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Real-time measurements and experimental analysis of material softening and total stresses of Si-composite electrode
Journal of Power Sources 424 (2019) 100–107
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Real-time measurements and experimental analysis of material softening and total stresses of Si-composite electrode
T
Haimei Xie, Yilan Kang, Haibin Song, Qian Zhang∗ Tianjin Key Laboratory of Modern Engineering Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350, PR China
H I GH L IG H T S
in situ method is used to measure modulus and total stresses in Si electrode. • An mechanical models are proposed including modulus, normal and shear stresses. • Four mechanical responses show hysteresis loops during lithiation and delithiation. • All correlation between modulus and Li content is not linear but likely exponential. • The • The softening relieves the total stresses greatly in lithiation and delithiation.
A R T I C LE I N FO
A B S T R A C T
Keywords: Si composite electrode Normal/shear stress Elastic softening Real-time measurement Mechanical models Lithiation/delithiation
The challenges facing high-performance lithium-ion batteries are not only chemical, but also key mechanical problems. Herein, we perform an experiment to investigate the crucial but difficult task of measuring the elastic modulus and total stress evolutions of a bilayer Si-composite electrode during electrochemical processes. Electrode bending deformation is measured in-situ through an optical system. And four mechanical models featuring Li concentration-dependent elastic modulus are used to quantitatively convert curvature into elastic modulus, normal stresses in electrode material and in current collector, and shear stress along interface. Experiments show that the elastic modulus and the three stresses decrease and increase nonlinearly with capacity, respectively, and all demonstrate hysteresis loops during lithiation and delithiation processes. The significant softening of electrode material indicates that the elastic modulus is not linear with Li content. And further discussions show that all the three stresses are significantly affected by elastic modulus, exhibiting a degree of relief similar to material softening. These results guide the mechanical modeling and provide experimental data for mechano-electro-chemical degradation for Si-composite electrode.
1. Introduction The rapid development of the applied fields of lithium-ion batteries (LIBs) demands the electrode materials with high specific capacity, in which silicon materials stand out owing to ten times higher capacity than the commercial carbon material [1]. However, the electrochemical lithiation and delithiation undergo complex mechano-electro-chemical multi-field coupling problems [2,3], where high stress, crack, fracture and delamination are induced and these in turn lead to battery degradation [1–3], making mechanics a key and basic problem for highcapacity electrode materials [4–6]. Therefore, real-time experimental measurements of the complex evolutions of material properties and stresses are crucial to provide effective data for quantifying the driving force for degradation during the cycling process. And this is one of the
∗
prerequisites for the design and development of LIBs with higher capacity and longer cycle life to promote the potential for commercialization. Several theoretical models, numerical simulation methods and experimental techniques and methods have recently been focused on the mechanical responses, mainly including the evolution of the elastic modulus and stress as well as fracturing and cracking in the electrodes. Continuum models and numerical methods of coupled Li diffusion and deformation have been widely developed across different length scales. Researchers have used molecular dynamic simulations and first-principles calculations to show that the elastic properties of Si and Ge electrodes decrease with increasing Li concentration [7,8], and the elastic modulus of the fully lithiated state, LiC6, is three times that of graphite [9]. Becoming aware of the intrinsic Li concentration-
Corresponding author. 135 Yaguan Road, Jinnan District, Tianjin University, Tianjin, 300350, PR China. E-mail address: [email protected] (Q. Zhang).
https://doi.org/10.1016/j.jpowsour.2019.03.107 Received 3 October 2018; Received in revised form 22 March 2019; Accepted 25 March 2019 0378-7753/ © 2019 Elsevier B.V. All rights reserved.
Journal of Power Sources 424 (2019) 100–107
H. Xie, et al.
dependent mechanical properties of the electrode materials, that has been incorporated into mechanical behaviors during the electrochemical processes [10–12]. The general results showed that the modulus softening/stiffening via Li concentration decreases/increases the stresses [3,13–15]. However, most of the above studies have been interested in the mechanical responses of the electrode material but ignored that of the collector. Further, the dependence of the elastic modulus on the Li concentration in stress models is a mixture of values between Li and active material in LixM1-x (M represents active material) by the volume fraction x, far removed from the experimental values. In the past few years, experimental techniques and methods have been developed rapidly for measurements of structural deformation, material properties, and stress responses. These techniques include nanoindentation [16], X-ray [17], digital image correlation [18], Raman spectroscopy [19], the probe technique [20] and the optical lever method [21], and have been extended to the electrochemistry field [4,5,22–25]. For the mechanical properties of the electrode materials, the results by nanoindentation and optical methods showed that the elastic modulus of Si electrodes decreases gradually with increasing degree of lithiation, exhibiting different decreasing trends [26–29]; and with delithiation increases gradually but only partially recovers [28,29]. In addition to material properties, combined with the Stoney equation, a multi-beam optical stress sensor (MOSS) has been proven an effective method for analyzing the stress during lithiation and delithiation processes, which is a major driving force for mechanical degradation. Based on this method, researchers have measured the stress responses in Si electrodes and reported that the maximum stresses in Sithin-film and Si-composite electrodes are found to be ± 1.75 GPa and about −100 MPa, respectively [30,31]. The influences of the solidelectrolyte interface, charge-rates and thickness on stress responses have been discussed [32–34]. However, these measurements do not take into account the close relationship existing between the elastic modulus of the electrode material and the Li concentration, which will inevitably result in errors, and especially in a Si electrode. Recently, Li et al. have reported the stress evolution of Si material in Si composite electrode with Li-dependent elastic modulus [29]. Xie et al. have proposed a new experimental method with a stress model that considers Li -dependent elastic modulus and demonstrated that material softening significantly relieves stress during the lithiation of Si-composite electrodes [35]. These studies provide some insights into the material properties and stress developments in Si electrodes but far form enough. For a commercial composite electrode, the stress responses must contain the normal stresses in the cross sections of active material and current collector and the shear stress at the interface. The characterization of the total stresses during electrochemical cycling is important for understanding the coupling mechanisms to develop high performance and durability of electrodes. However, there have been few experimental reports yet. The objective of this paper is to experimentally investigate the elastic modulus and the electrochemical-induced stresses of a bi-layer Si-composite electrode during lithiation and delithiation processes. To achieve this goal, first the deformation responses as a function of capacity during galvanostatic lithiation and delithiation are monitored in real-time and measured in situ via an optical acquisition system, where the influences that all non-Si parts have on the deformation are excluded. And then four mechanical models that consist of a modulus equation, two normal stress equations and a shear stress equation are proposed to quantify the evolutions of the elastic modulus of electrode material, the normal stresses in Si material and in current collector as well as the shear stress at the interface as a function of capacity during lithiation and delithiation processes. The effects of material softening during lithiation and delithiation on the stresses are further analyzed and discussed. This work enhances and advances the knowledge about mechanical responses and the coupling mechanism of a Si-composite electrode in the electrochemical process. And it also provides experimental basis for theoretical modeling of the elastic modulus and
Fig. 1. Schematic illustration of a customized electrochemical cell with a glass window and an optical acquisition system for curved deformation measurement. The inset shows the details of the electrode layered structure and an SEM surface morphology image of the electrode material. The schematic is not drawn to scale.
stresses.
2. Real-time experiments and methods 2.1. Electrode Preparation and cell assembly A Si-composite electrode was prepared by coating an electrodematerial slurry onto a Cu foil, where the slurry was composed of 70 wt % Si nanoparticles (∼80 nm diameter, 99% purity; Guangzhou Hongwu Material Technology Co., Ltd., China), 15 wt% binder (sodium alginate, 18th Research Institute, Tianjin, China) and 15 wt% conductive additive (Super P, Timcal, Switzerland). The layered structure of the electrode and thickness of the bi-layer (image in inset) are shown schematically in Fig. 1. The electrode exhibited a porous structure, as seen in the scanning electron microscope (SEM) surface morphology image of the electrode material shown in Fig. 1 inset. The Cu foil served as both a collector in the electrode and as a substrate that undergoes a curved deformation in response to stress in the electrode material bonded to it. A customized electrochemical cell was assembled in an argon-filled glove box, in which a glass window enabled in situ deformation measurements via the optical system, as illustrated schematically in Fig. 1. The Si-composite electrode (∼18 μm thickness) was used as the working electrode and a lithium metal foil (∼120 μm thickness, 99.9% purity; Tianjin Zhongneng Lithium Industry Co., Ltd., China) was used as the reference/counter electrode. The two electrodes exhibited a cantilever configuration whose upper end is fixed and whose lower end is free to deform. Further, the electrodes were separated by a Celgard microporous polypropylene separator and submerged in an electrolyte solution (analytical reagent, Tianjin Jingniu, China) comprising 1 M of LiPF6 in a 1:1 vol ratio of ethylene carbonate: dimethyl carbonate.
2.2. Electrochemical measurements Electrochemical experiments were conducted at room temperature and the data were collected by a CT2001A LAND cell tester (Wuhan LAND Electronics Co., Ltd., China). The Si-composite electrodes were galvanostatically lithiated to a lower cutoff potential of 0.01 V vs. Li/ Li+ at 532 μA, which corresponds to C/5 rate with a theoretical capacity of 3579 mAh g−1 [25,34]. Next, delithiation was performed at the same rate to a higher cutoff potential of 2 V vs. Li/Li+. To ensure the complete removal of Li, the potential was held constant at 2 V vs. Li/ Li+ until the current fell below 6 μA. 101
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H. Xie, et al.
Ee he3 + Ec hc 3 ] 6(he + hc ) he
h
6βc¯ ( he + 1)[Ee z e − c
σe =
1+
h E 4 he Ee c c
+
h2 E 6 e2 Ee hc c
h 3E 4 e3 Ee hc c
+
+
he 4 Ee 2 hc 4 Ec 2
he Ee , hc2 Ec
−0.5he < z e < 0.5he (1–2)
The normal stress along the thickness direction for current collector was expressed as [35]. h
σc =
6βc¯ ( he + 1)[Ec z c + c
1+
h E 4 he Ee c c
+
h2 E 6 e2 Ee hc c
+
Ee he3 + Ec hc 3 ] 6(he + hc ) hc
h 3E 4 e3 Ee hc c
+
he 4 Ee 2 hc 4 Ec 2
he Ee , hc2 Ec
−0.5hc < z c < 0.5hc (1–3)
Further, focused on the interface, the load along the horizontal direction was analyzed, as shown in Fig. 2. We simplified that the shear stress is uniform across the whole interface. Based on the balance along the horizontal direction of electrode material, that is l 0.5h ∫0 τdx = ∫−0.5hee σe dz , therefore, the shear stress was derived and expressed as
Fig. 2. Illustration of the bilayer electrode with a cantilever configuration for the initial (upper) and lithiated (lower) state. The interface load and the equivalent loads at the cross sections are shown. Schematic illustrations are not drawn to scale.
(1 +
During electrochemical lithiation/delithiation cycling, an expansion/contraction of electrode material layer appears, which induces a mismatch strain between the two layers. With a cantilever configuration of the electrode as shown in Fig. 1, the restriction of current collector causes the cantilever electrode to bend. Thus, the mechanical behaviors of the Si-composite electrode were measured by real-time collection of the curved deformation of the layered electrode during electrochemical lithiation and delithiation. Fig. 2 illustrates the bilayer electrode with a cantilever configuration before lithiation and during lithiation, where the interface load and equivalent loads at the cross sections are shown. Considering the Li concentration as analogous to a thermal expansion, and based on the balance equations, geometric equations, continuous conditions and constitutive equations, the modulus equation and normal stress equations with a Li-dependent elastic modulus were developed in our previous work [27,35] and were summarized here to convert curvature into modulus and stresses. The elastic modulus of electrode material was expressed as [27,35]. Ee Ec
=− +
hc he3 k
(4k 2 (he4 + hc4 ) + 12he hc k 2 (he2 + hc2) + 16he2 hc2 k 2
e
c
e c
h 4 he c
Ee Ec
+6
he2 Ee hc 2 Ec
+4
he3 hc3
Ee Ec
+
he 4 hc 4
Ee 2 )l Ec 2
he Ee hc3 Ec
(1–4)
where in the above equations, E is elastic modulus, h is thickness, σ is normal stress, z is distance offset from respective neutral layers of the electrode material (subscript e) and current collector (subscript c), respectively; τ is shear stress; l is electrode length; k is electrode curvature obtained by fitting the bending electrode measured in real-time via the optical acquisition system shown in Fig. 1, where the system comprises a telecentric lens, a charge-coupled device (CCD), image boards, acquisition cards, a monitor and a computer with a resolution of 0.05 mm/pixel; and β‾c s a thermally equivalent axial strain caused by the Li concentration, where ‾c is the normalized Li concentration and β is an equivalent dimensionless expansion coefficient. The normalized Li concentration‾c is determined by the expression of c/cmax, where c is the special capacity obtained from the cell tester in this experiment and cmax is the theoretical special capacity of 3579 mAh g−1. And its value varies between 0 and 1, that refers pure Si without expansion and the fully lithiated state Li3.75Si with 370% volume expansion, respectively [32]. The dimensionless expansion coefficient β is associated with the composition and structure of the electrode material and can be obtained from the maximum volume expansion of the electrode material when fully lithiated. For the Si-composite electrode, analogous to thermal expansion, β is calculated to be 0.33 through an expression of maximum volume expansion Vmax=(1+β)3. And Vmax is simplified calculation to be 235% that comprises two parts including expanded volume of the completely lithiated Si with 370%*50% (active Si volume fraction from Fig. 1) and volume of the inactive compositions of 50%. Owing to that the electrode material is constrained in-plane by the Cu collector, it is reasonable to assume that the lithiation-induced volume expansion is accommodated entirely by growth in the thickness direction. Reference to pervious work [30–35], a linear relationship between the thickness of Si-composite electrode is assumed and expressed as
{2he2 k + 3he hc k + 2khc2 − 3he βc¯ − 3hc βc¯
¯ (he3 + hc3) − 30βckh ¯ e hc (he + hc ) − 12βck 2 2 2 2 ¯ ¯ h + 9β c (h + h ) + 18βch
(Ee he 3 + Ec hc 3) βc¯
τ=
2.3. Mechanical models for elastic modulus and stresses
(1-1)
The normal stress along the thickness direction for electrode material was expressed as [35].
Table 1 Parameters for Si composite electrode. Parameter
Description
Value
Comments
Ec hc l he0 Vmax β cmax c ‾c k
Elastic modulus of current collector Thickness of current collector Electrode length Initial thickness of electrode material Max volume of electrode material Equivalent expansion coefficient Theoretical specific capacity Specific capacity Normalized Li concentration Electrode curvature
80 GPa 28 um 23.8 mm 18 um 235% 0.33 3579 mAh g−1 ∼ ∼ ∼
Measured by tensile machine Measured by microscope Measured by microscope Measured by microscope Calculated Calculated by max expansion Ref. 25,34 Measured by Land system Calculated by c/cmax Measured by optical system
102
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he = he0(1 + 1.35‾c), where he0 is initial thickness of electrode material. The total parameters are summarized in Table 1. Back to the four equations, Eqs. (1)–(1) shows that the elastic modulus of the electrode material is related to its composition and structure, electrode deformation and Li concentration. This is used to quantitatively present the elastic modulus evolution as a function of Li concentration. Eqs. ((1), (1), (2), (2) and (3) and (1-4) show that three stresses have a direct relationship with the Li concentration, composition and structure of electrode material, as well as the geometry and mechanical properties of the bilayer, and couple with the deformation owing to the elastic modulus of the electrode material. The normal stresses in the electrode material and collector as well as the shear stress at the interface can be quantitatively obtained by substituting the variable elastic modulus calculated from Eqs. (1)–(1) into Eqs. (1-2) and (1-3) and (1-4). 3. Results and discussion 3.1. Electrochemical potential and deformation responses As shown in Figs. 1 and 2, the layered Si-composite electrode in this experiment consists of a current collector and an electrode material that is a composite of active Si nanoparticles, binders and conductive additives. During electrochemical lithiation, lithium ions are continuously inserted into the active Si particles to participate in the Li–Si alloying reaction, accompanied by a volume expansion in the particles that results in an expansion of the electrode material. This expansion, however, is restricted by the Cu collector, and the bi-layer mismatch strain induces the layered electrode bending deformation. Conversely, Li is gradually extracted from the active Si particles for the de-alloying reaction during electrochemical delithiation. The resulting reduced volume expansion gradually causes the bending deformation of the layered electrode to recover. Fig. 3 shows the potential (Fig. 3a) and curvature (Fig. 3b) evolution of the Si-composite electrode as a function of capacity (i.e., Li concentration) during the second lithiation/delithiation cycle at the C/5 rate. The solid/open symbols represent the lithiation/delithiation process, and are used consistently as such throughout this entire work. As the Li concentration increases during the lithiation process, the potential of the Si-composite electrode gradually decreases to 0.01 V vs. Li/Li+ and the deformation varies nonlinearly. At the initial insertion, the curvature rapidly increases in an approximately linear fashion with capacity to ∼21.2 m−1 at 287 mAh g−1, beyond which it continues to increase slowly to a maximum value of 33.6 m−1 at 964 mAh g−1 at the cut-off potential. The slowed deformation implies that the mechanical properties of the electrode material may change with Li concentration. As the Li concentration decreases during the delithiation process, the potential gradually increases to 2 V vs. Li/Li+ and the deformation gradually recovers. In addition, Fig. 3b clearly shows that the curvature during lithiation/ delithiation is not identical when at the same capacity, indicating that the mechanical behaviors depend not only on the Li concentration, but also on the lithiation or delithiation process. In addition, it is noted that the electrode material contains both active Si and non-Si components. Therefore, a new electrode comprising no active parts, but 50 wt% binder and 50 wt% conductive additive, was prepared using the same procedure in the Electrode Preparation to exclude the influences that non-Si components and other factors such as wetting may have on the bending deformation. This new electrode was subjected to the same current value and the same deformation acquisition process as those used with the Si-composite electrode. The results show that the maximum curvature of the new electrode is 2.35 m−1 at the cut-off potential, accounting for about 7% of the measured k (33.6 m-1) of the Si-composite electrode. Therefore, all of the other factors are excluded in these results by multiplying the measured k by 0.93 to obtain the curvature of the active Si component, which is called the modified k and is shown in Fig. 3b. And the
Fig. 3. Responses in (a) potential vs. Li/Li+, and (b) curvature of the Si-composite electrode as a function of capacity during the second galvanostatic lithiation (solid symbol) and delithiation (open symbol) cycle at C/5 between 2 and 0.01 V vs. Li/Li+. The modified k is the curvature of the active Si component that excludes all other factors with a values of 93% measured k in Sicomposite electrode.
calculations and analyses in the next are based on the modified curvature. 3.2. Responses of elastic modulus during lithiation and delithiation processes To quantify the elastic modulus during lithiation and delithiation, the deformation results in Fig. 3b are substituted into the modulus equations (1)–(1). With the parameters in Table 1, the elastic modulus evolution of the Si-composite electrode material as a function of capacity during the second lithiation and delithiation is obtained, and is shown in Fig. 4. It shows that the mechanical properties of the Sicomposite electrode material soften significantly with increasing Li concentration during lithiation process. The elastic modulus decreases from an initial value of 966 to 82 MPa at 964 mAh g−1 (at lower cut-off potential), which is a decrease of about 91.5%. This is mainly owing to breakage of Si–Si bonds and the formation of weak Li–Si bonds during the alloying reaction. And the mechanical properties gradually recover with decreasing Li concentration during delithiation process, showing that the elastic modulus increases to 232 MPa at 80 mAh g−1 (at higher cut-off potential). This is mainly owing to the gradual recovery of the Si–Si bonds during the de-alloying reaction. As described in Eqs. (1)–(1), the elastic modulus depends on Li concentration, composition and structure, and deformation. With the deformation affected by porosity, ratio of active material and inactive composition, etc., therefore, the measured elastic modulus is equivalent 103
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are different from those reported in literature [25–29], which are a little larger than Si-composite electrodes and 2 orders of magnitude smaller than Si-thin film electrodes. This is mainly because the measured modulus is equivalent modulus of the composite film with porosity, inactive components and different Si content. 2. As shown in Fig. 4, the modulus decreases with capacity in a nonlinear fashion, exhibiting an initial fast and then slow trend. For further analysis, the modulus is plotted against volume fraction of Li, x, in LixSi(1-x), as shown in Fig. 4 inset. Obviously, the modulus is not linear with Li volume fraction. This demonstrates that the normal treatment of the elastic modulus, that is, simple mixtures between the properties of Si and Li cannot be applied to elastic modulus of composite electrode during electrochemical processes, which may be owing to the effects of inactive components and porosity. Further, it is found by fitting that an exponential function may better describe the relationship between the elastic modulus of composite electrode and Li volume fraction, as shown in Fig. 4 inset. 3. The modulus in the delithiation process recovers along a different path with a smaller value from that in the lithiation process, consistent with previous research [29]. The unexpected trend indicates that the mechanical property depends not only on the macroscopically-measurable capacity but also on film morphology during lithiation/delithiation process. The cracks appeared in the delithiation process is a reason for smaller modulus. Furthermore, in the complex composition and structure of composite electrode, the changes of elastic modulus mainly comes from Li content inside Si particle, so the concentration gradient inside particle may also be a reason for the modulus difference between lithiation and delithiation processes. In summary, the above experimental data and analysis provide guidance and basis for the mechanical modeling of composite electrode. If mechanical properties of original material or simple mixtures
Fig. 4. Elastic modulus of the Si-composite electrode material as a function of capacity and as a function of Li volume fraction (inset) during the second lithiation and delithiation processes. The plots are obtained by substituting the deformation data in Fig. 3b and parameters in Table 1 into the modulus equations (1)–(1).
modulus of the whole Si composite film structure that contains factors such as porosity, inactive components, active component as well as the film morphology. Based on this, the results of elastic modulus are analyzed. 1. The experimental results show that the elastic modulus decreases/increases with increasing/decreasing capacity during lithiation/delithiation process, that is generally consistent with the previously reports for Si electrodes, especially for Si-composite electrodes [25–29]. This validates our experiment data. And the modulus values
Fig. 5. The total stress evolutions for the (a) normal stress at the surface of electrode material and (b) normal stress at the interface of current collector and (c) shear stress along the interface as a function of capacity during the second lithiation and delithiation processes. The plots are obtained by substituting the variable elastic modulus in Fig. 4 and parameters in Table 1 into Eqs. ((1), (1), (2), (2) and (3) and (1-4). 104
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material associated with Li concentration, which significantly relieves not only the normal stress in the electrode material [35], but also that in the current collector as well as the shear stress along the interface during the entire electrochemical lithiation and delithiation processes. Quantitatively, a 91.5% softening of electrode material causes the stresses to decrease by about 90%. Such significant softening-induced stress reliefs are particularly important for fracture failure and interface failure during the lithiation and delithiation cycles of the Si-composite electrode. Second, comparing conditions 10 and 11 that only affect the delithiation process, as shown in Fig. 6 insets, the delithiated stresses with the same elastic modulus between lithiation and delithiation recover along the same path from lithiation, therefore are greater than the delithiated stresses calculated from the modulus in Fig. 4. The stress evolutions are seriously affected by elastic modulus, indicating the importance of elastic modulus measurements. In summary, to understand the mechano-electro-chemical mechanism for development of high-capacity electrode materials, an accurate characterization of the total stresses in a composite electrode during electrochemical lithiation and delithiation cycling must be carried out, displaying a significant dependence on the variable elastic modulus. Therefore, the Stoney equation with Li-independent elastic modulus is seriously challenged for in-situ total stress measurements of thin film electrodes during electrochemical processes, especially for electrodes comprising Si, C and Sn, whose mechanical properties change significantly with Li concentration. Thus, herein, the proposed mechanical models for elastic modulus, and normal stresses and shear stress with Li-dependent elastic modulus overcome the difficulty and realize the total stress measurements during electrochemical processes.
between of active material and Li are used, or the property difference between lithiation and delithiation is ignored, this will bring great errors to mechanical modeling. So the mechanical properties for each composite electrodes require experimental measurements. 3.3. Stress characterization during lithiation and delithiation processes The experimental results show that the elastic modulus of the electrode material softens during electrochemical lithiation/delithiation process. So in the following, the stress responses of the bi-layer electrode during lithiation and delithiation processes are characterized, and the influences of elastic modulus on the stress responses are discussed. Substituting the variable elastic modulus during lithiation and delithiation processes (as shown in Fig. 4) and the parameters in Table 1 into stress equations ((1), (1), (2), (2) and (3) and (1-4) the normal stresses and shear stress of the bilayer electrode can be obtained as a function of capacity. Fig. 5 shows the normal stress at the surface of electrode material σe-surface (Fig. 5a) and the normal stress at the interface of current collector σc-interface (Fig. 5b) and the shear stress along the interface τ (Fig. 5c) during the second lithiation and delithiation processes. During the electrochemical process, the electrode material experiences a compressive stress in the surface owing to the restriction of the substrate on free expansion of the electrode material, while the collector experiences a tensile stress in the interface. All the three stresses evolve nonlinearly with capacity. During the lithiation process, the normal stresses in electrode material and in current collector and the shear stress along the interface increase to their maximum values of −7.4 MPa and 41.3 MPa and 7.4 KPa, respectively, exhibiting an initially rapid and subsequently slow trend. And the stresses during the delithiation process recover along a different path from that in the lithiation process with a relatively stable trend. More details, normal stresses of the electrode material and current collector (never been experimentally reported) are several megapascals and several tens of megapascals, respectively, which are important for fracture failure during electrochemical processes. Shear stress (never been experimentally reported) is only several kilopascals, which is three orders of magnitude smaller than normal stresses and the values are helpful for understanding the interface state between the layers. Totally, the stresscapacity hysteresis loops provide basis data for mechanical energy consumptions and degradation driving force etc., which are very important for investigating mechano-electro-chemical coupling mechanisms and determining role of mechanics in electrochemical processes. Furthermore, the stress evolution with capacity is similar to modulus evolution with capacity and the normal stress in electrode material is smaller than that measured by MOSS for Si-composite electrode with a constant elastic modulus [31]. This makes us want to know the relationship between stress and elastic modulus during electrochemical processes. Here, three different cases for elastic modulus of electrode material are included: (1) constant modulus in lithiation/delithiation with value of 966 MPa, denoted by 00; (2) Li-dependent modulus but no difference between lithiation and delithiation, denoted by 10; and (3) Li-dependent modulus with different values in lithiation and delithiation, i.e., measured in Fig. 4, denoted by 11. Substituting all these modulus values into stress equations ((1), (1), (2), (2) and (3) and (1-4), the normal stresses and shear stress of the bilayer electrode can be obtained as a function of capacity for the three conditions, as shown in Fig. 6. First, conditions 00 and 11 are compared. The stresses with a constant elastic modulus increase linearly to maximum of −72.8 MPa for σe-surface, 436.8 MPa for σc-interface and 78.3 KPa for τ respectively during lithiation, and recover along the same path during the delithiation process. The stress trends are quite different from that in the case of Lidependent elastic modulus. And all the three stresses are much greater than that in the case of Li-dependent elastic modulus during electrochemical processes. These differences are owing to the softening of the
4. Conclusions The coupling of electrochemistry and mechanics determines the degradation process of Si electrodes. In parallel with research efforts to promote the electrochemical performance of Si electrodes, intensive research should be carried out to study the mechanical behaviors as well as the mechanisms during the electrochemical processes. Herein, in situ experiments are carried out to report the elastic modulus and total stresses of a Si-composite electrode during electrochemical lithiation and delithiation cycling. An optical system is applied to in situ measure the deformation and four mechanical models are applied to analyze the relationship between elastic modulus, normal stress in electrode material, normal stress in current collector, shear stress along interface, curvature and capacity. It is found that the elastic modulus of Si electrode material nonlinearly decreases and increases in different paths with capacity during lithiation and delithiation processes, exhibiting smaller values during delithiation process. The dependence of elastic modulus on Li content is more likely to be an exponential rather than a linear function. More importantly, the normal tensile stresses for current collector and normal compressive stresses for electrode material and shear stress along the interface also nonlinearly increase with capacity and show stress-capacity hysteresis loops during lithiation and delithiation cycle, which are significantly affected by the hysteresis loop of elastic modulus. This experimental results demonstrate the applicability and superiority of the proposed mechanical models for electrochemical processes and provide an experimental basis for quantification of mechano-electrochemical degradation and development of high-performance batteries. Declarations of interest None. Acknowledgments This work was financially supported by the the Major Program of 105
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Fig. 6. Stress evolution as a function of capacity for normal stresses in (a) electrode material and (b) current collector and (c) shear stress along interface under three different treatments of elastic modulus of electrode material.
the National Natural Science Foundation of China (grant numbers 11890683), the National Natural Science Foundation of China (grant numbers 11672203 and 11872269).
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SEM: scanning electron microscope CCD: charge-coupled device C: capacity cmax: theoretical capacity c¯ : normalized Li concentration Ee: elastic modulus of the electrode material Ec: elastic modulus of the collector he: thickness of the electrode material hc: thickness of the collector k: curvature of the electrode l: length of the electrode β: expansion coefficient σc: normal stress in the collector σe: normal stress in the electrode material τ: shear stress at the interface σe-surface: surface normal stress in the electrode material σc-interface: interface normal stress in current collector Vmax: maximum volume of the Si composite electrode x: volume fraction of Li in lithiated electrode material
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Real-time measurements and experimental analysis of material softening and total stresses of Si-composite electrode
T
Haimei Xie, Yilan Kang, Haibin Song, Qian Zhang∗ Tianjin Key Laboratory of Modern Engineering Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350, PR China
H I GH L IG H T S
in situ method is used to measure modulus and total stresses in Si electrode. • An mechanical models are proposed including modulus, normal and shear stresses. • Four mechanical responses show hysteresis loops during lithiation and delithiation. • All correlation between modulus and Li content is not linear but likely exponential. • The • The softening relieves the total stresses greatly in lithiation and delithiation.
A R T I C LE I N FO
A B S T R A C T
Keywords: Si composite electrode Normal/shear stress Elastic softening Real-time measurement Mechanical models Lithiation/delithiation
The challenges facing high-performance lithium-ion batteries are not only chemical, but also key mechanical problems. Herein, we perform an experiment to investigate the crucial but difficult task of measuring the elastic modulus and total stress evolutions of a bilayer Si-composite electrode during electrochemical processes. Electrode bending deformation is measured in-situ through an optical system. And four mechanical models featuring Li concentration-dependent elastic modulus are used to quantitatively convert curvature into elastic modulus, normal stresses in electrode material and in current collector, and shear stress along interface. Experiments show that the elastic modulus and the three stresses decrease and increase nonlinearly with capacity, respectively, and all demonstrate hysteresis loops during lithiation and delithiation processes. The significant softening of electrode material indicates that the elastic modulus is not linear with Li content. And further discussions show that all the three stresses are significantly affected by elastic modulus, exhibiting a degree of relief similar to material softening. These results guide the mechanical modeling and provide experimental data for mechano-electro-chemical degradation for Si-composite electrode.
1. Introduction The rapid development of the applied fields of lithium-ion batteries (LIBs) demands the electrode materials with high specific capacity, in which silicon materials stand out owing to ten times higher capacity than the commercial carbon material [1]. However, the electrochemical lithiation and delithiation undergo complex mechano-electro-chemical multi-field coupling problems [2,3], where high stress, crack, fracture and delamination are induced and these in turn lead to battery degradation [1–3], making mechanics a key and basic problem for highcapacity electrode materials [4–6]. Therefore, real-time experimental measurements of the complex evolutions of material properties and stresses are crucial to provide effective data for quantifying the driving force for degradation during the cycling process. And this is one of the
∗
prerequisites for the design and development of LIBs with higher capacity and longer cycle life to promote the potential for commercialization. Several theoretical models, numerical simulation methods and experimental techniques and methods have recently been focused on the mechanical responses, mainly including the evolution of the elastic modulus and stress as well as fracturing and cracking in the electrodes. Continuum models and numerical methods of coupled Li diffusion and deformation have been widely developed across different length scales. Researchers have used molecular dynamic simulations and first-principles calculations to show that the elastic properties of Si and Ge electrodes decrease with increasing Li concentration [7,8], and the elastic modulus of the fully lithiated state, LiC6, is three times that of graphite [9]. Becoming aware of the intrinsic Li concentration-
Corresponding author. 135 Yaguan Road, Jinnan District, Tianjin University, Tianjin, 300350, PR China. E-mail address: [email protected] (Q. Zhang).
https://doi.org/10.1016/j.jpowsour.2019.03.107 Received 3 October 2018; Received in revised form 22 March 2019; Accepted 25 March 2019 0378-7753/ © 2019 Elsevier B.V. All rights reserved.
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dependent mechanical properties of the electrode materials, that has been incorporated into mechanical behaviors during the electrochemical processes [10–12]. The general results showed that the modulus softening/stiffening via Li concentration decreases/increases the stresses [3,13–15]. However, most of the above studies have been interested in the mechanical responses of the electrode material but ignored that of the collector. Further, the dependence of the elastic modulus on the Li concentration in stress models is a mixture of values between Li and active material in LixM1-x (M represents active material) by the volume fraction x, far removed from the experimental values. In the past few years, experimental techniques and methods have been developed rapidly for measurements of structural deformation, material properties, and stress responses. These techniques include nanoindentation [16], X-ray [17], digital image correlation [18], Raman spectroscopy [19], the probe technique [20] and the optical lever method [21], and have been extended to the electrochemistry field [4,5,22–25]. For the mechanical properties of the electrode materials, the results by nanoindentation and optical methods showed that the elastic modulus of Si electrodes decreases gradually with increasing degree of lithiation, exhibiting different decreasing trends [26–29]; and with delithiation increases gradually but only partially recovers [28,29]. In addition to material properties, combined with the Stoney equation, a multi-beam optical stress sensor (MOSS) has been proven an effective method for analyzing the stress during lithiation and delithiation processes, which is a major driving force for mechanical degradation. Based on this method, researchers have measured the stress responses in Si electrodes and reported that the maximum stresses in Sithin-film and Si-composite electrodes are found to be ± 1.75 GPa and about −100 MPa, respectively [30,31]. The influences of the solidelectrolyte interface, charge-rates and thickness on stress responses have been discussed [32–34]. However, these measurements do not take into account the close relationship existing between the elastic modulus of the electrode material and the Li concentration, which will inevitably result in errors, and especially in a Si electrode. Recently, Li et al. have reported the stress evolution of Si material in Si composite electrode with Li-dependent elastic modulus [29]. Xie et al. have proposed a new experimental method with a stress model that considers Li -dependent elastic modulus and demonstrated that material softening significantly relieves stress during the lithiation of Si-composite electrodes [35]. These studies provide some insights into the material properties and stress developments in Si electrodes but far form enough. For a commercial composite electrode, the stress responses must contain the normal stresses in the cross sections of active material and current collector and the shear stress at the interface. The characterization of the total stresses during electrochemical cycling is important for understanding the coupling mechanisms to develop high performance and durability of electrodes. However, there have been few experimental reports yet. The objective of this paper is to experimentally investigate the elastic modulus and the electrochemical-induced stresses of a bi-layer Si-composite electrode during lithiation and delithiation processes. To achieve this goal, first the deformation responses as a function of capacity during galvanostatic lithiation and delithiation are monitored in real-time and measured in situ via an optical acquisition system, where the influences that all non-Si parts have on the deformation are excluded. And then four mechanical models that consist of a modulus equation, two normal stress equations and a shear stress equation are proposed to quantify the evolutions of the elastic modulus of electrode material, the normal stresses in Si material and in current collector as well as the shear stress at the interface as a function of capacity during lithiation and delithiation processes. The effects of material softening during lithiation and delithiation on the stresses are further analyzed and discussed. This work enhances and advances the knowledge about mechanical responses and the coupling mechanism of a Si-composite electrode in the electrochemical process. And it also provides experimental basis for theoretical modeling of the elastic modulus and
Fig. 1. Schematic illustration of a customized electrochemical cell with a glass window and an optical acquisition system for curved deformation measurement. The inset shows the details of the electrode layered structure and an SEM surface morphology image of the electrode material. The schematic is not drawn to scale.
stresses.
2. Real-time experiments and methods 2.1. Electrode Preparation and cell assembly A Si-composite electrode was prepared by coating an electrodematerial slurry onto a Cu foil, where the slurry was composed of 70 wt % Si nanoparticles (∼80 nm diameter, 99% purity; Guangzhou Hongwu Material Technology Co., Ltd., China), 15 wt% binder (sodium alginate, 18th Research Institute, Tianjin, China) and 15 wt% conductive additive (Super P, Timcal, Switzerland). The layered structure of the electrode and thickness of the bi-layer (image in inset) are shown schematically in Fig. 1. The electrode exhibited a porous structure, as seen in the scanning electron microscope (SEM) surface morphology image of the electrode material shown in Fig. 1 inset. The Cu foil served as both a collector in the electrode and as a substrate that undergoes a curved deformation in response to stress in the electrode material bonded to it. A customized electrochemical cell was assembled in an argon-filled glove box, in which a glass window enabled in situ deformation measurements via the optical system, as illustrated schematically in Fig. 1. The Si-composite electrode (∼18 μm thickness) was used as the working electrode and a lithium metal foil (∼120 μm thickness, 99.9% purity; Tianjin Zhongneng Lithium Industry Co., Ltd., China) was used as the reference/counter electrode. The two electrodes exhibited a cantilever configuration whose upper end is fixed and whose lower end is free to deform. Further, the electrodes were separated by a Celgard microporous polypropylene separator and submerged in an electrolyte solution (analytical reagent, Tianjin Jingniu, China) comprising 1 M of LiPF6 in a 1:1 vol ratio of ethylene carbonate: dimethyl carbonate.
2.2. Electrochemical measurements Electrochemical experiments were conducted at room temperature and the data were collected by a CT2001A LAND cell tester (Wuhan LAND Electronics Co., Ltd., China). The Si-composite electrodes were galvanostatically lithiated to a lower cutoff potential of 0.01 V vs. Li/ Li+ at 532 μA, which corresponds to C/5 rate with a theoretical capacity of 3579 mAh g−1 [25,34]. Next, delithiation was performed at the same rate to a higher cutoff potential of 2 V vs. Li/Li+. To ensure the complete removal of Li, the potential was held constant at 2 V vs. Li/ Li+ until the current fell below 6 μA. 101
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Ee he3 + Ec hc 3 ] 6(he + hc ) he
h
6βc¯ ( he + 1)[Ee z e − c
σe =
1+
h E 4 he Ee c c
+
h2 E 6 e2 Ee hc c
h 3E 4 e3 Ee hc c
+
+
he 4 Ee 2 hc 4 Ec 2
he Ee , hc2 Ec
−0.5he < z e < 0.5he (1–2)
The normal stress along the thickness direction for current collector was expressed as [35]. h
σc =
6βc¯ ( he + 1)[Ec z c + c
1+
h E 4 he Ee c c
+
h2 E 6 e2 Ee hc c
+
Ee he3 + Ec hc 3 ] 6(he + hc ) hc
h 3E 4 e3 Ee hc c
+
he 4 Ee 2 hc 4 Ec 2
he Ee , hc2 Ec
−0.5hc < z c < 0.5hc (1–3)
Further, focused on the interface, the load along the horizontal direction was analyzed, as shown in Fig. 2. We simplified that the shear stress is uniform across the whole interface. Based on the balance along the horizontal direction of electrode material, that is l 0.5h ∫0 τdx = ∫−0.5hee σe dz , therefore, the shear stress was derived and expressed as
Fig. 2. Illustration of the bilayer electrode with a cantilever configuration for the initial (upper) and lithiated (lower) state. The interface load and the equivalent loads at the cross sections are shown. Schematic illustrations are not drawn to scale.
(1 +
During electrochemical lithiation/delithiation cycling, an expansion/contraction of electrode material layer appears, which induces a mismatch strain between the two layers. With a cantilever configuration of the electrode as shown in Fig. 1, the restriction of current collector causes the cantilever electrode to bend. Thus, the mechanical behaviors of the Si-composite electrode were measured by real-time collection of the curved deformation of the layered electrode during electrochemical lithiation and delithiation. Fig. 2 illustrates the bilayer electrode with a cantilever configuration before lithiation and during lithiation, where the interface load and equivalent loads at the cross sections are shown. Considering the Li concentration as analogous to a thermal expansion, and based on the balance equations, geometric equations, continuous conditions and constitutive equations, the modulus equation and normal stress equations with a Li-dependent elastic modulus were developed in our previous work [27,35] and were summarized here to convert curvature into modulus and stresses. The elastic modulus of electrode material was expressed as [27,35]. Ee Ec
=− +
hc he3 k
(4k 2 (he4 + hc4 ) + 12he hc k 2 (he2 + hc2) + 16he2 hc2 k 2
e
c
e c
h 4 he c
Ee Ec
+6
he2 Ee hc 2 Ec
+4
he3 hc3
Ee Ec
+
he 4 hc 4
Ee 2 )l Ec 2
he Ee hc3 Ec
(1–4)
where in the above equations, E is elastic modulus, h is thickness, σ is normal stress, z is distance offset from respective neutral layers of the electrode material (subscript e) and current collector (subscript c), respectively; τ is shear stress; l is electrode length; k is electrode curvature obtained by fitting the bending electrode measured in real-time via the optical acquisition system shown in Fig. 1, where the system comprises a telecentric lens, a charge-coupled device (CCD), image boards, acquisition cards, a monitor and a computer with a resolution of 0.05 mm/pixel; and β‾c s a thermally equivalent axial strain caused by the Li concentration, where ‾c is the normalized Li concentration and β is an equivalent dimensionless expansion coefficient. The normalized Li concentration‾c is determined by the expression of c/cmax, where c is the special capacity obtained from the cell tester in this experiment and cmax is the theoretical special capacity of 3579 mAh g−1. And its value varies between 0 and 1, that refers pure Si without expansion and the fully lithiated state Li3.75Si with 370% volume expansion, respectively [32]. The dimensionless expansion coefficient β is associated with the composition and structure of the electrode material and can be obtained from the maximum volume expansion of the electrode material when fully lithiated. For the Si-composite electrode, analogous to thermal expansion, β is calculated to be 0.33 through an expression of maximum volume expansion Vmax=(1+β)3. And Vmax is simplified calculation to be 235% that comprises two parts including expanded volume of the completely lithiated Si with 370%*50% (active Si volume fraction from Fig. 1) and volume of the inactive compositions of 50%. Owing to that the electrode material is constrained in-plane by the Cu collector, it is reasonable to assume that the lithiation-induced volume expansion is accommodated entirely by growth in the thickness direction. Reference to pervious work [30–35], a linear relationship between the thickness of Si-composite electrode is assumed and expressed as
{2he2 k + 3he hc k + 2khc2 − 3he βc¯ − 3hc βc¯
¯ (he3 + hc3) − 30βckh ¯ e hc (he + hc ) − 12βck 2 2 2 2 ¯ ¯ h + 9β c (h + h ) + 18βch
(Ee he 3 + Ec hc 3) βc¯
τ=
2.3. Mechanical models for elastic modulus and stresses
(1-1)
The normal stress along the thickness direction for electrode material was expressed as [35].
Table 1 Parameters for Si composite electrode. Parameter
Description
Value
Comments
Ec hc l he0 Vmax β cmax c ‾c k
Elastic modulus of current collector Thickness of current collector Electrode length Initial thickness of electrode material Max volume of electrode material Equivalent expansion coefficient Theoretical specific capacity Specific capacity Normalized Li concentration Electrode curvature
80 GPa 28 um 23.8 mm 18 um 235% 0.33 3579 mAh g−1 ∼ ∼ ∼
Measured by tensile machine Measured by microscope Measured by microscope Measured by microscope Calculated Calculated by max expansion Ref. 25,34 Measured by Land system Calculated by c/cmax Measured by optical system
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he = he0(1 + 1.35‾c), where he0 is initial thickness of electrode material. The total parameters are summarized in Table 1. Back to the four equations, Eqs. (1)–(1) shows that the elastic modulus of the electrode material is related to its composition and structure, electrode deformation and Li concentration. This is used to quantitatively present the elastic modulus evolution as a function of Li concentration. Eqs. ((1), (1), (2), (2) and (3) and (1-4) show that three stresses have a direct relationship with the Li concentration, composition and structure of electrode material, as well as the geometry and mechanical properties of the bilayer, and couple with the deformation owing to the elastic modulus of the electrode material. The normal stresses in the electrode material and collector as well as the shear stress at the interface can be quantitatively obtained by substituting the variable elastic modulus calculated from Eqs. (1)–(1) into Eqs. (1-2) and (1-3) and (1-4). 3. Results and discussion 3.1. Electrochemical potential and deformation responses As shown in Figs. 1 and 2, the layered Si-composite electrode in this experiment consists of a current collector and an electrode material that is a composite of active Si nanoparticles, binders and conductive additives. During electrochemical lithiation, lithium ions are continuously inserted into the active Si particles to participate in the Li–Si alloying reaction, accompanied by a volume expansion in the particles that results in an expansion of the electrode material. This expansion, however, is restricted by the Cu collector, and the bi-layer mismatch strain induces the layered electrode bending deformation. Conversely, Li is gradually extracted from the active Si particles for the de-alloying reaction during electrochemical delithiation. The resulting reduced volume expansion gradually causes the bending deformation of the layered electrode to recover. Fig. 3 shows the potential (Fig. 3a) and curvature (Fig. 3b) evolution of the Si-composite electrode as a function of capacity (i.e., Li concentration) during the second lithiation/delithiation cycle at the C/5 rate. The solid/open symbols represent the lithiation/delithiation process, and are used consistently as such throughout this entire work. As the Li concentration increases during the lithiation process, the potential of the Si-composite electrode gradually decreases to 0.01 V vs. Li/Li+ and the deformation varies nonlinearly. At the initial insertion, the curvature rapidly increases in an approximately linear fashion with capacity to ∼21.2 m−1 at 287 mAh g−1, beyond which it continues to increase slowly to a maximum value of 33.6 m−1 at 964 mAh g−1 at the cut-off potential. The slowed deformation implies that the mechanical properties of the electrode material may change with Li concentration. As the Li concentration decreases during the delithiation process, the potential gradually increases to 2 V vs. Li/Li+ and the deformation gradually recovers. In addition, Fig. 3b clearly shows that the curvature during lithiation/ delithiation is not identical when at the same capacity, indicating that the mechanical behaviors depend not only on the Li concentration, but also on the lithiation or delithiation process. In addition, it is noted that the electrode material contains both active Si and non-Si components. Therefore, a new electrode comprising no active parts, but 50 wt% binder and 50 wt% conductive additive, was prepared using the same procedure in the Electrode Preparation to exclude the influences that non-Si components and other factors such as wetting may have on the bending deformation. This new electrode was subjected to the same current value and the same deformation acquisition process as those used with the Si-composite electrode. The results show that the maximum curvature of the new electrode is 2.35 m−1 at the cut-off potential, accounting for about 7% of the measured k (33.6 m-1) of the Si-composite electrode. Therefore, all of the other factors are excluded in these results by multiplying the measured k by 0.93 to obtain the curvature of the active Si component, which is called the modified k and is shown in Fig. 3b. And the
Fig. 3. Responses in (a) potential vs. Li/Li+, and (b) curvature of the Si-composite electrode as a function of capacity during the second galvanostatic lithiation (solid symbol) and delithiation (open symbol) cycle at C/5 between 2 and 0.01 V vs. Li/Li+. The modified k is the curvature of the active Si component that excludes all other factors with a values of 93% measured k in Sicomposite electrode.
calculations and analyses in the next are based on the modified curvature. 3.2. Responses of elastic modulus during lithiation and delithiation processes To quantify the elastic modulus during lithiation and delithiation, the deformation results in Fig. 3b are substituted into the modulus equations (1)–(1). With the parameters in Table 1, the elastic modulus evolution of the Si-composite electrode material as a function of capacity during the second lithiation and delithiation is obtained, and is shown in Fig. 4. It shows that the mechanical properties of the Sicomposite electrode material soften significantly with increasing Li concentration during lithiation process. The elastic modulus decreases from an initial value of 966 to 82 MPa at 964 mAh g−1 (at lower cut-off potential), which is a decrease of about 91.5%. This is mainly owing to breakage of Si–Si bonds and the formation of weak Li–Si bonds during the alloying reaction. And the mechanical properties gradually recover with decreasing Li concentration during delithiation process, showing that the elastic modulus increases to 232 MPa at 80 mAh g−1 (at higher cut-off potential). This is mainly owing to the gradual recovery of the Si–Si bonds during the de-alloying reaction. As described in Eqs. (1)–(1), the elastic modulus depends on Li concentration, composition and structure, and deformation. With the deformation affected by porosity, ratio of active material and inactive composition, etc., therefore, the measured elastic modulus is equivalent 103
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are different from those reported in literature [25–29], which are a little larger than Si-composite electrodes and 2 orders of magnitude smaller than Si-thin film electrodes. This is mainly because the measured modulus is equivalent modulus of the composite film with porosity, inactive components and different Si content. 2. As shown in Fig. 4, the modulus decreases with capacity in a nonlinear fashion, exhibiting an initial fast and then slow trend. For further analysis, the modulus is plotted against volume fraction of Li, x, in LixSi(1-x), as shown in Fig. 4 inset. Obviously, the modulus is not linear with Li volume fraction. This demonstrates that the normal treatment of the elastic modulus, that is, simple mixtures between the properties of Si and Li cannot be applied to elastic modulus of composite electrode during electrochemical processes, which may be owing to the effects of inactive components and porosity. Further, it is found by fitting that an exponential function may better describe the relationship between the elastic modulus of composite electrode and Li volume fraction, as shown in Fig. 4 inset. 3. The modulus in the delithiation process recovers along a different path with a smaller value from that in the lithiation process, consistent with previous research [29]. The unexpected trend indicates that the mechanical property depends not only on the macroscopically-measurable capacity but also on film morphology during lithiation/delithiation process. The cracks appeared in the delithiation process is a reason for smaller modulus. Furthermore, in the complex composition and structure of composite electrode, the changes of elastic modulus mainly comes from Li content inside Si particle, so the concentration gradient inside particle may also be a reason for the modulus difference between lithiation and delithiation processes. In summary, the above experimental data and analysis provide guidance and basis for the mechanical modeling of composite electrode. If mechanical properties of original material or simple mixtures
Fig. 4. Elastic modulus of the Si-composite electrode material as a function of capacity and as a function of Li volume fraction (inset) during the second lithiation and delithiation processes. The plots are obtained by substituting the deformation data in Fig. 3b and parameters in Table 1 into the modulus equations (1)–(1).
modulus of the whole Si composite film structure that contains factors such as porosity, inactive components, active component as well as the film morphology. Based on this, the results of elastic modulus are analyzed. 1. The experimental results show that the elastic modulus decreases/increases with increasing/decreasing capacity during lithiation/delithiation process, that is generally consistent with the previously reports for Si electrodes, especially for Si-composite electrodes [25–29]. This validates our experiment data. And the modulus values
Fig. 5. The total stress evolutions for the (a) normal stress at the surface of electrode material and (b) normal stress at the interface of current collector and (c) shear stress along the interface as a function of capacity during the second lithiation and delithiation processes. The plots are obtained by substituting the variable elastic modulus in Fig. 4 and parameters in Table 1 into Eqs. ((1), (1), (2), (2) and (3) and (1-4). 104
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material associated with Li concentration, which significantly relieves not only the normal stress in the electrode material [35], but also that in the current collector as well as the shear stress along the interface during the entire electrochemical lithiation and delithiation processes. Quantitatively, a 91.5% softening of electrode material causes the stresses to decrease by about 90%. Such significant softening-induced stress reliefs are particularly important for fracture failure and interface failure during the lithiation and delithiation cycles of the Si-composite electrode. Second, comparing conditions 10 and 11 that only affect the delithiation process, as shown in Fig. 6 insets, the delithiated stresses with the same elastic modulus between lithiation and delithiation recover along the same path from lithiation, therefore are greater than the delithiated stresses calculated from the modulus in Fig. 4. The stress evolutions are seriously affected by elastic modulus, indicating the importance of elastic modulus measurements. In summary, to understand the mechano-electro-chemical mechanism for development of high-capacity electrode materials, an accurate characterization of the total stresses in a composite electrode during electrochemical lithiation and delithiation cycling must be carried out, displaying a significant dependence on the variable elastic modulus. Therefore, the Stoney equation with Li-independent elastic modulus is seriously challenged for in-situ total stress measurements of thin film electrodes during electrochemical processes, especially for electrodes comprising Si, C and Sn, whose mechanical properties change significantly with Li concentration. Thus, herein, the proposed mechanical models for elastic modulus, and normal stresses and shear stress with Li-dependent elastic modulus overcome the difficulty and realize the total stress measurements during electrochemical processes.
between of active material and Li are used, or the property difference between lithiation and delithiation is ignored, this will bring great errors to mechanical modeling. So the mechanical properties for each composite electrodes require experimental measurements. 3.3. Stress characterization during lithiation and delithiation processes The experimental results show that the elastic modulus of the electrode material softens during electrochemical lithiation/delithiation process. So in the following, the stress responses of the bi-layer electrode during lithiation and delithiation processes are characterized, and the influences of elastic modulus on the stress responses are discussed. Substituting the variable elastic modulus during lithiation and delithiation processes (as shown in Fig. 4) and the parameters in Table 1 into stress equations ((1), (1), (2), (2) and (3) and (1-4) the normal stresses and shear stress of the bilayer electrode can be obtained as a function of capacity. Fig. 5 shows the normal stress at the surface of electrode material σe-surface (Fig. 5a) and the normal stress at the interface of current collector σc-interface (Fig. 5b) and the shear stress along the interface τ (Fig. 5c) during the second lithiation and delithiation processes. During the electrochemical process, the electrode material experiences a compressive stress in the surface owing to the restriction of the substrate on free expansion of the electrode material, while the collector experiences a tensile stress in the interface. All the three stresses evolve nonlinearly with capacity. During the lithiation process, the normal stresses in electrode material and in current collector and the shear stress along the interface increase to their maximum values of −7.4 MPa and 41.3 MPa and 7.4 KPa, respectively, exhibiting an initially rapid and subsequently slow trend. And the stresses during the delithiation process recover along a different path from that in the lithiation process with a relatively stable trend. More details, normal stresses of the electrode material and current collector (never been experimentally reported) are several megapascals and several tens of megapascals, respectively, which are important for fracture failure during electrochemical processes. Shear stress (never been experimentally reported) is only several kilopascals, which is three orders of magnitude smaller than normal stresses and the values are helpful for understanding the interface state between the layers. Totally, the stresscapacity hysteresis loops provide basis data for mechanical energy consumptions and degradation driving force etc., which are very important for investigating mechano-electro-chemical coupling mechanisms and determining role of mechanics in electrochemical processes. Furthermore, the stress evolution with capacity is similar to modulus evolution with capacity and the normal stress in electrode material is smaller than that measured by MOSS for Si-composite electrode with a constant elastic modulus [31]. This makes us want to know the relationship between stress and elastic modulus during electrochemical processes. Here, three different cases for elastic modulus of electrode material are included: (1) constant modulus in lithiation/delithiation with value of 966 MPa, denoted by 00; (2) Li-dependent modulus but no difference between lithiation and delithiation, denoted by 10; and (3) Li-dependent modulus with different values in lithiation and delithiation, i.e., measured in Fig. 4, denoted by 11. Substituting all these modulus values into stress equations ((1), (1), (2), (2) and (3) and (1-4), the normal stresses and shear stress of the bilayer electrode can be obtained as a function of capacity for the three conditions, as shown in Fig. 6. First, conditions 00 and 11 are compared. The stresses with a constant elastic modulus increase linearly to maximum of −72.8 MPa for σe-surface, 436.8 MPa for σc-interface and 78.3 KPa for τ respectively during lithiation, and recover along the same path during the delithiation process. The stress trends are quite different from that in the case of Lidependent elastic modulus. And all the three stresses are much greater than that in the case of Li-dependent elastic modulus during electrochemical processes. These differences are owing to the softening of the
4. Conclusions The coupling of electrochemistry and mechanics determines the degradation process of Si electrodes. In parallel with research efforts to promote the electrochemical performance of Si electrodes, intensive research should be carried out to study the mechanical behaviors as well as the mechanisms during the electrochemical processes. Herein, in situ experiments are carried out to report the elastic modulus and total stresses of a Si-composite electrode during electrochemical lithiation and delithiation cycling. An optical system is applied to in situ measure the deformation and four mechanical models are applied to analyze the relationship between elastic modulus, normal stress in electrode material, normal stress in current collector, shear stress along interface, curvature and capacity. It is found that the elastic modulus of Si electrode material nonlinearly decreases and increases in different paths with capacity during lithiation and delithiation processes, exhibiting smaller values during delithiation process. The dependence of elastic modulus on Li content is more likely to be an exponential rather than a linear function. More importantly, the normal tensile stresses for current collector and normal compressive stresses for electrode material and shear stress along the interface also nonlinearly increase with capacity and show stress-capacity hysteresis loops during lithiation and delithiation cycle, which are significantly affected by the hysteresis loop of elastic modulus. This experimental results demonstrate the applicability and superiority of the proposed mechanical models for electrochemical processes and provide an experimental basis for quantification of mechano-electrochemical degradation and development of high-performance batteries. Declarations of interest None. Acknowledgments This work was financially supported by the the Major Program of 105
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Fig. 6. Stress evolution as a function of capacity for normal stresses in (a) electrode material and (b) current collector and (c) shear stress along interface under three different treatments of elastic modulus of electrode material.
the National Natural Science Foundation of China (grant numbers 11890683), the National Natural Science Foundation of China (grant numbers 11672203 and 11872269).
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List of symbols
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SEM: scanning electron microscope CCD: charge-coupled device C: capacity cmax: theoretical capacity c¯ : normalized Li concentration Ee: elastic modulus of the electrode material Ec: elastic modulus of the collector he: thickness of the electrode material hc: thickness of the collector k: curvature of the electrode l: length of the electrode β: expansion coefficient σc: normal stress in the collector σe: normal stress in the electrode material τ: shear stress at the interface σe-surface: surface normal stress in the electrode material σc-interface: interface normal stress in current collector Vmax: maximum volume of the Si composite electrode x: volume fraction of Li in lithiated electrode material
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