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Lithium Diffusion in Graphitic CarbonKristin Persson,*,†,‡,z Vijay A. Sethuraman,†,§,z Laurence J. Hardwick,†,^,z Yoyo Hinuma,‡,#Ying Shirley Meng,‡,# Anton van der Ven, ) Venkat Srinivasan,† Robert Kostecki,† andGerbrand Ceder‡

†Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, ‡Massachusetts Institute of Technology,77 Mass Avenue, Cambridge, Massachusetts 02139, §Brown University, 182 Hope Street, Providence, Rhode Island 02906,^University of St. Andrews, North Haugh, St, Andrews, Fife KY16 9ST, Scotland, U.K., #University of California San Diego,Atkinson Hall 2703, La Jolla, California 92093, and )University of Michigan, 2300 Hayward Street, Ann Arbor, Michigan 48109

ABSTRACT Graphitic carbon is currently considered the state-of-the-artmaterialfor the negative electrode in lithium ion cells, mainly due to its high reversibilityand low operating potential. However, carbon anodes exhibit mediocre charge/discharge rate performance, which contributes to severe transport-induced sur-face structural damage upon prolonged cycling and limits the lifetime of the cell.Lithium bulk diffusion in graphitic carbon is not yet completely understood, partlydue to the complexity of measuring bulk transport properties in finite-sizednonisotropic particles. To solve this problem for graphite, we use the Devanathan-Stachurski electrochemical methodology combined with ab initio computationsto deconvolute and quantify the mechanism of lithium ion diffusion in highlyoriented pyrolytic graphite (HOPG). The results reveal inherent high lithium iondiffusivity in the direction parallel to the graphene plane (!10-7-10-6 cm2 s-1), ascompared to sluggish lithium ion transport alonggrainboundaries (!10-11 cm2 s-1),indicating the possibility of rational design of carbonaceous materials and com-posite electrodes with very high rate capability.

SECTION Energy Conversion and Storage

W hile commercial lithium ion batteries can consistof multiple cathode chemistries, a vast majorityof them use graphitic carbon as the negative-

electrode material because of its low cost, low operatingpotential, high capacity, high reversibility, and remarkablestructural and interfacial stability.1 The use of graphitic elec-trodes as ion-intercalation negative-electrode hosts for re-chargeable electrochemical power sources was suggestedfirst by Rudorff and Hofmann2 in 1938, and many scientistshave subsequently investigated them.3,4 Lithium diffusion ingraphitic carbon is not yet completely understood due toa lack of reliable theoretical and experimental methods.Impedance spectroscopy,5-8 potentiostatic intermittent titra-tion technique (PITT),9 and standard electrochemical meth-ods9,10 have been used to gauge the diffusion coefficient indifferent types of graphitized carbons in composite electrodesand to determine their overall rate performance in lithium ionsystems. However, the electrochemical response of a compo-site electrode consists of multiple components and, in princi-ple, fails to resolve the highly inherent anisotropic nature oflithium diffusion in graphitic carbon. Thus, the basic electro-chemical properties of graphite becomes convoluted with theparameters of mass and charge transfer involving par-ticle contact resistances, surface films, and side reactions.Moreover, the analysis of the experimental data is extre-mely complicated, and consequently, the lithium ion trans-port rates reported for various types of composite graphite

electrode architectures vary in the literature from 10-6 to10-16 cm2 s-1.5-12

In this Letter, we present a combination of electrochemicalmeasurements of lithium ion permeation and first-principlescalculations to clarify and quantify lithium ion diffusion inHOPG. The objective of this work is to (i) determine thediffusion paths and lithium ion transport parameters ingraphite and (ii) provide rational guidelines for design andsynthesis of high-rate graphitic materials.

In order to directly measure Li diffusion in graphite,a HOPG foil was used as a membrane in a Devanathan-Stachurski-type two-compartment cell.13 The HOPG usedwas made of single-crystal graphitic cuboids (i.e., graphenedomains) with an angular spread of the c-axes of the crystal-lites of less than 1!. The graphene basal planes are exposed atthe surface of the HOPG foil, whereas the plane edges are atthe foil perimeters. The HOPG membrane served as a com-mon working electrode for both compartments “A” and “B”(see Figures 1 and2), whichwere filledwith 1.2MLiPF6 inEC/EMC (1:1) electrolyte and equipped with two sets of metalliclithium reference and counter electrodes. Further details ofthe materials and cell setup are described in the Supporting

Received Date: February 10, 2010Accepted Date: March 16, 2010

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Information. Li permeation measurements were carried outwith two types of HOPGmembranes. In the first experiment,a thin and flat 20 !m thick HOPG membrane was used (seeinset, Figure 1), and in the second case, a 3 mm thick HOPGmembrane with two partial and overlapping holes (dia-meter = 1 mm, 0.5 mm apart) carefully drilled from theopposing sides of the membrane was used (see inset,

Figure 2). The objective of these experiments was tomeasurethe lithium ion diffusion perpendicular to the graphene layers(i.e., diffusion across thebasal plane; see Figure 1) andparallelto them (i.e., diffusion along the basal plane; see Figure 2).

The surface of the HOPG membrane in compartment Awas polarized galvanostatically with an applied current of25 !A cm-2, which enabled constant-rate lithium insertioninto the graphite, while the other side of the membrane incompartment B was maintained at a sufficiently high anodicpotential (3 V versus Li/Li!) to immediately oxidize all Li thatmoved across and appeared at the B side of the HOPGmembrane. The time delay between the lithium insertion atthe A side and the anodic current response at the B side of themembrane constitutes a direct measurement of the transportrate of lithium through HOPG. While the electrochemicalprocesses at the surface of the HOPGmembrane in compart-ment A also involve formation of the solid electrolyte inter-phase (SEI), its effect on the current response in compartmentB is negligible.

The anodic current response for the thinHOPGmembraneis shown in Figure 1. Because only basal planes were exposedto the electrolyte, lithium ions could diffuse through HOPGsolely between the graphene crystallites and then toward theB side along the grain boundaries. A small amountof Li! couldalso penetrate into the HOPG structure via defects and stepedges at the surface of the graphene planes, but their con-tribution to the transport mechanism in crystalline graphiteis insignificant. The current threshold in compartment B isobserved after !17 h, followed by a steep rise to reach aplateau after!80 h. Interestingly, only a small fraction of theLi! inserted in the HOPG membrane was detected on the Bside. The missing lithium most likely diffused into the part ofthe membrane that was not exposed to the electrolyte. Thelength and breadth of the HOPG membrane are much larger(a few centimeters) than its thickness (!60 !m). Becauseof this, it would take a very long time for all of the lithium(that was intercalated into the HOPG) to deintercalate onside B. Since the rise time (of the chronoameperometricresponse on side B) and the steady value of the current wereof interest, the experiment was not performed for such largetime scales.

The thick HOPG membrane with two partial and over-lapping holes offered two types of entry sites for lithium thatis, interplanar and graphene domain boundaries (Figure 2,inset). In this case, the current response in compartment Bwasobservedafteronly170 s to reach aplateauafter!20min(Figure 2). Theobservednearly 100%Coulombic efficiencyofredox processes in A and B compartments indicates thatalmost all Li! inserted in this HOPG membrane reached theother side of the membrane.

Using the chronoamperometric response obtained in com-partment B in both experiments together with Fick's secondlaw for the diffusion equation, along with the appropriateinitial and boundary conditions for the experimental setup(see Supporting Information), the lithium ion diffusion coeffi-cients in the directions perpendicular and parallel to thegraphene planes were estimated. Thus, the average diffusioncoefficient of lithium ions in graphite was determined to be8.7 ((0.4) " 10-12 cm2 s-1 in the direction perpendicular

Figure 1. The chronoamperometric response obtained on theHOPG membrane on Cell B in the basal-plane configuration. Thecurrent corresponds to the deintercalative flux of lithium ionsfrom the HOPG membrane into the electrolyte. Inset: Schematicshowing the diffusion pathway of lithium ions in the basal-planeconfiguration. A constant intercalative flux of lithium ions wasimposed on the electrolyte/HOPG interface in compartment Awhile a constant potential of 3 V vs Li/Li! was maintained on theHOPG/electrolyte interface in compartment B.

Figure 2. The chronoamperometric response obtained on theHOPG membrane in compartment B in the edge-plane configura-tion. The current corresponds to the deintercalative flux of lithiumions from the HOPG membrane into the electrolyte. Inset: Sche-matic showing the diffusion pathway of lithium ions in the edgeplane configuration. A constant intercalative-flux of lithium ionswas imposed on the electrolyte/HOPG interface in compartment Awhile a constant potential of 3 V vs Li/Li! was maintained on theHOPG/electrolyte interface in compartment B.

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to grapheneplanes inHOPGand4.4 ((0.1)"10-6 cm2 s-1 inthe direction parallel to graphene planes. The respective errormargins were obtained by setting the 95% confidence on theestimated parameters during the parameter estimation rou-tine.

There have been several ab initio studies on the lithium-graphite system,14-17 but the chemical diffusion coefficient oflithiumas a function of concentration has not been calculatedfromfirst principles. Verbruggeetal.10 treated theLi diffusivityin graphite within the 1-D continuum transport framework,and Toyoura et al16,17 recently calculated the Li diffusivity inordered LiC6, assuming a single vacancy or interstitial diffu-sion mechanism. In order to calculate a general concentra-tion-dependent lithium diffusivity in graphite from firstprinciples, without making any assumptions regarding thediffusionmechanism,we use the cluster expansionmethod18

to model partially disordered states at finite temperatures.Such an approach has, for example, been used successfully toelucidate the lithium ion diffusion in LixCoO2 and LixTiS2.

19,20

It has been shown that the lithium ion intercalation in graphiteoccurs in stages, where stage n contains (n- 1) empty layersbetween each lithium-filled layer.21,22 We chose to focus ourinvestigation on stage I and stage II compounds as thesephases dominate the lithium-graphite phase diagram23 (aswell as the concentrations that resulted inside of the HOPGmembrane in both experiments) and will therefore provide agood representation of lithium motion in graphite as a func-tion of concentration. Thus, the energies of 63 stage I andstage II structures of different lithium concentrations and Liarrangements were calculated through the generalized gradi-ent approximation24 to density functional theory as imple-mented in the Vienna Ab Initio Simulation Package (VASP).25

Projected augmented wave pseudopotentials26,27 were used,with an energy cutoff of 400 eV. Both internal coordinates andunit cell lattice parameters were fully relaxed, and the Bril-louin zones were sampled with a gamma-centered mesh sothat the energy convergence with respect to the k-pointsampling was better than 5 meV/6C. Further details andmotivations regarding the calculations can be found in theSupporting Information. The resulting energies were used tofit a cluster expansion, which was employed to calculate thelithium-graphite phase diagram through Monte Carlo simu-lations and benchmarked against experiments.23 The fulldetails of these calculations and extended analyses of thelithium-graphite thermodynamics will be published else-where.28

Kinetic Monte Carlo simulations were employed to calcu-late lithium diffusion coefficients as a function of lithiumconcentration in stage I and stage II compounds. In defect-free graphite, lithiummotion is restricted to two-dimensionaldiffusion because lithium hopping between layers through acarbon honeycomb is energetically extremely unfavorable.29

According to transition-state theory, the frequencywith whichlithium ions move to vacant neighboring sites is expressed as

! # "$ exp%-"Eh=kBT& %1&where "Eh is the difference between the energy at anactivated state and the initial equilibrium state, and "* is aneffective vibrational frequency, here taken to be 1 " 1013

s-1.17 The location and energy of the activated states, calcu-lated separately for stages I and II, were determined by thenudged elastic band method.30 The migration barriers werecombinedwith the cluster expansion for the lithium-vacancyconfiguration energy31 in graphite and used to constructactivation barriers in kinetic Monte Carlo simulations tocalculate the lithium diffusion coefficients. We have chosento show the diffusivity results for stage I (II) for the concentra-tion regions where experiments5 indicate average intralayerspacings characteristic of stage I (II). As can be seen inFigure 3, the chemical diffusivity in stage I (II) decreases asa function of increasing in-plane Li concentration. This is adirect result of repulsive lithium-lithium interactions, whichinhibit lithium mobility at higher lithium content. If we backout “effective” Li migration barriers from the chemical diffu-sivity, as a function of concentration, we find that theyincrease from 308 meV at x = 0.2 to 400 meV close to theordered LiC6 phase. Apart from the ordering effects, that is,some fluctuations and a sharp decrease in diffusivity at x =0.5 and 1.0, there are no other significant features in thediffusivity trend with concentration. Most importantly, wefind overall very fast intralayer lithium diffusion in bulkgraphite,!10-7 cm2 s-1 at room temperature. This is in verygood agreement with the experimental findings for diffusionparallel to graphene planes inHOPGat 4.4 ((0.1)"10-6 cm2

s-1 and gives further evidence for the extremely highmobilityof Li between the layers of graphite.

To conclude, we have studied, by highly controlled experi-ments combined with first-principles calculations, lithiumdiffusivity in HOPG as a function of transport direction. Thediffusivities obtained from these efforts show remarkableagreement between experiments and calculations and clearlyindicate that the lithium diffusion in graphite is several ordersofmagnitude faster between graphene planes than that alongthe grain boundaries or in the direction perpendicular tothe graphene sheets. While this is perhaps intuitively not

Figure 3. The chemical diffusivity for the stage II (blue squares)and stage I (red circles) phases in the Li-graphite system, obtainedfrom kinetic Monte Carlo simulations based on first-principlescalculations.25 The inset shows the Li (blue circles) path on thehoneycomb graphite lattice which was used to calculate the Limigration barriers.

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surprising, it has several important implications. First, itprovides a physical explanation for the very wide range oflithium diffusivity data that is reported in the literature fordifferent degrees of graphitized carbons. Traditionally, thisinconsistency has been attributed to the planar surfacemodels used in analysis of diffusivity experiments, whichcan differ significantly from the actual electrochemical inter-face area.12 While this uncertainty about the active areaundoubtedly contributes to the variation in the literature,the results presented in this paper also indicate that thelithium diffusivity in any graphitic carbon will depend criti-cally on the size of graphitized domains as well as its orienta-tion relevant to the intercalative/deintercalative flux. Second,the findings have immediate implications for potential ra-tional design of carbonaceous materials for high-rate anodesin lithium ion batteries. It is well-known that graphite anodessuffer severe transport-induced surface structural damageupon prolonged cycling (especially at high rates and atelevated temperatures) in rechargeable lithium ion bat-teries.32-35While well-controlled structure and performance-oriented design of cathode materials have recently beenexplored,36 there are currently no guidelines for designingcarbon-based electrode architectures for lithium ion batteries,especially for high-power applications. Assuming a designwhich efficiently utilizes the fast in-plane lithium diffusivity of10-7 cm2 s-1, graphitized natural graphite (MCMB) withtypical crystalline domain sizes around 45 nm could beintercalated/deintercalated in less than 0.2 ms. Such a ratewould competewith the fastest-rate cathodematerials seen todate.37 For example, a rate-promoting design could poten-tially be achieved by creating graphite particles with radiallyaligned crystallites, where the graphene planes are parallel tothe each other in radial direction. An anodematerial with thiskind of structural alignment should, by construction, exhibitvery little disordering, which minimizes the irreversible capa-city loss of lithium to the solid electrolyte interphase (SEI)formation38 and reduce Li plating, which is themain degrada-tionmechanism for Li ion batteries operating at low tempera-ture. While our work shows that graphitic carbon can, inprinciple, be a very high rate anode, and hence enable fastcharging batteries, it is important to understand that lithiumdiffusion in a composite electrode is only as fast as theweakest link in the chain. Hence, electronic and/or ionictransport through the SEI layer or Li ion transport throughthe electrode porosity may also have to be optimized in orderto enable high-rate anodes.

SUPPORTING INFORMATION AVAILABLE Experimentalsetup, diffusion equations, the estimation of transport parameters,and first-principles calculations. This material is available free ofcharge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author:*Towhom correspondence should be addressed. E-mail: kapersson@lbl.gov.

Author Contributions:z These authors contributed equally to this work.

ACKNOWLEDGMENT Work at the Lawrence Berkeley NationalLaboratory was supported by the Assistant Secretary for EnergyEfficiency and Renewable Energy, Office of Vehicle Technologiesof the U.S. Department of Energy, under Contract No. DE-AC02-05CH11231.Work at the Massachusetts Institute of Technology wassupported by Ford Motor Company under Grant Number 014502-010. A.V.D.V. acknowledges support from NSF under Grant No.DMR 0748516.

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