Electrochemical determination of the lithium ion diffusion coefficient in TiS2

Solid State Ionics 2 (1981) 337-340 North-Holland Publishing Company

ELECTROCHEMICAL DETERMINATION O F THE LITHIUM ION D I F F U S I O N C O E F F I C I E N T IN TiS 2 Anthony J. VACCARO Department of Chemistry, West Virginia University, Morgantown, WV 26506, USA T. PALANISAMY University of Dayton Research Institute, Dayton, 0H45469, USA

R.L. K E R R AFWAL/POOC-1, Wright-PattersonAFB, 0H45433, USA and J.T. MALOY * Department of Chemistry, Seton Hall University, South Orange,NJ07079, USA Received 17 September 1980 Long-time chronoamperometry of TiS2 electrodes immersed in saturated LiCIO4/DMF solution was employed to investigate the charge transport processes which govern the rate of Li+ intercalation in TiS2. The intercalation rate and hence, the current, appears to be controlled by the rate of Li+ diffusion within the TiS2. A model has been developed which predicts the current-time behavior under the control of Li+ solid state diffusion. The close agreement of this model with the experimental data allows the solid state diffusion coefficient and other transport parameters (such as effective electrode area) to be evaluated from the measured average grain boundary distance. Typical TiS2 grain boundary distances in the 3-10 #m range yield a geometric mean value of 1.3 × 10-9 cm2/s for the solid state diffusion coefficient; this is in close agreement with previously reported diffusivities as measured by NMR spin-lattice relaxation techniques.

1. Introduction The Li + intercalation reaction o f TiS 2 has received considerable attention because o f its application in secondary non-aqueous lithium battery development. The chemical diffusivity o f Li ÷ within the van der Waals gaps of TiS 2 limits the rate characteristics o f the positive electrode. Only a limited amount of data is available on the Li + diffusion in TiS 2 . Whittingham [1,2] and Basu and Worrell [3] have determined the Li ÷ diffusion coefficient within TiS 2 b y electrochemical techniques (chronoamperometry and chronopotentiometry, respectively); Silbernagel [4] has made this determination through NMR s p i n - l a t t i c e relaxation time * To whom correspondence should be addressed.

measurements. Either of the aforementioned electrochemical techniques requires the estimation of an effective electrode area; variation of surface structure during electrochemical intercalation, even at a singlecrystal electrode, m a y cause some uncertainty in this estimation and the resulting diffusion coefficient [3]. Because the chronoamperometric method requires the estimation of a charge carrier concentration within the TiS2, it has only been utilized previously on samples of LixTiS 2 o f known (and assumed invariant) stoichiometry. In this study, long-time chronoamperometry in conjunction with a recently developed theoretical model has been employed to determine the Li ÷ diffusion coefficient in TiS 2; this method eliminates the necessity of estimating an effective electrode area or an ionic charge

338

A.J. Vaccaro et al. / The diffusion coefficient of Li ~ in TiS2

carrier concentration within the TiS 2. This theoretical model predicts the current-time behavior of a TiS 2 electrode under the control of Li + diffusion within the TiS 2 [5,61. According to this model

i(t ) = nFAD1/2(Cs - Cb) ~ ( - 1 ) k exp(-k212/Dt), 7rl/2tl/2 k=-.~

(l) where C s is the concentration of Li+ within the TiS 2 at the solution interface (which is maintained constant at the applied potential) and Cb is the initial bulk Li+ concentration within the TiS 2; l represents the average grain boundary distance (the "average particle diameter") as determined by SEM studies. This model predicts that during the early stages of the electrolysis, Cottrell behavior will be obtained:

i(t) = nFAOl/2(Cs - Cb)/~rl/2tl[2.

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(2)

That is, a log i versus log t plot will have a slope of - 3 until D t = 0.25 l2. At that time a negative deviation from Cottrell behavior is predicted. The time corresponding to 12/D can be determined by fitting this theoretical log i versus log t curve to the data from a long-time chronoamperoL~etric experiment. By using this time, the Li + diffusion coefficient can be determined on the basis of the SEM estimate of the grain boundary distance. The diffusion coefficient obtained in this manner may then be used to determine A (C s - Cb) for the solid electrode material.

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Fig. 1. The electrochemical cell.

3. Results and discussion 2. Experiment~ The electrochemical cell used for this study is shown in fig. 1. The cell consisted of 0.025 cm 2 TiS 2 working electrode, a mercury pool counter electrode, and a saturated calomel (SCE) reference electrode. The TiS 2 was packed into the glass compartment of the working electrode; contact was made by a platinum button sealed at the top of the glass compartment. The TiS 2 was held in place against a porous separator and a coarse fritted glass disk. The reference electrode contacted the Solution through an agar salt bridge at the tip; two fritted glass disks were incorporated into the cell to minimize the diffusion of water or KC1 from the SCE electrode to the TiS 2 electrode. Reagents, apparatus, and procedure have been discussed previously [6].

The results of several long-time chronoamperometric experiments at a well conditioned TiS 2 electrode immersed in a saturated LiCIO4/DMF solution at different discharge potentials are shown in fig. 2; the theoretical log i versus log t plot for eq. (1) (solid line) was fit to each discharge curve independently. During the intermediate stages of the electrolysis (15 < t < 100 s), Cottrell behavior was obtained at each potential; at longer times, however, negative deviation from CottreU behavior occurred as predicted. The time corresponding to 12/D as a result of this fit and the average TiS 2 grain size were used to calculate the Li+ diffusion coefficient. Fig. 3 shows a typical SEM photograph of the TiS 2 material used in this study. Because of the variation in the size and the macrostructure of the particles, estl-

339

A.J. Vacearo et al. / The diffusion coefficient o f Li +in 77S2 O? 5 0

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Fig. 2. Long-time chronoamperometry at several discharge potentials. The experimental data (points) were fit independently with the theoretical model (solid line) at each potential. mating an average grain size was difficult. Therefore, the Li+ diffusion coefficient was calculated in a range corresponding to 3 - 1 0 ~'a particle sizes. This range of the Li+ diffusivity in TiS 2 at ambient temperature is shown in table 1 along with the previously reported Li÷ diffusion coefficients. The range determined by this study compares favorably with the self-diffusion coefficient determined from NMR data; this suggests that the self-diffusion and the chemical diffusion of Li÷ with. in TiS 2 are similar. Previous workers [1,2,7] have employed the Darken relationship [8] in order to achieve a correlation between the chemical diffusivity and selfdiffusion in solid state diffusion studies. Because the electrointercalation reaction involves the reaction of a solvated lithium ion with the positive electrode material, it is quite possible that the diffusivity of a solvated species within the TiS 2 is measured by this (or any) electrochemical technique. Significantly different values of D are obtained when other solvents or electrolytes are employed [9]. This observation illustrates the potential utility of this technique as a means to

characterize the electrochemical transport properties of different solution/electrode combinations. The possibility of significant electrolyte penetration into the TiS 2 electrode has been suggested [3]. This penetration can increase the true electrode area and cause some uncertainty in the determination of the diffusion coefficient by the previously employed electrochemical techniques. In general, the determination of a diffusion coefficient requires the estimation of one spatial parameter; however, an estimate of an average grain boundary distance (as determined by particle size) is believed to be more reliable than the estimate of the effective area of a variable electrode surface. The time corresponding to D f l 2 was found to be independent of the discharge voltage. However, the magnitude of the predicted deviation in the current from Cottrell behavior decreased as the discharge potential became more negative. The log i versus log t curve for a discharge at - 1.0 V versus SCE exhibited only Cottrell behavior during the time of the experiment. This observation suggests that the large negative potentials can

340

A.J. Vaccaro et al. / The diffusion coefficient o f Li + in TiS2

Table 1 Summary of solid state lithium diffusion coefficients in TiS2 at laboratory ambient temperature Technique

Ref.

D (10-9 cm2/s)

chronoamperometry chronoamperometry chronopotentiometry NMR relaxation this work

[ 1] [2] [3 ] [4 ]

32 a) 10 5 1 1.3 b)

a) Geometric mean of (10-7.-10-s) cmZ/s range. b) Geometric mean of (4.0-0.4) X 10-9 cm2/s range.

The determination o f the effective electrode area allows the charge carrier concentration at the surface of the TiS 2 to be measured as a function o f electrode potential. This measurement is useful in electrode kinetics studies which will be discussed in more detail in a future communication. Fig. 3. Scanning electron micrograph of the TiS2 used in this study. overcome the Li ÷ interparticle resistance and allow Li + transport across the grain b o u n d a r y , thereby increasing the average grain boundary distance. Short-time deviations from Cottrell behavior at less negative potentials may be attributed to the predominance o f the heterogenerous rate o f charge transfer in controlling the current during the early stages o f electrolysis at low overpotentials. The current corresponding to I / n F A D ( C s - Cb) as a result o f the fit in fig. 2 and the calculated Li + diffusion coefficient can be used to calculate A ( C s - C b ) for each discharge potential. The normalized A ( C s Cb) can be used to estimate an effective electrode area. For example, using the limiting data at - 0 . 9 V versus SCE in fig. 2, one may estimate that the effective surface area o f the electrode used in this study would be 30 times the apparent electrode area if the maximum solid state lithium concentration achieved at the surface o f the TiS 2 is assumed (albeit incorrectly) to be equal to the bulk concentration of lithium ion within the solution. This factor represents the error that would have been associated with the determination o f the diffusion coefficient for this electrode system b y conventional means.

Acknowledgement This work was supported b y the Air Force Systems Command through the sponsorship o f the Air Force Office o f Scientific Research and the Air Force Wright Aeronautical Laboratories.

References [I ] M.S. WhRtingham, in: Solid electrolytes,eds. P. Hagenmullq and W. van Gool (Academic Press,N e w York, 1978) p. 367 [2] M.S. Whittingharn, Progr. Solid State Chem. 12 (1978) 41. [3] B.G. Silbernagel,Solid State Commun. 17 (1975) 361. [4] S. Basu and W.L. Worrell, in: Fast ion transport in solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (NorthHolland, Amsterdam, 1979) p. 149. [5] T. Palanisamy, R.L. Kerr and J.T. Maloy, J. Electrochem.

Soc., to be pubfished. [6] AJ. Vaccaro, T. Palanisamy, R.L. Kerr and J.T. Maloy, Proceedings of the 29th Power Sources Conference (The Electrochemical Society), to be published. [7] T.A. Ramanarayanan and P.D. Jose, J. Electtochem. Soc. 125 (1978) 1684. [8] L.S. Darken, Trans AIMS 175 (1948) 184. [9] A.J. Vaccaro, T. Palanisamy, R.L. Kerr and J.T. Maloy, J. Electrochern. Soc., submitted for publication.