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Comparison of Li+ transport in Na1+xV3O8 and Li1+xV3O8 by 7Li NMR investigations
J. Phys. Chem. S&s Vol. 54, No. 7, pp. 85145, Printed in Great Britain.
195-3
0022-3697p3 s6.00 + 0.w 0 1993 Rrpmon Pms Ltd
COMPARISON OF Li+ TRANSPORT IN Na, +,V,O, AND Li, +nV3O8BY 7Li NMR INVESTIGATIONS G. Wmci,t$ J. Roos,t D. BRINKMANN,? M. PASQUALI§ and G. PISTDIAII TPhysik-Institut, Universitiit Zurich, 8001 Ztlrich, Switzerland &Xpartimento I.C.M.M.P.M., Universita di Roma “La Sapien&‘, Rome, Italy IlCentro di Studio per la Elettrochimica e la Chimica Fisica delle Interfasi, C.N.R.,
Via Castro Laumnziano 7, 00161 Rome, Italy (Received 17 August 1992; accepted in revisedform 19 January 1993) Abstract-‘Li NMR studies have been carried out on some vanadium bronzes of interest as cathodes in rechargeable Li cells. L&, NaV, Or , amorphous LiV,O, (both prepared at low temperature), L&NaV,Os and crystalline LiVr 0s (both prepared at high temperature) have been investigated by measuring linewidth, spin-lattice and spin-spin relaxation times. For the first three samples above, it was possible to calculate the self-diffusion coethcients (10-i’ cm2 s-l for the Na bronzes and 10e9 cm2 s-l for amorphous LiVrO,). These values are lower than those for the chemical diffusion coefficients measured by electrochemical techniques. This is explained by different contributions to the enhancement factor. Keywords: Vanadium bronzes, self-diffusion and chemical diffusion coefficients, ‘Li NMR, enhancement factor, Li+ transport.
1. INTRODUCTION
Intercalation compounds in recent years have proved to be of technological importance as cathode materials in rechargeable non-aqueous batteries. Because of its performance in secondary Li cells [I], LiV,OB has received a good deal of attention for possible use with both liquid and polymer electrolytes. In an attempt to improve the performance of cathode materials for such cells, amorphous LiV,Os (hereafter denoted as A) [2,3] and a low-temperature form of NaV,Os (noted as LT) [4] with reduced crystallinity, were recently synthesized by a simple precipitation technique. Their performance as cathodes for rechargeable Li cells is far superior to that of the analogous materials prepared at high-temperature, LiV,O,(C) and NaVsO,(HT), in terms of energy density, rate capability and cycle life. In order to gain further insight into the transport characteristics of these bronzes, we have carried out NMR measurements in order to probe the conduction mechanism at the atomic level [5]. We have studied the ‘Li NMR as a function of temperature in L&,NaV,O,(LT), %,NaV,O,(HT), LiV,Q(A) and LiV,O,(C), the last two compounds having about one Li atom per molecule, and measured the linewidth (Av), the spin-lattice and spin-spin relaxation times (T, and T2). The results reported here on these four samples show that the differences in the $ Permanent address: Institute of Physics, Academia Sinica. Reijing 100080, China.
ionic conductivities of the samples are reflected in the NMR parameters.
2. EXPERIMENTAL
2.1. Preparation of cathode materials LiV,O,(A) and NaV,O,(LT) were synthesized by a precipitation technique involving the addition of V,05 to solutions of LiOH and NaOH, respectively [2,4]. LiV,Os(C) was prepared by melting the proper amounts of Li,COX and VZO, at 680°C in air and then slowly cooling the melt, and NaV,O,(HT) was synthesized by reaction of Na*CO, and V,05 in air at 620°C for 24 h. All bronzes were found to contain a slight excess of alkali metal ions. However, the nominal stoichiometric formulas will be used here. For the measurements, samples of Li,,,NaV,O,(LT), Li,,NaV,O~(HT), NaV,O,(LT) and NaV,,O,(HT) powders were pressed into pellets for the cathodes. The button cells:
NaV,O,(LT)
or
NaV,Oa(HT)
were assembled and discharged at a low current density (0.2mAcm-*). From the calculated stoichiometries specific capacities, the nominal L&g NaV, O8(LT) and Li,,%NaV, 0s (HT) were deduced. 851
G. WANG et al.
852
The pellets of and Lksj NaV, 0, (LT) Li,,,NaV, 0, (HT) were washed with methyl formate and dried under vacuum at 100°C. Finally they were ground to fine powders. Fine powders of Lk3 NaV, 0, (IT), Li,,,NaV,OS(HT), LiV,(O*(A) and LiV,O*(C) were put in Pyrex tubes (o.d. 8 mm) in a nitrogen-filled glove box. The Pyrex tubes were then sealed under vacuum. 2.2. NA4R measurements The ‘Li NMR measurements were performed using a standard pulse spectrometer and a magnetic field of 2.11 T corresponding to a Larmor frequency of 34.977 MHz. The Free-Induction Decay (FID) and spin-echo signals were digitized by transient recorders, accumulated and then Fourier transformed by on-line computers. The Fourier transform, in the polar coordinate representation, of the FID, yields a magnitude spectrum with a linewidth Av, defined as the Full Width at Half Height (FWHH). The spin-lattice relaxation time T, data were obatined from the FID signal using the saturation method in which a n/2 pulse follows a comb of saturating a/2 pulses. The spin-spin relaxation time, T2, was deduced from the single-exponential decay as a function of delay time of the spin-echo signal. The temperatures were controlled to within +O.S K. 3. RESULTS AND DISCUSSION The ‘Li NMR spectra of the four samples were recorded as a function of temperature. At all tem-
peratures only a single resonance line was obtained, although a quadrupolar interaction of the Li nuclei with electric field gradients is expected which would result in a splitting of the NMR signal into a central line and satellite lines. However, it is a common feature of powder spectra that the splitting is “smeared” in the presence of structural disorder due to defects and strain, for example, thus leaving a central signal only. As in other vanadium bronzes containing Li [9], the quadrupolar interaction is rather weak and the linewidth is probably determined by magnetic interactions. Figures 1 and 2 show the temperature dependence of the ‘Li linewidth in the four samples. It can be seen that in each case considerable line narrowing takes place in tM temperature range examined, indicating diffusional motion of Li+ ions. Since the details of the mechanism causing line narrowing are not known, the temperature variation of the linewidth is analyzed in terms of the modified Bloembergen-Purcell-Pound (BPP) expression [6,7]
where l/r is the mean jump frequency of the diffusing ion and Av, is the residual linewidth at high temperatures due to mechanisms not affected by the line narrowing process. In our case, Av, is mainly determined by the magnetic field inhomogeneity caused by the slightly magnetic high-temperature probe insert.
TEMPERATURE[K] Fig. 1. Temperature dependence of the ‘Li NMR linewidth in LiV,O,(A) and LiV,O,(C).
Li+ transportin Na,+xVJ4 and Li,+,V,O, 16-
100
200
300
400
, 0
so0
Fig. 2. Temperature dependence of the ‘L.iNMR linewidth in L.& NaV, O,(L.T)and Li,,,NaV,Og (HT).
Avru is the rigid lattice linewidth, i.e. the linewidth at low temperatures. We also suppose that l/t obeys the Arrhenius law: l/r = (llrll)exP(~J~~), where l/r, is the prefactor or the attempt frequency. Then the activation energy E, can be obtained by using Av,, Av,, and different l/r, to fit the experimental points. In the above model, the diffusion coe&ient D+ is given by D + = r’/2 dr,
(2)
where r is the jump distance and d is the dimensionality of the system. In order to determined D*, we assume in our case that d = 2 and r = 3.5 A. Table 1 gives the activation energy E., the prefactor l/r, and the self-diffusion coefficient D* of Li+ ions in L&,6SNaV,0, (LT), L&,NaV, o&IT) and in LiV,O*(A). The prefactors are very low as found quite often in solid electrolytes [5J, however, we will not dwell on the possible reasons in this case. From the motional narrowing in Fig. 2, it can be seen that D * in Li,,NaV,08(LT) is a little larger
Table 1. !Somccbact&tk Sample L&UNaV, 4 (I-T) ~;l$59p(~)O80 I *
AMkHx) 13.8 14.3 17.0
than that in L&SNaV,O&IT), as conlhmed in Table 1. The values for the two Na bronxes are lower than that obtained for the amorphous Li bronze. Furthermore, they are three orders of magnitude lower than the chemical diffusion coefllcients, 6, obtained earlier by one of us (G.P.) with the longpulse galvanostatic technique [8] (Fig. 3) and with impedance measurements [4]. As shown in Fig. 3, b for L& NaV, Os(LT) and L&,NaV, 0, (HT) are higher than those of LiV,Os(A or C). Remarkable difference between the self-diffusion and chemical diffusion coefRcients have been previously reported. For instance, for y-LiV,05 [9] and LI,NiPS, [lo], D* values were found to be four orders of magnitude lower than the corresponding b values. It has been suggested that this discrepancy may result mainly from underestimation of the surface area in the calculation of B (111. However, at least in our case, this cannot be the sole reason. Also, with the long pulse galvanostatic technique, the surface area does not enter into the calculation of 6, since only the sample thickness needs to be known. Furthermore, NaV,O#IT) and LiV,O,(A) have a similar surface area (2-3 m2 g-i), but D* for the latter is two orders of magnitude higher (Table l), while B is somewhat lower [12] (Fig. 3).
parametu~ of Li and Na bronzes.
Av,OrHx) l/x,,(Hx) 4.2 4.6 x 10” 3.0 1.7
2.9 x l@ 3.7 lo’
%(ev) 0.09
D%mzs-‘, 300 R) 5.0 x IO-”
0.11 0.16
1.6 x lo-” 1.5 lo-’
WANG
et al. K, may simply be calculated, in this case, from the slope of the coulometric titration curve E/y through the relation: K_dhtai
yF
AE
‘--ii&Inc,TRT’&
v
cl
0.5 i x(Li/mol)
Fig. 3. Chemical Fusion coeflkients fi in NaV,O,(LT), NaV,O*(HT), LiV,Os(A) and LiV,O,(C).
Thus, the difference between fi and D * can only be reconciled by taking into account the enhancement (or Darken) factor k;: fi = K,D*.
(3)
As discussed by Weppner and Huggins [13], the enhancement factor can take quite different values depending on the number of ionic and electronic diffusing species and on their relative contribution to the transport process. A very common case is the one in which only One ionic and one electronic species are mobile. This corresponds to the present situation, where only Li+ and electrons move in the samples.? In this case, the enhancement factor may be written as:
-+-,
1
dIna, d In ci
wheret,=lti(re and ii being the transport numbers of the electron and the ion, respectively), 4 and ci are the activity and concentration of Li+, and a, is the activity of the electron. If the material intercalated by Li+ is a good electronic conductor, t,+l and
K
_dlnai ’ - d In c,
so that
(5)
t This is true also for the Na bronzes. Indeed, the Na+ ions residing in the octahedral sites of the unit cells, i.e. those correspondii to the nominal stoichiometry NaV,O,, are not mobile. A skcht Na+ excess (O.O2Na+ mol-9 has been determined in GaV,Os(LT) [S].‘These ions resize in tetrahedral sites and are mobile. However, for y ~0.6 in Li,,Na,,mV,O,,, their contribution to the transport process is obviously negligible.
Equation (5) has proved valid in a number of cases and we have ascertained that it holds true for LiV,O,(C). For this material, a K, of _ 15 has been determined [14]. If this value is also used for LiV,08(A) (which is justified by their very similar E/y curves) one obtains a a of 2.4 x 10-8cm2 s-r, in excellent agreement with the value reported in Fig. 3. On the other hand, for the two Na bronzes, if K, derived from eqn (5) is used (N 35 for y = 0.6) [8], one can only partially account for the difference between D* and a. It seems that in this case, the more general eqn (4), which allows for a non-negligible contribution of the electron to the transport process, must be used. The change in a, with the change in ci may give rise to a high value for the second term in square brackets in eqn (4). For Nata2V,08(LT), it has been ascertained that the overall resistance has a large contribution from the electronic mobility [4]. This seems to substantiate the need to use K, from eqn (4) in eqn (3). We could not obtain E,,, l/r, and D* for LiV,08(C) because of its complicated line narrowing (Fig. 1). There are two plateaus, perhaps indicating some restriction to translation [15]. However, it is very clear from Fig. 1 that the conduction of Li+ in LiV,O,(A) is faster than in LiV,O,(C), in agreement with the fi measured by the long-pulse galvanostatic technique (Fig. 3). The reason for this is that the pathways for Li” diffusion are shorter in LiV,O,(A) because only short-range crystalline order exists [4]. Finally, we comment on the ‘Li relaxation time measurements. In the temperature range studied, neither T, nor T2 exhibits a strong temperature dependence. For LiV,O,(A) and LiV308(C) the T, values are about 40 and 200 ms, respectively, while the T2 values are about 3 ms for both. One would expect the Li diffusion process to give rise to a strong temperature dependence of T, . In the absence of such a dependence, we presume that the underlying mechanism must be. different from the ion diffusion which causes line narrowing. The relaxation time measured probably arises from a dipolar interaction with the conduction electrons. Indeed, a simple estimate of a BPP-type T, which one would expect from diffusion, using the parameters of Table 1 for LiV,Os(A), yields a T, minimum
Li+ transport in Na, +xV,Q and Li,+,V,Os occurring around !JOO K, which is outside the temperature range studied. Assuming a fluctuating quadrupolar interaction field of the order of I5 kHz (which is comparable to the static amplitude found in [9], we obtain a T1 value of 500 ms, which is 10 times larger than the value measured.
4. CONCLUSION The cathode materials L&.63NaV308(LT), L&NaV, 0, (HT), LiV, 0, (A) and LiV, 0, (C) have been studied by ‘Li NMR, and the Li+ self-diffusion coefficients have heen estimated. The diffusion coefficients evaluated for the first three samples are lowe; than the chemical diffusional coefficients deterelectrochemical techniques. mined by For LiV,O,(A), the order-of-magnitude difference may be accounted for by an enhancement factor determined only by the transport characteristics of the Li+ ion. For the two Na bronzes, the three orders of magnitude difference can he reconciled if the contribution of the electrons to the transport resistance is recognized. of us (G. W.) is grateful to the “Schweizerischer Nationalfonds” for financial support.
Acknowledgement-One
855 REFEBENCES
Panero S., Paaquali M. and Pistoia G., J. elcclrochem. Sot. 13@,1226 (1983). 2. Pistoia G., Pasquali hi., Wang 0. and Li L.. J. Ekctrockm. Sot. 137,2365 (1990). 3. Pktoia G. and Pasquali M., prosnsS in Butteries& solar Cellv s, 143 (1989). 4. Pasquali M. and Pistoia G., EIectrochim. Actu 36, 1549 (1991). 5. BrinkmannD., Magnetic Resonance Rev. 14 lOl(l989). 6. Bloembergm N., Puree11E. M. and Pound R. V., Phys. Rev. 73, 679 (1948). 7. Abqam A., Principles of Nuclear Magnetic Resonance. Clarendon Press, Oxford (1961). 8. Pistoia G., Marassi R., Berrettoni M. and To&i R., lo be published. 9. (a) Cocciantelli J. M.. Sub K. S.. Sene8as J., Doumerc J. P., Soubeyroux J. L., Pouchard M. and Hagcnmulkr P., J. Phys. Ckem. Sol&b 9 51 (1992); (b) Coceiantelli J. M., Sub K. S., Sene8as J., Doumerc J. P. and Pouchard M., J. Phys. C/tern. Solid9 53, (1992) 57. 10. Berthier C., Cbabre Y., Minkr M. and Ouvrard G., Solid State Comm. 28, 327 (1978). 11. Matsumoto K., Na8ai R., Asai T. and Kawai S.. Solid 1.
Saute Ionics 25, 233 (1987).
12. Pistoia G.. Marassi R., Berrettoni M. and Tossici R., Solid State IO&S, in press. 13. Weppner W. and Huggins R. A., J. electrockm. Sot. 1% 1569 (1977). 14. Pistoia G., Divona M. L. and Tagliatesta P., Solid State Iottics 24, 103 (1987).
15. Whittingham M. S., in Fast Ion Transport in Soli& (Edited by W. Van Gool), p. 429. North-Holland/ American Elsevier, Amsterdam (1973).
195-3
0022-3697p3 s6.00 + 0.w 0 1993 Rrpmon Pms Ltd
COMPARISON OF Li+ TRANSPORT IN Na, +,V,O, AND Li, +nV3O8BY 7Li NMR INVESTIGATIONS G. Wmci,t$ J. Roos,t D. BRINKMANN,? M. PASQUALI§ and G. PISTDIAII TPhysik-Institut, Universitiit Zurich, 8001 Ztlrich, Switzerland &Xpartimento I.C.M.M.P.M., Universita di Roma “La Sapien&‘, Rome, Italy IlCentro di Studio per la Elettrochimica e la Chimica Fisica delle Interfasi, C.N.R.,
Via Castro Laumnziano 7, 00161 Rome, Italy (Received 17 August 1992; accepted in revisedform 19 January 1993) Abstract-‘Li NMR studies have been carried out on some vanadium bronzes of interest as cathodes in rechargeable Li cells. L&, NaV, Or , amorphous LiV,O, (both prepared at low temperature), L&NaV,Os and crystalline LiVr 0s (both prepared at high temperature) have been investigated by measuring linewidth, spin-lattice and spin-spin relaxation times. For the first three samples above, it was possible to calculate the self-diffusion coethcients (10-i’ cm2 s-l for the Na bronzes and 10e9 cm2 s-l for amorphous LiVrO,). These values are lower than those for the chemical diffusion coefficients measured by electrochemical techniques. This is explained by different contributions to the enhancement factor. Keywords: Vanadium bronzes, self-diffusion and chemical diffusion coefficients, ‘Li NMR, enhancement factor, Li+ transport.
1. INTRODUCTION
Intercalation compounds in recent years have proved to be of technological importance as cathode materials in rechargeable non-aqueous batteries. Because of its performance in secondary Li cells [I], LiV,OB has received a good deal of attention for possible use with both liquid and polymer electrolytes. In an attempt to improve the performance of cathode materials for such cells, amorphous LiV,Os (hereafter denoted as A) [2,3] and a low-temperature form of NaV,Os (noted as LT) [4] with reduced crystallinity, were recently synthesized by a simple precipitation technique. Their performance as cathodes for rechargeable Li cells is far superior to that of the analogous materials prepared at high-temperature, LiV,O,(C) and NaVsO,(HT), in terms of energy density, rate capability and cycle life. In order to gain further insight into the transport characteristics of these bronzes, we have carried out NMR measurements in order to probe the conduction mechanism at the atomic level [5]. We have studied the ‘Li NMR as a function of temperature in L&,NaV,O,(LT), %,NaV,O,(HT), LiV,Q(A) and LiV,O,(C), the last two compounds having about one Li atom per molecule, and measured the linewidth (Av), the spin-lattice and spin-spin relaxation times (T, and T2). The results reported here on these four samples show that the differences in the $ Permanent address: Institute of Physics, Academia Sinica. Reijing 100080, China.
ionic conductivities of the samples are reflected in the NMR parameters.
2. EXPERIMENTAL
2.1. Preparation of cathode materials LiV,O,(A) and NaV,O,(LT) were synthesized by a precipitation technique involving the addition of V,05 to solutions of LiOH and NaOH, respectively [2,4]. LiV,Os(C) was prepared by melting the proper amounts of Li,COX and VZO, at 680°C in air and then slowly cooling the melt, and NaV,O,(HT) was synthesized by reaction of Na*CO, and V,05 in air at 620°C for 24 h. All bronzes were found to contain a slight excess of alkali metal ions. However, the nominal stoichiometric formulas will be used here. For the measurements, samples of Li,,,NaV,O,(LT), Li,,NaV,O~(HT), NaV,O,(LT) and NaV,,O,(HT) powders were pressed into pellets for the cathodes. The button cells:
NaV,O,(LT)
or
NaV,Oa(HT)
were assembled and discharged at a low current density (0.2mAcm-*). From the calculated stoichiometries specific capacities, the nominal L&g NaV, O8(LT) and Li,,%NaV, 0s (HT) were deduced. 851
G. WANG et al.
852
The pellets of and Lksj NaV, 0, (LT) Li,,,NaV, 0, (HT) were washed with methyl formate and dried under vacuum at 100°C. Finally they were ground to fine powders. Fine powders of Lk3 NaV, 0, (IT), Li,,,NaV,OS(HT), LiV,(O*(A) and LiV,O*(C) were put in Pyrex tubes (o.d. 8 mm) in a nitrogen-filled glove box. The Pyrex tubes were then sealed under vacuum. 2.2. NA4R measurements The ‘Li NMR measurements were performed using a standard pulse spectrometer and a magnetic field of 2.11 T corresponding to a Larmor frequency of 34.977 MHz. The Free-Induction Decay (FID) and spin-echo signals were digitized by transient recorders, accumulated and then Fourier transformed by on-line computers. The Fourier transform, in the polar coordinate representation, of the FID, yields a magnitude spectrum with a linewidth Av, defined as the Full Width at Half Height (FWHH). The spin-lattice relaxation time T, data were obatined from the FID signal using the saturation method in which a n/2 pulse follows a comb of saturating a/2 pulses. The spin-spin relaxation time, T2, was deduced from the single-exponential decay as a function of delay time of the spin-echo signal. The temperatures were controlled to within +O.S K. 3. RESULTS AND DISCUSSION The ‘Li NMR spectra of the four samples were recorded as a function of temperature. At all tem-
peratures only a single resonance line was obtained, although a quadrupolar interaction of the Li nuclei with electric field gradients is expected which would result in a splitting of the NMR signal into a central line and satellite lines. However, it is a common feature of powder spectra that the splitting is “smeared” in the presence of structural disorder due to defects and strain, for example, thus leaving a central signal only. As in other vanadium bronzes containing Li [9], the quadrupolar interaction is rather weak and the linewidth is probably determined by magnetic interactions. Figures 1 and 2 show the temperature dependence of the ‘Li linewidth in the four samples. It can be seen that in each case considerable line narrowing takes place in tM temperature range examined, indicating diffusional motion of Li+ ions. Since the details of the mechanism causing line narrowing are not known, the temperature variation of the linewidth is analyzed in terms of the modified Bloembergen-Purcell-Pound (BPP) expression [6,7]
where l/r is the mean jump frequency of the diffusing ion and Av, is the residual linewidth at high temperatures due to mechanisms not affected by the line narrowing process. In our case, Av, is mainly determined by the magnetic field inhomogeneity caused by the slightly magnetic high-temperature probe insert.
TEMPERATURE[K] Fig. 1. Temperature dependence of the ‘Li NMR linewidth in LiV,O,(A) and LiV,O,(C).
Li+ transportin Na,+xVJ4 and Li,+,V,O, 16-
100
200
300
400
, 0
so0
Fig. 2. Temperature dependence of the ‘L.iNMR linewidth in L.& NaV, O,(L.T)and Li,,,NaV,Og (HT).
Avru is the rigid lattice linewidth, i.e. the linewidth at low temperatures. We also suppose that l/t obeys the Arrhenius law: l/r = (llrll)exP(~J~~), where l/r, is the prefactor or the attempt frequency. Then the activation energy E, can be obtained by using Av,, Av,, and different l/r, to fit the experimental points. In the above model, the diffusion coe&ient D+ is given by D + = r’/2 dr,
(2)
where r is the jump distance and d is the dimensionality of the system. In order to determined D*, we assume in our case that d = 2 and r = 3.5 A. Table 1 gives the activation energy E., the prefactor l/r, and the self-diffusion coefficient D* of Li+ ions in L&,6SNaV,0, (LT), L&,NaV, o&IT) and in LiV,O*(A). The prefactors are very low as found quite often in solid electrolytes [5J, however, we will not dwell on the possible reasons in this case. From the motional narrowing in Fig. 2, it can be seen that D * in Li,,NaV,08(LT) is a little larger
Table 1. !Somccbact&tk Sample L&UNaV, 4 (I-T) ~;l$59p(~)O80 I *
AMkHx) 13.8 14.3 17.0
than that in L&SNaV,O&IT), as conlhmed in Table 1. The values for the two Na bronxes are lower than that obtained for the amorphous Li bronze. Furthermore, they are three orders of magnitude lower than the chemical diffusion coefllcients, 6, obtained earlier by one of us (G.P.) with the longpulse galvanostatic technique [8] (Fig. 3) and with impedance measurements [4]. As shown in Fig. 3, b for L& NaV, Os(LT) and L&,NaV, 0, (HT) are higher than those of LiV,Os(A or C). Remarkable difference between the self-diffusion and chemical diffusion coefRcients have been previously reported. For instance, for y-LiV,05 [9] and LI,NiPS, [lo], D* values were found to be four orders of magnitude lower than the corresponding b values. It has been suggested that this discrepancy may result mainly from underestimation of the surface area in the calculation of B (111. However, at least in our case, this cannot be the sole reason. Also, with the long pulse galvanostatic technique, the surface area does not enter into the calculation of 6, since only the sample thickness needs to be known. Furthermore, NaV,O#IT) and LiV,O,(A) have a similar surface area (2-3 m2 g-i), but D* for the latter is two orders of magnitude higher (Table l), while B is somewhat lower [12] (Fig. 3).
parametu~ of Li and Na bronzes.
Av,OrHx) l/x,,(Hx) 4.2 4.6 x 10” 3.0 1.7
2.9 x l@ 3.7 lo’
%(ev) 0.09
D%mzs-‘, 300 R) 5.0 x IO-”
0.11 0.16
1.6 x lo-” 1.5 lo-’
WANG
et al. K, may simply be calculated, in this case, from the slope of the coulometric titration curve E/y through the relation: K_dhtai
yF
AE
‘--ii&Inc,TRT’&
v
cl
0.5 i x(Li/mol)
Fig. 3. Chemical Fusion coeflkients fi in NaV,O,(LT), NaV,O*(HT), LiV,Os(A) and LiV,O,(C).
Thus, the difference between fi and D * can only be reconciled by taking into account the enhancement (or Darken) factor k;: fi = K,D*.
(3)
As discussed by Weppner and Huggins [13], the enhancement factor can take quite different values depending on the number of ionic and electronic diffusing species and on their relative contribution to the transport process. A very common case is the one in which only One ionic and one electronic species are mobile. This corresponds to the present situation, where only Li+ and electrons move in the samples.? In this case, the enhancement factor may be written as:
-+-,
1
dIna, d In ci
wheret,=lti(re and ii being the transport numbers of the electron and the ion, respectively), 4 and ci are the activity and concentration of Li+, and a, is the activity of the electron. If the material intercalated by Li+ is a good electronic conductor, t,+l and
K
_dlnai ’ - d In c,
so that
(5)
t This is true also for the Na bronzes. Indeed, the Na+ ions residing in the octahedral sites of the unit cells, i.e. those correspondii to the nominal stoichiometry NaV,O,, are not mobile. A skcht Na+ excess (O.O2Na+ mol-9 has been determined in GaV,Os(LT) [S].‘These ions resize in tetrahedral sites and are mobile. However, for y ~0.6 in Li,,Na,,mV,O,,, their contribution to the transport process is obviously negligible.
Equation (5) has proved valid in a number of cases and we have ascertained that it holds true for LiV,O,(C). For this material, a K, of _ 15 has been determined [14]. If this value is also used for LiV,08(A) (which is justified by their very similar E/y curves) one obtains a a of 2.4 x 10-8cm2 s-r, in excellent agreement with the value reported in Fig. 3. On the other hand, for the two Na bronzes, if K, derived from eqn (5) is used (N 35 for y = 0.6) [8], one can only partially account for the difference between D* and a. It seems that in this case, the more general eqn (4), which allows for a non-negligible contribution of the electron to the transport process, must be used. The change in a, with the change in ci may give rise to a high value for the second term in square brackets in eqn (4). For Nata2V,08(LT), it has been ascertained that the overall resistance has a large contribution from the electronic mobility [4]. This seems to substantiate the need to use K, from eqn (4) in eqn (3). We could not obtain E,,, l/r, and D* for LiV,08(C) because of its complicated line narrowing (Fig. 1). There are two plateaus, perhaps indicating some restriction to translation [15]. However, it is very clear from Fig. 1 that the conduction of Li+ in LiV,O,(A) is faster than in LiV,O,(C), in agreement with the fi measured by the long-pulse galvanostatic technique (Fig. 3). The reason for this is that the pathways for Li” diffusion are shorter in LiV,O,(A) because only short-range crystalline order exists [4]. Finally, we comment on the ‘Li relaxation time measurements. In the temperature range studied, neither T, nor T2 exhibits a strong temperature dependence. For LiV,O,(A) and LiV308(C) the T, values are about 40 and 200 ms, respectively, while the T2 values are about 3 ms for both. One would expect the Li diffusion process to give rise to a strong temperature dependence of T, . In the absence of such a dependence, we presume that the underlying mechanism must be. different from the ion diffusion which causes line narrowing. The relaxation time measured probably arises from a dipolar interaction with the conduction electrons. Indeed, a simple estimate of a BPP-type T, which one would expect from diffusion, using the parameters of Table 1 for LiV,Os(A), yields a T, minimum
Li+ transport in Na, +xV,Q and Li,+,V,Os occurring around !JOO K, which is outside the temperature range studied. Assuming a fluctuating quadrupolar interaction field of the order of I5 kHz (which is comparable to the static amplitude found in [9], we obtain a T1 value of 500 ms, which is 10 times larger than the value measured.
4. CONCLUSION The cathode materials L&.63NaV308(LT), L&NaV, 0, (HT), LiV, 0, (A) and LiV, 0, (C) have been studied by ‘Li NMR, and the Li+ self-diffusion coefficients have heen estimated. The diffusion coefficients evaluated for the first three samples are lowe; than the chemical diffusional coefficients deterelectrochemical techniques. mined by For LiV,O,(A), the order-of-magnitude difference may be accounted for by an enhancement factor determined only by the transport characteristics of the Li+ ion. For the two Na bronzes, the three orders of magnitude difference can he reconciled if the contribution of the electrons to the transport resistance is recognized. of us (G. W.) is grateful to the “Schweizerischer Nationalfonds” for financial support.
Acknowledgement-One
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