Crystalline, Glassy and Molten Electrolytes: Conductivity Spectra and Model Consdderations
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Mat. Res. Soc. Symp. Proc. Vol. 455 0 1997 Materials Research Society
Glassy B2 0 3"0.56Li2 0-0.45LiBr, see Fig. 3, is a lithium ion conductor. As in crystalline electrolytes, there is an Arrhenius temperature dependence of the dc conductivity, and the III to II crossover line has a slope of one. Shifting the spectra taken at different temperatures along this line, we obtain one master curve, provided the frequencies included are not too high. This feature is called the time/temperature superposition principle; it was also encountered in Figs. 1 and 2.
log(oT.Q cmr/K)
log(aTQ cm/K)
3
.,3 1
2-
298 K ~
-•
0adc d0-
.....-.
--__.A |j
slope=l
\ lb.
~213 K
,,vib. 166 -0000"09v0"0.1 .K -
ARR
W-ARR
slope
O--
2 4 6 8
8
1000 KIT
1
0•:0 hf:
•I --am129K
-11
2
.. ---. . . . .. . ... . .- -----------0- - 123 I " i..• .---
-4
I
10
2 4 6 8
12
log(v/Hz)
1000 KIT
Fig. 1 Conductivity spectra of RbAg41 5 at different temperatures; temperature dependence of Gdc
and chf.
log (aT Qcm/K) 3
Iog(aTQ cm/K) slope =1 K-----
(do 450 K
1
ARR300 K 225 K
-1
---------------.--.
----
ARR
__
-3 sy) 23456 1000 KIT
-1
(&) -~~8-64tog(v/v0)
0K3
. -3 5
1000 KIT
Fig. 2 Set of conductivity spectra as derived from the jump relaxation model [6]. 320
1
a,1
o -__
3 0
Contrary to Figs. 1 and 2, however, there is no II to I crossover line. Rather, the dispersive hopping conductivity is found to merge into the broad vibrational contribution. The latter has a lowfrequency flank with a slope of two and almost no temperature dependence. Proceeding to a fragile glass-forming molten salt we once again observe similarities and differences in comparison to the previous examples. The spectra of Fig. 4 [11,12] have been taken log(aT-Qcm/K)
4
2
7
slop e =1,
473 K
0,
=2
0 373 K RdC 0---------323 K 0 ARR 0_ _ _641 -o
-2
/
-4
I
2.0 1000 K/T
1.0
6
3.0
8
10 log(v/Hz)
I 4 1/+
12
Fig. 3 Conductivity spectra of glassy B2 Oy0.56Li2 -0..45LiBrat different temperatures; temperature dependence of Gdc [9]. log (aT.fQcm/K)
/
31 2
slope =1Z// , 0 '-slope= 2 0
478 K c~o
0----------------
423 K
1
0--
d.
0 -
dc ,.0.
---
......
l
2.2
...
*
2.4
(,crossover from VFT to ARR
o/o000O .
,j,
2.6
/
0
-1
-1
Po/
o
000
7
8
.
,
I
I
9
10
11
12
•
log (v/Hz)
1000 K/T
Fig. 4 Conductivity spectra of the fragile glass-forming melt 0.6 KNOy3 0.4 Ca(N0 3)2 ; temperature dependence of 0 d,. 321
from 0.6 KNOy3 0.4 Ca(N0 3)2 , abbreviated as CKN. At far-infrared frequencies, the excitation of vibrational motion once again results in a frequency dependent conductivity that obeys a power law with an exponent of two. This c..comes more and more apparent as the temperature is decreased. At lower frequencies, the shape of the spectra is at first sight similar to those of the glass in Fig. 3. Contrary to the glass, however, the dc conductivity now has a different temperature dependence which can be described by the empirical Vogel-Fulcher-Tammann law. Most remarkably, there is a gradual crossover
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