A review on the solid-state ionics of electrochemical intercalation processes: How to interpret properly their electrochemical response

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Solid State Ionics 179 (2008) 742 – 751 www.elsevier.com/locate/ssi

A review on the solid-state ionics of electrochemical intercalation processes: How to interpret properly their electrochemical response Doron Aurbach ⁎, Mikhail D. Levi, Elena Levi Department of Chemistry, Bar-Ilan University, Ramat-Gan, 52900, Israel Received 27 July 2007; received in revised form 18 December 2007; accepted 20 December 2007

Abstract In this paper, we discuss the electrochemical response of three types of insertion electrodes: graphite and transition metal oxides that intercalate reversibly with lithium, electronically-conducting polymers with red-ox activity that can be doped reversibly, both positively and negatively (i.e., at high and low potentials), and Chevrel phases with Mo–S–Se elements, which intercalate reversibly with both lithium and magnesium. The main point of interest is the correlation among electrochemical kinetics, impedance, surface chemistry, 3D structure, and morphology of these systems, studied by the use of electroanalytical tools in conjunction with XRD, microscopy and spectroscopy. Magnesium insertion into Chevrel phases and Li insertion into most of the electrodes relevant to Li batteries involves phase transition. Thereby, the electrodes' kinetics are affected by interfacial charge transfer processes, solid-state diffusion, and the moving of boundaries between phases. The electrochemical response of the electrodes reflects all these processes. However, the identification of the relevant time constants that affect the measured electrochemical behavior is not trivial. Efforts are made in this paper to provide comprehensive guidelines regarding the proper use of fine electrochemical tools for the study of various types of insertion electrodes. © 2008 Elsevier B.V. All rights reserved. Keywords: Conjugated (conducting) polymers; Intercalation electrodes; Electroanalytical techniques; Li batteries; Mg batteries; SS diffusion

1. Introduction World-wide efforts are presently underway to develop new materials for rechargeable lithium batteries [1–3]. The most important hosts for negative, low potential electrodes (namely, the anodes), are based on graphitic carbons. Recent efforts to develop new anodes based on Li alloying with Sn and Si, as well as conversion reactions between Li and transition metal oxides (in composite structures) should also be mentioned [1–3]. The most important cathode materials for Li batteries are LiMO2 (M = Ni, Co, Mn, layered structure), LiMn2O4 (spinel structure), Li(CoxNiyAlz)O2,LiFePO4 (olivine) and Li(MnxNiyCoz)O2 and their modifications [1–3]. The electrolyte systems for these batteries mostly include polar aprotic, Li salt solutions based on ⁎ Corresponding author. Tel.: +972 3 5318317, +972 528 898 666 (Cellular); fax: +972 3 7384053. E-mail address: [email protected] (D. Aurbach). URL: http://www.ch.biu.ac.il/people/aurbach (D. Aurbach). 0167-2738/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2007.12.070

alkyl carbonate solvents [4]. Extensive R&D is also underway on solid electrolytes, including gel, all polymer electrolytes and Li-ion conducting glasses [1–3]. All the above electrode materials for Li batteries are intrinsically reactive with the polar aprotic electrolyte solutions suitable for nonaqueous batteries. Fortunately, in most cases, the electrode-solution reactions produce insoluble Li compounds that precipitate on the electrodes' surface thus forming passivating films that are electronic insulators, but Li-ion conductors (i.e., solid electrolyte interphases [5]). Hence, the electrochemical processes of all Li insertion electrodes are very complicated because they involve various kinds of interfacial transfer, Li-ion migration through surface films, solid-state diffusion (Li ions in the host's lattice), and in many cases, phase transitions. The thermodynamic and kinetic behavior of these insertion electrodes can be analyzed by electrochemical methods. In fact, they may be much more sensitive to structural variations than XRD, microscopy, and spectroscopy. However, they may provide too ambiguous information. Hence, the use of

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electrochemical means for the study of transport phenomena is not trivial and deserves special discussion. There are two other systems that should be included in such discussions, namely, electronically-conducting polymers with red-ox activity [6,7] and magnesium ion-insertion compounds [8,9]. This paper aims at reviewing our recent studies on the electrochemical response of various types of insertion electrodes (Li, Mg intercalation, electronically-conducting polymers), and at providing comprehensive guidelines for the use of fine electroanalytical techniques in the study of ion-insertion electrodes and the interpretation of the results. 2. Experimental The inorganic hosts related to this paper are graphite (powder obtained from Timrex, Inc.), and the Chevrel phases, synthesized as already described [10]. The electronically-conducting polymers relevant to this paper were derivatives of polythiophene, prepared as reported earlier [11]. For the study of Li and Mg insertion processes we used composite electrodes as was already described [12]. We used several types of electrodes of different loads of the active mass, in order to differentiate between the intrinsic behavior of the active mass and effects related to the electrodes' composite structure. The electrolyte solutions for Li insertion electrodes usually comprised a mixture of alkyl carbonates (ethylene carbonatedimethyl carbonate), LiPF 6 or LiClO 4 (Merck KGaA, Tomiyama, Inc.). For the study of electronically-conducting polymers, we used tetraalkyl ammonium salt solutions in solvents such as acetonitrile, propylene carbonate and sulfolene (Aldrich, Tomiyama, Merck, highly pure). For the study of Mg intercalation electrodes, we needed ethereal solutions (e.g., THF) with a complex of (MgR2)n(AlCl2R)m (R = alkyl groups), whose synthesis and properties were described earlier [13]. We applied fast and slow scan rate cyclic voltammetry (SSCV), potentiostatic intermittent titration (PITT), impedance spectroscopy (EIS), and chronopotentiometry, as already described [14−17] using standard equipment from Solartron, EG&G, EcoChemie, Arbin, and Maccor. VAC and M. Braun glove boxes were used for the preparation and measurements (highly pure argon atmosphere). Both two- and three-electrode flooded cells (made of polyethylene) and coin-type cells (standard parts, 2032 NRC, Canada) were used (Li and Mg counter and reference electrodes, where relevant). We also applied electron microscopic measurements (HRTEM, HRSEM, and SEM equipment from JEOL, Inc.), and XRD measurements (Advanced D8 from Bruker, Inc.), to electrodes after different stages of operation (pristine, cycled, aged. etc.). 3. Results and discussion

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(Cint), which is, in fact, the intercalation capacity that depends on the electrode's potential and the intercalation level. Each technique also has a typical time involvement parameter (Φ) from which the diffusion time, td ¼ l 2 =D ¼ f (Φ, Cint) can be calculated. Table 1 provides a summary of the four electrochemical techniques, their output, time invariant parameter (vs. what was plotted), and the specific term for Cint of each technique. Using each of these techniques, the electrochemical response has to be translated into plots that demonstrate that the expected Ф term (Table 1) is indeed invariant along the time domain relevant for diffusion processes. For instance, using PITT, following I vs. t resulting from the small potential steps applied to electrodes at equilibrium, plotting It1/2 vs. t is expected to show a plateau at small values of t (t b td, the diffusion time constant, which is equal to l2/D). The diffusion constant D, as a function of E, is calculated as follows.
2 Dð EÞ ¼ hpO l It O =Qm DX ð E Þ    2 ¼ pO l ItO =DE =Cint ð E Þ :

ð1Þ

Using EIS for the same electrode, the same function D(E) can be calculated from a “Warburg” domain in the spectrum (can be recognized from a linear Z″ vs. Z′ behavior at low ω values). For such a domain, D = 0.5 l2 [CintAw]− 2, where Aw is the slope of the linear response of Z′ vs. Z″ vs. ω− 1/2. The response of PITT and EIS applied to an electrode of the same equilibrium potential provides the constant term Aw[(It1/2))/ΔEPITT] = (2 п1/2)− 1/2 for all the measurement points. Obtaining this result verifies the validity of both types of measurements. Such a classical response was obtained indeed with doped electronicallyconducting polymers such as poly[2,7-fluorene-9-one-alt(5,5′-(3,3′-di-n-octyl-2,2′-bithiophene))] [18]. In general, electrodes comprising conducting polymeric films often show a classical, expected electrochemical response, from which their kinetic and thermodynamic properties can be calculated. 3.2. On the electrochemical response of Li insertion electrodes The electrochemical response of Li insertion electrodes is usually very complicated. In this paper, graphite electrodes are discussed as a typical example. Most of the practical Li insertion electrodes have a composite structure that includes active mass

Table 1 List of relevant techniques, namely, the fine electroanalytical tools, their input, output, time invariant parameter and differential (insertion capacity) form Technique Input E + νt ΔE I(Δt) Δ (Esin(ωt) 0

Output

Time invariant parameter, Φ Cint

I vs. E I vs. t E vs. t − Z″, Z' vs. ω

Ipν− 1/2 (vs. E) It 1/2/ΔE (vs. t) dE/dt1/2 (vs. t) Aw (the slope of Z″ or Z′ vs. ω1/2

Ipν ΔQ/ΔE I(Δt/ΔE) − 1/ω Z″ ω→0

3.1. On the relevant electroanalytical tools and demonstration of classical behavior

SSCV PITT GITT EIS

In this paper we discuss four electroanalytical techniques, SSCV, PITT, GITT and EIS, each of which has its own unique input, output and formula for calculating the different capacity

Comment: The diffusion time, τd, is a simple function of the time-dependent kinetic parameter (It 1/2/ΔE, Aw, Ipν− 1/2, etc), characteristic of the technique applied and of the differential intercalation capacity, Cint.

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particles (micro-nano size), conductive additives, and a polymeric binder. In addition to the complicated composite structure, Li insertion into graphite occurs in stages (Li layers inserted between graphene planes) via first order phase transitions. Hence, serious questions arise regarding the use of electrochemical techniques for such complicated electrochemical systems and the meaning of their response. The first problematic topic is the application of impedance spectroscopy to electrodes with a composite structure. These electrodes may suffer from several types of non-uniformity: different particle size and non-uniform thickness. For too-thick electrodes, their impedance reflects both the resistance of the active mass to interfacial charge transfer and solid-state diffusion, and the resistance of the solution in the porous structure, which supplies the ions for intercalation. Fig. 1 illustrates the two aspects of non-uniformity and shows calculated impedance spectra for different values of active mass and solution resistivity, different electrode thickness, and thickness non-uniformity. The relevant parameter values are indicated in the charts and the models used

for calculations, as described in Refs. [16,17]. The high frequency semicircles in the spectra are attributed to charge transfer phenomena related to the surface films, while the medium and low frequency semicircles that appear in the spectra of non-uniform, composite graphite electrodes, signify their non-uniformity: dispersion of time constants, e.g., coupling between the capacitance of the thinner part of the electrode with the charge transfer resistance of the thicker part of the electrode. Although a thorough discussion of these spectra is beyond the scope of this paper, the message is clear: the parameters of the composite electrodes may have a stronger impact on their impedance spectra than the intrinsic behavior of the active mass itself. Hence, in order to probe the intercalation reactions with micrometric-size particles by electrochemical measurements, it is important to work with as thin as possible electrodes, and with particles with a narrow size distribution. Another important question about the possible use of EIS for the study of intercalation reactions relates to the fact that many of them involve phase transitions.

Fig. 1. The impedance response of composite insertion electrodes, which suffers from non-uniformity. The illustrations (left side) demonstrate two aspects of nonuniformity [16,17]: I Different particle sizes; II Non -uniform thickness. The impedance spectra where calculated, as explained in Refs. [16,17] for different solution and particle resistivity, as marked. (The latter resistivity related to solid-state diffusion). a – Electrodes of uniform thickness, different particle size, the effect of resistivity values. b – Same as a, the effect of thickness. c – A typical spectrum of electrodes whose thickness is non-uniform.

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Electrochemical intercalation via phase transition has an intrinsic hysteresis between the intercalation and deintercalation processes (well reflected by a potential difference between the peaks related to these processes in the Cint vs. E curve). This hysteresis may be higher than the usual potential amplitude of a few millivolts, used in EIS, which raises a serious question regarding the validity of the data obtained: do the EIS measurements provide meaningful spectra? As discussed in Ref. [14], the simplest, general equivalent circuit analog of Li insertion electrodes comprises a ‘Voight’-type analog: several R||C circuits in series with a ‘Warburg’-type element and a capacitor. The ‘Voight’-type analog reflects the processes related to Li-ion migration through multilayer surface films, interfacial charge transfers, and related capacitances. The ‘Warburg’-type element reflects the solid-state diffusion of Li ions in the host, and the capacitor reflects the differential, intercalation capacitance of the electrode (potential dependent) due to the intercalation process and the accumulation of charge. Since the solid-state diffusion and the accumulation of charge (the arrangement of the inserted ions in their sites) may be rate determining, slow steps, the impedance spectra of these electrodes may resemble the EIS of blocked electrodes. Hence, in the worst case, the high frequency parts of the spectra, related to interfacial charge transfer and Li-ion migration processes through surface films, may be valid and

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significant. Consequently, EIS can definitely be a relevant electroanalytical tool for the study of surface/interface related phenomena of insertion electrodes. The next important point to consider, relates to the use of PITT for the study of insertion electrodes and the validity of this method for calculating the diffusion coefficient of the inserted ions in the host. As explained above (see Table 1 and related discussion), PITT measurements should provide plots of It1/2 vs. t or log t, in which a plateau should be observed for the short time domain (a typical Cottrellian behavior). D can then be calculated from the time invariant It1/2 (see above). In many cases, Li insertion electrodes provide, as a result of PITT measurements, It1/2 vs. log t plots with peaks instead of plateaus [18]. This is presented in Fig. 2a, which shows four It1/2 vs. log curves obtained from graphite electrodes in Li salt solutions at four temperatures, as indicated, when a potential step from 0.18 to 0.16 V (vs. Li/Li+) was applied [18]. The relevant process is Li intercalation, which leads to a phase transition between stage III and stage II (i.e., LiC18 → LiC12). The dashed (horizontal) line near each curve shows the expected shape of the It1/2 vs. log t curve for ideal Cottrellian behavior. We attribute the actual peak-shape behavior of the It 1/2 vs. t curves obtained experimentally, to the impact of all of the resistances, other than that related to solid-state diffusion (e.g., charge transfer and surface film resistance), which interfere with the expected

Fig. 2. A typical chronoamperometric response of graphite electrodes in PITT measurements, EC-DMC/LiAsF6 solutions [18]. (a) Plotting It1/2 vs. log t, 4 temperatures, as indicated. A peak-shaped response is realized. The horizontal lines beneath the curves, illustrate ideal Cottrellian behavior (plateau of It1/2 vs. t at short t. (b) Plots of the chronoamperometric response of the graphite electrode, presented in 2a, in the form of 1/It1/2 vs. t− 1/2, according to Eqs. (2) and (3).

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Cottrellian behavior at the short time, when the current is the highest, at the beginning of the transient, because then a pronounced IR drop exists (what distorts the voltage input in these potentiostatic measurements). This complication can be corrected as follows: at the small ΔE applied to PITT, the current I(t) measured should ‘obey’ Ohm's law according to the following equation: h i I ðt Þ ¼ DE= ðRsolution þ Rsurface−films þ RCT Þ þ ð DCint Þ1 lð pDt ÞO   Total high frequency resistance RP Diffusion resistance ð2Þ

Based on Eq. (2), the following plots should be used to provide a linear dependence between 1/ It1/2 and 1/ t1/2: 1=It O ¼ RP =DEt O þ pO l=DEDO Cint z z Readily obtained from the slope

Long−time intercept on the ordinate axis

ð3Þ From the slope of these plots, all the interfering resistances (R∑ = Rsolution + Rsurface films + Rcharge transfer) can be obtained, and from the intercept, D can be calculated, as all the other terms in Eq. (3) are known. Fig. 2b shows the relevant plots calculated according to Eq. (3), for the It1/2 vs. log t curves presented in Fig. 2a. Linear curves are indeed obtained. Moreover, the R∑ values obtained from the slopes of the curves in Fig. 2b can be easily verified by simple impedance measurements of the same electrodes at the same conditions (temperature, base equilibrium potential). The high frequency part of the impedance spectra exactly reflect all the resistances related to Rs, RCT, Rs films, etc., whose sum is directly obtained from the diameters of the semicircles that

characterize these spectra. Hence, a good matching between R∑ obtained from the slope of the plots according to Eq. (3) and from R∑ obtained directly from EIS measurements of the same systems, is the best verification that the above approach is valid, and that the correct D values thus calculated (from the intercept, Eq. (3)) are indeed relevant. As already reported [19], diffusion coefficient values of Li insertion into graphite, obtained as described above from PITT measurements, were found to be in good agreement with similar values calculated for Li insertion into graphite by Fischer et al. [20] using quasi electric neutron scattering (QENS). Fig. 3 shows a typical comprehensive response of thin graphite electrodes upon reversible lithiation–delithiation processes based on parallel studies by slow scan rate CV (solid line) PITT, from which D is calculated, vs. E (as explained above). See the dashed lines with the circles, referring to the right ordinate and EIS (see the family of Nyquist plots, related to the Li insertion process from 0.16 V to 0.105 V, LiC18 + 1/2Li + e− → LiC12, in the insert). The relevant phase compositions in each potential domain (measured by XRD) are also indicated in Fig. 3, above the potential scale. The voltammogram in Fig. 3 shows three sets of relatively sharp peaks. These sets of peaks reflect phase transitions and two phase domains upon the intercalation–deintercalation of lithium into graphite. Note that when very slow scan rates are applied, in the µV/s range, the voltammetric response of sufficiently thin insertion electrodes (such as the electrode of Fig. 3, that comprised one layer of synthetic graphite flakes) reflects the thermodynamics of these systems, beyond diffusion control. Hence, the potential difference between the corresponding peaks in a set, reflects a true, expected hysteresis whose source is thermodynamic, related to a process that involves a phase transition. A comparison between the voltammograms measured at very low scan rate (thus reflecting the differential intercalation

Fig. 3. A completed presentation of the electroanalytical response of a thin graphite electrode [14,15]. ❖ Solid line: typical steady slow scan rate voltammetry (I vs. E) that reflects the phase transitions (sets of peaks, right ordinate). ❖ Dashed line: D (diffusion coefficient) vs. E, obtained from PITT with corrections according to Eqs. (2) and (3) and the presentation in Fig. 2 (left ordinate). ❖ Insert: A family of Nyquist plots (EIS measurements) measured around equilibrium potentials in the potential domain of 0.16 → 0.105 V vs. Li/Li+), corresponding to the stage III → stage II transition. The dashed line corresponds to the points measured at the lowest frequency. From the Z″ at ω → 0, Cint vs. E can be calculated.

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capacity of these electrodes and its potential dependence) and the impedance spectra of the same electrode, is highly interesting. The simple equivalent circuit analog, which generally describes the electrical properties of insertion electrodes of these systems includes an high capacity element, namely, the intercalation sites that absorb the charges (ions + electrons). Hence, at ω → 0, the imaginary component of the impedance spectra of these electrodes should reflect their intercalation capacitance (which is potential dependent): Cint(E) = 1/ωZ″, ω → 0. Hence, such calculations from impedance measurements obtained at different potentials should provide Cint(E) curves similar to those obtained by SSCV and PITT. This is very true for thin enough electrodes and prolonged enough EIS measurements (so ω indeed approaches 0). The dashed line in the EIS chart of Fig. 3 reflects the peak-shaped behavior of Z″ vs. E at the lowest frequency used, for a family of spectra measured in the potential domain between 0.105 and 0.16 V, related to stage III → stage II phase transition. Therefore, the dashed line in the insert corresponds exactly to the peak in the voltammograms of Fig. 3, at the same potential domain. The peak-shaped D(E) curve (dashed line in Fig. 3), in which minima in D(E) are obtained at the SSCV (or Cint vs. E) peak potentials, is very typical to most of insertion electrodes, based on crystalline inorganic hosts (e.g., graphite, LixMOy; M = transition metal such as Mn, Co, Ni, V, etc.). The behavior of these systems, as reflected by the typical electrochemical + responses presented in Fig. 3 (Cint vs. E, DLI vs. E, EIS vs. E) raises the question about the general mechanisms of intercalation. One possibility is that phase transition occurs via moving boundaries with a sharp frontier. In such a case, the concentration gradient between the phases is infinite and hence, the theoretical curves of Cint vs. E should be delta functions (spike shaped). In reality, these theoretical spikes should be broadened to peaks (as indeed obtained by SSCV or PITT), due to kinetic limitations (e.g., different kinds of Ohmic drops, interfacial charge transfer, surface films, etc.). Another possibility, is that upon the electrochemical insertion of ions into hosts, even when phase transition is involved, there are no

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sharp boundaries between the phases. Instead, there is a diffusion process driven by a finite concentration gradient. Phase transition occurs due to segregation processes, which may involve the nucleating of the new phase into the pristine one. In fact, this is exactly what happens in many cases. There is clear evidence that Li insertion into hosts such as graphite or LixMn2O4 spinel, which leads to phase transitions, occurs via nucleating steps [21,22]. This is illustrated by the chronoamperometric response of graphite electrodes upon electrochemical lithiation, during the course of PITT measurements [21]. The process to which Fig. 4 relates, is the phase transition between LiC12 and LiC6 (stage II → stage I). Moving from 0.09 V to 0.083 V (vs. Li/Li+) via small potential steps, as indicated, shows the expected monotonous responses (current decay vs. t) for potential steps between 0.09 → 0.087 V and 0.085 → 0.683 V (vs. Li/Li+), but a peculiar non-monotonous response for a potential step between 0.087 and 0.085 V (Li/Li+). The current initially decays, but then rises before the expected decay at prolonged t (see Fig. 4). This special behavior upon ions' insertion via a phase transition can be explained by the mechanisms of phase formation via nucleation (in which the boundary between the phases initially increases [21,22]). Considering the typical features of these insertion processes, as reflected by Figs. 1-4, it seems correct and useful to apply as a first approximation, lattice gas models for the qualitative analysis of the thermodynamics of intercalation processes [23]. In fact, intercalation can be considered as a 3D adsorption process. Electroadsorption was thoroughly and rigorously studied in the past. Hence, it may prove beneficial to use the accumulated experience in the study of electroadsorption processes, for understanding the electrochemical response of intercalation electrodes. We can describe intercalation processes in terms of adsorption isotherms that take into account possible interactions between the insertion sites, which lead to the segregation of phases during the course of the process. The use of Frumkin-type isotherms for that purpose may be very appropriate, in which the factor g reflects to possible interactions among the sites (g N 0 → repulsion; g b 0 → attraction) [23]. This isotherm and the differential capacitance

Fig. 4. Evidence for nucleation during Li insertion into graphite. Chronoamperometric response during PITT measurements. Stage II → Stage I transition (LiC12 → LiC6). Note the monotonous response during the potential steps, 0.09 → 0.087 V; 0.085 → 0.083 V (Li/Li+), and the non-monotonous response to the potential step, 0.085–0.083 V, which indicates nucleation. (See Ref. [21]).

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and diffusion coefficient values derived from it are presented in the following formulae (Eqs. (4)–(7)) presented below [23]: ALiþ ¼ AoLiþ þ kT ln

X þ kTgð X  0:5Þ 1X

X =ð1  X Þ ¼ exp½f ð E  Eo Þexp½gð X  0:5Þ  Cdif =fQm ¼

gþ

1 1 þ X 1X

1

  Dei ¼ te a2 k4 ð1  X ÞX ðAALiþ =AX ÞðkT Þ1

ð4Þ

ð5Þ

ð6Þ

ð7Þ

te e1; D0 ¼ a2 k4; D=D0 ¼ ½1 þ gX ð1  X Þ X = the intercalation level (mole fraction); µ = the chemical potential; f = F/RT; F = Faraday constant; Qm = the total capacity of the electrodes; E, Eo are the electrode's potential; g = the interaction factor (g N 0 for repulsion and g b 0 for attraction), D, Do = chemical and self-diffusion coefficient (for insertion ions in the host). Fig. 5 shows the typical behavior of the intercalation process in terms of a Frumkin-type isotherm (x vs. E) with 3 g values (indicated). For values of g between zero (i.e., no interactions) and the critical value g = − 4 (attractive interactions), the isotherms show a monotonous behavior. For g values b − 4, this

isotherm shows an S shape (Fig. 5a). This relatively simple mathematics, reflects situations in which above a critical level of attractive interactions (g b − 4, in the Frumkin-type isotherm), there is a segregation of phases, and hence, intercalation occurs via a phase transition. The potential span of the S-shape feature of the curve is, in fact, the intrinsic hysteresis between the insertion and deinsertion processes, always observed by the fine methods of SSCVor PITT, in which the equilibrium states of the electrodes (i.e., the intercalation thermodynamics) can be approached (see the SSCV in Fig. 3). Fig. 5b and c show theoretical, dimensionless values of Cint and D vs. E, respectively, calculated using a Frumkin-type isotherm with different g values, as indicated. As g is lower, the attractive interactions are stronger, and the Cint vs. E peaks should be narrower and sharper. When repulsion interactions exist (g N 0), D vs. E is a function with a maximum (at Eo). With g = 0, i.e. no interaction, (Langmuirian-type behavior), D doesn't depend at all on E or X. At g b 0, when attractive interactions dominate, D vs. E is a function with a minimum of Eo. Hence, the sharp Cint vs. E peaks measured by SSCV or PITT for insertion electrodes, the intrinsic hysteresis between the insertion–deinsertion processes (peaks on the Cint vs. E curves), and the minima in D at the peak potentials of Cint vs. E (i.e., at Eo in the equation above and related Fig. 5b–c), are well explained in terms of 3D adsorption processes described by Frumkin-type isotherms, with attractive interactions between the sites. These attractive interactions lead to the segregation of phases, and hence, to intercalation processes that occur via phase transitions. It should be noted that the above simplified model relates to the active mass only. As shown in Fig. 1 and related discussion, when composite electrodes are used in real systems, their structure has

Fig. 5. The typical response of intercalation processes calculated using Frumkin-type isotherms. (See Ref. [23] for details). (a) X vs. E, three g values, as indicated. (b) Cint vs. E with different g values, as indicated. (c) D/Do values vs. E with different g values, as indicated.

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Fig. 6. A first and subsequent E vs. capacity curves for Mg insertion into Chevrel phase electrodes. Galvanostatic processes (constant I). During the first process, the maximal theoretical capacity, 122 mAh/g, is reached (2 Mg per Mo6S8). In subsequent processes, about 20% of the Mg ions are trapped at room temperature. The insert in the figure presents the crystal structure of the Chevrel phase.

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trapped in the structure so, subsequent reversible Mg insertion processes occur at about 80% of the theoretical capacity. It appears that the first Mg insertion process (to the inner sites, lower energy) is much slower than the second one (to the outer sites). Only at high enough temperature, de-magnesiation can be completed and hence, Mg insertion–deinsertion processes become fully reversible at capacities close to the theoretical one. Fig. 7 shows typical impedance spectra presented as Nyquist plots measured with MgxMo6S8 electrodes at different potentials (indicated) in the course of Mg insertion (full spectra in Fig. 7a and the frequency domain related to charge trapping in Fig. 7b) [25]. The most significant feature emphasized herein is the appearance of low frequency semicircle shown in Fig. 7b (around 1.25 V vs. Mg Ref.). At this potential, the slow process (first Mg insertion) takes place [25]. At the higher potentials, no significant process takes place and hence the impedance spectra reflect a capacitive behavior of the electrodes. At lower potentials, the faster Mg insertion process (the second

a dominant impact on their electrochemical response. Also, it is important to mention that the above discussion (while being focused on graphite electrodes) is relevant to many other types of intercalation electrodes. 3.3. On the electrochemical response of Mg insertion electrodes, compared to Li insertion processes The last topic dealt with in this review article, relates to Mg insertion processes, comparison between Mg and Li insertion, the phenomenon of charge trapping and its typical response by impedance spectroscopic measurements. About 8 years ago we demonstrated highly reversible Mg insertion into MgxMo6S8 (0 b x b 2) Chevrel phases [10]. New solution chemistry was developed for reversible Mg electrochemistry, based on ether solvents and complexes which are the reaction products between MgR2 Lewis bases and AlCl3−nRn Lewis acids, in which electrochemical Mg deposition–dissolution processes are fully reversible as well as Mg insertion– deinsertion processes with Chevrel phases. The basic crystal structure of the Chevrel phase (see the insert in Fig. 6) includes cubes of 8 sulfur atoms (the anionic framework) which confine octahedrons of molybdenum clusters of 6 atoms. Between each two Mo6S8 units, there are 12 possible insertion sites arranged as inner and outer rings of 6 sites each. Each set of sites can accommodate 2 Mg atoms. The first Mg atom inserted occupies an inner site, while the second one, inserted per unit, occupies an outer site [24]. Fig. 6 presents chronoamperometric response (V-t curves for constant current insertion–deinsertion processes) of MgxMo6S8 electrodes. It compares a first and subsequent Mg insertion into Mo6S8 electrodes. This figure demonstrates the problem of partial charge trapping which occurs upon magnesiation of all sulfur, Chevrel phase at low temperatures: while the first Mg insertion into a pristine electrode always occurs at the theoretical capacity, 122 mAh/g, corresponding to 2 Mg per Mo6S8 unit, a fraction of the inserted Mg atoms remained

Fig. 7. A family of Nyquist plots measured with MgxMo6S8 electrodes during intercalation (Mg counter and reference electrode, THF / Mg(AlCl2EtBu)2 solutions): (a) The whole frequency domain, (b) Emphasis on the high frequency domain. See Ref. [25].

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both MgxMo6S8 and MgxMo6Se8 [24,29], we can attribute the difference in kinetics of the first Mg insertion process into the two compounds, to a difference in the geometry of the inner sites for Mg insertion (hexagonal for MgxMo6S8 and tetragonal for MgxMo6Se8 [24,29]) and to a much higher polarizability of the anionic framework of the compound with Se atoms, what facilitates considerably Mg ions transport in this host. As demonstrated in Fig. 8b, Li insertion into the Chevrel compound, proceeds in three steps [28]: A first Li insertion step, parallel to the first magnesiation stage of the same compound (close potentials, around 1.25 vs. Mg), a second step in which two Li atoms are inserted, parallel to the second magnesiation process of Mo6S8, occurring at the same potential (1.1 V vs. Mg) and a third step of one Li insertion, occurring at about 0.9 V vs. Mg reference electrode. All the Li insertion processes into the Chevrel phase are very fast. Hence, Li insertion into Mo6S8,

Fig. 8. (a) Steady-state voltammograms related to Mg intercalation-deintercalation into Mo6S8 and Mo6Se8, as indicated. See Ref. [27] for details. (b) A steady-state voltammogram of Li insertion-deinsertion into Mo6S8. See Ref. [28] for details.

magnesiation step) takes place and hence, the impedance spectra are characterized by high frequency semicircles that reflect the main charge transfer process, a Warburg type element (straight lines with angles around 45°) which reflects solid-state diffusion of Mg ions in the host and a capacitive behavior (steep − Z″ vs. Z′ lines) which reflects the charge accumulation by the intercalation process. Very similar EIS response was obtained with electrodes comprising thin films of electronically-conducting polymers (derivative of polythiophene), with which a partial charge trapping was obtained, as already described in details [26]. It can be stated that whenever an insertion electrode suffers from a partial charge trapping, its impedance spectra (measured at the relevant potentials), include a typical low frequency semicircle as presented in Fig. 7b. Fig. 8 compares steady-state SSCV curves related to Mg insertion into MgxMo6S8 and into MgxMo6Se8 [27]and a SSCV curve related to Li insertion into LixMo6S8 [28] (the experimental details re: solutions, scan rates etc. are presented in the figure caption). As seen in this figure, Mg insertion into MgxMo6Se8 occurs in two stages in a similar manner to the same processes related to MgxMo6S8, at somewhat lower potentials (expected due to the higher electro-negativity of Se compared to S). However, the first magnesiation and last demagnesiation processes which are so sluggish with MgxMo6S8, are very fast with MgxMo6Se8. With the latter compound both Mg insertion processes, seems to have a similar, fast kinetics (Fig. 8a). Based on recent extensive studies of the structure of

Fig. 9. (a) A family of Nyquist plots measured with MgxMo6S8 electrodes during Mg intercalation. See Refs. [25] and [27] for details. The relevant potentials (vs. Mg Ref., are indicated). (b) A family of Nyquist plots measured with a LixMo6S8 electrode during Li intercalation. The relevant potentials (vs. Li/Li+) are indicated. See Ref. [25] for details.

D. Aurbach et al. / Solid State Ionics 179 (2008) 742–751

Mg insertion into Mo6Se8, the second Mg insertion process into Mo6S8 and their corresponding deinsertion processes, provide very good examples for fast intercalation–deintercalation processes, in contrast to the first Mg insertion process into Mo6S8 and its corresponding deinsertion process, which are slow. Fig. 9 presents the impedance response (as Nyquist plots) of Li insertion into Mo6S8 and Mg insertion into Mo6Se8 electrodes at the potentials relevant to the first intercalation step of these systems [25,27]. These spectra are typical to fast intercalation processes (see description and explanation related to Fig. 7 above). None of the spectra of these fast systems show any low frequency semicircle, as is observed for the slow, first magnesiation process of Mo6S8. The results presented in Figs. 7 and 9, demonstrates how EIS measurements indicate so clearly the phenomena of partial charge trapping with insertion electrodes. The typical low frequency semicircle (in Nyquist plots presentations of EIS) which characterizes the charge trapping phenomenon (as explained above), can be modeled by a system with two types of intercalation sites: sites with low barrier to transport (solid-state diffusion) of the intercalating ions and sites that bind the intercalation ions strongly. Using the approach of equivalent circuit analog, the former sites can be assigned as a branch with low capacitance while the latter sites (in which charge trapping occurs) can be described as a branch with high capacity. Both capacitive elements are connected in series to resistances related to charge transfer. As demonstrated in Ref. [30] simulations of Nyquist plots using equivalent circuit analogs containing such two branches provides indeed calculated spectra similar to that seen in Fig. 7b, measured at 1.25 V, which reflects the charge trapping phenomenon. At low frequency, the smaller capacity dominates the electrode's impedance and hence, coupling between the resistive element of the high capacity branch and the low capacitance at the parallel branch, provides the expected low frequency semicircle, which is always observed when an insertion process includes a partial charge trapping. 4. Conclusion We present in this review the application of several electroanalytical tools for the study of insertion electrodes including SSCV, PITT and EIS. Each technique probes precisely different processes and time constants. For instance: EIS probes clearly processes with short time constants, related to surface films and interfaces. SSCV and PITT approach better equilibrium condition and probe phase transitions. We have demonstrated analysis of ions' insertion into inorganic hosts via phase transition and nucleation. A simple procedure was suggested to correct the solid-state diffusion chronoamperometric response of insertion electrodes. It is important to apply several methods in parallel to the same electrodes, in order to confirm the validity of the results. Finally, some aspects of Mg and Li intercalation into Chevrel phases (Mo6T8, T = S,Se) were discussed. It was demonstrated how EIS measurements of these systems probe partial charge trapping phenomena, when it exist.

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