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Ionic transport properties in glasses
Journal of Non-Crystalline Solids 73 (1985) 287-303 North-Holland, Amsterdam
287
IONIC T R A N S P O R T P R O P E R T I E S IN GLASSES D. RAVAINE Laboratoire d'Energ~tique Electrochimique, LA C N R S 265, ENSEEG, BP 75. 38402 Saint Martin d'Hbres, France
The different glass compositions which exhibit ionic transport properties in the oxide, sulfide and fluoride systems, are presented. The main data concerning the conductivities and actiwition energies for conduction are given and compared to those of the best superionic conductors. The available models on ion transport in glasses are briefly discussed and the applicability' of the weak electrolyte theory emphasized. Future development concerns protonic conduction in glasses and "'sofl" methods for synthesis of new glass compositions.
1. Introduction
The ionic character of the conductivity in oxide glasses was established a century ago when Warburg experimentally demonstrated the transport of sodium between two amalgams separated by a glass membrane [1]. In the meantime, many experimental results concerning traditional oxide-glasses have been collected [2-4]. The conductivity of these glasses is cationic and highest for alkali and silver cations. Until about ten years ago, the best results in conductivity were around 10 s (f~ cm) -1 at room temperature which made ionic conductive glasses suitable only for very specific applications, such as glass membranes in pH sensitive electrodes. Recent progress and practical requirements have now focused more attention on glassy electrolytes. New sulfide glasses and doped inorganic glasses have led to much higher conductivities than traditional oxide-based glasses, from 10 5 to 10 3 (~2 cm) -1 at ambient temperature for some lithium conductive glasses [5-7]. In a short time, glasses have been synthesized that achieve performances comparable to those of the best solid electrolytes. In the field of battery applications, glasses offer a large number of advantages over crystalline solids. First. the ionic conductivity is isotropic and does not involve any gain boundary effects like in polycrystalline materials. Also, the electronic contribution to the total conductivity is usually very weak which is a consequence of the aperiodic potential fluctuations imposed by the disordered structure. Moreover, metal impurities are unable to enhance the electronic conductivity since they can exist in their own distinct local environment in the glass structure. Electronic leakage is then unlikely to occur in electrochemical devices using a glass membrane as an ionic separator. From a practical point of view, glasses have the advantage of being easilv obtainable in thin film configurations; layered microbatteries can then be 0022-3093/85/$03.30 < Elsevier Science Publishers B.V. INorth-Holland Physics Publishing Division)
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expected in the near future by using thin film glassy electrolytes. Extremely good contacts can be obtained between electrode materials and ionic conductive glasses of low glass transition temperatures Tg: this condition is expected to be especially critical for intercalation-type electrodes whose volume varies during charge-discharge cycles. Finally, one of the interesting features of glasses as electrochemically active materials is the possibility of continuously changing the composition through appropriate techniques. Bulk glass samples can be obtained with ionic transport properties at one end and electronic transport properties at the other end of the sample. Promising results have been obtained by the chemical intercalation of alkali ions in a phospho-vanadate glass [8]. This opens the way to make a compact battery with improved performance through the delocalization of the electrode/electrolyte interfaces. From a more fundamental point of view, varying the composition has been widely used as a means to investigate the ionic transport properties in glasses. This has led to an original approach to the interpretation of the ionic conduction mechanism in solid state conductors based on the existence of dissociation equilibria. The applicability of the weak electrolyte theory to glassy electrolytes [9] has attracted a revival of interest for the interpretation of poorly understood results like the mixed alkali effect [10], the magnitude of conductivity variations with the concentration of network modifiers or the electric field dependence [11].
2. Ionic conductive glass compositions 2.1. Oxide glasses In table 1 are summarized the different oxide glass compositions which are known to exhibit ionic transport properties. These are by far the most studied among amorphous electrolyte materials [2-4,12]. For simple glass composi-
Table 1 Oxide glass compositions Mobile ion
Ag +
Usual glass former cation
Si,
M+ (M = Li, Na, K... ) Ge,
B,
Unusual glass former cation
P,
AI.., Ta, Nb, W, Mo, La, Ga (ultrafast quenched)
Mo, As, Cr, W, Se, Te, V (quenched)
Doped by AgX or MX X = halides and sulfate X = CI and Br
X = halides and sulfate
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,o
@ o
O@o@o £ o < o .,,,o....
o . .
,o
@O o@o
o
(a) (h~ (c) Fig. 1. Schematic structure representation [71] for: (a) AgPO~ glass: (b) AgPO~-Agl glass: Ict Ag2 MoOa-Agl glass.
tions, such as binary network former/network modifier oxides, three dimensional covalent macromolecules are formed by an assembly of elementary units (SiO 4, BO4, PO4... tetrahedra) in which at least one atom of oxygen is shared (BO's). Some oxygen atoms that are non bridging (NBO's) are negatively charged keeping in their vicinity the alkali or silver (M) cations introduced by the network-modifier oxide (fig. la). Vitreous domains involving a wide concentration range in cation (M) content are obtained by dissolving alkali or silver salts in oxide-base glass in order to increase the number of charge carriers [13-17]. In that case, only large size anions (halides, sulfate) can be incorporated without affecting the macromolecular structure of the glassy network (fig. lb). For this reason, the term "doped" has been used to describe these types of more complex glass compositions although, in some cases, very high levels (up to 80 m / 0 ) of doping level can be attained [18]. For some silver glass compositions, this expression is not related to any structural evidence: due to the higher glass forming ability of silver glass, rapid quenching techniques can be used to obtain glass formation with unusual glass formers (see table 1) [19]. The addition of extra-silver salt leads to a disordered structure made of discrete anions (iodides, molybdates ... ) in which the doping agents are not discernible (fig. lc) [20,21]. Finally, unusual glass formers have also been used to obtain alkali conductive glasses. In that case, ultra-fast quenching techniques are necessary. (.}lass formation has been observed in systems of tantalates and niobates [22], aluminates, gallates and bismuthates [23], tungstate and molybdates [24], and sulfates [25]. Unlike the other glass systems, only small amounts of alkali sails can be incorporated before the occurrence of partial crystallisation [26]. 2.2. Sulfide glasses
Table 2 gives the different glass compositions investigated in the sulfide systems. Due to their hygroscopicity, the synthesis of sulfide glasses needs special attention. For this reason, the history of sulfide glasses is more recent [27] and the list of studied compositions is much less exhaustive than that of oxide glasses.
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Table 2 Sulfide glass compositions M+ (M = Li, Na, K... )
Doped by AgX or MX
Mobile ion
Ag+
Usual glass former cation
Si, Ge, B,
X = halides (excepted F)
Unusual glass former cation
As, Ga, La, Sb
X = halides (excepted F)
Table 3 Fluoride glass compositions Mobile ion Glass former
Additives
F Be, Zr, Hf Th, Sc, U transition metals rare earths Ba, AI, Y, Yb M(Li, Na, Rb... )
Nevertheless, the glass forming ability of the c o m m o n , as well as unusual (excepted for alkali glasses) glass formers has been tested in the sulfide systems, along with silver or alkali halide additions [28-30]. Transport n u m b e r measurements performed on N a z S - S i S 2 and N a 2 S - G e S 2 glass compositions show that the electronic contribution to the conductivity is quite negligible [27] and confirm the ionic character of the conduction in sulfide glasses. 2.3. Fluoride glasses
These glasses are currently under considerable development mainly because of their potential use for making infrared optical c o m p o n e n t s and ultra low-loss optical fibres. Their compositions are briefly reviewed in table 3. They exhibit relatively high fluorine ion conductivities and have been suggested as likely candidates for solid electrolytes [31]. Fluorine conductivity was confirmed on fluorozirconate glasses by the T u b a n d t test [32].
3. Data and striking features 3.1. D a t a
Fig. 2 shows an Arrhenius plot of conductivity measurements carried out on lithium and silver a m o r p h o u s electrolytes. All the data shown have come from
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291
t(°c)
IE
t3
2
3
4 10 3 ..-1',
~-- (,,
j
Fig. 2. Arrhenius diagram of conductivity for various glasses [33]. 1, AgPO 3 AgI; 2, Ag2MoO4 Agl; 3, AgPO3-AgBr; 4, GeS2-GeS AgI; 5, As2S 3 AgeS: 6, GeS: Li2S: 7, LiTaO~: 8, B:O~ LiCk 9, LiPO~ LiBr; 11, SiO2-Li20-Li2SO4; 12, P2Ss LieS-LiE
investigations within the past five years. At room temperature, the conductivity values are spread over more than 10 orders of magnitude though fig. 2 does not include much less conductive glasses (e.g. simple binary oxide glasses). Silver glasses (and copper glasses to a lesser extent) exhibit higher conductivities than alkali glasses. The performances of amorphous electrolytes are quite comparable to those of the best ionic conductive crystals. At the present time, silver conductivities in glasses are one order of magnitude below the best conductivity exhibited by the superionic-conductor RbAg415 (fig. 3). As a result of the research to improve ionic conductivity in glasses, the best lithium solid state conductor is a
D. Rauaine
292
-- 500
T(°c)
;~O0
f',,
,,L
",,
/ Ionic transport properties in glasses 100 ,
50
2,~
O0
-20
~RbAg415
I I , I ""L
o
? o
ssAg2~ \
\ 1,5
2
2,5
3,5 103(K1) "I'-
Fig. 3. Arrhenius diagram of conductivityfor silver conductingsolids [71]. glass ([30]), also in fig. 2) with a RT conductivity value of 10 3 (~ cm) -1. In any case, the search for highly conducting materials will be limited to a RT upper limit which can be estimated to be close to 1 ([2 cm) -1 (conductivity value of a molar solution of KC1 in water). Doped sulfide glasses have already been successfully tested in solid state cells [34,35] and they now appear as the most promising materials for solid state high energy batteries [36]. This remarkable improvement in glass conductivities has been obtained in less than ten years. It has been the result of several contributions: the replacement of oxygen by sulphur, the introduction of salts in base-glasses and the use of the maximum in conductivity observed when mixing two glass formers like in borophosphate glasses. The improvement in conductivity due to the first effect is always higher
D. Ra~aine / Ionic transport properties in ,glasses
293
Table 4 C o n d u c t i v i t i e s and a c t i v a t i o n energies for glasses c o n t a i n i n g salt additives o at 25°C (~2 1 cm
kiPO~ 0.7 LiP()~ + 0 . 3 LiCI 0.7 l,iP()~ + 0.3 LiBr 0.7 LiPO~ + 0 . 3 Lil
2x10-9 1 ×10 v 3 × 10 " v 3 × 10 -¢'
{t.70 0.60 0.55 0.52
1.1 × 1 0 a 1 . 0 × 1 0 -a
{).31
0.33 PeS5 + 0 . 6 6 L i e S 0.29 A + 0 . 7 1 Lil
A
(}lass c o m p o s i t i o n
o at 2 0 0 ° C (f~
{).64 B203 + 0 . 3 6 L i : O - B 0.54 B + 0 . 4 6 LiC1 0.62 B + 0 . 3 8 k i 2 S O 4
2 × 10- e' 2.5×10 3 4 × 10 -4
i cm
i)
Eo (eV)
Glass composition
1
Eo (eV) 0.72 0.46
than one order of magnitude. As a general trend, it appears that the smaller the difference in electronegativity between the modifier cation and the anion, the higher is the conductivity. This trend could also be suggested from considerations of the effectiveness of the non-bridging anions to trap the mobile cations. A few examples of doping effects are given in table 4. Its magnitude depends on the nature of the support glass (higher for borate glasses), thc halide size (higher for larger size anion), and the doping content (limited by the occurrence of partial crystallisation). Finally, conductivity maxima have been observed in the 40R,O .vB20~ ( 6 0 - x)PeOy(R = Li, Nay glass systems [72]. Starting from the alkali borate glass composition (x = 60), the conductivity increases by more than two orders of magnitude at 90°C. Considerations of the formation of BPO 4 and B O 4 groups have been underlined to interpret this property. The progressive replacement of one oxyanion by another can also lead to the appearance of a minimum in conductivity' like in phosphovanadate glasses and no general rulcs tire still available to a priori estimate the sign and the amplitude of lhe conductivity variations. Nevertheless this property has been used for the optimization of sulfide glass compositions. On the other hand, only a slight increase in ionic conductivity has been observed when mixing two halogenated anions [73]. 3.2. Features
The electrical conductivity of a glass is largely dependent on the concentration of its constituents. A simple example is given by the SiO,- Na~O system where increasing the concentration per unit volume of sodium atoms by a factor of 5 multiplies the conductivity by a factor 2000. The same behaviour is found in more complex glasses as shown in fig. 4 for silver conducting glasses.
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D. Ravaine / l o n i c transport properties in glasses
t~ I
I
I
I
I
I
-21.
-3
-4
• Ag2S- G e S 2 • Ag2S-As2S3 -5
Agl-
" A g 2 S - P2S5 Ag2S-As2S3 D A g 2 0 _ P205
-6
• Ag20-MoO 3
10
20
Fig. 4. Conductivity (~
30
40
50
60
(moles~)~Agl)
~ cm - t ) versus Agl content for various glass systems [63].
Such large effects of compositions can be considered as a unique feature among solid electrolytes. Considering that the conductivity is given by the product of the mobility and the charge carrier concentrations, only two ways are suitable for interpretation: either the mobility sharply increases, or the mobile ion concentration varies considerably which in turn implies that only part of the existing cations are free to move. Another feature of glass conductivity is the well known mixed alkali effect. It refers to a large deviation from linearity in glass conductivities as a function of composition as one alkali ion is replaced by another one. Although the effect is not unique in glasses, it is always associated with a structure exhibiting a high degree of disorder, like in /~-alumina [37,38] or in hydrate melts [39].
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295
4. Theoretical considerations on ion transport in glasses 4.1. Microscopic approach The classical microscopic approach of ionic transport in solids is a hopping mechanism. For a one-dimensional potential profile, the jump frequency is given by: v = vo e x p ( - E m / k T ),
(1)
where v0 is the attempt frequency corresponding to the oscillation frequency of the cation about an equilibrium position and E m the barrier height. Under an external electrical field E, the potential profile is slightly skewed and the jump frequency is split accordingly to the forwards direction, v, and the backwards direction, .v, with:
Um + zZefeP v = v0 e x p -
kT
'
(2)
where a is the jump distance and ze the particle charge. The average velocity, v, is given by: v = a(v. - . v ) .
(3)
In the linear approximation: azelEI > << kT, eq. (3) becomes: a2ze v= ~
( Em] Ely o exp - k T ] "
(4)
The conductivity, o, is given by: o = Czev/IEI,
(5)
where C is the concentration of mobile charge carriers per unit volume. Combining eqs. (4) and (5), the conductivity for a three dimensional network is: a2z2e 2
o-
6 k----~Cv° e x p ( - E m / k T ) "
(6)
When estimations of the preexponential term are possible (% lies in the vibrational frequency range of 10n-1013 Hz [40]), the calculated values always lie a few orders of magnitude below the experimental value [41]. The hopping mechanism appears to be oversimplified for the description of the conduction process in glasses. Correlation effects between consecutive jumps, local field considerations or ionic dissociation analogies for the calculation of mobile ion concentration have to be taken into account. Different attempts have been made to consider the random network of glass structure. Stevels [42], and Taylor [43] proposed a model in which there are potential barriers of various heights. It was assumed that for DC conduction the highest energy barrier had to be overcome, while for AC conduction the
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296
migration across the limited distance overcoming the lower energy barrier was responsible. Charles [44] postulated the existence of a number of equivalent positions for an alkali ion around each non-bridging oxygen. Different processes of alkali migration can take place involving defect formation (two alkali ions on the same NBO) and polarization (rotation of an alkali ion around one NBO). Quantitatively, the defect concentration is calculated using the procedure for estimating the point defect concentration in ionic crystals. These models imply the existence of dielectric relaxation effects in glasses. Actually, many papers deal with dielectric phenomena [45], including field distribution in inhomogeneous glass structure [46], and relaxation processes involving diffusion of defects [47]. They all invoke an ion migration mechanism over long distances. As mentioned in different papers [48,49], the low frequency dielectric characteristics are often difficult to obtain because of the DC conductivity contribution, which is the major portion of the loss, and which has to be subtracted from the total dielectric loss. From this point of view, the impedance spectroscopy method to investigate the AC electrical properties of ionically conducting glasses has brought a major contribution for the understanding of relaxation losses at low frequencies [50,51]. Other techniques have been used to investigate alkali-ion motion in silicate glasses, such as: tracer diffusion coefficient measurements [52,54] and thermally stimulated currents [55,56]. The values obtained for the correlation factor and the Haven ratio have been discussed using analogies with proposed diffusion mechanisms in crystalline solids. The overall picture of alkali diffusion is that, at low temperatures, the alkali ions diffuse by a 2-atom interstitialcy mechanism; as the temperature increases, a larger fraction of the alkali ions diffuses individually by a vacancy mechanism which consists of an alkali on a lattice site jumping to a vacancy at one of the 6 nearest-neighbor alkali lattice sites. 4.2. W e a k electrolyte m o d e l
These microscopic descriptions of conduction mechanisms in glasses are unable to predict or to explain the large variations observed for glass conductivities versus composition. Thermodynamic considerations are much more appropriate to provide an interpretation when large composition ranges are available for investigation. The conductivity of all electrolytes is given by the sum: o = ZCzeu,
(7)
where u is the mobility of ions of charge z e and concentration per unit volume C. If all the alkali (or silver ions) are equally mobile, then the situation is analogous to the complete dissociation of strong electrolytes in aqueous solution. If however the number of mobile ions is less than the stoichiometric concentration, then such glasses can be regarded as weak electrolytes. Earlier
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297
support for the weak electrolyte model in glasses came from Myuller [57] who postulated the formation of Frenkel defects, Proctor and Sutton [58] who studied space charge development in glass, and Haven and Verkerk [53] who discussed evidence for the interstitialcy mechanism in cationic transport. Let us consider conductive glasses as solid solutions in which the network former components or the doping salts, behave as weakly dissociated electrolyres; we can then write the following dissociation equilibria: M~O~M++OM which implies [M ~ ] =
K'/2a~2o
(8)
or (for doped glasses): MX ~ M + + X which in turn implies: [ M + ] = K 1 / 2 " ,I,2 MX,
(9)
where [M +] is the concentration of dissociated ions, K the dissociation constant (independent of concentration) and aM_,O, aMX the thermodynamic activities of the corresponding glass components. Although such an approach does not provide any description of the physical state of these species, M + may be regarded as dissociated "free" alkali (or silver) ions, M20 as trapped entities and OM as vacancies in the vicinity of non-bridging oxygens. Since only the first kind of species mentioned are able to move under an applied electric field, it is tempting experimentally to correlate the conductivity variations to those of thermodynamic quantities. This has been done for different silica glasses [9]: the ratios of the thermodynamic activities of two different glass compositions have been obtained from concentration cell emf measurements. Fig. 5 shows a plot of these ratios versus the corresponding ratios of the
~i~
I
I
I
2
o I
./'" /
I I
,
I 2
,
I 3
J
log/a,
Fig. 5. Conductivit) ratio versus activity ratio for various pairs of glasses [9 I.
D. Ravaine / Ionic transport properties in glasses
298
electrical conductivities for various pairs of glasses. In logarithmic scales, they fit a linear relationship, according to: [a(l) /~(2) ] 1/2 ol/o2= t M2°'"~2°1 " (10) A similar relation has been observed from calorimetric measurements for AgX (X = C1, Br, I)-doped phosphate glasses [59]. As a consequence of eqs. (7) and (8), relation (10) suggests that the mobility of the free ions is independent of concentration for a given glass system.
4.3. Using the weak electrolyte model 4.3.1. Temperature dependence for the conductivity From eqs. (7) and (8), the activation energy for conduction, Eo, can be calculated as a linear combination of three t e r m s : E m (migration energy corresponding to the activation energy for the mobility), H d (activation energy of the dissociation constant, independent of the concentration), HM2o (partial free enthalpy for the component M20): E°=Em+
Hd - AHM2o 2
(11)
Using a quasi-chemical model for calculating the mixing enthalpy, we can deduce AHM2o and estimate the concentration dependence of Eo. For sodium and potassium glass systems, it has been shown that they agree well with experimental variations of Eo [60] (fig. 6).
4.3.2. Observation of conductivity maximum Although in most glasses conductivity increases with the mole fraction of alkali, a maximum conductivity has been observed in ultra-fast quenched oxide glasses [24] and in boro-aluminate glass systems [61]. The structure of tantalate and niobate glasses is made of a random array of corner linked octahedra. The concentration of NBO's is a minimum for a L i / N b ratio value of 0.5, corresponding to the formula: 2[Nb 06/2 -- El] = Yb205 - Li20. At this concentration level, the disappearance of NBO's moves the dissociation equilibrium (eq. (8)) to the right hand side, and a maximum in mobile ion concentration and in conductivity may be expected in accordance with the experimental observation [24].
4. 3. 3. Mixed alkali effect A weak electrolyte model for the mixed alkali effect on electrical conductivity in glass has been developed for the dilute foreign alkali region [62]. It has been proposed that adding small amounts of foreign alkali leads to the formation of alkali-foreign alkali interstitial pairs which, by mass action, suppresses the mobile species concentration.
D. Ravaine / Ionic transportproperties in glasses
[
I
1
299
I
\
0
o
E
~---1 Ill
ILl
~3
--4
--
1
I
1
0.6
0.7
0.8
t X
0.9
Fig. 6. Comparison of calculated and experimental values of Eo for xSiO2 (1 x) Na20 gla~se~ [~o1. Kone et al. [74] show that a good agreement with experimental data can be obtained over the full range of mixed glass composition using a weak electrolyte description and with the assumption of low mobility complexes formation.
5. O u t s t a n d i n g p r o b l e m s and future d e v e l o p m e n t 5.1. Present problems
They mostly concern fundamental aspects. 5.1.1. Abou: the weak electrolyte theory
The weak electrolyte theory has been a very powerful tool to explain the variation in conductivity in many glass systems and also for proposing some new glass compositions to be investigated. But this theory is only a thermodynamic approach and the question arises of the applicability of a liquid model
300
D. Ravaine / Ionic transport properties in glasses
to glasses. The analogy with liquid weak electrolytes only holds if there are no structural limiting factors. This implies that eqs. (8) and (9) can be used to calculate the concentration of mobile ions if the number of available interstitial sites for the dissociated ions in the rigid glass network is large. It has been recently proved that up to 30% of sodium atoms per phosphorus atoms can be chemically intercalated in a phospho-vanadate glass without noticeable change in volume [8]. This proves the existence of energetically suitable interstitial sites for the alkali ions and gives some consistency to the applicability of the weak electrolyte model in glasses. But we need further investigation to identify these sites and to characterize the ion distribution over them. We need also physical experiments to show that only part of the ions are mobile and to describe the exchange mechanism between the trapped and the mobile ions.
5.1.2. Mixed alkali effect Although many interesting models have been developed to interpret this effect, there is still no generally accepted satisfactory explanation. For instance no direct proof for the formation of static alkali foreign alkali pairs has been given. 5.1.3. Doping effect A specific property has been observed in doped glasses: at very high concentrations of a given doping salt, experimental conductivity values all approach the same limit whatever the vitreous support [30,63] as shown by results collected in fig. 4 for silver iodide doped systems. Minami et al. [64], then Schiraldi [20], have proposed that the addition of AgI would lead to the formation of metastable microdomains of the AgI superionic conducting phase which would become joined as soon as their volume occupied about 70% of the total volume. Many crystalline compounds show superionic conducting phase transition at high temperature: it would therefore be interesting to test the validity of this model by stabilizing these superionic conducting phases in vitreous matrices. Another interpretation is based on a displacement of silver ions simply by rotating from one anion to another without loss of contact [63]. This displacement would take place as soon as the distance between the anions is close to 5
~.. Structural investigation in connection with the use of the concepts of the percolation theory should throw some light on this interesting property.
5.1.4. Decrease in conductivity with increasing alkali content A few examples have been given in the last section. This phenomenon is certainly related to the change of the network former cation symmetry when increasing the O / M ratio. Here again there is no structural evidence and only preliminary studies have been carried out.
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5.1.5. Anionic transport mechanism in fluoride glasses
The electrical properties of a wide range of fluoride glass compositions have recently been investigated [31,65]. N M R data [66] have shown the existence of local motions of low activation energies (0.2 eV) which disappear in the recrystallized samples. Point defects are not expected to play an important role in these disordered structures. Local motions should be mostly associated with a translocation mechanism in which two neighbouring metal cations exchange their coordinating polyhedra simultaneously with the jumping of the fluoride ion. Such a process would require a much higher energy barrier to be overcome in a well ordered crystalline phase. Long range displacements involve structural relaxations of the network which can account for the high activation energies (0.8 eV) observed for the conductivity. There is some similarity with the protonic conduction mechanism since in both cases the moving ions are part of the network forming species. However, all of these are proposed ideas and the anionic transport mechanism in fluoride glasses can in no way be considered as a solved problem. 5.2. Future development
In the future we should observe an increasing interest for protonic conduction in glasses. Although the glass literature is full of references to proton transport, by diffusive exchange with other monovalent cations, electromigration or mixed alkali effect induced by water (for basic references, see e.g. ref. [67]), very little is reported on protonic bulk conductivity in glasses [68]. Another area to be developed is the extension for the choice of available doping agents to low decomposition temperature or low melting temperature salts through the use of a "soft" method of glass synthesis. Interesting preliminary results show that alkali silicate dried gels behave as alkali conductive materials at temperatures corresponding to the pyrolisis of the organic residues [69]. The sol-gel process can also be of interest for the prepration of a wide range of new amorphous compounds, like the ORMOSILS (ORganic MOdified SILicateS) and provide new ways to obtain thin film layers by simple techniques (dipping, spinning ... ). Finally a great deal of research is expected to be developed during the next decade on the intercalation phenomena in amorphous semiconductors. A few experiments have already shown that semiconductive glasses can be lithiated through an insertion reaction [8,70]. They are now considered as possible candidates for positive electrode materials in lithium batteries. This opens the way for making monolithic vitreous batteries. By 2004, all integrated electronic circuits will be certainly powered by implanted vitreous microbatteries...
References
[1] G. Warburg, Ann. Phys. 21 (1884) 622. [2] G.W. Morey, The Properties of Glass, (Van Nostrand Reinhold, Princeton, 1954).
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D. Ravaine / Ionic transport properties in glasses
[3] K. Hughes and J.O. Isard, The Ionic Transport in Glasses, in Physics of Electrolytes, ed., J. Hladik (Academic Press, New York, 1972). [4] H.L. Tuller, D.P. Button and D.R. Uhlmann, J. Non-Crystalline Solids 40 (1980) 93. [5] A. Levasseur, J.C. Brethous, J.M. Reau and P. Hagenmuller, Mater. Res. Bull. 14 (1979) 921. [6] B. Barrau, M. Ribes, M. Maurin, A. Kone and J.L. Souquet, J. Non-Crystalline Solids 38/39 (1980) 271. [7] J.P. Malugani and G. Robert, Solid St. Ionics 1 (1980) 519. [8] T. Pagnier, M. Fouletier and J.L. Souquet, Solid St. Ionics 9-10 (1983) 649. [9] D. Ravaine and J.L. Souquet, Phys. Chem. Glasses 18 (1977) 27. [10] D.E. Day, J. Non-Crystalline Solids 21 (1976) 343. [11] M.D. Ingram, C.T. Moynihan and A.V. Lesikar, J. Non-Crystalline Solids 38-39 (1980) 371. [12] A.E. Owen, Prog. Ceram. Sci. 3 (1963) 77; D. Ravaine and J.L. Souquet, Ionic Conductive Glasses, in: Solid Electrolytes (Academic Press, New-York, 1978) p. 277. [13] J.P. Malugani and G. Robert, Mat. Res. Bull. 14 (1979) 1075. [14] A. Levasseur, M. Kbala, J.C. Brethous, J.M. Reau, M. Couzi and P. Hagenmuller, Solid St. Commun. 32 (1979) 839. [15] K. Otto, Phys. Chem. Glasses 7 (1966) 29. [16] J.P. Malugani, A. Wasniewki, M. Doreau, G. Robert and A. AI Rikabi, Mat. Res. Bull. 13 (1978) 427. [17] T. Minami, T. Shimizu and M. Tanaka, Solid St. Ionics 9/10 (1983) 577. [18] F. Bonino, M. Lazzari, A. Lonardi, B. Rivolta and B. Scrosati, Solid St. Chem. 20 (1977) 315. [19] M. Lazzari, B. Scrosati and C.A. Vincent, J. Am. Ceram. Soc. 61 (1978) 451. [20] A. Schiraldi, Electrochim. Acta 23 (1978) 1039. [21] T. Minami and M. Tanaka, J. Non-Crystalline Solids 38/39 (1980) 289. [22] A.M. Glass, K. Nassau and T.J. Negran, J. Appl. Phys. 49 (1978) 4808. [23] A.M. Glass and K. Nassau, J. Appl. Phys. 51 (1980) 3756. [24] K. Nassau, A.M. Glass, M. Grasso and D.H. Olson, J. Electrochem, Soc. 127 (1980) 2743. [25] K. Nassau, A.M. Glass, M. Grasso and D.H. Olson, J. Non-Crystalline Solids 46 (1981) 45. [26] D. Ravaine, K. Nassau and A.M. Glass, Solid St. Ionics 13 (1984) 15. [27] B. Barrau, J.M. Latour, D. Ravaine and M. Ribes, Silicates Ind. 12 (1979) 275. [28] M. Ribes, D. Ravaine, J.L. Souquet and M. Maurin, Rev. Chim. Min. 16 (1979) 339. [29] B. Carette, E. Robinel and M. Ribes, Glass Techn. 24 (1983) 157. [30] G. Robert, J.P. Malugani and A. Saida, Solid St. Ionics 3 / 4 (1981) 311. [31] D. Leroy, J. Lucas, M. Poulain and D. Ravaine. Mater. Res. Bull. 13 (1978) 1125. [32] D. Ravaine and D. Leroy, J. Non-Crystalline Solids 38 (1980) 353. [33] J.L. Souquet, Ann. Rev. Mater. Sci. 11 (1981) 211. [34] B. Carette, M. Maurin, M. Ribes and M. Duclot, Solid St. Ionics 9/10 (1983) 655. [35] J.P. Malugani, B. Fahys, R. Mercier, G. Robert, J.P. Duchange, S, Baudry, M. Broussely and J.P. Gabano, Solid St. Ionics 9/10 (1983) 659. [36] J.P. Gabano, Nato ASI Series: Glass Current Issues (1985) 457. [37] M.D. Ingram and C.T. Moynihan, Solid St. Ionics 6 (1982) 303. [38] C.C. Hunter, M.D. Ingram and A.R. West, Solid St. lonics 8 (1983) 55. [39] C.T. Moynihan, J. Electrochem. Soc. 126 (1979) 2144. [40] C.J. Exarhos and W.M. Risen, Solid St. Comm. 11 (1972) 755. [41] A. Doi, J. Non-Crystalline Solids 29 (1978) 131. [42] J.M. Stevels, in: Handbuch der Physik 20 (Springer, Berlin, 1957) p. 350. [43] H.E. Taylor, J. Soc. Glass Tech. 41 (1957) 350; 43 (1959) 124. [44] R.J. Charles, J. Appl. Phys. 32 (1961) 1115. [45] M. Tomozawa, in: Treatise on Mater. Sci. and Tech. 12 (Academic Press, New York, 1977) p. 283. [46] J.O. Isard, Proc. Instn. Electr. 44 (1962) 109B. [47] R.M. Hakim and D.R. Uhlmann, Phys. Chem. Glasses 14 (1973) 81. [48] M. Tomazawa, J. Cordaro and M. Singh, J. Mater. Sci. 14 (1979) 1945. [49] J.F. Cordaro and M. Tomozawa, J. Am. Ceram. Soc. 64 (1981) 713.
D. Ravaine / Ionic transport properties in glasses [50] [51] [52] [53] I54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69]
[70] [71] [72] [73] [74]
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D. Ravaine and J.L. Souquet, J. Chim. Phys. 5 (1974) 693. D. Ravaine, J. Non-Crystalline Solids 49 (1982) 507. R. Terai and R. Hayami, J. Non-Crsytalline Solids 18 (1975) 217. Y. Haven and B. Verkerk, Phys. Chem. Glasses 6 (1965) 38. C. Lim and D.E. Day, J. Am. Ceram. Soc. 60 (1977) 198. C.M. Hong and D.E. Day, J. Am. Ceram. Soc. 65 (1982) 2493. A.K. Agarwal and D.E. Day, J. Am. Ceram. Soc. 65 (1982) 111. R.L. Myuller, Sov. Phys. Solid State 2 (1960) 1213. T.M. Proctor and P.M. Sutton, J. Am. Ceram. Soc. 43 (1960) 173. J.C. Reggiani, J.P. Malugani and J. Bernard, J. Chem. Phys. 75 (1978) 849. D. Ravaine and J.L. Souquet, Phys. Chem. Glasses 19 (1978) 115. S.W. Martin, E.I. Cooper and C.A. Angell, Am. Ceram. Soc. Spring Meeting, Abstr. 87-6-83 (1982). C.T. Moynihan and A.V. Lesikar, J. Am. Ceram. Soc. 64 (1981) 40. E. Robinel, B. Carette and M. Ribes, J. Non-Crystalline Solids 57 (1983) 49. T. Minami, H. Nambu and M. Tanaka, J. Am. Ceram. Soc. 60 (1977) 467. D. Ravaine, W.G. Perera and M. Poulain, Solid St. tonics 9/10 (1983) 631. D. Ravaine, W.G. Perera and M. Minier, J. de Phys. 43 (1982) C9-407. F.M. Ernsberger, J. Non-Crystalline Solids 38/39 (1980) 557. I.M. Hodge and C.A. Angell, J. Chem. Phys. 67 (1977) 1647. D. Ravaine, J. Traore, L. Klein and I. Schwartz, Proc. 1984 Meeting of the MRS, Better Ceramics through Chemistry, Material Research Society Series 32 (Elsevier, Amsterdam, 1984). A.C. Leech, J.R. Owen and B.C.H. Steele, Solid St. lonics 9-10 (1983) 645. J.L. Souquet, Solid St. Ionics 5 (1981) 77. T. Tsuchiya and T. Moriya, J. Non-Crystalline Solids 38/39 (1980) 323. B. Carette, M. Ribes and J.L. Souquet, Solid St. Ionics 9/10 (1983) 7351. A. Kone, J.C. Reggiani and J.L. Souquet, Solid St. Ionics 9/10 (1983) 709.
287
IONIC T R A N S P O R T P R O P E R T I E S IN GLASSES D. RAVAINE Laboratoire d'Energ~tique Electrochimique, LA C N R S 265, ENSEEG, BP 75. 38402 Saint Martin d'Hbres, France
The different glass compositions which exhibit ionic transport properties in the oxide, sulfide and fluoride systems, are presented. The main data concerning the conductivities and actiwition energies for conduction are given and compared to those of the best superionic conductors. The available models on ion transport in glasses are briefly discussed and the applicability' of the weak electrolyte theory emphasized. Future development concerns protonic conduction in glasses and "'sofl" methods for synthesis of new glass compositions.
1. Introduction
The ionic character of the conductivity in oxide glasses was established a century ago when Warburg experimentally demonstrated the transport of sodium between two amalgams separated by a glass membrane [1]. In the meantime, many experimental results concerning traditional oxide-glasses have been collected [2-4]. The conductivity of these glasses is cationic and highest for alkali and silver cations. Until about ten years ago, the best results in conductivity were around 10 s (f~ cm) -1 at room temperature which made ionic conductive glasses suitable only for very specific applications, such as glass membranes in pH sensitive electrodes. Recent progress and practical requirements have now focused more attention on glassy electrolytes. New sulfide glasses and doped inorganic glasses have led to much higher conductivities than traditional oxide-based glasses, from 10 5 to 10 3 (~2 cm) -1 at ambient temperature for some lithium conductive glasses [5-7]. In a short time, glasses have been synthesized that achieve performances comparable to those of the best solid electrolytes. In the field of battery applications, glasses offer a large number of advantages over crystalline solids. First. the ionic conductivity is isotropic and does not involve any gain boundary effects like in polycrystalline materials. Also, the electronic contribution to the total conductivity is usually very weak which is a consequence of the aperiodic potential fluctuations imposed by the disordered structure. Moreover, metal impurities are unable to enhance the electronic conductivity since they can exist in their own distinct local environment in the glass structure. Electronic leakage is then unlikely to occur in electrochemical devices using a glass membrane as an ionic separator. From a practical point of view, glasses have the advantage of being easilv obtainable in thin film configurations; layered microbatteries can then be 0022-3093/85/$03.30 < Elsevier Science Publishers B.V. INorth-Holland Physics Publishing Division)
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D. Ravaine / Ionic transport properties in glasses
expected in the near future by using thin film glassy electrolytes. Extremely good contacts can be obtained between electrode materials and ionic conductive glasses of low glass transition temperatures Tg: this condition is expected to be especially critical for intercalation-type electrodes whose volume varies during charge-discharge cycles. Finally, one of the interesting features of glasses as electrochemically active materials is the possibility of continuously changing the composition through appropriate techniques. Bulk glass samples can be obtained with ionic transport properties at one end and electronic transport properties at the other end of the sample. Promising results have been obtained by the chemical intercalation of alkali ions in a phospho-vanadate glass [8]. This opens the way to make a compact battery with improved performance through the delocalization of the electrode/electrolyte interfaces. From a more fundamental point of view, varying the composition has been widely used as a means to investigate the ionic transport properties in glasses. This has led to an original approach to the interpretation of the ionic conduction mechanism in solid state conductors based on the existence of dissociation equilibria. The applicability of the weak electrolyte theory to glassy electrolytes [9] has attracted a revival of interest for the interpretation of poorly understood results like the mixed alkali effect [10], the magnitude of conductivity variations with the concentration of network modifiers or the electric field dependence [11].
2. Ionic conductive glass compositions 2.1. Oxide glasses In table 1 are summarized the different oxide glass compositions which are known to exhibit ionic transport properties. These are by far the most studied among amorphous electrolyte materials [2-4,12]. For simple glass composi-
Table 1 Oxide glass compositions Mobile ion
Ag +
Usual glass former cation
Si,
M+ (M = Li, Na, K... ) Ge,
B,
Unusual glass former cation
P,
AI.., Ta, Nb, W, Mo, La, Ga (ultrafast quenched)
Mo, As, Cr, W, Se, Te, V (quenched)
Doped by AgX or MX X = halides and sulfate X = CI and Br
X = halides and sulfate
289
D. Ravaine / Ionic transport properties in glasses
,o
@ o
O@o@o £ o < o .,,,o....
o . .
,o
@O o@o
o
(a) (h~ (c) Fig. 1. Schematic structure representation [71] for: (a) AgPO~ glass: (b) AgPO~-Agl glass: Ict Ag2 MoOa-Agl glass.
tions, such as binary network former/network modifier oxides, three dimensional covalent macromolecules are formed by an assembly of elementary units (SiO 4, BO4, PO4... tetrahedra) in which at least one atom of oxygen is shared (BO's). Some oxygen atoms that are non bridging (NBO's) are negatively charged keeping in their vicinity the alkali or silver (M) cations introduced by the network-modifier oxide (fig. la). Vitreous domains involving a wide concentration range in cation (M) content are obtained by dissolving alkali or silver salts in oxide-base glass in order to increase the number of charge carriers [13-17]. In that case, only large size anions (halides, sulfate) can be incorporated without affecting the macromolecular structure of the glassy network (fig. lb). For this reason, the term "doped" has been used to describe these types of more complex glass compositions although, in some cases, very high levels (up to 80 m / 0 ) of doping level can be attained [18]. For some silver glass compositions, this expression is not related to any structural evidence: due to the higher glass forming ability of silver glass, rapid quenching techniques can be used to obtain glass formation with unusual glass formers (see table 1) [19]. The addition of extra-silver salt leads to a disordered structure made of discrete anions (iodides, molybdates ... ) in which the doping agents are not discernible (fig. lc) [20,21]. Finally, unusual glass formers have also been used to obtain alkali conductive glasses. In that case, ultra-fast quenching techniques are necessary. (.}lass formation has been observed in systems of tantalates and niobates [22], aluminates, gallates and bismuthates [23], tungstate and molybdates [24], and sulfates [25]. Unlike the other glass systems, only small amounts of alkali sails can be incorporated before the occurrence of partial crystallisation [26]. 2.2. Sulfide glasses
Table 2 gives the different glass compositions investigated in the sulfide systems. Due to their hygroscopicity, the synthesis of sulfide glasses needs special attention. For this reason, the history of sulfide glasses is more recent [27] and the list of studied compositions is much less exhaustive than that of oxide glasses.
290
D. Ravaine / Ionic transport properties in glasses
Table 2 Sulfide glass compositions M+ (M = Li, Na, K... )
Doped by AgX or MX
Mobile ion
Ag+
Usual glass former cation
Si, Ge, B,
X = halides (excepted F)
Unusual glass former cation
As, Ga, La, Sb
X = halides (excepted F)
Table 3 Fluoride glass compositions Mobile ion Glass former
Additives
F Be, Zr, Hf Th, Sc, U transition metals rare earths Ba, AI, Y, Yb M(Li, Na, Rb... )
Nevertheless, the glass forming ability of the c o m m o n , as well as unusual (excepted for alkali glasses) glass formers has been tested in the sulfide systems, along with silver or alkali halide additions [28-30]. Transport n u m b e r measurements performed on N a z S - S i S 2 and N a 2 S - G e S 2 glass compositions show that the electronic contribution to the conductivity is quite negligible [27] and confirm the ionic character of the conduction in sulfide glasses. 2.3. Fluoride glasses
These glasses are currently under considerable development mainly because of their potential use for making infrared optical c o m p o n e n t s and ultra low-loss optical fibres. Their compositions are briefly reviewed in table 3. They exhibit relatively high fluorine ion conductivities and have been suggested as likely candidates for solid electrolytes [31]. Fluorine conductivity was confirmed on fluorozirconate glasses by the T u b a n d t test [32].
3. Data and striking features 3.1. D a t a
Fig. 2 shows an Arrhenius plot of conductivity measurements carried out on lithium and silver a m o r p h o u s electrolytes. All the data shown have come from
D. Ravaine / Ionic' transport properties in glasses
291
t(°c)
IE
t3
2
3
4 10 3 ..-1',
~-- (,,
j
Fig. 2. Arrhenius diagram of conductivity for various glasses [33]. 1, AgPO 3 AgI; 2, Ag2MoO4 Agl; 3, AgPO3-AgBr; 4, GeS2-GeS AgI; 5, As2S 3 AgeS: 6, GeS: Li2S: 7, LiTaO~: 8, B:O~ LiCk 9, LiPO~ LiBr; 11, SiO2-Li20-Li2SO4; 12, P2Ss LieS-LiE
investigations within the past five years. At room temperature, the conductivity values are spread over more than 10 orders of magnitude though fig. 2 does not include much less conductive glasses (e.g. simple binary oxide glasses). Silver glasses (and copper glasses to a lesser extent) exhibit higher conductivities than alkali glasses. The performances of amorphous electrolytes are quite comparable to those of the best ionic conductive crystals. At the present time, silver conductivities in glasses are one order of magnitude below the best conductivity exhibited by the superionic-conductor RbAg415 (fig. 3). As a result of the research to improve ionic conductivity in glasses, the best lithium solid state conductor is a
D. Rauaine
292
-- 500
T(°c)
;~O0
f',,
,,L
",,
/ Ionic transport properties in glasses 100 ,
50
2,~
O0
-20
~RbAg415
I I , I ""L
o
? o
ssAg2~ \
\ 1,5
2
2,5
3,5 103(K1) "I'-
Fig. 3. Arrhenius diagram of conductivityfor silver conductingsolids [71]. glass ([30]), also in fig. 2) with a RT conductivity value of 10 3 (~ cm) -1. In any case, the search for highly conducting materials will be limited to a RT upper limit which can be estimated to be close to 1 ([2 cm) -1 (conductivity value of a molar solution of KC1 in water). Doped sulfide glasses have already been successfully tested in solid state cells [34,35] and they now appear as the most promising materials for solid state high energy batteries [36]. This remarkable improvement in glass conductivities has been obtained in less than ten years. It has been the result of several contributions: the replacement of oxygen by sulphur, the introduction of salts in base-glasses and the use of the maximum in conductivity observed when mixing two glass formers like in borophosphate glasses. The improvement in conductivity due to the first effect is always higher
D. Ra~aine / Ionic transport properties in ,glasses
293
Table 4 C o n d u c t i v i t i e s and a c t i v a t i o n energies for glasses c o n t a i n i n g salt additives o at 25°C (~2 1 cm
kiPO~ 0.7 LiP()~ + 0 . 3 LiCI 0.7 l,iP()~ + 0.3 LiBr 0.7 LiPO~ + 0 . 3 Lil
2x10-9 1 ×10 v 3 × 10 " v 3 × 10 -¢'
{t.70 0.60 0.55 0.52
1.1 × 1 0 a 1 . 0 × 1 0 -a
{).31
0.33 PeS5 + 0 . 6 6 L i e S 0.29 A + 0 . 7 1 Lil
A
(}lass c o m p o s i t i o n
o at 2 0 0 ° C (f~
{).64 B203 + 0 . 3 6 L i : O - B 0.54 B + 0 . 4 6 LiC1 0.62 B + 0 . 3 8 k i 2 S O 4
2 × 10- e' 2.5×10 3 4 × 10 -4
i cm
i)
Eo (eV)
Glass composition
1
Eo (eV) 0.72 0.46
than one order of magnitude. As a general trend, it appears that the smaller the difference in electronegativity between the modifier cation and the anion, the higher is the conductivity. This trend could also be suggested from considerations of the effectiveness of the non-bridging anions to trap the mobile cations. A few examples of doping effects are given in table 4. Its magnitude depends on the nature of the support glass (higher for borate glasses), thc halide size (higher for larger size anion), and the doping content (limited by the occurrence of partial crystallisation). Finally, conductivity maxima have been observed in the 40R,O .vB20~ ( 6 0 - x)PeOy(R = Li, Nay glass systems [72]. Starting from the alkali borate glass composition (x = 60), the conductivity increases by more than two orders of magnitude at 90°C. Considerations of the formation of BPO 4 and B O 4 groups have been underlined to interpret this property. The progressive replacement of one oxyanion by another can also lead to the appearance of a minimum in conductivity' like in phosphovanadate glasses and no general rulcs tire still available to a priori estimate the sign and the amplitude of lhe conductivity variations. Nevertheless this property has been used for the optimization of sulfide glass compositions. On the other hand, only a slight increase in ionic conductivity has been observed when mixing two halogenated anions [73]. 3.2. Features
The electrical conductivity of a glass is largely dependent on the concentration of its constituents. A simple example is given by the SiO,- Na~O system where increasing the concentration per unit volume of sodium atoms by a factor of 5 multiplies the conductivity by a factor 2000. The same behaviour is found in more complex glasses as shown in fig. 4 for silver conducting glasses.
294
D. Ravaine / l o n i c transport properties in glasses
t~ I
I
I
I
I
I
-21.
-3
-4
• Ag2S- G e S 2 • Ag2S-As2S3 -5
Agl-
" A g 2 S - P2S5 Ag2S-As2S3 D A g 2 0 _ P205
-6
• Ag20-MoO 3
10
20
Fig. 4. Conductivity (~
30
40
50
60
(moles~)~Agl)
~ cm - t ) versus Agl content for various glass systems [63].
Such large effects of compositions can be considered as a unique feature among solid electrolytes. Considering that the conductivity is given by the product of the mobility and the charge carrier concentrations, only two ways are suitable for interpretation: either the mobility sharply increases, or the mobile ion concentration varies considerably which in turn implies that only part of the existing cations are free to move. Another feature of glass conductivity is the well known mixed alkali effect. It refers to a large deviation from linearity in glass conductivities as a function of composition as one alkali ion is replaced by another one. Although the effect is not unique in glasses, it is always associated with a structure exhibiting a high degree of disorder, like in /~-alumina [37,38] or in hydrate melts [39].
D. Ravaine / Ionic transport properties in glasses
295
4. Theoretical considerations on ion transport in glasses 4.1. Microscopic approach The classical microscopic approach of ionic transport in solids is a hopping mechanism. For a one-dimensional potential profile, the jump frequency is given by: v = vo e x p ( - E m / k T ),
(1)
where v0 is the attempt frequency corresponding to the oscillation frequency of the cation about an equilibrium position and E m the barrier height. Under an external electrical field E, the potential profile is slightly skewed and the jump frequency is split accordingly to the forwards direction, v, and the backwards direction, .v, with:
Um + zZefeP v = v0 e x p -
kT
'
(2)
where a is the jump distance and ze the particle charge. The average velocity, v, is given by: v = a(v. - . v ) .
(3)
In the linear approximation: azelEI > << kT, eq. (3) becomes: a2ze v= ~
( Em] Ely o exp - k T ] "
(4)
The conductivity, o, is given by: o = Czev/IEI,
(5)
where C is the concentration of mobile charge carriers per unit volume. Combining eqs. (4) and (5), the conductivity for a three dimensional network is: a2z2e 2
o-
6 k----~Cv° e x p ( - E m / k T ) "
(6)
When estimations of the preexponential term are possible (% lies in the vibrational frequency range of 10n-1013 Hz [40]), the calculated values always lie a few orders of magnitude below the experimental value [41]. The hopping mechanism appears to be oversimplified for the description of the conduction process in glasses. Correlation effects between consecutive jumps, local field considerations or ionic dissociation analogies for the calculation of mobile ion concentration have to be taken into account. Different attempts have been made to consider the random network of glass structure. Stevels [42], and Taylor [43] proposed a model in which there are potential barriers of various heights. It was assumed that for DC conduction the highest energy barrier had to be overcome, while for AC conduction the
D. Ravaine / l o n i c transport properties in glasses
296
migration across the limited distance overcoming the lower energy barrier was responsible. Charles [44] postulated the existence of a number of equivalent positions for an alkali ion around each non-bridging oxygen. Different processes of alkali migration can take place involving defect formation (two alkali ions on the same NBO) and polarization (rotation of an alkali ion around one NBO). Quantitatively, the defect concentration is calculated using the procedure for estimating the point defect concentration in ionic crystals. These models imply the existence of dielectric relaxation effects in glasses. Actually, many papers deal with dielectric phenomena [45], including field distribution in inhomogeneous glass structure [46], and relaxation processes involving diffusion of defects [47]. They all invoke an ion migration mechanism over long distances. As mentioned in different papers [48,49], the low frequency dielectric characteristics are often difficult to obtain because of the DC conductivity contribution, which is the major portion of the loss, and which has to be subtracted from the total dielectric loss. From this point of view, the impedance spectroscopy method to investigate the AC electrical properties of ionically conducting glasses has brought a major contribution for the understanding of relaxation losses at low frequencies [50,51]. Other techniques have been used to investigate alkali-ion motion in silicate glasses, such as: tracer diffusion coefficient measurements [52,54] and thermally stimulated currents [55,56]. The values obtained for the correlation factor and the Haven ratio have been discussed using analogies with proposed diffusion mechanisms in crystalline solids. The overall picture of alkali diffusion is that, at low temperatures, the alkali ions diffuse by a 2-atom interstitialcy mechanism; as the temperature increases, a larger fraction of the alkali ions diffuses individually by a vacancy mechanism which consists of an alkali on a lattice site jumping to a vacancy at one of the 6 nearest-neighbor alkali lattice sites. 4.2. W e a k electrolyte m o d e l
These microscopic descriptions of conduction mechanisms in glasses are unable to predict or to explain the large variations observed for glass conductivities versus composition. Thermodynamic considerations are much more appropriate to provide an interpretation when large composition ranges are available for investigation. The conductivity of all electrolytes is given by the sum: o = ZCzeu,
(7)
where u is the mobility of ions of charge z e and concentration per unit volume C. If all the alkali (or silver ions) are equally mobile, then the situation is analogous to the complete dissociation of strong electrolytes in aqueous solution. If however the number of mobile ions is less than the stoichiometric concentration, then such glasses can be regarded as weak electrolytes. Earlier
D. Ra~aine / Ionic transport properties in £1asses
297
support for the weak electrolyte model in glasses came from Myuller [57] who postulated the formation of Frenkel defects, Proctor and Sutton [58] who studied space charge development in glass, and Haven and Verkerk [53] who discussed evidence for the interstitialcy mechanism in cationic transport. Let us consider conductive glasses as solid solutions in which the network former components or the doping salts, behave as weakly dissociated electrolyres; we can then write the following dissociation equilibria: M~O~M++OM which implies [M ~ ] =
K'/2a~2o
(8)
or (for doped glasses): MX ~ M + + X which in turn implies: [ M + ] = K 1 / 2 " ,I,2 MX,
(9)
where [M +] is the concentration of dissociated ions, K the dissociation constant (independent of concentration) and aM_,O, aMX the thermodynamic activities of the corresponding glass components. Although such an approach does not provide any description of the physical state of these species, M + may be regarded as dissociated "free" alkali (or silver) ions, M20 as trapped entities and OM as vacancies in the vicinity of non-bridging oxygens. Since only the first kind of species mentioned are able to move under an applied electric field, it is tempting experimentally to correlate the conductivity variations to those of thermodynamic quantities. This has been done for different silica glasses [9]: the ratios of the thermodynamic activities of two different glass compositions have been obtained from concentration cell emf measurements. Fig. 5 shows a plot of these ratios versus the corresponding ratios of the
~i~
I
I
I
2
o I
./'" /
I I
,
I 2
,
I 3
J
log/a,
Fig. 5. Conductivit) ratio versus activity ratio for various pairs of glasses [9 I.
D. Ravaine / Ionic transport properties in glasses
298
electrical conductivities for various pairs of glasses. In logarithmic scales, they fit a linear relationship, according to: [a(l) /~(2) ] 1/2 ol/o2= t M2°'"~2°1 " (10) A similar relation has been observed from calorimetric measurements for AgX (X = C1, Br, I)-doped phosphate glasses [59]. As a consequence of eqs. (7) and (8), relation (10) suggests that the mobility of the free ions is independent of concentration for a given glass system.
4.3. Using the weak electrolyte model 4.3.1. Temperature dependence for the conductivity From eqs. (7) and (8), the activation energy for conduction, Eo, can be calculated as a linear combination of three t e r m s : E m (migration energy corresponding to the activation energy for the mobility), H d (activation energy of the dissociation constant, independent of the concentration), HM2o (partial free enthalpy for the component M20): E°=Em+
Hd - AHM2o 2
(11)
Using a quasi-chemical model for calculating the mixing enthalpy, we can deduce AHM2o and estimate the concentration dependence of Eo. For sodium and potassium glass systems, it has been shown that they agree well with experimental variations of Eo [60] (fig. 6).
4.3.2. Observation of conductivity maximum Although in most glasses conductivity increases with the mole fraction of alkali, a maximum conductivity has been observed in ultra-fast quenched oxide glasses [24] and in boro-aluminate glass systems [61]. The structure of tantalate and niobate glasses is made of a random array of corner linked octahedra. The concentration of NBO's is a minimum for a L i / N b ratio value of 0.5, corresponding to the formula: 2[Nb 06/2 -- El] = Yb205 - Li20. At this concentration level, the disappearance of NBO's moves the dissociation equilibrium (eq. (8)) to the right hand side, and a maximum in mobile ion concentration and in conductivity may be expected in accordance with the experimental observation [24].
4. 3. 3. Mixed alkali effect A weak electrolyte model for the mixed alkali effect on electrical conductivity in glass has been developed for the dilute foreign alkali region [62]. It has been proposed that adding small amounts of foreign alkali leads to the formation of alkali-foreign alkali interstitial pairs which, by mass action, suppresses the mobile species concentration.
D. Ravaine / Ionic transportproperties in glasses
[
I
1
299
I
\
0
o
E
~---1 Ill
ILl
~3
--4
--
1
I
1
0.6
0.7
0.8
t X
0.9
Fig. 6. Comparison of calculated and experimental values of Eo for xSiO2 (1 x) Na20 gla~se~ [~o1. Kone et al. [74] show that a good agreement with experimental data can be obtained over the full range of mixed glass composition using a weak electrolyte description and with the assumption of low mobility complexes formation.
5. O u t s t a n d i n g p r o b l e m s and future d e v e l o p m e n t 5.1. Present problems
They mostly concern fundamental aspects. 5.1.1. Abou: the weak electrolyte theory
The weak electrolyte theory has been a very powerful tool to explain the variation in conductivity in many glass systems and also for proposing some new glass compositions to be investigated. But this theory is only a thermodynamic approach and the question arises of the applicability of a liquid model
300
D. Ravaine / Ionic transport properties in glasses
to glasses. The analogy with liquid weak electrolytes only holds if there are no structural limiting factors. This implies that eqs. (8) and (9) can be used to calculate the concentration of mobile ions if the number of available interstitial sites for the dissociated ions in the rigid glass network is large. It has been recently proved that up to 30% of sodium atoms per phosphorus atoms can be chemically intercalated in a phospho-vanadate glass without noticeable change in volume [8]. This proves the existence of energetically suitable interstitial sites for the alkali ions and gives some consistency to the applicability of the weak electrolyte model in glasses. But we need further investigation to identify these sites and to characterize the ion distribution over them. We need also physical experiments to show that only part of the ions are mobile and to describe the exchange mechanism between the trapped and the mobile ions.
5.1.2. Mixed alkali effect Although many interesting models have been developed to interpret this effect, there is still no generally accepted satisfactory explanation. For instance no direct proof for the formation of static alkali foreign alkali pairs has been given. 5.1.3. Doping effect A specific property has been observed in doped glasses: at very high concentrations of a given doping salt, experimental conductivity values all approach the same limit whatever the vitreous support [30,63] as shown by results collected in fig. 4 for silver iodide doped systems. Minami et al. [64], then Schiraldi [20], have proposed that the addition of AgI would lead to the formation of metastable microdomains of the AgI superionic conducting phase which would become joined as soon as their volume occupied about 70% of the total volume. Many crystalline compounds show superionic conducting phase transition at high temperature: it would therefore be interesting to test the validity of this model by stabilizing these superionic conducting phases in vitreous matrices. Another interpretation is based on a displacement of silver ions simply by rotating from one anion to another without loss of contact [63]. This displacement would take place as soon as the distance between the anions is close to 5
~.. Structural investigation in connection with the use of the concepts of the percolation theory should throw some light on this interesting property.
5.1.4. Decrease in conductivity with increasing alkali content A few examples have been given in the last section. This phenomenon is certainly related to the change of the network former cation symmetry when increasing the O / M ratio. Here again there is no structural evidence and only preliminary studies have been carried out.
D. Rat,aine / Ionic transport properties in glasses
301
5.1.5. Anionic transport mechanism in fluoride glasses
The electrical properties of a wide range of fluoride glass compositions have recently been investigated [31,65]. N M R data [66] have shown the existence of local motions of low activation energies (0.2 eV) which disappear in the recrystallized samples. Point defects are not expected to play an important role in these disordered structures. Local motions should be mostly associated with a translocation mechanism in which two neighbouring metal cations exchange their coordinating polyhedra simultaneously with the jumping of the fluoride ion. Such a process would require a much higher energy barrier to be overcome in a well ordered crystalline phase. Long range displacements involve structural relaxations of the network which can account for the high activation energies (0.8 eV) observed for the conductivity. There is some similarity with the protonic conduction mechanism since in both cases the moving ions are part of the network forming species. However, all of these are proposed ideas and the anionic transport mechanism in fluoride glasses can in no way be considered as a solved problem. 5.2. Future development
In the future we should observe an increasing interest for protonic conduction in glasses. Although the glass literature is full of references to proton transport, by diffusive exchange with other monovalent cations, electromigration or mixed alkali effect induced by water (for basic references, see e.g. ref. [67]), very little is reported on protonic bulk conductivity in glasses [68]. Another area to be developed is the extension for the choice of available doping agents to low decomposition temperature or low melting temperature salts through the use of a "soft" method of glass synthesis. Interesting preliminary results show that alkali silicate dried gels behave as alkali conductive materials at temperatures corresponding to the pyrolisis of the organic residues [69]. The sol-gel process can also be of interest for the prepration of a wide range of new amorphous compounds, like the ORMOSILS (ORganic MOdified SILicateS) and provide new ways to obtain thin film layers by simple techniques (dipping, spinning ... ). Finally a great deal of research is expected to be developed during the next decade on the intercalation phenomena in amorphous semiconductors. A few experiments have already shown that semiconductive glasses can be lithiated through an insertion reaction [8,70]. They are now considered as possible candidates for positive electrode materials in lithium batteries. This opens the way for making monolithic vitreous batteries. By 2004, all integrated electronic circuits will be certainly powered by implanted vitreous microbatteries...
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