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MOBILE IONS IN AMORPHOUS
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SOLIDS
C. A. Angell
Department of Chemistry, Arizona State University, Tempe,
Arizona 85287- 1 604
KEY WORDS:
superionic glasses, decoupling index, conductivity, correlation
times
INTRODUCTION
Mobile ions in amorphous solids are interesting from both academic
and practical perspectives. They are of academic interest, because of the
challenge to explain how the structures of a wide variety of liquids can
change during cooling so as to permit truly enormous differences in their
particle mobilities (up to factors of 1 014) to develop. In the fluid states
of most nonpolymeric fast ion glass-forming liquids, the time scales for
electrical relaxation (by the most mobile species) and mechanical relaxation
(by the least mobile species) are within an order of magnitude ( 1 , 2). They
are of practical interest, because these materials may serve as the solid
electrolyte in a wide variety of electrical devices, such as primary and
secondary batteries, sensors, and electrochromic displays. The field of high
conductivity amorphous solids has been very active during the past two
decades, as it has become an increasingly important part of the broader
field of solid state ionics. With the urgent societal need for nonpolluting
vehicle power sources now being a subject of legislation in many states,
the importance of this subject area is destined to grow considerably.
The amorphous solid conductor field comprises two important subfields
and shares a further subfield with the crystalline branch of the su bject. The
subfields referred to are, respectively, fast ion-conducting ("superionic")
glasses and salt-in-solvating-polymer solutions. The shared subfield is that
of rotator phases and certain other highly disordered crystals that obey
the Vogel-Tammann Fulcher (VTF) equation and show glass transitions.
693
0066--426X/92j1 1 O 1 -0693$02.00
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694
ANGELL
These substances are crystalline with respect to the centers of mass of one
of the major constituent particles, but amorphous with respect to most,
or all, of their orientations, or with respect to the position coordinates of
other constituents. The rotator phase may be (and usually is) an ionic solid
with one or more quasispherical components (e.g. BF.j, R4N + ) or a molec­
ular substance [e.g. CN(CH2)2CN] containing small amounts of dissolved
ionic salt.
The salt-in-polymer class of conductor qualifies as a solid only when the
chain polymer solvent molecular weight is large enough to induce rubbery
behavior via the entanglement phenomenon (3), or when shorter chains
have been chemically cross-linked to induce a rubbery condition. The
rubbery condition implies that the relaxation time of the substance to
macroscopic shearing forces is very long, although the response to micro­
scopic shear and macroscopic electrical forces remains liquid-like. Indeed,
much of the research on this class of substance is, for convenience of
manipulation, performed on lower molecular weight polymer solutions,
which are truly liquid under most conditions. It is, in essence, a branch of
nonaqueous electrolyte solution chemistry; hence, it is given less attention
in this review than the glassy solid subfield.
Each of these subfields has been extensively reviewed by many expert
authors, both as select reviews (4-15) and as components of larger, edited
works on the whole solid state ionies field ( 1 5- 1 8). Earlier reviews of each
subfield by Souquet (5), Angell (6) (glasses), Armand (7), and Pethrick &
McLennaghan ( 1 5) (salt/polymers) tended to focus on classical transport
properties (dc conductivity, transport numbers) and the structures respon­
sible. M ore recent reviews, however, have been more phenomenologically
oriented and more detailed regarding kinetic processes. There has been
growing emphasis on frequency-dependent properties that delve into subtle
aspects of the ion dynamics problem. Finally, as the field has grown, whole
journal issues, which contain several specialized reviews of its component
parts, have appeared ( 1 9, 20), and separate detailed reviews of its parts,
e.g. of phosphate glasses (2 1 ), are also being published.
With such a wealth of information available, this review can only serve
a useful purpose if, after a summary of the basic phenomenology, it focuses
on the most current developments and contentious issues, and at least
partly succeeds in providing a broad and unifying view. Wc devote special
attention to the following controversial issues: factors limiting the
maximum conductivity provided by these systems; conductivity pathways
and microheterogeneity in superionic glasses; and problems in phenomen­
ology of relaxation caused by mobile ions, such as dielectric relaxation
versus conductivity relaxation in relation to nonexponential kinetics, the
emerging enigma of NMR correlation time versus dielectric/conductivity
MOBILE IONS
695
relaxation times discrepancies, and high frequency and/or low temperature
excitations.
The plastic crystal subfield, however, is underdeveloped, despite its
considerable promise. We discuss this subfield in the final section.
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BASIC PHENOMENOLOGY
Amorphous solid conductors form when liquids or solutions containing
ions cool from a high temperature liquid state (or dry by evaporation of
a volatile component) without crystallizing. To be solid, some process that
establishes a finite shear modulus must occur. For superionic glasses, this
process is the glass transition at which the shear and enthalpy (overall
structure) relaxation times become longer than ordinary experimental
2
times [usually considered as 1 0 sec (23), but somewhat arbitrarily, as the
two times are not necessarily the same, and for fragile glassformers they
can differ by one to four orders of magnitude (24; M. Tatsumisago,
in preparation)]. For salt/polymer systems, however, the shear modulus
becomes finite at the liquid-to-rubber transition.
To some extent, the properties of the glass, and to a lesser extent those
of the rubber, depend on the cooling rate at which the passage from the
liquid to solid state is carried out. However, for the interesting systems
with highest mobilities, the thermal history effect is not a very useful
variable for mobility enhancement. Thus, except for noting the interest
content of the study by Ingram et al (25), which showed that quenched,
but not anillealed, AgI-Ag2Mo0 4 glasses had non-Arrhenius conductivity
plots, we bypass this issue. (For the general case, see Refs 26-28b; for the
fast ion conductor case, see Refs. 5, 1 0, 28a,b.)
During cooling, all systems show enormous increases in viscosity (or
shear relaxation time), but favorable systems show only small increases in
conductivity relaxation time. Thus, a high conductivity is preserved in the
glassy statc�. This decoupling of conductivity modes from structural modes
is illustrated in Figure 1 and can be quantified by the ratio of shear
relaxation time to conductivity relaxation time, first utilized for this pur­
pose by M oynihan et al (29) and now generally called the decoupling index
� (6,8, 1 4),
1.
Because the shear relaxation times at and above T g are only available in a
few cases, we have found it more practical, for discussion of superionic
glass phenomology, to use the enthalpy relaxation time, 't'H, in place of't's
in Equation 1. LH is obtained directly from the conventional measurement
of the glass transition temperature Tg by differential scanning calorimetry
696
ANGELL
ref
...
..... .. ...
. .
2
1
0
OJ
(a)
•
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's
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--
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0>-.
...
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by ARIZONA STATE UNIV. on 06/30/09. For personal use only.
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..
u
::I
"0
c
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Oli
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•
+
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o
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C
..
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54
2
70Ag1.30AhMo<4
143
60Agl.40(Ag,O.2B20a:l
57AgzS.40Ag135B,S3
44LiI.56Li P2. S7
4
22 .5(LiCl)z27.5LizO.50Bl03
NaSi glass
84
66
59
57
Na2°.3SiOz
..
40Ca(NO�)2..60KN03
•
H3Uo}Q,.4HzO
•
-9
35AgC1.45Ag1.20CsCI
H,Zn2C1
162
36
163
.12HzO
-10
-II
-12
·13
·14
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-....-.-.-
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-15
-16
0
6
5
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A
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7
NaSi glass
8
1035
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323
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738
Tg/T
Figure I
(a)
Arrhenius plots of various interesting vitreous ionic conductors. The data
points indicate the lowest temperature studied and the conductivity at T. (sometimes by
extrapolation). In a few cases. additional data have been obtained in the liquid state, and
these are included. Note the proton conducting glass indicated by dashed line: Plot appears
Arrhenius but the Arrhenius law p reexponent
that a familiar
Uo
<To value
is unphysical. Dotted lines indicate
(10-'_10-3 0-1 em-I) is common to both excellent and poor conductors.
Arrow on conductivity axis indicates maximum conductivity for Liel aqueous solution at
10-14 Q-I em - I is conductivity at Tg expected for
Tg-reduced Arrhenius plots for a subset of part (a) systems, which
ambient temperature. Dot-dashed line at
fully coupled systems.
(b)
show how the systems may be ordered according to efficiency of decoupling of conductivity
modes from structural relaxation modes, by Tg scaling.
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MOBILE IONS
697
(DSC) or differential thermal analysis (DTA), and is 2 ± I x 102 s at Tg
when the latter is determined at 10 K/min scan rate (23). To characterize
the pToperties of a given amorphous phase conductor with respect to the
freedom of mobile ions from matrix interference, we are mainly interested
in the decoupling index at the point in temperature at which the structure
becomes fixed on cooling. This is closely related to Tg (depending on how
quickly relative to 10 K/min the glass was formed). Thus, the R, in which
we are interested for purposes of material property definition is R, (Tg),
hereafter called the decoupling index Ri:
R,*
=
LH(Tg)
Lu{Tg)
--
=
2 x 102
.
T:iTJ
-----
3
Because this quantity varies between 1014 and 10 - for different systems,
it is usually sufficient to have approximate values of Lu at Tg• Therefore, it
is convenient to choose the simple M axwell relaxation time, an average of
a distribution, defined by (30)
9+5xlO-13
2.
(ru) eOf.co /(Jdc �
-
=
(Jde
where (J is measured in n- 1/cm 1. The material property Ri can, therefore,
be defined simply in terms of the dc conductivity at the reference tem­
peratureT*
Tg, as determined by scanning calorimetry at 10 K min 1.
-
=
_ 2x102
><
9 10 13
Rt*
-
-
•
_
(Jdc(Tg)
-
1
2± 1 x 10 4 (Jdc(Tg)
3.
or
10g Ri
==
14.3+1og(JPg'
At the glass transition temperature, the temperature dependence of the
conductivity relaxation time changes to an Arrhenius form of lower slope
than that above Tg• Thus, the conductivity at room temperature (which is
the property of most practical interest) is determined by both the decou­
pIing index (which is the quantity of greatest phenomenological interest)
and the temperature interval between Tg and ambient. These features are
illustrated in Figure 1b, which is the reduced form used earlier by Angell
(13) and Kawamura & Shimoji (2), and is now updated to include recent
data on some new, highly decoupled systems (3 1 -34) and on some proton
conducting glasses (35, 36). Strategies that have been used to increase the
ambient temperature conductivity therefore aim either at diminishing the
mobile ion-to-matrix coupling, or at decreasing the glass transition tem­
perature. Their implementations are considered further below.
In the case of salt/polymer solutions, there is another feature to be
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698
ANGELL
considered: Most of the configurational (liquid-like) degrees of freedom
remain active as the rubbery (solid) state sets in; consequently, a glass
transition occurs only at much lower temperature. At the glass transition,
the rubbery character completely disappears. In this case, however, the
conductivity at the glass transition has become almost immeasurably small
« 1 0 - 14 n- I cm - I), because although the conducting modes are com­
pletely decoupled from the macroscopic (entanglement-based) viscosity,
they are very strongly coupled to the microviscosity. In fact, if the same
mechanical relaxation process that was used in defining the decoupling
index for superionic glasses is used to define mechanical relaxation for
the salt polymer systems, then the salt/polymer decoupling indices are
subunity-in fact, as low as 1 0 3 (37, 3S). Strategies for increasing the
conductivity of such systems must focus on understanding and eliminating
the source of this supercoupling, and on decreasing the glass transition
temperature for the salt/solvent as far below ambient as possible. The
supercoupling phenomenon has only recently been recognized (37), and
only one systematic study has been reported (39). Thus, solutions to the
problem are still far away. It appears to be a different problem from
that of ion pairing [which has long been recognized (7, 9, 40-42) and
characterized ( I 43-45)], because of the opposite composition dependences
(39). The primary problem of decreasing Tg (6) has been given some
attention (15, 46a,b), and recent progress has been reviewed (12, 14).
It is of both academic and practical importance to know which ionic
species is most responsible for an observed high conductivity. In many
cases, e.g. Li2S-SiS2 glasses (32-34), it is the Li+ ions. However, in such
glasses as LiF-PbF 2-AIF 3, it is by no means obvious whether Li + or F­
are the primary carriers. This issue is particularly important in the case of
salt/polymer systems, such as NaCI04 in polyethylene oxide and poly­
propylene oxide systems, in which it was initially supposed that the Na +
ion was the mobile species. It is very desirable, for the practical purpose
of avoiding polarization problems in salt/polymer-based batteries, that the
cation be the main current-carrying species, but mounting evidence now
indicates that the cation transport t+ number is very low, except at the
highest salt concentrations ( 1 2, 47, 4S). Even at a high concentration, t+
is still considerably below 0 5 (IS, 49-51), unless it is deliberately con­
strained to be unity by attaching the anions to the polymer backbone (52a-c).
In the latter case, the ambient temperature conductivity is unfortunately
very low (52a-c) unless crown ether additions are made to free the cations
(52b), or unless special high polarity side chains are attached to the polar
backbone (52c). In the case of the ionene polymers, in which the cations
are in the polymer backbone, the anionic transport number is clearly unity
(53), often involving a Grotthus mechanism.
-
,
.
MOBILE IONS
699
FACTORS LIMITING THE AMBIENT
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TEMPERATURE CONDUCTIVITY
The theoretical limit to ionic conductivity is necessarily far below that for
electronically conducting systems for reasons associated with the very
different masses and, hence quantum mechanical wavelengths, of the mov­
ing particle:s. Even in the case of protons, no equivalent of the Bloch waves
in metals can be identified in practice. The theoretical limit for ionic
conductivity is set by the current flowing instantaneously because of the
ions oscillating in their quasilattice sites; this can be measured by far
infrared (FIR) absorption or reflection spectroscopy (54, 55). This limit is
closely approached by hot ionic liquids, e.g. molten LiCI (see Ref. 8, Figure
10), but the best ambient temperature conducting glasses so far identified
have a conductivity almost two orders of magnitude smaller (see Figure
la), and one of them has the disadvantage of being unstable against
crystallization.
Figure Ib ranks the conductivity of different glasses against their struc­
tural relaxation times by normalizing the temperature scale to a tem­
perature of equal structural (not shear) relaxation time, viz. the calori­
metric glass transition temperature. This comparison shows that the
greatest progress in the effort to free the mobile ions from the frictional
effects of their more slowly relaxing neighbors, remains that made in 1983
by ChiodelIi et al (56) and Susman et al (57), with their respective
developments of the silver iodoborate and iodoborate-phosphate sys­
tems, and complex sodium zirconium phosphosilicate glasses (NaSi
glass). Although these are extremely conductive at their Tgs, they are not
the best ambient temperature conductors, because the Tgs are relatively
high.
Adding alkali halides to a base glass almost always increases the amb­
ient temperature conductivity (58-60), primarily because of the "plasticiza­
tion effect" (so named because of the analogy to the effect oflow molecular
weight solvents on polymer viscosities and glass transition temperatures).
The T g in these cases is lowered in proportion to the plasticizing alkali
halide mole fraction, but the decoupling remains the same. A good example
is provided by the early data of Malugani & Robert (58) on LiPOrLiX
(X CI, Hr, I), in which the iodide-doped glass with lowest Tg had the
highest conductivity at room temperature, but in which the conductivities
at Tg were: the same almost within experimental error, i.e. the decoupling
index was unaffected. This is demonstrated in Figure 2, which shows
conductivity Arrhenius plots for compositions at each extreme of several
families and the locus of conductivities at Tg for all members of each
family. Figure 2 also shows that the plasticization effect dominates in the
=
700
ANGELL
0
-I
'e
'"
�
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:&
:�
....
'"
:::I
"CI
c
0
'"
•
•
•
-2
-3
LiP03
33Lil.67LiPO 3
33LiBr.67LiP03
33LiC1.67LiPO�
�
A
20Agl.80AgPO 3
-5
II
40Agl.60AgP03
..
50Ag1.50AgPO�
55Agl.45AgPO,
+
..
III
-7
13
II
AgP03
lOAg1.90AgPO�
•
-6
14
12
-4
Oii
.g
0
R-r
10
30Agl.70AgPOs
\:;�;�;�:\!:
0.001
8
\i
AgI-TlPOl
0.000
9
0.003
0.002
0.004
1fT
Figure 2
Arrhenius-plots of conductivities of end members of families of vitreous conduc­
tors. For intermediate members, only conductivity at
Tg is shown. Locus of ITT values is
,
Tg is unchanged by
given by solid line for each family. For Li+ conductors, conductivity at
halide additions. For AgI-containing systems
short "incubation" interval.
ITT '
,
hence decoupling index Ri', increases after
more highly conducting Li halide + Li thiophosphate family (60). In the
AgPOrAgI system, on the other hand, the early study of Malugani et al
(61 b) shows that both decoupling and plasticization effects contribute to the
very high conductivity of the AgI-rich glasses (see Figure 2), once XAg1 >
0. 1 . The suggestion from the data that there is an initial plasticization­
only range seems to be supported by the more recent glass and liquid
study of Pathmanathan et al (61 a), and this is interesting in view of some
structural studies discussed later. The combination of plasticization and
decoupling effects also seems to be true for thc AgI-containing systems
reviewed by M inami & Tanaka (4) and for the iodoborate systems studied
by ChiodelIi et al (56). Finally, Figure 2 illustrates the case of TII-AgP03
glasses (62, 85), in which the conductivity initially increases despite
decreases in O'Tg (hence, in decoupling index), until at 20% TIl the decouJPling effect suddenly starts to increase sharply to the glass-forming comJPosition limit. This must be related to the Tl +-Ag+ exchange equilibrium
(between 1- and - p-o- sites discussed elsewhere) (62, 85).
Mixing of the glassformer components has frequently enhanced con­
ductivity (63-65b). From the data of M agistris et al (64), this is clearly
caused by an enhancement of the decoupling, because O'Tg increases with
second glassformer content despite increases in Tg• Pradel and Ribes
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MOBILE IONS
701
(65a,b) have suggested that this effect results from a tendency to micro­
scopically demix, with enhancement of mobile ion content (hence, of
conductivity) in one of the continuously connected microdomains.
Major improvements in room temperature conductivity have long been
known to occur in glasses when the oxide ion is replaced by sulfide or
selenide (5, 31 a,b), and such systems have recently been under intensive
study (32·-34, 68, 69). This improvement was thought to be due to the
easier passage ofthe mobile ion past the more polarizable nonmetal species.
However, this notion would imply decreased friction specifically for the
cation, hence an improved decoupling index, whereas examination of the
conductivity at Tg shows that scarcely any change in aTg (hence in Rn
occurs as a result of the sulfide substitution. The ambicnt temperature
conductivity increase, in other words, is primarily caused by the large Tg
decrease, which reflects the loosening of the entire structure, rather than
of the particular mobile ion-matrix interaction. In contrast, when selenide
replaces sulfide, the ambient temperature conductivity does not increase,
despite Tg decreases of some 50 K (69). Thus, in this case R1 has decreased,
making it evident that the decoupling is greatest in the more open
structures.
The greatest loosening, or Tg reduction, effects occur when the anion­
network, chain, or oligomeric structure is dismantled and when the anions
combine a low effective charge density with low polarizability. Thus, in
AgI-containing systems, the value of Tg decreases as metaphosphate is
replaced by pyrophosphate, when pyrophosphate is replaced by lower­
charged pyrosulfate or dichromate (70), and when dichromate is replaced
by chromate, which brings T g to room temperature. Finally, it can go to
well below room temperature, if all complex ions are removed and only
halide anions remain (71). Such systems can have a conductivity of almost
10-1 n-I cm- I at ambient temperature. Replacement of Ag+ by the
smaller Cu + in AgI-rich compositions gives lower conductivities in some
cases and higher conductivities in others (72; T. Minami, private com­
munication).
Likewise, if the silicate chains of Li20· Si02 glass (Tg 700 K) are
broken down to orthosilicate ions, Tg decreases to 500 K (73); replacing
SiO�- by CI04 or CIO] can yield Tg values well below room temperature.
However, somewhere in the sequence the high decoupling index becomes
lost. An extreme case is the high LiI content binary (LiI + organic cation
iodide) system studied by Cooper & Angell (74), in which R� falls to
about 102. Interestingly, in the related AgI-organic cation systems recently
reported by Kawamura & Hiyama (75), the conductivity remains very
high, 10-2 n-I cm - I at 25°C, and R: is �lO'2. This result presumably
reflects the: essential difference between AgI-containing and alkali-halide­
containing systems discussed earlier, viz. the AgI enhances the conductivity
=
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702
ANGELL
by providing new and more decoupled pathways, whereas the alkali salts
only plasticize the system to enhance existing pathways of constant de­
coupling index. If these do not pre-exist, then Lil addition leads to poor
conductors.
Recently, an extreme case of conductivity enhancement by AgI involved
actual precipitation of ct-AgI in microcrystals, which were stabilized
against the IX -+ f3 transition by the small size of crystals produced during
very rapid quenching in an AgB03 matrix (76).
In polymeric systems, different strategies must be followed; however,
we only summarize the principles involved. In the usual salt/polymer
solutions, the conductivity maximum observed around M: 0 1: 1 6
increases in magnitude with decreases in solution Tg and with increases
in solution fragility. Fragility (67) is defined by the parameter D (fragil­
ity oc D- ' ) of the modified VTF equation
=
4.
where To is related to the glass tranSItIOn temperature Tg by (67)
Tg/To I +0.0255D. Near the composition of maximum conductivity in
these systems, the system is supercoupled with R, ;::::::; 10- 3, almost inde­
pendent of temperature (37, 39). In the ionene polymers, however, there is
considerable conductivity at room temperature (53), despite Tg of;::::::; 100oe,
because of the decoupling of the anion motions, and R; may be of order
107• These polymers, which are effectively polymerized molten salts, pro­
vide one of the two conceptual bridges between polymeric and superionic
amorphous solid electrolytes. The other bridge is realized by the pro­
gressive addition of salt to polymer until the latter becomes the minority
component (39), as has been partially carried out by Przyluski & Wieczorek
(77), and now completed by Angell and Liu (in preparation).
=
CONDUCTIVITY PATHWAYS AND STRUCTURAL
MICROHETEROGENEITY IN SUPERIONIC
GLASSES
The structures responsible for the high conductivity obtained in superionic
glasses, have been of great interest and much controversy, particularly in
the case of the Ag+ -conducting glasses. Early in this subject's history, the
tendency of AgI-containing glasses to extrapolate conductivity (5) and
other properties (7) to the values for superionic crystalline ct-AgI had led
to the supposition that a-AgI-like clusters exist in the glass and that these
overlap increasingly with increasing AgI content. The existence of some
sort of inhomogeneity has been argued directly from small angle neutron
scattering (SANS) studies (79). These studies have suggested a dimension
MOBILE IONS
703
of some loA for the dispersed phase. An early calorimetric study on AgI­
AgP03 (80) has been used ( 1 7) to argue that, at least at low AgI content,
the tendenc:y is to order AgI within the AgP03 matrix, rather than to form
clusters. However, the partial molar heat of mixing of AgI seems to reverse
sign near XAg1 0.3, which implies clustering at higher XAg1• Indeed, the
opaque yellow appearance of slowly cooled AgI-AgP03 glasses of XAg1 >
0.50 strongly implies that a macroscopic phase separation can occur.
More recently, a new light has been thrown on these systems by the
elastic neutron scattering studies of Tachez et al (8 1 ) and Borjesson et al
(82-83). These authors have shown that, on doping a silver oxide-modified
oxide glass like AgP03 with AgI, a new sharp diffraction peak arises at very
low Q ( 0.7 A-I) with intensity proportional to AgI content. According to
Borjesson (83), this occurs not only in the complex P205- and B 20rbased
systems (8 1-82b), but also when there is no extended chain or network
structure present at all, viz. in the mixed salt glass (AgIh.75(Ag2Mo0 4)o25
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=
�
(see Figure 3). In the latter case, however, the low Q peak is distinctly
smeared out. Borjesson also shows that the peak is essentially absent from
AgCl-doped glasses and from the corresponding alkali halide (LiCI- and
...
t:
1.0
=
..
'OJ
°O�--+---"�O--�'5--�20
(a)
QrA_X
(e)
'.5
'.0
.,..
=
(b)
3.0
.9
u
�
(i)
1.5
(II)
(iii)
0.5
0.0
0
, Q/A,-'
�.7.
••��.�2
. �-'
�O'�f
' --��
O
Agi
concentration
X
(a) Reduced structure factors for four highly structured single-component glasses,
2 A - ' , and for silver iodoborate glass with prepeak at
which show prominent prepeaks at
0.7 A - '. (b) Structure factors showing low-Q prepeaks in three very different AgI-Ag oxanion
glasses: (i) Agl-Ag,O-2B ,0 3. (ii) (AgI)o 75' (Ag,MoO 4) 025. (iii) AgI-AgPO3. contrasted with
Figure 3
�
(iv) prepeakles.s structure factor for pure AgP03 (curves for i, ii, and iii displaced upward for
clarity).
(c) Intensity of low-Q peak in (AgI)x' (Ag,O' 2B,03) ,-x as function of AgI content.
Note how peak tends to vanish at XAg,
Research Soci'ety.)
=
0. 1 . (From Ref. 83, with permission of the Materials
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704
ANGELL
NaBr-doped) systems. Noting that the peakless systems are also relatively
poorer conductors, Borjcsson links the low Q peak and the associated
intermediate range order to the high conductivity known for the AgI­
doped systems. We would add that the systems with strongly increasing
prepeaks are those that owe their increasing conductivity to increased
decoupling, as well as to decreasing Tg (see earlier discussion of Figure 2).
Whether the low Q peak is equally prominent in the compound-related
glasses AgI-AgCI-CsCl [related to CsAg4Is (70)] and Ag2S-AgI-As2S 3
[related to Ag}SJ (20)], or in the mixed cation systems AgT-NaP03 (85)
and Til' AgP03 (62) is not yet known.
Sharp low Q diffraction peaks have long been recognized as indicators
of intermediate range order in the classical glassformers (86), although
their origin has been a subject of controversy (86, 87). The AgI-superionic
glass peak is at the lowest Q value observed for any nonmolecular system.
The authors observe that its value, �0.7 A, and width, 0. 5 A, imply an
intermediate range ordering of repeat length, 8-lO A, and correlation
length, 15 A, which is not inconsistent with the earlier SANS results.
However, Borjesson points out the difficulty raised by the failure of small
angle x-ray scattering, which should be sensitive to electron-rich AgI, to
detect a small angle peak (16 1). Most recently, Borjesson & McGreevy
(88) have tackled this problem by application of McGreevy's reverse
Monte Carlo computer simulation method and concluded that the low Q
peak is due to "local density fluctuations In the network of P0 4 tetrahedra
caused by the requirement to maintain connectivity while decreasing the
average density." From the form of the P-P radial distribution function,
they further suggest that there is a weakly fractal character in this expanded
network structure.
Before discussing how these notions may support alternative models
of the conduction mechanism, we draw attention to an interesting, and
probably diagnostic, correlation. Borjesson points out that the intensity
of the prcpeak extrapolates to zero not at XAgl 0, but rather at the point
XAgl
0.1. In discussing the difference between effects of alkali halide
additions to LiP03 and AgI addition to AgP03, we noted earlier (Figure
2) that only in the latter case did the decoupling increase with added
salt. We now further observe that the increase in decoupling index (or
conductivity at Tg) in AgI-AgP03 like the AgI activity coefficient only
begins to rise beyond X 0. 1 (see Figure 2). This would appear to connect
the structure behind the prepeak (and the break in FIR spectral shifts
discussed below) with the decoupling enhancement in AgI-based super­
ionics. Finally, we note that in the case of TII-AgPO 3 glasses (62), in which
an exchange of Ag between 1- neighbors and -O-P- neighbors can occur,
the increase in uT.' hence in decoupling index, only commences above 20%
�
=
=
=
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MOBILE IONS
705
TII, although the conductivity increases continuously. Clearly, the pre­
diction to test would be the absence of a prepeak at 20% Tii and a sharp
increase thereafter. A further test would be to see if the prepeak increases
with increasing [W04]/[W04+S04] at constant XAg1 in the system AgI­
Ag2S04-Ag2W04 (89), in which Tg, but not (J250, is a strong function of
the oxyanion ratio (90) (which implies that Ri can change at constant
XAg1).
Finally, we must consider the input into the structural character of
superionic glasses from vibrational spectroscopy. Many studies of glasses
containing polarizable components, like AgI, have been made by Raman
spectroscopy (97, 98). However, because the FIR bands represent the
attempt frequencies for activated conducting motions, we focus attention
on the FIR spectra in the quest for new indications of the structures
connected most directly to the conducting pathways. Alkali phosphates
were studied by Exarhos & Risen (9 1). Alkali silicates have been described
by Exarhos et al (92) and Gervais et al (93), and alkali borates have been
subject to detailed FIR study by Kamitsos and coworkers (94) and Liu &
Angell (54). Finally, Nazri et al (in preparation) and M artin et al (in
preparation) have examined AgI-AgP0 3 glasses.
Kamitsos and coworkers (94) observed asymmetry and structure in their
alkali metal borate FIR spectra, and Ingram et al (100) have deconvoluted
these into separate components, which they assign to distinct sites represent­
ing "cluster" and "tissue" components of the glass. In Ingram's "cluster­
bypass" model ( 10 1), the.conducting paths are conjectured to be localized
within a tissue component, which [in accord with concepts advanced first
by Tammann (102) and later Hayler & Goldstein (103) and Goodman
(104)] forms after denser clusters have impacted during cooling. The cluster
bypass model has the advantage of predicting that there should be more
tissue, hence higher conductivity, in quenched glasses, as is the case in
practice. It also seems compatible with the interpretation of the sharp
prepeak in AgI-containing glasses preferred by Borjesson & M cGreevy
(88). These: authors see the AgI filling out the low density fluctuations in
the oxyanion matrix, rather than forming distinct clusters that overlap or
percolate in the more common "cluster overlap" models ( 105, 106). An
element of confusion enters here, however, when the FIR spectra of AgI­
AgP03 glasses are examined because the most definitive evidence for
different oscillation sites might be expected in these cases. Although low
frequency Raman spectra show structure consistent with the presence of
Ag-halide like sites (97), the FIR spectrum, rather than developing new
low frequency components, and then moves systematically back to lower
frequencies, without any broadening, as XAg1 increase to 0.5 (Martin et ai,
in preparation). There is no obvious explanation for the absence of separate
706
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Ag site frequencies. However, the finding is consistent with the absence of
separate Ag+ jumping internal friction peaks ( 1 07). The only comparable
alkali halide-doped case, Button's ( l 08) study of LiCI-Li20�B203 glasses,
shows a simple and progressive shift to longer wavelengths, again without
obvious band broadening, as LiCI is added to lithium metaborate.
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FREQUENCY-DEPENDENT ION DYNAMICS AND
CORRELATION FUNCTIONS
The subject of relaxation kinetics, with its current emphasis on quantitative
treatment of nonexponential relaxation, is alive with controversy. This
follows a period in which many workers, including myself, had feIt matters
were reaching some consensus status, insofar as a certain ubiquity was
being recognized ( l 09-l l l b) for the stretched exponential (or KWW)
relaxation function ( 1 09):
8(t)
=
exp [
-
(t/r)/l].
5.
Its application was helping rationalize long-standing discrepancies between
nuclear spin-lattice relaxation (SLR) and conductivity relaxation (5, 17,
1 1 1 - 1 1 3) on the one hand, and quasielastic neutron scattering diffusivities
and conductivity ( 1 1 4) on the other. In addition, the treatment of electrical
properties of conducting solids by use of the complex modulus formalism
(30), which considerably simplified data manipulation, seemed to have
won broader acceptance, and the resulting spectral widths seemed con­
sistent with those from other spectroscopies. However, any tendency to
unwarranted complacency was halted by the confluence of experts pro­
moted by the 1 989 Heraklion conference organized by Ngai and Wright
and published in three volumes of the Journal of Non-Crystalline Solids
(131/133). In the following, we encapsulate some of the now troublesome
issues.
The first issue concerns the question of the appropriateness of the
modulus formalism both for electrical and mechanical relaxation
processes, and the consequences to nonexponentiality parameters if not.
Both Cole (116) and Kremer ( 1 1 7a) point out that only in the complex
susceptibility or complex conductivity formalisms are the quantities
directly defined by the fundamental Maxwell equations. Furthermore,
common relaxation times are only found for multilaterally. bonded liquids,
like glycerol, for which common relaxation functions are expected when
susceptibilities, not moduli, are compared ( 1 1 8, 1 1 9). A procedure for
combining the virtues of the modulus analysis (to suppress electrode
capacitance effects) with the notion that the electrical response of a con-
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MOBILE IONS
707
ductor should be treated as a dc conductance in parallel with a relaxing
dielectric, was suggested by Johari & Pathmanathan ( 1 20), who applied it
to several different glass systems. More recently, Cole & Tombari ( 1 2 1 ),
who used a direct susceptibility approach, found that their resistance-capa­
citance data on the NazO' 3SiOz glass previously studied by Moynihan
et al ( 1 22a,b) when first treated by removal of a Warburg surface im­
pedance, gave a good fit to a Davidson-Cole (DC) dielectric relaxation
function after subtraction of a dc conductance. The best fit DC parameter,
IX = 0.36, implies an equivalent KWW fJ parameter of 0.47, which is con­
siderably smaller than that of Moynihan et ai's KWW fit to the electrical
modulus spectrum (fJ 0.6) ( l 22a,b). This treatment, therefore, modifies
the electrical response spectral shape considerably and throws into
question, or at least modifies, some correlations made recently, e.g.
between conductivity and nuclear spin-lattice relaxation correlation func­
tions ( 1 1 1 b, 1 1 2) and between nonexponentiality parameter fJ and decou­
piing index ( 1 3). On the other hand, this treatment tends to reconcile those
cases in wlhich large differences have been noted, like the extremely broad
log TI versus l /Tcurve observed for 1 09Ag nuclear spin relaxation in AgI­
AgzO-Bz03 glasses studied by Chung et al ( 1 23). For instance, an analysis
by Niklassen et al ( 1 24), based on a complex capacitance representation
of the AgIx-(Ag20' 2B20 3)I x data almost equivalent to that of Cole &
Tombari (12 1 ), also gave best accord with a DC expression, the shape
parameter of which was compatible with the SLR findings. The detailed
comparison with SLR, however, raises a new question, which we discuss
below.
Another recent treatment of conductivity in fast ion glasses has been
the compkx conductivity analysis of Kremer et al ( 1 1 7b) for the interesting
case of anion conduction in polymeric organic salt glasses, viz. the poly­
ionenes [(CHr-CH2) 1O-NHi].Br';- (or [ZnBr:lln)' This has the advantage of
casting the real part of the conductivity in the form that has become well
known for its unification oflow frequency conductivity and high frequency
resonance absorption (optical phonon) regimes (see Ref. 1 2 1 , Figure 4,
and Ref. 13, equivalent diagrams for both AgI-based glasses and electrical
and mechanical absorption processes). For further details on the complex
conductivity analysis, refer to the discussion by Funke ( 1 25).
We now turn to a second problem area: the relation between conductiv­
ity and SLR. The manner in which the failure of the classical Bloembergen,
Purcell, and Pound (BPP) theory ( 1 26) for SLR in glasses and vis­
cous liquids is rectified by replacing the BPP exponential relaxation
assumption by the nonexponential kinetics characteristic of slow processes,
has become well recognized ( 1 09, 1 27a-c). In 1 986, we noted (8) that this
recognition is all that is necessary to explain the large and often-discussed
=
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708
ANGELL
difference between the activation energy usually observed for SLR in the
usual multi-MHz experiments, and that seen in conductivity. This has since
been explained in detail (17, 112, 129). Quite simply, the nonexponential
relaxation leads to frequency-dependent conductivity and frequency­
dependent NSR for frequencies above that of the system's internal relax­
ation frequency. For conductivity measurements conducted at constant
frequency, high temperature measurements "see" the frequency-independent
response and give the dc conductivity. At a temperature where the (fixed)
bridge frequency and the (temperature dependent) intrinsic relaxation
frequency coincide, there is a crossover to a lower activation energy regime.
This has rarely been discussed in the conductivity literature, although it is
obvious enough from the many figures of log a (O) versus log (frequency)
that have been presented (30, 122a,b, 130). lf the frequency of the bridge
is raised increasingly toward values typical of the SLR experiment, the
crossover temperature moves to temperatures, approaching or surpassing
the glass transition temperature. For most glasses, measurements made at
high SLR spectrometer frequencies see only the frequency-dependent
(lower activation energy) regime. This lower activation energy depends on
the departure from exponentiality of the dynamic process, approximately
according to the relation
6.
This relation was proposed on theoretical grounds by Ngai ( 1 09) and has
been supported by a variety of experiments ( 1 32a,b). Dyre ( 1 31 ) shows
that it is consistent with other empirical relations for glasses. Such a regime
has, for instance, been observed in the recent work on LizS' SiSz glass of
IPradel & Ribes (133), who deliberately extended the ac measurements to
low temperatures far into the frequency-dependent regime (see Figure 4).
However, other reports ( 17, 1 12, 134, 135) have suggested that Ea (ac)
increases with decreasing frequency. The general case remains to be clari­
lied. A feature of all these studies, however, is that the Arrhenius pre­
exponents of the plots in the frequency-dependent regime are unphysically
low. Because the activation energies are determined by the departure from
{�xponential relaxation, their interpretation must be intimately connected
to the model used to explain nonexponential relaxation, of which there
are now a considerable number ( 1 36-1 39).
Although a reconciliation of NSR with conductivity data, based on
nonexponential relaxation functions, has now been reported by several
laboratories (124, 133, 134, 139) and interpreted microscopically by Elliot
& Owens ( 140), there seems to be a problem that has not yet been discussed.
There is a tacit assumption that the correlation function for the spin­
relaxing and electrical field-relaxing fluctuations is the same. In the Elliott-
MOBILE IONS
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10 kHz (0).100 kHz (.).1 MHz (C). 10 MHz (e).
3
Figure 4
5
8
709
\r'
,;
3
4
5
Arrhenius plots for electrical conductivity at various fixed frequencies, for the
systems (AgI)o.37,(O.5Ag,SiS,)o 625 and (Li,S)o 5' (GeS,)o.,. Insert shows temperature depen­
dences of spin-lattice relaxation times [log (TI'ls) versus liT], from which the characteristic
time for SLR fluctuations at T(T" min) can be obtained. (Adapted from Ref. \33, with
permission of J. Non-Cryst. Solids.)
Owens treatment, this assumption is explicit. However, based on the data
discussed below, we suggest that this may be a poor assumption for
superionic glasses and that the agreement claimed between SLR and con­
ductivity behavior is only qualitative in nature. The problem is discussed
in more detail in a current paper ( l35), but the essential point is that in
superionic glasses, the fluctuations responsible for relaxing the weakly
coupled nuclear spin system seem to have a lower characteristic frequency
than those that relax the electric field. Furthermore, the opposite situation
appears to hold in polymer/salt solutions. It is probably more than coinci­
dence that the decoupling indices for conductivity (represented as log­
arithms), have opposite signs in these two cases. By way of confirmation,
we find that in the case of an aqueous lithium chloride solution,
LiCI· DH20, the relaxation of 8Li studied by the method of {3-radiation
detected NMR (]4 1 ) occurs on almost the same time scale as conductivity
relaxation (29, ]30). The decoupling index for this system (for the discussion
of which the rir:" ratio was first invented) is close to unity over the whole
temperature range of study (29).
To document the above, we consider the data of Refs. 123, 1 28, l 33,
134, and 141 , some of which are seen in Figure 4. Chung et al (123) noted
that their Tl minimum for 109Ag relaxation in an iodoborate glass implied
710
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a slower process (by approximately one order of magnitude) than for a
mechanical relaxation associated with Ag+ jumping, but attributed this to
failure of BPP theory. However, if we compare the simple Maxwell relax­
ation time (an average value) for conductivity in this glass (143), obtained
from the relation ( r.,. ) eoe",, /(Jde, with their 109Ag Le at the temperature
of the TI minimum (where WeLe � 1), we obtain Le/<L.,.)= 10-7.8/
10-9.3 = 101.5; This is much greater than any difference between (t.,.)
and La (most probable time) that could arise from any of the common re­
laxation functions for fast ion relaxation used to correct for the B PP
exponential relaxation assumption. The difference is even greater in the
silver iodogermanate case studied by Pradel & Ribes (133), Le/<L.,.)
10-7.8/10-10= 102.2, but about the same for their Li2S'SiS2 glass
(133), Lc/(r.,.) = 10-8.0/10-9.62 = 101.62, as can be confirmed from
data given in Figure 4 by using fL = 10.2 MHz and 1 5.8 MHz for 109Ag
and 7Li, respectively. The most detailed cases available, however, are those
reported by Martin et ai, in which several spectrometer frequencies have
been applied. They studied the cases of (Li20)x-(SiS2) I-x (134) and
(LiCl)x-(LizO· 2B 20 3 )I_x glasses ( 1 28) by using samples identical to those
studied by ac conductivity (134, 135). These studies not only confirm
the sort of differences seen in the above cases, but show that they are
t,emperature-dependent; the NMR correlation time has the larger acti­
vation energy, consistent with its longer relaxation time. This is, of course,
the opposite of the once-prevalent idea that SLR in conducting glasses
detects a fast low activation energy process.
In the case of salt-in-polymer electrolyte solutions, on the other hand,
23
comparison of data on Na relaxation reviewed by Greenbaum et al (144)
shows that Le/<L.,.) � 10-8.7/10-8.0 = 10-0.7• In the latter cases, which are
effectively liquids rather than glasses, the time scale for relaxation of the
matrix in which the ions move is about 102 shorter than the conductivity
relaxation time, as indicated by (composition-dependent) decoupling
indexes Rt = 10-3-10-I (37-39). These values contrast strongly with the
Rt values of � 1012, which characterize the superionic glasses. This implies
that the fluctuations (in electric field gradient, etc.) that couple most
effectively to the spin system (hence, that minimize TI/Le) are not those
determined by the frequency of ionic jumping, unless there is some error
in the common view that the conductivity relaxation time and mobile ion
jump time are very similar when many ions are present. The nature of
these less common but more effective fluctuations is, of course, of interest
in connection with migration models for glasses. For instance, it could be
argued that the larger activation energy for Le implies the presence of a
class of deep traps in which the electric field gradient is very different from
that in shallow traps in which the ions spend most of their time. To
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==
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MOBILE IONS
711
understand the domination of conductivity by shallow-trapped ions, one
must suppose that such traps are highly degenerate. Because of the field
gradient effect, however, the less frequent visits to the deeper traps would
dominat,e the SLR. An increase in shallow trap depth in poorer conducting
glasses would explain the tentative correlation of tc/tq with Rr•
This picture has much in common with that of the weak electrolyte
model ( 1 1 5). The emphasis on a trapping topology over an energy land­
scape provides an analogy with models of electron transport in glasses and
helps rationalize their common features (S. Sridhar et aI, in preparation).
Clearly, iit would be of value to follow both conductivity and SLR behavior
up into the liquid state, because the decoupling index there changes rapidly
towards unity. If, as we expect, tc then varies in a non-Arrhenius fashion
with changing temperature, then the phenomenon to which we have drawn
attention would be identified as another participant in the serial decoupling
phenomenon discussed recently by several authors ( 1 42a,b).
We now briefly address a third area of contention in frequency­
dependcnt behavior of fast ion conducting systems. This concerns fixed
temperature/very high frequency, or fixed frequency/very low temperature,
behavior. It deals with the problem of connecting resonance and relax­
ational modes of motion in amorphous materials and crossovers between
different power-law domains for frequency-dependent properties. It is
most actively studicd by NMR ( 1 39, 1 4 1 , 1 64), in which spin relaxation
by two-level systems (ADWS) is invoked (1 32a,b, 141), but has also been
studied by light-scattering ( 1 46a,b), ultrasonic relaxation ( 1 47), and dielec­
tric/conductivity relaxation ( 1 3, 1 48a), in which the role of fractal exci­
tations in geometrically non fractal amorphous Euclidean systems has been
suggested ( 1 3). Strom et al ( 1 49) provide a good overview. In all cases, the
question of interest concerns the source and nature of the apparently
universall excitations responsible for an excess absorption over that
expected from anharmonicity, and also over that predicted by most relax­
ation functions (165).
PLASTIC CRYSTALS AND RELATED SYSTEMS
We hav(: long known that some crystals with asymmetric constituent
particles can exhibit heat capacity anomalies on cooling (and subsequent
reheating) that are close analogues of the glass transition discussed earlier
(150, 1 5 1) . The motions being frozen out at Tg are, in most plastic crystal
cases, reorientational motions. Frequently associated with these reorien­
tational motions are diffusional modes, which, if the diffusing particles are
charged, lead to a high ionic conductivity in the solid state. Several well­
known fast ion conducting systems, such as Li2S0 4 ( 1 52, 1 53) and
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712
ANGELL
Li2MgCl 4 ( 1 54), fit this description with respect to conductivity, but never
t:xhibit the glass transition at lower temperatures because of the prior
intercession of an ordering phase transition. We restrict our discussion
here to the more limited range of systems that either exhibit the glass
transition directly or carry the other signature of typical glass-forming
systems, viz. non-Arrhenius transport behavior in the mobile state above
Tg•
We limit the scope in the latter manner so that we can relate the obser­
vations to the same parameters that have proven useful in discussing
superionic glasses on the one hand, and salt-in-polymer solutions on the
other. With these restrictions, this section can be very short, because the
number of systems investigated in the fast ion conductor context is very
small. It is, in any case, an open question whether many of the rotator
phases studied by solid state ionists (e.g. Refs. 1 52-1 54) could be quenched
t.o orientationally disordered glasses if specialized rapid quenching tech­
niques, such as those used in some glassy state studies (73), were employed.
For instance the threefold rotation of NO) in NaN0 3 cannot be quenched
in, and the transition being approached on cooling is not of the glass
transition type, but is a A. transition.
These materials are interesting because, like salt-in-polymer systems,
they have a mechanism for providing solid-like behavior above Tg (in this
case it is the crystal lattice); however, unlike the salt-in-polymer systems,
they have no obvious source of the supercoupling that depresses the salt­
in-polymer conductivity so seriously-indeed, they are more closely akin
to the ionene polymers, in which the conducting species motions are
decoupled, R� � 1 07 ( 1 1 7b). The first examples described were double salts
of LiBF 4, LiCIO 4, and LiI with tetraalkyl ammonium type cations, except
for having one R group methoxylated ( 1 55). They gave Tg values lower
than those of the best conducting PPO- or PEO-based salt-in-polymer
solutions, but yielded conductivities at 25°C that were only comparable,
1 0 - 5 a - I cm - I , probably because of a lower fragility ( 1 5 1 ). Since then, a
related compound has been shown to be about one order of magnitude
more conductive.
An alternative approach is to use a molecular plastic crystal, or a solid
solution of plastic crystals, as solvent for small amounts of ionic solute.
The advantage of this approach is that the Tg value of the room-tem­
perature-solid solvent can be very low, e.g. l I S K, for succinnonitrile­
malanonitrile mixtures ( 1 57). Because it is difficult to confirm that con­
ductivity occurs wholly within the large grains of the rotator phase crystals,
solute concentrations have been kept very small, 0.1 molar; nonetheless,
very high conductivities,
10 - 3 n- I cm I, have been observed. Opti­
mization of this approach could clearly yield interesting materials. These
�
-
MOBILE IONS
713
systems show highly non-Arrhenius conductivities and dielectric relax­
ations that fit the VTF equation well ( To :::::: 0.8Tg) ( 1 57; D. List and C. A .
Angell, in preparation). Conductivity and dielectric relaxations are well
separated in frequency, as expected ( 1 58), and dielectric relaxations are
nonexponential, with P(KWW) 0.7-0.8. In studies at different solvent
compositions (succinnonitrile : malanonitrile or succinnonitrile : glutaro­
nitrile ratios), some differences in VTF parameters may be seen; however,
values from conductivity (mobile species) and dielectric (matrix species)
relaxation are comparable, which implies coupled relaxation mechanisms,
as in pollymer/salts. The actual conductivity relaxation time is longer
because of the low ion concentration.
Anoth(�r crystalline solid case in which VTF behavior is observed
involves Ag7GeSesI, as reported recently by Ribes and coworkers (1 59).
In an Arrhenius plot, the conductivity of this compound shows strong
curvature that can be linearized by use of Equation 4 with To 90 K. This
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=
=
is 50 K bdow the temperature of an anomaly in the DSC scan (not shown
in Ref. 1 59), which was assumed to be a glass transition. The authors
analyze the data for this and several related compounds by using Equation
4 in the form
7.
with Ea in electron volts.
Ifwe convert their data from Equation 7 to Equation 4 using D
1 . 16 X
4
1 0 Ea/To, we find D values ranging from 5.92 to 33.6, which covers almost
the whole range of fragilities observed previously for plastic crystals ( 1 5 1 ,
157). A similar behavior has long been known for the case o f the compound
Ag 3 SI ( 1 60), but has never been analyzed in these terms. Clearly, the source
of non-Arrhenius behavior, and of excess heat capacity in these cases,
cannot lie in reorientations, but must lie somehow in the configurational
entropy associated with cation disordering. On the other hand, the relation
between what is jumping and what is freezing out is not clear, because the
DSC anomaly occurs at a temperature where (J :::::: 1 0 3 Q 1 cm - t, which
corresponds to a L" value of only 1 0 - 9 s, cf. 1 0 2 s for relaxation at a glass
transition. A glass transition due to freezing of mobile ions could only be
detected by DSC when (J :::::: 1 0 - 1 4 Q- I cm- I . The detailed study of these
compounds as a new class of plastic crystals, as well as an interesting class
of fast ion conductors, seems warranted.
=
A CKNOWLEDGMENTS
This work has been supported by the Department of Energy under grant
No. DE-F902-89ER4535398. The author thanks H. Senapati for assistance
with data and diagrams and for a critical reading of the manuscript.
714
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I . McLin, M . C., Angell, C. A. 1988. J.
Phys. Chern. 92: 2083
2. Kawamura, J. , Shimoji, M. 1986. J.
Non-Cryst. Solids 88: 295; Kawamura,
J., Shimoji, M. 1 989. Mater. Chern.
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