. the cell continues to shrink after current cutoff) is observed for low and high SOCs at all temperatures.
k [19], an explanation for the Based on the work of Heb and Nova staging-related relaxation of dilation after current pulses is proposed as follows. Two GICs Si and Siþ1 are assumed to coexist at the beginning of a current pulse. Under charge conditions (see Fig. 7(a)), GICs with higher lithiation are preferably located at the outside of the particle, where lithium ions enter the particle (vice versa for discharge in Fig. 7(b)). In case of low rate charging, the phase boundary is simply displaced, increasing the share of Siþ1 while decreasing the share of Si. At high rates, however, the lithium ion activity at the particle surface increases while diffusion processes inside the particles may become a limiting factor. Therefore, a higher-order compound Siþ2 (outer annulus) is formed while the lithiation of the particle core is delayed. With further increasing rate, we can expect even more than three GICs (Si, Siþ1, Siþ2, Siþ3, etc.) at the same time. Under nonequilibrium conditions, Gibbs' phase rule is not applicable, so there is no theoretical limitation of the number of phases which are formed. In an analogous manner, lower-order GICs (Si-1, Si-2, etc.) are formed during high-rate delithiation (Fig. 7(b)). With regard to dilation, the formation of these additional highrate induced phases leads to a deviation from the low-rate dilation curve. As soon as the current is cut off, the additional phases disappear and a two-phase equilibrium is re-established for energetic reasons. This relaxation process can explain the thickness changes after current pulses. 5.2. Example 1 (pulse from Fig. 6) Assuming the correspondencies Q ¼ 11.5 Ah ⇔ x ¼ 0.5 and Q ¼ 0 Ah ⇔ x z 0 in Fig. 4, the lithiation at the end of the current pulse to SOC ¼ 0.25 (Q ¼ 4Ah) is given by x z 0.17. Consequently, one can assume a relaxed state 4L 4 3L at the end of the pulse displayed in Fig. 6. During the high rate current pulse, however, outer annuli of higher-order GICs have been formed. Let us assume a significant share of dense stage 2 at the end of the pulse. During the subsequent relaxation this temporary stage 2 compound dissolves into 3L, releasing lithium ions which diffuse towards the 4L/3L phase boundary1, thus decreasing the share of 4L and increasing the share of 3L. In summary, 3L is formed from the stage 2 compound plus some part of the 4L compound. The phase shares a of stage 2 and b of stage 4L needed to form 3L are calculated from the lithiation
Fig. 2. (a) Scheme of the dilation components during the current pulse and during the subsequent relaxation phase of an individual GITT step (here for a charge pulse). (b) Overview of a GITT procedure as carried out at T ¼ 17.5 C.
1 Remark 1: As noted before, the formation of a dilute stage 2 compound 2L is neglected here. Nonetheless, the same reasoning can be applied if there are shares of both a dilute and a dense stage 2 compound.
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Fig. 3. Dilatometry of a graphite half-cell during the first one and a half cycles.
degrees in Table 1:
a ¼ 16 axð2Þ þ bxð4LÞ ¼ xð3LÞ 0 aþb¼1 b ¼ 56
(3)
=
=
With this, the average layer spacing d of the temporary 2 þ 4L shares can be calculated and compared to the layer spacing d(3L) of the additional share of 3L resulting from the relaxation process2.
) d ¼ adð2Þ þ bdð4LÞ ¼ 3:45 A 0dð3LÞ > d dð3LÞ ¼ 3:47 A
(4)
This finally explains both the positive relaxation after the current pulse in Fig. 6 as well as the positive values of Dsrel for lower SOCs in Fig. 5(a). Moreover, the temperature dependence of the time constant of relaxation in Fig. 6 is explained by the diffusion kinetics of lithium ions through the expanding layer (3L).
5.3. Example 2 (mid range SOCs) The analysis is now repeated for high-rate charge pulses ending at a mid-range SOC. The current cutoff is assumed at SOC ( 0.72. This is equivalent to x ( 0.5, as we find x ¼ 0.5 at Q ¼ 11.5 Ah ¼ 0.72 CN in Fig. 4. Thus, the corresponding two-phase equilibrium of the relaxed state is 3L 4 21. Again, high lithiation rates during the pulse can lead to the temporary formation of a higher-order staging compound, namely stage 1 in this case. By analogy with Example 1, we therefore expect that the stage 1 compound is dissolved entirely during the following relaxation period. In numbers, we get a ¼ 5/14 and b ¼ 9/14, where a/b is the ratio of stage 1 to stage 3L needed to form dense stage 2 during the relaxation. As seen from the average dilation d of the temporary phases
)
d ¼ adð1Þ þ bdð3LÞ ¼ 3:56 A 0dð2Þ < d; dð2Þ ¼ 3:51 A
(5)
the particle shrinks during the relaxation process explaining
Dsrel < 0 for mid-range SOCs in Fig. 5(a). For higher SOCs Dsrel tends to zero again, which is consistent with the model, because in the range of 2 4 1 there is no additional stage of higher order than
2 Remark 2: In addition to the dense stage 2 annulus, an outermost stage 1 annulus might be formed as well. For the corresponding relaxation process of stages 1 and 4L into 3L, we get a ¼ 1/15 (1), b ¼ 4=15 (4L) and dð3LÞ > d ¼ 3:46 A. Hence, this process would contribute to positive relaxation as well.
Fig. 4. Pseudo-equilibrium measurement at I ¼ C/40. Differential voltage (blue) and second derivative of dilation (olive) e both displayed for charging e show staging phenomena in graphite. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
stage 1 which could result in a relaxation phenomenon. 5.4. Comment on the discharge case The discharge data depicted in Fig. 5(b) can be analyzed in the same way. Dsrel < 0 for high SOCs (relaxed state is 2 4 1) is understood by assuming the formation of an outer 3L annulus or even lower-order annuli. As already elaborated in Example 2 for the charge case, layer spacings and cell thickness decrease during the relaxation process of 3L þ 1 / 2, thus explaining the observation. While we might expect Dsrel > 0 for mid-range SOCs (relaxed state 2 4 3L) due to the formation of an outer 4L annulus and subsequent relaxation of 4L and 2 to 3L, the data in Fig. 5(b) do not show this. We believe that this is caused by the charge/discharge asymmetry of staging phenomena, which was also described by k [19]. Due to comparatively high diffusion constants Heb and Nova of the liquid-like stages compared to the dense stages, one can suppose that all lithium ions can be provided by delithiation of stage 2 at the 2/3L phase boundary, with kinetically preferable ionic transport through the surrounding liquid-like stage 3L annulus. Hence, no outer annulus of lower order stages would be formed, explaining Dsrel z 0 in the discharge case. Due to a lack of data on the dilation behavior of the dilute stage 1 compound, we cannot present an explanation for the relaxation process leading to Dsrel < 0 at low SOCs. 5.5. Comment on possible effects on electrode level Depending on the kinetic properties of the electrode, the formation of additional phases may also occur on the electrode surface, while the lithiation/delithiation of the bulk is delayed [31]. In contrast to the core-shell model shown in Fig. 7, kinetic limitations on the electrode level would result in a layered staging structure with layers parallel to the current collector. The effects on external dilation are qualitatively equivalent to those resulting from kinetic limitations on the particle level. That means, the model introduced here likewise explains dilation phenomena on particle level and electrode level. 6. Conclusions The dilation behavior of a graphite half-cell and a graphite/NMC
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Fig. 5. Data from GITT with charge steps (a) and discharge steps (b). Step width is DSOC ¼ 0.1. The x-position of data points represents the SOC at the end of the underlying pulse. Pulses including a CV phase in order to meet voltage limits are marked by an asterix. Upper plots: Relative thickness change Dsdil during current pulse. Lower plots: Relative thickness change Dsrel during the subsequent relaxation phase.
commercial lithium-ion cell at low rates was analyzed. No major qualitative difference was observed, allowing for the conclusion that in both cases dilation at low rates is mainly influenced by graphite staging processes. It is shown that dilatometry is well suitable for the detection of graphite-staging-related data features. Furthermore we could demonstrate that at high rates the dilation can deviate from the dilation behavior observed at low current rates, due to the formation of over-next GICs under nonequilibrium conditions. As a result, both positive or negative dilation relaxation phenomena can occur. These phenomena could be systematically characterized for charge and discharge at different temperatures using a GITT measurement protocol. A model approach was presented which can explain such relaxation phenomena under the assumption that multiple (more than two) GICs coexist during high rate lithiation, giving rise to dilation changes as a two-phase equilibrium is re-established during relaxation. The consideration of these effects is for instance of great importance for the quantitative analysis of Li metal deposition based on dilatometry. The relaxation phenomena observed for charge and discharge
Fig. 6. Charge pulse from the discharged state to SOC ¼ 0.25 (DSOC ¼ 0.25): Positive or negative relaxation of cell thickness due to staging- and plating-related relaxation phenomena, respectively.
differ. Especially for mid-range SOCs during discharge, the formation of multiple GICs appears less pronounced compared to other SOC ranges and/or charge. This was explained by the higher diffusivity of lithium ions in the dilute staging compounds. We consider the dilation relaxation and the charge/discharge asymmetry as a clear confirmation of the shrinking annuli model proposed by Heb and Nov ak [19]. Additionally, we could prove that small variations of the cell temperature caused by dissipation of heat at constant ambient temperature do not severely affect the accuracy of our full-cell dilation experiments. In case of varying ambient temperatures, however, thermal expansion needs to be compensated for using an algorithm like the one introduced in A. Regarding automotive or stationary applications, where larger cells are employed and assembled into packs, dilatometry could be used as a sensitive measurement technique for monitoring kinetic limitations. Depending on SOC, these kinetic limitations can be detected either in the form of an excess-dilation during cycling or by analyzing the relaxation behavior after the current is cut off. As demonstrated by the results, both the formation of multiple phases and lithium plating lead to deviations from the low-rate dilation behavior. If it occurs, however, lithium plating is clearly dominant and the corresponding dilation is always positive. Based on these findings, an algorithm can be developed in order to decide whether only staging or even plating processes are present during real-time battery operation. Alternatively, the method can be used for creating look-up tables characterizing kinetic limitations at various operating conditions in order to feed BMS (battery management system) algorithms. As a limitation, moderate lithium plating and multi-phaseformation are difficult to discriminate during charge at mid-range SOCs because both processes lead to additional dilation (negative relaxation), here. Our future work will be dedicated to overcome this problem by an in-depth analysis of dilation dynamics. Remaining challenges also include the integration of a suitable sensor design into the battery system. (Wire) strain gauges need to be carefully integrated into the battery pack, either for monitoring individual cells or modules of multiple cells. Alternatively, force sensors can be taken into account as a cost-efficient solution, particularly with regard to prismatic or cylindrical cells. Dilatometry was shown to provide information on the kinetic limitations inside graphite anodes. The method is therefore highly interesting for monitoring purposes on a full cell level or even on a
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Fig. 7. Qualitative model of phase shares in graphite particles during high rate current pulses. If the pulse does not exceed the lithiation range of the two-phase equilibrium Si4Siþ1, we have j ¼ i, i. e. the same two stages coexist before the pulse and after the relaxation. Otherwise, j > i for charge and j < i for discharge. For more information on the morphology and characteristics of staging-related annuli in graphite particles please refer to [19].
pack level in electric vehicles. Acknowledgements This research project is supported by the German Federal Ministry for Economic Affairs and Energy (BMWi) under contract number 03ET4012C. Appendix A. Compensation of thermal expansion in dilatometry data In dilatometry measurements, the thermal expansion of both the measurement set-up and the cell is usually an undesired bias. It needs to be quantified and, optionally, compensated for. The total bias seen in dilatometry measurements like ours (see Fig. 1) is composed from shares caused by both the dilation of the measurement set-up and the cell. The set-up-related dilation offset cell is denoted by Dssetup Tref ðTsetup Þ, while DsTref ðTcell Þ is the dilation due to thermal expansion of the cell. Herein Tsetup and Tcell denote the surface temperatures of the set-up and the cell, respectively. Tref denotes the reference temperature which, by definition, corresponds to zero compensation offset regarding both the set-up- and the cell-related thermal expansion. In case of cell tests at constant ambient temperature, the temperature of the set-up (thread rods, aluminum plates, dial indicator) can be expected to be quasi-constant during the test (good thermal junction with ambient air), while the cell obviously heats up whenever high current loads are applied. In such a scenario, only the thermal expansion of the cell Dscell Tref ðTcell Þ contributes to the total bias. For more complex test procedures including a variation of the ambient temperature, the thermal expansion of both the cell and the set-up can be quite significant and need to be taken into account. In order to obtain quantitative results on that, load free
measurements with and without a cell mounted into the set-up are recorded at different temperatures. See Fig. 8 for the results. Fig. 8(a) directly presents data obtained from a temperature variation without a cell mounted in the set-up, i.e. the gauge tip rests on the lower aluminum plate. In Fig. 8(b), on the other hand, the curves are calculated by subtracting the dilation curve of the set-up (Fig. 8(a)) from aggregated dilation data obtained with a cell mounted into the measurement set-up. Thus, subfigure (b) shows the thermal expansion of the cell, only. For the quantification of thermal expansion in our measurements, a data-driven simulation model is used to calculate the expected offsets depending on the time series of surface temperatures (cell and set-up). The curves shown in Fig. 8 (a) and (b) are used to parametrize this simulation model. For demonstration, cell exemplary values of Dssetup Tref ðTsetup Þ and DsTref ðTcell Þ are sketched assuming Tref :¼ 20 C, Tsetup ¼ 25 C, Tcell ¼ 30 C and SOC ¼ 0.25. In our model we performed a piecewise cubic interpolation of these data with respect to both the temperature axis and the SOC axis. Based on the interpolated data, the simulation model calcucell lates both offsets Dssetup Tref ðTsetup Þ and DsTref ðTcell Þ for every data point in a dilatometry measurement for a given reference temperature, if the temperatures Tsetup and Tcell are provided. Thermally compensated dilation data Dscomp can now be calculated from the measured data Dsmeas by subtracting these offsets:
Dscomp ¼ Dsmeas Dssetup Tsetup Dscell Tref ðTcell Þ Tref
(A.1)
Fig. 8(c) shows an example of temperature compensation for GITT data at T ¼ 12.5 C (compare Section 4.3) based on sensor data for Tcell and Tsetup. For the compensation algorithm, Tref :¼ 12.5 C is chosen, so we may assume that all deviations between the compensated curve and the original data are due to self-heating of the cell. Obviously, the maximum deviation in Fig. 8(c) is not significant
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compared to the gauge resolution of 1 mm (0.125% in terms of relative cell dilation). We checked for these deviations in all our measurements and found that for the other temperatures investigated in Section 4.3, were even less than for T ¼ 12.5 C. Interestingly, the thermal expansion coefficient of the cell (i.e. the slope of Dscell Tref ðTcell Þ) exhibits a minimum for low temperatures around 0 C (compare Fig. 8(b)). This is why temperature induced dilation at T z 0 C is lower than one might expect due to high internal resistance and increased self-heating.
Fig. A8. (a) Temperature induced relative dilation of the measurement set-up. (b) Temperature induced relative dilation of the cell only. Relative Dilation is defined zero at T ¼ 0 C for every measurement. (c) Compensated and uncompensated dilation data during a GITT pulse from 40 to 50 % state of charge at an ambient temperature T ¼ 12.5 C (maximum bias).
Being negligible in our GITT-measurements, thermal expansion, however, needs to be compensated whenever there are significant temperature variations during a measurement. Regarding the application of dilatometry for the purpose of cell-monitoring in
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stationary or mobile power applications, a proper compensation of thermal expansion from the measured data is clearly necessary. Otherwise, staging- or plating-related information could be misinterpreted. References €hwald, T. Butz, A high resolution [1] W. Biberacher, A. Lerf, J. Besenhard, H. Mo dilatometer for in situ studies of the electrointercalation of layered materials, Mater. Res. Bull. 17 (11) (1982) 1385e1392, http://dx.doi.org/10.1016/00255408(82)90223-9. http://www.sciencedirect.com/science/article/pii/ 0025540882902239. €hwald, J. Nickl, W. Biberacher, W. Foag, Anodic [2] J. Besenhard, E. Wudy, H. Mo oxidation of graphite in H2SO4 dilatometry in situ X-ray diffraction Impedance spectroscopy, Synth. Met. 7 (3e4) (1983) 185e192, http://dx.doi.org/ 10.1016/0379-6779(83)90046-2. http://www.sciencedirect.com/science/ article/pii/0379677983900462. [3] J. Besenhard, M. Winter, J. Yang, W. 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Understanding the dilation and dilation relaxation behavior of graphite-based lithium-ion cells € we, Jon V. Persson, Michael A. Danzer Marius Bauer*, Mario Wachtler, Hendrik Sto Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW), 89081 Ulm, Germany
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
At high rates, dilation is affected by formation of >2 graphite staging compounds. There can be either positive or negative dilation relaxation after current pulses. A model explaining staging-related relaxation phenomena is presented. Staging relaxation and lithium plating are detectable in dilation data. A compensation procedure for thermal expansion in dilation data is presented.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 January 2016 Received in revised form 19 March 2016 Accepted 22 March 2016
The dilation of lithium-ion cells is sensitive towards swelling phenomena caused by both graphite staging processes and lithium plating on graphite anodes. In this work, the dilation behavior of graphite/ NMC pouch cells is studied with a focus on relaxation phenomena occurring after current pulses. In order to prevent misleading interpretations due to thermal effects, thermal expansion is quantified and a method for the thermal compensation of dilation data is developed. Dilation data are recorded for quasiequilibrium cycling as well as for current pulses at high rates. In the quasi-equilibrium case, the staging behavior is characterized based on dilation and voltage data. By comparison with a graphite half-cell measurement, the major effects in full cell dilation are confirmed to be anode related. In the high rate case, the dilation responses to the actual pulse and the subsequent relaxation phases are recorded systematically. Positive and negative relaxation phenomena are observed depending on the SOC. They are ascribed to both graphite staging and lithium plating processes. A model is presented explaining the unexpected relaxation effects by a temporary coexistence of three or more staging compounds during high rate lithiation and delithiation. Our data thereby confirm the shrinking annuli model introduced by k. Heb and Nova © 2016 Elsevier B.V. All rights reserved.
Keywords: Lithium-ion cell Dilation Relaxation of thickness Lithium plating Graphite staging Swelling
1. Introduction
* Corresponding author. E-mail address: [email protected] (M. Bauer). http://dx.doi.org/10.1016/j.jpowsour.2016.03.078 0378-7753/© 2016 Elsevier B.V. All rights reserved.
Over the last years, dilatometry has proven useful for characterizing lithium-ion cells and individual electrodes. Regarding individual electrodes, electrochemical in-situ dilatometry is a convenient tool to measure expansion/contraction
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during charge and discharge. In contrast to X-ray or neutron diffraction methods, dilatometry monitors the overall expansion of the whole composite electrode. Therefore, dilation data also include the influence of porosity within and between the active material particles, anisotropic expansion effects due to preferential particle orientation, swelling phenomena due to electrolyte uptake by the electrode and electrode binder, and the like. To our knowledge, the first dilatometric investigations of graphite were performed by J.O. Besenhard et al. [1,2], who studied the intercalation of HSO 4 /H2SO4. Furthermore, they investigated the intercalation of lithium ions [3,4] and demonstrated that the intercalation of solvated lithium ions is involved in the early stages of the formation of the solid electrolyte interphase (SEI) [3]. Similar investigations were performed by T. Ohzuku et al. [5]. More recently M. Hahn et al. developed dilatometers with improved resolution, and used it to study charge storage phenomena in supercapacitor electrodes [6,7] as well as to revisit the lithium ion intercalation into graphite for a more indepth analysis [8]. Lately, in-situ dilatometry has been used to study the intercalation of anions into graphite, viz. PF 6 anions from organic carbonate solutions at potentials >4.6 V vs. Li/Liþ, in view of using graphite as a cathode material, e.g. in dual carbon batteries [9]. Regarding the characterization of full-cell behavior, dilatometry is particularly interesting because of its non-destructive character and ability to provide information at low and high current rates. In contrast, many measurement techniques based on cell voltage require a quasi-equilibrium cell state in order to work. Electrochemical impedance spectroscopy, for instance, is only applicable to linear, time-invariant systems and therefore not valid for characterizing battery cells under high current loads [10]. Similar restrictions apply for methods based on a differential evaluation of the voltage response in quasi-equilibrium cycling (differential voltage analysis, incremental capacity analysis [11,12]). Obtaining valuable diagnostic information from voltage measurements at arbitrary current loads is obviously challenging. Dilatometry on full-cells, however, can fill this gap. It can be realized by measuring the external cell dilation using dial gauges, strain gauges, laser scanners, or, in a wider sense, pressure sensors fitted into battery packs. In this work, a dial gauge is used for the investigation of individual lithium-ion pouch cells. It has been shown already that dilation data allow for the online detection of lithium plating [13] and that also thermal expansion and lithium intercalation contribute to the swelling of the cell [14,15]. In this work, we present both half-cell and full-cell dilation experiments at low rates allowing us to identify the origin of dilation features observed for full-cells (graphite-anode-related or not). Based on the low rate results, the dilation behavior is then investigated for charge pulses at higher rates. For the first time, the relaxation phenomena after such high rate current pulses are analyzed, explained and modeled in detail.
2. Fundamentals During cycling, the cell thickness of lithium-ion pouch cells varies in the range of a few percent of the total cell thickness depending on the thickness shares and types of active material. For the cells investigated here, the relative dilation is in a range of 1 e 2 % during cycling. Both reversible and irreversible thickness changes can be observed and assigned to different effects in the cell. Contributions from the electrodes and thermal expansion can be distinguished.
2.1. Anode dilation 2.1.1. Dilation caused by intercalation of lithium ions (graphite staging) Graphite is well known for its ability to intercalate a large variety of guest species such as lithium and to form so-called graphite intercalation compounds (GICs), also known as staging compounds. The guest species are normally not uniformly distributed within the graphite lattice, but rather structures with periodically arranged intercalate layers are formed. This phenomenon is called staging. The GICs are usually labelled according to their stage index, which describes the number of graphene layers between two intercalant layers. Table 1 gives an overview of the lithium GICs formed during electrochemical charge and discharge, along with the approximate compositions x in LixC6, as proposed in Ref. [5], and with the average spacings d between the graphene layers, based on Refs. [5] and [16,17]. It should be noted that the stoichiometry of the staging compounds 3L and 4L is not well defined, and that also different compositions with less lithium have been reported [16e18]. The variations of average layer spacings d for the individual GICs explain why staging leads to reversible dilation during the lithiation and delithiation of the anode. At the beginning of the electrochemical lithiation of graphite a small amount of lithium is randomly distributed within the graphite lattice, forming a solid solution-type compound (1L). After exceeding a critical amount of lithium, an ordering of the lithium atoms takes place within the graphite lattice, and subsequently the stage 4L, 3L, 2L, 2, and 1 compounds are formed. In the dense stage 1 compound every gallery between two graphene layers is occupied by lithium. Within each gallery the lithium atoms are located at the centers of the hexagonal prisms formed by the carbon hexagons of the two adjacent graphene layers, and only every nextnearest site is occupied. This is the maximum amount of lithium which can be accommodated at room temperature and ambient pressure, yielding a lithiation of x ¼ 1 (LiC6) with a theoretical capacity of 372 mAh g1. In the dense stage 2 compound only every second gallery is filled, and all positions within a lithium gallery are occupied (as in the stage 1 compound), yielding a stoichiometry of x ¼ 0.5 (LiC12). For the dilute, liquid-like stage compounds 2L, 3L, and 4L, every 2nd, 3rd, or 4th gallery is filled with lithium. Unlike in the dense stage 1 and 2 compounds, however, the lithium layers are not completely filled, resulting in lower amounts of lithium stored than in the corresponding (hypothetical) dense stage compounds. The phase transitions 1L 4 4L, 3L 4 2L, 2L 4 2, and 2 4 1 are classical 2-phase reactions, giving rise to the typical potential plateaux in the charge/discharge curves, which are characteristic of graphite. The situation is less clear for the 4L 4 3L transition, and a sloping potential decrease is observed with a gradual shift of the Xray diffraction peaks, which points to a single-phase transition [18,5]. Also the transition from empty graphite (2H) to 1L is a single-phase transition. The stage 2L compound is given with values x z 0.25 [18] up to x ¼ 1/3 [16] in the literature. The formation of 2L may be suppressed depending on temperature [18]. (Note that the nomenclature of the stage 1L, 4L, and 3L comk [19] to pounds follows a recent proposal by M. Heb and P. Nova indicate their similarity with the 2L compound, with incompletely filled lithium layers. The same compounds are usually denoted as 10, 4, and 3, respectively.) 2.1.2. Dilation caused by lithium plating As already reported in the literature for a 20 Ah pouch cell [13], one can observe an additional thickness increase for high charge rates at low temperatures. This increase can be attributed to the
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deposition of lithium metal on the negative electrode (lithium plating) which occurs if the local potential drops below 0 V vs. Li/ Liþ [20]. After the charge current is switched off, there is a partial relaxation of this additional cell dilation, which can be explained by intercalation of a fraction of the plated lithium into the graphite electrode (compare [13]). Consequently there are both reversible and irreversible effects of lithium plating on cell thickness. 2.2. Cathode dilation Just like on the negative electrode (denoted as anode), lithium insertion into the positive electrode (cathode) will also have an effect on cell thickness. In our work, cells with an NMC (lithium nickel-manganese-cobalt oxide) chemistry for the positive electrode are investigated. Structural analyses of this material show monotonously decreasing unit cell volumes as the lithiation degree of NMC decreases (as the cell gets charged). The effect is slightly enhanced for low lithiation degrees y < 0.5 in LiyCo1/3Ni1/3Mn1/3O2 [21,22]. In a dilatometric study conducted by Nagayama et al. [23] with an LTO/NMC chemistry, NMC-related dilation was evaluated in a full-cell configuration (LTO is a zero strain material). The cell was shown to be dimensionally highly stable as long as the NMC electrode was operated at voltages up to 4.15 V vs. Li/Liþ. Only at high potentials, some cell shrinkage was detected. In summary, dimensional changes of the NMC cathode are always negative during delithiation (charge). In a wide range of SOC they can be neglected compared to anode-related effects. 2.3. Thermal expansion and its compensation in dilatometry data In addition to the dilation effects caused by lithium insertion or plating, dilatometry data always include contributions from thermal expansion or contraction of both the cell and the measurement set-up. It turns out that in the measurements carried out in this paper, where the ambient temperature is kept constant during each individual test, thermal expansion is negligible compared to the gauge resolution. From the thermal characterization presented in Appendix A, it is clear, however, that in an application of dilatometry for diagnostic purposes on commercial battery modules, where temperature is varying in a range of more than a few degree Celsius, the compensation of thermal expansion in the dilation data is essential to avoid misinterpretation of the data. Please refer to Appendix A for detailed results regarding thermal expansion and for an algorithm to compensate for it. 3. Experimental 3.1. Low-rate dilatometry of a graphite half-cell The half-cell dilatometry measurement of graphite has been performed with an ECD-1 dilatometer cell from El-Cell GmbH (Germany). The dilatometer cell employs a porous glass frit as separator, which serves as a rigid base on which the working electrode can expand. Therefore, only the expansion of the working electrode is measured. (It thus differs from the dilatometer described in Ref. [5] and from the measurement set-up used for the dilation measurements of the pouch-cells in the present work, where the expansion of the whole working electrode/separator/ counter electrode assembly is measured.) The electrode expansion is transmitted via a titanium membrane and a piston onto a linear variable differential transformer (LVDT), which produces a voltage output which varies linearly with the electrode expansion. The graphite electrode under investigation has the composition 92 wt.% graphite (SFG 6, Timcal) and 8 wt.% poly(vinylidene fluoride) (PVdF,
95
Solef 6020, Solvay Solexis), and is prepared by a doctor-blade coating process as described before [24]. The electrode has a diameter of 9 mm and contains ~3 mg of active material. It is used without previous pressing or calendering. Lithium metal is used as counter electrode (placed on the opposite side of the glass frit), and 1 M LiPF6/ethylene carbonate: dimethyl carbonate (1:1 by wt.) (battery grade, UBE Industries) as the electrolyte. Note, that the graphite electrode is charged to x z 0.75 only. This corresponds to the typical maximum lithiation state of graphite in a full-cell, where the anode capacity is over-dimensioned relative to the cathode capacity. 3.2. Low-rate dilatometry of a graphite/NMC commercial cell A quasi-equilibrium full-cell dilatometry experiment is conducted using pouch cells with a nominal capacity CN ¼ 16 Ah (Kokam SLPB 75106205). From a post-mortem analysis of the cell type [25], it is known to contain 16 anode sheets coated on both sides with graphite, 15 cathode sheets coated on both sides with NMC plus two single-sided cathode sheets. The nominal cell thickness is 8 mm. Before the actual test, five cycles are applied to the cell at Ich ¼ Idc ¼ 0.5 C, T ¼ 22.5 C in order to exclude formation effects. During the measurement, charge/discharge currents I ¼ 0.4 A ¼: C/40 are applied and the ambient temperature is set to T ¼ 27.5 C. The voltage range is limited to the boundaries given by the cell specification (2.7 V < V < 4.2 V). Due to the low current value and high temperature, overpotentials are expected to be very low, i.e. the measurements can be regarded as quasi-equilibrium (compare [12]). Dilation data are recorded using a dial gauge with a resolution of 1 mm (0.125‰ in terms of relative dilation of the cell). The measurement set-up (see Fig. 1) is similar to the one described by Bitzer and Gruhle [13] with two solid aluminum plates connected by four threaded metal rods. The cell is mounted on the lower plate and the measuring tip of the dial indicator is located in the middle of the cell surface. The upper plate serves as a mount for the dial indicator. By having a spring located between the point of measurement and the upper plate, a well defined pressure is applied to the small surface area around the measurement point on the cell. Therefore, the dilation data are not biased by gas generation in the pouch cell bag (compare ref. [13]). 3.3. High-rate dilatometry In addition, the dilation behavior is also investigated for high rate current pulses using the same set-up and cell type. For this purpose, a procedure of subsequent GITT (galvanostatic intermittent titration technique) pulses [26,27] is applied. An individual GITT step, comprising a charge pulse and a subsequent relaxation phase, is displayed in Fig. 2(a). GITT steps with discharge pulses are performed in an analogous manner. Our analysis of such GITT steps is focused on the dilation components Dsdil and Dsrel which represent the relative dilation during the current pulse and during the subsequent relaxation phase, respectively. Note that there can be either positive or negative relaxation Dsrel. Table 1 Relevant GICs and corresponding characteristics: x denotes the lithiation in LixC6 [5], d is the layer spacing as published in the referenced publications. Stage
2H
1L
4L
3L
2L
2
1
x d/Å [5] d/Å [16,17]
0 3.36 3.35
<0.04 N/A N/A
~1/6 3.44 N/A
~2/9 3.47 3.47
~1/3 N/A 3.53
1/2 3.52 3.51
1 3.70 3.71
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GITT steps of that kind are repeated from a discharged stage until the cell is fully charged (charge pulses) and vice versa (discharge pulses) as depicted in Fig. 2(b). A charge amount of DQpulse ¼ 1.6 Ah at I ¼ 1.5 C is chosen for the pulses, yielding individual state of charge steps equivalent to 10% of the nominal capacity. Throughout this work, state of charge (SOC) is defined zero at the discharged state (end of a constant current/ constant voltage cycle with Idc ¼ 1 C and Iend ¼ C/20 at Vend ¼ 2.7 V, T ¼ 22.5 C) and one for an amount of charge Q ¼ 16 Ah equal to the nominal capacity CN. The current-free relaxation time Dtrel after each current pulse is 1.5 h. Such GITT procedures (Fig. 2(b)) are applied to initially discharged cells at temperatures T 2 {27.5 C, 22.5 C, 17.5 C, 12.5 C, 5 C, 5 C}. If the upper or lower voltage limit is reached during one of the pulses, the current is reduced during the pulse (CV phase) in order to meet the cell specifications. Consequently, current reduction occurs at high SOCs for charge and low SOCs for discharge pulses. Despite this, the charge amount during the pulse is not varied. The last charge step is terminated according to a CV criterion (Iend ¼ C/ 20 at Vend ¼ 4.2 V) and the charge amount of the first discharge step is chosen equally to the last charge step. For later analyses, these two steps are excluded and not displayed in Fig. 5. Additionally, another cell of the same 16 Ah type is subjected to charge pulses with DSOC ¼ 0.25 from the discharged state to SOC ¼ 0.25 at T 2 {27.5 C, 22.5 C, 17.5 C, 12.5 C, 5 C, 5 C}. 4. Results and discussion 4.1. Quasi-equilibrium dilatometry of the graphite half-cell Fig. 3 shows the first one and a half cycles of an electrochemical in-situ dilatometric measurement of synthetic graphite. The results are in very good agreement with previously published data [8]. The intercalation of graphite starts with an initial strong expansion of about 1.5% between 800 and 200 mV vs. Li/Liþ (regions f þ e in Fig. 3) which can be ascribed to SEI formation via initial solvent cointercalation [3] as well as to an initial particle rearrangement during the first particle expansion upon charge/lithium intercalation. Also the initial lithium intercalation with the formation of the solid solution 1L is supposed to take place in this region. Between 200 and 100 mV vs. Li/Liþ the electrode expands for a further 1.5% which is ascribed to the transitions 1L / 4L / 3L (d þ c). Based on mere voltage and dilation data, we cannot clearly resolve data features indicating the formation of the 2L compound, although it might be there. Therefore, we continue with the simplified assumption of a 3L / 2 transition during the potential plateau at around 100 mV vs. Li/Liþ (b). This is in line with a previous suggestion by Hahn et al. [8]. At the final potential plateau at around 70 mV vs. Li/Liþ, again a strong expansion is observed which corresponds to the phase transition 2 / 1 (a). The overall expansion for the first charge cycle is 4.5% up to SOC ¼ 0.75 (which corresponds to a mixture of the phases 2 and 1). During the first discharge (lithium de-intercalation), the phase transitions occur in the reversed order, and the second charge is similar to the first charge except for the absence of SEI formation (f). The dilation curve can be roughly divided into four parts A to D, corresponding to the potential regions a (A), b (B), c þ d (C) and e (D). The slopes change in the order C > A > D [ B during charge and D > C > A [ B during discharge. The slopes A, B, and C are slightly higher for the second charge than for the first discharge, which might be an indication of further particle rearrangement (after all, we are still in the initial formation cycles). The slope D is an exception to this trend, being higher for the first discharge than for the second charge. The reason for this is not clear, yet. The slope ds/dQ of dilation during a two phase transition is
(ideally) expected to be proportional to the difference quotient of layer spacings over degrees of lithiation, i.e.
ds dðSi Þ d Sj ¼: DSi ;Sj ; ∝ dQ xðSi Þ x Sj
(1)
where Si and Sj symbolically denote the coexisting stages, d(Si/j) denote the corresponding layer spacings and x(Si/j) denote the degrees of lithiation (see Table 1). Using the values from Table 1, the flat dilation characteristic in region B (3L / 2) is explained by calculating the values of DS i ;S j :
9 D4L;3L z0:54 A > = ≪D4L;3L D 0 3L;2 D3L;2 z0:14 A D3L;2 ≪D2;1 > ; D2;1 z0:40 A
(2)
As discussed before, stage 2L is neglected, here. 4.2. Low-rate dilatometry of the graphite/NMC commercial cell The relative dilation of the cell during cycling is nonlinear with a hysteresis as shown in Fig. 4 for the quasi-equilibrium charge/ discharge at I ¼ C/40. At first sight, one recognizes a central region spanning from about 5.3 to 11.5 Ah with a low slope of relative dilation for charge and discharge. For lower and higher values on the charge axis the slope of dilation is significantly higher. In accordance with the half-cell data, we assume the transition 3L 4 2 (again neglecting 2L) in this central region. Consequently, we have 2 4 1 above 11.5 Ah and lower-order stage transitions for Q below 5.3 Ah. Comparing the peaks in differential voltage and the second derivative of dilation, we find perfect accordance at Q ¼ 11.5 Ah. This is the point of the stage 2 single phase configuration (neglecting inhomogeneous lithiation). After repeating similar tests for aged and unaged cells, we are convinced that dilatometry and its second derivative provide a very robust tool for detecting this feature and thus identifying the charge corresponding to an anode lithiation degree x equal to 0.5. Additionally, there is a strong, negative peak in d2/dQ2 at Q z 5.3Ah. In accordance with the half-cell data, we assume that it is related to the stage 3L single phase configuration. Assuming x z 0 at Q ¼ 0 Ah and x ¼ 0.5 at Q ¼ 11.5 Ah, one can calculate a lithiation degree of x z 0.23 at Q ¼ 5.3Ah, which is in good agreement with literature data (x z 0.22) for stage 3L (see Table 1). Obviously, dilatometry on full-cells can provide very useful information for algorithms requiring a reliable identification of graphite-staging-related data features. This is certainly the case regarding aging analyses based on the identification of active material loss vs. loss of cyclable lithium as introduced by Dubarry et al. [28e30]. 4.3. High-rate dilatometry 4.3.1. GITT pulses Fig. 5 shows the resulting dilation components Dsdil (during the current pulse) and Dsrel (during the subsequent relaxation) for the GITT procedure of step width DSOC ¼ 0.1 as introduced in Fig. 2. The data points where a current decay occurred (CV phase during the pulse) are marked by an asterix. In Fig. 5(a) (charge pulses), for higher temperatures, we see a minimum of Dsdil at mid-range SOCs, which is in accordance with the shape of the low-rate dilation curve (flat central region in Fig. 4). Only at T 2 {5 C,5 C}, Dsdil is significantly higher which is explained by lithium plating. Regarding Dsrel, there is a tendency
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4.3.2. Charge pulse 0 < SOC < 0.25 As shown in Fig. 6, it is even possible to observe negative or positive relaxation (depending on ambient temperature) for charge pulses starting at a discharged state and ending at SOC ¼ 0.25. Obviously, there are two distinct underlying processes. In the case of positive relaxation at temperatures T 5 C, we assume stagingrelated relaxation phenomena to be dominant (as explained in the following section). Please note that the time constant of this relaxation phenomenon decreases with increasing temperature (compare Fig. 6). After the pulse at T ¼ 5 C, negative relaxation occurs which indicates that the re-intercalation of plated lithium is the dominant phenomenon here. Fig. 1. Measurement set-up for recording dilatometry data during cycling e (1) Alplate (2) threaded rod (3) cell (4) dial gauge (5) tip with spring and metallic plate (1 cm2) (6) electric contact pads (gold plated). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
5. Modeling 5.1. Annuli model
towards positive relaxation (cell continues dilation after current stops) for low SOCs, towards negative relaxation for mid-range SOCs and negligible relaxation at high SOCs. At T 2 {5 C, 5 C} quite significant values of negative relaxation are observed at midrange and higher SOCs, which we ascribe to the re-intercalation of plated lithium. Due to the current decay for charge pulses at high SOCs, plating effects are reduced at very high SOCs. In the discharge case (Fig. 5(b)), there is a minimum of the absolute value of Dsdil at mid-range SOCs as expected from the lowrate dilation curve (low dilation in 3L 4 2). Regarding Dsrel, significant negative relaxation (i.e. the cell continues to shrink after current cutoff) is observed for low and high SOCs at all temperatures.
k [19], an explanation for the Based on the work of Heb and Nova staging-related relaxation of dilation after current pulses is proposed as follows. Two GICs Si and Siþ1 are assumed to coexist at the beginning of a current pulse. Under charge conditions (see Fig. 7(a)), GICs with higher lithiation are preferably located at the outside of the particle, where lithium ions enter the particle (vice versa for discharge in Fig. 7(b)). In case of low rate charging, the phase boundary is simply displaced, increasing the share of Siþ1 while decreasing the share of Si. At high rates, however, the lithium ion activity at the particle surface increases while diffusion processes inside the particles may become a limiting factor. Therefore, a higher-order compound Siþ2 (outer annulus) is formed while the lithiation of the particle core is delayed. With further increasing rate, we can expect even more than three GICs (Si, Siþ1, Siþ2, Siþ3, etc.) at the same time. Under nonequilibrium conditions, Gibbs' phase rule is not applicable, so there is no theoretical limitation of the number of phases which are formed. In an analogous manner, lower-order GICs (Si-1, Si-2, etc.) are formed during high-rate delithiation (Fig. 7(b)). With regard to dilation, the formation of these additional highrate induced phases leads to a deviation from the low-rate dilation curve. As soon as the current is cut off, the additional phases disappear and a two-phase equilibrium is re-established for energetic reasons. This relaxation process can explain the thickness changes after current pulses. 5.2. Example 1 (pulse from Fig. 6) Assuming the correspondencies Q ¼ 11.5 Ah ⇔ x ¼ 0.5 and Q ¼ 0 Ah ⇔ x z 0 in Fig. 4, the lithiation at the end of the current pulse to SOC ¼ 0.25 (Q ¼ 4Ah) is given by x z 0.17. Consequently, one can assume a relaxed state 4L 4 3L at the end of the pulse displayed in Fig. 6. During the high rate current pulse, however, outer annuli of higher-order GICs have been formed. Let us assume a significant share of dense stage 2 at the end of the pulse. During the subsequent relaxation this temporary stage 2 compound dissolves into 3L, releasing lithium ions which diffuse towards the 4L/3L phase boundary1, thus decreasing the share of 4L and increasing the share of 3L. In summary, 3L is formed from the stage 2 compound plus some part of the 4L compound. The phase shares a of stage 2 and b of stage 4L needed to form 3L are calculated from the lithiation
Fig. 2. (a) Scheme of the dilation components during the current pulse and during the subsequent relaxation phase of an individual GITT step (here for a charge pulse). (b) Overview of a GITT procedure as carried out at T ¼ 17.5 C.
1 Remark 1: As noted before, the formation of a dilute stage 2 compound 2L is neglected here. Nonetheless, the same reasoning can be applied if there are shares of both a dilute and a dense stage 2 compound.
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Fig. 3. Dilatometry of a graphite half-cell during the first one and a half cycles.
degrees in Table 1:
a ¼ 16 axð2Þ þ bxð4LÞ ¼ xð3LÞ 0 aþb¼1 b ¼ 56
(3)
=
=
With this, the average layer spacing d of the temporary 2 þ 4L shares can be calculated and compared to the layer spacing d(3L) of the additional share of 3L resulting from the relaxation process2.
) d ¼ adð2Þ þ bdð4LÞ ¼ 3:45 A 0dð3LÞ > d dð3LÞ ¼ 3:47 A
(4)
This finally explains both the positive relaxation after the current pulse in Fig. 6 as well as the positive values of Dsrel for lower SOCs in Fig. 5(a). Moreover, the temperature dependence of the time constant of relaxation in Fig. 6 is explained by the diffusion kinetics of lithium ions through the expanding layer (3L).
5.3. Example 2 (mid range SOCs) The analysis is now repeated for high-rate charge pulses ending at a mid-range SOC. The current cutoff is assumed at SOC ( 0.72. This is equivalent to x ( 0.5, as we find x ¼ 0.5 at Q ¼ 11.5 Ah ¼ 0.72 CN in Fig. 4. Thus, the corresponding two-phase equilibrium of the relaxed state is 3L 4 21. Again, high lithiation rates during the pulse can lead to the temporary formation of a higher-order staging compound, namely stage 1 in this case. By analogy with Example 1, we therefore expect that the stage 1 compound is dissolved entirely during the following relaxation period. In numbers, we get a ¼ 5/14 and b ¼ 9/14, where a/b is the ratio of stage 1 to stage 3L needed to form dense stage 2 during the relaxation. As seen from the average dilation d of the temporary phases
)
d ¼ adð1Þ þ bdð3LÞ ¼ 3:56 A 0dð2Þ < d; dð2Þ ¼ 3:51 A
(5)
the particle shrinks during the relaxation process explaining
Dsrel < 0 for mid-range SOCs in Fig. 5(a). For higher SOCs Dsrel tends to zero again, which is consistent with the model, because in the range of 2 4 1 there is no additional stage of higher order than
2 Remark 2: In addition to the dense stage 2 annulus, an outermost stage 1 annulus might be formed as well. For the corresponding relaxation process of stages 1 and 4L into 3L, we get a ¼ 1/15 (1), b ¼ 4=15 (4L) and dð3LÞ > d ¼ 3:46 A. Hence, this process would contribute to positive relaxation as well.
Fig. 4. Pseudo-equilibrium measurement at I ¼ C/40. Differential voltage (blue) and second derivative of dilation (olive) e both displayed for charging e show staging phenomena in graphite. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
stage 1 which could result in a relaxation phenomenon. 5.4. Comment on the discharge case The discharge data depicted in Fig. 5(b) can be analyzed in the same way. Dsrel < 0 for high SOCs (relaxed state is 2 4 1) is understood by assuming the formation of an outer 3L annulus or even lower-order annuli. As already elaborated in Example 2 for the charge case, layer spacings and cell thickness decrease during the relaxation process of 3L þ 1 / 2, thus explaining the observation. While we might expect Dsrel > 0 for mid-range SOCs (relaxed state 2 4 3L) due to the formation of an outer 4L annulus and subsequent relaxation of 4L and 2 to 3L, the data in Fig. 5(b) do not show this. We believe that this is caused by the charge/discharge asymmetry of staging phenomena, which was also described by k [19]. Due to comparatively high diffusion constants Heb and Nova of the liquid-like stages compared to the dense stages, one can suppose that all lithium ions can be provided by delithiation of stage 2 at the 2/3L phase boundary, with kinetically preferable ionic transport through the surrounding liquid-like stage 3L annulus. Hence, no outer annulus of lower order stages would be formed, explaining Dsrel z 0 in the discharge case. Due to a lack of data on the dilation behavior of the dilute stage 1 compound, we cannot present an explanation for the relaxation process leading to Dsrel < 0 at low SOCs. 5.5. Comment on possible effects on electrode level Depending on the kinetic properties of the electrode, the formation of additional phases may also occur on the electrode surface, while the lithiation/delithiation of the bulk is delayed [31]. In contrast to the core-shell model shown in Fig. 7, kinetic limitations on the electrode level would result in a layered staging structure with layers parallel to the current collector. The effects on external dilation are qualitatively equivalent to those resulting from kinetic limitations on the particle level. That means, the model introduced here likewise explains dilation phenomena on particle level and electrode level. 6. Conclusions The dilation behavior of a graphite half-cell and a graphite/NMC
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Fig. 5. Data from GITT with charge steps (a) and discharge steps (b). Step width is DSOC ¼ 0.1. The x-position of data points represents the SOC at the end of the underlying pulse. Pulses including a CV phase in order to meet voltage limits are marked by an asterix. Upper plots: Relative thickness change Dsdil during current pulse. Lower plots: Relative thickness change Dsrel during the subsequent relaxation phase.
commercial lithium-ion cell at low rates was analyzed. No major qualitative difference was observed, allowing for the conclusion that in both cases dilation at low rates is mainly influenced by graphite staging processes. It is shown that dilatometry is well suitable for the detection of graphite-staging-related data features. Furthermore we could demonstrate that at high rates the dilation can deviate from the dilation behavior observed at low current rates, due to the formation of over-next GICs under nonequilibrium conditions. As a result, both positive or negative dilation relaxation phenomena can occur. These phenomena could be systematically characterized for charge and discharge at different temperatures using a GITT measurement protocol. A model approach was presented which can explain such relaxation phenomena under the assumption that multiple (more than two) GICs coexist during high rate lithiation, giving rise to dilation changes as a two-phase equilibrium is re-established during relaxation. The consideration of these effects is for instance of great importance for the quantitative analysis of Li metal deposition based on dilatometry. The relaxation phenomena observed for charge and discharge
Fig. 6. Charge pulse from the discharged state to SOC ¼ 0.25 (DSOC ¼ 0.25): Positive or negative relaxation of cell thickness due to staging- and plating-related relaxation phenomena, respectively.
differ. Especially for mid-range SOCs during discharge, the formation of multiple GICs appears less pronounced compared to other SOC ranges and/or charge. This was explained by the higher diffusivity of lithium ions in the dilute staging compounds. We consider the dilation relaxation and the charge/discharge asymmetry as a clear confirmation of the shrinking annuli model proposed by Heb and Nov ak [19]. Additionally, we could prove that small variations of the cell temperature caused by dissipation of heat at constant ambient temperature do not severely affect the accuracy of our full-cell dilation experiments. In case of varying ambient temperatures, however, thermal expansion needs to be compensated for using an algorithm like the one introduced in A. Regarding automotive or stationary applications, where larger cells are employed and assembled into packs, dilatometry could be used as a sensitive measurement technique for monitoring kinetic limitations. Depending on SOC, these kinetic limitations can be detected either in the form of an excess-dilation during cycling or by analyzing the relaxation behavior after the current is cut off. As demonstrated by the results, both the formation of multiple phases and lithium plating lead to deviations from the low-rate dilation behavior. If it occurs, however, lithium plating is clearly dominant and the corresponding dilation is always positive. Based on these findings, an algorithm can be developed in order to decide whether only staging or even plating processes are present during real-time battery operation. Alternatively, the method can be used for creating look-up tables characterizing kinetic limitations at various operating conditions in order to feed BMS (battery management system) algorithms. As a limitation, moderate lithium plating and multi-phaseformation are difficult to discriminate during charge at mid-range SOCs because both processes lead to additional dilation (negative relaxation), here. Our future work will be dedicated to overcome this problem by an in-depth analysis of dilation dynamics. Remaining challenges also include the integration of a suitable sensor design into the battery system. (Wire) strain gauges need to be carefully integrated into the battery pack, either for monitoring individual cells or modules of multiple cells. Alternatively, force sensors can be taken into account as a cost-efficient solution, particularly with regard to prismatic or cylindrical cells. Dilatometry was shown to provide information on the kinetic limitations inside graphite anodes. The method is therefore highly interesting for monitoring purposes on a full cell level or even on a
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Fig. 7. Qualitative model of phase shares in graphite particles during high rate current pulses. If the pulse does not exceed the lithiation range of the two-phase equilibrium Si4Siþ1, we have j ¼ i, i. e. the same two stages coexist before the pulse and after the relaxation. Otherwise, j > i for charge and j < i for discharge. For more information on the morphology and characteristics of staging-related annuli in graphite particles please refer to [19].
pack level in electric vehicles. Acknowledgements This research project is supported by the German Federal Ministry for Economic Affairs and Energy (BMWi) under contract number 03ET4012C. Appendix A. Compensation of thermal expansion in dilatometry data In dilatometry measurements, the thermal expansion of both the measurement set-up and the cell is usually an undesired bias. It needs to be quantified and, optionally, compensated for. The total bias seen in dilatometry measurements like ours (see Fig. 1) is composed from shares caused by both the dilation of the measurement set-up and the cell. The set-up-related dilation offset cell is denoted by Dssetup Tref ðTsetup Þ, while DsTref ðTcell Þ is the dilation due to thermal expansion of the cell. Herein Tsetup and Tcell denote the surface temperatures of the set-up and the cell, respectively. Tref denotes the reference temperature which, by definition, corresponds to zero compensation offset regarding both the set-up- and the cell-related thermal expansion. In case of cell tests at constant ambient temperature, the temperature of the set-up (thread rods, aluminum plates, dial indicator) can be expected to be quasi-constant during the test (good thermal junction with ambient air), while the cell obviously heats up whenever high current loads are applied. In such a scenario, only the thermal expansion of the cell Dscell Tref ðTcell Þ contributes to the total bias. For more complex test procedures including a variation of the ambient temperature, the thermal expansion of both the cell and the set-up can be quite significant and need to be taken into account. In order to obtain quantitative results on that, load free
measurements with and without a cell mounted into the set-up are recorded at different temperatures. See Fig. 8 for the results. Fig. 8(a) directly presents data obtained from a temperature variation without a cell mounted in the set-up, i.e. the gauge tip rests on the lower aluminum plate. In Fig. 8(b), on the other hand, the curves are calculated by subtracting the dilation curve of the set-up (Fig. 8(a)) from aggregated dilation data obtained with a cell mounted into the measurement set-up. Thus, subfigure (b) shows the thermal expansion of the cell, only. For the quantification of thermal expansion in our measurements, a data-driven simulation model is used to calculate the expected offsets depending on the time series of surface temperatures (cell and set-up). The curves shown in Fig. 8 (a) and (b) are used to parametrize this simulation model. For demonstration, cell exemplary values of Dssetup Tref ðTsetup Þ and DsTref ðTcell Þ are sketched assuming Tref :¼ 20 C, Tsetup ¼ 25 C, Tcell ¼ 30 C and SOC ¼ 0.25. In our model we performed a piecewise cubic interpolation of these data with respect to both the temperature axis and the SOC axis. Based on the interpolated data, the simulation model calcucell lates both offsets Dssetup Tref ðTsetup Þ and DsTref ðTcell Þ for every data point in a dilatometry measurement for a given reference temperature, if the temperatures Tsetup and Tcell are provided. Thermally compensated dilation data Dscomp can now be calculated from the measured data Dsmeas by subtracting these offsets:
Dscomp ¼ Dsmeas Dssetup Tsetup Dscell Tref ðTcell Þ Tref
(A.1)
Fig. 8(c) shows an example of temperature compensation for GITT data at T ¼ 12.5 C (compare Section 4.3) based on sensor data for Tcell and Tsetup. For the compensation algorithm, Tref :¼ 12.5 C is chosen, so we may assume that all deviations between the compensated curve and the original data are due to self-heating of the cell. Obviously, the maximum deviation in Fig. 8(c) is not significant
M. Bauer et al. / Journal of Power Sources 317 (2016) 93e102
compared to the gauge resolution of 1 mm (0.125% in terms of relative cell dilation). We checked for these deviations in all our measurements and found that for the other temperatures investigated in Section 4.3, were even less than for T ¼ 12.5 C. Interestingly, the thermal expansion coefficient of the cell (i.e. the slope of Dscell Tref ðTcell Þ) exhibits a minimum for low temperatures around 0 C (compare Fig. 8(b)). This is why temperature induced dilation at T z 0 C is lower than one might expect due to high internal resistance and increased self-heating.
Fig. A8. (a) Temperature induced relative dilation of the measurement set-up. (b) Temperature induced relative dilation of the cell only. Relative Dilation is defined zero at T ¼ 0 C for every measurement. (c) Compensated and uncompensated dilation data during a GITT pulse from 40 to 50 % state of charge at an ambient temperature T ¼ 12.5 C (maximum bias).
Being negligible in our GITT-measurements, thermal expansion, however, needs to be compensated whenever there are significant temperature variations during a measurement. Regarding the application of dilatometry for the purpose of cell-monitoring in
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