Stress evolution in lithium metal electrodes

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Stress evolution in lithium metal electrodes Jung Hwi Cho a, **, Xingcheng Xiao b, Kai Guo a, ***, Yuanpeng Liu c, d, Huajian Gao a, Brian W. Sheldon a, * a

Brown University - School of Engineering, 182 Hope Street, Box D, Providence, RI, 02912, United States General Motors Global R&D Center, 30500 Mound Road, Warren, MI, 48090, United States c Center for Composite Materials, Harbin Institute of Technology, Harbin, 150001, China d National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150080, China b

1. Introduction Lithium metal anodes have higher theoretical capacity (3860 mAh/g) and lower reduction potential (
3.04 V vs. standard hydrogen) than other electrode materials. However, lithium metal has not been widely implemented in commercial rechargeable batteries because of poor electrochemical cycling. This is primarily due to difficulties that are associated with stabilizing the passivating surface films produced by electrolyte reduction (often referred to as the solid electrolyte interphase or SEI). The large volume changes that occur during Li plating and stripping subject the SEI films to coupled chemo-mechanical phenomena that produce complex interfacial morphologies such as mossy SEI and lithium dendrites [1,2]. These processes cause irreversible consumption of Li and electrolyte, leading to substantial capacity loss. Dendrite formation can also lead directly to battery failure by short-circuiting, and poses significant safety risks [1–4]. Uniform and smooth plating/stripping reduces capacity losses and dendrite formation, and widespread research efforts have focused on performance improvements via electrolyte additives, applying artificial SEI films, and improved configurational design of battery cell components [1,2,4,5]. In light of the volume changes that occur during lithium plating and stripping, the stresses that evolve in the electrode and the passivation films are critical [6]. There have been numerous studies of lithium metal deformation using tensile tests, nano-indentation, and acoustic methods [7–20]. These investigations provide important information about the mechanical properties of lithium metal, emphasizing its creep behavior [10,11,19] and visco-plasticity [10,12]. Recent work by LePage et al. shows that power-law creep models can accurately describe strain rate and temperature dependent deformation of lithium over a wide range of real-life battery conditions [17]. While the bulk yield stress of lithium is

quite low (<1 MPa), the onset of plastic flow at smaller length scales occurs at stresses that are ~30–200 times higher [7,9–11,14,17]. Nanoindentation study by Herbert et al. reported diffusion-mediated flow at low strain rates, with a transition to dislocation-mediated flow with increasing indentation depth and strain rate [19,20]. These higher yield stresses are also consistent with in situ compression testing on micro-pillars [14]. This existing information about the mechanical properties of lithium metal is very valuable, however, very little is currently known about the deformation that occurs during electrochemical cycling. Recently, Kushima et al. speculated that the compressive stress in lithium metal during plating is one of the main driving forces for dendrite growth [21]. Similarly, Wang et al. reported compressive residual stress during lithium plating, and also proposed that dendrites propagate as a stress-driven whisker-growth process [22]. Both describe morphological instabilities due to growth stress in the lithium metal, but neither provides a direct measurement of this stress nor do they consider the possible role of stress in the SEI. One notable study by Yoon et al. shows that reaction between lithium metal and a liquid electrolyte without an applied voltage produces an SEI-like interphase with significant compressive stress [23]. In the study reported here, in situ wafer curvature measurements were employed to monitor stress evolution during the plating and stripping of lithium metal films. This investigation shows that compressive stress is initially observed during the Li plating process. Measurements made under a variety of cycling conditions indicate that these stresses are primarily caused by processes that occur in the multiphase SEI that forms on the metal surface. Analytical modeling is also presented here to demonstrate that the observed compressive stress in the surface layer is expected to impact morphology evolution in ways that differ substantially from the effects of compressive stress in the lithium metal

* Corresponding author. ** Corresponding author. *** Corresponding author. E-mail addresses: [email protected] (J.H. Cho), [email protected] (X. Xiao), [email protected] (K. Guo), [email protected] (Y. Liu), huajian_gao@ brown.edu (H. Gao), [email protected] (B.W. Sheldon). https://doi.org/10.1016/j.ensm.2019.08.008 Received 20 April 2019; Received in revised form 26 July 2019; Accepted 8 August 2019 Available online xxxx 2405-8297/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: J.H. Cho et al., Stress evolution in lithium metal electrodes, Energy Storage Materials, https://doi.org/10.1016/ j.ensm.2019.08.008

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analysis is modified for the bilayer film structure. If the SEI is fully stabilized (i.e., unchanging), then the derivative of the curvature K with respect to the lithium thickness, hLi , can be used to obtain the steady-state growth stress in the Li metal, σ GLi . The following expression is obtained by rearranging Eq. (S6) in the Supplementary Information:

that have been proposed by other researchers [21,22]. 2. Materials and methods 2.1. Experimental procedures

  B2 dK Bq þ 4 BLi η þ 6 BLi η2 þ 4 BLi η3 þ Li η4 h2q dhLi Bq   ½hσ Li ihLi  B2 þ 6 þ 4 BLi þ 3 BLi η þ 3 BLi η2 þ Li η3 hq K hq Bq    12 Bq þ BLi η þ ½hσ S ihS  Bq hq 1 6ð1 þ ηÞ

Each specimen was prepared with an Au current collector film on a 250 μm thick quartz glass wafer (double-side polished, 100 diameter). A reflective/bonding layer of 15 nm Ti and 200 nm Ni was deposited first, followed by 50 nm of Au. These were deposited via electron-beam evaporation at rates of 0.7 A/s and 1A/s respectively. MOSS (Multi-beam Optical Stress Sensor) measurements were then conducted in custom-made electrochemical cells that permit optical access, using Li foil as the counter electrode [24]. This technique measures wafer curvature changes during electrochemical cycling, by monitoring the spacing between reflected laser beams. The electrolyte for this study was 0.4 M LiNO3 0.6 M LiTFSI in DOL:DME (1:1). Each experiment was started by plating a relatively thick Lithium film, using the galvanostatic sequences shown in Supplementary Information Section I. These films were then used for two types of experiments: Plating-only cycles: Repeated galvanostatic plating at i ¼
0.265 mA/cm2 for 10 h, followed by OCV (open circuit voltage) holds for 14 h. Asymmetric cycles: Galvanostatic plating at i ¼
0.265 mA/cm2 for 10 h followed by OCV holds for 14 h (first half cycle), then stripping at i ¼ 0.1325 mA/cm2 for 10 h followed by OCV holds for 14 h (second half cycle). The film surfaces were examined with scanning electron microscopy after disassembling the tested electrodes in an argon glovebox, and gently washing with dimethyl carbonate (DMC, Aldrich). This was used to verify that the plated Lithium was uniformly deposited on the Au current collector.

σ GLi ¼


The value of σ GLi (hLi Þ is the stress in the incremental amount of new film material that is added to the Li metal (i.e., at the position hLi ). If lithium film growth is conducted under conditions where the growth stress is constant for most of the plating process, then hσ Li i  σ GLi . In this case, Eq. (3) can be simplified to give:   1 B2 dK Bq þ 4 BLi η þ 6 BLi η2 þ 4 BLi η3 þ Li η4 h2q 6ð1 þ 2ηÞ dhLi Bq   B2 þ 4 BLi þ 3 BLi η þ 3 BLi η2 þ Li η3 hq K Bq    12 Bq þ BLi η ½hσ S ihS  þ Bq hq

σ GLi ffi


3.1. Stress during lithium plating To investigate the stresses that arise during Li plating, relatively thick films were first electrodeposited onto Au surfaces. Fig. 1(a) shows the top surface of a 31 μm thick Li film created in this way. These films were then equilibrated with a 24-h OCV (open circuit voltage) hold. This served as the initial state for the plating studies, where subsequent cycling was conducted using the sequence shown in Fig. 2(a). This consists of repeated galvanostatic plating at i ¼ 0.265 mA/cm2 for 10 h, followed by OCV holds for 14 h. The primary purpose of this methodology was to incrementally increase the thickness of plated lithium from cycle to cycle. In general, making measurements at different thicknesses makes it possible to separate stress contributions that occur in the bulk film material from those that occur near the surface [24]. Our interpretations and analyses of stress evolution behaviors during these plating experiments are based on the type of in situ curvature data reported in Fig. 2(a). The sharp initial compressive stress (i.e., decrease in K) that occurs at the beginning of each plating cycle is a key feature. This response is almost identical in each cycle, and thus independent of the thickness of the underlying Li film. In general, stress-generating mechanisms that affect the entire film will lead to curvature values that change proportionally with the plated lithium thickness (i.e., a thicker film with the same average stress will cause more bending). In contrast to this, a response that does not vary with the film thickness is indicative of surface processes [24]. Based on this the initial compressive stress transient in each of these cycles is attributed to phenomena occurring near the surface. With this in mind, quantitative analysis of the curvature measurements is based on the two-layer description in section 2.2, where the surface contribution is viewed as the stress-thickness product in the SEI, Δ½hσ S ihS . On pure lithium these surface layers are generally thicker and less chemically stable than the SEI’s that form on other negative electrodes (e.g., graphite and silicon) [5]. In all of these systems the SEI is largely composed of electrolyte decomposition products. Direct imaging of SEI films is generally very challenging, particularly with lithium metal. For this reason, there is very little information about the internal microstructure of these films, and thus the depiction in Fig. 1(d) provides only an approximate representation of several general features.

The measured curvature is attributed to contributions from both the plated Li and the SEI. To analyze the data, these are treated as two layers: Z 0

hLi

σ Li ðzÞ dz;

hσ S ihS ¼

Z

hLi þhS

σ S ðzÞ dz

(1)

hLi

where σ Li ðzÞ and σ S ðzÞ are the stress profiles across the Li and surface layers respectively, and hLi and hS are the corresponding film thicknesses. Note that σ Li ðzÞ and σ S ðzÞ are average in-plane stresses at position z (the distance normal to the current collector surface), and hσ Li i and hσ S i are then the overall average stresses in the films. Film curvature measurements are often interpreted with the Stoney equation, which is only applicable for films that are very thin relative to the substrate. This is not valid for the thicker Li metal in the current experiments, and thus a modified description of the curvature, K, is used here (refer to Supplementary Information Section II for derivation). K¼

   
6 Bq ð1 þ ηÞ½hσ Li ihLi  þ Bq ð1 þ 2ηÞ þ BLi η2 ½hσ S ihS  h i       h2q B2q þ 4 BLi Bq η þ 6 BLi Bq η2 þ 4 BLi Bq η3 þ B2Li η4

(4)

3. Results

2.2. Relationships between curvature and stress

hσ Li i hLi ¼

(3)

(2)

where η ¼ hLi = hq , hLi is the plated Lithium thickness, hq is the quartz substrate thickness, and BLi ¼ ELi =ð1
νLi Þ and Bq ¼ Eq =ð1
νq Þ are the biaxial modulus of Lithium and the quartz glass substrate. The SEI here is assumed to be relatively thin (hS ≪ hq ). During film growth processes it is also useful to consider the derivative of curvature with respect to time or film thickness [25–27]. Under conditions where the Stoney equation is valid, the derivative of stress-thickness with respect to thickness is equal to the incremental growth stress in the film. To apply this to our Li plating experiments, the 2

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Fig. 1. (a) Lithium film created via electrochemical deposition. Before cycling, ~31 μm of Li was plated onto the Au current collector. SEM image of the top-surface is shown. (b) Curvature versus time during initial Li film deposition. (c) Steady-state stress obtained with Eq. (4) during the latter part of the plating step in (b). (d) Schematic of SEI on Li during plating. The volume expansion of lithium inclusions inside the surface layer can induce stress in the SEI.

are well established, and with the idea that the incremental stress here is associated solely with steady-state growth of the Li underneath a fixed SEI film. This type of steady-state stress is commonly observed during film growth in other materials [24,26,28,29]. Growth stresses in other metal films are often larger [26,28,29]. However, in our experiments a low value is reasonable, given the low yield stress of lithium metal [7, 9–11,14,17]. This value of σ GLi is also more than two orders of magnitude smaller than the value reported in another recent study [22]. Possible reasons for this discrepancy are discussed further in Section 4. Fig. 1(b) also shows that tensile stress evolution occurs during the OCV hold after the initial plating step. There is no addition of Li during this hold, and thus we attribute the OCV behavior to the relaxation of compressive stress in the surface layer. This interpretation is further justified by the analysis of the subsequent cycles that is discussed in more detail below. Based on the assessments above, we attribute most of the measured tensile stress during initial plating to phenomena that occur during the growth of the lithium metal film. The curvature data in Fig. 2(a) were evaluated with Eq. (5), using the estimated Li thicknesses and setting hσ Li i to the σ GLi value obtained from the data in Fig. 1(b). These plots in Fig. 2(b) show values of Δ½hσ S ihS  that are attributed to the SEI surface layer, where the starting point for each cycle was set to zero to facilitate direct comparisons. There are several key observations that are evident here:

To interpret the curvature measurements in terms of the stress contribution from the SEI, Eq. (2) can be rearranged to give: ½hσ S ihS  ¼  


Kh2q Bq þ 4BLi η þ 6BLi η2 þ 4BLi η3 þ B2Li Bq η4
ð1 þ ηÞ½hσ Li ihLi      6 ð1 þ 2ηÞ þ BLi Bq η2 (5) These stress-thickness values are the “membrane force” (N/m) applied by the SEI film, which are analogous to the result which is obtained with the Stoney equation for simpler systems. The change in Δ ½hσ S ihS  can then be obtained from the measured curvature change (ΔK ¼ K
Ko ) if values for hLi and hσ Li i are available. The Li thicknesses are estimated from the total current integrated over time. This simple approach is commonly used, but it is subject to errors since it assumes that the plated Li is fully dense and it neglects Li losses due to SEI formation and other side reactions. Application of Eq. (5) also requires an assessment of hσ Li i. The curvature increase throughout the plating step in Fig. 1(b) indicates that a net tensile stress occurs. Evaluation of the stress-generating mechanisms during this initial growth process are beyond the scope of our current investigation. In particular, during the first hours it is difficult to disentangle the contributions from SEI formation and the changing grain structure in the Li. These variations are the primary reason for using the long initial plating cycle, with the expectation that this will stabilize the structures of both the Li metal at the top of the film and the SEI. Once this occurs, using Eq. (2) to obtain Δ½hσ S ihS  from the curvature changes in Fig. 2(a) requires an assessment of the concurrent changes in ½hσ Li ihLi . At a fixed current the steady-state growth stress in the Li film should be constant. This implies that Δ½hσ Li ihLi  ¼ σ GLi ΔhLi . This value of σ GLi can be obtained by applying Eq. (4) to the end of the initial Li plating process, where the current is the same as that used in Fig. 2 and where the Li and the SEI structures are stabilized. This quantity is plotted in Fig. 1(c), where the results over the last 1 h give a near constant value of σ GLi ¼ 0.22 MPa. This constant value of σ GLi during the latter portion of the initial plating cycle is consistent with our assertion that the film structures here

 The measured negative curvature changes indicate that a net compressive stress occurs during initial plating.  Most of the stress generated during plating relaxes during the OCV hold.  The stress response in each plating/hold cycle is very similar. During each plating step, the initial sharp increase in compressive stress occurs over approximately 1 h. After this initial transient the change in hσ S ihS is very small for the remaining 9 h. Initial stress transients followed by steady-state behavior are commonly observed during the deposition of many types of films [25,26,28–30]. In Fig. 2(b) the nearly flat response after the first hour indicates that 3

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Fig. 2. (a) Curvature and voltage vs. time for the 2nd-6th cycles of plating only half-cycles. The missing data in the 2nd cycle occurred when the optical measurements were accidently disrupted (the electrochemical measurements ran normally during this time). (b) Change in Δ½hσ S ihS  in the SEI versus time for respective cycles (via Eq. (5) in Section 2.2). The starting value of Δ½hσ S ihS  in each cycle was adjusted to zero for facile comparison. Colored points are stress-thickness values obtained from the MOSS data. The dotted lines show the voltage response during cycling. (c) Magnitude of stress-thickness changes during different cycles. These changes occur in opposite directions, and thus the maximum compressive changes at time tSAT are plotted as
Δ½hσ S ihS SAT so that these are positive values (blue dots). This facilitates direct comparisons with the tensile relaxations, Δ½hσ ih OCV (turquoise crosses). The Li thicknesses on the horizontal axis are upper bound estimates based on the assumption that all of the current was converted to plated Li (discussed further in the text), using tSAT values for the plating stresses and times at the end of plating for the relaxation stresses at OCV. The inset (3rd cycle plot from (b)) shows how the data was acquired. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

compressive stress in Fig. 2(b) is very similar in all cycles, as seen in Fig. 2(b) and (c). As noted at the beginning of this section, stressgenerating mechanisms that affect the entire film will lead to hσ ih values that change proportionally with the plated lithium thickness (i.e., a thicker film with the same average stress will cause more bending). In contrast to this, stress-thickness values that do not vary with the film thickness are indicative of surface processes [24]. In Fig. 2(c) the ½hσ S ihS SAT values decrease somewhat from cycles 3 to 6, and the cycle 2 value is also somewhat lower (the latter may include some continuing effects from the OCV tensile relaxation observed after the long initial plating cycle). Clearly these values do not exhibit the type of increase with thickness that is indicative of growth stress in the metal film. Two other observations that support the conclusion that the initial compressive stress during plating is primarily caused by surface effects are: (1) at the same current density, the observed growth stress is tensile in both Figs. 1(b) and 2(b), (2) at higher current densities the stress transient during initial plating becomes more compressive (see Supplementary Material section III). The latter is in contrast to other materials (including many electrodeposited metals), where growth stresses become more tensile at higher deposition rates. At the higher current densities, note that Fig. S5 also shows that the portion of the data that we attribute to growth stress becomes more tensile, which is consistent with widespread observations in other materials [26,30]. Based on the evidence described above, the experiments indicate that the initial compressive stress (i.e. the large transient contribution at the

the incremental stress here can be attributed to a steady-state growth stress, σGLi , in the Li metal. As outlined above, the results plotted here are based on the specific value of σGLi that was inserted into Eq. (5). This means that a growth stress equal to this value during Li plating will lead to an unchanging value of Δ½hσ S ihS  after the initial transient in Fig. 2(b). Within the accuracy of these data and the model, this is essentially what is observed here. Small deviations from zero slope after reaching ½hσ S ihS SAT can be interpreted in several ways. One possibility is that the σ GLi value in each plating cycle is not exactly equal to the value obtained from the analysis of the data in Fig. 1. The use of Eq. (5) is also subject to other uncertainties, such as errors in the Li thickness estimates and the assumption of plasticity in the Li. These possible effects were tested by varying the model accordingly (i.e., by assuming that the amount of plated Li corresponds to only 50% or 75% of the current and by Li deformation with and without plasticity). These alterations (not shown) lead to plots that are very similar to Fig. 2(b), with only small variations in the slope after reaching ½hσ S ihS SAT . Based on these sensitivity tests, we believe that the basic bilayer model used here provides a reasonable basis for calculating ½hσ S ihS SAT and for understanding the basic trends in the curvature data. It is important to emphasize that the large transient compressive stress that occurs during the first hour of plating in Fig. 2(b) is not consistent with growth stress in the lithium for several reasons. The primary basis for this interpretation is that the magnitude of the initial

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σ max  -275 MPa. The actual limiting stress is expected to be smaller, since only part of the total overpotential will act across the surface layer. With this mind, the value of σ max obtained from Eq. (6) is in reasonable agreement with the experimental range above. Thus the thermodynamic limit imposed by the local overpotential provides a plausible explanation for the observation that the stress reaches a limiting value. During the OCV holds the driving force that produces the stress in Eq. (6) is removed, and thus it is reasonable that the stress relaxes. Simply reversing the incorporation of electrochemically active Li within the SEI corresponds to explanation I above (i.e., there is a net flux of Li ions back into the electrolyte). This only requires dissolution of a small amount of the Li. The relationship between the volume loss (i.e., strain) in the Li and the stress relaxation requires an appropriate model of the composite SEI structure. However, to demonstrate that the experiments are consistent with small changes it is convenient to use a simple approximation that is based on SEI with a uniform modulus of 5 GPa (consistent with some reported SEI measurements and close to the value for Li). For this highly oversimplified case a stress relaxation of
50 MPa stress corresponds to a composite strain relaxation of
1%. Based on a simple rule of mixtures estimate, a
2% strain in the Li would then produce this
50 MPa change in a film composed of 50% Li [32]. This very rough estimate indicates that the measured stress relaxation can be realized via the dissolution of a relatively small fraction of the total Li in the SEI. Other stress relaxation mechanisms that involve redistributing lithium would then correspond to explanation II. Plasticity in both organic decomposition products and Li inclusions is possible. For the latter, the stress estimates of
30 to
300 MPa based on the experiments are well above the yield strength of bulk lithium, but comparable to values reported in recent studies of Li yielding at small length scales [14]. Thus, plastic flow of Li in the surface layer cannot be disregarded. Recent nanoindentation experiments suggest that this will be dominated by diffusional creep at the small length scales in the SEI [19]. However, this work also indicates that the corresponding diffusion times should be much shorter than those observed in Fig. 2. This suggests that the process occurring here is rate limited by another mechanism. In summary, the two general mechanisms based on Li metal inclusions that are described above provide possible explanations for the experimental results in Fig. 2. Stress generated in the surface layer could also be due to the formation of solid phases other than lithium metal [40]. However, for explanation I this requires electrolyte decomposition products in the SEI that form reversibly (i.e., such that they dissolve back into the electrolyte. With SEI components that do not form reversibly, other mechanisms associated with explanation II are required to explain the full stress relaxation observed during the OCV holds.

beginning of each cycle) is mostly due to processes occurring relatively close to the film surface. Our basic interpretation is that the behaviors observed in Fig. 2(a) are then caused by the following proposed phenomena:  The transient behavior measured during the first hour in each plating cycle is primarily associated with changes in the stress-thickness of this surface layer, Δhσ S ihS .  The onset of plating produces this initial response, and the nearly constant stress-thickness value that follows indicates that the surface layer reaches a limiting value, ½hσ S ihS SAT .  Once saturation is reached, additional plating in the steady-state regime only adds lithium to the film underneath the SEI. Additional small curvature changes here occur because of the growth stress in the Li metal.  The stress created in the SEI at the onset of each plating cycle fully relaxes during the OCV hold. 3.2. Stress saturation and relaxation Compressive hσ S ihS values during plating indicate that volume expansion occurs inside of the surface layer, presumably due to electrochemical reactions that create additional material. This is consistent with a recent study showing that direct reactions between Li metal and a liquid electrolyte can produce compressive stress (in the absence of an applied voltage) [23]. Several other observations in Fig. 2 must also be reconciled with this proposed mechanism: (1) the stress reaches a limiting value, ½hσ S ihS SAT (i.e. the stress does not continue to increase); (2) most of this stress disappears during the OCV hold; and (3) this stress reappears at the onset of the next plating cycle. Two general explanations that can explain this reversible stress relaxation are: I. Active lithium inclusions incorporated in the SEI during plating are dissolved at open circuit, and then reform when plating is resumed. II. Alternatively, when the driving force for plating is altered during the OCV hold, the stresses in the SEI could relax because of solid state processes. To more clearly demonstrate the logic behind these two scenarios, we first consider the case where σ S is largely produced by the growth of lithium metal inclusions in the SEI. Evidence for this behavior has been observed during SEI morphological evolution with ether-based electrolytes, where the surface layer on Li metal typically contains intricate conductive paths of lithium surrounded by the passivating layer [31,32]. This is shown schematically in Fig. 1(d). The thermodynamic limit on the hydrostatic stress in a constrained particle is given by:

σ max ¼

F Δφ VmLi S

3.3. Plating and stripping cycles

(6)

Asymmetric cycles with both plating and stripping steps were also investigated, using the sequence shown in Fig. 3(a). The current density during plating was the same, but only 50% of the plating current was used during stripping (0.1325 mA/cm2). This change in the current led to a net increase in the lithium layer thickness during each full cycle. Fig. 3 shows results from these experiments, where a sharp compressive stress is again observed at the start of each plating step. A primary reason for employing asymmetric plating-stripping cycles here was to again verify that the initial stress during plating is not proportional to the total lithium thickness (i.e., similar to the comparison in Fig. 2(c)). The same initial plating conditions were employed for the experiments in Figs. 2 and 3. The starting curvature values for the cycling experiments shown in Figs. 2(a) and 3(a) are somewhat different because of the initial stripping cycle, and also due to experiment-to-experiment variation. However, the measurements during the first plating cycle that follows the initial OCV hold show identical trends for both experiments (Supplementary Fig. S6). This indicates that the differences in the initial curvature do not significantly alter the main trends that are reported here.

where F is Faraday’s constant, VmLi is the molar volume of Li, and ΔφS is the local overpotential (i.e., between the electrolyte and the solid Li in the SEI). Note that Eq. (6) is based on the thermodynamic balance between the overpotential and the elastic strain energy in the metal, and thus it does not depend on the structure of the surface layer which forms. In general Li addition to an inclusion will cause a volume expansion, which will lead to stress when this is constrained by other SEI constituents. The growth of an inclusion will stop when the stress reaches σ max (i.e. at this point the stress counteracts the local overpotential). This behavior is consistent with the observation that the initial transient in our experiments reaches a limiting value, ½hσ S ihS SAT . To evaluate the measured stress here, a value of hS is needed. Limited information about SEI thicknesses on Li metal suggests that this is likely to be 0.1–1 μm [3,5,33–39]. This range and the measured value of ½hσ S ihS SAT ¼
30 MPa μm (average max stress from all cycles) then implies that hσ S iSAT falls in the range  -30 to
300 MPa. In these experiments ΔφS is not directly known, however, using the externally measured overpotential of
0.037 V as an upper bound in Eq. (6) gives 5

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Fig. 3. (a) Curvature and voltage vs. time for the 2nd-7th cycles of plating and stripping with asymmetric cycling. P and S indicate plating and stripping half cycles, respectively. (b) Change in Δ½hσ ih  in the SEI vs. time for respective plating half-cycles of the asymmetric cycles with both plating and stripping (via Eq. (5) in Section 2.2). The starting value of Δ½hσ S ihS  in each cycle was adjusted to zero for facile comparison. Colored points are the stress-thickness values measured via MOSS. Dotted lines indicate voltage response during cycling. (c) Magnitude of the stress-thickness changes during different cycles versus plated Li thickness. Blue dots and turquoise crosses indicate Δ½hσ S ihS SAT and Δ½hσ ih OCV values respectively. These changes occur in opposite directions, and thus the compressive changes during plating are plotted as
Δ½hσ S ihS SAT so that these are positive values. The Li thicknesses shown here are upper bound estimates based on the assumption that all of the current was converted to plated Li (discussed further in the text). The inset (2nd cycle plot from Fig. 3(b)) shows how the data was acquired. (For interpretation of the references to colour in this figure legend, the reader is referred to the online version of this article.)

assuming that only 50% or 75% of the current was converted to plated Li. These plots (not shown) exhibit the same key trends that are shown in Fig. 3. The idea that stripping will significantly alter the SEI structure has been widely discussed in the literature [1,4]. “Dead lithium” in the SEI is an important factor here, where Li near the surface layer can become disconnected from the underlying lithium layer during stripping, such that it becomes electrochemically inactive [1–4,41,42]. Using 0.5 M LiTFSI in DOL/DME, Fang et al. recently reported an SEI that consists of almost ~50% of isolated Li, largely surrounded by electronically insulating SEI after multiple plating/stripping cycles [32]. With the Li-based mechanism discussed in the previous section, “dead” lithium will presumably not contribute to stress generation because the local overpotential ΔφS Eq. (6) will not lead to additional Li incorporation in these electronically isolated regions. As dead lithium builds up during repeated plating-stripping cycles, the value of ½hσ S ihS SAT might be expected to decrease. This is potentially consistent with the decrease seen in Fig. 3(c). In Fig. 3(b) there is a transition between the initial compressive transient and subsequent steady-state plating that resembles the behavior in Fig. 2 (the similarity is more apparent in later cycles). One difference here is that the compressive stress continues to evolve after the initial compressive transient. In the later cycles where the slope of the hσ ih data is relatively constant (e.g., cycle 7), Eq. (4) gives a σ GLi  -0.2 MPa. This relatively small measured value should be due, at least in part, to steadystate growth stresses (i.e., the conventional interpretation of this slope, as noted in connection with Eq. (4)). In the earlier cycles where the

The results in Fig. 3(c) clearly show that the magnitude of the ½hσ S ihS SAT values during the initial transient are decreasing as the film thickness increases (in contrast to the plating only results in Fig. 2 where these differences are smaller). This again confirms that these initial stresses are not associated with the bulk Li film material (i.e., since ½hσ S ihS SAT would then increase with Li thickness). The decrease in ½hσ S ihS SAT values as cycling proceeds provides further support for the idea that plating-stripping cycles are likely to alter the surface layer structure, in contrast to the sequential plating results in Fig. 2 where the SEI stress level stays relatively constant in each cycle. The difference between the magnitudes of the ½hσ S ihS SAT and Δ½hσ ih OCV values in Fig. 3 are also somewhat larger than the corresponding differences in Fig. 2. This appears to be correlated with slower stress relaxation at OCV. The larger changes that occur at the end of the OCV hold may also affect subsequent stress evolution in the SEI during stripping. Further study of the processes occurring here are clearly needed. Note also that the voltage overpotentials during the plating step of the asymmetric cycles in Fig. 3 are slightly higher than those during the plating-only cycles. This suggests that there is higher impedance in the SEI, which is consistent with the idea that a different SEI structure is created when the stripping half-cycles were included. The thicknesses in Fig. 3(c) are based on the same method (integrated current) used in Fig. 2. Thus, they are again an upper bound. It is likely that more lithium is consumed by SEI formation when the stripping cycles are included [32], and thus our analysis was also conducted by 6

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stresses appear to be small. In contrast, the much larger compressive stress that we measure in the surface layer has very different implications for the propagation of morphological instabilities. To further evaluate this possibility, consider a bilayer structure with an SEI film on a thick Li metal layer, as illustrated in Fig. 4(a). Although the Young’s modulus for lithium (~4.9 GPa [46]) is comparable to that of the SEI layer [23], the yield strength of bulk Li metal is reported to be ~0.4–0.8 MPa [7,9–11, 14,17]. This is comparable to the small steady-state growth stresses measured during Li plating. The relatively low yield stress of Li means that the metal is soft in comparison with the surface layer. The compressive stress in the SEI can then lead to film wrinkling (Fig. 4(b)). During cyclic plating and stripping, plastic ratcheting in the metal can also produce accumulative increases in the wrinkling amplitude, and ultimately lead to interfacial delamination between the SEI and Li. An analytical model is developed here to evaluate the “wrinkling-toratcheting-to-delamination” sequence in Fig. 4. This analysis demonstrates that the measured stress in the surface layer can induce roughening due to deformation of the softer underlying lithium metal. We recently developed a similar wrinkling and ratcheting model where the film stress is induced by lateral deformation [47]. This is now modified slightly to describe our experiments, where the plated Li metal is bonded to a stiff substrate. Thus a boundary condition is set to confine the SEI and Li metal so that no lateral expansion or contraction is allowed. The following assumptions are also employed:

transition from the initial transient to the steady-state portion is not as sharp, there may be simultaneous contributions from both growth stress in the lithium film and the surface layer. This would mean the surface layer changes occur over longer times here, compared to the plating-only experiments in Fig. 2. This is consistent with the idea that stripping cycles (Fig. 3) lead to the formation of a different surface layer structure. In all cases the measured σ GLi values are relatively small compared to growth stresses in other electrodeposited metals [26,28,29]. It is possible that the growth stress is limited by the yield stress, σ y , since the reported values for bulk lithium metal are generally less than 1 MPa [7,9–11,14,17]. In all of our experiments the steady-state stresses during plating are significantly smaller than those during the initial transient, which confirms the conclusion that the surface layer is the dominant cause of the measured stresses. At first glance, a direct comparison between Figs. 2(b) and 3(b) suggests that σ GLi values obtained at the same current density are tensile in Fig. 2 and compressive in Fig. 3. In both cases these values are very small, and thus this difference may not be meaningful in light of the accuracy of Eq. (4), as noted in section 3.1. However, differences in the growth stress of the Li metal are possible. It is well established that several different mechanisms dictate intrinsic stress evolution during the deposition of polycrystalline films [26,28–30], and for a given material, the competition between these mechanisms can cause the net growth stress to shift from tensile to compressive [26]. Two factors that are expected to be important here are the low Li yield stress and the relatively large surface roughness of passivation films on Li metal. The observation that the measured σ GLi values for both experiments are comparable to the bulk yield stress suggests that the growth stresses may be limited by plasticity. The heterogeneity of the surface layer may also promote small differences between the relative contributions from mechanisms that lead to tensile and compressive stresses, leading to σ GLi variations in different experiments.

 The SEI layer is a purely elastic film of thickness hS .  The underlying Li metal film is elastic - perfectly plastic (i.e., the yield stress of the Li provides a simple one parameter description of plastic flow).  The SEI film is initially flat with a biaxial compressive stress, hσ S i, that is set to the experimentally measured value (i.e., Fig. 2(b)). The stress relaxation during the OCV hold has not been included, but its implications for the wrinkling and delamination criteria are discussed further below.  Stresses in the SEI and Li metal prior to wrinkling are biaxial. The Young’s modulus and Poisson’s ratio of the SEI film and Li metal are ES , νS and ELi , νLi , respectively, and σ y is the Li yield stress.

3.4. Film stress and lithium wrinkling The measurements reported in Figs. 2 and 3 indicate that electrochemical reactions inside of the SEI during plating induce net compression in the surface layer. The growth stress in the lithium film is significantly smaller, which appears to contradict a recent report of larger compressive growth stress during lithium plating [22]. These results are based on wrinkling that occurs during Li film growth on soft PDMS substrates. The authors propose that plating produces a compressive membrane strain of εm ffi
0:047% in the Li metal, and that this induces the observed wrinkling. In contrast to this our measurements indicate that the magnitude of the strains produced by the Li growth process are more than an order of magnitude lower (~0.0037% for σ GLi ¼ 0.2 MPa and BLi ¼ 4.9 GPa). Their experiments were conducted at a higher current density than the value in Fig. 2, but as noted above and in Fig. S5, the resulting higher growth rate is unlikely to increase compressive growth stresses (i.e., the opposite trend is expected). Based on these considerations and our measurements, the observed wrinkling does not appear to be caused by compressive growth stress in the Li metal film. However, the dominant compressive stress that we attribute to surface processes is instead a plausible cause of the type of wrinkles observed in reference [22]. The idea of large compressive growth stresses in the Li metal led Wang et al. to develop a model for stress-driven dendrite propagation. However, their analysis is not consistent with the revised interpretation that we propose here. While the plating only experiments in Fig. 2 show small tensile growth stress, other measurements also show that small compressive growth stress in the lithium can occur under some conditions (e.g., during the plating-stripping experiments in Fig. 3). It is well established that stresses in a thin film will create a driving force for surface roughening effects [43–45]. However, these effects are expected to be minimal in the Li metal based on our observations, where these

These assumptions provide a relatively simple basis for evaluating surface roughening due to the measured compressive stress in the SEI. The primary properties that are expected to dictate wrinkling and ratcheting phenomena are the elastic moduli of the two materials, the yield stress of the Li metal, and the thickness and compressive stress of the SEI. All of these are included in the initial model that is presented here, with the understanding that more complex behaviors such as

Fig. 4. Schematics of SEI states on Li metal: (a) initial state, (b) wrinkling, and (c) delamination. (d) SEI failure map based on analytical models of wrinkling and delamination. 7

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leads to a delamination criterion:

plasticity in the SEI are also possible. During plating lithium is added to the metal film that is underneath the stiffer SEI. Building a growth model of this process is beyond the scope of this paper. However, the existing static model can be used to predict wrinkling criteria for conditions where the Li plating process creates small uniform in-plane stress (tensile or compressive) in the metal film. The lithium undergoes elastic deformation until the yield stress, σ y , is reached. A small value of σ y for Li indicates that the metal yields easily and is then subject to extensive plastic deformation. This creep dominant behavior in bulk lithium is generally consistent with prior experiments [7–17,19,20]. Here, we take a Li film of thickness hLi at its yielding point as the initial state and assume it is much thicker than the SEI (i.e., hLi ≫ hS ). During cyclic plating and stripping, the thickness change is described as ΔhLi . The derivation of the modified analytical solution is similar to the previously published analysis [47], based on the revised assumptions above (see details in Supplementary Information Section V). This model predicts criteria for wrinkling and interfacial delamination between the SEI and Li metal. Based on this analysis, one dimensional wrinkling occurs if the magnitude of the compressive stress in the SEI hσ S i exceeds a critical value. For the limiting case where there is no excess Li inserted (i.e., ΔhLi ¼ 0), this gives the standard wrinkling model for an elastic thin film on an elastic substrate [48,49]: jhσ S ij  σ elas crit ≝

 1=3 1 2 9ELi E S 4

G¼



9 2 2 α ELi ES 16

where εS ¼ ð1
νS Þjhσ S ij=ES . Here we assume that all of the elastic energy [49] stored in the wrinkled SEI can be released. This is an upper bound which in some sense overestimates the risk of delamination. However, this captures the relationship between this failure mechanism and key physical quantities. The analytical model predicts the failure regimes in Fig. 4(d), as a function of the normalized modulus and the initial compressive stress in the SEI. The boundaries in Fig. 4(d) are based on an elastic limit of 0.01% elastic strain for the Li metal (i.e., σ y =ELi ¼ 0.01%), ΔhLi =hLi of   10% and a normalized interfacial toughness of Γ int ¼ Γ int = σ y hS ¼ 10. The oblique blue and red lines are then the critical conditions for wrinkling and delamination predicted by Eqs. (8) and (12), respectively. The assumption that the SEI is purely elastic is no longer valid towards the top left corner of the failure map, as it is unphysical that the compressive stress is comparable to the modulus. To address this issue, an elastic limit of 2% elastic strain for the SEI is shown by the black dotted line. Any point higher than this elastic upper bound will yield to this limiting value (i.e., this is taken as the threshold for plastic deformation in the SEI). To represent this the critical conditions for wrinkling and delamination are plotted as vertical blue and red lines, which connect to the critical lines that are predicted with the analytical model at points that are at the elastic limit (i.e., on the dotted black line). The boundaries for wrinkling and delamination conveniently divide the failure map into three regions, representing the final configurations of the SEI after multiple plating and stripping cycles (i.e., no wrinkling or delamination). For lower ΔhLi =hLi , there is less plastic deformation in the Li and the wrinkling boundary moves up (see Fig. S9), indicating that under these conditions wrinkling requires a stiffer SEI film with higher compressive stresses. The failure map in Fig. 4(d) qualitatively illustrates a design space for stable SEI when there are relatively small stresses in the Li metal. Modulus values of 1–5 GPa that are consistent with several recent experimental reports [23,50] imply that the ES =σ y ratio is on the order of 104 or higher, and the estimated SEI stress based on our experiments (see section 3.2) indicates that jhσ S ij =σ y > 102. Based on these values Fig. 4(d) indicates that surface wrinkling can potentially occur. As noted above, the simplified model developed here is only presented to demonstrate the general possibility of wrinkling. More complex behavior is likely to occur in the actual materials. In particular, recent studies by Herbert et al. indicate that σ y increases significantly at small lengths and high strain rates [19]. The time scales in our experiments are much longer than these and applying the results obtained from shallow nanoindentation experiments to the plating configuration requires detailed analysis that is beyond the scope of our current simple model. Ultimately, plasticity variations over a range of time and length scales will potentially lead to a variety of effects that require more detailed consideration. Also, the mechanical properties of the SEI will vary significantly depending on the electrolyte and cycling condition. In general, the magnitude of the compressive stress in the SEI is likely to be correlated with its modulus (i.e., the stress level will be lower with decreasing modulus). With this in mind, reducing the SEI modulus is a potential strategy to avoid delamination. The analytical model also suggests that delamination due to ratcheting can be suppressed with higher Γ int (i.e., lower SEI thickness and/or higher interfacial toughness between the Li metal and SEI). These effects will move the position of the delamination boundary (see Fig. S10). The experiments also show different stress variations inside of the SEI during

(7)

1=3 (8)

where: 1
ν2 σy s s  Li ; ELi ¼ s σ y ELi þ ΔhLi =ð3hLi Þ ð2
νLi ÞELi ELi þ νLi ð1
2νLi ÞELi ELi

α¼

(9) approximate To demonstrate the relationship between σ and σ values for the other quantities here were taken as ELi ¼ 4.9 GPa [46], νLi ¼ νS ¼ 0.3, ES ¼ 5 GPa, σ y ¼ 0.5 MPa [9,10], and hσ S i ¼
100 MPa. elas crit

plas crit ,

elas When ΔhLi ¼ 0, σ plas crit reduces to σ crit  2:7 GPa, which is comparable to the SEI modulus and thus far beyond the stress expected in the SEI.

However, Eq. (9) indicates that σ plas crit decreases with increasing ΔhLi since plastic flow lowers the effective stiffness of the Li metal near the SEI/Li interface (see Fig. S8). Once σ plas crit is less than jhσ S ij, wrinkling occurs. The wavenumber of the wrinkled SEI is expressed as: k¼

2 hS

sffiffiffiffiffiffiffiffiffiffiffi jhσ S ij ES

(10)

If wrinkling occurs, the plastic deformation in the Li metal near the SEI film accumulates during each subsequent cycle. This phenomenon, often referred to as “ratcheting”, incrementally increases the amplitude of the wrinkled SEI with cycle number. However, the ratcheting rate gradually decreases with increasing cycle number, such that after a sufficiently large number of cycles, the wrinkling amplitude approaches a steady state value which is found to be: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3ELi Ae ¼ hS j1
αj 4jhσ S ij

# "  2 1 2 2 1 k Ae
hεS i þ hεS i2
ES hS νS k 2 A2e 4 4

(12)

where E Li ¼ ELi =ð1
ν2Li Þ and ES ¼ ES =ð1
ν2S Þ are the plane strain modulus of the Li metal and SEI film, respectively. During plating, lithium insertion into the underlying metal leads to the following modified wrinkling criterion: jhσ S ij  σ plas crit ≝

1 ES hS ES h3S k 4 A2e þ 48 2 
hεS i hεS i  Γ int

(11)

Interfacial delamination between the SEI and Li metal occurs when the energy release rate G exceeds the interface toughness Γ int , which then 8

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mechanisms. A variety of processes that can create and relax stresses are potentially relevant, and evaluating these effects requires more detailed study.

plating and stripping cycles (i.e., Fig. 3), however we have not yet included this effect in the analytical model, largely due to the absence of a quantitative understanding of the mechanisms that lead to the stress changes during plating, stripping, and OCV holds. Nevertheless, the repeated compression and relaxation in the SEI film is similar to the loading condition adopted in our previous work [24]. Thus, from a qualitative point of view, we speculate that accounting for reaction-induced stress variations will not alter the wrinkling boundary in the failure map but will instead facilitate plastic ratcheting and move the delamination boundary to lower threshold values. Ultimately, quantitative prediction of whether wrinkling or delamination will occur requires more accurate property values from experiments or atomistic simulations.

5. Conclusions In summary, the work presented here provides the first observation of stress evolution in surface layers on Li metal anodes. The in-situ curvature experiments and analysis lead to the following key findings: (1) During plating, there is a sharp increase and saturation in compressive stress in the surface layer. This initial transient stress ½hσ S ihS SAT is the largest contribution to the stress evolution during plating. (2) After the stress saturates in the surface layer, much smaller growth stress in lithium metal persists until the end of plating. (3) When plating is stopped (i.e., under open circuit), the surface layer stresses relax over a period of several hours. (4) Analytical modeling shows that the compressive stress in the surface layer can lead to surface wrinkling and strain in the underlying soft Li metal. Subsequent cycling may eventually lead to ratcheting and delamination of the surface layer. (5) The model also indicates that long-term cyclability of lithium metal electrodes can be enhanced by decreasing SEI thickness and modulus, and by increasing interfacial toughness between Li metal and the SEI.

4. Discussion The in situ measurements reported here indicate that compressive stresses that evolve during Li plating are primarily caused by electrochemical reactions that occur inside of the surface layer, while stresses in the underlying bulk Li metal are considerably smaller. Compared to the relatively large growth stresses estimated by Wang et al. [22], the growth stresses that we measure during steady-state plating are roughly consistent with the reported Li yield stress (<1 MPa) [7,9–11,14,17]. It is well established that surface stresses in a thin film will create a driving force for surface roughening effects [43–45]. Wang et al. present this type of analysis and also propose that larger stresses in the Li metal can promote dendrite formation. However, the much smaller stresses in the Li observed in our experiments do not support the idea that overall stress in the plated lithium directly promotes dendrite formation. Instead, the much larger compressive stress that we measure in the surface layer has very different implications for the propagation of morphological instabilities. This is illustrated with the initial “wrinkling-to-ratcheting-to-delamination” model presented above. Here, the map in Fig. 4 indicates that compressive stress in the SEI can lead to surface instabilities that differ from those predicted by Wang et al. [22]. Our analysis does not evaluate dendrite formation. However, a likely possibility is that fracture and delamination that is caused by stress in the SEI can lead to dendrite initiation via localized deposition of new Li. Our analyses also suggest that stiffer, thicker SEI films are more susceptible to wrinkling and subsequent failure mechanisms, and that stronger bonding between the surface layer and the underlying Li should logically reduce delamination. An important experimental finding in Wang et al. is that dendrite formation is suppressed when Li plating is conducted on the soft PDMS substrates. They propose that this occurs because the wrinkling reduces compressive stress in the Li film. However, our results indicate that an alternative explanation for their observations is needed. In their experiments the film wrinkling should also relax the compressive stress that we observe in the surface layer. This is consistent with the predictions of the model presented in the previous section. For example, reducing the stress in the surface layer (i.e., hσ S i) will move the system to a lower value on the vertical axis in Fig. 4, and thus potentially prevent wrinkling of the SEI layer. It is important to note here that our analysis is based on wrinkling of the SEI/Li bilayer, rather than the wrinkling of the Li/PDMS bilayer reported in Wang et al. [22]. Both phenomena are based on the idea that strain energy will be reduced by wrinkling of a stiff film on a soft substrate, but our interpretation is based on a surface layer with substantially different dimensions and properties. The mechanisms outlined in the previous section are facilitated by the stress and plasticity in the Li metal. However, based on our experiments and analysis the stresses in the Li metal are too small to enable wrinkling of just this layer. In addition to demonstrating that significant stress creation and relaxation mechanisms operate during Li plating and stripping cycles, the experiments presented here provide some initial insight into relevant

Data availability The raw data required to reproduce these findings are available upon request at [email protected]. The processed data required to reproduce these findings are available for request at jung_hwi_cho@ brown.edu. Author contributions J.C., X.X., and B.S. designed the experiments. J.C., K.G., Y.L, and H.G. carried out the experiments and analysis. J.C., K.G., and B.S. wrote the paper. Acknowledgements This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Vehicle Technologies Office of the U.S. Department of Energy, Award Number DE-EE0007787, under the Battery Material Research (BMR) Program. The authors also thank Profs. Neil Dasgupta (Michigan) and Hanqing Jiang (Arizona State) for valuable discussions of their work. Appendix A. Supplementary data Supplementary data to this article can be found online at https://do i.org/10.1016/j.ensm.2019.08.008. References [1] D. Lin, Y. Liu, Y. Cui, Reviving the lithium metal anode for high-energy batteries, Nat. Nanotechnol. 12 (2017) 194, https://doi.org/10.1038/nnano.2017.16. [2] W. Xu, et al., Lithium metal anodes for rechargeable batteries, Energy Environ. Sci. 7 (2) (2014) 513–537, https://doi.org/10.1039/C3EE40795K. [3] D. Aurbach, et al., A short review of failure mechanisms of lithium metal and lithiated graphite anodes in liquid electrolyte solutions, Solid State Ion. 148 (3) (2002) 405–416. https://doi.org/10.1016/S0167-2738(02)00080-2. [4] S. Li, et al., Developing high-performance lithium metal anode in liquid electrolytes: challenges and progress, Adv. Mater. 30 (17) (2018) 1706375, https://doi.org/ 10.1002/adma.201706375.

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