Temperature Dependence of Dendritic Lithium Electrodeposition: A Mechanistic Study of the Role of Transport Limitations within the SEI

The accelerated failure of rechargeable Li-metal batteries due to dendritic Li electrodeposition particularly during charging at low temperatures is not well-understood. In this work, we investigate the effect of temperature on the initiation of Li dendrites during galvanostatic lithium electrodeposition. Using electrochemical measurements coupled with optical microscopy, we show that the dendrite onset time increases monotonically with temperature in the range 5 °C – 35 °C. This observation is explained by incorporating temperature effects into an analytical transport model for Li dendrite initiation [ J. Electrochem. Soc. , 165, D696 (2018)], which considers solid state Li + diffusion through a gradually thickening solid electrolyte interphase (SEI) layer. We conclude that sluggish Li + transport at lower temperatures accelerates the depletion of Li + at the Li-SEI interface, and this effect causes earlier initiation of dendrites at lower temperatures. Electrochemical impedance spectroscopy measurements of the temperature-dependent transport properties of the SEI, as well as plating ef ﬁ ciency measurements, are used to support the model. on of The Limited. an

Meeting the demand for high-energy density "beyond Li-ion" batteries remains a challenge due to the rapid capacity fade and safety concerns of secondary Li-metal anodes. [1][2][3][4] The key bottleneck in adopting rechargeable Li-metal anodes is the uneven or dendritic morphology evolution during battery charging. [5][6][7] A comprehensive understanding of the dendrite initiation process is still lacking. [8][9][10][11][12] Whereas a number of studies have attributed the initiation of dendrites to non-uniformities in the solid electrolyte interphase (SEI), [13][14][15][16][17][18][19][20] our recent work suggests the critical role of Li + transport through a uniform but gradually thickening SEI. 21 Specifically, we have shown 21 that a model incorporating Li + transport limitations in the SEI explains the influence of important factors on the dendrite initiation time. These factors include the Li plating current density, SEI thickness, and the application of pulsed currents.
Low temperature charging shortens the cycle life of Li-ion and Li-metal batteries. [22][23][24] Li-ion batteries experience detrimental Li plating when charged at low temperatures. 25 The similarity of these two systems (i.e., the presence of an SEI) and their issues with respect to sub-ambient temperature charging suggests an analogous transport limitation is at work.
The transport of Li + through the SEI is critical in determining the kinetics and stability of Li-metal in electrochemical systems. 9,26,27 Effects of temperature on Li battery performance and surface film growth were reported by Dey in the 1970 s. 28 Churikov studied the role of temperature on charge-transfer kinetics at a Li electrode limited by transport processes within the SEI using pulse voltammetry, 29,30 as well as photoemission spectroscopy. 31 Heins et al. reported the energetics of SEI formation on intercalation electrodes during charging by using temperature-dependent electrochemical impedance spectroscopy (EIS). 32 Despite intensive research activity characterizing and modeling the SEI, 33-36 the precise mechanism of Li + transport within the SEI is presently not well-understood. 37 Hess recently extended studies of the nonlinearity in the SEI overpotential 38 to a wide temperature range for several alkali metal anodes, and found that conduction mechanisms through SEI exhibit distinct temperature dependencies. 39 Shi et al. performed experimental and DFT simulation studies to investigate the hopping of Li + within the SEI, enabling the prediction of Li + diffusion coefficients and the Li + concentration evolution. 40 Benitez and Seminario carried out molecular dynamics simulations of Li + diffusional transport in the SEI in the temperature range 250-400 K. 41 In relation to mechanisms of Li surface morphology evolution and dendrite formation, Mogi et al. studied the effect of temperature on SEI and Li deposition morphology using AFM. 42 While they found that the SEI became uniform and Li dendrites were suppressed at elevated temperatures, the uniform surface film formed at high temperatures did not prevent dendrite growth when plating was carried out at room temperature. Ota et al. also studied the correlation between Li surface film formation and plating morphology at various temperatures. 43 Using diffusion-reaction modeling, 44 Akolkar predicted a critical temperature below which uncontrolled Li dendrite propagation occurs. 45 This prediction was a consequence of increased mass transport resistance at low temperature and decreased reaction resistance provided by a thinner SEI. Love et al. performed experimental studies of dendrite initiation times at ambient and sub-ambient temperatures and observed an increase in the propensity for Li dendrites at low temperatures, 22 which was in qualitative agreement with the Akolkar model. 45 Hao et al. proposed that Li dendrites are initiated by two possible mechanisms: (i) Li + depletion at the Li-SEI interface, and (ii) nonuniformity of the SEI, causing non-uniform local deposition rates. 46 Recently, Mistry et al. presented a model of electrolyte confinement 47 to explain Li dendrite initiation beyond the Sand criteria. 48 Sano et al. reported the effects of temperature on Li electrodeposition in an ionic liquid electrolyte. 12 To explain the effect of temperature on the dendrite initiation time, a mechanistic model that incorporates Li + diffusion through a dynamic SEI layer is needed. Herein, we provide electrochemical measurements of the dendrite onset time onset t as a function of temperature. Chronopotentiometry and optical imaging are used to quantify the time at which Li dendrites initiate. This initiation occurs at a temporal maximum in the surface overpotential-a unique electrochemical signature that corresponds with and thus helps easily identify the first morphological appearance of Li dendrites. 21 Electrochemical impedance spectroscopy (EIS) is used to measure the growth of the SEI before and during Li electrodeposition over a range of temperatures. The continuous growth of the SEI leading to the depletion of Li + at the Li-SEI interface during electrodeposition, and the eventual onset of Li dendritic growth is considered. The diffusional transport of Li + through the SEI is shown to be the z E-mail: rna3@case.edu *Electrochemical Society Student Member. **Electrochemical Society Member. critical temperature-dependent process that explains the early initiation of Li dendrites at sub-ambient temperatures.

Experimental
Cell materials and construction.-Li ribbon (99.9%, Sigma-Aldrich) with 0.38 mm thickness was used to prepare the working (WE), counter (CE), and reference (RE) electrodes. The electrode surfaces were polished with 400 grit sanding sheets. Discs were cut from the Li ribbon using a 0.5″ diameter punch. Chemical-resistant compression tee fittings for 0.5″ OD plastic tubing were used to construct the electrochemical cells (McMaster Carr). Stainless steel rod 0.5″ in diameter was inserted into the compression fittings, sealing the Li WE and CE in place (Fig. 1). The projected area of the exposed Li WE and CE was 0.672 cm 2 . A length of 18-gauge copper wire, which was used to contact the RE, was guided through the PTFE stopper inserted into the top of the tee fitting. The tip of the wedge-shaped Li RE exposed to electrolyte was cleaved prior to each experiment. Battery grade 1.0 M LiPF 6 solution in 1:1 (v/v) EC/DMC electrolyte (MilliporeSigma) was dispensed into the cell by pipet. The total electrolyte volume in the cell was ∼3 ml.

Methods
Cells were prepared within an Ar-purged glovebox (MBraun). Moisture inside the glovebox was maintained below 5 ppm. A water circulating bath located outside the glovebox pumped chilled or heated water through tubing into a jacketed beaker, controlling the temperature of the electrolyte within the glovebox prior to cell fabrication. After fabrication, the cells were removed from the glove box for electrochemical characterization. During characterization, the temperature of the sealed cells was maintained by immersion in sand at controlled temperatures. The sand was either heated using a hot plate or cooled using refrigeration.
Chronopotentiometry and electrochemical impedance spectroscopy (EIS) experiments were performed using a VersaSTAT 4 potentiostat/galvanostat with built-in frequency response analyzer (Ametek). Chronopotentiometry was performed at an applied current density (i). Here, i refers to the applied current normalized to the exposed geometric surface area of the WE. For simplicity and consistency, we used the sign convention that cathodic (plating) current densities and overpotentials are positive quantities. The EIS experiments and analysis were performed using the methods described in our previous publication. 21 In brief, galvanostatic EIS was performed with a direct current of 0 A and the RMS amplitude was 45 μA cm −2 . The frequency range used was 100 kHz to 1 Hz. The ohmic resistance R , e determined at the high frequency limit, was used to subtract the iR drop in the liquid electrolyte. The surface resistance R s was determined from the diameter of a circle fit to the Nyquist impedance plot.
The faradaic efficiency of plating was measured via anodic stripping coulometry. A 0.127 mm thick Cu foil (99.9%, Alfa Aesar) was used as substrate for galvanostatic Li plating and subsequent anodic stripping coulometry. Prior to Li plating, the Cu foil was cleaned in 2 M H 2 SO 4 for 10 min, then rinsed with acetone and deionized water (Millipore). Li plating onto and stripping from the Cu foil were performed in the cell described above. The Cu substrate was used in place of the polished Li foil WE for plating efficiency studies. The electrolyte, RE, and CE were otherwise used in the same manner as above.

Results and discussion
In this section, we first describe experimental investigations of the temperature effects on Li dendrite initiation using chronopotentiometry, EIS, and plating efficiency studies. Next, we present a mechanistic model to explain the temperature effects invoking Li + transport through the SEI. ) coincided with temporal maximum in surface overpotential, V iR s e h = - (Fig. 2). In the present work too, similar behavior was observed at a variety of temperatures: s h increased during an initial SEI growth phase, reached a local maximum at t , onset t = and then decreased during the period of dendrite growth. A moderate increase in the temperature of the cell was found to increase . onset t For instance, at 8°C the measured onset t was 30 s, while at 34°C onset t was 240 s. Thus, increasing the temperature of Li deposition by 26°C resulted in an eight-fold increase in the plating time at which the first dendrite appeared. The increase in temperature also lowered the initial t 0 ( ) = surface overpotential, and broadened the peak in the surface overpotential (at t onset t = ). Interestingly, the difference in s h between t onset t = and t 0 = was roughly constant (∼290 mV) and independent of temperature.
The dependence of onset t on temperature at i = 1 mA cm −2 is shown over the range from 5 to 35°C (Fig. 3). A monotonic increase in dendrite onset time was observed over the range of temperatures studied. This temperature dependence within the range studied does not suggest the presence of a distinct critical temperature below which dendrites are initiated. On the contrary, while Li dendrites were found to initiate at all temperatures, lower temperatures favored an earlier onset (shorter onset t ) of Li dendrites. This effect of temperature on dendrite initiation will be discussed within the context of Li + transport through the SEI layer in the following sections. Electrochemical impedance spectroscopy.-EIS was used to characterize the SEI growth on the Li WE both during the soaking step and during Li electrodeposition. A fixed period (t soak = 30 min) of exposing the Li WE to liquid electrolyte before plating was used to establish an initial SEI before Li electrodeposition. Under open circuit conditions, the surface resistance R s of the WE in contact with liquid electrolyte increased due to SEI growth. 49,50 Nyquist plots for soaking at 22°C are shown in Fig. 4a for various values of t . soak In the absence of an externally applied field, as is the case during soaking, the magnitude of R s and thus the SEI thickness 26,51 is expected to increase roughly in proportion to t . ( ) This parabolic growth is typical for surface films growing under mass transport limitations of the reacting (e.g., Li + ) species. 52 Mathematically, R s depends on t soak as: In Eq. 1, A and B are constants. The data in Fig. 4b when fitted to Eq. 1 provided values of the parameter α, which was 0.5 at 22°C and 31°C, but 0.2 at 12°C. The mechanistic origin of the temperature-dependence of α particularly at low temperatures is presently unknown. Nyquist plots immediately prior to plating t 30 min, are shown for 12, 22, and 31°C in Fig. 5. The electrolyte resistance R e was found to be a weak function of temperature, while the surface resistance R s was observed to be strongly dependent on temperature. The weak temperature-dependence of R , e a liquidphase property that remains constant during plating, further strengthens the conclusion that liquid-phase transport limitations are not critical in Li dendrite initiation, as was shown in our previous work. 21 The solid-state property R s depends on the SEI conductivity k and the SEI thickness L as: The quantitative temperature-dependence of k in the temperature range of interest is not known to us. While the theoretical temperature-dependence was given by Peled, 26 we do not have access to the parameters needed to calculate .
k Thus, at the present time, quantitative determination of L at a variety of temperatures is not feasible. We estimate L after t soak to be between 5-8 nm based on k = 10 -9 S cm −1 for Li 2 CO 3 at room temperature. 51 In order to confirm that k is indeed the relevant temperaturedependent property, EIS measurements were performed on a Li WE immersed in liquid electrolyte while the cell temperature was varied. In this experiment, the Li WE in the cell was allowed to soak for 22 h until R s reached an approximately constant value at 35 ± 3°C. The temperature of the cell was then decreased to 15°C until equilibrium was reached, and EIS was performed again (Fig. 6). The figure shows that the value of R s dropped measurably when the temperature was increased from 15°C to 35°C; however, returning the temperature to 15°C produced nearly the same value of R s as was measured at 15°C before the temperature increase. That is, R s was roughly the same before (1) and after (3) the temperature increase (2) shown in Fig. 6. Such reversibility implies that the SEI thickness L remained relatively constant during the temperature changes, and that R s changed due to temperature-effects on .
k A rough estimate of the energy barrier for the conduction of Li + ions was obtained from the slope of the ln ( R 1 s / ) vs T -1 curve. The energy barrier was calculated to be 0.4 eV, which is comparable to the energetics of an ion hopping transport mechanism reported by Churikov, 29 albeit for a different electrolyte composition. This suggests that transport of Li + ions through the SEI is a temperaturedependent process, and thus it is a factor that must be accounted for in understanding temperature effects on Li dendrite initiation.
In Fig. 7, the surface resistance R s is plotted as a function of plating time (t plate ) during galvanostatic Li electrodeposition at an applied current density i 1 = mA cm −2 . Three temperatures (12, 22, and 31°C) were evaluated. During the initial phase of Li plating, i.e., prior to reaching , onset t a fraction of the applied current is consumed by the formation of additional SEI while the rest of the current results in Li plating. A more quantitative study of these competing processes is conducted in the next section. In Fig. 7, the slope of the R s vs t plate curve must be proportional to the SEI growth rate and inversely proportional to k in accordance with Eq. 2. This slope is observed to decrease with increasing temperature. Indeed, the general shape of the R s vs t plate curve (Fig. 7) is similar to that of the surface overpotential ( s h ) time trend seen during galvanostatic Li electrodeposition (Fig. 2). This is expected because s h predominantly represents the Li + transport resistance through the SEI. 26,27 While the general form of the time evolution of R s and s h are similar, it must be noted that the SEI is not strictly an ohmic resistor. 39 This is  evident from comparing the surface resistance R s (= 594 W cm 2 ) at t plate = 15 s and at 22°C to the surface overpotential s h (= 245 mV) under similar conditions. The surface overpotential (measured at 1 mA cm −2 ) corresponds to an area normalized surface resistance ( i s / h = ) of 245 W cm 2 , which is significantly lower than that provided by EIS.
It should be noted that while the change in R s due to temperature was explained by changes in , k the change in R s during plating is not due to a transient change in .
k This was shown previously by current interrupt experiments. 21 The rise in R s and s h during plating is explained neither by concentration effects nor by conductivity effects. These changes due to SEI growth are irreversible and stable until dendrites pierce the SEI.
Lithium plating efficiency.-Coulometric measurements during Li plating and its subsequent anodic stripping were used to study the effect of temperature on the Li plating efficiency. Li was plated on a Cu substrate in a two-step process. First, an average current density of 2 mA cm −2 was applied for 5 s to facilitate high nucleation density Li plating on Cu leading to uniform substrate coverage by Li.
Next, a current density of 1 mA cm −2 was applied for 120 s. The Li deposited on the Cu substrate was immediately stripped by applying an anodic potential of +0.5 V vs Li/Li + RE (Fig. 8a). The charge corresponding to Li stripping (Q strip ) was compared to the total charge passed during plating (Q plate ), thus yielding the plating efficiency : e The experiments were repeated 3 times each at 20 ± 1.0°C and at 30.5 ± 1.0°C. As shown in Fig. 8b, the Li plating efficiency was not found to be a strong function of temperature. The average ε at 20°C was 44%, while at 30.5°C ε was 48%. The fraction of the charge that contributed to SEI growth during plating was (1 − ε) and was related to the SEI growth rate as follows: s The size of the Nyquist plot semicircle increased during t soak due to SEI growth. (b) Surface resistance R s plotted as a function of t soak at temperatures 12, 22, and 31°C. The period t soak = 30 min when the Li WE was exposed to liquid electrolyte before plating was used to establish an initial SEI after removing the native oxide layer. Figure 5. Nyquist plots after t soak = 30 min immediately prior to Li plating at temperatures 12, 22, and 31°C. The electrolyte resistance R e was weakly temperature-dependent, whereas the Li surface resistance R s was a strong function of temperature. Figure 6. Nyquist plots on a Li electrode over a swing in temperature from 15°C to 35°C and back to 15°C. The 3-electrode Li cell was first allowed to soak for 22 h until R s reached an approximately constant value at 35 ± 3°C before the cell temperature was lowered. Roughly the same value of R s was measured at 15°C before (1) and after (3) swinging the temperature to 35°C (2).
In Eq. 4, G is a constant which incorporates the physicochemical properties of the SEI such as density and molecular weight. Since ε is not a strong function of temperature (Fig. 8b), Eq. 4 implies that the SEI growth rate L  at a fixed applied current density i is also relatively independent of temperature. This conclusion will be used in the model development in the following section.
Model incorporating Li + transport through the SEI.-In this section, we propose a model for explaining the temperature effects on Li dendrite initiation reported in Figs. 2 and 3. As a basis for the model development, we use the framework outlined in our previous publication. 21 Briefly, the model we have proposed earlier considers the diffusional transport of Li + through a temporally evolving SEI layer. Whereas a typical SEI formed in EC/DMC with LiPF 6 salt has a complex bilayer structure with an outer organic layer and an inner compact layer composed of inorganic Li compounds, 36 the present model assumes for simplicity a single uniform layer composed of Li 2 CO 3 . The SEI layer grows in thickness on the Li surface during soaking as well as during Li electrodeposition (Fig. 9). The SEI growth that occurs during the time period t soak (prior to commencement of Li plating) forms the initial SEI thickness L . 0 During Li electrodeposition, the SEI grows at a roughly constant rate L  proportional to (1 − e) as in Eq. 4. The steady growth of the SEI layer manifests in experiments as a steady increase in the surface resistance R s seen in EIS data, and a steady increase in the surface overpotential s h seen in chronopotentiometry. To model transport of Li + ions across the SEI, we neglect electric field induced migrational transport (t  + 1) and assume the development of a linear Li + concentration profile within the SEI that drives diffusional transport. At pseudo steady-state, the Li + diffusional flux is proportional to the applied current density i. Under galvanostatic conditions, this provides the Li + concentration at the Li-SEI interface (C e ): In Eq. 5, C 0 is the constant Li + concentration in the SEI at the SEI-electrolyte interface (Fig. 9), and  SEI is the solid-state Li + diffusion coefficient in the SEI. As the Li plating progresses, the SEI layer thickness L increases causing the gradual depletion of Li + at the Li-SEI interface. Eventually, as the plating time reaches , onset t C e approaches 0 and, as demonstrated previously, 21 this depletion is responsible for the initiation of Li dendrites. Assuming that L increases linearly with time (L L Lt 0 plate  = + ), the critical time onset t at which C e approaches 0 leading to onset of dendrites is: provides insights into the effect of temperature on . onset t First, as described above (Eq. 4 and related discussion), the SEI growth rate L  at a fixed applied current density i is not a strong function of temperature. Furthermore, the initial thickness L 0 (which depends on t soak ) should increase with temperature because of faster transport through the SEI at elevated temperatures; however, per Eq. 6, this effect would lead to a decrease in onset t at higher temperatures, which is inconsistent with the experimental data in Figs. 2 and 3. Thus, temperature-dependencies of L  and L 0 do not explain the temperature-dependence of . onset t Now, we examine the lumped parameters  C SEI 0 comprising the diffusion coefficient ( SEI ) and the maximum concentration of mobile Li + species in the SEI (C 0 ). Although the precise temperature-dependence of  C SEI 0 is not known, both parameters  SEI and C 0 are expected to increase with temperature, causing an increase in onset t per Eq. 6. Therefore, one or both of these parameters is responsible for the  At low temperatures, fewer defects are present in the SEI (lower value of C 0 ) and solid-state diffusivity ( SEI ) is lowered too. 36,40,41 This causes lower onset t and thus an earlier onset of Li dendrite growth. At higher temperatures, a greater number of defects (C 0 ) and an elevated diffusion coefficient ( SEI ) permits the SEI to grow to a greater thickness L before reaching the critical condition C e  0 for dendrite initiation. Consequently, at elevated temperatures, Li dendrite initiation is delayed. Thus, our model qualitatively explains the observed temperature-dependence of onset t based on changes in Li + transport ( C SEI 0 ) through the SEI.

Conclusions
The temperature-dependence of Li dendrite initiation during galvanostatic electrodeposition was investigated using experiments and modeling. The following main conclusions can be drawn from this work: during galvanostatic Li electrodeposition was found to increase monotonically with an increase in temperature from 5°C to 35°C. (ii) During Li electrodeposition, the SEI continued to grow in thickness (for t onset t < ), as evidenced by an increase in surface overpotential and surface resistance, until the onset of dendritic growth. (iii) Temperature affects the solid state ionic conductivity (k) of the SEI. (iv) The Li plating efficiency, and thus the SEI growth rate during galvanostatic electrodeposition, was shown not to be a strong function of temperature. (v) The temperature-dependence of the Li dendrite initiation time was explained within the framework of a previously-developed transport model. The bulk concentration C 0 and diffusion coefficient  SEI of Li + within the SEI are suggested to be the temperature-dependent parameters responsible for the effect of temperature on onset t per Eq. 6.
The sluggish transport of Li + through the SEI imposes a major limitation during low-temperature charging of Li-metal batteries. The sluggish transport leads to faster depletion of Li + at the Li-SEI interface, triggering earlier initiation of Li dendrites at lower temperatures. Our work implies that while Li dendrite initiation during battery charging may be inevitable even at low current densities, avoiding low temperatures thereby facilitating faster Li + transport is critically essential in delaying dendrites. Other strategies such as artificial SEI layers, including materials with Li + transference numbers approaching unity, or solid electrolytes that do not continue to evolve in thickness, may hold the promise to preventing altogether the formation of Li dendrites. Figure 9. Schematic showing Li electrodes submerged in liquid electrolyte and covered with SEI of thickness L . onset During t soak the SEI grows to thickness L . 0 During t plate the SEI continues to grow at the rate L.  The concentration gradient with slope  i nF SEI / develops due to the consumption of Li + at the Li-SEI interface. At low temperatures, the bulk concentration of Li + C 0 ( ) is lower and the concentration gradient is steeper due to lower  .

SEI
Faster dendrite initiation time onset t at low temperatures is explained by the increased resistance associated with Li + diffusional transport.