Solid State Ionics 187 (2011) 58–63

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Solid State Ionics

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Determination of the chemical diffusion coefficient of Li+ in intercalation-typeLi3V2(PO4)3 anode material

X.H. Rui, N. Yesibolati, S.R. Li, C.C. Yuan, C.H. Chen ⁎CAS Key Laboratory of Materials for Energy Conversion, Department of Materials Science and Engineering, University of Science and Technology of China, Anhui Hefei 230026, China

⁎ Corresponding author: Tel.: +86 551 3606971; faxE-mail address: cchchen@ustc.edu.cn (C.H. Chen).

0167-2738/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.ssi.2011.02.013

a b s t r a c t

a r t i c l e i n f o

Article history:Received 25 November 2010Received in revised form 15 February 2011Accepted 16 February 2011Available online 10 March 2011

Keywords:Lithium vanadium phosphateLithium ion batteryAnodeChemical diffusion coefficient

The chemical diffusion coefficients of lithium ion (DLi+) in intercalation-type Li3V2(PO4)3 (LVP) anodematerial as a function of cell voltage between 3.0 and 0.0 V are systematically determined by cyclicvoltammetry (CV), electrochemical impedance spectroscopy (EIS) and galvanostatic intermittent titrationtechnique (GITT). The true chemical diffusion coefficients (DLi+

true) obtained from EIS and GITT for the single-

phase region (1.6–0.0 V vs. Li+/Li) are in the range of 10−10 to 10−9 cm2s−1 and 10−11 to 10−10 cm2s−1,respectively, and exhibit a decreasing trend of the change of DLi+

truevs. voltage as the discharge and charge

proceeded. The apparent chemical diffusion coefficients (DLi+app

) measured from CV and GITT for the two-phaseregions (around 2.5–1.6 V) are in the range of 10−10 cm2s−1 and 10−12 to 10−10 cm2s−1, respectively. ForGITT, DLi+

appvs. voltage plots display a characteristic of “W” shape due to the strong interactions of Li+ with

surrounding ions. Finally, the DLi+ values of LVP anode are compared with other anode materials, illustratingthat LVP can also be used as a potential anode material to achieve high rate capability.

: +86 551 3601592.

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

The monoclinic lithium vanadium phosphate, Li3V2(PO4)3 (LVP),has been employed as a promising cathode material in rechargeablelithium ion batteries, due to its good ionic mobility, high reversiblecapacity and relatively high operating voltage [1–3]. The 3D frame-work structure of LVP is built from slightly distorted VO6 octahedraand PO4

3− tetrahedral anions [4]. Each VO6 octahedron is surroundedby six PO4 tetrahedra, whereas each PO4 tetrahedron is surrounded byfour VO6 octahedra. This configuration containing relatively largeinterconnected interstitial space is potentially a fast ionic conductor.One of the major problems limiting the application of LVP cathode inhigh power density batteries is its low intrinsic electronic conductiv-ity (about 10−8 Scm−1 [5]). As a result, many investigations havebeen focused on its synthesis and improvement of electrochemicalcapacities in non-queous electrolytes [6–8]. In the past few years,conductivity is usually enhanced appreciably by coating LVP particleswith electrically conductive carbon materials [6–8].

Interestingly, in our recent work, we have successfully confirmedthat the carbon coated Li3V2(PO4)3 (LVP/C) can also be used as anintercalation-type anode material with superior electrochemical per-formance [9]. It exhibits a stable reversible capacity of 203 mAh g−1

in the voltage range of 3.0–0.0 V vs. Li+/Li, and the Coulombic efficiencyis close to 100% after the third cycle. In addition, the monoclinic LVP

structure can be still retained during the lithium ions insertion/extraction process. In the discharge process, there are initially asequence of two-phase transition processes taking place at 1.95 V(Li3V2(PO4)3→Li3.5V2(PO4)3), 1.86 V (Li3.5V2(PO4)3→Li4V2(PO4)3),1.74 V (Li4V2(PO4)3→Li4.5V2(PO4)3) and 1.66 V (Li4.5V2(PO4)3→Li5V2

(PO4)3), respectively. Subsequently, a single-phase region between1.6 V and 0.0 V is occurred, corresponding to 2 Li+ insertion (Li5V2

(PO4)3→Li7V2(PO4)3) associated with the V2+/V+ redox couple. Andthe lithium ions extraction is a reversible process. Furthermore, withincreasing interest in high power density of Li-ion batteries, kinetics oflithium ions transfer in LVP anode material is also necessary to beevaluated and understood since they govern the intercalation/deinter-calation rate.

In literatures, several techniques including cyclic voltammetry (CV)[10,11], electrochemical impedance spectroscopy (EIS) [12,13] andgalvanostatic intermittent titration technique (GITT) [14,15], have beenextensively used to study the diffusion kinetics of Li+ intercalation/deintercalation and to estimate the chemical diffusion coefficients ofLi+ in solid electrodes. Here, it should be noted that, for the diffusioncoefficient with a physical meaning (named true diffusion coefficient,DLi+true

), the Li+ concentration of electrodes must be changed mono-tonically as intercalation proceeds [16], which is valid only fortopotactic solid-state intercalation reactions. When the intercalationof lithium ions is accompanied by strong electron–ion interactions, theintercalation proceeds following one or several reaction fronts, andleads to the coexistence of two phases [15]. Thus, the physical meaningof the chemical diffusion coefficient, DLi+, as a function of lithiumcomposition becomes obscure. However, the obtainedDLi+ can be taken

Fig. 1. Galvanostatic charge–discharge curves of the LVP anode at a constant currentdensity of 0.013 mA cm−2 between 3.0 and 0.0 V during the 1st and 2nd cycles. Inset isthe amplification of four plateaus in the first discharge process.

Fig. 2. Cyclic voltammetry curves of the LVP anode during the third cycle at differentscan rates of 0.05, 0.1 and 0.2 mV s−1 between 3.0 and 0.0 V.

59X.H. Rui et al. / Solid State Ionics 187 (2011) 58–63

as an effective measurement to reflect the intensity of long- and short-range interactions of lithium ions. At this condition, the DLi+ is called asapparent diffusion coefficient, DLi+

app. We have reported the diffusion

coefficients (DLi+true

and DLi+app

) of LVP cathode in the voltage window of 3.0–4.8 V throughCV, GITT andEISmethods [17].DLi+

truemeasured in the single-

phase region is in the range of 10−10 to 10−9 cm2s−1, and DLi+app

derived from two-phase regions by the CV and GITT is in the range of10−11 to 10−10 cm2s−1 and 10−13 to 10−8 cm2s−1, respectively. In thepresent paper, a systematic measurement and discussion of the DLi+

trueand

DLi+app

of LVP anodewas conducted, using three different techniques, CV, EISand GITT.

2. Experimental

The monoclinic LVP/C sample was synthesized by the carbother-mal reduction method. The detailed sample preparation, structuraland morphological characterization have been described elsewhere[9].

The electrochemical tests of LVP/C composites were carried out incoin-type cells. The working electrodes were prepared by mixing80 wt.% LVP/C composites, 10 wt.% acetylene black and 10 wt.% poly(vinylidene fluoride) in N-methyl pyrrolidone to ensure homogene-ity, and then followed by coating the slurry onto Cu foil currentcollector and drying at 70 °C. The electrolyte was a solution of 1 MLiPF6 dissolved in EC/DMC (1:1 w/w), and lithium metal was chosenas the counter electrode. The coin-cells (CR2032 size) were fabricatedin an argon-filled glove box (MBraun Labmaster 130) with a porouspolypropylene membrane (Celgard 2400) as the separator. The cellswere tested on a multi-channel battery test system (NEWARE BTS-610) with galvanostatic charge and discharge in the voltage range of3.0–0.0 V at a constant current of 0.1 mA. The cyclic voltammetry (CV,scan rate: 0.05, 0.1 and 0.2 mV s−1) and electrochemical impedancespectroscopy (EIS, frequency range: 0.001–105Hz) at differentcharge–discharge states were performed on a CHI 604B electrochem-ical workstation. In order to realize an equilibrium state, all cells forEIS were kept at open circuit condition for 30 min before measure-ment. The galvanostatic intermittent titration technique (GITT)measurement was programmed to supply a constant current flux of0.1 mA for 10 min followed by an open circuit stand for 40 min. Thesequence was continued for the composition (x in Li3+xV2(PO4)3 orvoltage) of interest.

3. Results and discussion

The X-ray diffraction (XRD), scanning electron microscope (SEM)and high-resolution transmission electron microscope (HRTEM)results have been discussed in our previous work [9].

Galvanostatic charge–discharge curves of the LVP anode at aconstant current density of 0.013 mA cm−2 between 3.0 and 0.0 Vduring the 1st and 2nd cycles are shown in Fig. 1. From inset of Fig. 1,as described in the Introduction part, in the first discharge process(Li+ insertion), four plateaus located at around 1.95, 1.86, 1.74 and1.66 V correspond to a sequence of phase transition processes.Subsequently, a solid solution behavior (i.e. single-phase region) isdisplayed as indicated by a smoothly sloped curve down to 0.0 Vwith a capacity of about 310 mAh g−1. Then, the Li+ extraction is areversible process. In addition, a large irreversible capacity originatedfrom the single-phase region can be observed on the initial cycle,which is mainly attributed to the formation of the solid electrolyteinterphase (SEI) film [18,19]. On the subsequent cycles, there is about2 Li+ insertion/extraction (Li5V2(PO4)3↔Li7V2(PO4)3) in the single-phase region associated with the V2+/V+ redox couple.

The cyclic voltammetry (CV) is widely used to study the oxidation/reduction characteristics in electrochemical reactions and to obtainthe apparent chemical diffusion coefficient of lithium ions. Fig. 2shows CV curves of the LVP anode during the third cycle at different

scan rates of 0.05, 0.1 and 0.2 mV s−1 between 3.0 and 0.0 V. At a slowscan rate of 0.05 mV s−1, it can be clearly seen that, on the Li+

insertion, there are four cathodic peaks at around 1.91 V (C1), 1.83 V(C2), 1.70 V (C3) and 1.62 V (C4) as well as a sloping curve down to0.0 V, which are indicative of the coexistence of two intercalatedphases and a solid solution behavior. On the Li+ extraction, thesloping curve is up to about 1.6 V and three anodic peaks are located ataround 1.82 V (A1), 1.94 V (A2) and 2.04 V (A3). The cyclic voltam-metry peaks coincide well with the voltage plateaus in the galvano-static charge–discharge curves (Fig. 1). The anodic peak A1corresponds to two discharge plateaus around 1.70 and 1.77 V inFig. 1. In CV scan, the heights of the anodic and cathodic peaks increasewith increasing of the potential sweep rate. It is because of the peakarea divided by the scan rate yields the capacity of the electrodewhichis a constant. Noting that, at a high scan rate (N0.2 mV s−1), the redoxpeaks have a trend of combination and become difficult to distinguish,thus, we only conducted the CV curves at three low scan rates. Asshown in Fig. 3, each redox peak current (ip) shows a linear rela-tionship with the square root of scan rate (ν1/2), which is expected forthe diffusion-limited intercalation/deintercalation processes of Li-ion.Herein, the classical Randles–Sevchik equation for a semi-infinitediffusion of Li+ into LVP anode can be applied. This equation is derivedfrom the similar adsorption process theory at the metal/solutioninterface [12,20] as shown below:

ip = 2:69 × 105� �

n3=2SD1 = 2Liþ C⁎Liν

1=2 ð1Þ

Fig. 3. The linear relationship of the peak current (ip) and the square root of scan rate(ν1/2).

Fig. 4. The Nyquist plots under different discharge (a) and charge (b) states for thesingle-phase region of LVP anode.

60 X.H. Rui et al. / Solid State Ionics 187 (2011) 58–63

where ip is the peak current (A), n is the charge-transfer number, S isthe contact area between LVP anode and electrolyte (here thegeometric area of electrode, 1.54 cm2, is used for simplicity), DLi+ isthe chemical diffusion coefficient (cm2s−1), CLi is the concentration oflithium ions in the LVP anode and ν is the potential scan rate (V s−1).Based on Eq. (1) and the slope values from Fig. 3, the apparentdiffusion coefficients for the peaks of C1, C2, C3, C4, A1, A2 and A3 arecalculated, which are listed in Table 1. As can be seen, the DLi+

appvalues

are all in a magnitude of 10−10 cm2s−1 and close to each other.Moreover, with a careful observation, in these two-phase regions, theDLi+app

values show a roughly increasing trend as discharge proceeds,and then a decreasing trend displayed as the charge process proceeds.

Electrochemical impedance spectroscopy (EIS) is a powerful tool toidentify the kinetics of lithium ions intercalation/deintercalation intothe electrodes [21]. The measured cell impedance is a collectiveresponse of kinetic processes occurring in the electrode. The Nyquistplots under different discharge and charge states for the single-phaseregion (between 1.6 V and 0.0 V) of LVP anode are shown in Fig. 4a andb. Each Nyquist plot is composed of two high- and medium-frequencydepressed semicircles and a Warburg region followed by a straightsloping line at low frequencies. Such a pattern in the impedance spectracan be simply explained by an equivalent circuit shown in Fig. 4c. The Rbrepresents bulk resistance of the cell, which reflects the overall ohmicresistance of electrolyte and electrodes. Rct1 and Cdl1 are the charge-transfer resistance and its related double-layer capacitance between theelectrolyte and lithium metal electrode, which correspond to thesemicircle at high frequencies. Rct1 is relatively stable with values ofabout 65Ω (discharge) and 100Ω (charge). Rct2 and Cdl2 are the charge-transfer resistance and its related double-layer capacitance between theelectrolyte and LVP electrode, corresponding to the semicircle atmedium frequencies. Rct2 changes and depends on the depth of dis-charge and charge processes (Fig. 4a and b), illustrating a general trendof increasing of Rct2 as the voltage increased. W is the Warburg impe-dance related to the diffusion of lithium ions in the LVP electrode, whichis indicated by a straight slopping line at low frequencies.

Based on the Warburg impedance and the model proposed by Hoet al. [22], the true diffusion coefficient of Li+ in LVP anode can becalculated as the following equation:

DLiþ =12

VM

SFσW

� �δEδx

� �2ð2Þ

Table 1The apparent diffusion coefficients of Li+ in LVP anode calculated from CV.

Cathodic/anodic peaks C1 C2 C3 C4 A1 A2 A3

DLi+app

/×10−10cm2s−1 1.48 2.78 2.77 2.98 4.04 3.69 2.74

where F is the Faraday constant (96 486 Cmol−1), and σW is theWarburg coefficient. The σw is obtained from the slope of Z′ vs.ω−1/2 or−Z″ vs. ω−1/2 plot (ω is the angular frequency) in the Warburg region(Fig. 5). δE/δx is the slope of the open circuit voltage vs. mobile Li+

concentration x, which is not shown here. Since δE/δx is almost zerowithout any meaning in the two-phase regions, we only investigate thetrue chemical diffusion coefficient (DLi+

true) in the single-phase region.

Based on σW and δE/δx values, the DLi+true at various open circuit voltages

can be calculated from Eq. (2). As shown in Fig. 6, the DLi+true

values fromEIS measurement are in the range of 10−10 to 10−9 cm2s−1 dependingon the voltages. On the other hand, DLi+

truevalues have a trend of

decreasing as the cell discharged down to 0.0 V and charged up to about1.6 V. It is probably because that as discharge proceeding, the availablespace for lithium ions insertion in the lithiated LVP 3D structurebecomes smaller and smaller, implying that Li+ insertion becomesextremely difficult at the end of discharge. On the other hand, at theinitial charge process, the concentration of lithium ions is the highest,thus, the Li+ extraction at initial stage is much easier.

Among the current pulse methods, the galvanostatic intermittenttitration technique (GITT) proposed by Weppner and Huggins [23]has been used as a standard method to obtain chemical diffusioncoefficients of Li+ in electrode materials. This technique is based onchronopotentiometry, where the host electrode with a known Li+

composition in thermodynamic equilibrium is subjected to lithiation

Fig. 5. The plots of the real part of impedance (Z′) as a function of the inverse squareroot of angular frequency (ω−1/2) at different voltages in the Warburg region.

Fig. 7. The GITT curves of LVP anode during the 4th cycle as a function of time in thevoltage range of 3.0–0.0.

61X.H. Rui et al. / Solid State Ionics 187 (2011) 58–63

or delithiation by applying a constant current flux (I0) for a limitedtime period τ, at the end of which the electrode material has a knownlithium content, x±Δx, depending on the direction of the current[21,24]. After the current is interrupted at τ, the cell is allowed to relaxto its new steady-state potential (Es), from which the change in thesteady-state voltage (ΔEs) over the galvanostatic titration can bedetermined. The procedure is then repeated until the compositioninterval of interest (x) is covered. Here, GITT is used to determine theDLi+true

(single-phase region) and DLi+app

(two-phase region) of LVP anodeas a function of voltage for the entire voltage range of discharge/charge cycling (3.0–0.0 V).

Fig. 7 shows the GITT curves of LVP anode during the 4th cycle as afunction of time in the voltage range of 3.0–0.0 V. During the GITTmeasurement, the cell was discharged/charged at a constant currentflux (I0=0.1 mA) for an interval of 10 min followed by an open circuitstand for 40 min to allow the cell voltage to relax to its steady-statevalue (Es). This procedure was repeated for the full voltage window,3.0–0.0 V. The applied current flux and the resulting voltage profile fora single titration at around 1.75 V during the fourth discharge processof LVP anode is shown in Fig. 8a with schematic labeling of differentparameters. The values of chemical diffusion coefficients (DLi+) in LVPanode can be determined by applying the Fick's second law ofdiffusion. After a series of assumptions and simplifications, forsufficiently small current where ΔEs for a single titration is small,the equation for DLi+ can be written as [14,21,24–26]:

DLiþ =4π

mBVM

MBS

� �2 ΔEsτ dEτ =d

ffiffiffiτ

p !2

ðτbbL2 =DLiþ Þ ð3Þ

Fig. 6. The true chemical diffusion coefficients of Li+ in the single-phase regions of LVPanode calculated from EIS.

wheremB, VM,MB and L are themass, themolar volume, themolecularweight and the thickness of the electrode material. It may be noticedthat mBVM/MB represents the volume of the electrode material. As anexample, Fig. 8b shows a straight line behavior on the variation of cellvoltage during titration vs. τ1/2. Thus, the Eq. (3) can be furthersimplified as:

DLiþ =4πτ

mBVM

MBA

� �2 ΔEsΔEτ

� �2ð4Þ

Fig. 8. (a) Scheme for a single step of a GITT experiment at around 1.75 V during thefourth discharge process of LVP anode: τ (constant current pulse time), ΔEτ (totalchange of cell voltage during constant current pulse neglecting the IR-drop) and ΔEs(change of the steady-state voltage). (b) Variation of cell voltage for the above titrationplotted against τ1/2 to show the linear fit.

Fig. 9. The chemical diffusion coefficients (DLi+trueand DLi+

app) of Li+ in LVP anode forwhole voltage range of 3.0–0.0 calculated from GITT.

62 X.H. Rui et al. / Solid State Ionics 187 (2011) 58–63

Here, in calculations, the molar volume (VM) is assumed to remainstable as lithium content varying in LVP anode or its possible changecan be ignored. Based on Eq. (4), the chemical diffusion coefficients ofLi+ in LVP anode calculated from GITT as a function of cell voltage areplotted in Fig. 9. It can be seen that, in the two-phase regions, log(DLi+)vs. voltage profiles display a characteristic of “W” shape with fourminima not only in the discharge process but also in the chargeprocess. These minima are consistent with the voltage plateaus ofgalvanostatic charge–discharge curve (Fig. 1) and CVpeaks in Fig. 2. Theexistence of minima in the DLi+

appis because of the phase transition for

strong attractive interactions between the intercalation species and thehostmatrix or someorder–disorder transitionduring cycling,which canbe commonly observed in the electrodematerials of LiCoO2 [27], spinel-type LiMn2O4 [24], LiFePO4 [15] and LVP cathode [17]. As shown in Fig. 9,the DLi+

appvalues for two-phase regions calculated from GITT measure-

ment are in the range of 10−11 to 10−10 cm2s−1 apart from minimaaround 2.0 V (10−12 cm2s−1) during discharge and charge processes.Here, it shouldbenoted that the chemical diffusioncoefficientmeasuredin the two-phase regionswould be a resultant average value, where Li+

diffusion can occur through the phase boundary and also within eachphase, and hence DLi+ can be treated as an apparent rather than truevalue. On the other hand, in the single-phase region, the DLi+

truevalues

are in the range of 10−11 to 10−10 cm2s−1 for the discharge process and10−10 cm2s−1 for the change process, which are comparablewith thoseobserved in EIS measurement. In addition, the change of DLi+

truevalues

with cell voltage is the same with EIS results, displaying a decreasingtrend as the discharge and charge proceeded.

Fig. 10. A comparison of chemical diffusion coefficients of Li+ in LVP anode determinedby CV, EIS and GITT.

At the end, the chemical diffusion coefficients of Li+ in LVP anodemeasured by CV, EIS and GITT are compared in Fig. 10. As can be seen,nomatter whichmethod is used, the change of the DLi+ vs. cell voltageis almost the same. In addition, the W-shaped curve from GITT is acommon characteristic of the insertion-host electrode materialswith the phase transition or order–disorder transition. Furthermore,the DLi+

appvalues for the two-phase region obtained from CV

(10−10 cm2s−1) are a little higher than those gained from GITT(10−12 to 10−10 cm2s−1), which difference may be caused by Li-iontransfer within the grain boundaries. The DLi+

truevalues for the single-

phase region obtained from EIS and GITT are in the range of 10−10

to 10−9 cm2s−1 and 10−11 to 10−10 cm2s−1, respectively, and DLi+true

(EIS) is consistently higher than that from GITT under the samevoltage. Here, it should be mentioned that, in our calculations, thesurface area (S) in contact with the electrolyte is taken as the geome-tric area of the electrode. In fact, the actual contact area between LVPanode and electrolyte will be larger than the geometric surface areadue to the penetration of electrolyte into the LVP anode, which willresult a reduction of DLi+ but the change of DLi+ with cell voltage (orlithium content, x) is still retained. On the other hand, comparing withother anode materials, DLi+ values for LVP anode in our work arehigher than those for nano-Si obtained from EIS by Ding et al. [28](10−13 to 10−12 cm2s−1), manganese oxide obtained from CV by Wuet al. [29] (10−13 cm2s−1) and LixAg0.5V2O5 (x=0, 1, 2, 3) compositefilms obtained from EIS by Huang et al. [30] (10−14 to 10−12 cm2s−1)as well as comparable with those for 62 at.% Sn–Ni alloy obtained fromEIS by Mukaibo et al. [31] (10−10 to 10−9 cm2s−1), TiO2/WOxHy

obtained from GITT by Facci et al. [32] (10−13 to 10−11 cm2s−1) andgraphite obtained from CV by Shim et al. [33] (10−11 to 10−10 cm2s−1).Therefore, Li3V2(PO4)3 can also be used as a potential anode material toachieve high rate capability.

4. Conclusions

CV, EIS and GITT have been successfully employed to determine thechemical diffusion coefficient of Li+ in LVP anode. The DLi+

appvalues

calculated from CV for four cathodic and three anodic peaks are all in therange of 10−10 cm2s−1. The EIS measurement was conducted in thesingle-phase region (1.6–0.0 V) and the calculated DLi+

truevalues are in the

range of 10−10 to 10−9 cm2s−1. GITT measurement provides a moreaccurate chemical diffusion coefficient in the whole voltage range of 3.0–0.0 V. For the single-phase region, the DLi+

truevalues from GITT during the

discharge and charge processes are in the rangeof 10−11 to 10−10 cm2s−1

and 10−10 cm2s−1, respectively, and the DLi+app

values for two-phaseregions are in the range of 10−11 to 10−10 cm2s−1 apart from minimaaround 2.0 V (10−12 cm2s−1). In addition, the change of DLi+

appvalues with

cell voltage in the two-phase regions exhibits a characteristic of “W” shapedue to the strong interactions of Li+ with surrounding ions.

Acknowledgments

This study was supported by National Science Foundation of China(grant no. 20971117 and 10979049) and Education Department ofAnhui Province (grant no. KJ2009A142). We are also grateful to theSolar Energy Operation Plan of Academia Sinica.

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