Intercalation of Lithium Ions into Graphite Electrodes Studied by AC ...

2794 Journal of The Electrochemical Society, 146 (8) 2794-2798 (1999) 

S0013-4651(98)02-016-5 CCC: $7.00 © The Electrochemical Society, Inc. 

Intercalation of Lithium Ions into Graphite Electrodes Studied by AC 

Impedance Measurements 

Tiehua Piao, a, * ,c Su-Moon Park,* ,a Chil-Hoon Doh, b and Seong-In Moon b 

a Department of Chemistry, Pohang, University of Science and Technology, Pohang 790-784, Korea 

b Korea Electrotechnology Research Institute, Changwon, Korea 

Effects of electrolyte concentrations and the level of preintercalation (x values in Li x C 6 ) on the lithium ion intercalation into 

graphite lattices have been examined in propylene carbonate-ethylene carbonate mixed solutions with LiClO 4 as an electrolyte by 

ac impedance measurement techniques. Exchange current densities were determined for reductive intercalation of lithium by ac 

impedance measurements to range between 1.4 and 2.4 mA/cm 2 depending on the amount of intercalated lithium ions with a transfer 

coefficient (�) of 0.65. Diffusion coefficients during the deintercalation process have also been determined at various preintercalation 

levels. The dependence of diffusion coefficients and exchange currents on the x values in Li x C 6 (x � 1) is discussed. 

© 1999 The Electrochemical Society. S0013-4651(98)02-016-5. All rights reserved. 

Manuscript submitted February 4, 1999; revised manuscript received May 1, 1999. 

The electrochemistry of the lithium-ion intercalation process into 

the graphite lattices has received much attention in the battery community 

because of its practical applications to rechargeable lithium 

batteries. 1-10 Metallic lithium presents serious problems as an anode 

material in lithium rechargeable batteries. These problems include (i) 

poor plating/stripping efficiencies in organic electrolyte solutions, (ii) 

formation of lithium dendrites during charge and discharge cycles, and 

(iii) unsafe operating characteristics due to high reactivity of the lithium 

metal. Therefore, much effort has been focused on search for suitable 

materials as an alternative anode for lithium rechargeable batteries 

in the last decade. 11-16 Among many types of materials reported, 

graphite appears to be the most desirable candidate. 

Graphite has a nearly perfect lamellar structure. 17 Lithium is 

known to intercalate and deintercalate into its lattices upon charging 

and discharging. This property can be used to make graphite as an 

anode in secondary lithium batteries. Graphite has two major advantages 

as an anode material 2 :(i) a high storage capacity, as Li � can 

intercalate into graphite lattices to make a graphite intercalation 

compound (GIC) with a stoichiometry of Li x C 6 with x � 1; and (ii) 

a relatively flat potential profile near the redox potential of the 

Li/Li � couple during charge-discharge processes. 

The intercalation of lithium into graphite lattices is an electrochemical 

process similar to an underpotential deposition and can be 

described as an electrochemical reaction 3 

Li � � 6C � e � } LiC 6 

The reaction mechanism is more complicated than that represented 

by reaction 1 due to the phase transition related to the staging phenomenon 

of the GIC. 4,18 The electrochemical kinetics of reaction 1 

determines the power densities of lithium batteries. Despite a number 

of reports on the performance of graphite as an anode material, few 

addressed the reaction kinetics. 5,6 Yazami and Touzain measured diffusion 

coefficients of Li � within the graphite lattice by potentiometric 

and galvanometric intermittent titration techniques. 5 Recently, 

Tokami and co-workers 6 studied the diffusion kinetics of lithium-ion 

intercalation into various carbons by ac impedance techniques. To our 

knowledge, no kinetic parameters such as exchange current densities 

and transfer coefficients of lithium-ion intercalation reaction into 

graphite electrodes have been reported. 

The aim of this study is to investigate the reaction kinetics of the 

electrode/electrolyte interfaces for the lithium intercalation process. 

In the present work, the exchange current densities and the transfer 

coefficient have been determined using ac impedance measurements. 

Diffusion coefficients of the Li � ion in the graphite lattices 

* Electrochemical Society Active Member. 

c Present address: Arbin Instruments, College Station, Texas 77845, USA. 

[1] 

during deintercalation processes have been determined by the 

steady-state ac techniques. 

Experimental 

Lithium perclorate (LiClO 4 , Alfa Chemical) was dried under vacuum 

(10 �4 mmHg) below its melting point for 2 days before use. 

Propylene carbonate (PC, Aldrich 99�%) and ethylene carbonate 

(EC, Aldrich 98%) were fractionally distilled under reduced pressure 

with a reflux ratio of 5:1 after week-long storage over activated molecular 

sieves (Acros, 4A). Distilled PC and EC were degassed by 

three freeze-pump-thaw cycles and introduced into the dry box. 18- 

Crown-6 (Aldrich, 99%) and 12-crown-4 (Aldrich, 98%) cyclic 

ethers were used as received. Unless otherwise stated, the electrolyte 

used in this study is 1.0 M LiClO 4 dissolved in a 50:50 mixture of 

PC and EC by volume. 

A single-compartment cell was used for all the electrochemical 

measurements inside an inert atmosphere glove box. The working 

electrode was made of a graphite sheet (Alfa, 99.9%) with a geometric 

area of about 1.0 cm 2 and a total weight of 15-20 mg. The 

electrode thickness was approximately 0.1 mm. Lithium foils (Alfa 

Chemical, 99.9%) were used as a reference and counter electrodes. 

All the experiments including the electrolyte preparation and cell assembly 

were carried out under an argon atmosphere in a glove box 

(Innovative Technology MB-150-M). The Ar atmosphere was continuously 

circulated through a purification train containing molecular 

sieves and the copper metal to remove trace oxygen and water 

vapor. The O 2 content was monitored by diethylzinc mixed with nheptane. 

The absence of a vapor cloud indicates less than 5 ppm O 2. 

An EG&G Princeton Applied Research model 273 potentiostatgalvanostat 

was used for electrochemical measurements. The lithium 

intercalation was conducted by passing a constant current of 

0.25 mA. The x values in Li xC 6 were determined from the amount 

of electrical charge passed and the initial weight of the graphite 

electrode. 18 

The instrument used for impedance measurements consisted of a 

PAR 5210 lock-in amplifier and the PAR 273 potentiostat-galvanostat. 

The impedance data were obtained in a frequency range of 

50 kHz-0.005 Hz. The ac amplitude was 5 mV peak-to-peak and the 

sampling rate of 15 samples per dec was used. In the frequency 

range 50 kHz-5 Hz, single-sine measurements were employed with 

the lock-in amplifier, whereas multisine measurements were conducted 

at frequencies between 5 and 0.005 Hz. The impedance data 

reported here were the ones merged from both single and multisine 

measurements. 

The impedance data were analyzed using a computer software 

program, Equivalent Circuit, provided by Universiteit Twente 

through EG&G. 19 The program used a variety of electrical circuits 

to numerically fit measured impedance data. The program is capable

of conducting analysis of heavily convoluted frequency dispersion 

data by deconvoluting the complex responses into those of simple 

subcomponents. This approach combined with the general nonlinear 

least-squares fitting procedure allowed us to construct equivalent circuits 

whose simulated responses describe actually measured data 

well. From this simulation, values of various circuit components 

were obtained. 

In the present work, a constant phase element (CPE or Q) is used 

for equivalent circuits except for resistors, R. The general expression 

for the admittance response of the CPE is 19 

YCPE � Yc�n cos(n�/2) � jYC�n sin(n�/2) [2] 

where � is the angular frequency, which is 2�f with f being frequency 

and j � (�1) 1/2 . Depending on the n value, the CPE can have 

a variety of responses. If n � 0, it represents a resistance with R � 

Y �1 

c ; if n � 1, a capacitance with C � YC, and if n � 0.5, a Warburg 

response. 

Results and Discussion 

Chronopotentiometric responses.—A major problem encountered 

during the electrochemical lithium intercalation reaction in the PCbased 

electrolytes is the excessive electrolyte decomposition reaction 

during the first lithiation process. Much effort has been expended to 

overcome these problems. 7-10,20 Fong et al. 10 reported that introducing 

a cosolvent, EC, into the PC-based electrolyte improves the reversibility 

of Li/graphite cells. Other workers8,9,20 suggested that 

crown ethers reduce the degree of PC decomposition reactions when 

used as an additive. We examined effects of the electrolyte composition 

on the PC decomposition by recording chronopotentiograms in 

four different electrolyte solutions (see Fig. 1) under otherwise-identical 

experimental conditions. In Fig. 1, the period during which the 

potential plateau is maintained at around �0.8 V corresponding to the 

PC decomposition reaction21 changes with the electrolyte composition. 

In 0.1 M LiClO4-PC/EC with 0.1 M 12-crown-4 added, the period 

for the plateau is the shortest. A serious capacity loss is observed 

in the 0.1 M LiClO4-PC solution, as can be seen from the long potential 

plateau corresponding to the PC decomposition reaction. Similar 

results were reported by Shu and co-workers. 9 Fong et al. 10 concluded 

that the PC decomposition reaction at the graphite electrode is 

associated with Li� solvated with PC molecules which become cointercalated 

into the graphite layers. The addition of EC or crown ethers 

to the electrolyte may change the solvation structure and appears to 

suppress the cointercalation process, resulting in the reduction of the 

PC decomposition reaction. 

According to Fong et al., 10 the PC decomposition reaction results 

in the formation of passive films on the graphite electrode surface. Reversible 

Li intercalation still takes place on the film-covered graphite 

Figure 1. Chronopotentiometric results obtained at graphite electrodes with an 

applied current of 0.2 mA in (a) 0.1 M LiClO 4 in PC, (b) 0.1 M LiClO 4 in 

PC/EC (50:50), (c) 0.1 M LiClO 4 in PC/EC (50:50) with 0.1 M 18-crown-6 

added, and (d) 0.1 M LiClO 4 in PC/EC with 0.1 M 12-crown-4 added. 

Journal of The Electrochemical Society, 146 (8) 2794-2798 (1999) 2795 


Figure 2. Chronopotentiometric results obtained at the graphite electrode at an 

applied current of 0.2 mA in 0.1 M LiClO 4 in PC/EC during (a) first and (b) 

second cycles. 

surface even after the surface is passivated. Figure 2 shows the 

chronopotentiograms recorded at the graphite electrode for the first 

two consecutive runs. It is clearly seen in this figure that the length of 

the plateau at about �0.8 V is significantly shorter during the second 

than the first run. This means that the PC decomposition reaction 

mainly takes place during the first intercalation cycle. After the first 

cycle, the dominant process is the lithium intercalation reaction. For 

this reason, we used a 1.0 M LiClO4 solution in PC/EC (50:50) as an 

electrolyte in order to minimize the effect of solvent decomposition 

reactions on the electrochemical measurements and ran each electrochemical 

experiment after the first cycle, during which the PC decomposition 

is a predominant reaction. For kinetic measurements, crown 

ethers were not added to the electrolyte solutions. 

AC impedance studies.—Shown in Fig. 3 are (a) a typical electrochemical 

impedance spectrum at a preintercalated graphite electrode 

with x � 0.330 at an open-circuit potential and (b) an equivalent 

circuit obtained by fitting the impedance responses. The GIC, 

LixC6 , with various x values was prepared by passing a given amount 

of cathodic charge. The x value is then calculated from the increase 

in mass of the electrode from the Faraday law using the amount of 

current applied and the duration of the current flow. 18 The irreversible 

capacity loss was not taken into account in the calculation 

of x values, assuming that the loss is not significant compared to the 

total amount of Li� intercalated. 

The impedance responses shown in Fig. 3a consist of a depressed 

semicircle in the high-frequency range (50 kHz-0.35 Hz) and a linear 

portion with a slope close to unity in the low-frequency range 

(0.41-0.005 Hz). The features shown here are in good agreement 

with those reported in the literature6,22 under similar experimental 

conditions. The depressed semicircle is shown to consist of two arcs 

from the curve-fitting procedure. The small arc in the high-frequency 

range (50 kHz-150 Hz) is attributed to the formation of a passive 

film on the graphite surface. 22 The large semicircle in the mediumfrequency 

range (0.5-145 Hz) is ascribed to the charge-transfer reaction 

of Li intercalation into graphite. 6,22 The linear portion observed 

in the low-frequency region (0.41-0.005 Hz) is characteristic of a 

diffusion-limited process, which is discussed in more detail later. 

The equivalent circuit presented in Fig. 3b describes the impedance 

spectra shown in Fig. 3a; solid lines are calculated responses using the 

circuit shown in Fig. 3b. Values obtained from the simulation for various 

circuit elements shown in Fig. 3b at various x values in LixC6 are 

listed in Table I. The equivalent circuit consists of two parallel RC circuits 

in series, one for the passive film formation and the other for 

lithium intercalation, respectively, as pointed out previously. Three 

CPEs, Q1 � Q3 , are included in the equivalent circuit. From Table I 

we see that Q3 is basically the Warburg impedance with n � 0.5. The 

charge-transfer resistance (R2) associated with Li intercalation varies 

depending on the composition of the graphite electrode.



Figure 3. (a) Impedance responses recorded at the graphite electrode in 1.0 

M LiClO 4 in PC/EC at an x value of 0.33 in Li x C 6 at an open-circuit potential 

of 0.20 V; (b) an equivalent circuit describing the impedance responses 

shown in (a). 

The charge-transfer resistance, R CT , is related to the exchange 

current (i 0 ) by the equation 23a 

R CT � RT/(nFi 0 ) [3] 

The exchange current densities were calculated using Eq. 3 for various 

x values in Li x C 6 as listed in Table I. The result is shown in Fig. 

4. The exchange current densities range between 1.4 and 2.4 mA/cm 2 

and decrease monotonously with an increase in the x value of Li x C 6 

with some scattered points. The dependence of the exchange current 

on the amount of Li � is readily expected because of the different 

equilibrium potentials at the interface. While we found no reported 

exchange current density data for lithium intercalation into the 

graphite electrode in the literature, there are reports 6,24 about the 

charge-transfer resistance at various carbon electrodes determined by 

ac impedance methods. These values were reported to range between 

5 and 20 � depending on the carbon types, which are in good agreement 

with ours listed in Table I. A similar but more drastic change in 

the exchange current has been reported by Colson et al. 25 for sodium 

intercalation in sodium molybdates. This result suggests that the 

interfacial charge-transfer process is associated with the electron 

transfer rather than the Li � transfer. 

Shown in Fig. 5 are the impedance spectra recorded at fresh electrodes 

(without preintercalation) in 0.1, 0.2, 0.5, 0.8, and 1.0 M 

LiClO 4 in the PC/EC mixed solvent at an applied potential of 0.20 V 

with no crown ethers added. The equivalent circuit presented in Fig. 

3b also applies to the data shown in Fig. 5. Values obtained for the 

various circuit elements at different LiClO 4 concentrations are listed 

in Table II. As expected, the solution resistance (R s ) estimated from 

the high-frequency intercept and the charge-transfer resistance (R 2 ) 

obtained from the larger semicircle for the Li intercalation decrease 

as the Li � concentration increases in solution. The exchange current 

also increases with an increase in the Li � concentration as shown in 

Fig. 6. From the dependence of i 0 on the Li � concentration, one can 

calculate the transfer coefficient (�) for the Li intercalation process 

represented by Eq. 1. The relationship between the exchange current, 

i 0 , and the concentrations is 23 

i0 � nFk0C Li� 

(l��) � 

CLi While this equation is for solution species, it should be applicable to 

the interfacial electron transfer as the equilibrium potential at the elec- 

Table I. Values obtained for simulation of the elements in equivalent circuit shown in Fig. 6 at various x in Li x C 6 . a,b 

Open-circuit 

Q1 Q2 Q3 x in LixC6 potential, V R1 , � R2 , � Y, S n Y S n Y, S n x2 0.000 — 2.01 10.77 1.35 � 10 �4 0.858 6.82 � 10 �3 0.614 0.125 0.543 1.3 � 10 �3 

0.166 0.20 2.91 11.20 6.70 � 10 �4 0.676 6.53 � 10 �3 0.613 0.141 0.555 1.7 � 10 �4 

0.330 0.20 3.02 14.65 6.27 � 10 �4 0.702 6.51 � 10 �3 0.619 0.167 0.588 2.5 � 10 �4 

0.429 0.077 3.44 14.35 2.40 � 10 �4 0.808 5.91 � 10 �3 0.652 0.266 0.514 1.9 � 10 �4 

0.444 0.080 4.10 11.70 8.36 � 10 �4 0.649 5.32 � 10 �3 0.675 0.216 0.401 4.1 � 10 �4 

0.576 0.070 4.42 12.99 7.89 � 10 �4 0.661 4.97 � 10 �3 0.679 0.253 0.490 4.3 � 10 �4 

0.680 0.060 2.96 9.46 6.13 � 10 �4 0.704 5.63 � 10 �3 0.624 0.203 0.453 2.0 � 10 �4 

0.740 0.072 4.46 15.83 3.75 � 10 �3 0.547 5.10 � 10 �3 0.762 0.219 0.394 2.7 � 10 �4 

1.000 0.061 4.37 18.68 4.37 � 10 �4 0.928 6.14 � 10 �3 0.717 0.188 0.481 2.6 � 10 �4 

a Rs values are constant to 13.50 ∀ 1.0 �. 

b Impedance measurement under dc potential stepped to �0.2 V. 

Figure 4. The exchange current plotted vs. x in Li x C 6 . 

[4]

Figure 5. Impedance spectra recorded at the graphite electrode at 0.20 V in 

1.0 M LiClO 4 in PC/EC at various Li � concentrations. 

trode is determined by the activity of Li intercalated and the concentration 

of Li � in solution. From the log(i 0 ) vs. log(C Li�) plot shown in 

Fig. 6, we calculate the transfer coefficient (�) of 0.65 for the intercalation 

process, indicating that the electron transfer is reasonably 

reversible. 

From the analysis of the impedance spectrum shown in Fig. 3a, the 

diffusion coefficient of Li � in the graphite electrode can also be determined. 

As mentioned already, the impedance responses (see Fig. 3a) 

contain linear portions in the low-frequency range with an angle close 

to 45� from which diffusion coefficients can be obtained. This straight 

line in the low-frequency region is caused by the Warburg impedance 

due to the diffusion. The slope of the straight line in the Randles plot 

(Z � vs. � 2 plot) in the low-frequency region is related to the Warburg 

coefficient, �, according to the equation 26 

Journal of The Electrochemical Society, 146 (8) 2794-2798 (1999) 2797 


� � RT/{n 2 F 2 A 1/2 [1/(D O 1/2 CO ) � 1/(D R 1/2 CR )]} [5] 

where R is the gas constant, T the absolute temperature, n the number 

of electrons transferred, A the electrode area, and C the concentrations 

with subscripts representing the oxidant (O) and reductant (R), respectively. 

Since D O 1/2 CO >> D R 1/2 CR under the experimental conditions 

used in this experiment, Eq. 5 reduces to 

� � RT/(n 2 F 2 A 1/2 D R 1/2 CR ) [6] 

The value of C R (mol/cm 3 ) is calculated from the molar volume of 

graphite and the quantity of lithium intercalated. A typical Randles 

plot is shown in Fig. 7. While this equation was for the solution redox 

species, a reasonably good linearity observed in the frequency range 

0.025-0.145 Hz indicates that it is applicable to situations like the one 

currently considered. Nonetheless, use of Eq. 4-6 may provide only an 

indication of how the calculated parameters vary depending on the experimental 

conditions. The data points deviate from the linearity at 

Figure 6. Effects of [Li � ] on exchange current densities. 

Table II. Values obtained for simulation of the elements in equivalent circuit (Fig. 6) for data shown in Fig. 8. a 

very low frequencies (



Figure 7. A typical Randles plot in a lower frequency region shown in Fig. 5b. 

et al. 28 This is perhaps because the structures of the carbon they used 

were different from ours and Takami’s. In our case, the diffusion coefficient 

is seen to decrease significantly between x � 0.1 and 0.4 and 

then levels off when x is greater than 0.4. We believe that the break 

point of the two domains is related to the structural change of graphite 

during intercalation. Also, the intercalation between Li � and the 

graphite host lattice would be responsible for the changes in diffusion 

coefficients. 25,29 While abrupt changes in diffusion coefficients were 

observed due to the structural modification in the host material during 

the intercalation of Li into a cathode material such as V 2 O 5 25 or that 

Na into molybdates 29 depending on the x values, the change is relatively 

smooth and continuous in our case. This means that graphite undergoes 

its structural modification gradually in a continuous fashion 

rather than an abrupt change in the crystal structure. 

Conclusion 

We see from our results that the diffusion coefficients are strongly 

dependent on the electrode composition. The diffusion coefficients decrease 

with an increase in x in the GIC, Li x C 6 . There are two domains 

in how the diffusion coefficients are distributed depending on the level 

of preintercalation. When x < �0.4 or so, the diffusion coefficients 

decrease rapidly with an increase of the x value. Above this, the diffusion 

coefficients stay approximately constant. 

The kinetic parameters of lithium intercalation have been obtained 

from ac impedance measurements. The exchange current densities are 

in the range 1.4-2.4 mA/cm 2 depending on the Li content of the graphite 

electrode, and the transfer coefficient was determined to be 0.65. 

Overall, the lithium intercalation/deintercalation reaction is electrochemically 

reversible, although it displays chemical irreversibility at 

initial stages due to the effective reaction of intercalated lithium with 

solvent. Once its surface is passivated, a reasonably reversible lithium 

intercalation reaction takes place. 

The solution resistance decreases as the electrolyte concentration 

increases. The decrease, however, slows down beyond about 0.8 M 

LiClO 4 . It appears that the electrolyte concentration higher than 1 M 

does not provide benefits in terms of solution resistance for actual battery 

operations. The drastic decrease in diffusion coefficients beyond 

x > 0.4 would result in a decrease in power densities of the lithium-ion 

intercalation batteries. 

Acknowledgment 

This work was supported by a grant from Korea Electrotechnology 

Research Institute (KERI) and Research and Development Man- 

Figure 8. Effects of x values in Li x C 6 on diffusion coefficients. The values 

determined by the ac impedance method refer to diffusion coefficients of Li 

atom, while those determined by the chronoamperometric method refer to diffusion 

coefficients of Li � ion. 

agement Center for Energy and Resources (RACER). This work was 

performed at the Department of Chemistry, University of New Mexico, 

Albuquerque, NM, as part of the T.P.’s dissertation. 

Pohang University of Science and Technology assisted in meeting the publication 

costs of this article. 

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