7Li and 11B nuclear spin lattice relaxation in B2O3 + 0.7Li2O + XLiCl glassy fast ionic conductors

] O U R N A L OF

NON-CRYSTALLINE SOLIDS

Journal of Non-Crystalline Solids 139 (1992) 257-267 North-Holland

7Li and 11B nuclear spin lattice relaxation in B203 + 0.7Li20 + XLiC1 glassy fast ionic conductors M. T r u n n e l l a n d D . R . T o r g e s o n Ames Laboratory USDOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

S.W. Martin Department of Material Science and Engineering, Iowa State University, Ames, IA 50011, USA

F. B o r s a Ames Laboratory USDOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA and Dipartimento di Fisica dell' Universitd di Pavia, 27100 Pavia, Italy Received 3 July 1991 Revised manuscript 30 September 1991

Nuclear spin-lattice relaxation rates, R1, are reported for lithium chloro-borate glassy fast ionic conductors for both the mobile 7Li nuclei and the stationary lIB nuclei, as functions of temperature and NMR resonance frequency. The 7Li relaxation is driven by the lithium diffusion via quadrupole interactions. The data for all frequencies can be fitted by assuming a single correlation function of the form e x p ( - ( t / z * ) ~ ) . In the fit a thermally activated correlation time, rc*, is assumed with an effective activation energy E * = 7400 K, higher than the one deduced from dc conductivity measurements. It is argued that the correlation function (CF) which determines the conductivity and the CF which determines the NMR relaxation may differ in the presence of collective effects in the lithium diffusion. The liB data indicate that the nuclear relaxation proceeds via a Raman two phonon process involving internal vibrational modes of the BO 4 units heavily damped by reorientational motion. The data are fitted by an expression for R 1 derived from an extension of the Van Kranendonk two phonon relaxation mechanism in insulators. The activation energy for the damping frequency is compared with E a =/3E* which should represent the 'single particle' energy barrier for the lithium motion.

1. Introduction

There is wide interest in fast ion conducting glasses formed from B203, a network modifier oxide (eg. A g 2 0 or L i 2 0 ) and a metal halide salt as a dopant (eg. AgI, LiC1 or LiI). These glasses have dc conductivities which can exceed 10 -4 ( ~ cm)-1 at room temperature [1] and find applications in battery and fuel-cell technology. The atomic level mechanisms for fast cation conduction in glass are still poorly understood particularly with regards to the effects of intermediate range order. One of the most striking measures is the large decoupling of the ionic diffusive motion,

as measured by the electric conductivity, and the viscous motions of the matrix as probed by the low frequency mechanical relaxation time [2]. On the other hand, phonon-like local disorder modes or two-level-systems (TLS) are known to exist in these glassy materials [3] and can be detected directly by ultrasonic attenuation [4]. Thus, although the metal ion sublattice may be decoupled from the glass matrix on a long range order scale it may still couple on a short or medium range order scale. N M R has been used for some time as a microscopic probe to study ionic motion in fast ionic glassy conductors [5,6]. In this paper, we use both

0022-3093/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

258

NL Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

the N M R of the mobile nuclei (7Li) and of the stationary nuclei (aaB) to investigate the coupling between the translational motion of the cation and the local disorder modes of the BO 4 groups in B 2 0 3 + 0.7Li20 + X L i C 1 glassy ionic conductors, a system known to have high conductivity.

2. Experimental procedure and materials

2.1. Sample preparation The glass samples were p r e p a r e d * by mixing LiC1 (Wako, > 99%), LizCO 3 (Wako, > 99%) and dried B 2 0 3 (Kishida, > 90%). The mixtures were then placed in Pt crucibles and heated for 30 min at increasing t e m p e r a t u r e plateaus at 600, 700, 800, 900 and 1000 ° C. Then the mixtures were poured onto metal plates and pressed with another plate. The samples used for N M R measurements were sealed under vacuum in 10 m m quartz ampoules.

2.2. Instrumentation The 7Li relaxation m e a s u r e m e n t s were performed at 4.0, 12.2 and 40.0 M H z and the liB relaxation m e a s u r e m e n t s were performed at 12.2, 24.0 and 32.5 M H z over the t e m p e r a t u r e range 100-500 K using a phase coherent N M R spectrometer. The spectrometer employed a programmable pulse sequencer, a double sideband rf switch and a wide bandwidth receiver described in ref. [7]. The N M R signal was digitized by means of a Nicolet 1170 signal averager and transferred to a D E C model LSI 11/73 computer for analysis. The rf intensity varied as a function of operating frequency. Typical "rr/2 pulse lengths for 7Li r~mged from 3 Ixs at 4.0 M H z to 5 ~s at 40 MHz. A variable t e m p e r a t u r e chamber with a vacu u m jacketed counter flow heat exchanger design was used in connection with a three term temperature control based on an O m e g a Engineering * Samples were prepared by Masahiro Tatsumisago of the University of Osaka Prefecture, Department of Applied Chemistry.

2012 programmable t e m p e r a t u r e control. A temperature stability much better than _+ 1 K was achieved with t e m p e r a t u r e gradients over the sample volume less than 2 K.

2.3. Data analysis The 7El N M R spectrum above room temperature is made up of a single narrow line ( < 1 kHz width) as expected in presence of motional narrowing due to the fast Li-ion diffusion. Below room temperature, the 7Li line broadens and develops a broad base due to a random distribution of satellite lines ( + 1 / 2 ~ _+3/2)which are shifted with respect to the central line transition by first order nuclear electric quadrupole effects [8]. The full width of the 7Li N M R spectrum is obtained below 200 K and is shown in fig. l(a). The structureless broad shape of the line in fig. l(a) results from an N M R powder pattern with a distribution of perturbing quadrupole frequencies, vQ, and electric field gradient (EFG) asymmetry parameters, ~7. This is consistent with a local disorder in the 'frozen-in' positions of the Li-ions in the glass. The recovery of the nuclear magnetization following x r - r r / 2 rf pulse sequence used in measuring spin-lattice relaxation rates, R I , was found to be exponential at all temperatures. If the relaxation mechanism is of quadrupolar rather than of magnetic dipole-dipole origin, one expects, in general, a multiexponential recovery when static quadrupole effects are present [9]. However, if the relaxation transition probabilities W 1 (for Am = +_ 1) and W 2 (for Am = -+2) are of the same order of magnitude and if the initial conditions correspond to saturation (or magnetization inversion) of both central and satellite lines, the recovery will be exponential [9]. Since the overall frequency distribution width of satellites lines is 60-70 kHz (see fig. l(a)), which is of the same order of magnitude of the intensity of the irradiating rf magnetic field, all transitions are irradiated in these materials, even at low temperatures. Thus the relaxation mechanism can be of quadrupole origin (with W 1 - W z) even in presence of an exponential recovery of the magnetization at low temperatures.

M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

The l i b spectrum is shown in fig. l(b). The narrow line at the center of the spectrum arises from the N M R central transition ( + 1/2, - 1 / 2 ) of the liB nuclei in BO4 units in tetrahedral coordination with oxygens. For those nuclei, the quadrupole coupling frequency is only u o ~ 200 kHz [10] sufficient to generate only first order quadrupole perturbation effects. The Tr/2 pulse length for the narrow line is reduced by a factor

259

of 2 with respect to the pulse length for liB in a liquid reference solution. This is due to the increase of the effective gyromagnetic ratio expected when only the central line is irradiated: 7' = ,/(I + 1 / 2 ) [8]. The broad component in the liB N M R spectrum in fig. l(b) shows a visible structure. Measurements performed at two different values of the external magnetic field, H, indicated the separation between the two maxima

(a)

o .<

'

-50

-40

-30

-20

Frequency

I

10

-10

'

I

'

20

f

I

30

40

'

50

(kHz)

(b)

2 c

©

' -40

I -.30

'

J -20

'

1 -20 Frequency

'

I 10

'

I 2O

'

I 30

' 40

(kHz)

Fig. 1. (a) 7Li N M R s p e c t r u m in B 2 0 3 + 0 . 7 L i 2 0 + 0.6LiCl glass at = 80 K a n d 22.0 M H z o b t a i n e d from the F o u r i e r t r a n s f o r m of the free i n d u c t i o n decay. B o t h the n a r r o w c e n t r a l line t r a n s i t i o n and the b r o a d d i s t r i b u t i o n of satellites are visible. (b) 11B N M R

spectrum in B203 +0.7Li20+0.6LiC1 glass at room temperature and 32.5 MHz. The narrow strong signal is from the central transition of boron in B O 4 units.

M. Trunnell et a L / Nuclear spin lattice relaxation in glassy conductors

260

in the broad signal is inversely proportional to H. This result is clear evidence of a second order quadrupole splitting of the liB central line [8,11]. For ~7 -- 0 the separation of the two singularities in the powder pattern is given by (25/49) (u~/u L) [8]. From fig. l(b) we measure a separation of 30 kHz which for u L = 32.5 MHz, leads to an estimate of v o = 1.4 MHz. The broad line in fig. l(b) is very similar to the 11B N M R spectrum in vitreous B 2 0 3 shown on p. 21 of ref. [11]. There, the quadrupole frequency was found to be u o = e2qQ/2h = 1.38 MHz, almost identical to our result. We conclude the broad line in fig. l(b) arises from UB nuclei belonging to the BO 3 arrangements with triangular coordination with oxygens, as in B 2 0 3 [11]. From the ratios of the areas under the narrow and broad NMR lines components, we estimate a fraction of liB nuclei in BO 4 sites of the order of 0.5 in general agreement with accurate studies by Bray et al. [12]. The results of ~IB relaxation rate presented in this paper refer only to the boron nuclei in BO 4 units. This can be achieved quite easily by monitoring the recovery of the narrow central line only (see fig. l(b)). The measurements were per-

formed by saturating the central line transition and part of the satellite transitions with a long sequence of r r / 2 pulses. The recovery of the nuclear magnetization is slightly nonexponential. The relaxation rate, R1, was determined by forcing the fit to a single exponential function. This leads to larger systematic errors than for the 7Li NSLR. The measured 11B Rxs are an ill-known combination of the quadrupole relaxation transition probabilities W 1 and W2, but this should not affect the relative temperature dependence of R~ which is the main scope of this work.

3. Results

3.1. 7Li nuclear spin lattice relaxation rate The 7Li NSLR data as a function of temperature are shown in fig. 2 for different measuring frequencies. The data are limited at high temperature by the glass transition occurring at Tg = 680 K.

10 • [3 I

4.0MHz 12.2MHz 40.OMHz

0.1 T m E "" 0.01

0.001

0.0001

'

'

I

2

'

I

3

'

I

'

4

1000/T (K-') Fig. 2. 7Li nuclear spin lattice relaxation rate, R1, plotted versus ] 0 0 0 / T for B203 + 0.7Li20 + 0.6LiC] glass at different resonance frequencies. T h e full lines are theoretical fits according to eqs. (1)-(3) for the choice of parameters in table 1.

M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

261

0.1 0 I A

12.2MHz 24.0MHz 32.SMHz

i

co

E

0.01 [3

Od

0.001

'

I

0

'

I

1

'

2

I

'

3

I

'

I

4

'

I

5

'

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6

'

7

I

'

8

I

'

9

10

IO00/T Fig. 3. 11B relaxation rate versus 1 0 0 0 / T in B 2 0 3 + 0.7Li20 +0.6LiC1 glass for three resonance frequencies. T h e full line is the theoretical fit according to eqs. (5) and (6)with E" = 3570 K, hzl 0 / e = 800 and B = 2.8 × 10 - 4 (s-1 K - 2 ) .

3.2. 11B nuclear spin lattice relaxation rate

suring frequency indicating the relaxation mechanism for the non-diffusing UB is different from the one responsible for the 7Li NSLR. Different NSLR mechanisms for the diffusing and the non-diffusing nuclei have been previously re-

The 11B nuclear spin-lattice relaxation rate is shown as a function of temperature in fig. 3. The R 1 maximum is almost independent of the mea0.1

7Li

I B203+O.7Li20 +0.6LiCI B B20~+O.5Ag20+O.93Agl

'O:Ag 00000 0

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0.01

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0

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0 rq

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5

~

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6

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7

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8

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1

9

0

I O 0 0 / T (K-') Fig. 4. Comparison of I1B relaxation rate, R~, versus 1 0 0 0 / T for lithium chloro-borate (our m e a s u r e m e n t s at 12.2 MHz) and silver borate (from ref. [13] at 16 MHz). The arrows indicate the temperature at which the 7Li R I m a x i m u m occurs for the same resonance frequency and for the same sample. For 7Li see fig. 2 and for l°7Ag see ref. [14].

M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

262

0.1 FI 1

0.6LiCI 0.2LICI

0.01 tl /

E

/ i

i D iE

/ l

0.00!

0.0001

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1000/T

Fig. 5. Comparison of 11B relaxation rates for two samples of B20 3 + 0.7Li20 + XLiCI glass with different LiC1 concentrations, X. Both sets of measurements were done at 32.5 MHz. The solid and dashed curves are the theoretical fits according to eq. (5). The fitting parameters are: £" = 3570 K (for both samples); B = 2.8× 10 -4 (s -1 K -2) and hAo/E = 800 for X = 0.6; B = 1.9 x 10 4 (s -~ K -2) and hAo/E = 200 for X = 0.2.

ported for (Ag20 --}-nB203)1_ x -t- (AgI) x superionic glass [13]. The 11B NSLR for the lithium chloro-borate glasses and for the silver borate glasses are compared in fig. 4. In both cases the n B NSLR maxima occur at temperatures lower than the NSLR maximum for the nuclei of the mobile ions (Li, Ag), the comparison being made for the same frequency. The liB NSLR in glasses with two different amounts of LiC1 are shown in fig. 5 as a function of temperature.

4. Discussion

4.1. 7Li N S L R rate In order to extract information about the 7Li ion translational motion from the NSLR data, one must adopt an interpretive scheme. It is well known that in glassy fast ionic conductors the NSLR rate results cannot be explained by assuming a single Debye type exponential decay for the correlation function (CF) of the appropriate local lattice variables, such as in the BPP model [5].

Attempts have been made to fit the results by using a distribution of exponential correlation functions [5,15-17] or by using a single CF described by a stretched exponential [5,18] (see eq. (1) below). The two formalisms, however, have certain similarities. In fact, a stretched exponential can always be expressed as a sum of exponential functions with a given distribution of correlation times but the inverse is not always possible [19]. Moreover, the use of a single homogeneous CF could reflect the more fundamental effect of the slowing down of the decay of the correlations at long times due to cooperative effects [20]. The theoretical expression which describes the NSLR in terms of a distribution of activation energies (and hence a distribution of correlation times) is valid only for independent ionic motion [21]. Further, a consistent interpretation and comparison of both N H R and conductivity data in terms of a distribution of activation energies appears more difficult. Recently, it has been shown [22] that a consistent interpretation of both conductivity and NSLR measurements over a wide range of temperature

a/L Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

and frequency can be achieved in glassy superionic conductors by using the stretched exponential CF of the form

f(t)

= exp( -

(t/r*)t~),

(1)

)

(2)

values of the parameters chosen in the fit are listed in table 1. The value of the constant C gives indications on the dominant interaction driving the relaxation. For a dipole-dipole nuclear interaction, C is related to the rigid lattice second moment Ccx (Wd2), while for a quadrupole interaction C c~ (w~), where w 0 is the root-mean-square value of the time dependent quadrupole interaction frequency which is modulated by the lithium ionic diffusion. The order of magnitude of the 7Li rigid lattice second moment can be estimated from the width of the central line in fig. l(a). One has o92 -~ (2Tr X 4 X 1 0 3 ) 2 - 6 X 108 ( r a d / s ) 2. The same can be done for the average quadrupole interaction from the satellite distribution in fig. l(a). One has N~ = (2rr × 40 X 103) 2 = 6 × 101° ( r a d / s ) 2. The value found for C (see table 1) exceeds the rigid lattice second moment by more than an order magnitude, while it is of the same order of magnitude as the satellite splitting observed at low temperature (see fig. l(a)). This difference allows us to conclude that the 7Li NSLR is driven by the fluctuating electric field gradient due to the diffusive motion. From eqs. (1)-(3), one can deduce [22] the following limiting behaviors which can be tested independently:

where r* = r~ exp(E*/kBT

is an effective correlation time which is assumed to be thermally activated. The effective activation energy, E * , should be related to the microscopic energy barrier of the diffusive motion but includes effects due to the averaging over a distribution of barriers a n d / o r to collective effects associated with the ion-ion interactions [20,23]. The activation energy, E * , is obtained from the temperature dependence of the dc conductivity and from the NSLR data on the high temperature side of the relaxation rate maximum since in both cases the measured quantity probes the long time behavior of the corresponding CF [5,22]. The 7Li NSLR is related to the spectral density of the fluctuations due to lithium ion diffusive motion by [5,6,8] R 1 = C[J(WL)

+ 4J(2WL) ] ,

263

(3)

with J ( w ) = R e f _ i f ( t ) e -i°'t dt,

WLT* << 1

R 1 ot Z*c,

where w L is the Larmor frequency in the external static magnetic field. A theoretical expression for R 1 can be obtained from eqs. (1)-(3) by using numerical integration and series expansion methods [24] for given values of the parameters 13, r~, E * and C. The theoretical curves are compared with the experimental data in fig. 2 and the

(.OLT£ >> 1

e 1 (x (DL(1 +'8)(Tc* ) - f l ,

(4a)

(4b)

Ea* ] R1

(OLTc* ~ 0 . 6 4

max

cxexp-

kBrmax ]

,

where Rlm~x is the maximum value of R 1 (see fig. 2) found at the temperature Tm~x. In fig. 6 and

Table 1 Glass Composition

/3

E * (K)

r~' (s)

E 2 (K)

E ( l l B ) (K)

C(rad/s) 2

B 2 0 3 + 0.7Li 2 0 + 0.6LIC1 B 2 0 3 + 0.7Li20 + 0.2LiC1 B;O 3 +0.7Li20

0.35

7400 _+200

0.8 × 10 - I4

5500 6300 7000 7500

3600 _+200 3600 _+200

11.5 N 109

~) Extrapolated from ref. [32]. b) See ref. [31].

(4c)

a) a) b) a)

264

M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors 10 O 346K

,

E

0.1

r.~

-

.5

0.01

0.001

i

d

i

i~lll

I

0.1

1

i

i

ii1,1

1

I

i

i

J

iiii1[

i

10

i

i

itlll

100

1000

Frequency (xlO 6 r a d / s e c ) Fig. 6. 7Li relaxation rates versus resonance frequency for B203 4-0.7Li20 + 0.6LiC1 glass at two different temperatures. The full lines represent the behavior predicted by eq. (4b) for low temperature (wLr* >> 1) with the fitting parameter/3 = 0.35 (see table 1).

fig. 7, the limiting behaviors predicted by eq. (4b) and eq. (4c), respectively, are confirmed for the parameters listed in table 1. On the low temperature side of Rlm~, (0)L'rc~ >> 1), the NSLR probes the short time behavior

of the CF, whereas on the high temperature side of R l m a x (the fast motion regime wLz* << 1), the NSLR probes the long time behavior of the CF [5,15,22]. Thus the activation energy derived from the dc conductivity, E a, should be compared with

10

i

v

E

0.1

0.01

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.6

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1.7

'

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1.8

'

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1.9

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2

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2.1

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2.2

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2.3

IO00/T~,, ("K-') Fig. 7. Maximum value of the 7Li relaxation rate for B203 + 0.7Li20 + 0.6kiC1 glass (from fig. 2) plotted as a function of reciprocal temperature at which the maximum occurs. The straight line represent the behavior predicted by eq. (4c) with the parameter E * = 7400 K (see table 1).

M. Trunnell et a L / Nuclear spin lattice relaxation in glassy conductors

E * . In fact, the dc conductivity which probes the long time behavior of the polarization correlation function which, although differing from the CF describing R 1 in eq. (3), also decays as a consequence of the lithium ionic diffusion [20]. From table 1 one can see that E * for B 2 0 3 + 0.7Li20 + 0.6LiC1 is closer to E~ for B203 + 0.7Li20 than the E a for B 2 0 3 + 0.7Li20 + 0.6LiC1. Note the activation energy derived by fitting the R~ data on the low temperature side of the maximum (see fig. 1) yields E a = / 3 E * . This lower value of E a should be close to the microscopic single particle energy barrier [25] and should be compared with the results of the high frequency, low temperature conductivity, while the effective energy, E * , includes the effects of the ion-ion interactions on the cooperative long range diffusion [20,23] and thus should be compared with the results of dc conductivity [22].

4.2. JiB nuclear spin lattice relaxation rate We argue here that the HB nuclei are relaxed by the fluctuations of the electric field gradient due to the dynamics of the internal modes of the BO 4 units in a way similar to that found for other borate glasses [26]. In the case of silver borate glass, the 11B NSLR was found to be frequencydependent, indicating that the nuclear relaxation proceeds via direct interaction with the reorientational modes of groups of BO 4 units [13]. In the present case, the frequency independence of the 11B NSLR (see fig. 3) points towards a Raman process involving excitations and de-excitations of two internal vibrational or librational modes. A model which was successfully used in explaining the 11B NSLR frequency-independent maximum in B203 involves low frequency phonons heavily damped by structural relaxation of two level defects (TLS) [26]. For the case of optical modes, the following expression was obtained [26] (by extending the Van Kranendonk theory [27,28] for the NSLR driven by a Raman two phonon process): R 1 = - - T 2 2 tan -1

rr

-

e

in 1 +

h~

(5)

265

where a is the phonon damping frequency due to the structural relaxation associated with reorientation of BO 4 units or groups of units. The damping zl could also be affected by the lithium long range diffusion. In either case we assume a thermally activated relaxation rate: A = , r - 1 - - A 0exp - ~

,

(6)

with an average activation energy, E. Other parameters in eq. (5) are the width, e, of the dispersion for the optical modes and the interaction strength, B, describing the coupling between the laB nuclear quadrupole moment and the local electric field gradient [26]. A best fit of the experimental data in fig. 3 to eq. (5) yields: B = 2.8 × 10 - 4 (S 1 K - z ) ; h A o / E = 800; and /~ = 3600 K. The theoretical curve appears to give a satisfactory description of the experimental data (see fig. 3). T h e deviation of the R 1 values from the theoretical fit at low temperature (T < 150 K) is probably due to an additional relaxation mechanism such as the one due to paramagnetic impurities a n d / o r direct relaxation by two level systems (TLS) [13,29]. The relaxation data for the sample with composition B 2 0 3 + 0.7Li20 + XLiC1 with X = 0.6 are compared in fig. 5 with the data for the sample with X = 0.2. The two set of data can be fitted with eq. (5) by using the same activation energy, E (see table 1), but differing values of B and h a o l e as shown in the caption of fig. 5. The l i B relaxation rate in B 2 0 3 glass displays a weakly frequency-dependent maximum [26] similar to the one observed here but with R a smaller by one order of magnitude.

5. Summary and conclusions

The 7Li relaxation rate in lithium chloro-borate glassy fast ionic conductors is driven by the quadrupoie interaction of the 7Li electric quadrupole moment with the fluctuating electric field gradient due to the ionic diffusive motion. Within the framework of the stretched exponential description for the CF, the activation energy derived from NMR, Ea* = 7400 K, represents an

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M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

effective e n e r g y b a r r i e r for t h e long r a n g e diffusive m o t i o n o f t h e l i t h i u m ion which i n c l u d e s a v e r a g i n g over a d i s t r i b u t i o n o f m i c r o s c o p i c b a r r i ers a n d / o r c o r r e l a t i o n effects. T h e fact t h a t E * from N M R is s o m e w h a t h i g h e r t h a n E a f r o m the dc conductivity (see t a b l e 1) suggests t h a t c o o p e r ative effects in lithium ionic long r a n g e diffusion a r e i m p o r t a n t . I n fact, in t h e p r e s e n c e of c o o p e r ative effects, t h e C F s h o u l d b e e x p r e s s e d in t e r m s of q ( m o m e n t u m ) - d e p e n d e n t collective v a r i a b l e s as is d o n e c u s t o m a r i l y to d e s c r i b e m a c r o s c o p i c r e s p o n s e functions a n d N M R r e l a x a t i o n r a t e s in m a g n e t i c a n d s t r u c t u r a l p h a s e t r a n s i t i o n s [30]. N o t e t h e C F d e s c r i b i n g t h e conductivity is a m a c r o s c o p i c C F at q = 0, while the local C F d e s c r i b i n g N M R results involves a s u m o f fluctuations at all q vectors. W e p r o p o s e t h e f r e q u e n c y - i n d e p e n d e n t relaxa t i o n r a t e of n B i n d i c a t e s t h e s t a t i o n a r y b o r o n is r e l a x e d by a two p h o n o n R a m a n p r o c e s s involving i n t e r n a l v i b r a t i o n a l o r l i b r a t i o n a l m o d e s which a r e highly d a m p e d by t h e t h e r m a l l y a c t i v a t e d m o t i o n of B O 4 units or g r o u p s of units a m o n g different metastable equilibrium configurations (TLS). T h e activation e n e r g y for t h e l a t t e r p r o cess is E = 3600 K a n d it s h o u l d r e p r e s e n t t h e m i c r o s c o p i c e n e r g y b a r r i e r of t h e TLS. T h e mic r o s c o p i c single p a r t i c l e b a r r i e r for t h e l i t h i u m h o p p i n g m o t i o n , on t h e o t h e r h a n d , m a y b e estim a t e d [25] as E a = / 3 E * = 2600 K (see t a b l e 1). Thus, it a p p e a r s t h a t the b a r r i e r for t h e l i t h i u m m o t i o n is d i f f e r e n t f r o m t h e b a r r i e r for t h e T L S dynamics. T h e I1B r e l a x a t i o n r a t e d a t a in glasses with d i f f e r e n t LiC1 c o n c e n t r a t i o n (see fig. 5) a r e diff e r e n t suggesting a c o u p l i n g b e t w e e n l i t h i u m m o bility a n d B O 4 d i s o r d e r m o d e s m a y b e p r e s e n t . I n o r d e r to investigate t h e p r o b l e m m o r e q u a n t i t a tively, a d d i t i o n a l m e a s u r e m e n t s in glass with varia b l e c o n c e n t r a t i o n s a r e n e e d e d t o g e t h e r with a r e f o r m u l a t i o n o f t h e N S L R in t e r m s o f qd e p e n d e n t collective variables, b o t h efforts a r e u n d e r way. T h e a u t h o r s wish to t h a n k Kevin G o r m a n a n d H u i W a n g for assisting with the r e l a x a t i o n m e a s u r e m e n t s . A m e s L a b o r a t o r y is o p e r a t e d u n d e r C o n t r a c t No. W-7405-Eng-82. This w o r k was sup-

p o r t e d by the D i r e c t o r of E n e r g y R e s e a r c h , Ofrice o f Basic E n e r g y Sciences (M.T., D.R.T., F.B.), a n d by N S F - D M R g r a n t n u m b e r 87-01077, I o w a S t a t e University A c h i e v e m e n t a n d R e s e a r c h F o u n d a t i o n (S.W.M.). O n e of us (F.B.) was p a rtially s u p p o r t e d by a g r a n t f r o m Consiglio N a z i o n a l e d e l l a R i c e r c h e for I t a l y - U S A c o l l a b o rations.

References [1] C.A. Angell, Solid State Ionics 18&19, (1985) 72. [2] A. Angell, Solid State Ionics 9&10 (1983) 3. [3] W.A. Phillips, J. Low Temp. Phys. 7 (1972) 351; P.W. Anderson, B.I. Halperin and C.M. Varma, Philos. Mag. 25 (1972) 1. [4] J~ickle, Z. Phys. 257 (1972) 212; S. Humklinger and A.M. Raychaudhuri, Progress in Low Temperature Physics, Vol. 9 (Elsevier, Amsterdam, 1986). [5] S.W. Martin, Mater. Chem. Phys. 23 (1989) 225 and references therein. [6] D. Brinkman, Solid State Ionics 5 (1981) 53. [7] D.J. Adduci and B.C. Gerstein, Rev. Sci. Instrum. 50 (1979) 1403; D.J. Adduci, P.A. Hornung and D.R. Torgeson, Rev. Sci. Instrum. 47 (1976) 1503. [8] A. Abragam, The Principles of Nuclear Magnetism (Clarendon, Oxford, 1961) p. 36. [9] M.I. Gordon and M.J.R. Hoch, J. Phys. C: Solid State Phys. 11 (1978) 783. [10] K.S. Kim and P.J. Bray, J. Non-met. 2 (1974) 95; C. Rhee and P.J. Bray, Phys. Chem. Glasses 12 (1971) 165. [11] P.J. Bray, J. Non-Cryst. Solids 73 (1985) 19. [12] J. Zhang and P.J. Bray, J. Non-Cryst. Solids 111 (1989) 67. [13] A. Avogadro, F. Tabak, M. Corti and F. Borsa, Phys. Rev. B41 (1990) 6137. [14] S.W. Martin, H.J. Bischof, M. Mali, J. Roos and D. Brinkmann, Solid State Ionics 18&19 (1986) 421. [15] M. Villa and J.L. Bjorkstam, Solid State Ionics 9&10 (1983) 1421; J.L. Bjorkstam, J. Listerud, M. Villa and C.I. Massara, J. Magn. Res. 65 (1985) 383. [16] E. Gobel, W. Miiller-Warmuth, H. Olyschlager, and H. Dutz. J. Magn. Res. 36 (1979) 371. [17] J. Roos, D. Brinkmann, M. Mali, A. Pradel and M. Ribes, Solid State Ionics 28-30 (1988) 710. [18] S.H. Chung, K.R. Jeffrey, J.R. Stevens and L. B6rjesson, Phys. Rev. B41 (1990) 6154. [19] C.P. Lindsey and G.D. Patterson, J. Chem. Phys. 73 (1980) 3348; E. Helfald, J. Chem. Phys. 78 (1983) 1931. [20] K.L. Ngai, R.W. Rendell, A.K. Rajagopal and S. Teifler, Ann. NY Acad. Sci. 484 (1986) 150;

M. Trunnell et al. / Nuclear spin lattice relaxation in glassy conductors

[21] [22]

[23] [24] [25] [26]

K.L. Ngai, R.W. Rendell, A.K. Rajagopal and S. Teitler, Ann. NY Acad. Sci 484 (1986) 321. R.E. Walstedt, R. Dupree, J.P. Remeika and A. Rodriguez, Phys. Rev. B15 (1977) 3442. S.W. Martin, H. Patel, F. Borsa and D.R. Torgeson, J. Non-Cryst. Solids 131-133 (1991) 1041, and to be published. K. Funke and R. Hoppe, Solid State Ionics 40&41 (1990) 200, and references therein. M. Disllon, G.H. Weiss and J.T. Bendler, J. Res. Nat. Bur. Stand. 90 (1985) 27. G. Balzer-J611enbeck, O. Kanert, H. Jain and K.L. Ngai, Phys. Rev. B30 (1989) 6071. M. Rubinstein, H.A. Resing, T.L. Reinecke and K.L. Ngai, Phys. Rev. Lett. 34 (1975) 34;

[27] [28] [29] [30]

[31] [32]

267

M. Rubinstein and H.A. Resing, Phys. Rev. B13 (1976) 959. J. Van Kranendonk, Physica (Utr.) 20 (1954) 781. K.R. Jeffrey and R.E. Armstrong, Phys. Rev. 174 (1968) 253. J. Szeftel and M. Alloul, J. Non-Cryst. Solids 29 (1978) 253. See various contributions in: K.A. Muller and A. Rigamonti, eds., Local Properties at Phase Transitions (North-Holland, Amsterdam, 1976). H.L. Tuller, D.P. Button and D.R. Uhlmann, J. NonCryst. Solids 40 (1980) 93, and references therein. A. Lavasseur, J.C. Brethous, J.M. Reau and P. Hagenmuller, Mater. Res. Bull. 14 (1979) 921.