In situ healing of dendrites in a potassiummetal batteryPrateek Hundekara Swastik Basua Xiulin Fanb Lu Lia Anthony Yoshimurac Tushar Guptaa Varun SarbadadAniruddha Lakhnota Rishabh Jaina Shankar Narayanana Yunfeng Shid Chunsheng Wangb and Nikhil Koratkarad1

aDepartment of Mechanical Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Troy NY 12180 bDepartment of Chemical andBiomolecular Engineering University of Maryland College Park MD 20742 cDepartment of Physics Applied Physics and Astronomy Rensselaer PolytechnicInstitute Troy NY 12180 and dDepartment of Material Science and Engineering Rensselaer Polytechnic Institute Troy NY 12180

Edited by John A Rogers Northwestern University Evanston IL and approved February 7 2020 (received for review September 5 2019)

The use of potassium (K) metal anodes could result in high-performance K-ion batteries that offer a sustainable and low-costalternative to lithium (Li)-ion technology However formation ofdendrites on such K-metal surfaces is inevitable which preventstheir utilization Here we report that K dendrites can be healed insitu in a K-metal battery The healing is triggered by current-controlled self-heating at the electrolytedendrite interface whichcauses migration of surface atoms away from the dendrite tipsthereby smoothening the dendritic surface We discover that thisprocess is strikingly more efficient for K as compared to Li metal Weshow that the reason for this is the far greater mobility of surfaceatoms in K relative to Li metal which enables dendrite healing totake place at an order-of-magnitude lower current density Wedemonstrate that the K-metal anode can be coupled with a potas-sium cobalt oxide cathode to achieve dendrite healing in a practicalfull-cell device

potassium-ion battery | dendrite healing | safety

Rechargeable lithium (Li)-ion batteries (LIBs) have emergedas the preeminent energy storage technology over the past

few decades owing to their high energy density and extraordi-nary cycling characteristics (1 2) However the uneven distri-bution and scarcity of Li in the earthrsquos crust (sim20 ppm) makesrelying on LIBs as the sole source of energy storage highly im-practical and uneconomical (3) Alkaline metal-ionndashbased bat-teries such as sodium (Na)-ion batteries (NIBs) and potassium(K)-ion batteries (KIBs) have garnered extensive attention overthe past few years in the hope that their abundant presence inthe earthrsquos crust (sim236 wt and sim209 wt respectivelycompared to sim00017 wt of Li) and lower costs would aidlarge-scale energy storage applications (4 5) NIBs have beenintensively investigated in the past few years while KIBs aregradually gaining widespread attention (6 7)The standard potential for K+K is minus293 V versus the stan-

dard hydrogen electrode (SHE) which is comparable to minus304 Vfor Li+Li Also K theoretically offers a higher operating voltagethan Na since the standard redox potential for Na+Na is minus271 Vversus SHE In the commonly used ethylene carbonatediethylcarbonate (ECDEC) electrolyte it was determined that K+Kis minus015 V versus the Li+Li (ref 7) This low potential providesKIBs a superior position among possible alternatives to replaceLi-based batteries It should also be noted that K unlike Li doesnot alloy with aluminum at low potentials (8) enabling the uti-lization of low-cost aluminum foils as the current collector forthe anode Compared to LIBs and NIBs another importantbenefit of KIBs is that the K ion exhibits much weaker Lewisacidity (9 10) and forms smaller solvated ions than those of Li andNa This allows for higher ionic conductivity and faster transportof solvated K ions with prospects of improved high-power per-formance for KIBsA variety of anode and cathode materials for K secondary

batteries have been explored Owing to the larger ionic size andmass of K+ only a few cathode materials have been reported for

KIBs Among these Prussian Blue and its analogs have beenreported to reversibly store K ions in nonaqueous electrolytesbut poor volumetric capacity due to the low density of hexa-cyanoferrates limits their practical applications (8 11 12) Re-cently Deng et al synthesized a hierarchically structured P2-typelayered K06CoO2 cathode which not only delivered a high spe-cific capacity but was also capable of cycling K+ ions at rea-sonably high rates (13) On the anode side a variety of materialssuch as graphite (14) hard carbons (15) soft carbons (16) as wellas phosphorous-based alloys (17) have been explored in sec-ondary K batteries In contrast to this the direct use of K metalas the anode would allow for superior specific capacity thancarbonaceous alloying or intercalation compounds as thepacking density of K atoms is the highest in its metallic formHowever similar to Li the K-metal anode is observed to developdendritic projections during the electrochemical platingndashstrip-ping processes which occur when the battery is being chargedand discharged The growth of dendrites is associated with ir-reversible capacity loss a reduced Coulombic efficiency as wellas drying and degradation of the electrolyte (18) Most impor-tantly these dendritic projections can pierce through the sepa-rating membrane and electrically short the battery leading to asevere thermal runaway which could result in a catastrophicfire hazardKinetically the nucleation and growth of metal dendrites is

highly favorable during electrochemical plating and strippingprocesses It is generally accepted that a higher current density(ie faster chargedischarge) would promote dendritic growthsince the diffusion-limited aggregation of dendrites should befavored under such conditions In previous work (19 20) on Li-metal systems we demonstrated that this is not always the caseIn particular we demonstrated a distinct regime in which the

Significance

Historically battery self-heating has been viewed negatively asan undesirable attribute However we report that battery self-heat if properly controlled can smoothen dendritic features inpotassium metal batteries This could open the door to highgravimetric and volumetric energy density potassium-ion bat-teries that could offer a sustainable and low-cost alternative tothe incumbent lithium-ion technology

Author contributions PH LL and NK designed research PH SB AY TG AL RJand NK performed research PH SB XF LL AY TG VS AL RJ SN YS CWand NK contributed new reagentsanalytic tools PH SB AY TG AL RJ SN YSCW and NK analyzed data and PH SB and NK wrote the paper

The authors declare no competing interest

This article is a PNAS Direct Submission

Published under the PNAS license1To whom correspondence may be addressed Email koratnrpiedu

This article contains supporting information online at httpswwwpnasorglookupsuppldoi101073pnas1915470117-DCSupplemental

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opposite was true where at very high current densities (sim15mA cmminus2)the internal self-heating of the battery triggers extensive surfacediffusion of Li which smoothens (heals) the dendrites In this studywe investigate how K dendrites in K-metal batteries respond to self-heat We discover that the process of self-heatndashdriven healing(smoothening) of dendrites is strikingly more effective in K ascompared to Li metal The parameter used to control the batteryself- (Joule) heating is the operating current density (or chargendashdischarge rate) of the cell Because K dendrites are far easier to healwhen compared to their Li counterparts the current density requiredto trigger the healing was an order-of-magnitude lower for K(sim15 mA cmminus2) as compared to that of Li metal (sim15 mA cmminus2)This markedly lower current density suggests that a smaller rise intemperature while cycling is required for self-diffusion assistedhealing of K dendrites which would make electrolyte degradation ordamage to the separator less likely Therefore the thermally acti-vated healing of K dendrites is not only more efficient but also muchsafer when compared to that of LiTo uncover the mechanism as to why K dendrites heal much

easier than Li we used first-principles density-functional theory(DFT) calculations to estimate the extent of surface diffusion ofK metal atoms by calculating activation energy barriers for sur-face diffusion via hopping and exchange diffusion mechanisms(20) Similar calculations were also performed for self-diffusionof Li Further we look at an Arrhenius picture to investigate Ksurface diffusion as a temperature-activated process and com-pare the results to that of Li (20) Our theoretical study revealsthat the activation barrier for surface diffusion in K (sim01 eV) issignificantly lower than that in Li (sim015 eV) Consequentlyeven at a moderately high temperature of sim50 degC the rateconstant of surface diffusion of K is about fivefold higher thanthat of Li at the same temperature The drastically higher self-diffusion for K as compared to Li metal explains why K dendritesare much easier to heal when compared to Li We also show thatK dendrites can be healed in a full-cell device that consists of aK06CoO2 cathode and a K-metal anodeBattery self-heating typically has a negative connotation

however our results indicate that battery self-heat if properlycontrolled can smoothen dendritic features in K-metal batteriesThis could lead to high-performance K-ion batteries that couldoffer a sustainable and low-cost alternative to Li-ion technology

ResultsTo study the morphology of the K-metal electrode after cyclingwe tested K-K symmetric cells over a wide range of operatingcurrent densities (Fig 1 A and B) ranging from low (sim001mA cmminus2) to moderately high values (sim2 mA cmminus2) We imagedthe surfaces of the K-metal foils used in the experiments by exsitu scanning electron microscopy (SEM) Shown in Fig 1 CndashJare the SEM images of the K-metal electrode surface after 50cycles of charge and discharge at current densities of sim001 sim01sim05 sim075 sim15 and sim2 mA cmminus2 As expected large isolatedhemispherical deposits (Fig 1C) were observed after operationat a low current density (sim001 mA cmminus2) At such low currentdensities the deposition of K is considered to be charge-transfercontrolled (21) As the operation current density increases (Fig1 DndashF) nuclei grow in a dendritic form and the deposition isdiffusion controlled (21) The dendrites formed are more denselypacked and their diameter decreases with increasing currentdensity However with further increase in the current density(sim2 mA cmminus2) the morphology of the K-metal surface appears tobe smooth and nondendritic in nature (Fig 1H) At a currentdensity of 15 mA cmminus2 partial healing can be observed (Fig 1G)where the individual dendritic structures seem to have fused (ormerged) together Cross-sectional images of the electrode cycledat sim001 and sim2 mA cmminus2 are shown in Fig 1I and J respectivelyDue to their porous nature deposition of platinum and ion millingof the dendrites leads to their structural collapse (Fig 1I)

However the cross-sectional image clearly reveals a high degreeof porosity which is to be expected for the dendritic layer Bycontrast the cross-section of the K-metal electrode cycled atsim2 mA cmminus2 exhibited a compacted (or healed) sublayer in whichthe individual K dendrites have merged and fused together (Fig1J) which confirms the effectiveness of the healing phenomenonThese results are also consistent with the voltage profiles in Fig1B The voltage profile of the cell cycled at sim05 mA cmminus2 is in-dicative of extensive dendritic growth and increasing cell imped-ance By contrast the cell cycled at sim2 mA cmminus2 exhibits highimpedance initially but the voltage profile stabilizes which indi-cates that the dendrites formed in the initial cycles get healedover timeWe used first-principles DFT calculations to study the surface-

diffusion characteristics of Li and K metal To study surfacediffusion we consider both hopping and exchange mechanismsIn the hopping mechanism we consider that the adatom movesfrom one equilibrium adsorption position to another (Fig 2 Aand B) The rate of diffusion is estimated by the calculated en-ergy barrier along the path The diffusion path is determined bycomparing the adsorption energy of the adatoms on the high-symmetry sites of their respective most stable surface termina-tions The adatom is allowed to relax in the direction perpen-dicular to the (001) surface The adsorption energy (Eads) iscalculated by subtracting the energy of the clean metal electrodewithout the adatom (Eslab) and the energy of the single adatom(Eatom) from the energy of the system with the relaxed adsorbateadatom (Esys) ie Eads = Esys ndash Eslab ndash Eatom (20)The exchange or the concerted displacement mechanism of

diffusion involves the cooperative motion of several surfaceatoms To determine the activation barrier in this mechanism anexchange diffusion pathway (20) (ie the preferred adsorptionsite to the nearest surface neighbor then to the next preferredadsorption site) is considered as follows Adatom A sits originallyin the fourfold hollow site while surface atom B is one of itsnearest neighbors on the (001) surface Both atoms move co-operatively such that adatom A replaces surface atom B whilesurface atom B becomes an adatom in the next fourfold hollowsite This is illustrated in Fig 2C and has been adopted from theapproach used in ref 22 The nudged elastic band (NEB) method(23) was utilized to find the minimum energy path (MEP) andactivation 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 hinderedby an activation energy barrier (sim015 eV for Li and sim01 eV forK) This energy barrier for exchange is much lower than thecorresponding barrier for the hopping mechanism For examplein the case of K the barrier for the exchange mechanism (sim01eV) is less than half the barrier for the hopping mechanism(sim023 eV) and therefore we conclude that the exchangemechanism is the predominant mechanism for self-diffusion inK This barrier of diffusion in K is also significantly lower thanthe barrier for both types of diffusion (ie exchange as well ashopping) in Li Consequently K exhibits a much higher rate ofself-diffusion [calculated using the Arrhenius equation (24) Fig2E] when compared to that of Li For example at a temperatureof sim50 degC the rate constant of surface diffusion for K is aboutfivefold higher (Fig 2E) than that of Li at the same temperatureWhile modeling effects of the solid electrolyte interface (SEI)and solvent (electrolyte) is challenging using DFT due to thesystem size and complexity such work should be pursued as partof future studies

DiscussionThe magnitude of the metal self-diffusion energy barrier hasbeen proposed as a descriptor for occurrence of dendrite growth(25) and growth phenomena at interfaces are closely related tothe diffusion coefficient (26 27) Considering the link between

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lower self-diffusion barrier and growth of smooth surface struc-tures we infer that K metal can present a relatively smoothsurface 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 thatprovide sufficient thermal energy for self-diffusion The predicted

Fig 1 Dendrite morphology in K-K symmetrical cells (A) Schematic of a symmetric K-K cell (B) Potential-time profiles for K-K symmetric cells operated atlow and high current densities SEM images depicting the surface morphology of the K-metal electrode in K-K symmetric cells cycled at different currentdensities (C) sim001 mA cmminus2 (D) sim01 mA cmminus2 (E) sim05 mA cmminus2 (F) sim075 mA cmminus2 (G) sim15 mA cmminus2 and (H) sim2 mA cmminus2 Cross-sectional images of the K-metal electrode operated at (I) sim001 mA cmminus2 and (J) sim2 mA cmminus2 produced by FIB milling

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temperature rise in the dendrites as a function of current density isprovided in SI Appendix Fig S3 along with details of the thermalmodeling approach (SI Appendix Fig S1) With electrical re-sistance of the electrolyte and SEI far exceeding that of the metaldendrite it is assumed that Joule heating is predominantly in theelectrolyte and SEI and that heat is transferred to the K-metaldendrite at the dendriteSEIelectrolyte interface (SI AppendixFig S2) The computational thermal modeling results indicatethat temperatures on the order of 30ndash40 degC (in the K dendrites SIAppendix Fig S3A) and 40ndash50 degC (in the electrolyteSEI SI Ap-pendix Fig S3B) are possible at current densities of sim20 mA cmminus2Note that these temperatures are well below the melting tem-perature of K (sim635 degC) or the onset temperature at whichdegradation of the electrolyteseparator (about 80ndash90 degC) wouldbe initiatedA thermal annealing control experiment was also carried out

to confirm the thermally assisted surface diffusion mechanismfor healing of the K dendrites For this cells were cycled at acurrent density of sim05 mA cmminus2 for about 200 h (50 chargendashdischarge cycles) to generate dense regions of closely spaceddendrites (SI Appendix Fig S4A) The cells were then thermallyannealed at sim40 degC on a hot plate for up to 72 h The annealingwas carried out without opening the cells to ensure that theannealing took place in the presence of the battery electrolyteInspection of these electrodes after thermal annealing by SEM(SI Appendix Fig S4 B and C) indicates diffused or mergedsurfaces and a smooth morphology that is similar to the elec-trodes cycled at high current density (sim2 mA cmminus2 see Fig 1H)Such healing of the dendrites in a high current density regimesubstantially reduces the risk of dendrite penetration through theseparator improving the safety of secondary batteries using Kmetal as the anodeTo analyze the structurechemistry of the SEI of the K-metal

anode run at low (sim001 mA cmminus2) and high (sim2 mA cmminus2)current densities we carried out depth profiling (SI AppendixFig S5) via X-ray photoelectron spectroscopy (XPS) O1s scansreveal the presence of CndashO bond at about 530 eV C =O bond at5318 eV and CO3

2minus at 5335 eV K2p scans indicate doubletscorresponding to K-F (2935 2958 eV) and KndashO bonds (292295 eV) Additionally a peak corresponding to K4XK3X (2908eV) where X is a counterion was also detected In general wefound that much sharper peaks (SI Appendix Fig S5 C and D)

were observed for the sample cycled at 2 mA cmminus2 which sug-gests less diversity in the SEI composition By contrast thesample cycled at 001 mA cmminus2 exhibited more diffused andbroader peaks (SI Appendix Fig S5 A and B) which is indicativeof a more diverse SEI with significant contribution from multiplecompounds For example the K4XK3X (where X is a counter-ion) contribution is prominent at a current density of 001mA cmminus2 but is negligibly small at 2 mA cmminus2 These observa-tions can be explained based on reaction kinetics At low currentdensities (eg 001 mA cmminus2) reactions with slow kinetics havesufficient time to complete as opposed to cycling at high currentdensities (such as 2 mA cmminus2) where the plating and stripping ofpotassium dominates over reactions with slow kinetics Thus athigh current densities fewer compounds are present in largeramounts resulting in sharp peaks in the XPS spectra At lowcurrent densities a more diverse set of compounds are present inrelatively smaller amounts which results in a broadening of theXPS responseAnother 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 compoundsthrough the depth of the SEI for samples cycled at 2 mA cmminus2 SIAppendix Fig S5 C and D indicates that there is virtually nochange in the XPS K2p and O1s spectra with depth The situationis different for samples cycled at 001 mA cmminus2 with significantchanges in the relative intensities of the XPS peaks with depth (SIAppendix Fig S5 A and B) The variation of the types andquantities of compounds through the thickness of the SEI on thepotassium-metal anode cycled at 001 mA cmminus2 indicates in-creased nonuniformity in the SEI On the other hand at thehealing current density of 2 mA cmminus2 the SEI is far more uniformin the thickness direction when compared to the SEI that developsat low current densitiesTo investigate the effect of current density on SEI thickness

we carried out electrochemical impedance spectroscopy onK-K symmetric cells cycled at low (001 mA cmminus2) and high(2 mA cmminus2) current densities (SI Appendix Fig S6) It is clear thatthe SEI resistance from intercepts of the high-frequency semicir-cles are lower for the cell cycled at 2 mA cmminus2 as compared tothat cycled at 001 mA cmminus2 Due to the much lesser resistanceof the K-K cell cycled at 2 mA cmminus2 the two semicircles repre-senting charge transfer (CT) and SEI resistance tend to overlap

Fig 2 First-principles DFT calculations of surface diffusion Adsorption energy landscape for (A) Li adatom on Li (001) and (B) K adatom on K (001) (C)Snapshots of the atomic configuration along the MEP for self-diffusion with the adatom in a fourfold hollow in the exchange mechanism (D) Activationenergy barrier calculated by NEB method for the diffusion by exchange mechanism for Li and K (E) In an Arrhenius picture the diffusion rate constant (kSTST)at a temperature T is computed using a simple approximate form (24) of STST in which kSTST = npv0exp[minus(Esaddle ndash Emin)kBT] (Materials and Methods) Thevariation of the diffusion rate constant with temperature for both Li and K is plotted

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temperature rise in the dendrites as a function of current density isprovided in SI Appendix Fig S3 along with details of the thermalmodeling approach (SI Appendix Fig S1) With electrical re-sistance of the electrolyte and SEI far exceeding that of the metaldendrite it is assumed that Joule heating is predominantly in theelectrolyte and SEI and that heat is transferred to the K-metaldendrite at the dendriteSEIelectrolyte interface (SI AppendixFig S2) The computational thermal modeling results indicatethat temperatures on the order of 30ndash40 degC (in the K dendrites SIAppendix Fig S3A) and 40ndash50 degC (in the electrolyteSEI SI Ap-pendix Fig S3B) are possible at current densities of sim20 mA cmminus2Note that these temperatures are well below the melting tem-perature of K (sim635 degC) or the onset temperature at whichdegradation of the electrolyteseparator (about 80ndash90 degC) wouldbe initiatedA thermal annealing control experiment was also carried out

to confirm the thermally assisted surface diffusion mechanismfor healing of the K dendrites For this cells were cycled at acurrent density of sim05 mA cmminus2 for about 200 h (50 chargendashdischarge cycles) to generate dense regions of closely spaceddendrites (SI Appendix Fig S4A) The cells were then thermallyannealed at sim40 degC on a hot plate for up to 72 h The annealingwas carried out without opening the cells to ensure that theannealing took place in the presence of the battery electrolyteInspection of these electrodes after thermal annealing by SEM(SI Appendix Fig S4 B and C) indicates diffused or mergedsurfaces and a smooth morphology that is similar to the elec-trodes cycled at high current density (sim2 mA cmminus2 see Fig 1H)Such healing of the dendrites in a high current density regimesubstantially reduces the risk of dendrite penetration through theseparator improving the safety of secondary batteries using Kmetal as the anodeTo analyze the structurechemistry of the SEI of the K-metal

anode run at low (sim001 mA cmminus2) and high (sim2 mA cmminus2)current densities we carried out depth profiling (SI AppendixFig S5) via X-ray photoelectron spectroscopy (XPS) O1s scansreveal the presence of CndashO bond at about 530 eV C =O bond at5318 eV and CO3

2minus at 5335 eV K2p scans indicate doubletscorresponding to K-F (2935 2958 eV) and KndashO bonds (292295 eV) Additionally a peak corresponding to K4XK3X (2908eV) where X is a counterion was also detected In general wefound that much sharper peaks (SI Appendix Fig S5 C and D)

were observed for the sample cycled at 2 mA cmminus2 which sug-gests less diversity in the SEI composition By contrast thesample cycled at 001 mA cmminus2 exhibited more diffused andbroader peaks (SI Appendix Fig S5 A and B) which is indicativeof a more diverse SEI with significant contribution from multiplecompounds For example the K4XK3X (where X is a counter-ion) contribution is prominent at a current density of 001mA cmminus2 but is negligibly small at 2 mA cmminus2 These observa-tions can be explained based on reaction kinetics At low currentdensities (eg 001 mA cmminus2) reactions with slow kinetics havesufficient time to complete as opposed to cycling at high currentdensities (such as 2 mA cmminus2) where the plating and stripping ofpotassium dominates over reactions with slow kinetics Thus athigh current densities fewer compounds are present in largeramounts resulting in sharp peaks in the XPS spectra At lowcurrent densities a more diverse set of compounds are present inrelatively smaller amounts which results in a broadening of theXPS responseAnother 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 compoundsthrough the depth of the SEI for samples cycled at 2 mA cmminus2 SIAppendix Fig S5 C and D indicates that there is virtually nochange in the XPS K2p and O1s spectra with depth The situationis different for samples cycled at 001 mA cmminus2 with significantchanges in the relative intensities of the XPS peaks with depth (SIAppendix Fig S5 A and B) The variation of the types andquantities of compounds through the thickness of the SEI on thepotassium-metal anode cycled at 001 mA cmminus2 indicates in-creased nonuniformity in the SEI On the other hand at thehealing current density of 2 mA cmminus2 the SEI is far more uniformin the thickness direction when compared to the SEI that developsat low current densitiesTo investigate the effect of current density on SEI thickness

we carried out electrochemical impedance spectroscopy onK-K symmetric cells cycled at low (001 mA cmminus2) and high(2 mA cmminus2) current densities (SI Appendix Fig S6) It is clear thatthe SEI resistance from intercepts of the high-frequency semicir-cles are lower for the cell cycled at 2 mA cmminus2 as compared tothat cycled at 001 mA cmminus2 Due to the much lesser resistanceof the K-K cell cycled at 2 mA cmminus2 the two semicircles repre-senting charge transfer (CT) and SEI resistance tend to overlap

Fig 2 First-principles DFT calculations of surface diffusion Adsorption energy landscape for (A) Li adatom on Li (001) and (B) K adatom on K (001) (C)Snapshots of the atomic configuration along the MEP for self-diffusion with the adatom in a fourfold hollow in the exchange mechanism (D) Activationenergy barrier calculated by NEB method for the diffusion by exchange mechanism for Li and K (E) In an Arrhenius picture the diffusion rate constant (kSTST)at a temperature T is computed using a simple approximate form (24) of STST in which kSTST = npv0exp[minus(Esaddle ndash Emin)kBT] (Materials and Methods) Thevariation of the diffusion rate constant with temperature for both Li and K is plotted

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and cannot be distinguished Therefore for the 2-mA cmminus2 case asingle semicircle is used for fitting to obtain the total impedance(ie SEI + CT) of the cell The SEI + CT resistance was calcu-lated to be sim468 Ω (at 2 mA cmminus2) which is considerably lesserthan the SEI resistance of the anode cycled at 001 mA cmminus2

(sim1683 Ω) with a dendritic morphology This reduction in theresistance is indicative of a relatively thinner SEI for the K-metalfoil that is cycled at the healing current density of 2 mA cmminus2 ascompared to 001 mA cmminus2Based on SI Appendix Figs S5 and S6 we conclude that the

SEI that forms at the healing current density of 2 mA cmminus2 is farmore uniform (ie less heterogeneous) and thinner than the SEIcreated at low current densities It is well established that thenucleation of dendrites is exacerbated for a more heterogeneousand thicker SEI due to nonuniform diffusion of K+ through suchlayers Consequently in our system once the dendrites get healed(due to surface diffusion triggered by battery self-heat) they areless likely to renucleate due to the enhanced uniformity and

reduced thickness of the SEI layer that is formed at the healingcurrent densityTo 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 K06CoO2(s-KCO) (13) as cathode The s-KCO cathode possess micrometer-sized hierarchical structured spheres assembled from nano- orsubmicrometer primary particles The nanosized primary parti-cles assist with fast ion intercalationdeintercalation (SI Appen-dix Table S1) while the microsized spheres minimize parasiticreactions and improve the volumetric energy density of thebattery These s-KCO cathodes not only maintained a high ca-pacity with a low fade rate at a current density of sim500 mA gminus1

(13) but were also capable of being operated at the currentdensities (Fig 3B) required to heal the dendrites The full cellswere cycled at low current density of sim05 mA cmminus2 (Fig 3C)and in another experiment were cycled at low current density ofsim05 mA cmminus2 with bursts of higher current density (sim2 mA cmminus2)

Fig 3 Dendrite healing in a full cell with K metal as anode and s-KCO as cathode (A) Schematic of the full-cell device (B) Voltage profiles of the s-KCOjK celloperated at low and high current densities Cycle stability of the full cells indicating specific charge capacity (red) and Coulombic efficiency of KCO (blue)when cycled at (C) low current density (sim05 mA cmminus2) and (E) low current density (sim05 mA cmminus2) with bursts of high current density (sim2-mA cmminus2) cyclesSEM images of the K-metal electrode after cycling at (D) low current densities (sim05 mA cmminus2) exhibit a dendritic surface morphology while the surface of theK metal after cycling at (F) low current density (sim05 mA cmminus2) with bursts of high current density (sim2 mA cmminus2) cycles is devoid of any distinct dendriticprojections

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cycles (Fig 3E) to study the dendritic morphology on the cycledmetal anode Ex situ SEM images of the K-metal anode aftercycling reveal a rough dendritic surface at low current densities(sim05 mA cmminus2) (Fig 3D) However the surface of the K-metalanode cycled with bursts of higher current densities (sim2 mA cmminus2)was observed to have a smooth surface (Fig 3F) due to healing ofthe K dendrites by Joule-heating-assisted surface diffusion con-sistent with the observations made in a symmetric cell system Asexpected the cell cycled at low current density (Fig 3C) has alower average Coulombic efficiency (sim9643) than the cell cy-cled at low current density with repeated doses of high currentdensity (Fig 3E) healing cycles (sim9892)It should be noted that the melting of potassium takes place at

a much lower temperature (635 degC) as compared to lithium(1805 degC) However at a current density of sim2 mA cmminus2melting does not take place in our potassium battery The typicalvoltage profile at this current density is shown in Fig 1B Duringthe dendrite growth as well as healing process the voltage profileshows large fluctuations (or spikes) that are associated with thechanging morphology of the dendritic surface and the SEI layerAfter the healing is completed a stable voltage profile is ob-served As is evident from Fig 1B it takes about 30 h for thepotassium surface and SEI to stabilize and heal Such timescalesare not consistent with a melting process which would proceedmuch more rapidly if the dendrite temperature were to exceedthe melting point of potassium On the other hand surface-diffusion-induced healing is consistent with the timescales ob-served in our experiments Further our thermal modeling (SIAppendix Fig S3) predicts maximum dendrite temperatures ofsim40 degC at an operating current density of sim2 mA cmminus2 This iswell below the melting temperature of potassium metal Theheating (annealing) of the coin cell on a hot plate at sim40 degC alsosupports the surface-diffusion hypothesis since it takes over 36 hfor the healing to be completed (SI Appendix Fig S4) which iscomparable to the timescales in the electrochemical test (Fig1B) These results indicate that dendrite healing is a surfacediffusion rather than a melting processIt is possible that while healing the dendrites the battery

management system (BMS) could accidently malfunction andapply current densities that are much larger than 2 mA cmminus2 Insuch a scenario could melting of the potassium-metal anode be apossibility Certainly this could take place in a K-K symmetricalcell since in such a cell the current density can be raised to anarbitrarily large value at which point the temperature rise in theK-metal foil could exceed the melting temperature resulting incatastrophic failure However this is not the case in a practicalfull-cell configuration Among cathodes for nonaqueous KIBss-KCO offers among the best high-rate capabilities reported todate (13) However even the s-KCO electrode (which is opti-mized for high-rate operation) is unable to operate effectivelyabove 2 mA cmminus2 current density as shown in SI Appendix FigS7 At a current density of 2 mA cmminus2 we predict maximumdendrite temperatures of about 40 degC based on our thermalmodeling (SI Appendix Fig S3) which is significantly below themelting point of potassium metal Other high-performing cath-odes (SI Appendix Table S1) for potassium-ion batteries are alsounable to operate at current densities above 2 mA cmminus2 Thus inour practical full-cell device we do not cycle and more impor-tantly even in the event of a BMS failuremalfunction we cannotcycle at rates that might lead to melting of potassium Furthersince the capacity of the s-KCO drops to almost zero at currentdensities such as 5 mA cmminus2 increasing current densities beyond2 mA cmminus2 for the s-KCO cathode would not aid in dendritehealing on the K-metal anodeThe full-cell tests in Fig 3 were conducted with sim08 M KPF6

in dimethyl ether (DME) as the electrolyte We also assembledK-K symmetric cells in an electrolyte of sim08 M KPF6 in DME toconfirm that the healing mechanism still applies in the ether-

based electrolyte SEM images of the cycled K-metal anodes atvarying current densities is shown in SI Appendix Fig S8 Thedendrite evolution with current density is very similar to theresults shown in Fig 1 for the carbonate-based electrolyte Atcurrent densities of sim2 mA cmminus2 a smooth surface indicative ofdendritic healing was observed From these results we concludethat the K-dendrite healing phenomena applies to both car-bonate as well as ether-based electrolytesTo summarize we have studied how K dendrites respond to

self-heat and compared our results to that of Li Testing ofsymmetric cells indicates that the self-heatingndashdriven healing ofdendrites is far more effective in K as compared to Li metal Thisenables dendrite healing to take place at an order-of-magnitudelower current density for K relative to Li Detailed DFT calcu-lations were used to explain the underlying reason for this be-havior It was found that the energy barriers for self-surfacediffusion in K are much lower than in Li metal which explainswhy K dendrites are easier to heal when compared to their Licounterparts Finally we show that self-heatingndashinduced healingof the K-metal anode can also be accomplished in a full-cellsetting which indicates that this healing concept has importantpractical implications

Materials and MethodsElectrode Preparation All procedures were carried out in an Ar-filled glo-vebox (MBraun Labstar) For the synthesis of s-KCO sim095 g of CoCl26H2Owas added into a solution containing sim20 mL of H2O sim55 mL of glyceroland sim25 g of urea at room temperature under stirring After stirring forsim2 h and making sure all of the chemicals were dissolved the mixture wastransferred to an sim100-mL Teflon-lined stainless-steel autoclave and reactedin a laboratory oven at sim180 degC for sim12 h The precursors (CoCO3) werecollected by centrifugation and washed with water and ethanol severaltimes and dried at sim80 degC overnight The as-obtained CoCO3 microsphereswere calcined at sim500 degC for sim4 h in air to obtain the Co3O4 microspheresThen sim3 mM of Co3O4 together with sim6 mM of KOH pellets were dispersedin sim1 mL of H2O After being homogeneously mixed the suspension wasdried at sim80 degC overnight Finally the solid mixture was preheated atsim350 degC for sim2 h and sim700 degC for sim10 h in an O2 environment to obtain theP2-type K06CoO2 microspheres After natural cooling the temperaturewas held at sim200 degC before the samples were collected in an argon-filledglovebox to prevent contamination from moisture in the air To prepare theworking electrode the as-synthesized P2-type K06CoO2 (s-KCO) super-Pcarbon black and polyvinylidene fluoride binder with a mass ratio ofsim511 were hand milled with an adequate amount of N-methyl 2-pyrroli-done into a homogeneous slurry using a pestle and mortar under an argonatmosphere The slurry mixture was coated onto an Al-foil current collectorand then dried at sim100 degC for sim12 h under vacuum The mass loading of theactive materials for the electrode was sim10 mg cmminus2

Electrochemical MeasurementsArbin BT2000was used to run all galvanostaticchargedischarge and platingstripping tests To assemble KK symmetric cellsand s-KCOK full cells 2032-type coin cells were used For the KK symmetriccells potassiummetal (995 trace-metal basis Sigma-Aldrich) was used bothas anode and cathode and sim08 M KPF6 in ECDEC (11 vol) was used as theelectrolyte For the s-KCOK full cell potassium metal was used as the anodewhile s-KCO (13) was used as the cathode with sim08 M KPF6 in DME as theelectrolyte KK-symmetric cells with sim08 M KPF6 in DME were also assem-bled The salt (KPF6) and solvents (EC DEC and DME) were purchased fromSigma-Aldrich The symmetric cells were cycled at various current densitieswith same cycle times (2-h charge 10-min rest 2-h discharge 10-min rest)For the s-KCOK cell galvanostatic chargedischarge cycles were performedover the voltage range from 17 to 375 V (vs KK+) The capacity was nor-malized to the active mass loading of s-KCO The current densities men-tioned are with respect to the K-metal anode Celgard 2340 were used as themembrane separator in all of our testing

Electrode Characterization The cells were opened in the Ar-filled glovebox toprocure the cycled K-metal electrode The electrode was washed with DECsolvent to remove any salt precipitates and dried The K electrode was thensealed in an Ar-filled container and transferred for further characterization Kdendrites were imaged using the Carl Zeiss Supra 55 field-emission scanningelectron microscope An aperture of sim30 μm and beam energy of sim5 kV was

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used The cross-section of the sample was obtained by gallium focused ion-beam (FIB) sputtering at sim30 keV using FEI VERSA three-dimensional dual-beam system Coarse sputtering was carried out at sim15 nA and final cleaningof the cross-section surface was carried out at sim1-nA beam current Ion-beam-deposited platinum at the top surface protects the sample surfacefrom damage due to sputtering at higher ion-beam currents Secondaryelectron images of the cross-section were obtained by incident electronbeam at sim10 keV and the sample at a sim52deg tilt SEI characterization wascarried out by using XPS Al Kα radiation (sim1486 eV) in a PHI 5000 Versaprobesystem (20)

First-Principles Calculations The Vienna ab initio simulation package programwas used for the first-principle DFT (28) calculations Core electrons weredescribed by the projector augmented-wave pseudopotentials (29) andexchange-correlation energies of electrons used the Perdew Burke andErnzerhof functional (30) for generalized gradient approximation Theplane-wave energy cutoff for different interfaces (for all of the calculations)was taken as 550 eV All ions were fully relaxed during the structural opti-mization until the total energy was converged within 10minus5 eV per cell andthe total energy was calculated with the linear tetrahedron method withBlochl corrections The electrode surfaces are modeled by five-layer slabs

The vacuum layer for the slab models is around 115 Aring Adsorption energiesand diffusion paths have been determined within a 4 times 4 geometry using a5 times 5 times 1 k-point grid For all adsorption calculations the atoms of the twouppermost surface layers have been allowed to relax in all directions (20)

We calculated the rate constants using a simple approximate form (24) of

transition-state theory (STST) in which kSTST =npv0 expminusEdiff

kBT

where np is

the number of possible exit directions v0 is the harmonic frequency Ediff isthe activation energy barrier for the diffusion process kB is the Boltzmannconstant and T is the temperature np = 4 due to the fourfold symmetry ofthe diffusion mechanism Here the rate constant has been calculated for theexchange mechanism and the harmonic frequency has been approxi-mated from a harmonic fit to the potential energy curve for the exchangemechanism (20)

Data Availability All relevant data are provided as Datasets S1ndashS16

ACKNOWLEDGMENTS This work was supported by the NSF (Award1922633) NK also acknowledges funding support from the John A Clarkand Edward T Crossan endowed Chair Professorship at the RensselaerPolytechnic Institute

1 S Hong et al Charge carriers in rechargeable batteries Na ions vs Li ions EnergyEnviron Sci 6 2067 (2013)

2 V Palomares et al Na-ion batteries recent advances and present challenges to be-come low cost energy storage systems Energy Environ Sci 5 5884 (2012)

3 X Wang et al Sodium-ion batteries Novel K3V2(PO4)3C bundled nanowires as su-perior sodium-ion battery electrode with ultrahigh cycling stability Adv EnergyMater 5 1500716 (2015)

4 I Sultana T Ramireddy M M Rahman Y Chen A M Glushenkov Tin-basedcomposite anodes for potassium-ion batteries Chem Commun (Camb) 52 9279ndash9282 (2016)

5 N Yabuuchi K Kubota M Dahbi S Komaba Research development on sodium-ionbatteries Chem Rev 114 11636ndash11682 (2014)

6 G Kresse et al Modeling microstructural effects on deformation resistance andthermal conductivity Phys Rev B Condens Matter Mater Phys 62 11169ndash11186(2000)

7 P Hohenberg W Kohn Inhomogeneous electron gas Phys Rev 136 B864ndashB871(1964)

8 A Eftekhari Z Jian X Ji Potassium secondary batteries ACS Appl Mater Interfaces9 4404ndash4419 (2017)

9 M Okoshi Y Yamada S Komaba A Yamada H Nakai Theoretical analysis of in-teractions between potassium ions and organic electrolyte solvents A comparisonwith lithium sodium and magnesium ions J Electrochem Soc 164 A54ndashA60 (2017)

10 K Lei et al High K-storage performance based on the synergy of dipotassium tere-phthalate and ether-based electrolytes Energy Environ Sci 10 552ndash557 (2017)

11 X Bie K Kubota T Hosaka K Chihara S Komaba A novel K-ion batteryHexacyanoferrate(ii)graphite cell J Mater Chem A Mater Energy Sustain 5 4325ndash4330 (2017)

12 C D Wessells S V Peddada R A Huggins Y Cui Nickel hexacyanoferrate nano-particle electrodes for aqueous sodium and potassium ion batteries Nano Lett 115421ndash5425 (2011)

13 T Deng et al Self-templated formation of P2-type K06CoO2 microspheres for highreversible potassium-ion batteries Nano Lett 18 1522ndash1529 (2018)

14 S Komaba T Hasegawa M Dahbi K Kubota Potassium intercalation into graphiteto realize high-voltagehigh-power potassium-ion batteries and potassium-ion ca-pacitors Electrochem Commun 60 172ndash175 (2015)

15 Z Jian Z Xing C Bommier Z Li X Ji Hard carbon microspheres Potassium-ionanode versus sodium-ion anode Adv Energy Mater 6 1ndash5 (2016)

16 Z Jian W Luo X Ji Carbon electrodes for K-ion batteries J Am Chem Soc 13711566ndash11569 (2015)

17 W Zhang J Mao S Li Z Chen Z Guo Phosphorus-based alloy materials for ad-vanced potassium-ion battery anode J Am Chem Soc 139 3316ndash3319 (2017)

18 Y Lu Z Tu L A Archer Stable lithium electrodeposition in liquid and nanoporoussolid electrolytes Nat Mater 13 961ndash969 (2014)

19 L Li et al Self-heating-induced healing of lithium dendrites Science 359 1513ndash1516(2018)

20 P Hundekar et al Exploiting self-heat in a lithiummetal battery for dendrite healingEnergy Storage Materials 20 291ndash298 (2019)

21 H Sano H Sakaebe H Senoh H Matsumoto Effect of current density on mor-phology of lithium electrodeposited in ionic liquid-based electrolytes J ElectrochemSoc 161 1236ndash1240 (2014)

22 P J Feibelman Diffusion path for an Al adatom on Al(001) Phys Rev Lett 65 729ndash732 (1990)

23 G Henkelman B P Uberuaga H Joacutensson Climbing image nudged elastic bandmethod for finding saddle points and minimum energy paths J Chem Phys 1139901ndash9904 (2000)

24 A F Voter Classically exact overlayer dynamics Diffusion of rhodium clusters onRh(100) Phys Rev B Condens Matter 34 6819ndash6829 (1986)

25 M Jaumlckle A Groszlig Microscopic properties of lithium sodium and magnesium batteryanode materials related to possible dendrite growth J Chem Phys 141 174710(2014)

26 H Brune Microscopic view of epitaxial metal growth Nucleation and aggregationSurf Sci Rep 31 125ndash229 (1998)

27 H Gao B Guo J Song K Park J B Goodenough A composite gel-polymerglass-fiber electrolyte for sodium-ion batteries Adv Energy Mater 5 1ndash8 (2015)

28 W Kohn L Sham Self-consistent equations including exchange and correlation ef-fects Phys Rev 140 A1133ndashA1138 (1965)

29 G Kresse J Furthmuumlller Efficient iterative schemes for ab initio total-energy calcu-lations using a plane-wave basis set Phys Rev B Condens Matter 54 11169ndash11186(1996)

30 J P Perdew K Burke M Ernzerhof Generalized gradient approximation madesimple Phys Rev Lett 77 3865ndash3868 (1996)

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