Stability and surface diffusion at lithium-electrolyte interphases withconnections to dendrite suppression

Yalcin Ozhabes,1, a) Deniz Gunceler,1, b) and T. A. Arias1

Department of Physics, Cornell University, Ithaca, New York, 14853, USA

This work presents an ab initio exploration of fundamental mechanisms with direct relevance to dendriteformation at lithium-electrolyte interfaces. Specifically, we explore surface diffusion barriers and solvatedsurface energies of typical solid-electrolyte interphase layers of lithium metal electrodes. Our results indicatethat surface diffusion is an important mechanism for understanding the recently observed dendrite suppressionfrom lithium-halide passivating layers, which were motivated by our previous work. Our results uncoverpossible mechanisms underlying a new pathway for mitigating dendridic electrodeposition of lithium on metaland thereby contribute to the ongoing efforts to develop stable lithium metal anodes for rechargeable batterysystems.

Keywords: Density Functional Theory, Lithium battery

I. INTRODUCTION

Development of more efficient energy storage technolo-gies is needed to build a more sustainable future. Un-derstanding physical processes at the atomic scale onelectrode-electrolyte interfaces is an important interme-diate step towards realizing this goal. Motivated by thedesire to help enable many new applications, rangingfrom grid storage to long-ranged electric cars, researchershave also been using the tools of ab initio electronicstructure to help develop better rechargeable lithiumbatteries.1–18

The current state-of-the-art in rechargeable batteries islithium-ion technology, where the presence of a graphiticanode host results in deadweight (carbon) to be car-ried along with the battery. Metallic anodes would bea better choice due to their increased energy density(∼ 3860 mAhg−1),19,20 but they suffer from localizednucleation while charging and form needle-like structurescalled dendrites.20–22 Despite many years of concentratedeffort, there are still many unanswered questions aboutthe underlying physical mechanisms of lithium dendriteinitiation and growth. This is partly due to the com-plex nature of the passivation layer, also called the solid-electrolyte interphase (SEI), that forms when the metal-lic electrode comes in contact with the electrolyte.23–25

Existing ideas and models on dendritic electrodepositionof lithium suggest that chemical inhomogeneities in theSEI layer result in spatially varying rates of deposition onthe surface, which then lead to instabilities because anyprotrusion tends to concentrate electric field lines.26–32

Recent experiments have shown that the compositionof the SEI layer has a dramatic effect on the performanceof the battery cell. Based on our previous theoreticalwork,2,3 Tu et. al. have managed to suppress dendritegrowth in liquid and nanoporous electrolytes by passivat-ing the surface of the anode with lithium-halides.33 Like-

a)ao294@cornell.edu; Contributed equally to this workb)dg544@cornell.edu; Contributed equally to this work

wise, researchers from Stanford have succeded in design-ing an interfacial layer from carbon nanospheres whichimproves cycling efficiency.19 Understandably, these re-sults and many others stimulate a strong interest instudying the fundamental physical mechanisms withinthe SEI layer, and to date, many studies have investi-gated the bulk properties of these materials (e.g. bulkdiffusion of Lithium).10–12

The rich physics at the interface between anode andliquid electrolyte is much less understood, though therehave been very promising new developments in this fieldas well.2,4,19,34 Very recently, Jackle and Groß have pub-lished a comparative study of metallic Lithium, Sodiumand Magnesium surfaces.4 Their DFT calculations sug-gest that surface diffusion is significantly faster on mag-nesium metal than on lithium metal, which may be im-portant to understand why lithium forms dendrites whilemagnesium does not. While this work is very important,we believe (and the authors themselves also point out)that more investigation in this area is needed becausethat work does not address the presence and the effect ofthe electrolyte and, critically, the fact that metallic elec-trodes do not present pure surfaces to the electrolyte butrather complex non-metallic passivating layers known asSEI.

In this paper, we focus on the physical processes onthe surfaces of various SEI materials for metallic lithiumanodes. In particular, we provide an explanation of thephysical mechanisms by which halogen additives (espe-cially F−) to the electrolyte suppress dendrites and im-prove cycling efficiency33,35–39. To this end, we utilizedensity functional theory to calculate surface cleavageenergies and surface diffusion barriers for the most com-monly reported SEI materials in the literature,40–42 andthen use these results to help understand the experimen-tally observed trends. Our hope is that such understand-ing will accelerate the development of novel anode ma-terials to improve battery performance. Our results sup-port the growing belief2–4,27,33 that anode materials withhigh surface energy and surface mobility are desirable.We also detail our previous claim,2 recently supported byexperiment,33 that Lithium-halide SEI layers have these

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FIG. 1. The percentage error in DFT lattice constants, plot-ted as a function of the experimental lattice constants. Thesolid black line represents exact agreement of theory and ex-periment. The dashed black lines represent ±2.5% deviationsfrom experiment.

desirable properties and that they are effective in sup-pressing dendrite growth on metallic lithium anodes.

II. COMPUTATIONAL METHODS

To perform first principles DFT calculations, we usethe open source JDFTx software43 which is based on thedirect minimization of an analytically continued total en-ergy functional.44 Ultra-soft pseudopotentials45 from theGBRV library46 are generated using the Vanderbilt pseu-dopotential code.47 To account for electronic exchangeand correlation, we use the PBE flavour of generalizedgradient approximation.48 Throughout this methods sec-tion, we work in standard atomic units; i.e. bohr (B)for distances and hartree (H) for energies. All results inthe sections below will be presented in more familiar SIunits.

For the Brillouin zone sampling of bulk units, we usea k-point grid of 4× 4× 4 which we determined by con-verging the total energy to a level of 0.1 mH. The energycut-off for the plane wave basis was 20 Hartree which wasalso consistent with the same convergence threshold. aThe nuclei were relaxed until the root mean square of theforces were below 0.1 mH/Bohr.

To test our choice pseudopotentials as well as othercalculation parameters, we calculated lattice constantsof various Lithium SEI materials. The results, plottedin figure 1, were satisfactory. (It is our belief that DFThas the largest error in the lattice constant of LiOH be-cause LiOH has a layered structure where long-rangeddispersion interactions play an important role.)

To calculate the surface formation energies, we createslabs varying in size from compound to compound. To

determine the thickness of each slab, we take the numberof layers that are necessary to converge the surface en-ergy to a level of 0.1 mH per unit cell. The vacuum layer(or solvent for fluid calculations) between the slabs is 20Bohr, allowing us to collapse the three dimensional k-point grid to a planar grid. The center layer is held fixedand the rest of the slab is relaxed with the same conver-gence criteria mentioned for the bulk calculations. Whereneeded, we use a truncated Coulomb kernel50 along theslab axis to prevent spurious electrostatic interactions be-tween slabs. Then we calculate surface formation ener-gies by taking the difference of the slab energy and theenergy of equal number of formula units in the bulk andthen dividing by the surface area.

Esurf =1

2A(Eslab − Ebulk) (1)

To study surface diffusion, we consider the hoppingprocess of an adatom that moves from one equilibriumposition to the other and whose rate depends on the en-ergy barrier along that path. We determine the diffusionpath by comparing the binding energies of the adatom atthe high symmetry points along the surface, letting theadatom relax in the direction parallel to the slab nor-mal. Once we determine the endpoints of the diffusionpathway, we carry out a series of intermediate calcula-tions by putting the adatom in a series of sites equallyspaced on the line connecting the two binding sites. Forthese calculations, the entire slab relaxes except the mid-dle layer, while the adatoms are restricted to stay on theplane perpendicular to the diffusion path. To minimizethe interactions between periodic images of adatoms, weuse 3×3 supercells.

Standard plane-wave electronic structure methodshave difficulty handling interfaces between battery elec-trodes and the electrolyte,51 largely due to the needto thermodynamically sample the configuration spaceof the liquid electrolyte. As a result, there have beenfewer ab inito investigations of lithium metal anode-electrolyte interfaces compared to, for example, the inves-tigations of the bulk properties of lithium intercalationcompounds.5–9,18

In principle, one can sample the configuration space ofthe electrolyte using ab initio molecular dynamics,17,34

and further accelerate the calculation using hybrid tech-niques such as QM/MM.52 However, calculation of freeenergies with these methods are difficult and these ap-proaches often do not easily scale to the large number ofmaterials we want to study. An alternative approach isthat of continuum solvation models,3,53,54 where the in-dividual molecules in the liquid electrolyte are replacedwith a continuum field, and thus free energies can becomputed with a single density-functional calculation.Fortunately, recent developments in continuum solvationmodels3,53–55 have made it feasible to efficiently studythe solid-liquid interfaces for a large number of mate-rial/electrolyte combinations.

In this work, we use a nonlinear polarizable continuum

3

FIG. 2. From left to right: rocksalt (Li-halides), anti-fluorite (Li2O), zabuyelite (Li2CO3) and LiOH. Pictures were madeusing VESTA.49

model which models the electrolyte environment as a con-tinuous field of interacting dipoles.3 This approach canalso capture dielectric saturation effects, which are im-portant near the surfaces of highly polar materials suchas the Lithium SEI surfaces we consider here. In thisnonlinear continuum model, the density profile of theelectrolyte (s(~r)) is computed self-consistently from theelectron density of the surface slab (n(~r)) as

s(~r) = erfcln(n(~r)/nc)

σ√

2, (2)

where σ (= 0.6) determines the width of the transi-tion region that is set to be resolvable on the FFT gridand nc is a (solvent-dependent54) critical electron densityvalue that determines the location of the solute-solventinterface. For the non-electrostatic terms in the surface-electrolyte interaction, (such as cavitation entropy andlong-ranged van der Waals) we make use of the effec-tive surface tension approximation,53 which modifies thebulk (macroscopic) surface tension of the electrolyte toapproximate these contributions.

III. SURFACE ENERGIES AND DIFFUSION

The formation of dendrites represents an increase insurface area. The thermodynamic perspective would thusindicate that SEI materials with greater surface energiesshould offer greater dendrite resistance. Furthermore,dendrite nucleation may be driven by cracks in the SEI,20

so that a stable SEI with a high surface formation energywould offer resistance to this mechanism as well.

However, the kinetics during electrodeposition mightvery well drive the system far from equilibrium. There-fore, one must also consider the mechanism by whichsurface energy would tend to suppress dendrites, namelysurface diffusion. Following the same train of thought,one expects that materials with fast surface diffusion, forexample those with small diffusion barriers for adatoms,would be less likely to form dendrites.

This section is broken into four parts: In the first part,we obtain order-of-magnitude estimates for those diffu-sion barrier heights which would make diffusion an im-portant process during electro-deposition. We find that,

indeed, most SEI materials in the following sections dohave diffusion barriers in the relevant range. In the sec-ond part, we investigate a binding-site switching mecha-nism that results in unusually low diffusion barriers forsome lithium halides. In the third part, we summarizeour results for the surface energies and diffusion barrierheights for many candidate lithium SEI materials, anddiscuss the trends we observe. We investigate multi-ple classes of materials: rocksalt halides (LiF, LiCl, LiI,LiBr), layered (LiOH) and multivalent (Li2O, Li2CO3).In the final part of this section, we present an intriguingcorrelation between our diffusion barrier results and theexperimentally observed time to short circuit.

A. Comparing rates of deposition and diffusion

cat: rates/main.tex: No such file or directoryIt is important to know whether, at experimental con-

ditions, surface diffusion can be competitive with elec-trodeposition. We now probe this question with a simpleorder-of-magnitude analysis. We assume that diffusion isa random walk where the hop rate is given by the Arrhe-

nius equation R = R0e−∆E

kT , where kT is thermal energy,∆E is the diffusion barrier and R0 is a base attempt raterelated to the material’s phonon frequencies. To deter-mine the balance between surface diffusion and deposi-tion, let qe be the charge of the arriving ions, J be thecurrent density and a be the dimension of the surface unitcell. Under these conditions, we expect that dendritesform when the local current density becomes high enoughto overcome surface diffusion, specifically when the meandistance traveled by a diffusing atom (d(t) =

√Rta) in

the (mean) time interval between two deposition eventsat the same site (t = qe/

(Ja2

)) is smaller than the grow-

ing dendrite tip. In this simple scenario, the critical bar-rier at which the rate of electrodeposition equals the rate

of diffusion, is given by ∆Ec = 2kT ln

[1d

√R0qeJ

].

Experiments typically use current densities on the or-der of 1.0 mA/cm2, but owing to the highly non-uniformrate of deposition on the surface, especially near anyprotrusion, the relevant current densities can be ordersof magnitude higher. Indeed, measurements of lithium

4

dendrite growth56,57 have yielded the current densitiesat the dendrite tip in the 100− 1000 mA/cm2 range. Asfor R0, following previous studies,4 we assume a standardphonon frequency of ∼ 10 THz. For any microscopic pro-trusions in the order of 1-100 micrometers, we see thatthe critical diffusion barriers that result in competitiverates are of a few tenths of an electron volt. At 100mA/cm2 current density the critical barrier for a protru-sion of size 5 micrometers is approximately 0.1 eV, whichwould mean that for such a system diffusion on a surfacewith a barrier above this value would be too slow to miti-gate the growth of dendrites regardless of themodynamicunfavourability. In fact, we do find that surface diffusionbarriers on typical SEI materials are in this range andso a detailed study of surface diffusion is necessary forunderstanding dendritic processes. Finally we note that,one must take this very simple analysis with care, asquantitative predictions other than order-of-magnitudeestimates are likely to be beyond its capabilities.

B. Change in the binding sites of Li-halides

Below we find that of all the SEI materials we havestudied, the lithium-halides are the most promising fromthe above point of view, with diffusion barriers rangingfrom 0.03 to 0.15 eV. The physical reason for these lowbarriers are as follows. Even though the bulk structureof all the lithium-halide materials we consider here is thesame (rocksalt), the binding site for adatoms changes asthe anion size increases. For halides with small anions (Fand Cl) the binding site for the adatom is directly abovethe anion (“anion site”), and in the transition state fordiffusion, the adatom sits between two anions and twocations (“in-between site”). See figure 3 (a) for an il-lustration. On the contrary, for large anions, the roles ofthese two sites are reversed and the binding site sits at the“in-between site” (slightly off-center) while the transitionstate has the adatom at the “anion site”. (See figure 3(b)) Now, the diffusion barrier is equal to the energy dif-ference between the binding site and the transition-site.Because of this, halide surfaces that are in the neighbour-hood of this change (LiCl and LiBr), where the sign ofthis difference changes, have very low diffusion barriers.On the other hand, LiF, which is far from this change,have a relatively larger barrier, but still small comparedto non-halide SEI materials.

The reason for the change in the binding site with an-ion size is steric interactions. For the two smaller halo-gens, the in-between site is too close to the two cations,which makes it energetically less favorable. However, asthe anions get bigger, the distance from the in-betweensite to the cations increases and the adatom prefers toplace itself in this halfway point where it can also inter-act with two anions simultaneously. Finally we note thateven though the binding site changes as one goes fromLiCl to LiBr, the diffusion path remains the same.

C. Predictions for battery performance

Figure 4 summarizes all of our results, not only for thediffusion barriers for all of our surfaces (including halides,as well as the hydroxide, carbonate and oxide) but alsofor the corresponding surface energies. The data showthat the presence of the electrolyte has significant impact,especially on the surface diffusion barriers. The surfaceenergies of all ionic crystals go down (often by 5− 15%),owing to the strong electrostatic interaction between thesurface and the solvent. The surface diffusion barriers,however, change more dramatically, by up to as much asa factor of 2. The diffusion barrier for all materials butone (Li2CO3) decrease when the electrolyte is includedin the calculation. These changes in diffusion barriers aresignificant because the rate depends exponentially on thebarrier height and because these energy changes are onthe order of several kT (which, at room temperature isapproximately 0.025 eV).

The data also suggest a strong positive correlation be-tween surface energies and surface diffusion barriers formost, but not all, SEI materials. The most severe trendbreakers are Magnesium metal (black hexagon), lithiummetal (black plus) and LiOH (blue square). Of these,the metals break the trend likely due to their very dif-ferent electronic structure, where Li is not in an oxidized(positively charged) state. LiOH likely breaks the trendbecause its layered structure and large intra-layer dis-tance cause it to have a very low surface energy alongthe z-axis.

Li2CO3, present in the SEI layer formed in the pres-ence of many commonly used electrolytes (propylene car-bonate, ethylene carbonate and others), is a less severetrend breaker. It has low surface energy and high dif-fusion barrier, both of which are undesirable quantitiesin a SEI material. Lithium halides, on the other hand,have lower surface diffusion barriers than Li2CO3 whilealso having either equal or higher surface energies. Ourhypothesis, first put forth in an earlier work,2 is thatthe low barriers may help explain the experimentallyobserved phenomenon33 in which the formation of anlithium-halide SEI is effective in suppressing dendrites.We further hypothesize that these mechanisms may berelevant not only in experiments where the electrolytehas been seeded with a Li-halide crystal,33 but also in ex-periments where other additives containing fluorine (e.g.hydrofloric acid or fluoroethylene carbonate)37–39 havebeen used to improve stability and suppress dendridicgrowth.

As for LiOH and Li2O, which are also occasionally ob-served in experiments,33 LiOH appears to be undesirablebecause of its low surface energy, whereas Li2O appearsto be undesirable because of its high diffusion barrier.However, the superiority of Li-halides over LiOH/Li2Ois not as conclusive because the halides are superior inonly one of the two indicators.

Finally, among halides, figure 4 shows that the stabil-

5

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0.00 2.88 5.760.00

2.88

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-0.9 eV

-0.8 eV

-0.6 eV

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0.0 eV

FIG. 3. Surface binding energies versus its binding site. LiF is in the left, LiBr is on the right. The lowest energy binding sitesare indicated with a green circle and the diffusion path is as shown with the green arrows. The black cross markers indicateour data points, the whole contour plot is generated using symmetries of the surface and cubic interpolation.

0.0 0.1 0.2 0.3 0.4 0.5Diffusion Barriers (eV)

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LiF in vacuum LiCl in vacuum LiBr in vacuum LiI in vacuum LiOH in vacuum Li2O in vacuum Li2CO3in vacuum LiF in CH3CN LiCl in CH3CN LiBr in CH3CN LiI in CH3CN LiOH in CH3CN Li2O in CH3CN Li2CO3 in CH3CN Li metal in vacuum Na metal in vacuum Mg metal in vacuum

FIG. 4. The surface diffusion barrier (x-axis) and the sur-face energy (y-axis) of various Lithium SEI materials. Hol-low data points represent surfaces in contact with vacuumwhereas filled data points represent the same surfaces in con-tact with the electrolyte (CH3CN, modeled with a polarizablecontinuum model). The black markers indicate the bare metalcalculations by Jackle and Groß.4

ity (i.e. surface energy) decreases as one goes down thecolumn of the peridic table, from F to Cl to Br to I. Thisis likely due to some combination of the decrease in theelectronegativity of the ions (which weakens the strengthof the ionic bonds) and the steric interactions increasingthe size of the lattice (which decreases the electrostaticstability of the lattice). Decreased stability is an unde-sirable property in battery materials as it tends to lower

the voltage at which the surface breaks down.D. Comparisons with measurements of short-circuit time

From a practical perspective, the ultimate figure ofmerit is the length of time before the battery short cir-cuits. Figure 5 plots this quantity, as measured by Lu,Tu, and Archer 33 in a symmetric cell, as a function of ourcalculated diffusion barriers. Because diffusion is an acti-vated process, we choose a logarithmic scale for the verti-cal axis. Moreover, for Li2CO3, Li2O and LiOH there areno separate data, instead, for this single measurementthat we have, where there are no halide additives, thesurface of the anode contains spatially-varying fractionsof all three of these species. The observed breakdown islikely due to the most-dendrite prone among these threematerials, and thus represents a lower bound for the life-time of each of the materials. Due to the notably lowerbarrier which we calculate for the hydroxide, we stronglysuspect that the observed cycle lifetime is associated ei-ther with the carbonate or the oxide. Finally, becausethe barriers we calculate for these latter two materialsare so close, we can not determine unambiguously whichof these two materials fails first. Accordingly, the figureincludes the experimental lifetime twice, once for eachone of these two materials.

The data in figure 5 show a clear linear trend consistentwith an Arrhenius-like behaviour. However, the slopedoes not appear to be exactly unity, demonstrating theimportance of other factors beyond the diffusion barrier.Additionally, one point, lithium fluoride, appears to bean outlier, requiring additional explanation. LiF has thehighest barrier among the halides but the second longesttime to short circuit. We suspect that this deviation

6

0 2 4 6 8 10 12Diffusion Barriers (in units of kT)

100

101

102

Tim

e to

sho

rt c

ircui

t (ho

urs)

LiF in CH3CN LiCl in CH3CN LiBr in CH3CN LiI in CH3CN Li2O in CH3CN Li2CO3 in CH3CN

FIG. 5. Battery short circuit times (from Lu, Tu, andArcher 33) plotted as a function of the surface diffusion bar-rier. The green line is the best fit line, excluding the oneoutlier. The blue line shows has the slope for an Arrheniusprocess.

from the trend may be tied to it having the most stablesurface among the halides (see figure 4), thus affordingit additional stability. Lithium fluoride’s high surfaceenergy derives not only from the high electronegativityof the fluoride atom, but also from its very small latticeconstant and surface area per formula unit. (LiCl, thesecond smallest halide, has a surface area ∼ 60% largerthan LiF.)

While it is not suprising that a single quantity (thediffusion barrier) is not enough to fully explain the ex-perimental lifetimes, we find it encouraging that thereis such strong correlation between diffusion barriers andthe experimental lifetimes.

IV. CONCLUSION

Recent experiments, prompted by earlier theoreticalwork,2 confirm the success of Lithium-halide additivesin suppressing dendrite growth,33,35,36 consistent withthe findings of previous experiments with other fluoride-containing electrolyte additives.37–39 Prompted by this,we set out to explore more deeply the mechanisms ofdendrite suppression at the atomic level.

We performed density-functional calculations to deter-mine the surface energies and the surface diffusion barri-ers of lithium solid-electrolyte interphase materials. Ourcalculations show that a lithium-halide SEI layer resultsin increased stability of the surface (higher surface en-ergy) and faster diffusion along the surface (lower sur-face diffusion barrier for adatoms), both of which arelikely important in explaining the above phenomenon.Furthermore, our results provide an explanation for theunusually low diffusion barries on halide surfaces, trac-

ing this effect back to a change in the binding site. Thischange in binding site, in turn, is driven by the trendsin the electronegativity and the sizes of the anions inthe halide crystals. Finally, we observe a clear, approx-imately Arrhenius correlation between battery time toshort circuit and surface diffusion barriers, that can beused as a guide to suggest new material systems to fur-ther enhance stability against dendrite formation.

This work, which focused on solid-electrolyte inter-phase materials, leaves many directions yet to be ex-plored. In mitigating dendrite growth, multiple diffu-sion pathways are available, including surface diffusion,bulk diffusion, and diffusion at the SEI-metal interface.A study similar to this one, but for the SEI-metal inter-face, would be illuminating. Finally, with the potentialimportance of surface diffusion established, results fromab initio studies should be incorporated into macroscopicmodels of dendrite growth.

ACKNOWLEDGMENTS

The authors would like to thank Prof Lynden Archer,Prof Ersen Mete, Mukul Tikekar, Pooja Nath and Sne-hashis Choudhury for encouragement and useful discus-sions, and Christine Umbright for her help in writing thismanuscript. This work was supported as a part of theEnergy Materials Center at Cornell (EMC2), an EnergyFrontier Research Center funded by the U.S. Departmentof Energy, Office of Science, Office of Basic Energy Sci-ences under Award Number de-sc0001086.

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