Lithium ion transport in Li2SO4–Li2O–P2O5 glasses

Solid State Ionics 122 (1999) 23–33

Lithium ion transport in Li 2 SO 4 –Li 2 O–P2 O 5 glasses Munia Ganguli, M. Harish Bhat, K.J. Rao* Solid 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 to the ternary glass system Li 2 SO 4 –Li 2 O–P2 O 5 have been carried out over a wide range of temperature (150 K to 450 K) and frequencies (10 Hz–10 7 Hz). DC conductivities exhibit two different activation regions. This seems to be suggestive of the presence of a cluster-tissue texture in these glasses. The clusters may be of both Li 2 SO 4 and lithium phosphate and are held together by a connective tissue of average composition. This conjecture seems to be well-supported by the ac conductivity behaviour 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 The need for electrolytes suitable for lithium battery application has spurred investigations into a number of lithium ion containing inorganic glass systems. Preparation and properties of several of these systems have been reviewed extensively in the literature [1–10]. It is apparent that two strategies have been used in the design of lithium ion conducting electrolytes. The first is to use a combination of two anionic species which has been known to give increased ionic conductivity and is attributed to the so-called mixed anionic effect [11]. The second

*Corresponding author. Tel.: 191-80-309-2583; fax: 191-80334-1683. E-mail address: [email protected] (K.J. Rao)

strategy is to dissolve a highly ionic lithium salt in a conventional polymeric lithium silicate, borate or phosphate glass [1–4]. The increased conductivity is attributed to a volume increasing effect of the dissolved ionic salt [1–3]. Several studies have been reported on lithium silicate, lithium phosphate and lithium borate glasses to which lithium halides and lithium oxysalts have been added [1–3,12–16]. In general, introduction of LiX (X 5 Cl, Br, I) or Li 2 SO 4 has been found to increase the conductivity. Introduction of LiF, however, has been known to produce the opposite effect (decrease of Li 1 ion conductivity) [17,18] and is attributed to the formation of local columbic traps of F 2 ions which impede Li 1 ion motion. Although the glasses containing dissolved lithium halides are entirely homogeneous as reported in these studies, there has been no evidence of the halide being incorporated as a

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

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

network element [1–3]. However, in the case of lithium sulphate introduced into lithium silicate and lithium phosphate glasses, there have been suggestions of SO 22 ions being incorporated into the 4 network [16,19]. It has been suggested that SO 422 ions behave similarly to O 22 ions whereby the SO 422 ions modify the silicate or phosphate network. Thus there appears to be a qualitative difference in the roles played by LiX (X 5 halogen) and Li 2 SO 4 in affecting the lithium ion conductivities of the respective glass systems. However there has been no clear experimental evidence for the incorporation of SO 22 4 ions into the network. How specifically this feature influences lithium ion transport is also unclear. We have recently investigated Li 2 SO 4 –Li 2 O–P2 0 5 glass systems using a variety of thermal and spectroscopic techniques [19] which have a bearing on the structure of these glasses. The role of Li 2 O as a modifier of the phosphate network is the most dominant and it follows the well known successive degradation of the phosphate network [20] and results in the formation of a variety of phosphate anionic species. The SO 22 ions are largely dissolved 4 in the phosphate glass matrix. However, SO 22 ions 4 and metaphosphate ions appear to be interacting weakly, resulting in a small dynamic concentration of dithiophosphate (DTP) units. The dynamic feature consists of an association–dissociation equilibrium. In fact this dynamical character of DTP was suggested as capable of assisting lithium ion transport as well [19]. It is therefore necessary to investigate the ion transport behaviour of Li 2 SO 4 containing lithium phosphate glasses over a wide range of compositions in order to understand better the role of Li 2 SO 4 in the lithium ion transport in these glasses. In this paper we report both ac and dc conductivity measurements performed on these glasses which contain up to 30 mole % of Li 2 SO 4 in a phosphate host matrix so modified as to cover a wide range of meta and pyrophosphate compositions. We have discussed the possible role of Li 2 SO 4 as a plasticiser not just of the mechanical properties, but of the electrical properties as well. This is a consequence of smoothening the electrical charge distribution and hence of the columbic field felt by the Li 1 ions.

2. Experimental The nominal compositions of the glasses studied in this work and the designations are listed in Table 1. Also listed in the same table are the concentrations of the metaphosphate (designated by P2 ) and pyrophosphate (designated by P1 ) species which were calculated on the basis of hierarchial modification. The details of this calculation, along with the method of preparation of these glasses by the conventional melt quenching method have been given elsewhere [19]. Electrical conductivity measurements were carried out on a Hewlett-Packard HP 4192A impedance-gain phase analyser from 10 Hz to 10 MHz in the temperature range of 150 K to 450 K. A laboratory built cell assembly (having a 2-terminal capacitor configuration and silver electrodes) was used for the measurements. The sample temperature was measured using a Pt–Rh thermocouple positioned very close to the sample. Annealed circular glass bits, coated with silver paint on both sides and having thickness of about 0.1 cm and diameter of about 1 cm were used for the measurements.

3. Analysis of data The capacitance (Cp ) and conductance (G) of all the samples were measured from the impedance analyser. These were used to evaluate the real and imaginary parts of the complex impedance using standard relations [21]. The dc conductances were determined from the semicircular complex impedance (Z9 versus Z0) plots by taking the value of intersection of the low frequency end of the semicircle with the Z9 axis. The dc conductivity (s ) for each sample was estimated using the expression s 5G.(d /A) where G is the conductance and d and A are the thickness and area of the sample, respectively. Arrhenius plots of the conductivities were made using the expression s 5 s0 exp(2Ea (dc) /kT ) where Ea (dc) is the dc activation energy and T is the temperature in K. Values of Ea (dc) and s0 were estimated through linear regression analysis of log s versus 1 /T plots.

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

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

P1 1P2

Composition (mole %)

Ea (ac)

Ea (dc)

(eV)

(eV)

Li 2 SO 4

Li 2 O

P2 O 5

CLSP1 CLSP2 CLSP3 CLSP4

30 30 30 30

35 39 42 45

35 31 28 25

70P2 46P2 116P1 28P2 128P1 10P2 140P1

0.46 0.41 0.31 0.25

0.39 0.37 0.39 0.39

CLOP1 CLOP2 CLOP3 CLOP4

10 15 25 30

45 45 45 45

45 40 30 25

90P2 70P2 110P1 30P2 130P1 10P2 140P1

0.33 0.38 0.44 0.25

0.40 0.31 0.39 0.39

CP1 CP2 CP3 CP4

10 15 25 30

55 50 40 35

35 35 35 35

30P2 140P1 40P2 130P1 60P2 110P1 70P2

0.40 0.43 – 0.46

0.40 0.39 0.35 0.39

CLP1 CLP2 CLP3 CLP4

0 10 20 30

50 45 40 35

50 45 40 35

100P2 90P2 80P2 70P2

0.48 0.33 0.48 0.46

0.39 0.40 0.39 0.39

The dielectric constants, dissipation factor and dielectric moduli have also been estimated using standard relations [21].

4. Results and discussion

4.1. dc conductivity behaviour of the glasses The impedance (Z0 vs. Z9, where Z9 and Z0 are the real and imaginary parts of the impedance) plots for all the samples were found to be good semicircles. In several cases more than one semicircle was observed, particularly at high temperatures because of the effect of electrode polarisation. In those cases the intersection point of the low frequency end of the high frequency arc was used to estimate the dc conductance. The intersection points of the semicircles shifted to lower and lower Z9 values with increasing temperature indicating that the dc conductivity is thermally activated. The variation of dc conductivities with temperature of the four series of glasses are shown in Fig. 1. In all the series there appears to be a change of slope

at low temperatures between 250 K and 300 K as shown in Fig. 1. Activation energies (Ea (dc)) were determined using the two straight line portions from the plot of log s with (1 /T ) using standard relations [21]. These activation barriers and the conductivities of the glasses at 298 K are listed in Table 2. The variation of log s at 298 K, which is in the high temperature region, is shown as a function of Li 2 SO 4 mole percent in Fig. 2(a). In Fig. 2(b) we show the variation of log s at 298 K as a function of lithium mole number (i.e. the total number of moles of lithium ions in the glass). The conductivity of the pure lithium metaphosphate glass itself appears to be the least, suggesting that the lithium ions are located near the P–O 2 on the metaphosphate chain and are trapped in deeper potential wells. This is also seen in the higher activation barrier of CLP1 glass (see Table 2). Two influences are noticeable from Table 2 on the lithium ion conductivities. Increasing the Li 2 SO 4 mole fraction, as in the CLP series, increases the conductivity by almost two orders of magnitude. Increasing modification at constant Li 2 SO 4 level also increases conductivity, but to a much lower extent by a factor of only three as evidenced in the CLSP

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

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 in lithium ion mole numbers is 0.3 and 0.2, respectively, and therefore the increase in conductivity cannot be simply associated with the availability of lithium ions. It is also evident from both Fig. 2(a) and Table 2 that when a high percentage of Li 2 SO 4 is present, the alteration in the level of modification does not have much influence on the conductivity.

Therefore the dc conductivities of the glasses in the high temperature region is suggestive of the presence of two different populations of lithium ions, the one which is associated with the deeper columbic wells near the P–O 2 units and the other which is possibly associated with the SO 22 ions. The presence of 4 P–O 2 entities on the phosphate chains in which the oxygen carries a unit negative charge requires that

M. Ganguli et al. / Solid State Ionics 122 (1999) 23 – 33 Table 2 Room temperature conductivities and dc activation energies for the different compositions

s (298 K)

Ea (dc)

(S / cm)

High temp. (eV)

Low temp. (eV)

CLSP1 CLSP2 CLSP3 CLSP4

1.3310 27 1.4310 27 2.0310 27 4.2310 27

0.39 0.37 0.39 0.39

0.02 0.03 0.02 0.06

CLOPl CLOP2 CLOP3 CLOP4

4.3310 29 1.9310 28 2.8310 27 4.2310 27

0.40 0.31 0.39 0.39

0.02 0.02 0.07 0.06

CPl CP2 CP3 CP4

6.4310 28 1.1310 27 3.8310 27 1.3310 27

0.40 0.39 0.35 0.39

0.10 0.05 0.02 0.02

CLP1 CLP2 CLP3 CLP4

2.8310 29 4.3310 29 8.0310 28 1.3310 27

0.53 0.40 0.39 0.39

0.06 0.02 0.06 0.02

Sample

P–O 2 and P=O do not resonate in the structure and hence do not reduce the effective charge as it is often argued. This is consistent with the observation of an infrared absorption at ¯1300 cm 21 due to P=O present in all these compositions [19]. In the case of discrete SO 22 ions however the partial charge on 4 oxygen is formally 0.5 and in fact the partial charge calculated using Sanderson’s procedure [22] is also similar (0.45) [19]. Therefore the Li 1 ions present in the columbic wells surrounded by a larger number of sulphatic oxygens are expected to be shallow and therefore are characterised by a lower activation barrier for Li 1 ion transport. Such Li 1 ions therefore are likely to dominate the conduction even when only a small concentration of SO 22 ions is intro4 duced in the glass, as reflected in the variation of measured Ea values (for the high temperature region) in Fig. 2(c). This characteristic barrier, as expected, remains independent of further increase in SO 22 ion 4 concentration. When the columbic wells are surrounded by a combination of sulphatic and pyrophosphatic oxygens rather than sulphatic and metaphosphatic oxygens, the wells would deepen and hence the activation barriers would be higher than in the

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case of pure metaphosphate because of higher partial charge on pyrophosphatic oxygen. Conductivities have been extrapolated to 1 /T50 and values of s0 have been evaluated. Most of them lie in the region 10 0 to 10 1 S / cm. These values compare well with those reported in the literature [23]. The low temperature region of conductivity is very intriguing in these materials. The elbow region of the conductivity variation, as pointed out earlier, lies in the range of 250–300 K. The activation barriers for this region are very low and lie in the range of 0.02 eV to 0.1 eV which is characteristic of hopping barriers in several low temperature transport phenomena [24]. Since the conductivities in this region are low and the barriers are also low, the concentration of lithium ions which contribute to the dc conductivity can be expected to be much smaller than the concentration of Li 1 ions involved in the conductivity of the high temperature region. Further, it is suggestive of the presence of a connected (percolating) pathway characterised by low barriers and a small population of Li 1 ions. We would like to consider that the glass has a cluster-tissue structure discussed extensively in earlier publications from this laboratory [25–27]. Such a model has been found to be particularly wellsupported by the behaviour of highly ionic glasses. The small population of Li 1 ions having a low barrier for transport can be attributed to the transport in the connective tissue region in the glass structure. The low temperature transport is essentially confined to the transport in this disordered connective tissue. Although the barriers are low there is a high degree of disorder related scattering and the mean free paths are low, which diminishes the conductivity. On the contrary the conduction in the cluster regions which, according to the cluster model of glasses, has a more ordered structure than the tissue, is characterised by a high barrier but a low degree of scattering. Therefore the lithium ion motion in the clustered region dominates the transport at higher temperatures. It may be noted that at laboratory temperature (298 K) the (extrapolated) tissue conductivity is about (1 / 10)th of the total conductivity. However, pressure dependent conductivity measurements can further confirm the appropriateness of the cluster model for these glasses.

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

Fig. 2. (a) Variation of log of room temperature conductivity (s (298 K)) of all the glasses with Li 2 SO 4 mole per cent; (b) variation of log of room temperature conductivity (s (298 K)) of all the glasses with total lithium mole number; (c) variation of dc activation energies (Ea (dc)) of all the glasses with Li 2 SO 4 mole per cent.

In order to derive further support for the suitability of the cluster-tissue model to these glasses, the relation between the glass transition temperatures to the cage vibrational frequencies of lithium ions has been examined. With the very limited data on cage vibrational frequencies (n ) available from our own investigations, T g was found to vary with the cage vibrational frequencies thus confirming the applicability of the cluster-tissue model. It is possible to make further use of the results of the model

described earlier [26] in the relation RT g /DE5RT g / Nhn. RT g /DE is found to be equal to 25 / 10.8. This actually represents a cluster / tissue volume ratio of 1.6 [26] and is suggestive of the involvement of several excited states near the glass transition.

4.2. ac conductivity behaviour of the glasses The ac conductivities and the dielectric relaxation behaviour of the glasses were studied between 150 K

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

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and 450 K and over a wide frequency range (10 Hz to 10 MHz). Typical log s versus log f variations at different temperatures are shown for the case of CLSP1 glass in Fig. 3. The behaviour of all the other glasses is qualitatively similar. The ac conductivities exhibited change of slope to higher values as the frequency is increased, and the nearly flat portion at lower frequencies increased to higher values of conductivity at higher temperatures. The conductivity behaviour has been examined using Almond– West type of power law [28–30] using a single exponent of v :

s (v ) 5 A 1 Bv s

(1)

Typical conductivity fits to Eq. (1) are shown in Fig. 4(a) and 4(b). In Fig. 4(a), different glass compositions have been chosen and the s versus v (52pf ) logarithmic plots refer to the same temperature (298 K) while in Fig. 4(b) the plots refer to the same glass (CLP3) at various temperatures. It is evident 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 are listed in Table 3 at 298 K. Further, s values have

Fig. 3. Variation of log s with frequency at different temperatures for CLSP1 glass.

Fig. 4. (a) Typical ac conductivity plots (at 298 K) of different glasses fitted to the power law equation s 5 s0 1 Av s ; (b) typical ac conductivity data of CLP3 glass at different temperatures fitted to the single exponent power law equation.

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

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Table 3 Values of the fitting parameters and the goodness of fit ( x 2 ) for the log(s ) versus log v plots at 298 K Sample

A (S / cm)

B (S / cm)

s

x2

CLSP1 CLSP2 CLSP3 CLSP4

4.99310 28 1.18310 27 1.73310 27 3.37310 27

4.56310 211 1.58310 210 1.11310 210 2.13310 210

0.6 0.55 0.57 0.55

0.0005 0.0002 0.0002 0.0001

CLOP1 CLOP2 CLOP3 CLOP4

2.59310 29 1.66310 28 2.46310 27 3.37310 27

5.56310 212 1.77310 211 1.29310 210 2.13310 210

0.7 0.65 0.58 0.55

0.004 0.0007 0.0003 0.0001

CP1 CP2 CP3 CP4

5.22310 28 8.79310 28 2.66310 26 4.99310 28

5.42310 211 3310 211 1.02310 28 4.56310 211

0.59 0.64 0.37 0.6

0.0005 0.0008 0.0001 0.0005

CLP1 CLP2 CLP3 CLP4

1.2310 29 2.59310 29 7.27310 28 4.99310 28

8.9310 213 5.56310 212 2.15310 10 4.56310 211

0.77 0.7 0.54 0.6

0.0006 0.004 0.0002 0.0005

been determined in each case for various temperatures. Variation of s values with temperature are shown for typical compositions in all the four series of glasses in Fig. 5(a). In general, s values are high at low temperatures and below 200 K, exceed unity. Values of s also decrease rapidly towards room temperature and tend to level off in the neighbourhood of 0.5. In few of the glasses (not shown here) occurrence of s minimum was noted. Observation of s minimum has been observed in other systems [31–33] and discussed widely [34–38]. However the phenomenon is absent in all glasses, even though belonging to the same category, and therefore is not discussed in this paper. The tendency towards levelling off of s values around 0.5 above 250 K seems to be a more general phenomenon. It lends credence to the suggestion that there are two regimes of s values: one is where s is high, strongly temperature dependent and often exceeds unity at very low temperatures; the second, where s is low and fairly insensitive to temperature. Since a two term Almond–West expression was found to give satisfactory fits over the entire range of frequencies, the corresponding regimes of s values may not be associated with distinct frequency re-

Fig. 5. (a) Variation of the power law exponent s with temperature for some typical glasses. n denotes CLSP1, s denotes CLOF2, d denotes CP3 and h denotes CLP2; (b) variation of the stretched exponent b with temperature for some typical glasses. n denotes CLSP1, s denotes CLOP2, d denotes CP3 and h denotes CLP2.

gimes. We would like to attribute the change of high to low temperature regimes of s values to a structural origin consistent with the dc conductivity behaviour. We noted earlier that glasses discussed here are likely to conform to a cluster-tissue model texture. Both Li 2 SO 4 and modified phosphate can give rise to clustered regions with different structures. The intercluster region constitutes the tissue and is considered to be truly amorphous. Li 1 ions are present in all the

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

three regions and their transport is characterised by different activation barriers. If the transport barriers are E Ia , E IIa and E III a , respectively, in the phosphate (dominated) clusters, sulphate (dominated) clusters and the inter-cluster tissue, then E Ia .E IIa because in the phosphate clusters, the partial charge on oxygen in P–O 2 (20.36) is higher than the oxygen in sulphate groups (20.45). E III a is least because the tissue is of lower density and the inter-ionic distances are larger. Also, since the number of ions in Li 2 SO 4 clusters is higher than both, in phosphate type clusters and the tissue, the conduction process is dominated at higher temperatures by the sulphate clusters. The presence of a high density of Li 1 ions, which are also more mobile (lower value of E IIa ), seems to be associated with a low and essentially temperature insensitive Almond– West expression for ac conductivity, At lower temperatures, the ac conductivity is largely confined to the tissue in which Li 1 ions are in lower density and reduced inter-lithium ion interactions. The increases in the values of s appear to be associated with this situation. A transition therefore manifests in increased s values as a function of decreasing temperature. However, the foregoing only establishes that the Li 1 ion transport, as observed in these measurements, is a composite of at least three contributions. The relaxation mechanisms and characteristic relaxation times are expected to be different for the three types of Li 1 ions, and hence their contribution to polarisation current measured in ac conductivity studies. In order to examine this aspect further, we have used the results of dielectric relaxation spectroscopy which are discussed below.

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M9 and M0 of all the glasses investigated here was similar. The measurements were performed at a number of temperatures between 170 K and 450 K for all the glasses. It was found that the amplitude (height of M0 peak) was not constant at various temperatures. Therefore there may not be a single relaxation mechanism operating in these glasses. This was confirmed by considering the superimposability of M9 /M0(max) versus log ( f/f (max)) for the glasses obtained at different temperatures as shown in Fig. 6 for CLSP1 glass. The plots were clearly not superimposable. It may also be noted that the FWHM is significantly lower at lower temperatures than at higher temperatures for these glasses. In fact at 226 K, the FWHM for CLSP1 glass is 1.5 decades, suggesting that it is almost a Debye type of relaxation characterised by a single relaxation frequency. Since the low temperature transport is dominated by the tissue region in which the Li 1 ion population is low, the dipoles in this region are well separated and non-interacting. Hence it is not surprising that the behaviour is Debye-like. As the temperature is increased, the relaxational process is dominated by transport in the Li 2 SO 4 cluster region and the relaxation becomes increasingly non-Debye like. It is interesting to note that in the regime II of

4.3. Dielectric relaxation behaviour of the glasses The dielectric constants e 9 and e 0 were measured for all the glasses between 10 Hz and 10 MHz. Since these are highly ionic glasses, the low frequency dispersion of the dielectric constant was found to be very high because of the electrode polarisation. Electrode polarisation effects at ordinary temperatures (298 K) are manifest even at kHz frequencies. It was therefore appropriate to examine the dielectric data using the modulus representation which suppresses the dc polarisation effect. The behaviour of

Fig. 6. Typical normalised plot of M0 against normalised frequency for the glass CLSP1 from 180 K to 370 K. Inset: for CLSP1 from 328–403 K.

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

ac conductivity, where the s values are insensitive to temperature, the reduced semilog plots of M0 / M0(max) versus f/f (max) were quite superimposable (see inset to Fig. 6). Non-Debye like behaviour of dielectrics is generally examined by the use of a stretched exponential function for the relaxation times:

f 5 f0 exp[2(t /t0 ) b ] where t0 is the characteristic relaxation time and b is the stretching exponent. b is generally determined by fitting M0 plots to analytical functions [39]. b is however fairly accurately determined by using the full width at half maximum (FWHM) of M0 together with b vs half width plots. The b values thus determined at a number of temperatures from the FWHM values as a function of temperature are plotted in Fig. 5b for a few typical systems. The b values in general decrease as the temperature is increased in a qualitatively similar manner as s itself (Fig. 5a). However, the scatter in b values is much higher than in the s values. This behaviour is also unusual in the sense that the sum of ( b 1s) is evidently not a constant [38]. The value of b reaches a limiting value of 1.0 at low temperatures. This is Debye like and, as noted earlier, dominated by the transport in the tissue region. The gradual increase of transport in the cluster region which occurs when the temperature is increased is associated with a decrease in b, because Li 1 ion conductivity in clusters is characterised by reduced inter-lithium ion distances and a greater interaction among the mobile lithium ions [40]. This interaction is now well known to lead to the formation of a significant density of low energy states and leads to low b values [41]. An interesting feature to note is that the transition between different s regimes and the b regimes (Fig. 5) occurs at almost similar temperatures which is again the regime of transition from the low activation barrier to the high activation barrier in dc conductivities. This is a further indication of the suitability of the cluster-tissue description of these glasses. Neither dc nor ac activation energies in the high temperature regime are well correlated to b because of the complex nature of transport in these glasses.

5. Conclusions Conductivity measurements and dielectric relaxation behaviour have been examined over a wide range of compositions in the ternary glass system Li 2 SO 4 –Li 2 O–P2 0 5 in the temperature range of 150 K to 450 K. The dc conductivity is thermally activated and exhibits two different activation barriers in the high and low temperature regimes. This seems to suggest the presence of an ultramicroscopic cluster-tissue texture in these glasses. Activation barriers for lithium ion transport in the clustered regions of Li 2 SO 4 and the semicontinuous lithium phosphate are higher than in the amorphous tissue regions. Such a model is well supported by the ac conductivity and dielectric relaxation behaviour also. ac conductivity variation with frequency has been fitted to an Almond–West type of expression using a single exponent s. Variation of s with temperature also shows a rapid decrease with temperature in the low temperature regime, followed by a nearly constant value of around 0.5 above 250 K. The dielectric data has been analysed using a modulus formalism and b values have been calculated from the dielectric relaxation peaks. Variation of b with temperature shows a similar behaviour as s, lending further support to the cluster-tissue model.

Acknowledgements The authors are thankful to the Commission of the European Communities for financial support. One of the authors (M.G.) is grateful to the Council for Scientific and Industrial Research (CSIR), India for a senior research fellowship.

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