NMR study of Li diffusion in β-LiAl

Solid State Communications, Vol. 53, No. 1, pp. 55-58, 1985. Printed in Great Britain

0038-1098/85 $3.00 + .00 Pergamon Press Ltd.

NMR STUDY OF Li DIFFUSION IN/3-LIA1 T. Asai, M. Hiratani and S. Kawai The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki 567, Japan

(Received 8 August 1984 by J. Kanamori) Diffusion of a Li atom in an anode material/3-LiA1 was studied over the composition range of 48.0-50.2 at % Li by the 7Li magnetic relaxation times. Dependence of 7'1 upon temperature and the resonance frequency was successfully explained by a vacancy diffusion on the Li sublattice involving a distribution of the activation energy for migration, Ea. The central value of Ea was almost independent of the composition (~-- 13.8 kJ mo1-1), while the width of distribution increased with increase of the number of substituted Li on the A1 sublattice. The obtained diffusion constants, extrapolated to 415°C, were larger by a factor of 1.8-3.4 than those obtained by the electrochemical method. AN INTERMETALLIC compound/3-LiA1 is one of candidate materials for the anode of a molten salt secondary battery. It belongs to the so-called Zintl structure [ 1]. Lithium atoms form a sublattice of the diamond arrangement, and so do A1 atoms. The two sublattices interpenetrate to form a cubic lattice in such a manner that each atom has four nearest neighbours of the like atom and four further neighbours of the unlike atom at the same distance. It is a non-stoichiometric compound and the composition changes between 48 and 55 at % Li [2]. Two types of point defect co-exist over the whole composition range. They are a vacancy on the Li sublattice, VLi, and a substituted Li atom on the AI sublattice, LiA1. Their concentration depends largely on the composition of the sample and stabilizes the structure [3]. /3-Lithium aluminium is a mixed conductor. The electronic conductivity, ae, was measured on single crystals [4, 5] as well as on powder samples [6]. It is metallic. The temperature-dependent part of ae obeys the Grtineisen formula, and is almost independent of the composition. The absolute value of Oe, however, has a large contribution from the residual resistivity, Rres, and because Rre s is mainly due to LiA1, the total ae changes sensitively with the composition [4]. On the other hand, because the ionic conductivity, oi, is much less than oe, the direct measurement of ai has not been made. Several other methods have been employed to obtain an information concerning to the ionic motion in ~-LiAI: that is, electrochemical [7] and NMR [8-11] studies to obtain a diffusion constant of a Li atom and its activation energy, and an X-ray diffraction study [12] to elucidate a diffusion path. In the present NMR study, temperatme dependence of the

7Li spin-lattice relaxation time was similar to that of the previous studies [10, 11 ], but another explanation of the data will be given. Samples were prepared in a similar way as in [13]. Their chemical composition was determined by the gravimetric analysis of A1 as oxinate. Pulverized samples, passed through a seive of 200 mesh, were taken in a glass tube of 8 mm~b, added with a mineral oil under the Ar atmosphere and sealed off. Three samples were used: their composition, x in LixA1l_x, is 0.480, 0.500 and 0.502. Relaxation times, T1, T2 and Tip, of a 7Li nucleus were measured by a pulsed NMR spectrometer Bruker 322s. Pulse sequences of 1 8 0 ° - r - 9 0 ° and 9 0 ° - r - 9 0 ° were employed for the T1 measurement, the CurrPurcell sequence for 7"2, and the spin-locking method with H1 of 0.5 mT for Tip. Resonance frequencies were 23.3 and 7.8 MHz. Results are shown in Figs. 1-3. Figure 1 shows T1, 7"2 and T~p of the sample Lio. 48oAlo.s2o. Below 400 K the V-shaped temperature dependence of T~ was observed for both resonance frequencies. Values of the 7"1 minimum are 220 and 70 ms for 23.3 and 7.8 MHz, respectively, and are in good agreement with the reported values [ 9 - I 1]. At high temperatures both Tl'S coincided. Both T2 and Tip below 300 K had the same activation energy as T1 and coincided with T1 at high temperatures. These facts are expected in the case of a relaxation of the normal BPP-type. On the other hand, the ratio of 7'1 (23.3 MHz)/ T1 (7.8 MHz)were 4.9 (at 103 KIT = 7.0)instead of 9 (= 23.32/7.82). The activation energy in this region was smaller by -~ 4 kJ mo1-1 than that in high temperatures and the V-shape is asymmetric. 55

NMR STUDY OF Li DIFFUSION IN 13-LiA1

56 10 +1

J

i

i

6

7

8

10+o

a" I-,. 10-1

10-2

10-3

2

3

4

5 103K/T

Fig. 1. Temperature dependence of T1, Tz and Tip of Lio.48oAlo.s2o. A: T1 at 23.3 MHz, A: TI at 7.8 MHz, ca: 7/2, #: Tip (H1 = 0.5 roT) and o: TI at 23.3 MHz after the heating above 400 K.

10 +1

,

,

,

Vol. 53, No. 1

It was noticed that when the sample was heated above 400 K, a thermal hysteresis was observed: after heating, T1 was longer by "" 20% in the low temperature region while it was the same in the high temperature region (Fig. 1). For x = 0.500 and 0.502, the similar behaviour of T1 was observed as shown in Figs. 2 and 3. The T1 minimum was slightly longer (270 ms). The temperature where the T1 minimum appears also shifted from 220 to 270 K with increase ofx. Tip for x = 0.500, however, showed a different behaviour than the one in Fig. 1 and has shorter values than were expected. Willhite et al. [9] reported similar deviation from T1 for Lio.sAlo.s. T~ above 440 K and T2 and T~p above 300 K for x = 0.480 decreased again with increase o f temperature. A similar indication was observed also in the other samples. Tokuhiro and Susman [10] reported similar behaviour. It suggests presence of another relaxation mechanism which may be related with the intrinsic formation of defects [10] or with the beginning of Li diffusion through a new pathway [12]. The T~ minimum for this relaxation mechanism was not observed in the present study because a reaction of ~-LiA1 with the mineral oil inhibited measurements at higher temperatures, and a further analysis was discontinued. The T1 minimum at --~ 250 K was attributed to the Li diffusion on the Li sublattice by exchanging sites with V L i [9, 11 ]. Willhite et al. [9] and Kishio et al. [11] explained the asymmetric temperature dependence of 7Li T~ by the superposition of the dipolar and the quadrupolar relaxation mechanisms. The former is a main component to the observed Tt. It is one of possible

10 +0

10

I

I

I

I

I

I

I 6

I 7

~Az~

0~0

03

I~

10 -1

0

•

I&zX/2 *

gx

10 -= ZX~X

10-3

I 2

3

4

5

6

7

8

0.1

103K/T

Fig. 2. Temperature dependence of T~ and TIp of Lio.sooAlo.soo. Symbols are the same as in Fig. 1.

L 2

I 3

I 4

I 5

8

103K/T

Fig. 3. Temperature dependence of Tl at 23.3 MHz of tio.so2Alo.498.

NMR STUDY OF Li DIFFUSION IN 3-IAAi

Vol. 53, No. 1

explanations; and the separated Ta minimum for the quad~upolar relaxation had a right order of magnitude when it is estimated with the eZqQ/hvalue of 340 kHz [8]. Some inconsistency, however, was seen among their obtained parameters, e.g., ro'S for the vacancy diffusion, and their explanation does not seem definite. Present authors agreed that T1 is determined by the dipolar relaxation through the Li diffusion, but attributed the asymmetry to a distribution of the activation energy for migration, E a. Because the intrinsic formation of defects is seen only at high temperature [10], a locally inhomogeneous distribution of Linl seems to be frozen at ordinary temperature and to result in the distribution of Ea. Heating of samples above 400 K is expected to reduce the inhomogeneity and to narrow the distribution of fla. This is qualitatively consistent with the noticeable feature of the thermal hysteresis mentioned above. With this picture the observed Tl'S were analyzed as follows. Because an ZTAl nucleus relaxes much faster than a VIA nucleus [9, 11 ], the dipolar relaxation time for 7Li is described by equations (1) and (2) [14]. T11

(3/2)7]h2I(I + 1)k[I(1)(w,) 4- I{:)(2COl)] + ~,272sh2S(S + 1)fs [(1/12)K(°)(wx -- Ws) + (3/2)K(l)(wl) + (3/4)K(2)(wt + COs)]

T~'

(1)

~ h2I(I + 1)fl [(3/8)I(°)(0) + (15/4)1 (1)(wt) + (3/8)I(2)(2wi)] + T~y~hZS(S + 1 ) f s x [(1/6)K(°)(0) + (1/24)Kt°)(wl -- Ws)

+ (3/4)K(1)(coI) + (3/2)Ktl)(Ws) + (3/8)K(2)(oox + 6Os)].

(2)

Here I is a spin quantum number of 7Li and S of 27Al, f is the natural abundance, and other symbols have the usual meaning. In the case of diffusion, the spectral densities, I (i) and K (i), are usually calculated by means of the Bessel function. In the present analysis, however, /(i)'s, and similarly K ( i ) ' s , w e r e described by the following equation for a powder sample [15] in order to simplify computation. 1 (1) = (4/15) ~r/6

1 + c 7" o2r 2'

1(2) :

41(1). (3)

Distribution of the activation energy was assumed to be Gaussian, centering around E ° and with a width of oE. In computation it was treated after the analysis of 3--Na ÷ alumina by Walstedt et al. [16]. Parameters obtained by fitting the T1 data to equations (1) and (3) are given in Table 1, and the calculated T1 and 7"2 are shown by the solid lines in Figs. 1 - 3 . As seen in Figs. 1 - 3 , the present analysis explains

57

Table 1. Motional parameters obtained by fitting T1 data to the theory E~a

OE

7o

e (LiA1)

lax All -x

kJ mo1-1

kJ mo1-1

ps

%

0.480 0.500 0.502

14.0 13.5 13.8

1.8 2.8 2.9

3.3 11 14

--~ 0* 1.6 1.9

x

in

* Values are taken from [3]. well both the assymetry and the frequency dependence of T1. Although the coefficients in equations ( 1 ) - ( 3 ) were fixed at the theoretical values, agreement of T1 minima are satisfactory. For x = 0.480, T2 and Tlo were also reproduced well with the same parameters as for T1. Small deviation at the lowest temperature may be a result from the Tlo minimum which is expected to appear at 103K/T -~ 8 - 9 . On the other hand, the calculated T2's for x = 0.500 deviated much from the observed Tip even in the region of coir c < 1. Therefore, 7"2 may have a contribution from some mechanism other than the dipolar one in contrast with T1. Table 1 shows that aE increases with the number of Lial defect. This is consistent with the present model that the LiA1 defects bring a distribution of Ea. On the other hand, E ° is almost constant in the whole range of composition, and may be regarded as an activation energy of migration in the ideal 3-IDA[ lattice. The correlation time re, which is regarded as an interval between two jumps, is usually connected with a diffusion constant, D, by equation (4).

D = (12)/6rc.

(4)

Taking x/(l 2) as a nearest neighbour distance of Li (2.76 A), the pre-exponential factor of the diffusion constant, Do, was obtained. When these values are plotted against the number of VLi [3], they show a linear dependence as shown in Fig. 4. This means that a vacancy on the Li sublattice diffuses with a constant velocity (D~ = 4.4 x 10 -4 c m 2 S-1), irrespective of its concentration. The diffusion constant of Li in 3-LiA1 was reported using an electrochemical method [7]. They are 1.0 x 10 - 6 , 4.7 x 10 -7 and 4.6 x 10 -7 cm 2 s -1 at 415°C for x = 0.480, 0.500 and 0.502, respectively. Extrapolation to 415°C o f the present data gives diffusion constants of 3.4 x 10 -6, 1.2 x 10 - 6 and 8.6 x 10 -7 c m 2 s -1 . The present extrapolated values are larger by a factor of 1.8-3.4. Agreement between two sets of data is very good when a possibility of the grain boundary effect on the electrochemical method is taken into account.

NMR STUDY OF I5 DIFFUSION IN/3-LiA1

58 50

I

I

I

2.

I

'7u)

E u O

3.

40

4.

30

m-

5.

20

/4

10 El

0

6.

I

I

[

I

2

4

6

8

10

CVLi//% Fig. 4. Pre-exponential factor of the Li diffusion constant plotted against the concentration of the I5 vacancy. In conclusion, the defect VLi concerns directly with the Li diffusion on the Li sublattice, while the substituted Li for A1 affects the activation energy of migration. The distribution of the activation energy is narrowed to some extent by thermal treatment above 400 K. The defect structure of/3-LiA1 thus plays a very important role to determine two essential properties of the electrode material, the ionic diffusion and the electronic transport [ 4 - 6 ] .

7. 8. 9. 10. 11. 12. 13. 14. 15.

1.

REFERENCES E. Zintl & G. Braun, Z. Phys. Chem. 20B, 245 (1933).

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Vol. 53, No. 1

K.M. Myles, F.C. Mrazek, J.A. Smaze-& J.L. Settle, U.S. ERDA Report ANL-76-8 (1976)." K. Kishio & J.O. Brittain, J. Phys. Chem. Solids 40, 933 (1979). T. Asai, M. Hiratani & S. Kawai, Solid State Commun. 48, 173 (1983). L.N. Hall, T.O. Brun, G.W. Crabtree, J.E. Robinson, S. Susman & T. Tokuhiro, Solid State Commun. 48, 547 (1983). K. Kuriyama, T. Kamijoh & T. Nozaki, Phys. Rev. B22,470 (1980). C.J. Wen, B.A. Boukamp, R.A. Huggins & W. Weppner, J. Electroehem. Soe. 126, 2258 (1979). H.E. Schone & W.D. Knight, Acta Metall. 11, 179 (1963). J.R. Willhite, N. Karnezos, P. Cristea & J.O. Brittain, J. Phys. Chem. Solids 37, 1073 (1976). T. Tokuhiro & S. Susman, Solid State Ionics 5, 421 (1981). K. Kishio, J.R. Owers-Bradley, W.P. Halperin & J.O. Brittain, Solid State Ionics 5,425 (1981); J. Phys. Chem. Solids 42, 1031 (1981). K. Kitahama, M. Hiratani & S. Kawai, (unpublished data). K. Kitahama, M. Hiratani & S. Kawai, J. Cryst. Growth 62, 177 (1983). M. Eisenstadt & A.G. Redfield, Phys. Rev. 132, 635 (1963). R.M. Cotts, Ber. Bunsenges. Phys. Chem. 76, 760 (1972). R.E. Walstedt, R. Dupree, J.P. Remaika & A. Rodriguez, Phys. Rev. B15, 3442 (1977).