Fast lithium growth and short circuit induced by localized-temperature hotspots in lithium batteries.

Fast-charging and high-energy-density batteries pose significant safety concerns due to high rates of heat generation. Understanding how localized high temperatures affect the battery is critical but remains challenging, mainly due to the difficulty of probing battery internal temperature with high spatial resolution. Here we introduce a method to induce and sense localized high temperature inside a lithium battery using micro-Raman spectroscopy. We discover that temperature hotspots can induce significant lithium metal growth as compared to the surrounding lower temperature area due to the locally enhanced surface exchange current density. More importantly, localized high temperature can be one of the factors to cause battery internal shorting, which further elevates the temperature and increases the risk of thermal runaway. This work provides important insights on the effects of heterogeneous temperatures within batteries and aids the development of safer batteries, thermal management schemes, and diagnostic tools.


Line heating experiment
To further validate that the morphology change of the deposited Li originated from the local high temperatures and not the photons in the laser, a set of line heating experiments was also conducted. We investigated the same coin cells (CR 2032) as described in Methods. However, instead of creating a hotspot with laser, a thin-film (Pt) resistive line heater (2 mm long, 100 µm wide) was patterned on the backside of the Cu plated thin glass (145 μm thick). A power of 0.03 W was applied to the heater. The temperature distribution was modeled in COMSOL assuming joule heating in the line heater (Supplementary Figure 1a). The result suggests a localized ellipticalshaped hot region with a peak temperature of 54 ºC. The widening of the hot region was mainly due to heat spreading in the 145 µm thick glass which separated the heater and the Cu current collector.
During the experiment, Li was deposited at 1 mA/cm 2 for 2 minutes. The coin cells after Li deposition were then disassembled immediately inside the glove box. The working electrodes were rinsed with DEC to remove salts for SEM imaging. The Li deposition morphology to the uniform temperature experiments, where Li formed at high temperature was less dendritic, and vice versa. In addition, Li deposited in the hot region was densely packed, whereas the deposited Li was sparser in the low temperature region. This suggests that Li deposition rate was higher in the high temperature region, which agrees with the hotspot experiment.

Uniform temperature experiment
To investigate lithium (Li) deposition morphology at uniform temperature conditions, we tested the same coin cells (CR 2032) as described in Methods in a temperature controlled environmental chamber (BTU-133, ESPEC). The entire coin cell was placed in the environmental chamber for two hours to reach the desired temperature. The same Li deposition current (1 mA/cm 2 ) was applied for the same period of time (2 minutes) for all the coin cells at different temperatures (room temperature, 30 ºC, 50 ºC, 70 ºC and 90 ºC). The coin cells after Li deposition were then disassembled immediately inside the glove box. The working electrodes were rinsed with diethyl carbonate (DEC) to remove salts for SEM imaging (Supplementary Figure 2).
The morphology of Li was more dendritic at lower deposition temperature, compared to Li deposited at higher temperature. More specifically, the deposited Li formed whiskers at room temperature. When the temperature increased, the diameter of Li whiskers increased. At 90 ºC, pancake shaped Li with less dendrites was formed.

Model description
The temperature profile as a result of the laser heating was simulated using COMSOL Multiphysics with the "Heat Transfer in Solids" module. A two-dimensional (2D) geometry with rotation was built which forms a three-dimensional (3D) spatial model. The domain consists of a glass disk (145 μm thick, 5.6 mm in radius), a Cu layer (170 nm thick, 5.6 mm in radius) and electrolyte (100 μm thick, 5.6 mm in radius) which represents the experimental conditions. The porous separator which is soaked in the electrolyte domain was not considered in the simulation. This is because it is far from the hotspot, and its thermal conductivity is similar with the electrolyte where T is the temperature, ⃗ is the heat flux, k is the thermal conductivity, and Q is volumetric heat generation.
The boundary conditions were set as follows: (1) the bottom surface of the electrolyte was fixed at room temperature, since it is in contact with high thermal conductivity Li metal on top of a thick stainless steel at room temperature; (2) the vertical z axis is axi-symmetric; and (3) the remaining surfaces are adiabatic.
For boundary condition (3), we neglected natural convection and radiation through the top glass surface, since the temperature on the top glass surface is estimated to be near room temperature, and heat transfer coefficient of natural convection of air is also small (~ 10 W/m 2 K).
This assumption was validated by additional simulation where the top glass surface has a heat transfer coefficient of 20 W/m 2 K, which resulted in the same hotspot temperature.

Mesh
Due to the various length scale involved (from 50 nm to 5.6 mm) in the COMSOL model, meshing was constructed with very fine meshes near the hotspot to capture the detailed physics, and coarse mesh at a distance from the hotspot to reduce computation time, where it is anticipated that the temperature is basically at room temperature. The meshes (Supplementary Figure 4) were constructed with sizes of (1) 25 nm for the heat source domain (500 nm in radius, 50 nm in thickness); (2) 25 nm to 200 nm for the copper layer; (3) For the glass and electrolyte, the minimum mesh sizes were the same with the hotspot and Cu where the domains connect, and the maximum size was 100 μm (the entire disk is 5.6 mm in radius). To ensure the meshes are fine enough, we reduced the minimum mesh sizes from 25 nm to 10 nm in the heat source domain. The resulting peak temperature was 362.394 K for the original mesh, and 362.395 K for the finer mesh (incident laser energy of 13.4 mW, absorption of 0.4). This suggests that the original mesh is sufficiently fine for the modeling.

Results of the temperature distribution
Results of the temperature distribution with parameters in Supplementary Table 2

Dependence on the laser beam profile
Another factor to consider is the shape of the laser beam. In the COMSOL model we approximated the laser beam with a top-hat shape (uniform heating within the laser spot radius of 500 nm, and no heating outside the laser spot). For comparison, we also performed simulation using a more detailed Gaussian profile spot. Here the beam radius corresponds to the location where the laser power decays to 1/e 2 of the peak intensity. To result in the same total heating power, the constant A in the Gaussian profile ( ) =

Dependence on thermal conductivity of Cu and electrolyte
We would like to note that the thermal conductivity listed in Supplementary

Effect of the heat source spot size
In the experiment the focused laser spot size was 1 μm, which was non-adjustable. To investigate the effect of the heat source size, we performed simulation varying the spot size of the heat source, while conserving the total energy input (13.4 mW incident laser with an absorption of 0.4). The radius of the laser spot was varied from 300 nm, 500 nm, 1 μm to 2 μm. The results of the temperature distribution are shown in Supplementary Figure 9a-d, and the radial temperature profile on the Cu-electrolyte interface is shown in Supplementary Figure 9e. Accordingly, lithium deposition current density is also affected, as shown in Supplementary Figure 16.

Heat spreading in the deposited Li
The thermal simulations discussed above was only appropriate for the initial stage (t=0 s), where Li has not formed on the Cu current collector. After Li deposition, the Li layer with higher thermal conductivity than the electrolyte could spread the heat from the laser hotspot and therefore change the temperature distribution. Although the exact model is difficult to construct since the deposited Li is nanostructured, for an estimation we constructed a simplified model which included a Li disk (1 μm thick, 5 μm in radius) (Supplementary Figure 10). We assumed an effective thermal conductivity of 68 W/mK for the Li disk (80% lithium (85 W/mK) and 20% electrolyte (0.3 W/mK)). The peak temperatures are 47.6, 75.3 and 89.1 ºC respectively which are lower than the peak temperatures without the Li disk (55, 90 and 108 ºC). In addition, the temperatures on the bottom surface of the Li (or the Li-electrolyte interface) are even lower with a wider width (Supplementary Figure 10). These results suggest that thermal spreading may be one of the reasons that the deposited Li on the hotspot in Figure 2 in the manuscript is much wider than the width of the initial temperature distribution.

COMSOL simulation -Lithium deposition rate
The electrochemical simulations were performed using COMSOL Multiphysics with the physics module "Tertiary Current Distribution, Nernst-Planck" and a 2D geometry with rotation, forming a 3D spatial model. The simulation cell (Supplementary Figure 11) Electrolyte neutrality: Overpotential of electrochemical reaction (η), where φs is the electrode potential and Eeq is the equilibrium potential of the Li/Li + couple.

= − −
Butler-Volmer equation, which governs the local current density, with j0 being the exchange current density, αa and αc being the anodic and cathodic charge transfer coefficient, respectively, R, the gas constant, and T, the temperature: The boundary conditions and initial conditions are as follows. The diffusion coefficient of Li + in the electrolyte was set to 3.2x10 -6 cm 2 /s from reference 8   , also discussed later in this section ** estimated from reference [3][4][5][6][7], also discussed later in this section