In situ healing of dendrites in a potassium metal battery

To study the morphology of the K-metal electrode after cycling, we tested K-K symmetric cells over a wide range of operating current densities (Fig. 1 A and B), ranging from low (∼0.01 mA cm⁻²) to moderately high values (∼2 mA cm⁻²). We imaged the surfaces of the K-metal foils used in the experiments by ex situ scanning electron microscopy (SEM). Shown in Fig. 1 C–J are the SEM images of the K-metal electrode surface after 50 cycles of charge and discharge at current densities of ∼0.01, ∼0.1, ∼0.5, ∼0.75, ∼1.5, and ∼2 mA cm⁻². As expected, large isolated hemispherical deposits (Fig. 1C) were observed after operation at a low current density (∼0.01 mA cm⁻²). At such low current densities, the deposition of K is considered to be charge-transfer controlled (21). As the operation current density increases (Fig. 1 D–F), nuclei grow in a dendritic form and the deposition is diffusion controlled (21). The dendrites formed are more densely packed and their diameter decreases with increasing current density. However, with further increase in the current density (∼2 mA cm⁻²), the morphology of the K-metal surface appears to be smooth and nondendritic in nature (Fig. 1H). At a current density of 1.5 mA cm⁻², partial healing can be observed (Fig. 1G), where the individual dendritic structures seem to have fused (or merged) together. Cross-sectional images of the electrode cycled at ∼0.01 and ∼2 mA cm⁻² are shown in Fig. 1I and J, respectively. Due to their porous nature, deposition of platinum and ion milling of the dendrites leads to their structural collapse (Fig. 1I). However, the cross-sectional image clearly reveals a high degree of porosity, which is to be expected for the dendritic layer. By contrast, the cross-section of the K-metal electrode cycled at ∼2 mA cm⁻² exhibited a compacted (or healed) sublayer in which the individual K dendrites have merged and fused together (Fig. 1J), which confirms the effectiveness of the healing phenomenon. These results are also consistent with the voltage profiles in Fig. 1B. The voltage profile of the cell cycled at ∼0.5 mA cm⁻² is indicative of extensive dendritic growth and increasing cell impedance. By contrast, the cell cycled at ∼2 mA cm⁻² exhibits high impedance initially, but the voltage profile stabilizes, which indicates that the dendrites formed in the initial cycles get healed over time.

We used first-principles DFT calculations to study the surface-diffusion characteristics of Li and K metal. To study surface diffusion, we consider both hopping and exchange mechanisms. In the hopping mechanism, we consider that the adatom moves from one equilibrium adsorption position to another (Fig. 2 A and B). The rate of diffusion is estimated by the calculated energy barrier along the path. The diffusion path is determined by comparing the adsorption energy of the adatoms on the high-symmetry sites of their, respective, most stable surface terminations. The adatom is allowed to relax in the direction perpendicular to the (001) surface. The adsorption energy (E_ads) is calculated by subtracting the energy of the clean metal electrode without the adatom (E_slab) and the energy of the single adatom (E_atom) from the energy of the system with the relaxed adsorbate adatom (E_sys), i.e., E_ads = E_sys – E_slab – E_atom (20).

The exchange, or the concerted displacement mechanism of diffusion involves the cooperative motion of several surface atoms. To determine the activation barrier in this mechanism, an exchange diffusion pathway (20) (i.e., the preferred adsorption site to the nearest surface neighbor, then to the next preferred adsorption site) is considered as follows. Adatom A sits originally in the fourfold hollow site, while surface atom B is one of its nearest neighbors on the (001) surface. Both atoms move cooperatively such that adatom A replaces surface atom B, while surface atom B becomes an adatom in the next fourfold hollow site. This is illustrated in Fig. 2C and has been adopted from the approach used in ref. 22. The nudged elastic band (NEB) method (23) was utilized to find the minimum energy path (MEP) and activation barrier in the exchange mechanism (Fig. 2D).

The minimum energy path for self-diffusion of both Li on Li (001), and K on K (001) in the exchange mechanism is hindered by an activation energy barrier (∼0.15 eV for Li and ∼0.1 eV for K). This energy barrier for exchange is much lower than the corresponding barrier for the hopping mechanism. For example, in the case of K, the barrier for the exchange mechanism (∼0.1 eV) is less than half the barrier for the hopping mechanism (∼0.23 eV), and therefore we conclude that the exchange mechanism is the predominant mechanism for self-diffusion in K. This barrier of diffusion in K is also significantly lower than the barrier for both types of diffusion (i.e., exchange as well as hopping) in Li. Consequently, K exhibits a much higher rate of self-diffusion [calculated using the Arrhenius equation (24), Fig. 2E] when compared to that of Li. For example, at a temperature of ∼50 °C, the rate constant of surface diffusion for K is about fivefold higher (Fig. 2E) than that of Li at the same temperature. While modeling effects of the solid electrolyte interface (SEI) and solvent (electrolyte) is challenging using DFT due to the system size and complexity, such work should be pursued as part of future studies.

The magnitude of the metal self-diffusion energy barrier has been proposed as a descriptor for occurrence of dendrite growth (25), and growth phenomena at interfaces are closely related to the diffusion coefficient (26, 27). Considering the link between lower self-diffusion barrier and growth of smooth surface structures, we infer that K metal can present a relatively smooth surface with suppression of dendrite growth. This inference is consistent with our experimental findings as suppression of K-dendrite growth is clearly observed at current densities that provide sufficient thermal energy for self-diffusion. The predicted temperature rise in the dendrites as a function of current density is provided in SI Appendix, Fig. S3 along with details of the thermal modeling approach (SI Appendix, Fig. S1). With electrical resistance of the electrolyte and SEI far exceeding that of the metal dendrite, it is assumed that Joule heating is predominantly in the electrolyte and SEI and that heat is transferred to the K-metal dendrite at the dendrite/SEI/electrolyte interface (SI Appendix, Fig. S2). The computational thermal modeling results indicate that temperatures on the order of 30–40 °C (in the K dendrites, SI Appendix, Fig. S3A) and 40–50 °C (in the electrolyte/SEI, SI Appendix, Fig. S3B) are possible at current densities of ∼2.0 mA cm⁻². Note that these temperatures are well below the melting temperature of K (∼63.5 °C) or the onset temperature at which degradation of the electrolyte/separator (about 80–90 °C) would be initiated.

A thermal annealing control experiment was also carried out to confirm the thermally assisted surface diffusion mechanism for healing of the K dendrites. For this, cells were cycled at a current density of ∼0.5 mA cm⁻² for about 200 h (50 charge–discharge cycles) to generate dense regions of closely spaced dendrites (SI Appendix, Fig. S4A). The cells were then thermally annealed at ∼40 °C on a hot plate for up to 72 h. The annealing was carried out without opening the cells, to ensure that the annealing took place in the presence of the battery electrolyte. Inspection of these electrodes after thermal annealing by SEM (SI Appendix, Fig. S4 B and C) indicates diffused or merged surfaces and a smooth morphology that is similar to the electrodes cycled at high current density (∼2 mA cm⁻², see Fig. 1H). Such healing of the dendrites in a high current density regime substantially reduces the risk of dendrite penetration through the separator, improving the safety of secondary batteries using K metal as the anode.

To analyze the structure/chemistry of the SEI of the K-metal anode run at low (∼0.01 mA cm⁻²) and high (∼2 mA cm⁻²) current densities, we carried out depth profiling (SI Appendix, Fig. S5) via X-ray photoelectron spectroscopy (XPS). O1s scans reveal the presence of C–O bond at about 530 eV, C = O bond at 531.8 eV, and CO₃²⁻ at 533.5 eV. K2p scans indicate doublets corresponding to K-F (293.5, 295.8 eV) and K–O bonds (292, 295 eV). Additionally, a peak corresponding to K₄X/K₃X (290.8 eV), where X is a counterion, was also detected. In general, we found that much sharper peaks (SI Appendix, Fig. S5 C and D) were observed for the sample cycled at 2 mA cm⁻², which suggests less diversity in the SEI composition. By contrast, the sample cycled at 0.01 mA cm⁻² exhibited more diffused and broader peaks (SI Appendix, Fig. S5 A and B), which is indicative of a more diverse SEI with significant contribution from multiple compounds. For example, the K₄X/K₃X (where X is a counterion) contribution is prominent at a current density of 0.01 mA cm⁻², but is negligibly small at 2 mA cm⁻². These observations can be explained based on reaction kinetics. At low current densities (e.g., 0.01 mA cm⁻²), reactions with slow kinetics have sufficient time to complete as opposed to cycling at high current densities (such as 2 mA cm⁻²), where the plating and stripping of potassium dominates over reactions with slow kinetics. Thus, at high current densities, fewer compounds are present in larger amounts, resulting in sharp peaks in the XPS spectra. At low current densities, a more diverse set of compounds are present in relatively smaller amounts, which results in a broadening of the XPS response.

Another key observation was how the SEI composition changes with respect to its thickness. Sputter-down XPS of the potassium-metal anodes revealed a uniform distribution of compounds through the depth of the SEI for samples cycled at 2 mA cm⁻². SI Appendix, Fig. S5 C and D indicates that there is virtually no change in the XPS K2p and O1s spectra with depth. The situation is different for samples cycled at 0.01 mA cm⁻², with significant changes in the relative intensities of the XPS peaks with depth (SI Appendix, Fig. S5 A and B). The variation of the types and quantities of compounds through the thickness of the SEI on the potassium-metal anode cycled at 0.01 mA cm⁻² indicates increased nonuniformity in the SEI. On the other hand, at the healing current density of 2 mA cm⁻², the SEI is far more uniform in the thickness direction when compared to the SEI that develops at low current densities.

To investigate the effect of current density on SEI thickness, we carried out electrochemical impedance spectroscopy on K-K symmetric cells cycled at low (0.01 mA cm⁻²) and high (2 mA cm⁻²) current densities (SI Appendix, Fig. S6). It is clear that the SEI resistance from intercepts of the high-frequency semicircles are lower for the cell cycled at 2 mA cm⁻² as compared to that cycled at 0.01 mA cm⁻². Due to the much lesser resistance of the K-K cell cycled at 2 mA cm⁻², the two semicircles representing charge transfer (CT) and SEI resistance tend to overlap and cannot be distinguished. Therefore, for the 2-mA cm⁻² case, a single semicircle is used for fitting to obtain the total impedance (i.e., SEI + CT) of the cell. The SEI + CT resistance was calculated to be ∼46.8 Ω (at 2 mA cm⁻²), which is considerably lesser than the SEI resistance of the anode cycled at 0.01 mA cm⁻² (∼168.3 Ω) with a dendritic morphology. This reduction in the resistance is indicative of a relatively thinner SEI for the K-metal foil that is cycled at the healing current density of 2 mA cm⁻² as compared to 0.01 mA cm⁻².

Based on SI Appendix, Figs. S5 and S6 we conclude that the SEI that forms at the healing current density of 2 mA cm⁻² is far more uniform (i.e., less heterogeneous) and thinner than the SEI created at low current densities. It is well established that the nucleation of dendrites is exacerbated for a more heterogeneous and thicker SEI, due to nonuniform diffusion of K⁺ through such layers. Consequently, in our system once the dendrites get healed (due to surface diffusion triggered by battery self-heat), they are less likely to renucleate due to the enhanced uniformity and reduced thickness of the SEI layer that is formed at the healing current density.

To demonstrate the application of healing of K dendrites in a working secondary battery, we assembled a full cell (Fig. 3A) with K-metal foil as the anode and the P2-type layered K_0.6CoO₂ (s-KCO) (13) as cathode. The s-KCO cathode possess micrometer-sized hierarchical structured spheres assembled from nano- or submicrometer primary particles. The nanosized primary particles assist with fast ion intercalation/deintercalation (SI Appendix, Table S1), while the microsized spheres minimize parasitic reactions and improve the volumetric energy density of the battery. These s-KCO cathodes not only maintained a high capacity with a low fade rate at a current density of ∼500 mA g⁻¹ (13), but were also capable of being operated at the current densities (Fig. 3B) required to heal the dendrites. The full cells were cycled at low current density of ∼0.5 mA cm⁻² (Fig. 3C) and in another experiment were cycled at low current density of ∼0.5 mA cm⁻² with bursts of higher current density (∼2 mA cm⁻²) cycles (Fig. 3E) to study the dendritic morphology on the cycled metal anode. Ex situ SEM images of the K-metal anode after cycling reveal a rough, dendritic surface at low current densities (∼0.5 mA cm⁻²) (Fig. 3D). However, the surface of the K-metal anode cycled with bursts of higher current densities (∼2 mA cm⁻²) was observed to have a smooth surface (Fig. 3F), due to healing of the K dendrites by Joule-heating-assisted surface diffusion, consistent with the observations made in a symmetric cell system. As expected, the cell cycled at low current density (Fig. 3C) has a lower average Coulombic efficiency (∼96.43%) than the cell cycled at low current density with repeated doses of high current density (Fig. 3E) healing cycles (∼98.92%).

It should be noted that the melting of potassium takes place at a much lower temperature (63.5 °C) as compared to lithium (180.5 °C). However, at a current density of ∼2 mA cm⁻², melting does not take place in our potassium battery. The typical voltage profile at this current density is shown in Fig. 1B. During the dendrite growth as well as healing process, the voltage profile shows large fluctuations (or spikes) that are associated with the changing morphology of the dendritic surface and the SEI layer. After the healing is completed, a stable voltage profile is observed. As is evident from Fig. 1B, it takes about 30 h for the potassium surface and SEI to stabilize and heal. Such timescales are not consistent with a melting process, which would proceed much more rapidly, if the dendrite temperature were to exceed the melting point of potassium. On the other hand, surface-diffusion-induced healing is consistent with the timescales observed in our experiments. Further, our thermal modeling (SI Appendix, Fig. S3) predicts maximum dendrite temperatures of ∼40 °C at an operating current density of ∼2 mA cm⁻². This is well below the melting temperature of potassium metal. The heating (annealing) of the coin cell on a hot plate at ∼40 °C also supports the surface-diffusion hypothesis, since it takes over 36 h for the healing to be completed (SI Appendix, Fig. S4), which is comparable to the timescales in the electrochemical test (Fig. 1B). These results indicate that dendrite healing is a surface diffusion rather than a melting process.

It is possible that while healing the dendrites, the battery management system (BMS) could accidently malfunction and apply current densities that are much larger than 2 mA cm⁻². In such a scenario, could melting of the potassium-metal anode be a possibility? Certainly, this could take place in a K-K symmetrical cell, since in such a cell the current density can be raised to an arbitrarily large value, at which point the temperature rise in the K-metal foil could exceed the melting temperature, resulting in catastrophic failure. However, this is not the case in a practical full-cell configuration. Among cathodes for nonaqueous KIBs, s-KCO offers among the best high-rate capabilities reported to date (13). However, even the s-KCO electrode (which is optimized for high-rate operation) is unable to operate effectively above 2 mA cm⁻² current density as shown in SI Appendix, Fig. S7. At a current density of 2 mA cm⁻², we predict maximum dendrite temperatures of about 40 °C based on our thermal modeling (SI Appendix, Fig. S3), which is significantly below the melting point of potassium metal. Other high-performing cathodes (SI Appendix, Table S1) for potassium-ion batteries are also unable to operate at current densities above 2 mA cm⁻². Thus, in our practical full-cell device, we do not cycle and more importantly even in the event of a BMS failure/malfunction, we cannot cycle at rates that might lead to melting of potassium. Further, since the capacity of the s-KCO drops to almost zero at current densities such as 5 mA cm⁻², increasing current densities beyond 2 mA cm⁻² for the s-KCO cathode would not aid in dendrite healing on the K-metal anode.

The full-cell tests in Fig. 3 were conducted with ∼0.8 M KPF₆ in dimethyl ether (DME) as the electrolyte. We also assembled K-K symmetric cells in an electrolyte of ∼0.8 M KPF₆ in DME to confirm that the healing mechanism still applies in the ether-based electrolyte. SEM images of the cycled K-metal anodes at varying current densities is shown in SI Appendix, Fig. S8. The dendrite evolution with current density is very similar to the results shown in Fig. 1 for the carbonate-based electrolyte. At current densities of ∼2 mA cm⁻², a smooth surface indicative of dendritic healing was observed. From these results, we conclude that the K-dendrite healing phenomena applies to both carbonate as well as ether-based electrolytes.

To summarize, we have studied how K dendrites respond to self-heat and compared our results to that of Li. Testing of symmetric cells indicates that the self-heating–driven healing of dendrites is far more effective in K as compared to Li metal. This enables dendrite healing to take place at an order-of-magnitude lower current density for K relative to Li. Detailed DFT calculations were used to explain the underlying reason for this behavior. It was found that the energy barriers for self-surface diffusion in K are much lower than in Li metal, which explains why K dendrites are easier to heal when compared to their Li counterparts. Finally, we show that self-heating–induced healing of the K-metal anode can also be accomplished in a full-cell setting, which indicates that this healing concept has important practical implications.

This work was supported by the NSF (Award #1922633). N.K. also acknowledges funding support from the John A. Clark and Edward T. Crossan endowed Chair Professorship at the Rensselaer Polytechnic Institute.