Chemical Physics Letters 485 (2010) 265–274

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Chemical Physics Letters

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FRONTIERS ARTICLE

Direct in situ measurements of Li transport in Li-ion battery negative electrodes

Stephen J. Harris a,*, Adam Timmons a, Daniel R. Baker a, Charles Monroe b

a Electrochemical Energy Research Lab, General Motors R&D Center, Mail Code 480-102-000, Warren, MI 48090, United Statesb Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, United States

a r t i c l e i n f o

Article history:Received 14 November 2009In final form 10 December 2009Available online 22 December 2009

0009-2614/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cplett.2009.12.033

* Corresponding author. Address: Electrochemical EMotors R&D Center, Mail Code 480-102-000, 30500 M9055, United States. Fax: +1 586 986 2244.

E-mail address: stephen.j.harris@gm.com (S.J. Harr

a b s t r a c t

We describe the first direct in situ measurements of Li transport in an operating cell. Motion of the lith-iation front in the graphite electrode suggests that transport could be controlled by liquid-phase diffu-sion. The electrochemical (current–voltage) data are successfully modeled with a diffusion equationthat contains no material or microstructural information. The model is only qualitatively successful inpredicting observed Li transport rate data, suggesting that microstructural information is required andthat the actual process is more complex than simply diffusion. The technique can provide data for study-ing Li plating and Li dendrite growth, both of which can cause battery degradation.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Because of their high energy density and long cycle life, Li-ionbatteries are used today in many practical devices including cellphones and laptop computers, and they are now being contem-plated for mass-produced hybrid and electric vehicles [1]. A typicalLi-ion battery is shown schematically in Fig. 1a and as an SEM inFig. 1b. As the battery is charged and discharged, Li, originally pres-ent in the electrolyte and in the positive electrode*, chemically re-acts with the negative electrode, inserting or intercalating into thebulk material. This lithiation process changes the chemistry of theelectrode particles, so the properties of the Li-ion battery dependcritically on the chemical nature of the electrode material. Since,by definition, Li is thermodynamically more stable in the positiveelectrode, a power supply is required to detach Li from the positiveelectrode (usually a transition metal oxide or phosphate) to formLi+ ions and then to push them into the negative electrode* (almostalways a form of graphite or carbon) for charging, as illustrated inFig. 1a. Because lithium reacts with practically everything, thenumber of potential lithium-ion battery electrode materials—and,therefore, the number of potential lithium-ion battery types—is al-most limitless.

Li-ion batteries are generally analyzed using the macro-homo-geneous porous electrode model developed by Newman and co-workers [2,3]. The model consists of equations for: (1) electroniccharge balance in the solid phase (Ohm’s law); (2) electrolytecharge and mass balance for Li+ using concentrated electrolyte the-ory; (3) diffusion of lithium in the electrode particles (Fick’s law);(4) Butler–Volmer* charge transfer kinetics at the electrolyte-solid

ll rights reserved.

nergy Research Lab, Generalound Rd., Warren, MI 48090-

is).

phase boundary; (5) and associated boundary conditions. Themodel requires as input no microstructural information beyondparticle radius, electrode thickness, and electrode porosity. Other-wise, it assumes that the microstructure can be described as an iso-tropic, homogeneous, 1-dimensional porous material made upfrom monodisperse non-porous isotropic spherical particles thatare small compared to the electrode thickness.

Of course, none of these assumptions and approximations canbe truly correct. For example, significant inhomogeneity in theelectrodes and in the state of lithiation within an electrode thatshould be at equilibrium has been observed [4–6]. The chargetransfer step is modeled as a single global chemical reaction inwhich Li+ ions in the electrolyte solution de-solvate, transportthrough a �1–10 nm thick solid electrolyte interphase (SEI) layer[7–12] consisting of various degradation products, and react withthe electrode material. Remarkably little is known about the de-tailed chemistry of the Butler–Volmer step [12–14], even thoughit is involved in many proposed degradation mechanisms[11,15,16]. Diffusion of lithium in the solid phase active particlesis treated with a shrinking core diffusion model [17,18] althoughits validity is at best uncertain for many commonly used elec-trodes, and although it has been shown to be invalid for at leastone material [19]. Properties of the conductive carbon and binder,while of considerable importance to battery performance, are ab-sorbed into other parameters.

In the years since the model appeared, a number of papers,some from Newman’s group, have examined the effects of relaxingsome of the microstructural assumptions of the original model. Forexample, Darling and Newman [20] analyzed the effects of multi-ple particle sizes, Yi and Sastry [21] considered particles with ellip-soidal shapes, and Santhanagopalan et al. [22] and Yi et al. [23]looked at extending the model to higher dimensions. These andother efforts notwithstanding, the original macro-homogenousmodel performs very well and is still widely and successfully used

Fig. 1. (a) Schematic of a lithium-ion battery being charged. Each electrode is acomposite made from �10 lm particles (red and green balls, �80% by mass) withwhich Li+ ions react and into which the lithium inserts. By definition, lithium bindsstrongly with positive electrode* material (low DG ? high voltage) and weakly withnegative electrode* material (high DG ? low voltage). The particles are held togetherand attached to a metal current collector with a minimal amount of binder (light blue,polyvinylidene fluoride PVDF,�10% by mass). In order to ensure that electrons have alow-resistance path for electrons to get from the current collector to active particles,which are often electrical insulators such as LiCoO2, a minimal amount of conductivecarbon (black squiggles, soot or carbon black,�10% by mass) is also added. Electrodeporosity is�15% in a laptop battery, but it may be much greater when high power isrequired; and electrode thickness is 50–100 lm. The electrolyte solution—LiPF6 saltin a diethyl carbonate/ethylene carbonate solvent—functions as a filter that passesions but not electrons. The electrolyte solution fills the pores, but there is no freeliquid. Electrodes are prevented from short-circuiting with a 10–20 lm thick porouspolymeric separator. (Thanks to V. Srinivasan of LBNL for the diagram) (b) SEM crosssection of a LiCoO2 (positive) electrode, potted in epoxy, which fills the pores.Electrode material coats both sides of the aluminum current collector, seen runningtowards the upper left corner. This double-sided arrangement allows electrodes to beeasily stacked in parallel. (a) shows electrode on only 1 side.)

266 S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274

[24] for optimizing electrode parameters such as thickness andporosity. It is, in fact, the basis for COMSOL’s commercial Li-ionbattery code.

On the other hand, the ability to predict cell degradation re-mains a challenge because so many unaccounted for and seem-ingly unrelated micro-scale degradation mechanisms have beenidentified or postulated [4,21,25–39]. Experimental measurementsdescribing local chemistry, details of the microstructure and trans-port, and an understanding of how these factors evolve are re-quired in order to sort out the issues involved with degradation.At present, analysis of specific degradation mechanisms cansometimes offer explanations for experimentally observed degra-dation [22,29,40,41], but without additional experimental data

and associated theoretical analysis, cause-and-effect relationshipsbetween observation and degradation pathway can be difficult todemonstrate. For example, a widely invoked degradation mecha-nism is loss of internal ‘electrical connectivity.’ The loss of connec-tivity has been directly observed by Kostecki and McLarnon [4],and they attributed it to the movement of conductive carbon (‘car-bon retreat’), reducing electron transport within the electrode. Butloss of internal electrical connectivity has also been attributed toparticle fracture [36,38,42], to precipitation of thick surface films[30,35], to gas generation [43], to loss of contact between activematerial and the current collector [44] or between the current col-lector and the cell housing [45], and to degradation of the binder[46]. As a result, there has not appeared to be any experimentalor modeling strategy that elucidates degradation as a general phe-nomenon. Because a lower degradation rate translates directly intolower-cost batteries, the ability to predict, mitigate, and deal withdegradation by understanding fundamental chemical and materialproperties is critical if batteries for transportation are to becomeeconomically viable.

In an ideal Li-ion battery, the only process that should occur atthe mesoscale (smaller than an electrode, larger than a molecule) istransport of lithium ions through the electrolyte and in the activeparticles, accompanied by reversible reactions of lithium at appro-priate locations within the electrodes. All of the seemingly dispa-rate mechanisms of battery degradation lead in some way toinefficiency or irreversibility of these fundamental transport andassociated chemical processes. The present work is predicated onthe notion that a general study of degradation can begin with mea-surements of Li transport and insertion into porous electrodes.These measurements could then guide researchers towards otherexperiments and models that provide fundamental knowledge ofdegradation. With this goal in mind, we provide here in situtime-dependent Li spatial maps and transport rate measurementsat the mesoscale.

2. Experimental

Charging and discharging experiments were carried out in anoptical half-cell*. Fig. 2 shows the optical half cell as seen fromthe side (schematic) and from above (photograph). The cell wasassembled in a glove box under an Ar atmosphere (<1 ppm oxygenand water), since even N2 reacts with Li. A brushed piece of Li foilacted as the negative electrode, while a porous graphite electrodecut from an LR1865AH 18650* laptop battery made by TianjinLishen Battery Co. served as the positive electrode. The electrodematerial coated both sides of a copper current collector, as canbe seen for a different electrode in Fig. 1b.

Conventionally, electrodes are stacked (or wound) facing eachother with a separator keeping them apart so they do not short,as shown in Fig. 1a. (Putting electrode material on both sides ofthe current collector allows this stacking arrangement.) This geom-etry minimizes Li+ transport barriers and in-plane gradients. Forour system, the electrodes, each roughly 1 cm square, were insteadplaced side-by-side on separate spring-loaded stainless steel sup-ports that were separated by a Teflon spacer, Fig. 2. The electrodesand supports were electrically isolated, but they could be con-nected through an external circuit. The electrodes were soakedwith electrolyte (1 M LiPF6 salt in 1:2 volumetric ratio ethylenecarbonate: diethyl carbonate solvent), which also filled the gapabove the Teflon spacer and between the electrodes. The cell wasthen covered with a quartz window, sealing it. (Quartz is graduallyattacked by lithium. Sapphire is a better choice.) The pressure ofthe window on the electrodes was approximately 1 bar.

The arrangement shown in Fig. 2 allows transport of Li+ ionsfrom the metal, above the spacer, and into the edge of the porous

Fig. 2. (a) Side view schematic of the optical half-cell. (A) Quartz window. (B) Li foilelectrode, 0.38 mm thick. (C) Graphite electrode showing current collector bisectingit. (D) Teflon spacer. (E) Coin cell springs. (F) Stainless steel supports and cellhousings. (G) Keithley 237 source/measure unit, external to the cell. (H) Workingelectrode wire. (I) Reference electrode wire. (J) Counter electrode wire. Optical dataare taken with a microscope viewing the quartz window from above. Electrolytewets the electrodes and also fills cavities between the electrodes and surroundingthe Teflon spacer. Cell housing is not shown. (b) Photograph of the graphiteelectrode positioned about 2 mm from a Li metal electrode on electrically separatedstainless steel supports. Electrolyte fills the gap between the electrodes (above theTeflon) so that there is an unimpeded pathway for Li+ ions to travel between theelectrodes. The electrodes are positioned on spring-loaded supports such that theyare pressed against the quartz window (pressure about 1 bar) that seals the cell.

S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274 267

graphite electrode. Within the graphite electrode, Li+ ions mayeither insert into the graphite or diffuse through the electrolyte,which fills the pores between the particles. Although a direct diffu-sion path perpendicular to the lithium and graphite edges is mostfavorable, other Li pathways were observed. For example, lithiumcould electrodeposit directly on the stainless steel or travel aroundthe edges of the graphite far from the Teflon spacer. In principle, itcould also move through pores that are between the window andthe electrode top surface. In order to confirm that such transportwas not dominant, we imaged the edge of the electrode duringthe lithiation step in a separate experiment to determine the lith-iation rate just under the quartz window compared to that for therest of the electrode.

After assembly, the cell was removed from the glove box andput under an Olympus SZX12 optical microscope at 90�magnifica-tion. The brushed lithium metal electrode showed no obvious oxi-dation or nitride formation over a time scale of up to a week.

Cells were placed under either current or voltage control using ahigh precision source/measure unit (Keithley 237) in an externalcircuit. Current densities, defined with respect to the nominal geo-

metric surface area of the electrode edge, were in the range 1–10 mA/cm2.

Digital micrograph images of the electrodes were recordedevery 15 min, with the microscope focused near the edge of thegraphite electrode closest to the Li metal electrode. Experimentstypically ran for a couple of days. Videos, some of which are avail-able online [47], were constructed from the sequence of images.Because of the color change that occurs when graphite is lithiated[48–50], these images provide approximate time-dependent Liconcentration maps or spatial profiles in the graphite electrode.(For the images shown in this Letter and on the web [47], we haveenhanced the colors using Photoshop.)

Our experimental arrangement (Fig. 2) has several advantagesfor performing studies on Li transport compared to a more conven-tional face-to-face arrangement (Fig. 1a).

(1) By placing the electrodes ‘face up’ we can take advantage ofgraphite’s color changes upon lithiation to measure in situspatial profiles of intercalated Li. Bazant et al. [51] used aconceptually similar geometry to follow transport and reac-tion in a copper–chlorine corrosion system.

(2) The side-by-side arrangement leads to large concentrationgradients. While undesirable in a conventional cell, largegradients are useful when the goal is to make transportmeasurements.

(3) Our arrangement, in effect, converts the problem of measur-ing Li transport perpendicular to the current collectorthrough a distance of about 0.1 mm, to the problem of mea-suring Li transport parallel to the current collector through adistance of about 10 mm, making the measurement easier.

3. Color of lithiated graphite

Graphite possesses a P63/mmc layered structure [52], wherelayers of graphene composed of hexagonally arranged sp2 hybrid-ized carbon are weakly bonded to each other by van der Waalsforces along the c-axis, resulting in 0.34 nm-wide galleries be-tween the graphene layers. The layer stacking of lithium-freegraphite is A–B–A–B, with layers translated but not twisted rela-tive to each other. In order to allow lithium intercalation into a gal-lery space, the graphene layers slide with respect to each other,creating domains with A–A or B–B stacking [53,54]. At room tem-perature, electrochemically lithiated graphite at the LiC18 [55] con-centration has Li in every other gallery (‘dilute stage 2’) on average,although the Li is not well ordered within each gallery [53]. Thisphase is dark blue colored. Additional Li inserts in every secondgallery through a two-phase transition to the well ordered (‘stage2’) [50] LiC12 phase, which grows as the LiC18 phase shrinks [53].This phase is red colored. Once LiC12 is reached, additional Li goesinto the unoccupied galleries through another two-phase transi-tion with a phase of well ordered lithium in every layer growingas the LiC12 phase shrinks until a fully ordered (‘stage 1’) LiC6 is ob-tained. This phase is gold colored [56].

There are a variety of factors that can lead to color variation be-tween a particle and its neighbors, even if they are all at the samenominal potential. The need for graphene layers to slide with re-spect to one another when Li is intercalating (to form A–A stackingfrom A–B stacking) means that defects in the graphite structuremay prevent full lithiation [57]. As a result, the color homogeneityof lithiated graphite held at a given potential can depend on howdefect density varies from particle to particle [57]. Any variationin the electrical contact of a particle to its neighbor or to the cur-rent collector may also lead to variation in color if the color is ob-served before the family of particles has been given sufficient timeto reach equilibrium. A similar logic could explain variation in

268 S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274

color within a single particle [6]. As a result, even when the poten-tial is such that all of the graphite should, for example, be LiC12, asmeasured by the electrical potential, it is likely that some of thegrains will have a greater lithium concentration and some of thegrains will have a lower lithium concentration. However, fromthe perspective of canonical mesoscopic transport models [2], onlya locally averaged graphite color is meaningful; additional micro-scopic details would be needed to rationalize these fine-grainedcolor variations.

Conversion of color to Li concentration should be taken as onlysemi-quantitative. Various attempts have been made to correlategraphite’s color with intermediate lithium contents [48], but coloris difficult to calibrate (for example, it depends significantly onambient lighting conditions [58]). Furthermore, it is difficult to en-sure that electrochemical equilibrium has been reached when esti-mating an electrode’s lithiation state.

4. Model

To model the insertion experiments, it will be assumed that theprocess of lithium insertion obeys the transient diffusion equation

@c@t¼ Deff

@2c@x2 ; ð1Þ

where c is the (molar) concentration of lithium with respect to avolume element containing both graphite and pore-filling electro-lyte, x is the distance from the electrode’s edge at the electrode/sep-arating electrolyte boundary, and t is time. The effective diffusioncoefficient Deff is intended to lump together microscopic processessuch as diffusion and migration* of lithium through the liquidphase, solid-phase lithium transport, and electrochemical kineticsby which lithium crosses solid–liquid boundaries in the cell’sinterior.

Although it has been observed that the diffusion coefficient oflithium in graphite electrodes (lithium exists in graphite as nearlyionic, with a positive charge of about 0.8 [59]) varies with lithiumconcentration [60,61], for the sake of simplicity it will be assumedhere that Deff is constant. For extensions of the model, we believethat it would be better to consider that diffusion of lithium inthe pore-filling electrolyte and the solid graphite occur in parallellocally, as in Tobias and Newman’s porous-electrode theory [62],rather than to give the effective diffusion coefficient in equation1 a locally variable value.

Although more sophisticated theories applicable to porousinsertion electrodes exist [2,63], Eq. (1) could suffice to approxi-mate experimental results if any of the diffusion processes associ-ated with lithium insertion is rate-limiting. Use of Eq. (1) also hasthe advantage that it is amenable to analytical solution. The ad hocassumption that diffusion is rate-limiting will be revisited later,but it is consistent with experimental observations shown belowand with the common observation that lithium insertion kineticstends to be fast—i.e., ion transfer between pore-filling electrolyteand graphite requires a low overpotential*.

To convert the concentration variable into a more meaningfulparameter, we introduce the maximum molar lithium content cmax.If the quantity of lithium dissolved in the pore-filling electrolyte isnegligible,

h ¼ ccmax

ð2Þ

represents the local fractional lithiation of the porous electrode.A typical electrochemical experiment begins with a porous

graphite electrode that has been drained to a fully de-lithiatedstate. After a step designed to remove impurities, the experimentthen takes place in two steps:

(A) Lithium is inserted into the electrode at constant current for aperiod t0, at which time the electrode/liquid boundary hasreached lithiation hmax (determined by the color at the bound-ary). At this time the voltage has attained a value U0(t0).

(B) The cell is held at the constant voltage U0 from t = t0 onward.Experimentally, it is observed that this condition maintains aconstant lithiation state (gold color) at the electrode/liquidboundary. During this period the current decays over timeas the lithiation state (color) gradually becomes uniformthroughout the electrode.

Formally, the initial condition of the experiment is

hð0; xÞ ¼ 0: ð3Þ

Step A corresponds to the condition

�Deff@h@x

����ðt;0Þ¼ i0

nFc0if 0 < t 6 t0; ð4Þ

where i0 is the current density during the constant-current step (A),F is Faraday’s constant, and n is the number of electrons transferredduring an insertion event; typically n = 1 for lithium insertion. (Notethat current density is expressed with respect to the nominal geo-metric surface area of the electrode’s edge.) Assuming that a con-stant voltage maintains constant lithiation state (color) at theelectrode/electrolyte boundary, step B is described by the condition

hðt; xÞ ¼ hmax if t > t0: ð5Þ

The electrode size is chosen such that

hðt;1Þ ¼ 0; ð6Þ

that is, the initial lithiation state is maintained far from the graph-ite/liquid interface (off the top of the figures).

An analysis of step A shows that the maximum lithium contentat the electrode boundary depends on the constant-current pulseduration, effective diffusion coefficient, and maximum inserted-lithium concentration, through

hmax ¼2i0

nFc0

ffiffiffiffiffiffiffiffiffiffiffit0

pDeff

r: ð7Þ

The solution to Eq. (1) that satisfies initial and boundary condi-tions (3)–(6) can be obtained using a combination of Laplace trans-formation and Duhamel’s superposition integral, which show that

hðg; sÞhmax

¼

ffiffiffiffiffiffip1�s

pierfcðgÞ s 6 0;ffiffiffiffiffiffip

1�s

pierfcðgÞ �

ffiffiffiffiffiffips1�s

pierfcðg=

ffiffiffispÞ

þ 12ffiffiffiffiffiffi1�sp

R 10

ffiffiffiffiffiffiffis1�u

p� sffiffiffiffiffiffiffiffi

1�sup

� �erfc g=

ffiffiffiffiffiffisup� �

dus > 0;

8>><>>:

ð8Þ

where the integrated error function complement function is definedas

ierfcðgÞ ¼ 1ffiffiffiffipp e�g2 � gerfcðgÞ ¼ 1ffiffiffiffi

pp e�g2 � g

2ffiffiffiffipp

Z 1

ge�u2

du ð9Þ

and the independent variables g and s relate to time, position, andconstant current duration through

gðt; xÞ ¼ x2ffiffiffiffiffiffiffiffiffiffiDeff tp and sðt; t0Þ ¼ 1� t0

t: ð10Þ

Note that 0 < s < 1 when t > t0 and s < 0 when t < t0.Eq. (8) can be used to determine the flux at the electrode

boundary when t > t0 (or s > 0). Faraday’s law then shows howthe current relaxes during step B:

iðt > t0Þi0

¼ 2p

arccos

ffiffiffiffiffiffiffiffiffiffiffiffit � t0

t

r !: ð11Þ

S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274 269

Eq. (8) can also be applied to obtain the position of the movingboundary between colors as a function of time. The gold/red bound-ary position, for instance, corresponds to a given fractional lithia-tion, hg/r. Since the constant-current duration t0 is setexperimentally, s(t, t0) is known from Eq. (10); moreover, the exper-iment is constructed to set hmax = 1; that is, t0 is selected such thatthe electrode/electrolyte boundary is fully lithiated (gold). A mastercurve for gg/r(s), the value of the similarity variable that corre-sponds to the transient location of the gold/red boundary, is foundby solving the implicit equation h(gg/r,s) = hg/r for gg/r at each exper-imental dimensionless time s. This curve is determined by theparameters t0 and hg/r alone; no other properties are required. Toobtain x(t), the transient position of the gold/red boundary, Eq.(10) can be rearranged to the form xðtÞ ¼ 2gg=r

ffiffiffiffiffiffiffiffiffiffiDeff tp

, which intro-duces the effective diffusion coefficient. Thus the position of themoving boundary depends on the parameters t0, hmax, hg/r, and Deff.The first two of these are controlled experimentally and hg/r can befound by auxiliary measurements. The only unknown is Deff, whichcan be determined by a best-fit of an experimental measurement ofx(t) by the method of nonlinear least squares.

5. Results

5.1. Experimental

Fig. 3a and b show a pair of images taken about 45 min apartduring lithiation. The camera angle gives a view of the edge of

Fig. 3. A pair of images showing the gold color climbing up the edge of theelectrode, indicated by the region between the white dashed lines. (a) Taken earlier,shows the gold color only at the bottom of the edge, near the current collector. (b)Taken about 45 min later, shows the gold color covering the entire edge. SeeSupplementary video.

the electrode. The gold color rises from the current collector(Fig. 3a) toward the top face of the electrode (Fig. 3b), where thequartz window sits. The fact that lithiation occurs first at the cur-rent collector and only later at the top of the electrode suggeststhat the pore space between the top surface of the electrode andthe quartz window is not the main transport pathway for Li+ ions;rather, Li+ ions travel predominantly through the porous electrode.The result suggests that the state of lithiation at the top surface,which we observe, lags by less than an hour that at the bottom sur-face, only a few percent of the duration of the experiment.

Fig. 4 shows an SEM micrograph of a cross section of the dou-ble-sided graphite electrode after the pores have been filled withepoxy and the electrode cut with a microtome blade, which is a de-vice that cuts very thin slices. The �10 lm thick copper currentcollector runs from the top to the bottom, bisecting the electrode,with epoxy filling the balance of the image, including the voids inthe electrode. Striations outside the electrode that run from top to

Fig. 4. Cross section of the graphite electrode made with a microtome and imagedwith an SEM. The electrode was filled with epoxy before being microtomed. Verticalscratches made by the microtome are visible on either side of the electrode. Thecurrent collector, approximately 10 lm thick, runs top-to-bottom, bisecting theelectrode. Individual particles are difficult to make out.

Fig. 5. Experimental (dots) and theoretical (solid line) data for the transient currentand voltage during the galvanostatic/potentiostatic lithium insertion experimentdescribed in the Model section. The duration of the galvanostatic control was28694 s, around 8 h, with I0 = 150 lA.

270 S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274

bottom were made by the microtome blade and are clearly visiblein the epoxy. Each electrode, on either side of the current collector,is about 70 lm thick. Examination with Energy Dispersive Spec-troscopy, a variant of X-ray fluorescence that provides elementalanalysis of a sample, shows that the graphite particles are complexin shape and generally 5–20 lm across.

Fig. 5 shows the electrochemical data for our experiment, whileFig. 6 shows some of the corresponding electrode optical micro-graph images. Fig. 6(a) shows the initially grey electrode that con-tains minimal Li. We first applied a constant voltage of 1 V to thecell for 28 h. Since Li insertion does not occur at 1 V, we assumethat the current measured during this period (preceding step A,see Section 4) involves side reactions of lithium with impurities.When the measured current dropped to �15 lA we switched tocurrent control at �150 lA for t0 = 8 h (step A). Fig. 6b, taken dur-ing this period of constant current, shows that a blue color gradu-ally covered the electrode, starting from the edge nearest the

Fig. 6. A sequence of four optical micrographs showing the time-evolution of color in thtaken approximately 6 h after t = 0 in Fig. 5 (t/t0 � 0.75). (c) Three graphite stages visible:the image shown in (b). (d) Two graphite stages visible: red (stage 2), and gold (stage 1dependence of the lithiation process are available on the internet at www.lithiumonthe

lithium metal and moving away from the edge. Fig. 6c shows thatthis was followed by red and then gold bands, where the red–blueand gold–red boundaries started at the electrode edge and movedaway from that edge. The voltage eventually dropped to 2 mV, atwhich point we put the cell under voltage control (step B).Fig. 6d shows that while under voltage control, the gold regioncontinued to expand into the red region until most of the visibleelectrode was gold. Videos of the process are available on the inter-net [47].

The most obvious feature of these images is the relatively sharpboundaries between the colored areas, particularly between redand gold. We note that although the lithium content in a volumeelement of graphite will in general vary continuously as latticevacancies are filled, the color of the graphite can change sharplydepending on which types of vacancies are being occupied.Lithiated graphite will appear blue when every other galleryis partially full at LiC18; it will appear red once every other

e electrode. (a) Initial, de-lithiated. (b) Graphite mainly in the blue, dilute stage 2;blue (dilute stage 2), red (stage 2), and gold (stage 1); taken approximately 3 h after); taken approximately 4 h after the image shown in (c). Videos showing the timeweb.com [47].

S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274 271

gallery is full; and it will appear gold after some stage when‘almost every’ gallery is full. That is, the state of lithiation variescontinuously, but the changes in color are discrete. We are observ-ing phase boundaries.

The sharp gold–red boundary, corresponding roughly to a 90%[13] state of lithiation (Li0.9C6), allows its advance to be easily mea-sured as a function of time. Fig. 7 shows a plot of the width of thegold region, measured in Photoshop pixels, as a function of time ona log–log scale. The data fall closely on a straight line, especially atlonger times, with a slope of 0.52. This value close to 0.5 suggeststhat, while any number of processes may be occurring, the rate ofadvance of inserted Li can be modeled as a diffusion process. Wetake this experimental result as justifying the use of Eq. (1),although we will point out below that more complex processesare not precluded.

5.2. Model

Some fraction of the experimentally measured current I is dueto ‘stray current’ Istray, which drives either lithium insertion alongthe sides of the electrode or other electrochemical side reactionsparallel to the insertion of lithium in graphite. To assess the effectsof stray currents in the experimental cell, transient data were ana-lyzed using a variant of Eq. (11) that includes a stray-currentcorrection,

Iðt > t0Þ � Istray

I0 � Istray¼ 2

parccos

ffiffiffiffiffiffiffiffiffiffiffiffit � t0

t

r !: ð12Þ

Here we assume that stray currents are constant. (Although not rig-orously justifiable, we believe that this assumption is valid withinexperimental uncertainty.) Best fits of experimental data show thatapproximately 10% of the current supplied by the potentiostat dur-ing an experiment is stray. The best-fit current corresponds toIstray = 12.7 lA.

It is notable that Eq. (11) does not involve any material proper-ties, which is helpful in the processing of experimental data. Thereare two consequences of this result. First, there are no adjustablematerial parameters of which we can avail ourselves (apart fromthe fitted stray current in Eq. (12))—the data and predictions either

Fig. 7. Time evolution of the width of the gold band, from the electrode/separatingelectrolyte edge to the gold–red boundary. The equation for the least squares line fithas a slope very close to 0.5.

agree or they do not. Second—a corollary—there is no materialproperty information that can be learned from comparing thisequation to experimental data.

Fig. 5 compares the experimental transient current with thetheoretical expression given in Eq. (12), along with transient volt-age measurements. The excellent agreement between experimen-tal and theoretical currents suggests that the ad hoc model oflithium insertion from Eq. (8) is reasonable, despite its neglect ofalmost all microscopic detail.

To obtain the theoretical curve, a value of hg/r = 0.9 was chosen,in line with the colorimetric observations of Maire et al. [48]; thatis to say, the red/gold boundary was assumed to correspond to 90%of the theoretical maximum lithiation of the graphite. A best-fityields Deff = 4 � 10�10 m2/s. Since this value is typical of organic li-quid-phase diffusion coefficients [64], the analysis suggests thatthe color advance in our system is limited by transport of Li+ inthe pores rather than in the bulk graphite.

In processing the boundary-motion data, a lag of 30 min wasintroduced to account for the time that changing color took topropagate through the porous graphite in the direction perpendic-ular to the copper current collector (i.e., toward the optical win-dow). This lag was suggested by the results shown on Fig. 3.Fig. 8 compares the model predictions with the experimentallymeasured rate of advance of the gold–red boundary, as determinedfrom micrographs taken during the galvanostatic/potentiostaticinsertion experiment depicted in Fig. 6. The agreement in Fig. 8 be-tween the experimental data and the model is only fair.

The ‘open face’ geometry that we use here can facilitate studyof other important phenomena related to battery degradation.For example, Fig. 9 shows micrographs of an MCMB* electrodetaken several hours apart as it is being plated with Li [47]. Ourobservations indicate that (1) Li particles appear to nucleatereadily but sparsely; however, they grow relatively slowly; (2)The front (lower, in the figure) edge of the electrode, which isnearest the Li electrode, is free of plated lithium; (3) Li particlesdo not preferentially form on the most lithiated (gold) graphiteparticles; (4) A Li particle can sit on a stage 2 (red) graphite par-ticle for many hours without lithiating the particle to stage 1(gold); and (5) Lithium plating occurs while the electrode poten-tial is set at +0.002 V, although thermodynamically, Li should not

Fig. 8. Position of the gold/red boundary relative to the electrode/separatingelectrolyte edge during the experiment described in Fig. 5. The points areexperimental data; the solid line is a best-fit of Eq. (8) with a boundary Li contentof 0.9, which yielded Deff = 4 � 10�10 m2/s.

Fig. 9. Li plating on an MCMB electrode. The plating occurred while the voltage applied to the current collector was +2 mV, with (a) imaged about 8 h before (b). Videosshowing the time dependence of the lithiation plating is available on the internet at www.lithiumontheweb.com [47].

272 S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274

plate significantly unless the voltage is 0 or negative. Analyses ofthese observations will be the subject of future work. Fig. 10shows an electrode that has been electrically shorted by a Li den-drite that grew from the Li electrode during de-lithiation. Shortcircuits caused by Li dendrites penetrating through the separator(Fig. 1a) are a common cause of failure in Li-ion batteries.

6. Summary and future work

In this work we have presented what we believe are the first di-rect in situ measurements of Li transport in an operating Li-ion cell.Such transport measurements could be useful for relating themany degradation modes that have been observed or proposed,to material properties and operating conditions, since most suchmechanisms involve Li ‘not getting to the right place at the righttime.’ We showed that for our conditions the lithium transport rate

Fig. 10. View of the interface of the Teflon spacer and the negative (graphite)electrode. A Li dendrite that formed on the Li electrode crossed the gap betweenelectrodes and short-circuited the cell.

scales as t0.5. A model developed to describe the experiments givesgood agreement with the experimentally measured current re-sponse. The result shows that for this system, chronoamperometricdata contain minimal microstructural information. The model is inonly fair agreement with the observed motion of color boundaries,indicating that microstructural information or a more sophisti-cated model is required to predict Li transport within the electrode.The model allowed us to extract an effective Li diffusion coefficientthat is in reasonable agreement with values determined for pore(liquid phase) diffusion in more conventionally designed cells.

We conclude by pointing out several caveats that should bekept in mind with respect to our experimental arrangement andour modeling process.

(a) It is not at all clear that the effective diffusion coefficientthat was fit to the data has a simple physical interpretationin terms of fundamental material properties. A first attemptat clarifying this issue can be made by applying the muchmore sophisticated transport model of Doyle et al. [2,3]to this experimental situation to see if it too is capable ofreproducing the square-root-of-time front propagationand also of matching the current decay in step B of theexperiment. Preliminary investigations indicate that this isindeed the case, provided one assumes that the kineticsof the intercalation reaction at the boundary of the carbonparticles is close to equilibration during this experiment. Inthis case, the current would not be determined by a simplediffusion equation; rather, the more complicated modelpredicts that lithium transport is occurring through a com-bination of both diffusion and migration. If this is true, thecorrect interpretation of the fit diffusion coefficient mayturn out to be a rather complicated functional combinationof the lithium salt diffusion coefficient and the electricalconductivity in such a way that a general application ofthese results to other situations becomes difficult. It is nec-essary to perform these more complicated simulations anddo the corresponding analysis to determine a more preciseinterpretation for Deff.

S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274 273

(b) If we wish to associate our transport data with those deter-mined in more conventional architectures, we need toassume that the composite electrode is isotropic (transportparallel to the current collector is equivalent to transportperpendicular to the current collector).

(c) Color is only a semi-quantitative and subjective measure ofLi state of charge. Other techniques such as Raman spectros-copy [65–67] will be required for more quantitative work ongraphite electrodes or for non-graphite electrodes that donot change color upon lithiation.

(d) The color represents only the concentration of the insertedLi. We do not have any measure of the spatial dependenceof the Li+ concentration in the electrolyte or of the electro-lyte potential.

We will address each of these concerns in future work.

Acknowledgements

Valuable discussions with Prof. Martin Bazant of MIT and Drs.Yue Qi and Mark Verbrugge of GM R&D are gratefully acknowl-edged. SJH acknowledges support for this work from the TankAutomotive Research, Development and Engineering Center (TAR-DEC) under Contract N61339-03-D-0300.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.cplett.2009.12.033.

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Glossary

18650 battery: A standard size cylindrical cell, 18 mm in diameter and 65 mm long.Butler–Volmer equation: This equation, which describes how the current in an

electrochemical cell depends on the electrode potential, models an elementarycharge transfer step. It includes Arrhenius dependences for forward and reversereactions; the activation energies also depend on overpotential.

Half-cell: An electrochemical cell in which one electrode is a reference electrodethat is thermodynamically equilibrated and whose potential is assigned thevalue zero. In half-cells pertinent to Li-ion batteries, Li metal is typically used asa reference; the reaction Li ? Li+ + e� is taken as the zero of potential.

MCMB: Meso-carbon micro-beads, spherical particles of artificial graphite.Electrodes made with MCMB can be of very high quality, with long lifetimes,but the cost of MCMB can be prohibitive.

Migration: Transport driven by a potential gradient; in contrast to diffusion, whichis driven by a concentration gradient; or convection, driven by bulk flow.

Negative and positive electrodes: At thermodynamic equilibrium, DG = �nFe, whereDG is the free energy difference of lithium between the two electrodes; n is thenumber of electrons transferred in the reaction, F is Faraday’s constant (whichconverts coulombs into moles); and e is the cell potential. Materials such asLiFePO4 and LiCoO2, in which Li is strongly bound, have a much lower freeenergy for lithium oxidation than does lithium metal and exhibit a high voltagerelative to it. Thus, they can be identified as positive electrodes. Graphite andlithium metal, on the other hand, have higher free energies for lithiumoxidation, making them negative electrodes. In fact, the free energy of lithiummetal is so high that all known electrodes have a positive voltage with respectto it. Although both electrodes in a Li-ion battery may operate as cathodes oranodes (during discharge or charge), positive electrodes are often called cath-odes in the battery literature, with negative electrodes called anodes.

Overpotential: The difference between a half-reaction’s thermodynamic andobserved potentials. This difference, which is lost as heat, can act as a kineticbarrier and appears in the Butler–Volmer equation.

274 S.J. Harris et al. / Chemical Physics Letters 485 (2010) 265–274

Stephen J. Harris received his B.S. in Chemistry at theUniversity of California, Los Angeles in 1971 and hisPh.D. in Physical Chemistry at the Harvard University in1975. He was a Miller Institute Fellow at the Universityof California, Berkeley from 1975 to 1977. Since then hehas spent his career at the General Motors ResearchLabs (1977–1998), Ford Research Labs (1998–2007),and back at General Motors Research since 2007. He hasworked in the areas of laser diagnostics of combustion,soot formation and aerosol dynamics, chemical vapordeposition of diamond and boron carbide, contactmechanics modeling and prediction of fatigue lifetimes,

microscopic basis for ductile fracture in cast aluminum, and battery degradation.

Adam Timmons received a BSc and CAS in Science andEngineering from Acadia University (Canada) in 2001and a Ph.D. in Physics from Dalhousie University (Can-ada) in 2007. Adam performed his doctoral work underthe supervision of Prof. Jeff Dahn concluding in thedissertation titled ‘Visible Changes in Lithium-IonElectrodes Upon Lithium Insertion and Removal’. He isthe recipient of a Presidents Graduate Teaching Awardat Dalhousie University as well as master’s and doctorallevel scholarships from the Natural Science and Engi-neering Research Council of Canada. In 2007, Adamjoined General Motors Global Research and Develop-

ment where he executes a portfolio of research endeavors that pursue an enhancedunderstanding of the mechanisms and materials of advanced batteries.

Daniel R. Baker received his Bachelor’s degree inmathematics in 1971 from Brandeis University and hisPh.D. in theoretical mathematics in 1976 from S.U.N.Y.Stony Brook. In 1979 he took his first job in appliedmathematics, simulating melt water run-off from aglacier in the Austrian Alps. In 1985 he joined GeneralMotors R&D Center, where he is currently a StaffResearch Scientist. For the last twenty years, his workhas focused on electrochemical modeling.

Charles Monroe received a BSE from Princeton Universityin 1999 in Chemical Engineering, and a Ph.D. in ChemicalEngineering from UC Berkeley in 2004. He was a researchassociate in the Chemistry Department at ImperialCollege from 2004 to 2007, and he was a post doctoralfellow in the Chemistry Department at Simon FrasierUniversity from 2007 to 2008. He joined the faculty of theChemical Engineering Department at the University ofMichigan in the fall of 2008. His work involves modelingof batteries, fuel cells, and other electrochemical systems;nonequilibrium statistical mechanics; and coupled andmulticomponent transport theory.