ISSN 1023-1935, Russian Journal of Electrochemistry, 2008, Vol. 44, No. 5, pp. 550–557. © Pleiades Publishing, Ltd. 2008. Original Russian Text © A.V. Churikov, K.I. Pridatko, A.V. Ivanishchev, I.A. Ivanishcheva, I.M. Gamayunova, K.V. Zapsis, V.O. Sycheva, 2008, published in Elektrokhimiya, 2008, Vol. 44, No. 5, pp. 594–601.

Impedance Spectroscopy of Lithium–Tin Film Electrodes1 A. V. Churikovz, K. I. Pridatko, A. V. Ivanishchev, I. A. Ivanishcheva, I. M. Gamayunova, K. V. Zapsis, and V. O. Sycheva Chernyshevsky Saratov State University, ul. Astrakhanskaya 83, 410012 Saratov, Russia Received December 26, 2006

Abstract—A method of electrochemical impedance spectroscopy was used to study the reversible lithium intercalation from nonaqueous electrolyte into tin films with the thickness of 0.1–1 µm. The impedance spectra of lithium–tin (LixSn) electrodes have a complicated shape depending on the electrode state and prehistory; they reflect the occurrence of several consecutive and parallel processes, including the lithium migration, diffusion, and accumulation. The formation of a solid-electrolyte layer on the surface at Li intercalation into Sn is observed. Equivalent circuits are proposed that adequately model the experimental data on the LixSn electrodes both freshly prepared and after prolonged cycling. Problems associated with the choice of equivalent circuits and determination of their parameters, the accuracy of the diffusion coefficient determination, the trends in the parameters' variation with electrode potential (composition) are discussed. Key words: electrode impedance spectroscopy, equivalent circuits, lithium, tin, intercalation, diffusion DOI: 10.1134/S1023193508050078 1

INTRODUCTION

Lithium intercalation into the structure of the anodic material of lithium-ion batteries can proceed by three major mechanisms: intercalation [1], alloy formation [2], and the reaction of lithium substitution for transition metals in their oxides [3]. Our paper focuses on the phenomena related to the alloy formation mechanisms. Lithium alloys attracted the attention of researchers for a long time due to their high capacity parameters. The main advances of recent years in this field were associated with the employment of micro- and nanotechnologies in the synthesis scheme [4] and also with the implementation of a concept of a composite electrode containing a matrix component that prevents considerable bulk changes at the lithium intercalation– extraction [5]. Among lithium alloys and compounds, the most promising are tin alloys that combine reasonable energy properties and adequate kinetic characteristics [6]. In studying such objects, the electrode impedance spectroscopy (EIS) often works as an electrochemical method supplementing the data of direct methods [7–10]. In many cases, the use of EIS is limited to the mere estimation and discussion of the system impedance or the effective electrode resistance. However, the possibilities of this method are essentially wider. Based on EIS, it is possible to determine the main kinetic and diffusion mass transfer parameters, find the approaches 1 The

paper is published based on the materials presented at the International Conference “Fundamental Problems of Energy Conversion in Lithium Electrochemical Systems”, Ufa, 2006. z Corresponding author: [email protected] (A.V. Churikov).

towards determination of the electrode reaction mechanism [11, 12]. The EIS method is based on the registration of frequency dependences (spectra, complex plane plots) of the electrochemical cell impedance and their further interpretation using the technique of equivalent circuits (EC). It is often possible to satisfactorily describe a sufficiently complicated spectrum by several circuits with different sets of parameters. Such an ambiguity is considered to be a fault of this method, as it complicates the verification of the system’s model, i.e. the attribution of a definite physical meaning to EC parameters. In any case, the large number of parameters involved cannot be considered as advantageous, because the model becomes more reliable with minimization of the number of EC elements [13]. To substantiate the choice of a particular model, it is necessary to study the behavior of the system with the varied potential or concentration. In the present paper, the impedance spectra of tin film electrodes are analyzed in the course of lithium intercalation from nonaqueous electrolytes. EXPERIMENTAL Planar working electrodes represented tin chemically deposited on a nickel support. Their surface area was 2 cm2 (a 1 × 1 cm square with the both sides accessible for lithium), the tin layer thickness determined gravimetrically was 0.1–1 µm. In [14], the electrochemical behavior of such electrodes was studied by a chronopotentiometric method. The reference and auxiliary electrode were made of metal lithium, the electrolyte was 1 M LiClO4 solution in a mixture of propylene

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carbonate (PC) and dimethoxyethane (DME). The design of electrochemical cells is described in more detail in [15, 16]. The study was performed by varying the composition of LixSn electrodes of one and the same series but with different prehistory; namely, in the course of primary lithiation of a tin electrode, after the first charge–discharge cycle, and after 40 charge–discharge cycles. The impedance measurements were carried out using a Solartron electrochemical complex (1286 Electrochemical Interface, 1255 HF Frequency Response Analyzer) in the frequency range from 0.01 Hz to 100 kHz, the voltage amplitude was 10 mV. In specified cases, the measurements were performed from 0.001 Hz. A Zview software package (Scribner Associates Inc., USA) was used in calculations. All potentials Ö are presented vs. the lithium reference electrode in the same solution. RESULTS AND DISCUSSION The beginning of the measurement cycle started corresponded to the initial (nonlithiated) state of a Sn electrode. The thin-film tin electrodes immersed into the 1 M LiClO4, PC + DME solution were characterized by a sufficiently stable steady-state potential in the range of 2–2.3 V. The impedance spectrum of a nonlithiated Sn electrode is presented in Fig. 1a in the Nyquist coordinates Z'' vs. Z' (Z' and Z'' are the real and imaginary components of impedance Z, respectively). In the absence of intercalated lithium, the complex plane plots have a simple form of an incomplete semicircle arc with a very large diameter (Fig. 1a). The high-frequency cutoff value Rohm obtained by the interpolation of the complex-plane plot to the real axis includes the external and internal Ohmic resistances (for the largest part, the resistance of the electrolyte layer between the working and reference electrodes), does not change with the electrode potential, and remains constant for a given electrochemical cell. A close Rohm value can be calculated theoretically for the given cell geometry. Further registration of impedance frequency spectra of the lithiated electrode was carried out in the potentiostatic mode at a gradual increase in the amount of intercalated lithium Q as the potential was shifted in the cathodic direction from 2 to 0.01 V. Typical complex plane plots are presented in Figs. 1b, 1c. Insofar as the spectrum scale dramatically changed during the lithium intercalation and its specific features could be observed only in the high-frequency region, the complex-plane presentation of our curves covers only a limited frequency range. For example, at Ö = 1.25 V, the emergence of a new semicircle was observed in the high-frequency range (Fig. 1b). The appearance of this arc was due to the formation of a new interface in the system. In our case, bearing in mind the chemistry of Li and Sn interactions [6], it is reasonable to attribute the latter interface to formation of a passive layer also known as the solid electrolyte interphase (SEI). The appearance RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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Fig. 1. Evolution of impedance diagrams of a tin electrode in 1 MLiClO4, PC + DME in the course of primary lithiation. The electrode potential (vs. Li/Li+), V: (a) 2.0; (b) 1.25; (c) 0.5. No. 5

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of a clearly distinguishable semicircle corresponding to the SEI was observed the further potential shift in the cathodic direction (Fig. 1c). For all electrodes studied, the general trend towards the reduction of the electrode impedance was observed at the cathodic shift from 2 to 0.01 V (Figs. 1a–1c). The high-frequency arc was formed virtually completely at Ö = 0.8 V and the further lithium intercalation induced no essential changes in its shape or size. Thus, one can assume that the main irreversible lithium losses, which are observed in the first cycle and associated with the electrolyte decomposition and the formation of a passive film on tin, start at Ö ≈ 1.25 V and end at Ö ≈ 0.8 V. To the negative of 0.8 V, the reaction of lithium and tin alloy formation is predominant (available capacity). Such conclusions agree both with the voltage profiles presented in the literature [17–19] and with our own data on the cycling of tin electrodes [14]. It is pointed out in many papers that the rational choice of the upper voltage limit is required for the successful cyclic performance of LixSn electrodes. We limited the range of electrode tests in the “charge–discharge” mode by a potential of 0.8 V, which a fortiori eliminated the formation of the pure tin phase at more positive potentials and the concomitant wide fluctuations of the alloy volume during lithium intercalation– extraction [14]. The authors of [20] evidenced that irreversible capacity losses occur at Ö > 1.5 V due to the catalytic acceleration of the electrolyte decomposition reaction at the Sn surface. Lithium is alloyed with tin to form seven phases, from Li2Sn5 to Li22Sn5; in chronopotentiograms, the equilibria of lithium-rich phases with very close formation potentials are undistinguishable from one another, and the individual phases cannot be identified by X-ray analysis. The theoretically calculated potentials of the plateau corresponding to phase transitions between lithium–tin phases with close compositions at room temperature are as follows: ~0.76 V for the Li2Sn5 phase; 0.66 V for the LiSn phase (x = 0.4–0.7 in LixSn); 0.53 V for Li7Sn3; 0.485 V for the Li5Sn2 and Li13Sn5 phases (x = 2.33–2.63 in LixSn); 0.420 V for Li7Sn2; 0.38 V for Li22Sn5 [17]. Typical Ö vs. x curves of electrodeposited thin tin films were characterized by several horizontal plateaus. The real plateau potentials depend on not only by the thermodynamics and the kinetic hindrances but also by the electrode prehistory. For example, with the increase in the number of charge–discharge cycles, a tin layer is developed and the potential profiles undergo considerable changes. The gradual smoothening of the charge–discharge curves correlates with attainment of stable LixSn electrode performance with a high degree of reversibility [14]. This is even clearer in the differential capacitance dQ/dE vs. potential plots [19]. It is assumed that the highest stability is typical of electrodes with flat dQ/dE vs. E dependences that feature no pronounced peaks. The constant shape for the dQ/dE vs. E dependence cor-

responds to the steady state of the material with the steady-state grain size [19]. The use of EIS and chronopotentiometry for the determination of the diffusion rate of guest species in an intercalation electrode requires the knowledge of the relationship between the electrode potential Ö and the lithium concentration c in the alloy [21, 22]. The Ö vs. Ò dependence used in calculations must be obtained under conditions maximally close to the equilibrium conditions. Cyclic charge–discharge curves are unsuitable for this purpose, being characterized by a considerable hysteresis and a strong dependence on the current density. According to detailed studies, even reducing the polarization current density to the limiting value does not always allows obtaining a quasi-equilibrium E vs. c dependence, due to the increase in the role of side processes [23]. We used the coulometric titration method [14, 21, 22]. Typical impedance spectra of a LixSn electrode recorded after prolonged cycling and after the first charge–discharge cycle are shown in Fig. 2. The highfrequency parts of spectra are presented separately in Fig. 3. First, let us consider the spectrum at Ö = 0.65 V. In the high-frequency range, the spectrum represents a depressed distorted semicircle arc. At lower frequencies, this arc transforms into a straight line situated at an angle of 45° to the Z' axis. The high frequency semicircle arc is characteristic of many lithium electrode systems that include a passive film [24–26]. The presence of such characteristic geometric features of the impedance complex plane plots allows two successive stages of the electrochemical process to be identified with sufficient reliability. The first stage is the transfer of Li+ cations through the “electrolyte | SEI | matrix” structure, the second stage is the diffusion of lithium intercalated into the alloy in LixSn. As the studied spectra are sufficiently clearly divided into high- and low-frequency parts, it is expedient to consider them separately by determining the individual contributions of the passive layer and the tin matrix into the general impedance of a LixSn electrode. Accordingly, in addition to Rohm, the equivalent circuit should include elements that model the SEI behavior and describe the lithium transport in the tin matrix. A common EC version for modeling a passive film represents a SEI ionic resistance and an interface capacitance connected in parallel. The complex plane plot of such a R||C circuit consists of a regular semicircle with the center on the Z' axis. Insofar as the high-frequency arc is usually distorted (depressed and/or asymmetric), it can be presented as the sum of several semicircles. Its modeling requires the use of a set of R||C circuits connected in series. The physical meaning of such an EC is as follows: SEI has a multilayer structure in which each circuit corresponds to a layer. However, if the satisfactory agreement between experiment and calculation requires that more than two R||C circuits with close characteristic frequencies were connected, then their

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Fig. 2. Impedance diagrams of LixSn electrodes in 1 M LiClO4, PC + DME: (a) after prolonged cycling; (b) after the first charge–discharge cycle. The potential of a LixSn electrode, V (vs. Li/Li+) is shown near the curves.

Fig. 3. The high-frequency range of impedance diagrams of LixSn electrodes in 1 M LiClO4, PC + DME: (a) after prolonged cycling; (b) after the first charge–discharge cycle. The potential of a LixSn electrode V (vs. Li/Li+) is shown near the curves.

parameters turn out to be interdependent (cross-correlation) and thus cannot be determined unambiguously. To describe the behavior of a LixSn electrode in the low-frequency range, it is necessary to introduce additional elements into the EC. As was found, “pure diffusion”, i.e., free of complications due to superposition of other processes, occurs at 0.65 V and is reflected in the complex plane as a straight line at 45° (Fig. 2b). It is logical to assume that favorable conditions that allow one to observe diffusion in its pure form are realized at E = 0.65 V. Hence, it is expedient to introduce the Warburg diffusion element W into EC in modeling the low-

frequency impedance spectrum. At other potentials, the lithium diffusion in the matrix is masked either partly or completely by the other processes including the charge accumulation or the charge leakage through the blocking LixSn|Ni interface, which is reflected in the deflection of the low-frequency line from 45° or its transformation into an arc of a large semicircle at some potentials (0.6, 0.7, and 0.8 V). The domination of any of these processes is reflected in the EC pattern by connecting the leakage resistance R3 or the matrix capacitance C3 in parallel to W. Ultimately, we obtain circuit 1 in Fig. 4 that models very well the impedance of a fresh LixSn

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impedance, namely, a constant phase angle (Fig. 2a). The noncoincidence of the line angle with 45° requires that W and C3 were replaced by a constant phase ele-

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ment (CPE) ZCPE = ( iω ) /σ with the variable exponent n = 0–1. Herewith, the circuit 1 in Fig. 4 is transformed into circuit 2. The results of modeling based on circuit 2 are presented in Table 2. The use of CPE with variable exponent simplifies considerably the choice of EC but creates uncertainty in the interpretation of the low-frequency equivalent circuit component. The replacement of capacitance by a CPE is usually explained by the roughness and nonhomogeneity of the solid electrode surface [13]. For our electrodes, the surface can indeed be developed by multiply repeated charge-discharge cycles and undergo considerable morphologic changes. But the interpretation of CPE is problematic if n differs noticeably from 1 and 1/2, as in our case.

C2

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Fig. 4. Equivalent circuits modeling the impedance spectra of LixSn electrodes (1, 3) after the first charge–discharge cycle and (2, 4) after prolonged cycling.

electrode at all potentials under study. Certain results of such modeling are presented in Table 1. However, LixSn electrodes after prolonged cycling demonstrated a different shape of low-frequency

Another possible explanation for the appearance of a constant phase angle can be given in terms of the existence of a phenomenon of anomalous diffusion, as in paper [27]. The authors studying the ac conductivity of disordered materials pointed to the frequency dispersion of the conductivity mechanism. The conductivity was constant up to a certain frequency, while at higher frequencies, it depended exponentially on the frequency with the exponent n = 0–1. Formally, this should result in the appearance of a constant phase angle in the impedance diagram. The authors of [27] suggested that the appearance of ac conductivity is due to the transition from the ordinary (Fick) diffusion to the anomalous diffusion mechanism. In terms of the hopping transport mechanism in disordered materials, the anomalous diffusion can be caused by the dispersion of both the barrier height and the jump distance [28, 29].

Table 1. Results of modeling of impedance spectra of a LixSn electrode after the first charge–discharge cycle Equivalent circuit no. 1 E, V

Rohm, Ω cm2

R1, Ω cm2

C1, µF/cm2

R2, Ω cm2

C2, µF/cm2

R3, Ω cm2

C3, µF/cm2

W, Ω cm2/s0.5

0.01 0.30 0.65 0.80

36.3 36.2 34.6 35.7

13.0 14.3 11.5 24.1

1.6 1.7 1.8 1.9

27.4 26.8 19.4 23.6

7.7 9.4 15.1 36.2

– – – 1531

61.9 105 – 1.26

18.9 36.6 73.6 346.7

Equivalent circuit no. 3 E, V

Rohm, Ω cm2

R1, Ω cm2

C1, µF/cm2

W1, kΩ cm2/s0.5

R2, Ω cm2

C2, µF/cm2

0.01 0.30 0.65 0.80

33.0 32.5 30.5 30.3

44.4 45.5 39.5 61.8

5.6 6.7 – –

2.032 2.094 2.409 2.701

– – – 1408

65.3 108 – 1.5

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Table 2. Results of modeling of impedance spectra of a LixSn electrode after prolonged cycling Equivalent circuit no. 2 E, V 0.01 0.25 0.5 0.6

Rohm, Ω cm2

R1, Ω cm2

52.7 52.9 53.0 55.6

5.3 5.9 6.4 8.1

C1, µF/cm2 6.5 8.2 22.2 19.6

R2, Ω cm2

C2, µF/cm2

σ, cn/Ω cm2

n

10.5 12.4 14.7 21.5

138 184 290 243

0.1056 0.0752 0.0649 0.0876

0.670 0.746 0.705 0.665

Equivalent circuit no. 4 E, V

Rohm, Ω cm2

R1, Ω cm2

C1, µF/cm2

W, Ω cm/s0.5

0.01 0.25 0.5 0.6

52.2 52.3 52.2 54.7

16.3 19.8 22.5 31.9

132 340 348 344

418 419 289 321

Yet another version of high-frequency EC and its physical meaning were suggested in our papers [24–26]. This high-frequency circuit includes a SEI resistance R1, a Warburg diffusion impedance W1 associated with the ionic transport in the passive film, and a capacitance ë1 interpreted as the capacitance of a solid-electrolyte double layer or a space charge layer in the SEI. Then, in place of circuits 1 and 2 in Fig. 4, we obtain circuits 3 and 4, respectively. Such circuits contain a smaller number of elements, so that the standard deviations of their parameters are lower (the parameters are determined with higher precision). At the same time, circuits 3 and 4 adequately model an important peculiarity of the LixSn electrode impedance spectrum in the high-frequency limit, namely, the arc transformation into a straight line that resembles the diffusion impedance (Fig. 3). This provides grounds to assume that the diffusion component of the SEI polarization is of a significant magnitude at small times, which justifies the use of the corresponding element in the EC design. Thus, circuit 3 contains two Warburg diffusion impedances with different meaning, namely, the element W1 is related to the ion transport in SEI and the element W2 is associated with the lithium diffusion in the tin matrix. These processes differ in the rate so widely that the elements W1 and W2 correspond to different frequency ranges and the relevant Warburg constants differ by several orders of magnitude. Let us consider the dependence of EC parameters on the potential (on the lithium concentration in the alloy). First, note that in addition to four EC shown above, other versions with comparable standard deviations of parameters are possible, which were also considered (on the whole, 12 circuits were analyzed). Different circuits give different interpretations of the transport process in SEI but contain virtually similar parameters RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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n 0.674 0.751 0.715 0.679

related to the lithium alloy. Thus these circuits can be equally well used in, e.g., the determination of the lithium diffusion coefficient in thin tin layers. Besides, as seen from Table 1, the selected circuits can be further simplified, which is reflected in the absence of some elements at certain potentials. The size and shape of the high-frequency semicircle arc (and, therefore, the SEI parameters) exhibit a certain dependence on the lithium content in the electrode. The tin matrix begins to affect the SEI properties at potentials to the positive from 0.65 V where the electrode is lithium-depleted. In the range from 0.01 to 0.65 V, where lithium-enriched phases exist, the differences between the spectra in the high-frequency range are negligible and the spectra virtually coincide (Fig. 3b). We have also found a similar behavior of lithium–carbon intercalation compounds [30]. According to Tables 1 and 2, in all the cases, the electrolyte solution resistance Rohm is independent of both the electrode potential and chosen circuit and could be determined with high precision (error of about 1%). The passive layer resistance is comparable with the electrolyte resistance, independent of the lithium concentration in the alloy virtually throughout the studied range, and starts to increase only at E > 0.7 V. The error of the SEI parameter determination using circuit 3 or 4 is at the level of several per cent, the resistance R1 is determined with the highest precision and the capacitance ë1 is determined with the least precision because its role is insignificant. The errors are considerably higher for circuits 1 and 2 due to the cross-correlation of parameters R1 and R2, ë1 and ë2, i.e., it is reasonable to analyze only the overall SEI characteristics rather than the individual parameters of these circuits. In earlier studies of the evolution of the high-frequency arc in the complex plane plot for a LixSn elecNo. 5

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10 11 12 13 14 –logD [cm2/s] Fig. 5. Dependence of the lithium diffusion coefficient D in tin on the potential of a LixSn electrode.

trode subjected to aging in electrolyte, another trend was revealed, namely, the corrosion-induced decrease in the lithium concentration in alloy during the storage is simultaneously accompanied by an increase in the high-frequency impedance due to increasing SEI thickness and decreasing conductivity [24]. It can be concluded that the passive film does not grow in the course of the LixSn electrode cycling, being almost completely formed in the first cycle. But the SEI-related capacitance components increase by virtually two orders of magnitude after prolonged cycling, which can evidence the increase in the electrode roughness. Diffusion coefficient D of lithium in tin was calculated from the low-frequency Warburg constant W (or W2) that can be determined with high precision (standard deviation of 1–7%). As seen from Table 1, this parameter depends weakly on the chosen EC. In calcudE/dc lation, we used the general expression of W = ------------------ , F 2D that takes into account the non-Nerstian relationship between the electrode potential and the concentration of intercalated species [21, 22, 30]. As noted above, the derivative dE/dc was determined by coulometric titration [14], its role in calculations was very significant. The results of calculations are presented in Fig. 5. The dependence of D on the potential is very close to analogous curves obtained in [14] by pulse chronopotentiometry for tin plate electrodes (a thin tin layer on an iron support). The phase formation was manifested as the extremums in D vs. E curves. The lithium diffusion coefficient varied in the range from 10–9 to 10–14 cm2/s, increasing by several orders of magnitude with the enrichment of the alloy in lithium, which was accompanied by the transition via a series of successive phases from Li2Sn5 to Li22Sn5.

CONCLUSION Thus, impedance spectroscopy allows reliable registration of all the major events that occur in the course of primary lithiation and the further cycling of LixSn film electrodes in nonaqueous electrolytes. These include the formation of a passive surface layer with a high ionic conductivity, the cycling stability of their properties as opposed to very considerable changes in diffusion properties of the tin matrix with varied lithium concentration, and the changes in the tin electrode morphology on prolonged cycling. In the considered case, the choice of equivalent circuit is not the major concern due to the well-separated contributions of the electrode surface and bulk on the frequency scale. ACKNOWLEDGEMENTS The authors are grateful to the researchers of the Frumkin Institute of Physical Chemistry and Electrochemistry of the Russian Academy of Sciences T.L. Kulova and A.M. Skundin for their help in performing the impedance measurements. The work was financially supported by the Russian Foundation for Basic Research (project no. 06-03-32803) and a Grant of the President of the Russian Federation for Young Russian Researchers (project no. MK-2222.2006.3). REFERENCES 1. Nagaura, T. and Tozawa, T., Prog. Batt. Solar Cells, 1990, vol. 9, p. 209. 2. Idota, Y., Kubota, T., Matsufuji, A., Maekawa, Y., and Miyasaka, T., Science, 1997, vol. 276, p. 1395. 3. Poizot, P., Lauruelle, S., Grugeon, S., Dupont, L., and Tarascon, J.-M., Nature, 2000, vol. 407, p. 496. 4. Schoonman, J., Solid State Ionics, 2000, vol. 135, p. 5. 5. Boukamp, B.A., Lesh, G.C., and Huggins, R.A., J. Electrochem. Soc., 1981, vol. 128, p. 725. 6. Pridatko, K.I. and Churikov, A.V., Elektrokhimicheskaya Energetika, 2005, vol. 5, p. 16. 7. Dimov, N., Fukuda, K., Umeno, T., Kugino, S., and Yoshio, M., J. Power Sources, 2003, vol. 114, p. 88. 8. Zhang, X.-W., Wang, C., and Appleby, A.J., J. Power Sources, 2003, vol. 114, p. 121. 9. Chu, Y.-Q., Fu, Z.-W., and Qin, Q.-Z., Electrochim. Acta, 2004, vol. 49, p. 4915. 10. Choi, W.C., Byun, D., Lee, J.K., and Cho, B., Electrochim. Acta, 2004, vol. 50, p. 523. 11. Li, H., Huang, X., and Chen, L., J. Power Sources, 1999, vol. 81–82, p. 340. 12. Levi, M.D., Gofer, Y., and Aurbach, D., Elektrokhimiya, 2004, vol. 40, p. 310. 13. Elektroanaliticheskie metody. Teoriya i praktika (Electroanalytical Methods. Theory and Practice), Sholts, F., Ed., Moscow: BINOM. Laboratoria Znanii, 2006. 14. Pridatko, K.I., Elektrokhimiya, 2006, vol. 42, p. 72. 15. Churikov, A.V., Volgin, M.A., and Pridatko, K.I., Electrochim. Acta, 2002, vol. 47, p. 2857.

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IMPEDANCE SPECTROSCOPY OF LITHIUM–TIN FILM ELECTRODES 16. Churikov, A.V., Volgin, M.A., Pridatko, K.I., Ivanishchev, A.V., Gridina, N.A., and L’vov, A.L., Elektrokhimiya, 2003, vol. 39, p. 591. 17. Winter, M. and Besenhard, J.O., Electrochim. Acta, 1999, vol. 45, p. 31. 18. Wang, J., Raistrick, I.D., and Huggins, R.A., J. Electrochem. Soc., 1986, vol. 133, p. 457. 19. Courtney, I.A., McKinnon, W.R., and Dahn, J.R., J. Electrochem. Soc., 1999, vol. 146, p. 59. 20. Beattie, S.D., Hatchard, T., Bonakdarpour, A., Hewitt, K.C., and Dahn, J.R., J. Electrochem. Soc., 2003, vol. 150, p. A701. 21. Churikov, A.V. and Ivanishchev, A.V., Electrochim. Acta, 2003, vol. 48, p. 3677. 22. Ivanishchev, A.V. and Churikov, A.V., Elektrokhimicheskaya Energetika, 2003, vol. 3, p. 174.

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No. 5

2008