Fast Li+ conduction in fluoroborate glasses

Mat. Res. B u l l . , Vol. 15, p p . 421-425, 1980. P r i n t e d in t h e USA. 0025-5408/80/040421-05502.00/0 C o p y r i g h t (e) 1980 Pergamon P r e s s Ltd.

FAST Li + CONDUCTION IN FLUOROBORATE GLASSES

S. I. Smedley and C. A. Angell Chemistry Department Purdue University West Lafayette, Indiana 47907

(Received F e b r u a r y 8, 1980; Communicated by R. A. Huggins) ABSTRACT Following recent measurements of very high d.c. conductivities in complex Li fluorlde-borate-sulfate glasses, we have performed systematic measurements in the Li20-LIF-B20 S system. All glasses studied have essentially the same Arrhenius pre-exponential constant. Converting the data to conductivity relaxation times the pre-exponentlal constant corresponds to a frequency considerably higher than the Li + - cage "rattling" frequency. Connections between the a.c. conductivity and the IR absorptivity are discussed. + Recently we reported conductivities in a multicomponent Li - conducting glass, the conductivity of which exceeded that of Li + ~-AI20 S above 200°C (i). In the present article we describe somewhat lower, but more systematicallybehaving, conductances in the basic ternary system Li20-LiF-B20 S. This system clearly will have certain features in common with boracite type (Li20-LiCI-B20 S) glasses recently described by Reau et al (2) on the one hand, and the Li20-LiF-AI(POs) glasses described by Evstrop'ev et al (3), on the other, s The glasses were prepared by fusion of thoroughly dried components in a platinum crucible, followed by quenching between metal plates separated by 2mm spacers, to give a common thermal history to all samples irrespective of glassformlng ability. Gold electrodes were deposited, and conductances were measured by a guarded 3 terminal technique described in detail elsewhere (4). Conductances were measured using a combination of bridges covering 8 decades of frequency, and wide frequency-lndependent (hence d.c. conductivity) plateaus were found at all except the lowest temperatures. In view of this behavior most cases were studied at only sufficient frequencies to establish that the measurement was being made in the 'd.c.' region.

On leave from Victoria University of Wellington, Department of Chemistry, Private Bag, Wellington, New Zealand. 421

422

Smedley, et al.

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Vol. 15, No. 4

Glasses studied, and their temperature and composition dependences, are shown in Fig. i. The highest-conducting glass is, not surprisingly, that which is richest in Li + (however see ref. i). It is close to the limit of glass formation in this system. It was the extension of the glass-forming region to higher alkali contents by addition of 4th and 5th components which made possible the exceptionally high glass conductivities reported in our earlier communication (i). Unexpectedly, replacement of Li20 by LiF at constant mole fraction of B20 3 decreases the conductance. The behavior in the present system is particularly simple to describe analytically. All compositions follow Arrhenius behavior in either of the common Eq. (i) or Eq. (2) forms and only the activation energy is significantly composition-dependent, 0 T = A exp (-E./RT) o i

(I)

~o

(2)

= A'exp (-E /RT)

for the ith composition. The constancy of the pre-exponential term A, shown in Fig. I by the common intersection at I/T = 0, implies that conductance in this system is dominated by a simple "rattle and jump" process involving Li +

T/°C 400

3OO 2OO i

I00

i

50

7 6

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\

O .,

*1(! -II

\\\

\

-I

\

"-..

\\

\

\,

LifO I

I

0,4

:i

LiF i

i

0.8

i

i

1.2

i

l

\\ i

I. 6

I

2.0

i

I

2.4

I

I

2.8

I

I

3.2

I

3.6

I0' K/T FIG. i Arrhenius plots of the conductivity as the OT product for all glasses (and as o alone for glass 3). Inset shows glass-forming region and indicates compositions of glass studied (glasses I and 3 contained 43% Li20 and LiF, respectively, glass 2 has 21.5% each of Li20 and LiF, glass 5 contains 23% Li20, glass 4 contains 24.3% each of Li20 and LiF; glass 6 contains 20% Li20 , 36% LIF).

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FLUOROBORATE GLASSES

423

ions in potential wells of composition-independent form such that there is a characteristic frequency of escape attempt. The average distance moved when the "escape attempt" is successful must also be approximately constant, though experimental accuracy is insufficient to resolve very small changes in A of Eq. (i) beyond those due to increasing concentrations of Li + ions. The escape attempt frequency, fo' may be obtained by converting the d.c. conductivity to an average conductivity relaxation time using (5) e g o ~

=

(3)

O where E is the high frequency dielectric constant obtained from measurements made at frequencies well above 2~/ (4), and e is the permittlvity of free space. We then write, for the average relaxatlo~ frequency

i = ~

>

.

~o . . 2~e e O

~

A~ .

-E /RT e

2~e e O

-E /RT = f e o

(4)

~

lies close to the maximum in the plot of the imaginary part of the electrical modulus M" (M* = l/E* = M' + IM"), so in seeking fo we are asking what is the limiting value of the electrical loss maximum frequency. This should correspond wlth the quasi-lattice vibrational frequency in the low frequency IR region wlth which the M" peak must ultimately merge, so in the simplest case we expect fo to correspond with the measured IR peak frequency of 400 cm -I found for Li20 • B203, and other oxide glasses wlth Li + modifier, by Exarhos and Risen (6). Using eM = I0 (4), e o = 8.85 x i0 -~ and log AO = 2.15 ± 0.2 (corresponding to Eq. ~2) - see dashed plot for glass 3 shown in Fig. i), we obtain fo = 2.9 ± 1.5 x 1013 Hz or 950 ± 450 cm -I. Since any imperfections In the glass or electrode contacts wlll tend to inflate the experimental value of £ used in Eq. (3), the f value obtained above will tend to be an overestimate. On the other hand,°the lles to the low side of the M" maximum. On balance we conclude f = 2~(lattlce). O

A value higher than the observed lattice frequency would imply a positive activation entropy for the Jumping process. Thls could be interpreted quite naturally in terms of a jumping process in which the Ion continues to execute an oscillatory motion but at a reduced frequency corresponding to shallower repulsive walls in the "saddle point" region. To obtain an entropy contribution of e AS/R > 2 to A G as implied above, the oscillation frequency in the transition state would correspond to ~2 in the expression AS = R In 91/~2. With ~i = 400 cm -I V2 ~ 200 cm -I, which would imply a tendency of far-IR bands to broaden to low frequencies at high temperatures as the moving ion fraction increases towards unity. Such effects should be observable by Fourier transform IR spectroscopy of low-meltlng Li + glasses. We note that Eq. (2) preexponential constants of 2 - 2.3 were also found for a large number of Li ~ oxide glasses in the system LI20-B203-SiO2by Otto (7). From the present measurements we can map out, approximately, the relation between low and high frequency ionic motions by plotting conductivities as absorption coefficients using the relationship (8)

424

S.I.

SMEDLEY, et al.

~(~)

=

C

o(m)

n(~)

Vol. 15, No. 4

(5)

e O

and assuming the ~ dependence of n is weak, crystal-like absorption line).

(which is valid except at a sharp

f / c m-I

IO IO3

2, I

-

o~

~ / '

i

T

-i I"

.. 4o0~

-,:'. ~

-

iooo

I

I00

..~'

lO

~

O-Ol~.

_ 7~12o¢~o.~ _

o

0J

_lOt,",l"

0

",

,

'

,

,

,

5

,

o ,,

I0

,

,

5

log f / H z FIG. 2 Frequency dependence of conductivity of glasses of this study and relaxation to IR conductivity assessed from "lattice vibration" infra red spectra.

Some results for glasses 2, 4, and 6 are shown in Fig. 2, and parallel the more extensively documented behavior of the sodium silicate glass discussed in detail elsewhere (9). The dashed lines are calculated from d.c. conductivity values at higher temperatures (taken from the Fig. i plots) and imply that temperatures well above the glass transition temperature range of 400 - 500°C would be needed for the low frequency absorptivity to approach that of the high frequency quasi-resonance mode and thereby produce an easily observed far IR band broadening.

Acknowledgement Support of this work was provided by the NSF-MRL program under Grant No. DMR-76-O0889. Thanks are due to Doug Blough, Steve Holland, and Harold Harrison for technical assistance, and to I. M. Hodge for advice on data processing.

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FLUOROBORATE GLASSES

425

References i.

S. I. Smedley and C. A. Angell, Solid State Comm. 27, i (1978).

2.

M. M. A. Levasseur, B. Calks, J. M. Reau, and P. Hagenmuller, Mat. Res. Bull. 13, 205 (1978).

3.

K. K. Evstrop'ev, G. I. Veksler, B. S. Kondrateva, Doklady Akademii Nauk SSR 215, 902 (1974).

4.

S. I. Smedley and C. A. Angell,

5.

P. B. Macedo, C. T. Moynihan and R. Bose, Phys. Chem. Glasses 13, 171 (1972).

6.

G. J. Exarhos, P. J. Miller, and W. M. Risen, Jr., J. Chem. Phys. 60, 4145 (1974).

7.

K. Otto, Phys. Chem. Glasses ~, 29 (1966).

8.

T. Moss, "Optical Properties of Semiconductors," Butterworth, London, 1961.

9.

J. Wong and C. A. Angell, "Glass: Structure by Spectroscopy," Marcel Dekker, New York, New York (1976).

submitted to J. Am. Ceram. Soc.