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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 Moonb

aDepartment of Chemistry, Pohang, University of Science and Technology, bKorea Electrotechnology Research Institute, Changwon, Korea

Pohang 790-784, Korea

Effects of electrolyte concentrations and the level of preintercalation (x values in LixC6) on the lithium ion intercalation into graphite lattices have been examined in propylene carbonate-ethylene carbonate mixed solutions with LiClO4 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/cm2 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 LixC6 (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 material2: (i) a high storage capacity, as Li can intercalate into graphite lattices to make a graphite intercalation compound (GIC) with a stoichiometry of LixC6 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 reaction3 Li 6C e } LiC6 [1]

during deintercalation processes have been determined by the steady-state ac techniques. Experimental Lithium perclorate (LiClO4, 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. 18Crown-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 LiClO4 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 cm2 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 O2 content was monitored by diethylzinc mixed with nheptane. The absence of a vapor cloud indicates less than 5 ppm O2. 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 LixC6 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

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-workers6 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.

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

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


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 is19 YCPE Yc


cos(n /2)



sin(n /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 Yc 1; 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 2. Chronopotentiometric results obtained at the graphite electrode at an applied current of 0.2 mA in 0.1 M LiClO4 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 1. Chronopotentiometric results obtained at graphite electrodes with an applied current of 0.2 mA in (a) 0.1 M LiClO4 in PC, (b) 0.1 M LiClO4 in PC/EC (50:50), (c) 0.1 M LiClO4 in PC/EC (50:50) with 0.1 M 18-crown-6 added, and (d) 0.1 M LiClO4 in PC/EC with 0.1 M 12-crown-4 added.


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

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

Figure 4. The exchange current plotted vs. x in LixC6.

Figure 3. (a) Impedance responses recorded at the graphite electrode in 1.0 M LiClO4 in PC/EC at an x value of 0.33 in LixC6 at an open-circuit potential of 0.20 V; (b) an equivalent circuit describing the impedance responses shown in (a).

The charge-transfer resistance, RCT, is related to the exchange current (i 0) by the equation23a RCT RT/(nFi 0) [3]

The exchange current densities were calculated using Eq. 3 for various x values in LixC6 as listed in Table I. The result is shown in Fig. 4. The exchange current densities range between 1.4 and 2.4 mA/cm2 and decrease monotonously with an increase in the x value of LixC6 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 reports6,24 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 LiClO4 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 LiClO4 concentrations are listed in Table II. As expected, the solution resistance (Rs) estimated from the high-frequency intercept and the charge-transfer resistance (R2) 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, i0, and the concentrations is23 i0 nFk 0C Li

(l )



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 LixC6.a,b Open-circuit potential, V -- 0.20 0.20 0.077 0.080 0.070 0.060 0.072 0.061 Q1 R1, 2.01 2.91 3.02 3.44 4.10 4.42 2.96 4.46 4.37 R2, 10.77 11.20 14.65 14.35 11.70 12.99 9.46 15.83 18.68 Y, S 1.35 6.70 6.27 2.40 8.36 7.89 6.13 3.75 4.37 10 10 10 10 10 10 10 10 10

4 4 4 4 4 4 4 3 4

Q2 n 0.858 0.676 0.702 0.808 0.649 0.661 0.704 0.547 0.928 6.82 6.53 6.51 5.91 5.32 4.97 5.63 5.10 6.14 YS 10 10 10 10 10 10 10 10 10

3 3 3 3 3 3 3 3 3

Q3 n 0.614 0.613 0.619 0.652 0.675 0.679 0.624 0.762 0.717 Y, S 0.125 0.141 0.167 0.266 0.216 0.253 0.203 0.219 0.188 n 0.543 0.555 0.588 0.514 0.401 0.490 0.453 0.394 0.481 1.3 1.7 2.5 1.9 4.1 4.3 2.0 2.7 2.6 x2 10 10 10 10 10 10 10 10 10

3 4 4 4 4 4 4 4 4

x in LixC6 0.000 0.166 0.330 0.429 0.444 0.576 0.680 0.740 1.000

a b

Rs values are constant to 13.50 1.0 . Impedance measurement under dc potential stepped to

0.2 V.

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

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


Figure 6. Effects of [Li ] on exchange current densities. Figure 5. Impedance spectra recorded at the graphite electrode at 0.20 V in 1.0 M LiClO4 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(CLi ) 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 equation26

1/2 RT/{n2F 2A1/2[1/(DO CO)

very low frequencies (<0.010 Hz), which is attributed to the finite diffusion effects of lithium in the graphite.27 In order to see how the lithium content affects the diffusion coefficient, diffusion coefficients during the deintercalation processes were determined at different x values from the analysis described. The results are shown in Fig. 8. The diffusion coefficients are in the range 1 10 12 to 1 10 8 cm2/s. The diffusion coefficients were also determined by a conventional potentiostatic chronoamperometric technique and extracted from the Cottrel equation i(t ) nFAD1/ 2 C 1/ 2t1/ 2 [7]

1/(D1/2CR)]} R


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 D1/2 CO >> D1/2CR under the experimental conditions O R used in this experiment, Eq. 5 reduces to RT/(n2F 2A1/2D1/2CR) R [6]

The value of CR (mol/cm3) 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

where i(t) is the current at time t after a potential step to a given value with other symbols having their usual meanings. The i(t) vs. t 1/2 plot should be a straight line with its slope containing the diffusion coefficient from which its value is estimated. The results thus obtained are also shown in Fig. 8; the diffusion coefficients obtained by the two techniques agree reasonably well with each other. The diffusion coefficients shown in Fig. 8 are strongly dependent on the lithium content of the graphite electrode, decreasing with an increase in x values. A similar effect was also observed by other investigators.6,27 Takami et al.6 measured the diffusion coefficients at various types of carbon electrodes by ac impedance techniques. Their values were in the range 9.0 10 10 to 2.0 10 8 cm2/s. They observed that the diffusion coefficient decreased almost linearly with an increase in the x values of up to x 0.5. The decrease was slower between x 0.5 and 1.0. Jean et al.28 determined diffusion coefficients in the carbon electrode made with petroleum coke by the galvanometric intermittent titration technique and obtained values of 1.0 10 8 to 2.0 10 7 cm2/s. They found two concentration domains; when x < 0.1, the diffusion coefficient is independent of the preintercalation level, while it decreases with the increasing lithium content when 0.1 < x < 1.0. Our diffusion coefficients are comparable with those of Takami et al.6 but are about two orders of magnitude smaller than those reported by Jean

Table II. Values obtained for simulation of the elements in equivalent circuit (Fig. 6) for data shown in Fig. 8.a LiClO4 concentration, M Rs, 0.1 0.2 0.5 0.8 1.0


Q1 R1, 32.98 12.58 11.44 8.53 11.10 R2, 88.34 72.46 58.15 58.30 56.85 Y, S 4.26 5.45 1.20 3.97 1.06 10 10 10 10 10

5 5 4 5 4

Q2 n 0.739 0.789 0.711 0.840 0.710 3.16 4.41 4.84 5.22 5.10 Y, S 10 10 10 10 10

4 4 4 4 4

Q3 n 0.793 0.741 0.745 0.751 0.769 Y, S 3.73 7.27 9.42 1.14 1.12 10 10 10 10 10

2 2 2 2 1

n 0.538 0.573 0.602 0.641 0.622 3.2 1.8 7.2 8.3 6.8


91.54 54.98 35.38 33.40 31.38

10 10 10 10 10

4 4 5 5 5

Impedance measurement under dc potential stepped to

0.2 V.


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

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

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 V2O5 25 or that Na into molybdates29 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, LixC6. 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/cm2 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 LiClO4. 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 LixC6 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.


1. B. Scrosati, J. Electrochem. Soc., 139, 2776 (1992). 2. D. Aurbach and Y. Ein-Eli, J. Electrochem. Soc., 142, 1746 (1995). 3. K. Tatsumi, N. Iwashita, H. Sakaebe, H. Shioyama, and S. Higuchi, J. Electrochem. Soc., 142, 716 (1995). 4. T. Ohzuku, Y. Iwakoshi, and K. Sawai, J. Electrochem. Soc., 140, 2490 (1993). 5. R. Yazami and Ph. Touzain, J. Power Sources, 9, 365 (1983). 6. N. Takami, A. Satoh, M. Hara, and T. Ohsaki, J. Electrochem. Soc., 142, 371 (1995). 7. Z. Jiang, M. Alamgir, and K. M. Abraham, J. Electrochem. Soc., 142, 333 (1995). 8. M. Morita, H. Hayashida, and Y. Matsuda, J. Electrochem. Soc., 134, 2107 (1987). 9. Z. X. Shu, R. S. McMillan, and J. J. Murray, J. Electrochem. Soc., 140, 922 (1993). 10. R. Fong, U. von Sacken, and J. R. Dahn, J. Electrochem. Soc., 137, 2009 (1990). 11. J. Farcy, R. Messina, and J. Perichon, J. Electrochem. Soc., 137, 1337 (1990). 12. N. Kumagai, Y. Matsuura, and K. Tanno, J. Electrochem. Soc., 139, 3553 (1992). 13. N. Kumagai, T. Fujiwara, and K. Tanno, J. Electrochem. Soc., 140, 3194 (1993). 14. K. Kanehori, F. Kirino, T. Kudo, and K. Miyauchi, J. Electrochem. Soc., 138, 2216 (1991). 15. D. Guyomard and J. M. Tarascon, J. Electrochem. Soc., 139, 937 (1992). 16. A. S. Baranski and W. R. Fawcett, J. Electrochem. Soc., 129, 901 (1982). 17. J. E. Fischer and T. E. Thompson, Physics Today, 31, 36 (1978). 18. J. R. Dahn, Phys. Rev. B, 44, 9170 (1991). 19. B. A. Boukamp, Equivalent Circuit User's Manual, University of Twente, 2nd ed., (1989). 20. J. R. Dahn, R. Fong, and M. J. Spoon, Phys. Rev. B, 42, 6424 (1990). 21. A. N. Dey and B. P. Sullivan, Phys. Rev., 117, 222 (1970). 22. R. Yazami and D. Guerard, J. Power Sources, 43-44, 39 (1993). 23. A. J. Bard and L. R. Faulkner, Electrochemical Methods, Fundamentals and Applications, Chap. 3 and 9, John Wiley & Sons, Inc., New York (1980). 24. N. Takami, A. Satoh, M. Hara, and T. Ohsaki, J. Electrochem. Soc., 142, 2564 (1995). 25. S. Colson, L. C. Klein, J. M. Tarascon, and D. Guyomard, J. Electrochem. Soc., 139, 2359 (1992). 26. A. J. Bard and L. R. Faulkner, Electrochemical Methods, Fundamentals and Applications, p. 328, John Wiley and Sons, Inc., New York (1980). 27. C. Ho, I. D. Raistrick, and R. A. Huggins, J. Electrochem. Soc., 127, 343 (1980). 28. M. Jean, C. Desnoyer, A. Tranchant, and R. Messina, J. Electrochem. Soc., 142, 2122 (1995). 29. J. Farcy, R. Messina, and J. Perichon, J. Electrochem. Soc., 137, 1337 (1990).


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