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Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries
ARTICLE IN PRESS Materials Science and Engineering B ■■ (2016) ■■–■■
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Materials Science and Engineering B j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m s e b
Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries Jean-Claude Badot a,*, Bernard Lestriez b, Olivier Dubrunfaut c a Institut de Recherche de Chimie Paris, UMR CNRS 8247, Réseau sur le Stockage Electrochimique de l’Energie (RS2E), Chimie Paris Tech, PSL*, 11 rue P. et M. Curie, 75231 Cedex 05 Paris, France b Institut des Matériaux Jean Rouxel, UMR CNRS 6502, Université de Nantes, 2 rue de la Houssinière, BP32229, 44322 Nantes, France c GeePs | Group of electrical engineering – Paris, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Universités, UPMC Univ Paris 06, 3 & 11 rue Joliot-Curie, Plateau de Moulon, 91192 Gif-sur-Yvette CEDEX, Paris, France
A R T I C L E
I N F O
Article history: Received 15 February 2016 Received in revised form 9 May 2016 Accepted 12 May 2016 Available online Keywords: Dielectric spectroscopy Multiscale conductivity and permittivity Lithium batteries Composite electrodes Interfaces Electronic conductivity
A B S T R A C T
Broadband dielectric spectroscopy (BDS) is used to measure complex permittivity and conductivity of conducting materials for lithium batteries at frequencies from a few Hz to several GHz with network and impedance analysers. Under the influence of an electric field, there will be charge density fluctuations in the conductor mainly due to electronic transfer. These fluctuations result in dielectric relaxations for frequencies below 100 GHz. The materials are compacted powders in which each element (particles, agglomerates of particles) can have different sizes and morphologies. In the present review, studies are reported on the influence of surface states in LiNiO2 (ageing and degradation in air) and LiFePO4 (carbon coating thin layer), and on a composite electrode based on the lithium trivanadate (Li1.1V3O8) active material. The results have shown that the BDS technique is very sensitive to the different scales of materials architectures involved in electronic transport, from interatomic distances to macroscopic sizes. © 2016 Published by Elsevier B.V.
1. Introduction Upcoming hybrid electric and pure electric vehicles (HEV and EV) applications require the development of new lithium batteries with high energy density, high power and high cyclability. To reach these goals, a more fundamental understanding of the so called “formulation” of the composite electrode, i.e. the relationships between the processing, the morphology at its different scales, the electrical and mechanical properties and the electrochemical performance of the composite electrode, is needed. Electronic conductivity is one of the two major electrical properties (the other is the ionic conductivity) of the composite electrode with respect to its electrochemical behaviour. The broadband dielectric spectroscopy (hereafter called BDS) allows the study of the electronic conductivity of a composite electrode at all the scales of its architecture (from interatomic distances to macroscopic lengths) as function of the temperature usually between 200 and 400 K [1–5]. This technique thus allows the clarification of the charge transport mechanisms and the origin of the limitations in these
* Corresponding author. Tel.: +33 1 44 27 80 15. E-mail address: [email protected] (J.-C. Badot).
mechanisms, depending on the composition, processing and morphology of the composite electrode. Understanding the electrical properties of such hierarchical materials is difficult due to their complexity. First of all, to study each electrode component taken separately is mandatory. We must be aware that the electrical properties of composite electrode are not the sum of all the contributions of its different components taken separately. We must indeed also consider the existence of interfaces (or contacts) at the different levels of the composite electrode: sample/current collector interface, junctions between CB agglomerates, junctions between AM agglomerates, grain boundaries in AM agglomerates, AM/CB interfaces, binder layers (gaps) present at some these interfaces (Fig. 1). The surface effects are thus of the greatest importance to understand the multiscale electronic transfer in composite electrodes. In the present review, we compare previous studies on the influence of surface states for LiNiO2 [6] and LiFePO4 [1,2] active materials. In the first case, the influence of surface ageing and degradation is considered and in the second one, the influence of a carbon coating is analysed. Moreover, the nature of the electronic transfer in composite electrode based on the Li1.1V3O8 active material is investigated [4]. Permittivity and conductivity measurements have been recorded in a wide frequency range from 10 Hz to 10 GHz in the temperature range 200 to 300 K.
http://dx.doi.org/10.1016/j.mseb.2016.05.012 0921-5107/© 2016 Published by Elsevier B.V.
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centred on the ε’ axis. Two approaches are considered to interpret the different relaxations: the first one is geometrical and the second is kinetic. In the geometrical approach, when the size of a system increases, its response appears at lower frequency (e.g. agglomerate polarization fluctuates slower than particle polarization). In the kinetic approach, when the mobility of charge carrier increases, its response is shifted to higher frequencies (e.g. ions contributions are generally observed at lower frequencies than the electrons). Consequently, several types of polarizations involving dielectric relaxations can appear from low to high frequencies in the following order: (a) space-charge polarization (low-frequency range) due to the sample/current collector interface; (b) polarization of agglomerates (or clusters) of particles (micronic scale) and (c) polarization of particles due to the existence of resistive junctions between them; d) electron transfers (nanometric or interatomic scale). The resistivity ρ(ω) and conductivity σ(ω) relaxations also described by the same functions as before are thus given by
Fig. 1. Schematic representation of a composite electrode.
ρ (ω ) = ρH +
2. Theoretical background
ρL − ρH
1−δ γ
ρ
The electrical response of a material results from charge density fluctuations, when it is submitted to a time-dependent electric field E (t ) . This response is given by a time dependent current density J(t) and dielectric displacement D(t),
dD (t ) J (t ) = Jc + dt
(1)
The first term on the right hand side is the direct current density Jc = σ dcE where σdc is the direct current conductivity of the material. The second term is the displacement current density Jd = dD dt = ε 0d ε E dt where ε0 is the vacuum permittivity and ε
( )
the relative permittivity. In harmonic regime (i.e. E(t) ∝ exp(iωt)), from equation 1 the relationship between frequency-dependent complex conductivity σ(ω) = σ’(ω) + iσ”(ω) and relative permittivity ε(ω) = ε’(ω) – iε”(ω) can be defined as follows,
σ (ω ) = ρ (ω ) = σ dc + iωε 0 ε (ω ) = (σ dc + ωε 0 ε ′′ (ω )) + iωε 0 ε ′ (ω ) −1
(2)
The real part of the conductivity is the sum of the DC-conductivity (i.e. at zero frequency) and of a term proportional to the imaginary part ε” (i.e. dielectric losses) of the permittivity (Fig. 2a). In electronic conductors, several polarization mechanisms occur at different scales (from interatomic to macroscopic sizes) [7] with distinct characteristic frequencies (Fig. 2b). At frequencies below 1011 Hz, the dielectric spectra of conducting materials can be generally summarized by the following expression:
⎡ ε mL − ε mH ε (ω ) = ε ∞ + ⎢ ∑ ⎢ m 1 + (iωτ m )1−αm ⎣
(
)
βm
⎤ ⎥ + A (iω )s−1 + σ dc ⎥ iωε 0 ⎦
(3)
where ε∞ is the residual (network) permittivity and A is a fitting parameter. The term in brackets in expression (3) is the sum of m dielectric relaxations described by empirical Havriliak–Negami (HN) functions [8]. For each relaxation, εmL and εmH are the low- and highfrequency limits of the permittivity, τm the mean relaxation time; αm and βm are fitting parameters. The HN-function is the generalization of the Cole–Cole (CC) function with βm = 1, of the Cole– Davidson (CD) function with αm = 0 and of the Debye function (D) with αm = 0 and βm = 1 [8]. CC, CD and HN functions result from distributions of relaxation times, which are symmetrical for CC function and asymmetric for CD and HN functions [8]. The Nyquist plots of the complex permittivity (i.e. ε” vs. ε’) are circular arcs with centres below the ε’ axis for CC function and skewed arcs for CD and HN function. Note that Nyquist plot of the D function is a semi-circle
(4a)
(1+ (iωτ ) )
σ (ω ) = σ H −
σH −σL
(1+ (iωτ
)1−η )
κ
σ
(4b)
where the indices L and H mean the low- and high-frequency limits of resistivity and conductivity, τρ and τσ the resistivity and conductivity relaxation times; δ, γ, η and κ are fitting parameters similar to those of equation (3). If we examine the influence of surface effects on the electrical properties, we can consider the two extreme cases most frequently observed: the first one is formed by conducting grains surrounded by a quasi-insulating thin layer (Fig. 3a) and the second one insulating grains surrounded by a conducting thin layer (Fig. 3b). In the first case, the electrical equivalent circuit of the system can be schematized as two parallel combinations of resistance and capacitance in series: the first one is associated with the grains (higher frequencies) and the second with the interfacial region (lower frequencies) (Fig. 3a). The Nyquist plot of the resistivity is the sum of two relaxations often illustrated by two circular arcs (CC functions). The circular arc corresponding to the bulk or grain response crosses the ρ’ axis at the origin when ν → ∞. The shape of the conductivity spectrum is similar to a sigmoid curve (Fig. 3a): the lowfrequency part (sample conductivity) corresponds to the conductivity of the quasi-insulator phase (σs) and the high frequency part to the grain bulk conductivity (σg > > σs). In the second case, the interface forms a continuous conducting medium giving rise to a constant conductivity in all the frequency range (Fig. 3b). The Nyquist plot of the resistivity (impedance) shows only one relaxation described by a circular arc (CC function) or a skewed arc (CD or HN function) for highly disordered conducting network (e.g. percolated conductor with concentration slightly higher than the percolation threshold) (Fig. 3b). 3. Experimental devices The broadband dielectric spectroscopy requires some devices and instruments (network and impedance analysers) for complete coverage of the frequency range. Complex resistivity and permittivity spectra are recorded over a broad frequency range of 40 Hz to 10 GHz, using simultaneously impedance and network analysers Agilent 4294 (40 Hz–110 MHz), 4291 (1 MHz–1.8 GHz), PNA E8364B (10 MHz– 10 GHz). The experimental devices, fully described in previous papers [9,10], consists of a coaxial cell (APC7 standard) in which the cylindrically shaped sample fills the gap between the inner conductor and a short circuit (Fig. 4). The samples are powders that are pressed
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Fig. 2. a) Schematic representation of the real (ε’) and imaginary (ε”) parts of the permittivity vs. frequency for a solid. εlat is the lattice permittivity of the solid, einf the permittivity of induced polarization, n the refractive index; χint, χdip, χlat and χel are interfacial, dipolar, lattice and electronic electrical susceptibilities, respectively. b) Schematic description of a hierarchical architecture at different scales of a powdered material: different sources of polarization vs. frequency and size. (b) Reproduced from Ref. [7] with permission of the PCCP Owner Societies.
at about 0.7 GPa. Two sample diameters are considered: the first one is similar to the inner conductor diameter equal to 3 mm (Fig. 4a) [9] and the second to the outer conductor with diameter of 7 mm (Fig. 4b) [10]. Sample thickness lies between 0.4 and 1 mm in both cases. To ensure good contacts (junctions) between the sample/
inner conductor and sample/short-circuit, its front faces are covered with silver or gold thin layers. After a relevant calibration of the analysers, the sample admittance is computed from measurements of the complex reflection coefficient of the device. The knowledge of the admittance allows
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Fig. 3. Influence of the surface states on the electrical properties of powdered materials. a) Insulating layer around the conducting phase: layer resistivity ρs > > grain resistivity ρg, electrical equivalent scheme and frequency dependent real part of the conductivity σ with σs = 1/ρs and σg = 1/ρg surface layer and grain conductivities, respectively. b) Conducting layer around the insulating phase: layer resistivity ρs < < grain resistivity ρg, electrical equivalent scheme and frequency dependent real part of the conductivity σ with σs = 1/ρs conducting layer conductivity.
the determination the complex (relative) permittivity of the sample. Complete dielectric spectra are made from about 600 measurements with an accuracy of approximately 3 to 5% in the whole frequency range. The knowledge of the complex permittivity allows the calculation of complex resistivity and conductivity. The measurements are recorded in the range of 190 to 300 K under dry N2 flux and 300 to 450 K in a furnace. Since all the polarizations at different scales are generally additive (assumed in Eq. 3), their contributions can be thus evidenced by the decomposition of the different dielectric spectra using Nyquist plots (imaginary part vs. real part of the permittivity, the conductivity and the resistivity). Spectra analyses are recorded by home-made software [9,10].
4. Influence of the surface states on the conductivity and permittivity spectra For the purpose of this study, the influence of the surface states of two types of compounds, LiNiO2 [6] and LiFePO4 [1,2], on their dielectric spectra, is here detailed. LiNiO2 degrades when exposed to ambient atmosphere with the formation of a quasi-insulating thin layer on aggregates (i.e. clusters of particles) and particles surface. LiFePO4 has low intrinsic conductivity and is embedded by a thin conducting carbon coating layer on aggregates and particles surface.
Fig. 4. a) Coaxial cell used to make measurements of permittivity and conductivity of materials vs. frequency from 10 Hz to 10 GHz [9]; b) Coaxial cell used to make measurements of permittivity and conductivity of materials vs. frequency from 10 Hz to 18 GHz [10]. Adapted with permission from Ref. [9]. Copyright (2010) American Chemical Society.
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4.1. Insulating layer on conducting LiNiO2 aggregates and particles [6] Fig. 5 shows the frequency dependence of the real parts of the conductivity and permittivity of pure (hereafter called A1) and damaged (hereafter called A2) LiNiO2 at room temperature. Below 3 × 109 Hz, the conductivity of A1 is independent of the frequency (Fig. 5a) and is equal to the sample DC conductivity (σ = 0.18 S m−1 at room temperature) at low-frequency (i.e. ν = ω/2π < 1 × 104 Hz). Such a behaviour is seen as a ω−1 frequency response on the dielectric losses (imaginary part of ε). The real part ε’(ω) of the complex permittivity shows a low-frequency dispersion of A1 (Fig. 5b), which can be approximated by a straight line with a slope close to −1. This corresponds to a ν−1 frequency response in the low-frequency range (ν < 2 × 103 Hz). Furthermore, ε’(ω) rises to high values between 105 and 106 at 10 Hz, which indicates a high capacitive effect of the semiconductor–metal junction. The semiconductor–metal junction is a Schottky barrier, which produces a limited charge flow (resistive part) and a polarization (capacitive part) at the junction. In the low-frequency domain, the electrical equivalent circuit of the system can be schematized as Fig. 3a. The dielectric response is described by the Debye relaxation model, for which ε’ and ε” follow respectively ω−2 and ω−1 frequency responses for frequencies above
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the relaxation frequency. The dielectric losses ε” are here due to the DC conductivity of the sample. Unfortunately, the Debye model cannot explain the experimental ω−1 frequency response of the real part ε’. The sample surface roughness involves a distribution of interfacial resistances and capacitances, and thus a distribution of relaxation times with a dielectric response fitted by the CC function. In this model, ε’ and ε” are proportional to ωα−1 for frequencies above the relaxation frequency. This behavior is identical to the universal dielectric response (UDR) depicting the low-frequency dispersion of the dielectric spectra. The ω−1 experimental lowfrequency response of ε’ results from a very narrow distribution of relaxation times with negligible α parameter (i.e. α < <1). After a few weeks under air, the sample A1 was damaged and became A2 (Fig. 5a). The sharp decrease of the DC-conductivity by about two orders of magnitude is due to the formation of a quasi-insulating layer (in fact ionic conducting layer) of Li2CO3 on the grain boundaries, while the high-frequency conductivity is not modified for ν > 1 × 109 Hz and is thus intrinsic to the grain bulk (electronic conductor) of the sample. The evolution of the spectra with the formation of Li2CO3 during the ageing has provided evidence of two regimes: the first one is an interfacial (low-frequency) regime and the second a bulk (high-frequency) regime. The crossover frequency νco between the two regimes is 3 × 109 Hz at 293 K and decreases
Fig. 5. (a, b) Real parts of the conductivity σ’ and permittivity ε’ as functions of frequency ν = ω/2π at room temperature for the compound Li0.97Ni1.03O2. The curves A1 correspond to the sample of the pure compound (A1); the curves A2 correspond to the sample damaged (A2) (after a few weeks under air), which contains a low content of Li2CO3. Reprinted from Ref. [6]. Copyright Institute of Physics (the “Institute”) and IOP Publishing 2010.
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down to 108 Hz at 220 K, which broadens the frequency range of the bulk regime. The damaging in air of LiNiO2 is here a necessary drawback, since it allows the attribution of the dielectric relaxations to interfacial polarizations due to metal/sample junction and grain boundaries for frequencies below νco. 4.2. Conducting carbon black coating on insulating LiFePO4 aggregates and particles [1,2] Carbon and non-carbon coated (carbon content: 0 to 4 wt%) LiFePO4, whose particle size is between 50 and 150 nm, were studied. LiFePO4 is a mixed conductor whose electronic conductivity, which is between 10−7 and 10−8 S m−1, is due to small-polaron transfer [11–13]. LiFePO4 is usually embedded by a carbon coating with thickness from 3 to 5 nm (Fig. 6a). The carbon coating sharply increases the conductivity of the material, provides better electronic contacts between submicronic particles within large clusters, and thus improves the electrochemical performance. In previous works, the electrochemical performance of LiFePO4 composite electrodes was closely correlated to macroscopic conductivities of the active ma-
terial [14]. Higher discharge capacities and better rate capability of LiFePO4 composite electrodes were directly correlated with increased content of sp [2] (vs. sp [3]) carbon domains, a trend that can be interpreted in terms of the increasing amount of larger graphite nanodomains in the disordered carbon structure. The macroscopic conductivity data are limited because the direct current techniques do not give information on conduction mechanisms in powdered systems. Real parts of the conductivity and permittivity for LiFePO4 (LFP) at room temperature are shown in Fig. 6b. The lowest measured value is about 10−7 S m−1 at 40 Hz and the lack of DC-conductivity plateau shows that our device does not access to lower frequencies. The carbon coating sharply increases the electrical conductivity in the whole frequency range: the sample DC-conductivity σ S is 4 × 10−4 S m−1 below 105 Hz and the high frequency conductivity reaches almost 10−1 S m−1 in the GHz region at room temperature. This type of frequency dependence shows that the carbon-coating creates a percolated conducting network throughout the sample (hereafter called CLFP). This situation can be realized with a small volume fraction of conductor because of the core-shell morphol-
Fig. 6. a) TEM picture of coated LiFePO4; b) Real parts of the conductivity (σ) and of the permittivity (ε’) as functions of the frequency for both carbon-coated (c LFP) and uncoated (LFP) LiFePO4 samples at 298 K; c) Real parts of the conductivity (σ) and of permittivity (ε’) as functions of the frequency for two types of metallizations (gold and silver) on c LFP at 298 K. Adapted from Ref. [1] with permission of The Royal Society of Chemistry.
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ogy of the carbon-coated LiFePO4 material (Fig. 3b). At the highest frequencies (Fig. 4b), CLFP and LFP permittivities converge toward the constant residual permittivity ε∞ which is the effective (bulk) permittivity of LiFePO4. Indeed, the volume fraction of the carbon coating is too small to play significantly on the bulk permittivity ε∞. Moreover, it has been previously shown that the type of metallization (i.e. silver and gold paints) affects the spectra at frequencies below 106–107 Hz [1]. For frequencies above 107 Hz, the dielectric spectra correspond to the intrinsic spectra of the composite sample because they are not depending on the nature of the metallization. The dielectric relaxation, which appears around 104 Hz at room temperature is thus due to the interfacial polarization resulting from the sample/metal contact. Consequently, we demonstrate again that some variations in the interfaces at the macroscopic and microscopic levels permit the attributions of the electric polarizations occurring within the samples.
5. Composite electrode based on lithium trivanadate (Li1.1V3O8) as active material [3] The composite electrodes studied here are based on the lithium trivanadate (Li1.1V3O8) active material that offers a high theoretical capacity of 360 mAh/g, which makes it a promising positive electrode AM. Various composite electrodes have been prepared in which the surrounding of the same Li1.1V3O8 is changed by pre-plasticizing the poly(methyl methacrylate) (PMMA) binder with ethylene carbonate (EC) + propylene carbonate (PC). Tape casting, a fluid forming process using a volatile solvent, is used to prepare the composite electrodes. In previous works, an astonishing 50% increase in the cycling capacity was obtained in Li1.1V3O8-based electrodes after adding EC + PC as a non-volatile co-solvent during the fabrication step of the composite electrode. The increased cycled capacity could be interpreted as a more efficient electronic wiring of the AM particles due to a better distribution of both the AM and carbon black (CB) particles within the EC + PC pre-plasticized composite electrode. This makes the Li1.1V3O8/CB/PMMA (hereafter called TC) and Li1.1V3O8/CB/PMMA/EC + PC (hereafter called TCEC) composite electrodes very interesting materials to characterize with broadband dielectric spectroscopy [3]. Compositions of TC and TCEC are the following in weight percentages: - TC: Li1.1V3O8 = 73%wt; CB = 8%wt; PMMA = 19%wt. - TCEC: Li 1.1 V 3 O 8 = 58.4%wt; CB = 6.4%wt; PMMA = 15.2%; EC + PC = 20%wt. CB is made of elementary spheres (crystallites), whose diameter ranges from 10 to 90 nm, made up of the stacking of broken quasi-graphitic layers. These spheres are fused together by chemical bonds in various forms of aggregation, usually named primary aggregates (hereafter called particles) with an average diameter of 100–300 nm. Four shapes can be recognized for carbon-black particles: spherical, ellipsoidal, linear, and branched. Several shapes may coexist in a given grade. CB particles consist however of the smallest dispersible unit. They further give larger secondary structures of particles held together with only physical bonds, often-denoted agglomerates, hereafter called clusters. The diameter of elementary spheres of the CB used in this study ranges from 30 to 50 nm and the spheres are fused together to form linear and branched particles. The binder is deposited at the surface of Li1.1V3O8 and CB in the form of a thin layer and the binder/CB mixture forms a continuous 3D network, which connects the Li1.1V3O8 particles. The real parts of the permittivity (ε’) and the conductivity (σ) for composite electrodes without EC + PC (TC) and with EC + PC (TCEC) are shown in Fig. 7a and b. For both samples, the real part
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of the permittivity ε’ decreases by about six orders of magnitude from 105 to negative values (see insert of Fig. 7a) between 10 and 1010 Hz. The conductivities of the two composite electrodes are due to the percolated CB network because the conductivity of LiV3O8 is negligible compared to that of CB. The conductivities of TC and TCEC increase by about half an order of magnitude in the same frequency range. The conductivity of TCEC is higher owing to the presence of the EC + PC. This is likely due to a better distribution of CB clusters giving rise to a better connectivity between them. This results in lower percolation threshold in TCEC than in TC. Fig. 7c shows the complex resistivity plots, ρ” vs. ρ’ of TC (black colour) and TCEC (red colour) at 300 K. These plots are well fitted by CC-functions with α parameters of about 0.2 whatever the temperature. The electrode DC-conductivity σ e = ρ e −1 = ρ L −1 is determined from the intersection of the low-frequency part of the circular arc with the real ρ’ axis. A second type of conductivity σc = ρc−1 = ρH−1 is defined from the intersection of the high frequency part of the same circular arc with the real ρ’ axis. Since a cluster of particles is the second object after the electrode (sample) as regards the size scale, σc corresponds thus to its conductivity. Similar resistivity diagrams were obtained whatever the temperature. Fig. 8a show the entire Cole–Cole plots of TCEC at 300 K. The first dispersion domain (P1) is fitted between 40 and 6 × 107 Hz by quasivertical straight lines, which corresponds to a να−1 frequency response of the complex permittivity with the exponent α = 5 × 10−3. The real part of the permittivity ε’ rises to high values around to 105 at 50 Hz, which is due to high capacitive effects of the sample–metal junction. This type of junction is a partially blocking and ohmic contact, involving a limited charge flow (resistive part) and a polarization (capacitive part) at the junction. The domain (P1) is the high frequency part of a “quasi-Debye” dielectric relaxation due to junction polarization. Upon subtracting this low frequency contribution P1, a second dispersion domain P2 (Fig. 8b) is evidenced and well fitted by a circular arc corresponding to a CC-function. The relaxation frequency (ν2) is 6 × 108 Hz at room temperature, the α parameters (α2) is 0.08. By the same procedure, the higher frequency relaxation domain P3 (Fig. 8c) is unambiguously defined and described by a semi-circle centred on the ε’-axis, i.e.; with α3 = 0. The relaxation frequency (ν3) is 4 × 109 Hz at room temperature. The attributions of these relaxations depend on the architecture of the composite electrode. Apart from the sample/silver interface, the polarization sources are thus the clusters and the particles in TC and TCEC electrodes. Since the clusters are less conductive and have higher sizes, the relaxation of their polarization occurs at lower frequency than that of the particles. The relaxations P2 and P3 are thus attributed to the polarizations of the clusters and particles, respectively. P2 is a quasi-Debye relaxation, which indicates the lack of relaxation times distribution and the presence of smaller monodisperse CB clusters in TCEC, in agreement with previous morphological analysis. Otherwise, P3 is a Debye-type relaxation, owing to a monodisperse distribution of the particle size. The high frequency limit of the permittivity for relaxation P3 (Fig. 8c) corresponding to the static permittivity εp of the particles is negative and equal to −30. This agrees with the Drude model valid for the (quasi) metallic compounds. To find the conductivity σp of the particles, we must add the incremental conductivity δσ3 given by the strength Δε3 of the relaxation P3 to the conductivity σc of the clusters. In the case of a Debye relaxation such as P3, σ p may be written by σ p = σ c + 2πν 3ε 0 Δε 3 . In summary, different electrical relaxations were evidenced on the composite electrodes, resulting from the polarizations at the different scales of the CB network: a) the electrode conductivity (macroscopic size) σ e = 10 S m −1 ; b) the cluster conductivity σc = 25 S m−1; c) the particle conductivity σp = 40 S m−1. Higher effective conductivities, as well as narrower distribution of relaxation times of the clusters, were measured for the electrode containing
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Fig. 7. Real parts of permittivity ε’ (a) and conductivity σ (b) vs. frequency for composite electrode without EC: PC (TC) and with EC + PC (TCEC) at 300 K. (c) Nyquist plots of the imaginary part ρ” vs. the real part ρ’ of the complex resistivity at 300 K for composite electrodes without EC + PC (TC) (black colour) and with EC + PC (TCEC) (red colour). Reprinted from Ref. [3], copyright (2009), with permission from Wiley-VCH Verlag GmbH & Co.
EC + PC, in good agreement with the morphological features, i.e. a better developed percolating network of smaller CB clusters [3]. 6. Conclusion The results demonstrate that the broadband dielectric spectroscopy technique is very sensitive to the different scales of material architectures involved in the electronic transport, from interatomic distances to macroscopic sizes, as well as to the morphology at these scales, coarse or fine distribution of the constituents. The interpretation of dielectric and conductivity spectra was made only possible through the knowledge of the chemical properties (composition, ageing and surface states, structure and microstructures of the samples [15]). We must not forget that the elaboration processing of the samples also plays an important role on the electrical properties of the electrode (pressure to obtain samples, mixture process and environmental humidity). The BDS data depend on the
porosity and the density of the samples. At very low frequencies, the contact pressure applied to the sample has an influence on the measurement because of the contact resistances between the sample and the current collector. At higher frequencies, this effect is negligible because the contact pressure is far below the synthesis pressure of sample pellets (i.e. lower than 0.7 GPa). When the frequency increases, different kinds of polarizations appear from macroscopic sizes to interatomic distances and give rise to dielectric relaxations in the following order: a) Polarization (low-frequency range) due to the interface between the electrode and the conductive metallic layer (i.e. current collector) deposited on it; b) Polarization due to the existence of boundaries (direct contacts or B gaps) between clusters of C or AM particles (micronic and/or submicronic scales); c) Interfacial polarization due to the existence of particle and grain boundaries within the CB or AM clusters (nanoscales); and d) Charge motion (free electrons in quasi-metals, small-polarons hopping in oxides) at interatomic scale (microwave frequency range). Surface
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Fig. 8. Nyquist plots of the imaginary part ε” vs. the real part ε’ of the complex permittivity at 300 K for the composite electrode with EC + PC (TCEC). a) Entire plots from 40 to 1010 Hz: only the contribution (P1) of the DC-conductivity is visible. b) Plot obtained upon subtracting the domain P1 and evidence of the relaxation P2. (c) Plot obtained upon subtracting the domain P2 and evidence of the relaxation P3. Reprinted from Ref. [3], copyright (2009), with permission from Wiley-VCH Verlag GmbH & Co.
states of grains (crystallites), particles (aggregates of grains) and agglomerates of particles significantly influence the electrical response of samples: a) at lower frequencies for insulating layers (Li2CO3 layer after ageing of LiNiO2 [6]); and b) in all the frequency range for conducting layer [1,2] (carbon coating layer on LiFePO4 particle surface). Moreover, different electrical relaxations have been evidenced on composite electrode based on lithium trivanadate (Li1.1V3O8) [3] as active material, resulting from electron transfer at the different scales of the CB network: a) the electrode conductivity (i.e. CB conductivity at macroscopic size); b) the CB cluster conductivity; and c) the CB particle conductivity. The surface states of the CB are of the highest importance to understand the electrical properties of the composite electrodes. The analysis of the various functional groups on the CB surface is therefore necessary to control the electronic transfer in composite electrodes. References [1] K.A. Seid, J.C. Badot, O. Dubrunfaut, S. Levasseur, D. Guyomard, B. Lestriez, J. Mater. Chem. 22 (2012) 2641.
[2] K.A. Seid, J.C. Badot, O. Dubrunfaut, S. Levasseur, D. Guyomard, B. Lestriez, J. Mater. Chem. 22 (2012) 24057. [3] J.C. Badot, E. Ligneel, O. Dubrunfaut, D. Guyomard, B. Lestriez, Adv. Funct. Mater. 19 (2009) 2749. [4] J.C. Badot, E. Ligneel, O. Dubrunfaut, J. Gaubicher, D. Guyomard, B. Lestriez, Phys. Chem. Chem. Phys. 14 (2012) 9500. [5] K.A. Seid, J.C. Badot, C. Perca, O. Dubrunfaut, P. Soudan, D. Guyomard, et al., Adv. Energy Mater. 5 (2015) 1400903. [6] J.C. Badot, V. Bianchi, N. Baffier, N. Belhadj-Tahar, J. Phys. Condens. Matter 14 (2002) 6917. [7] K.A. Seid, J.C. Badot, O. Dubrunfaut, M.T. Caldes, N. Stephant, L. Gautier, et al., Phys. Chem. Chem. Phys. 15 (2013) 19790. [8] C.J.F. Böttcher, P. Bordewijk, Theory of Electric Polarization, Vol. II: Dielectrics in Time-dependent Fields, Elsevier, Amsterdam, 1996. [9] S. Berthumeyrie, J.-C. Badot, J.-P. Pereira-Ramos, O. Dubrunfaut, S. Bach, P. Vermaut, J. Phys. Chem. C 114 (2010) 19803. [10] N. Belhadj-Tahar, A. Fourrier-Lamer, IEEE Trans. Microwave Theory Tech. 34 (1986) 346. [11] K. Zaghib, A. Mauger, J.B. Goodenough, F. Gendron, C.M. Julien, Chem. Mater. 19 (2007) 3740. [12] C. Delacourt, L. Laffont, R. Bouchet, C. Wurm, J.B. Leriche, M. Morcrette, et al., J. Electrochem. Soc. 152 (2005) A913. [13] T. Maxish, F. Zhou, G. Ceder, Phys. Rev. B 73 (2006) 104301. [14] M.M. Doeff, J.D. Wilcox, R. Yu, A. Aumentado, M. Marcinek, R. Kostecki, J. Solid State Electrochem. 12 (2008) 995. [15] F. Ragot, J.C. Badot, N. Baffier, A. Fourrier-Lamer, J. Mater. Chem. 5 (1995) 1155.
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Materials Science and Engineering B j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m s e b
Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries Jean-Claude Badot a,*, Bernard Lestriez b, Olivier Dubrunfaut c a Institut de Recherche de Chimie Paris, UMR CNRS 8247, Réseau sur le Stockage Electrochimique de l’Energie (RS2E), Chimie Paris Tech, PSL*, 11 rue P. et M. Curie, 75231 Cedex 05 Paris, France b Institut des Matériaux Jean Rouxel, UMR CNRS 6502, Université de Nantes, 2 rue de la Houssinière, BP32229, 44322 Nantes, France c GeePs | Group of electrical engineering – Paris, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Universités, UPMC Univ Paris 06, 3 & 11 rue Joliot-Curie, Plateau de Moulon, 91192 Gif-sur-Yvette CEDEX, Paris, France
A R T I C L E
I N F O
Article history: Received 15 February 2016 Received in revised form 9 May 2016 Accepted 12 May 2016 Available online Keywords: Dielectric spectroscopy Multiscale conductivity and permittivity Lithium batteries Composite electrodes Interfaces Electronic conductivity
A B S T R A C T
Broadband dielectric spectroscopy (BDS) is used to measure complex permittivity and conductivity of conducting materials for lithium batteries at frequencies from a few Hz to several GHz with network and impedance analysers. Under the influence of an electric field, there will be charge density fluctuations in the conductor mainly due to electronic transfer. These fluctuations result in dielectric relaxations for frequencies below 100 GHz. The materials are compacted powders in which each element (particles, agglomerates of particles) can have different sizes and morphologies. In the present review, studies are reported on the influence of surface states in LiNiO2 (ageing and degradation in air) and LiFePO4 (carbon coating thin layer), and on a composite electrode based on the lithium trivanadate (Li1.1V3O8) active material. The results have shown that the BDS technique is very sensitive to the different scales of materials architectures involved in electronic transport, from interatomic distances to macroscopic sizes. © 2016 Published by Elsevier B.V.
1. Introduction Upcoming hybrid electric and pure electric vehicles (HEV and EV) applications require the development of new lithium batteries with high energy density, high power and high cyclability. To reach these goals, a more fundamental understanding of the so called “formulation” of the composite electrode, i.e. the relationships between the processing, the morphology at its different scales, the electrical and mechanical properties and the electrochemical performance of the composite electrode, is needed. Electronic conductivity is one of the two major electrical properties (the other is the ionic conductivity) of the composite electrode with respect to its electrochemical behaviour. The broadband dielectric spectroscopy (hereafter called BDS) allows the study of the electronic conductivity of a composite electrode at all the scales of its architecture (from interatomic distances to macroscopic lengths) as function of the temperature usually between 200 and 400 K [1–5]. This technique thus allows the clarification of the charge transport mechanisms and the origin of the limitations in these
* Corresponding author. Tel.: +33 1 44 27 80 15. E-mail address: [email protected] (J.-C. Badot).
mechanisms, depending on the composition, processing and morphology of the composite electrode. Understanding the electrical properties of such hierarchical materials is difficult due to their complexity. First of all, to study each electrode component taken separately is mandatory. We must be aware that the electrical properties of composite electrode are not the sum of all the contributions of its different components taken separately. We must indeed also consider the existence of interfaces (or contacts) at the different levels of the composite electrode: sample/current collector interface, junctions between CB agglomerates, junctions between AM agglomerates, grain boundaries in AM agglomerates, AM/CB interfaces, binder layers (gaps) present at some these interfaces (Fig. 1). The surface effects are thus of the greatest importance to understand the multiscale electronic transfer in composite electrodes. In the present review, we compare previous studies on the influence of surface states for LiNiO2 [6] and LiFePO4 [1,2] active materials. In the first case, the influence of surface ageing and degradation is considered and in the second one, the influence of a carbon coating is analysed. Moreover, the nature of the electronic transfer in composite electrode based on the Li1.1V3O8 active material is investigated [4]. Permittivity and conductivity measurements have been recorded in a wide frequency range from 10 Hz to 10 GHz in the temperature range 200 to 300 K.
http://dx.doi.org/10.1016/j.mseb.2016.05.012 0921-5107/© 2016 Published by Elsevier B.V.
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centred on the ε’ axis. Two approaches are considered to interpret the different relaxations: the first one is geometrical and the second is kinetic. In the geometrical approach, when the size of a system increases, its response appears at lower frequency (e.g. agglomerate polarization fluctuates slower than particle polarization). In the kinetic approach, when the mobility of charge carrier increases, its response is shifted to higher frequencies (e.g. ions contributions are generally observed at lower frequencies than the electrons). Consequently, several types of polarizations involving dielectric relaxations can appear from low to high frequencies in the following order: (a) space-charge polarization (low-frequency range) due to the sample/current collector interface; (b) polarization of agglomerates (or clusters) of particles (micronic scale) and (c) polarization of particles due to the existence of resistive junctions between them; d) electron transfers (nanometric or interatomic scale). The resistivity ρ(ω) and conductivity σ(ω) relaxations also described by the same functions as before are thus given by
Fig. 1. Schematic representation of a composite electrode.
ρ (ω ) = ρH +
2. Theoretical background
ρL − ρH
1−δ γ
ρ
The electrical response of a material results from charge density fluctuations, when it is submitted to a time-dependent electric field E (t ) . This response is given by a time dependent current density J(t) and dielectric displacement D(t),
dD (t ) J (t ) = Jc + dt
(1)
The first term on the right hand side is the direct current density Jc = σ dcE where σdc is the direct current conductivity of the material. The second term is the displacement current density Jd = dD dt = ε 0d ε E dt where ε0 is the vacuum permittivity and ε
( )
the relative permittivity. In harmonic regime (i.e. E(t) ∝ exp(iωt)), from equation 1 the relationship between frequency-dependent complex conductivity σ(ω) = σ’(ω) + iσ”(ω) and relative permittivity ε(ω) = ε’(ω) – iε”(ω) can be defined as follows,
σ (ω ) = ρ (ω ) = σ dc + iωε 0 ε (ω ) = (σ dc + ωε 0 ε ′′ (ω )) + iωε 0 ε ′ (ω ) −1
(2)
The real part of the conductivity is the sum of the DC-conductivity (i.e. at zero frequency) and of a term proportional to the imaginary part ε” (i.e. dielectric losses) of the permittivity (Fig. 2a). In electronic conductors, several polarization mechanisms occur at different scales (from interatomic to macroscopic sizes) [7] with distinct characteristic frequencies (Fig. 2b). At frequencies below 1011 Hz, the dielectric spectra of conducting materials can be generally summarized by the following expression:
⎡ ε mL − ε mH ε (ω ) = ε ∞ + ⎢ ∑ ⎢ m 1 + (iωτ m )1−αm ⎣
(
)
βm
⎤ ⎥ + A (iω )s−1 + σ dc ⎥ iωε 0 ⎦
(3)
where ε∞ is the residual (network) permittivity and A is a fitting parameter. The term in brackets in expression (3) is the sum of m dielectric relaxations described by empirical Havriliak–Negami (HN) functions [8]. For each relaxation, εmL and εmH are the low- and highfrequency limits of the permittivity, τm the mean relaxation time; αm and βm are fitting parameters. The HN-function is the generalization of the Cole–Cole (CC) function with βm = 1, of the Cole– Davidson (CD) function with αm = 0 and of the Debye function (D) with αm = 0 and βm = 1 [8]. CC, CD and HN functions result from distributions of relaxation times, which are symmetrical for CC function and asymmetric for CD and HN functions [8]. The Nyquist plots of the complex permittivity (i.e. ε” vs. ε’) are circular arcs with centres below the ε’ axis for CC function and skewed arcs for CD and HN function. Note that Nyquist plot of the D function is a semi-circle
(4a)
(1+ (iωτ ) )
σ (ω ) = σ H −
σH −σL
(1+ (iωτ
)1−η )
κ
σ
(4b)
where the indices L and H mean the low- and high-frequency limits of resistivity and conductivity, τρ and τσ the resistivity and conductivity relaxation times; δ, γ, η and κ are fitting parameters similar to those of equation (3). If we examine the influence of surface effects on the electrical properties, we can consider the two extreme cases most frequently observed: the first one is formed by conducting grains surrounded by a quasi-insulating thin layer (Fig. 3a) and the second one insulating grains surrounded by a conducting thin layer (Fig. 3b). In the first case, the electrical equivalent circuit of the system can be schematized as two parallel combinations of resistance and capacitance in series: the first one is associated with the grains (higher frequencies) and the second with the interfacial region (lower frequencies) (Fig. 3a). The Nyquist plot of the resistivity is the sum of two relaxations often illustrated by two circular arcs (CC functions). The circular arc corresponding to the bulk or grain response crosses the ρ’ axis at the origin when ν → ∞. The shape of the conductivity spectrum is similar to a sigmoid curve (Fig. 3a): the lowfrequency part (sample conductivity) corresponds to the conductivity of the quasi-insulator phase (σs) and the high frequency part to the grain bulk conductivity (σg > > σs). In the second case, the interface forms a continuous conducting medium giving rise to a constant conductivity in all the frequency range (Fig. 3b). The Nyquist plot of the resistivity (impedance) shows only one relaxation described by a circular arc (CC function) or a skewed arc (CD or HN function) for highly disordered conducting network (e.g. percolated conductor with concentration slightly higher than the percolation threshold) (Fig. 3b). 3. Experimental devices The broadband dielectric spectroscopy requires some devices and instruments (network and impedance analysers) for complete coverage of the frequency range. Complex resistivity and permittivity spectra are recorded over a broad frequency range of 40 Hz to 10 GHz, using simultaneously impedance and network analysers Agilent 4294 (40 Hz–110 MHz), 4291 (1 MHz–1.8 GHz), PNA E8364B (10 MHz– 10 GHz). The experimental devices, fully described in previous papers [9,10], consists of a coaxial cell (APC7 standard) in which the cylindrically shaped sample fills the gap between the inner conductor and a short circuit (Fig. 4). The samples are powders that are pressed
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Fig. 2. a) Schematic representation of the real (ε’) and imaginary (ε”) parts of the permittivity vs. frequency for a solid. εlat is the lattice permittivity of the solid, einf the permittivity of induced polarization, n the refractive index; χint, χdip, χlat and χel are interfacial, dipolar, lattice and electronic electrical susceptibilities, respectively. b) Schematic description of a hierarchical architecture at different scales of a powdered material: different sources of polarization vs. frequency and size. (b) Reproduced from Ref. [7] with permission of the PCCP Owner Societies.
at about 0.7 GPa. Two sample diameters are considered: the first one is similar to the inner conductor diameter equal to 3 mm (Fig. 4a) [9] and the second to the outer conductor with diameter of 7 mm (Fig. 4b) [10]. Sample thickness lies between 0.4 and 1 mm in both cases. To ensure good contacts (junctions) between the sample/
inner conductor and sample/short-circuit, its front faces are covered with silver or gold thin layers. After a relevant calibration of the analysers, the sample admittance is computed from measurements of the complex reflection coefficient of the device. The knowledge of the admittance allows
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Fig. 3. Influence of the surface states on the electrical properties of powdered materials. a) Insulating layer around the conducting phase: layer resistivity ρs > > grain resistivity ρg, electrical equivalent scheme and frequency dependent real part of the conductivity σ with σs = 1/ρs and σg = 1/ρg surface layer and grain conductivities, respectively. b) Conducting layer around the insulating phase: layer resistivity ρs < < grain resistivity ρg, electrical equivalent scheme and frequency dependent real part of the conductivity σ with σs = 1/ρs conducting layer conductivity.
the determination the complex (relative) permittivity of the sample. Complete dielectric spectra are made from about 600 measurements with an accuracy of approximately 3 to 5% in the whole frequency range. The knowledge of the complex permittivity allows the calculation of complex resistivity and conductivity. The measurements are recorded in the range of 190 to 300 K under dry N2 flux and 300 to 450 K in a furnace. Since all the polarizations at different scales are generally additive (assumed in Eq. 3), their contributions can be thus evidenced by the decomposition of the different dielectric spectra using Nyquist plots (imaginary part vs. real part of the permittivity, the conductivity and the resistivity). Spectra analyses are recorded by home-made software [9,10].
4. Influence of the surface states on the conductivity and permittivity spectra For the purpose of this study, the influence of the surface states of two types of compounds, LiNiO2 [6] and LiFePO4 [1,2], on their dielectric spectra, is here detailed. LiNiO2 degrades when exposed to ambient atmosphere with the formation of a quasi-insulating thin layer on aggregates (i.e. clusters of particles) and particles surface. LiFePO4 has low intrinsic conductivity and is embedded by a thin conducting carbon coating layer on aggregates and particles surface.
Fig. 4. a) Coaxial cell used to make measurements of permittivity and conductivity of materials vs. frequency from 10 Hz to 10 GHz [9]; b) Coaxial cell used to make measurements of permittivity and conductivity of materials vs. frequency from 10 Hz to 18 GHz [10]. Adapted with permission from Ref. [9]. Copyright (2010) American Chemical Society.
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4.1. Insulating layer on conducting LiNiO2 aggregates and particles [6] Fig. 5 shows the frequency dependence of the real parts of the conductivity and permittivity of pure (hereafter called A1) and damaged (hereafter called A2) LiNiO2 at room temperature. Below 3 × 109 Hz, the conductivity of A1 is independent of the frequency (Fig. 5a) and is equal to the sample DC conductivity (σ = 0.18 S m−1 at room temperature) at low-frequency (i.e. ν = ω/2π < 1 × 104 Hz). Such a behaviour is seen as a ω−1 frequency response on the dielectric losses (imaginary part of ε). The real part ε’(ω) of the complex permittivity shows a low-frequency dispersion of A1 (Fig. 5b), which can be approximated by a straight line with a slope close to −1. This corresponds to a ν−1 frequency response in the low-frequency range (ν < 2 × 103 Hz). Furthermore, ε’(ω) rises to high values between 105 and 106 at 10 Hz, which indicates a high capacitive effect of the semiconductor–metal junction. The semiconductor–metal junction is a Schottky barrier, which produces a limited charge flow (resistive part) and a polarization (capacitive part) at the junction. In the low-frequency domain, the electrical equivalent circuit of the system can be schematized as Fig. 3a. The dielectric response is described by the Debye relaxation model, for which ε’ and ε” follow respectively ω−2 and ω−1 frequency responses for frequencies above
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the relaxation frequency. The dielectric losses ε” are here due to the DC conductivity of the sample. Unfortunately, the Debye model cannot explain the experimental ω−1 frequency response of the real part ε’. The sample surface roughness involves a distribution of interfacial resistances and capacitances, and thus a distribution of relaxation times with a dielectric response fitted by the CC function. In this model, ε’ and ε” are proportional to ωα−1 for frequencies above the relaxation frequency. This behavior is identical to the universal dielectric response (UDR) depicting the low-frequency dispersion of the dielectric spectra. The ω−1 experimental lowfrequency response of ε’ results from a very narrow distribution of relaxation times with negligible α parameter (i.e. α < <1). After a few weeks under air, the sample A1 was damaged and became A2 (Fig. 5a). The sharp decrease of the DC-conductivity by about two orders of magnitude is due to the formation of a quasi-insulating layer (in fact ionic conducting layer) of Li2CO3 on the grain boundaries, while the high-frequency conductivity is not modified for ν > 1 × 109 Hz and is thus intrinsic to the grain bulk (electronic conductor) of the sample. The evolution of the spectra with the formation of Li2CO3 during the ageing has provided evidence of two regimes: the first one is an interfacial (low-frequency) regime and the second a bulk (high-frequency) regime. The crossover frequency νco between the two regimes is 3 × 109 Hz at 293 K and decreases
Fig. 5. (a, b) Real parts of the conductivity σ’ and permittivity ε’ as functions of frequency ν = ω/2π at room temperature for the compound Li0.97Ni1.03O2. The curves A1 correspond to the sample of the pure compound (A1); the curves A2 correspond to the sample damaged (A2) (after a few weeks under air), which contains a low content of Li2CO3. Reprinted from Ref. [6]. Copyright Institute of Physics (the “Institute”) and IOP Publishing 2010.
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down to 108 Hz at 220 K, which broadens the frequency range of the bulk regime. The damaging in air of LiNiO2 is here a necessary drawback, since it allows the attribution of the dielectric relaxations to interfacial polarizations due to metal/sample junction and grain boundaries for frequencies below νco. 4.2. Conducting carbon black coating on insulating LiFePO4 aggregates and particles [1,2] Carbon and non-carbon coated (carbon content: 0 to 4 wt%) LiFePO4, whose particle size is between 50 and 150 nm, were studied. LiFePO4 is a mixed conductor whose electronic conductivity, which is between 10−7 and 10−8 S m−1, is due to small-polaron transfer [11–13]. LiFePO4 is usually embedded by a carbon coating with thickness from 3 to 5 nm (Fig. 6a). The carbon coating sharply increases the conductivity of the material, provides better electronic contacts between submicronic particles within large clusters, and thus improves the electrochemical performance. In previous works, the electrochemical performance of LiFePO4 composite electrodes was closely correlated to macroscopic conductivities of the active ma-
terial [14]. Higher discharge capacities and better rate capability of LiFePO4 composite electrodes were directly correlated with increased content of sp [2] (vs. sp [3]) carbon domains, a trend that can be interpreted in terms of the increasing amount of larger graphite nanodomains in the disordered carbon structure. The macroscopic conductivity data are limited because the direct current techniques do not give information on conduction mechanisms in powdered systems. Real parts of the conductivity and permittivity for LiFePO4 (LFP) at room temperature are shown in Fig. 6b. The lowest measured value is about 10−7 S m−1 at 40 Hz and the lack of DC-conductivity plateau shows that our device does not access to lower frequencies. The carbon coating sharply increases the electrical conductivity in the whole frequency range: the sample DC-conductivity σ S is 4 × 10−4 S m−1 below 105 Hz and the high frequency conductivity reaches almost 10−1 S m−1 in the GHz region at room temperature. This type of frequency dependence shows that the carbon-coating creates a percolated conducting network throughout the sample (hereafter called CLFP). This situation can be realized with a small volume fraction of conductor because of the core-shell morphol-
Fig. 6. a) TEM picture of coated LiFePO4; b) Real parts of the conductivity (σ) and of the permittivity (ε’) as functions of the frequency for both carbon-coated (c LFP) and uncoated (LFP) LiFePO4 samples at 298 K; c) Real parts of the conductivity (σ) and of permittivity (ε’) as functions of the frequency for two types of metallizations (gold and silver) on c LFP at 298 K. Adapted from Ref. [1] with permission of The Royal Society of Chemistry.
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ogy of the carbon-coated LiFePO4 material (Fig. 3b). At the highest frequencies (Fig. 4b), CLFP and LFP permittivities converge toward the constant residual permittivity ε∞ which is the effective (bulk) permittivity of LiFePO4. Indeed, the volume fraction of the carbon coating is too small to play significantly on the bulk permittivity ε∞. Moreover, it has been previously shown that the type of metallization (i.e. silver and gold paints) affects the spectra at frequencies below 106–107 Hz [1]. For frequencies above 107 Hz, the dielectric spectra correspond to the intrinsic spectra of the composite sample because they are not depending on the nature of the metallization. The dielectric relaxation, which appears around 104 Hz at room temperature is thus due to the interfacial polarization resulting from the sample/metal contact. Consequently, we demonstrate again that some variations in the interfaces at the macroscopic and microscopic levels permit the attributions of the electric polarizations occurring within the samples.
5. Composite electrode based on lithium trivanadate (Li1.1V3O8) as active material [3] The composite electrodes studied here are based on the lithium trivanadate (Li1.1V3O8) active material that offers a high theoretical capacity of 360 mAh/g, which makes it a promising positive electrode AM. Various composite electrodes have been prepared in which the surrounding of the same Li1.1V3O8 is changed by pre-plasticizing the poly(methyl methacrylate) (PMMA) binder with ethylene carbonate (EC) + propylene carbonate (PC). Tape casting, a fluid forming process using a volatile solvent, is used to prepare the composite electrodes. In previous works, an astonishing 50% increase in the cycling capacity was obtained in Li1.1V3O8-based electrodes after adding EC + PC as a non-volatile co-solvent during the fabrication step of the composite electrode. The increased cycled capacity could be interpreted as a more efficient electronic wiring of the AM particles due to a better distribution of both the AM and carbon black (CB) particles within the EC + PC pre-plasticized composite electrode. This makes the Li1.1V3O8/CB/PMMA (hereafter called TC) and Li1.1V3O8/CB/PMMA/EC + PC (hereafter called TCEC) composite electrodes very interesting materials to characterize with broadband dielectric spectroscopy [3]. Compositions of TC and TCEC are the following in weight percentages: - TC: Li1.1V3O8 = 73%wt; CB = 8%wt; PMMA = 19%wt. - TCEC: Li 1.1 V 3 O 8 = 58.4%wt; CB = 6.4%wt; PMMA = 15.2%; EC + PC = 20%wt. CB is made of elementary spheres (crystallites), whose diameter ranges from 10 to 90 nm, made up of the stacking of broken quasi-graphitic layers. These spheres are fused together by chemical bonds in various forms of aggregation, usually named primary aggregates (hereafter called particles) with an average diameter of 100–300 nm. Four shapes can be recognized for carbon-black particles: spherical, ellipsoidal, linear, and branched. Several shapes may coexist in a given grade. CB particles consist however of the smallest dispersible unit. They further give larger secondary structures of particles held together with only physical bonds, often-denoted agglomerates, hereafter called clusters. The diameter of elementary spheres of the CB used in this study ranges from 30 to 50 nm and the spheres are fused together to form linear and branched particles. The binder is deposited at the surface of Li1.1V3O8 and CB in the form of a thin layer and the binder/CB mixture forms a continuous 3D network, which connects the Li1.1V3O8 particles. The real parts of the permittivity (ε’) and the conductivity (σ) for composite electrodes without EC + PC (TC) and with EC + PC (TCEC) are shown in Fig. 7a and b. For both samples, the real part
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of the permittivity ε’ decreases by about six orders of magnitude from 105 to negative values (see insert of Fig. 7a) between 10 and 1010 Hz. The conductivities of the two composite electrodes are due to the percolated CB network because the conductivity of LiV3O8 is negligible compared to that of CB. The conductivities of TC and TCEC increase by about half an order of magnitude in the same frequency range. The conductivity of TCEC is higher owing to the presence of the EC + PC. This is likely due to a better distribution of CB clusters giving rise to a better connectivity between them. This results in lower percolation threshold in TCEC than in TC. Fig. 7c shows the complex resistivity plots, ρ” vs. ρ’ of TC (black colour) and TCEC (red colour) at 300 K. These plots are well fitted by CC-functions with α parameters of about 0.2 whatever the temperature. The electrode DC-conductivity σ e = ρ e −1 = ρ L −1 is determined from the intersection of the low-frequency part of the circular arc with the real ρ’ axis. A second type of conductivity σc = ρc−1 = ρH−1 is defined from the intersection of the high frequency part of the same circular arc with the real ρ’ axis. Since a cluster of particles is the second object after the electrode (sample) as regards the size scale, σc corresponds thus to its conductivity. Similar resistivity diagrams were obtained whatever the temperature. Fig. 8a show the entire Cole–Cole plots of TCEC at 300 K. The first dispersion domain (P1) is fitted between 40 and 6 × 107 Hz by quasivertical straight lines, which corresponds to a να−1 frequency response of the complex permittivity with the exponent α = 5 × 10−3. The real part of the permittivity ε’ rises to high values around to 105 at 50 Hz, which is due to high capacitive effects of the sample–metal junction. This type of junction is a partially blocking and ohmic contact, involving a limited charge flow (resistive part) and a polarization (capacitive part) at the junction. The domain (P1) is the high frequency part of a “quasi-Debye” dielectric relaxation due to junction polarization. Upon subtracting this low frequency contribution P1, a second dispersion domain P2 (Fig. 8b) is evidenced and well fitted by a circular arc corresponding to a CC-function. The relaxation frequency (ν2) is 6 × 108 Hz at room temperature, the α parameters (α2) is 0.08. By the same procedure, the higher frequency relaxation domain P3 (Fig. 8c) is unambiguously defined and described by a semi-circle centred on the ε’-axis, i.e.; with α3 = 0. The relaxation frequency (ν3) is 4 × 109 Hz at room temperature. The attributions of these relaxations depend on the architecture of the composite electrode. Apart from the sample/silver interface, the polarization sources are thus the clusters and the particles in TC and TCEC electrodes. Since the clusters are less conductive and have higher sizes, the relaxation of their polarization occurs at lower frequency than that of the particles. The relaxations P2 and P3 are thus attributed to the polarizations of the clusters and particles, respectively. P2 is a quasi-Debye relaxation, which indicates the lack of relaxation times distribution and the presence of smaller monodisperse CB clusters in TCEC, in agreement with previous morphological analysis. Otherwise, P3 is a Debye-type relaxation, owing to a monodisperse distribution of the particle size. The high frequency limit of the permittivity for relaxation P3 (Fig. 8c) corresponding to the static permittivity εp of the particles is negative and equal to −30. This agrees with the Drude model valid for the (quasi) metallic compounds. To find the conductivity σp of the particles, we must add the incremental conductivity δσ3 given by the strength Δε3 of the relaxation P3 to the conductivity σc of the clusters. In the case of a Debye relaxation such as P3, σ p may be written by σ p = σ c + 2πν 3ε 0 Δε 3 . In summary, different electrical relaxations were evidenced on the composite electrodes, resulting from the polarizations at the different scales of the CB network: a) the electrode conductivity (macroscopic size) σ e = 10 S m −1 ; b) the cluster conductivity σc = 25 S m−1; c) the particle conductivity σp = 40 S m−1. Higher effective conductivities, as well as narrower distribution of relaxation times of the clusters, were measured for the electrode containing
Please cite this article in press as: Jean-Claude Badot, Bernard Lestriez, Olivier Dubrunfaut, Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries, Materials Science and Engineering B (2016), doi: 10.1016/j.mseb.2016.05.012
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Fig. 7. Real parts of permittivity ε’ (a) and conductivity σ (b) vs. frequency for composite electrode without EC: PC (TC) and with EC + PC (TCEC) at 300 K. (c) Nyquist plots of the imaginary part ρ” vs. the real part ρ’ of the complex resistivity at 300 K for composite electrodes without EC + PC (TC) (black colour) and with EC + PC (TCEC) (red colour). Reprinted from Ref. [3], copyright (2009), with permission from Wiley-VCH Verlag GmbH & Co.
EC + PC, in good agreement with the morphological features, i.e. a better developed percolating network of smaller CB clusters [3]. 6. Conclusion The results demonstrate that the broadband dielectric spectroscopy technique is very sensitive to the different scales of material architectures involved in the electronic transport, from interatomic distances to macroscopic sizes, as well as to the morphology at these scales, coarse or fine distribution of the constituents. The interpretation of dielectric and conductivity spectra was made only possible through the knowledge of the chemical properties (composition, ageing and surface states, structure and microstructures of the samples [15]). We must not forget that the elaboration processing of the samples also plays an important role on the electrical properties of the electrode (pressure to obtain samples, mixture process and environmental humidity). The BDS data depend on the
porosity and the density of the samples. At very low frequencies, the contact pressure applied to the sample has an influence on the measurement because of the contact resistances between the sample and the current collector. At higher frequencies, this effect is negligible because the contact pressure is far below the synthesis pressure of sample pellets (i.e. lower than 0.7 GPa). When the frequency increases, different kinds of polarizations appear from macroscopic sizes to interatomic distances and give rise to dielectric relaxations in the following order: a) Polarization (low-frequency range) due to the interface between the electrode and the conductive metallic layer (i.e. current collector) deposited on it; b) Polarization due to the existence of boundaries (direct contacts or B gaps) between clusters of C or AM particles (micronic and/or submicronic scales); c) Interfacial polarization due to the existence of particle and grain boundaries within the CB or AM clusters (nanoscales); and d) Charge motion (free electrons in quasi-metals, small-polarons hopping in oxides) at interatomic scale (microwave frequency range). Surface
Please cite this article in press as: Jean-Claude Badot, Bernard Lestriez, Olivier Dubrunfaut, Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries, Materials Science and Engineering B (2016), doi: 10.1016/j.mseb.2016.05.012
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Fig. 8. Nyquist plots of the imaginary part ε” vs. the real part ε’ of the complex permittivity at 300 K for the composite electrode with EC + PC (TCEC). a) Entire plots from 40 to 1010 Hz: only the contribution (P1) of the DC-conductivity is visible. b) Plot obtained upon subtracting the domain P1 and evidence of the relaxation P2. (c) Plot obtained upon subtracting the domain P2 and evidence of the relaxation P3. Reprinted from Ref. [3], copyright (2009), with permission from Wiley-VCH Verlag GmbH & Co.
states of grains (crystallites), particles (aggregates of grains) and agglomerates of particles significantly influence the electrical response of samples: a) at lower frequencies for insulating layers (Li2CO3 layer after ageing of LiNiO2 [6]); and b) in all the frequency range for conducting layer [1,2] (carbon coating layer on LiFePO4 particle surface). Moreover, different electrical relaxations have been evidenced on composite electrode based on lithium trivanadate (Li1.1V3O8) [3] as active material, resulting from electron transfer at the different scales of the CB network: a) the electrode conductivity (i.e. CB conductivity at macroscopic size); b) the CB cluster conductivity; and c) the CB particle conductivity. The surface states of the CB are of the highest importance to understand the electrical properties of the composite electrodes. The analysis of the various functional groups on the CB surface is therefore necessary to control the electronic transfer in composite electrodes. References [1] K.A. Seid, J.C. Badot, O. Dubrunfaut, S. Levasseur, D. Guyomard, B. Lestriez, J. Mater. Chem. 22 (2012) 2641.
[2] K.A. Seid, J.C. Badot, O. Dubrunfaut, S. Levasseur, D. Guyomard, B. Lestriez, J. Mater. Chem. 22 (2012) 24057. [3] J.C. Badot, E. Ligneel, O. Dubrunfaut, D. Guyomard, B. Lestriez, Adv. Funct. Mater. 19 (2009) 2749. [4] J.C. Badot, E. Ligneel, O. Dubrunfaut, J. Gaubicher, D. Guyomard, B. Lestriez, Phys. Chem. Chem. Phys. 14 (2012) 9500. [5] K.A. Seid, J.C. Badot, C. Perca, O. Dubrunfaut, P. Soudan, D. Guyomard, et al., Adv. Energy Mater. 5 (2015) 1400903. [6] J.C. Badot, V. Bianchi, N. Baffier, N. Belhadj-Tahar, J. Phys. Condens. Matter 14 (2002) 6917. [7] K.A. Seid, J.C. Badot, O. Dubrunfaut, M.T. Caldes, N. Stephant, L. Gautier, et al., Phys. Chem. Chem. Phys. 15 (2013) 19790. [8] C.J.F. Böttcher, P. Bordewijk, Theory of Electric Polarization, Vol. II: Dielectrics in Time-dependent Fields, Elsevier, Amsterdam, 1996. [9] S. Berthumeyrie, J.-C. Badot, J.-P. Pereira-Ramos, O. Dubrunfaut, S. Bach, P. Vermaut, J. Phys. Chem. C 114 (2010) 19803. [10] N. Belhadj-Tahar, A. Fourrier-Lamer, IEEE Trans. Microwave Theory Tech. 34 (1986) 346. [11] K. Zaghib, A. Mauger, J.B. Goodenough, F. Gendron, C.M. Julien, Chem. Mater. 19 (2007) 3740. [12] C. Delacourt, L. Laffont, R. Bouchet, C. Wurm, J.B. Leriche, M. Morcrette, et al., J. Electrochem. Soc. 152 (2005) A913. [13] T. Maxish, F. Zhou, G. Ceder, Phys. Rev. B 73 (2006) 104301. [14] M.M. Doeff, J.D. Wilcox, R. Yu, A. Aumentado, M. Marcinek, R. Kostecki, J. Solid State Electrochem. 12 (2008) 995. [15] F. Ragot, J.C. Badot, N. Baffier, A. Fourrier-Lamer, J. Mater. Chem. 5 (1995) 1155.
Please cite this article in press as: Jean-Claude Badot, Bernard Lestriez, Olivier Dubrunfaut, Interest in broadband dielectric spectroscopy to study the electronic transport in materials for lithium batteries, Materials Science and Engineering B (2016), doi: 10.1016/j.mseb.2016.05.012