Lithium ion transport in Li2SO4–Li2O–P2O5 glasses

Solid State Ionics 122 (1999) 23–33

Lithium ion transport in Li SO –Li O–P O glasses2 4 2 2 5

*Munia Ganguli, M. Harish Bhat, K.J. RaoSolid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

Received 10 October 1998; accepted 8 February 1999

Abstract

Electrical conductivity and dielectric relaxation studies on a large number of lithium ion conducting glasses belonging tothe ternary glass system Li SO –Li O–P O have been carried out over a wide range of temperature (150 K to 450 K) and2 4 2 2 5

7frequencies (10 Hz–10 Hz). DC conductivities exhibit two different activation regions. This seems to be suggestive of thepresence of a cluster-tissue texture in these glasses. The clusters may be of both Li SO and lithium phosphate and are held2 4

together by a connective tissue of average composition. This conjecture seems to be well-supported by the ac conductivitybehaviour of these glasses which have been analysed using both power law and stretched exponential relaxation functions. 1999 Elsevier Science B.V. All rights reserved.

Keywords: Lithium ion conductivity; Lithium phosphate glasses; Lithium sulphate glasses

1. Introduction strategy is to dissolve a highly ionic lithium salt in aconventional polymeric lithium silicate, borate or

The need for electrolytes suitable for lithium phosphate glass [1–4]. The increased conductivity isbattery application has spurred investigations into a attributed to a volume increasing effect of thenumber of lithium ion containing inorganic glass dissolved ionic salt [1–3]. Several studies have beensystems. Preparation and properties of several of reported on lithium silicate, lithium phosphate andthese systems have been reviewed extensively in the lithium borate glasses to which lithium halides andliterature [1–10]. It is apparent that two strategies lithium oxysalts have been added [1–3,12–16]. Inhave been used in the design of lithium ion conduct- general, introduction of LiX (X 5 Cl, Br, I) oring electrolytes. The first is to use a combination of Li SO has been found to increase the conductivity.2 4

two anionic species which has been known to give Introduction of LiF, however, has been known to1increased ionic conductivity and is attributed to the produce the opposite effect (decrease of Li ion

so-called mixed anionic effect [11]. The second conductivity) [17,18] and is attributed to the forma-2tion of local columbic traps of F ions which impede

1Li ion motion. Although the glasses containingdissolved lithium halides are entirely homogeneous*Corresponding author. Tel.: 191-80-309-2583; fax: 191-80-as reported in these studies, there has been no334-1683.

E-mail address: [email protected] (K.J. Rao) evidence of the halide being incorporated as a

0167-2738/99/$ – see front matter 1999 Elsevier Science B.V. All rights reserved.PI I : S0167-2738( 99 )00059-4

24 M. Ganguli et al. / Solid State Ionics 122 (1999) 23 –33

network element [1–3]. However, in the case of 2. Experimentallithium sulphate introduced into lithium silicate and

The nominal compositions of the glasses studiedlithium phosphate glasses, there have been sugges-22 in this work and the designations are listed in Tabletions of SO ions being incorporated into the4

22 1. Also listed in the same table are the concentrationsnetwork [16,19]. It has been suggested that SO422 22 of the metaphosphate (designated by P ) and pyro-ions behave similarly to O ions whereby the SO 24

phosphate (designated by P ) species which wereions modify the silicate or phosphate network. Thus 1

calculated on the basis of hierarchial modification.there appears to be a qualitative difference in theThe details of this calculation, along with the methodroles played by LiX (X 5 halogen) and Li SO in2 4of preparation of these glasses by the conventionalaffecting the lithium ion conductivities of the respec-melt quenching method have been given elsewheretive glass systems. However there has been no clear

22 [19].experimental evidence for the incorporation of SO4Electrical conductivity measurements were carriedions into the network. How specifically this feature

out on a Hewlett-Packard HP 4192A impedance-gaininfluences lithium ion transport is also unclear.phase analyser from 10 Hz to 10 MHz in theWe have recently investigated Li SO –Li O–P 02 4 2 2 5 temperature range of 150 K to 450 K. A laboratoryglass systems using a variety of thermal and spectro-built cell assembly (having a 2-terminal capacitorscopic techniques [19] which have a bearing on theconfiguration and silver electrodes) was used for thestructure of these glasses. The role of Li O as a2 measurements. The sample temperature was mea-modifier of the phosphate network is the mostsured using a Pt–Rh thermocouple positioned verydominant and it follows the well known successiveclose to the sample. Annealed circular glass bits,

degradation of the phosphate network [20] andcoated with silver paint on both sides and having

results in the formation of a variety of phosphatethickness of about 0.1 cm and diameter of about 122anionic species. The SO ions are largely dissolved4 cm were used for the measurements.22in the phosphate glass matrix. However, SO ions4

and metaphosphate ions appear to be interactingweakly, resulting in a small dynamic concentration 3. Analysis of dataof dithiophosphate (DTP) units. The dynamic featureconsists of an association–dissociation equilibrium. The capacitance (C ) and conductance (G) of allpIn fact this dynamical character of DTP was sug- the samples were measured from the impedancegested as capable of assisting lithium ion transport as analyser. These were used to evaluate the real andwell [19]. imaginary parts of the complex impedance using

It is therefore necessary to investigate the ion standard relations [21].transport behaviour of Li SO containing lithium2 4 The dc conductances were determined from thephosphate glasses over a wide range of compositions semicircular complex impedance (Z9 versus Z0) plotsin order to understand better the role of Li SO in2 4 by taking the value of intersection of the lowthe lithium ion transport in these glasses. In this frequency end of the semicircle with the Z9 axis. Thepaper we report both ac and dc conductivity mea- dc conductivity (s) for each sample was estimatedsurements performed on these glasses which contain using the expression s 5G.(d /A) where G is theup to 30 mole % of Li SO in a phosphate host conductance and d and A are the thickness and area2 4

matrix so modified as to cover a wide range of meta of the sample, respectively.and pyrophosphate compositions. We have discussed Arrhenius plots of the conductivities were madethe possible role of Li SO as a plasticiser not just of using the expression s 5 s exp(2E (dc) /kT ) where2 4 0 a

the mechanical properties, but of the electrical E (dc) is the dc activation energy and T is thea

properties as well. This is a consequence of temperature in K. Values of E (dc) and s werea 0

smoothening the electrical charge distribution and estimated through linear regression analysis of log s1hence of the columbic field felt by the Li ions. versus 1 /T plots.

M. Ganguli et al. / Solid State Ionics 122 (1999) 23 –33 25

Table 1Compositions of the glasses prepared, along with codes of designation, relative amounts of the phosphate units present and ac and dcactivation energies at room temperature

Code Composition (mole %) P 1P E (ac) E (dc)1 2 a a

Li SO Li O P O (eV) (eV)2 4 2 2 5

CLSP1 30 35 35 70P 0.46 0.392

CLSP2 30 39 31 46P 116P 0.41 0.372 1

CLSP3 30 42 28 28P 128P 0.31 0.392 1

CLSP4 30 45 25 10P 140P 0.25 0.392 1

CLOP1 10 45 45 90P 0.33 0.402

CLOP2 15 45 40 70P 110P 0.38 0.312 1

CLOP3 25 45 30 30P 130P 0.44 0.392 1

CLOP4 30 45 25 10P 140P 0.25 0.392 1

CP1 10 55 35 30P 140P 0.40 0.402 1

CP2 15 50 35 40P 130P 0.43 0.392 1

CP3 25 40 35 60P 110P – 0.352 1

CP4 30 35 35 70P 0.46 0.392

CLP1 0 50 50 100P 0.48 0.392

CLP2 10 45 45 90P 0.33 0.402

CLP3 20 40 40 80P 0.48 0.392

CLP4 30 35 35 70P 0.46 0.392

The dielectric constants, dissipation factor and at low temperatures between 250 K and 300 K asdielectric moduli have also been estimated using shown in Fig. 1. Activation energies (E (dc)) werea

standard relations [21]. determined using the two straight line portions fromthe plot of log s with (1 /T ) using standard relations[21]. These activation barriers and the conductivities

4. Results and discussion of the glasses at 298 K are listed in Table 2. Thevariation of log s at 298 K, which is in the high

4.1. dc conductivity behaviour of the glasses temperature region, is shown as a function of Li SO2 4

mole percent in Fig. 2(a). In Fig. 2(b) we show theThe impedance (Z0 vs. Z9, where Z9 and Z0 are the variation of log s at 298 K as a function of lithium

real and imaginary parts of the impedance) plots for mole number (i.e. the total number of moles ofall the samples were found to be good semicircles. In lithium ions in the glass). The conductivity of theseveral cases more than one semicircle was ob- pure lithium metaphosphate glass itself appears to beserved, particularly at high temperatures because of the least, suggesting that the lithium ions are located

2the effect of electrode polarisation. In those cases the near the P–O on the metaphosphate chain and areintersection point of the low frequency end of the trapped in deeper potential wells. This is also seen inhigh frequency arc was used to estimate the dc the higher activation barrier of CLP1 glass (seeconductance. The intersection points of the semicir- Table 2). Two influences are noticeable from Table 2cles shifted to lower and lower Z9 values with on the lithium ion conductivities. Increasing theincreasing temperature indicating that the dc con- Li SO mole fraction, as in the CLP series, increases2 4

ductivity is thermally activated. the conductivity by almost two orders of magnitude.The variation of dc conductivities with tempera- Increasing modification at constant Li SO level also2 4

ture of the four series of glasses are shown in Fig. 1. increases conductivity, but to a much lower extent byIn all the series there appears to be a change of slope a factor of only three as evidenced in the CLSP


Fig. 1. Arrhenius plots of dc conductivity of (a) CLSP series (b) CLOP series (c) CP series (d) CLP series of glasses. n denotes the first, s

the second, 3 the third and 1 the fourth glass in each series.

series. In fact in CLP and CLSP series the increase Therefore the dc conductivities of the glasses in thein lithium ion mole numbers is 0.3 and 0.2, respec- high temperature region is suggestive of the presencetively, and therefore the increase in conductivity of two different populations of lithium ions, the onecannot be simply associated with the availability of which is associated with the deeper columbic wells

2lithium ions. It is also evident from both Fig. 2(a) near the P–O units and the other which is possibly22and Table 2 that when a high percentage of Li SO associated with the SO ions. The presence of2 4 4

2is present, the alteration in the level of modification P–O entities on the phosphate chains in which thedoes not have much influence on the conductivity. oxygen carries a unit negative charge requires that


Table 2 case of pure metaphosphate because of higher partialRoom temperature conductivities and dc activation energies for charge on pyrophosphatic oxygen.the different compositions

Conductivities have been extrapolated to 1/T50Sample s (298 K) E (dc)a and values of s have been evaluated. Most of them0

0 1(S/cm) High temp. Low temp. lie in the region 10 to 10 S/cm. These values

(eV) (eV) compare well with those reported in the literature27 [23].CLSP1 1.3310 0.39 0.0227CLSP2 1.4310 0.37 0.03 The low temperature region of conductivity is very27CLSP3 2.0310 0.39 0.02 intriguing in these materials. The elbow region of the27CLSP4 4.2310 0.39 0.06 conductivity variation, as pointed out earlier, lies in29 the range of 250–300 K. The activation barriers forCLOPl 4.3310 0.40 0.0228 this region are very low and lie in the range of 0.02CLOP2 1.9310 0.31 0.0227CLOP3 2.8310 0.39 0.07 eV to 0.1 eV which is characteristic of hopping27CLOP4 4.2310 0.39 0.06 barriers in several low temperature transport phe-

nomena [24]. Since the conductivities in this region28CPl 6.4310 0.40 0.1027 are low and the barriers are also low, the con-CP2 1.1310 0.39 0.0527 centration of lithium ions which contribute to the dcCP3 3.8310 0.35 0.0227CP4 1.3310 0.39 0.02 conductivity can be expected to be much smaller

1than the concentration of Li ions involved in the29CLP1 2.8310 0.53 0.06 conductivity of the high temperature region. Further,29CLP2 4.3310 0.40 0.0228 it is suggestive of the presence of a connectedCLP3 8.0310 0.39 0.0627 (percolating) pathway characterised by low barriersCLP4 1.3310 0.39 0.02

1and a small population of Li ions.We would like to consider that the glass has a

2P–O and P=O do not resonate in the structure and cluster-tissue structure discussed extensively in ear-hence do not reduce the effective charge as it is often lier publications from this laboratory [25–27]. Suchargued. This is consistent with the observation of an a model has been found to be particularly well-

21infrared absorption at ¯1300 cm due to P=O supported by the behaviour of highly ionic glasses.1present in all these compositions [19]. In the case of The small population of Li ions having a low

22discrete SO ions however the partial charge on barrier for transport can be attributed to the transport4

oxygen is formally 0.5 and in fact the partial charge in the connective tissue region in the glass structure.calculated using Sanderson’s procedure [22] is also The low temperature transport is essentially confined

1similar (0.45) [19]. Therefore the Li ions present in to the transport in this disordered connective tissue.the columbic wells surrounded by a larger number of Although the barriers are low there is a high degreesulphatic oxygens are expected to be shallow and of disorder related scattering and the mean free pathstherefore are characterised by a lower activation are low, which diminishes the conductivity. On the

1 1barrier for Li ion transport. Such Li ions therefore contrary the conduction in the cluster regions which,are likely to dominate the conduction even when according to the cluster model of glasses, has a more

22only a small concentration of SO ions is intro- ordered structure than the tissue, is characterised by4

duced in the glass, as reflected in the variation of a high barrier but a low degree of scattering.measured E values (for the high temperature region) Therefore the lithium ion motion in the clustereda

in Fig. 2(c). This characteristic barrier, as expected, region dominates the transport at higher tempera-22remains independent of further increase in SO ion tures. It may be noted that at laboratory temperature4

concentration. When the columbic wells are sur- (298 K) the (extrapolated) tissue conductivity isrounded by a combination of sulphatic and pyrophos- about (1 /10)th of the total conductivity. However,phatic oxygens rather than sulphatic and metaphos- pressure dependent conductivity measurements canphatic oxygens, the wells would deepen and hence further confirm the appropriateness of the clusterthe activation barriers would be higher than in the model for these glasses.


Fig. 2. (a) Variation of log of room temperature conductivity (s(298 K)) of all the glasses with Li SO mole per cent; (b) variation of log of2 4

room temperature conductivity (s(298 K)) of all the glasses with total lithium mole number; (c) variation of dc activation energies (E (dc))a

of all the glasses with Li SO mole per cent.2 4

In order to derive further support for the suitability described earlier [26] in the relation RT /DE5RT /g g

of the cluster-tissue model to these glasses, the Nhn. RT /DE is found to be equal to 25/10.8. Thisg

relation between the glass transition temperatures to actually represents a cluster / tissue volume ratio ofthe cage vibrational frequencies of lithium ions has 1.6 [26] and is suggestive of the involvement ofbeen examined. With the very limited data on cage several excited states near the glass transition.vibrational frequencies (n) available from our owninvestigations, T was found to vary with the cage 4.2. ac conductivity behaviour of the glassesg

vibrational frequencies thus confirming the ap-plicability of the cluster-tissue model. It is possible The ac conductivities and the dielectric relaxationto make further use of the results of the model behaviour of the glasses were studied between 150 K


and 450 K and over a wide frequency range (10 Hzto 10 MHz). Typical log s versus log f variations atdifferent temperatures are shown for the case ofCLSP1 glass in Fig. 3. The behaviour of all the otherglasses is qualitatively similar. The ac conductivitiesexhibited change of slope to higher values as thefrequency is increased, and the nearly flat portion atlower frequencies increased to higher values ofconductivity at higher temperatures. The conduc-tivity behaviour has been examined using Almond–West type of power law [28–30] using a singleexponent of v :

ss(v) 5 A 1 Bv (1)

Typical conductivity fits to Eq. (1) are shown in Fig.4(a) and 4(b). In Fig. 4(a), different glass com-positions have been chosen and the s versus v

(52pf ) logarithmic plots refer to the same tempera-ture (298 K) while in Fig. 4(b) the plots refer to thesame glass (CLP3) at various temperatures. It isevident from Fig. 4 that the goodness of fit is high(as listed in Table 3 for the room temperature fits)and therefore single exponential fit seems adequate.The values of the fitting parameters A, B and s arelisted in Table 3 at 298 K. Further, s values have

Fig. 4. (a) Typical ac conductivity plots (at 298 K) of differentsglasses fitted to the power law equation s 5 s 1 Av ; (b) typical0

Fig. 3. Variation of log s with frequency at different temperatures ac conductivity data of CLP3 glass at different temperatures fittedfor CLSP1 glass. to the single exponent power law equation.


Table 32Values of the fitting parameters and the goodness of fit (x ) for

the log(s) versus log v plots at 298 K2Sample A B s x

(S /cm) (S/cm)28 211CLSP1 4.99310 4.56310 0.6 0.000527 210CLSP2 1.18310 1.58310 0.55 0.000227 210CLSP3 1.73310 1.11310 0.57 0.000227 210CLSP4 3.37310 2.13310 0.55 0.0001

29 212CLOP1 2.59310 5.56310 0.7 0.00428 211CLOP2 1.66310 1.77310 0.65 0.000727 210CLOP3 2.46310 1.29310 0.58 0.000327 210CLOP4 3.37310 2.13310 0.55 0.0001

28 211CP1 5.22310 5.42310 0.59 0.000528 211CP2 8.79310 3310 0.64 0.000826 28CP3 2.66310 1.02310 0.37 0.000128 211CP4 4.99310 4.56310 0.6 0.0005

29 213CLP1 1.2310 8.9310 0.77 0.000629 212CLP2 2.59310 5.56310 0.7 0.00428 10CLP3 7.27310 2.15310 0.54 0.000228 211CLP4 4.99310 4.56310 0.6 0.0005

been determined in each case for various tempera-tures. Variation of s values with temperature areshown for typical compositions in all the four seriesof glasses in Fig. 5(a). In general, s values are high atlow temperatures and below 200 K, exceed unity.Values of s also decrease rapidly towards roomtemperature and tend to level off in the neigh-bourhood of 0.5. In few of the glasses (not shownhere) occurrence of s minimum was noted. Observa-tion of s minimum has been observed in other

Fig. 5. (a) Variation of the power law exponent s with temperaturesystems [31–33] and discussed widely [34–38].for some typical glasses. n denotes CLSP1, s denotes CLOF2, dHowever the phenomenon is absent in all glasses,denotes CP3 and h denotes CLP2; (b) variation of the stretchedeven though belonging to the same category, andexponent b with temperature for some typical glasses. n denotes

therefore is not discussed in this paper. CLSP1, s denotes CLOP2, d denotes CP3 and h denotes CLP2.The tendency towards levelling off of s values

around 0.5 above 250 K seems to be a more generalphenomenon. It lends credence to the suggestion that gimes. We would like to attribute the change of highthere are two regimes of s values: one is where s is to low temperature regimes of s values to a structuralhigh, strongly temperature dependent and often origin consistent with the dc conductivity behaviour.exceeds unity at very low temperatures; the second, We noted earlier that glasses discussed here arewhere s is low and fairly insensitive to temperature. likely to conform to a cluster-tissue model texture.Since a two term Almond–West expression was Both Li SO and modified phosphate can give rise to2 4

found to give satisfactory fits over the entire range of clustered regions with different structures. The inter-frequencies, the corresponding regimes of s values cluster region constitutes the tissue and is considered

1may not be associated with distinct frequency re- to be truly amorphous. Li ions are present in all the


three regions and their transport is characterised by M9 and M0 of all the glasses investigated here wasdifferent activation barriers. similar. The measurements were performed at a

I II IIIIf the transport barriers are E , E and E , number of temperatures between 170 K and 450 Ka a a

respectively, in the phosphate (dominated) clusters, for all the glasses. It was found that the amplitudesulphate (dominated) clusters and the inter-cluster (height of M0 peak) was not constant at various

I IItissue, then E .E because in the phosphate clus- temperatures. Therefore there may not be a singlea a2ters, the partial charge on oxygen in P–O (20.36) relaxation mechanism operating in these glasses.

is higher than the oxygen in sulphate groups This was confirmed by considering the superim-III(20.45). E is least because the tissue is of lower posability of M9 /M0(max) versus log ( f/f (max)) fora

density and the inter-ionic distances are larger. Also, the glasses obtained at different temperatures assince the number of ions in Li SO clusters is higher shown in Fig. 6 for CLSP1 glass. The plots were2 4

than both, in phosphate type clusters and the tissue, clearly not superimposable. It may also be noted thatthe conduction process is dominated at higher tem- the FWHM is significantly lower at lower tempera-peratures by the sulphate clusters. The presence of a tures than at higher temperatures for these glasses. In

1high density of Li ions, which are also more mobile fact at 226 K, the FWHM for CLSP1 glass is 1.5II(lower value of E ), seems to be associated with a decades, suggesting that it is almost a Debye type ofa

low and essentially temperature insensitive Almond– relaxation characterised by a single relaxation fre-West expression for ac conductivity, At lower tem- quency. Since the low temperature transport is

1peratures, the ac conductivity is largely confined to dominated by the tissue region in which the Li ion1the tissue in which Li ions are in lower density and population is low, the dipoles in this region are well

reduced inter-lithium ion interactions. The increases separated and non-interacting. Hence it is not sur-in the values of s appear to be associated with this prising that the behaviour is Debye-like. As thesituation. A transition therefore manifests in in- temperature is increased, the relaxational process iscreased s values as a function of decreasing tempera- dominated by transport in the Li SO cluster region2 4

ture. and the relaxation becomes increasingly non-DebyeHowever, the foregoing only establishes that the like. It is interesting to note that in the regime II of1Li ion transport, as observed in these measure-

ments, is a composite of at least three contributions.The relaxation mechanisms and characteristic relaxa-tion times are expected to be different for the three

1types of Li ions, and hence their contribution topolarisation current measured in ac conductivitystudies. In order to examine this aspect further, wehave used the results of dielectric relaxation spec-troscopy which are discussed below.

4.3. Dielectric relaxation behaviour of the glasses

The dielectric constants e9 and e0 were measuredfor all the glasses between 10 Hz and 10 MHz. Sincethese are highly ionic glasses, the low frequencydispersion of the dielectric constant was found to bevery high because of the electrode polarisation.Electrode polarisation effects at ordinary tempera-tures (298 K) are manifest even at kHz frequencies.It was therefore appropriate to examine the dielectric Fig. 6. Typical normalised plot of M0 against normalised fre-data using the modulus representation which sup- quency for the glass CLSP1 from 180 K to 370 K. Inset: forpresses the dc polarisation effect. The behaviour of CLSP1 from 328–403 K.


ac conductivity, where the s values are insensitive to 5. Conclusionstemperature, the reduced semilog plots of M0 /M0(max) versus f/f (max) were quite superimposable Conductivity measurements and dielectric relaxa-(see inset to Fig. 6). tion behaviour have been examined over a wide

Non-Debye like behaviour of dielectrics is gener- range of compositions in the ternary glass systemally examined by the use of a stretched exponential Li SO –Li O–P 0 in the temperature range of 1502 4 2 2 5

function for the relaxation times: K to 450 K. The dc conductivity is thermallyactivated and exhibits two different activation bar-riers in the high and low temperature regimes. Thisb

f 5 f exp[2(t /t ) ]0 0 seems to suggest the presence of an ultramicroscopiccluster-tissue texture in these glasses. Activation

where t is the characteristic relaxation time and b is barriers for lithium ion transport in the clustered0

the stretching exponent. b is generally determined by regions of Li SO and the semicontinuous lithium2 4

fitting M0 plots to analytical functions [39]. b is phosphate are higher than in the amorphous tissuehowever fairly accurately determined by using the regions. Such a model is well supported by the acfull width at half maximum (FWHM) of M0 together conductivity and dielectric relaxation behaviour also.with b vs half width plots. ac conductivity variation with frequency has been

The b values thus determined at a number of fitted to an Almond–West type of expression using atemperatures from the FWHM values as a function single exponent s. Variation of s with temperatureof temperature are plotted in Fig. 5b for a few typical also shows a rapid decrease with temperature in thesystems. The b values in general decrease as the low temperature regime, followed by a nearly con-temperature is increased in a qualitatively similar stant value of around 0.5 above 250 K. The dielectricmanner as s itself (Fig. 5a). However, the scatter in b data has been analysed using a modulus formalismvalues is much higher than in the s values. This and b values have been calculated from the dielec-behaviour is also unusual in the sense that the sum of tric relaxation peaks. Variation of b with temperature(b 1s) is evidently not a constant [38]. The value of shows a similar behaviour as s, lending furtherb reaches a limiting value of 1.0 at low tempera- support to the cluster-tissue model.tures. This is Debye like and, as noted earlier,dominated by the transport in the tissue region. Thegradual increase of transport in the cluster region Acknowledgementswhich occurs when the temperature is increased is

1associated with a decrease in b, because Li ion The authors are thankful to the Commission of theconductivity in clusters is characterised by reduced European Communities for financial support. One ofinter-lithium ion distances and a greater interaction the authors (M.G.) is grateful to the Council foramong the mobile lithium ions [40]. This interaction Scientific and Industrial Research (CSIR), India for ais now well known to lead to the formation of a senior research fellowship.significant density of low energy states and leads tolow b values [41]. An interesting feature to note isthat the transition between different s regimes and Referencesthe b regimes (Fig. 5) occurs at almost similartemperatures which is again the regime of transition [1] D. P Button, R. P Tandon, H.L. Tuller, D.R. Uhlmann, J.from the low activation barrier to the high activation Non-Cryst. Solids 42 (1980) 297.barrier in dc conductivities. This is a further indica- [2] H.L. Tuller, D. R Button, D.R. Uhlmann, J. Non-Cryst.

Solids 40 (1983) 93.tion of the suitability of the cluster-tissue description[3] D. R Button, R. R Tandon, C. King, M.H. Velez, H.L. Tuller,of these glasses. Neither dc nor ac activation ener-

D.R. Uhlmann, J. Non-Cryst. Solids 49 (1982) 129.gies in the high temperature regime are well corre- [4] A.R. Kulkarni, H.S. Maiti, A. Paul, Bull. Mater. Sci. 6lated to b because of the complex nature of transport (1984) 201.in these glasses. [5] C.A. Angell, Solid State lonics 9–10 (1983) 3.


[6] C.A. Angell, Solid State lonics 18–19 (1986) 72. [23] K.C. Sobha, K.J. Rao, Solid State Ionics 81 (1995) 145.[7] C.A. Angell, Chem. Rev. 90 (1990) 523. [24] K. Funke, Solid State Ionics 22 (1992) 111.[8] C.A. Angell, Annu. Rev. Phys. Chem. 43 (1992) 693. [25] K.J. Rao, C.N.R. Rao, Mater. Res. Bull. 17 (1982) 1337.[9] M.D. Ingram, Phys. Chem. Glasses 28 (1987) 215. [26] K.J. Rao, Proc. Indian Acad. Sci. (Chem. Sci.) 93 (1984)

[10] K.J. Rao, M. Ganguli, in: M.A.Z. Munshi (Ed.), Handbook 389.of Solid State Batteries and Capacitors, World Scientific, [27] R. Parthasarathy, K.J. Rao, C.N.R. Rao, Chem. Soc. Rev. 12Singapore, 1995. (1983) 361.

[11] B. Carette, M. Ribes, J.L. Souquet, Solid State Ionics 9 (10) [28] D. P Almond, G.K. Duncan, A.R. West, Solid State Ionics 8(1983) 735. (1983) 159.

[12] A. Levasseur, B. Cales, J.M. Reau, P. Hagenmuller, Mater. [29] D. P Almond, C.C. Hunter, A.R. West, J. Mater. Sci. 19Res. Bull. 14 (1979) 921. (1984) 3236.

[13] P.R. Gandhi,V.K. Deshpande, K. Singh, Solid State Ionics 36 [30] D. R Almond, A.R. West, R.J. Grant, Solid State Commun.(1989) 97. 44 (1982) 1277.

[14] J. P Malugani, G. Robert, Mater. Res. Bull. 14 (1979) 1075. [31] H. Jam, J.N. Mundy, J. Non-Cryst. Solids 91 (1987) 315.[15] J. P Malugani, A. Wasnieroski, M. Doreau, G. Robert, C.R. [32] S.R. Elliott, F.E.G. Henn, J. Non-Cryst. Solids 116 (1990)

Acad. Sci. (Paris) 287 (1978) 455. 179.[16] J.L. Souquet, A. Kone, M. Ribes, J. Non-Cryst. Solids 38–39 [33] S.R. Elliott, Adv. Phys. 35 (1987) 135.

(1980) 307. [34] S.R. Elliott, Solid State Ionics 70/71 (1994) 27.[17] J.O. Isard, K.K. Mallick, M. Jagla, Solid State Ionics 9–10 [35] S.R. Elliott, J. Non-Cryst. Solids 170 (1994) 97.

(1983) 623. [36] S.R. Elliott, A. P Owens, Philos. Mag. B 60 (1989) 777.[18] H.S. Maiti, A.R. Kulkarni, A. Paul, Solid State Ionics 9–10 [37] K.J. Rao, C. Estournes, M. Menetrier, A. Levasseur, Philos.

(1983) 605. Mag. B 70 (1994) 809.[19] M. Ganguli, K.J. Rao, J. Non-Cryst. Solids. 243 (1999) 251. [38] S. Muthupari, S. Lakshmi Raghavan, K.J. Rao, J. Phys.[20] S.W. Martin, Eur. J. Solid State Chem. 28 (1991) 163. Chem. 100 (1996) 4243.[21] J. Ross MacDonald, Impedance Spectroscopy, Emphasizing [39] C.T. Moynihan, L.P. Boesch, N.L. Laberge, Phys. Chem.

Solid Materials and Systems, John Wiley and Sons, New Glasses 14 (1973) 122.York, 1967. [40] H.K. Patel, S.W. Martin, Phys. Rev. B 45 (1992) 10292.

[22] R.T. Sanderson, Polar Covalence, Academic Press, New [41] S.W. Martin, C.A. Angell, J. Non-Cryst. Solids 83 (1986)York, 1983. 185.

Documents

Lithium ion transport in Li2SO4–Li2O–P2O5 glasses