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Chemical Physics Letters 424 (2006) 295–299

Relaxation of silver ions in superionic borate glasses

S. Bhattacharya, A. Ghosh *

Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, West Bengal, India

Received 11 April 2006; in final form 20 April 2006Available online 29 April 2006

Abstract

We have investigated the conductivity spectra at different temperatures for the AgI doped silver borate superionic glasses and esti-mated the concentration of mobile Ag+ ions as a function of temperature and composition. It is observed that the concentration ofmobile Ag+ ions is independent of temperature and only a fraction of the total Ag+ ions in these glasses participate in the diffusion pro-cess. The increase in conductivity due to the insertion of AgI can be attributed to the increase in hopping rate of Ag+ ions which is sup-ported by FT-IR results.� 2006 Elsevier B.V. All rights reserved.

1. Introduction

The understanding of ion diffusion process in superionicglasses is of both practical and academic interest [1–4].These materials are currently under investigation for tech-nical application as solid electrolytes in electrochemicaldevices such as batteries, sensors, electrochromic displays,etc. due to their high ionic conductivity, high stabilityand large available composition ranges. It is also interest-ing in the academic level to understand the nature of iondiffusion in these materials.

A particularly interesting class of fast-ion conductors isthe AgI-doped silver borate glasses which can accommo-date a high content of AgI in a disordered phase withoutany evidence of crystallization [1,2]. The best conductingglasses may reach conductivity up to 10�2 S/cm at roomtemperature [2]. The role of Ag2O seems to be quite differ-ent from other modifying cations, because the local coordi-nation is characterized by an unusually low coordinationnumber and a short distance, as shown by EXAFS mea-surements [5]. Much attention has been focused on howAgI is introduced into the glassy borate network. Mainlytwo models have been proposed: first suggests that AgI iscoordinated with the BO4 units and thus is homogenously

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doi:10.1016/j.cplett.2006.04.077

* Corresponding author. Fax: +91 33 2473 2805.E-mail address: sspag@iacs.res.in (A. Ghosh).

dispersed in the host Ag2O–2B2O3 network [6] and the sec-ond proposes that AgI forms small clusters or microdo-mains of an ‘amorphous-like’ AgI with tetrahedralcoordination to that of crystalline superionic a-AgI [7].Raman spectroscopy result [8] suggests existence of sucha-AgI domains, especially at higher AgI concentrationsalthough (EXAFS) [9], 109Ag NMR [10] and X-ray diffrac-tion [11] support absence of an ordered AgI phase resem-bling a-AgI. In the microdomain model, the Ag+ cationsexist in two coordination environments, one related tothe iodide anion and the other with oxygen ions (bridgingor non-bridging oxygens) [6]. In the latter model, the Ag+

cations share a common coordination with iodide anionsand oxygen atoms [5]. Recently X-ray and neutron-diffrac-tion data of silver borate glasses have been used [12] forstructural modelling for fast ion conducting glass systemsusing the reverse Monte Carlo method [13] which predictsthat most of the Ag+ ions are coordinated to both I� ionsand BO4 units in the network [12]. It is concluded that,while the short-range order of the borate network is unaf-fected by AgI doping, by increasing the amount of AgIcontent improves the medium-range order of the glass byinducing ordering between the neighboring boron–oxygenchain segments. It is therefore proposed that the improve-ment of medium-range order in glass can be connected withthe network expansion and the creation of new pathwaysfor ion transport [13].

103 105 107

10-9

10-8

10-7

10-6

1x10-5

104 105 106 10710-9

10-8

10-7

10-6

(b)

(a)

T = 1 5 3 K T = 1 5 8 K T = 1 6 3 K T = 1 7 3 K T = 1 8 3 K T = 1 9 3 K T = 2 0 3 K T = 2 1 3 K T = 2 2 3 K

σ' (

ω)

(Ω-1

cm

-1)

ω [rad s-1]

ω [rad s-1]

(σ' (

ω)-

σ dc)

(Ω-1

cm-1)

T = 1 5 3 K T = 1 5 8 K T = 1 6 3 K T = 1 7 3 K T = 1 8 3 K T = 1 9 3 K T = 2 0 3 K T = 2 1 3 K T = 2 2 3 K

Fig. 1. (a) Conductivity spectra for the 0.2AgI � 0.8(Ag2O–2B2O3) glasscomposition at different temperatures shown in the inset. The solid linesare best fits to Eq. (1). (b) Variation of the dispersive conductivity(r 0(x) � rdc) with frequency for the same glass composition and temper-atures as in (a).

296 S. Bhattacharya, A. Ghosh / Chemical Physics Letters 424 (2006) 295–299

However, despite many experimental and theoreticalefforts [1–3,12,13] the mechanism of Ag+ ion dynamics inAgI doped borate glasses is partly understood yet due tothe difficulty in separating the contribution of the ion con-centration and the mobility from the measured conductiv-ity. There is no general agreement about the fraction ofAg+ ions participating in the dynamic process, which isone of the most critical parameters to explore the transportmechanism of the presently studied system.

Conductivity spectroscopy is a well established methodfor characterizing the hopping dynamics of the ions. Avariety of different materials have been studied using thistechnique. It is well documented in the literature [14,15]that in the usual experimental frequency window and tem-perature range, the overall frequency response of the realpart of the conductivity can be described by

r0ðxÞ ¼ rdc½1þ ðx=xcÞn�; 0 6 n < 1 ð1Þwhich is the sum of a constant dc conductivity, rdc and afractional power law dependence with an exponent n. xc

is a characteristic crossover frequency from dc to dispersiveconductivity. Both the dc conductivity and the crossoverfrequency, above which r 0(x) � xn, are thermally acti-vated. However, there is another contribution to the dis-persive conductivity, which consists of a nearly frequencyindependent dielectric loss and corresponds to an almostlinear frequency dependent term of the form r 0(x) = Axfor the real part of the complex conductivity. At sufficientlylow temperatures or high frequencies, the Ax term domi-nates over the power law dependence of the conductivitygiven by Eq. (1) [16].

In this Letter, we have investigated the conductivityspectra for AgI doped silver diborate glasses at differenttemperatures and estimated Ag+ ions participating in thetransport process. We have shown that the increase in theconductivity due to the AgI doping is not due to theincrease in the number of mobile Ag+ ions, but is due tothe increase in the mobility of Ag+ ions. The results areclarified also by the analysis of the FT-IR absorption spec-tra of the glasses.

2. Experimental

Glass samples of compositions xAgI � (1 � x)(Ag2O–2B2O3), where x = 0–0.5 were prepared in two steps. First,Ag2O–2B2O3 base glass was obtained by melting AgNO3

and H3BO3 at 750 �C for 6 h in a platinum crucible andthen quenching the melt in an aluminum mould. In the sec-ond step, appropriate amounts of AgI and the base glasswere mixed, melted in platinum crucible at 750 �C for30 min and poured in an aluminum mould to get final glasssamples. Glass samples of thickness �0.1 cm were obtainedfor x = 0–0.5. Glass formation was confirmed from X-raydiffraction. The density of the samples was measured usingArchimedes’ principle with acetone as an immersion liquid.The FT-IR spectra of the bulk glass samples in absorptionmode were recorded in a Nicolet FT-IR spectrophotometer

(Magna IR-750, Series II) at 25 �C and at relative humidityof 50–60%. For FT-IR measurements, pellets of thickness1 mm and diameter 13 mm were obtained by pressing amixture of 1 part of glass and 60 parts of KBr at a pressureof 200 kg/cm2. The electrical measurements such as capac-itance and conductance of the samples were carried out ongold coated samples of diameter �1 cm in the frequencyrange 10 Hz to 2 MHz using a RLC meter (QuadTech,model 7600)and in the temperature range 93–393 K.

3. Results and discussion

The frequency dependence of the conductivity at differ-ent temperatures for a typical glass composition is shownin Fig. 1a. At low frequencies the conductivity is indepen-dent of the frequency corresponding to the dc conductivity.The frequency dispersion starts at a higher frequency as thetemperature is increased. The dispersive portion is firstanalyzed by subtracting the dc conductivity from the mea-sured conductivity as shown in Fig. 1b. It is noted that in

3 4 5 6 7 8 9

2

3

4

5

6

7

0.0 0.1 0.2 0.3 0.4 0.55

6

7

8

9

10

(a)

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5

log 10

[ωh (r

ads-1

)]

log 10

[ωh (r

ads-1

)]

1000 / T (K -1)

(b)

x

Fig. 2. (a) Arrhenius plots of the hopping frequency of xAgI � (1 � x)-(Ag2O–2B2O3) glasses, obtained from the best fits of conductivity spectra,for different values of x, to Eq. (1). The solid lines are the least-squarestraight line fits of the data. (b) Compositional variation of the hoppingfrequency of mobile ions xh at room temperature (298 K).

S. Bhattacharya, A. Ghosh / Chemical Physics Letters 424 (2006) 295–299 297

the frequency window the slopes give power law exponent(0.65) which is much less than unity and independent oftemperature. Thus, the nearly constant loss region is absentin the investigated frequency window and the temperaturerange, and the data can be described by the power lawmodel (Eq. (1)). The conductivity spectra for all composi-tions were then fitted to Eq. (1). We have replaced rdc inEq. (1) by the following expression for rdc given by theNernst–Einstein relation

rdc ¼ q2d2ncxh=12pkT ; ð2Þwhere nc and d is the mobile ion concentration and thejump distance, respectively. It has been pointed out [17]that short range displacements of the ions at higher fre-quencies are thought to be coupled to the ionic environ-ment. Interionic interactions become important, and theshort range hopping is often viewed as the highly correlatedmotion in which the ions perform several reiterated for-ward–backward hops before completing any successful for-ward displacement [17,18]. The power law dispersion (Eq.(1)) is thus a consequence of this reiterated hopping and oc-curs down to the crossover frequency xc below which suc-cessful hops can be completed [17]. Thus in the presentapproach it can be tacitly assumed [17–19] that the cross-over frequency, xc in Eq. (1) is close to the hopping fre-quency of the mobile Ag+ ions, presented as xh in Eq.(2). Recent NMR and conductivity experiments of somecrystals and AgI-doped fast ion conducting glasses [20–22] have indicated that xc is slightly longer than xh, whichdoes not change the values of nc drastically, justifying ourassumption for the present AgI-doped glasses. Threeparameters nc, xh and n were obtained at different temper-atures for all glass compositions. We have taken the jumpdistance as the nearest Ag–Ag distance for these glasses ob-tained from structural studies [12].

We note that the values of power law exponent n arealmost independent to AgI content within experimentalerrors. The temperature dependency of xh is shown inFig. 2a. Fig. 2b shows the variation of the hopping ratexh of mobile Ag+ ions at room temperature as functionAgI content. It is observed that the hopping rate increaseslinearly with the increase of AgI content in the host glassnetwork. From Fig. 2a it is noteworthy that xh showsArrhenius behavior with activation energy (Eh) very closeto the activation energy (Er) for the dc conductivity rdc

(Fig. 3). The Arrhenius temperature dependence of nc isshown in Fig. 4a, which indicates that nc is almost indepen-dent of temperature. The variation of the estimated mobileion concentration nc with AgI content in the compositionsis shown in Fig. 4b. The variation of the total Ag+ ion con-centration is also shown in the same figure. It is clear in thefigure that the mobile Ag+ ion concentration obtainedfrom the analysis is much less than the total Ag+ ion con-centration. Thus, a fraction of the Ag+ ions are mobile andare weakly dependent on composition.

It is worthy to mention here that the NMR experimentsof AgI doped borate glasses [23] have also demonstrated

that a fraction of Ag+ ions participate in the dynamic pro-cess. In Fig. 4b, we have also included the mobile ion con-centration obtained from NMR experiments [23]. We notethat the fraction of mobile ions obtained from the presentanalysis are comparable with those reported from NMRexperiments [23].

The FT-IR absorbance spectra of AgI doped andundoped silver diborate glasses is shown in Fig. 5a in thefrequency range 500–1550 cm�1. Strong band envelopescentered at 1350 and 1000 cm�1 are observed in all glasscompositions. These features are attributed to the asymmet-ric stretching of B–O bonds in borate triangles BO3 andBO2O� (1350 cm�1) and in tetrahedral units, BO�4(1000 cm�1), respectively [24,25]. The remaining band enve-lopes centered at 700 cm�1 arise from the deformationmodes of borate network structures [7]. All the spectra inFig. 5a present quite similar band shapes, indicating thatAgI addition does not cause the formation of new structuralunits in the borate network, although the AgI content arevaried in a rather broad range, 0 6 x 6 0.5. However, it is

3 4 5 6 7 81020

1021

1022

0.0 0.2 0.4 0.6 0.8 1.01021

1022

(b)

(a)

n c (cm

-3)

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5

1000/T ( K -1)

[Ag+

] (c

m- 3

)

x

Fig. 4. (a) Arrhenius plots of the mobile Ag+ ion concentration obtainedfrom the analysis of the conductivity spectra of xAgI � (1 � x)(Ag2O–2B2O3) glasses, for different values of x. (b) Variation of Ag+ ionconcentration with composition for xAgI � (1 � x)(Ag2O–2B2O3) glasses:(h) total Ag+ ion concentration obtained from the composition anddensity; (e) mobile Ag+ ion concentration nc obtained from the analysisof the conductivity spectra; ($) mobile Ag+ ion concentration obtainedfrom NMR experiments [23].

600 900 1200 1500

0.0 0.1 0.2 0.3 0.4 0.50.6

0.9

1.2

(b)

(a)

x=0.5

x=0.1

x=0.2

x=0.3

x=0.4

x=0.0

arb.

uni

ts

Wavenumbers (cm-1)

A 4 /

A 3

x

Fig. 5. (a) FT-IR absorption spectra for xAgI � (1 � x)(Ag2O–2B2O3)glasses for different values of x. (b) Relative absorption A4/A3 as afunction of AgI content in xAgI � (1 � x)(Ag2O–2B2O3).

2 3 4 5 6 7 8 9-8

-6

-4

-2

0 x = 0 . 0 x = 0 . 1 x = 0 . 2 x = 0 . 3 x = 0 . 4 x = 0 . 5

log 10

[σdc

T (

Ω-1 c

m-1

K)]

1000 / T (K-1)

Fig. 3. Arrhenius plots of dc conductivity obtained from compleximpedance plots of xAgI � (1 � x)(Ag2O–2B2O3) glasses, for differentvalues of x. The solid lines are the least-square straight line fits of thedata.

298 S. Bhattacharya, A. Ghosh / Chemical Physics Letters 424 (2006) 295–299

observed that AgI addition induces a change in the relativeintensities of the envelopes at 1350 and 1000 cm�1. The nar-rowing of the 1350 cm�1 envelope indicates the occurrenceof AgI-induced structural rearrangements in these glasses.

The integrated absorption of the characteristic bandenvelopes between 780 and 1180 cm�1 (A4) and between1180 and 1570 cm�1 (A3) was calculated to probe the rela-tive population of borate tetrahedra (BO�4 ) and triangles(BO3 and B2O�), respectively, in the glasses. The A4/A3

ratio presented in Fig. 5b demonstrates a strong depen-dence on the AgI doping into the host network. It is note-worthy from Fig. 2b that hopping rate xh also varies in thesame manner with AgI content. Since addition of AgI toAg2O–2B2O3 glass is not expected to change the total for-mal negative charge on the borate network, the dependenceof the A4/A3 ratio on AgI content can be understood interm of changes in the population of borate species. Thiscan be expressed by the following chemical equilibrium[26] that takes place in the melt and involves the isomericB2O� and BO�4 species

BO�4 �B2O� ð3ÞThe data presented in Fig. 5b indicate that when the AgIcontent is increased the above equilibrium shifts progres-

S. Bhattacharya, A. Ghosh / Chemical Physics Letters 424 (2006) 295–299 299

sively to the left. Thus the Ag+ ions coordinate with bothI� ion and BO�4 units with the insertion of AgI into thehost glass network. The host glass network expands consid-erably to accumulate the dopant ions [12,13] and changesof the intermediate structure are indicated. This expansionenhances the hopping rate of mobile Ag+ ions as shown inFig. 2b and hence increases the ionic conductivity.

4. Conclusions

We have studied the dynamics of Ag+ ions in superionicsilver borate glasses by conductivity spectroscopy and esti-mated the mobile Ag+ ions participating in the transportprocess. We have observed that the mobile Ag+ ion con-centration is less than the total Ag+ ions estimated fromglass compositions and density and is independent of AgIdoping. Thus AgI insertion into the host network primarilyenhances the mobility, i.e. the hopping rate of mobile Ag+

ions by the improvement of the medium-range order of theglass as observed from the analysis of FT-IR absorptionspectra.

Acknowledgements

The work is supported partly by the Department of Sci-ence and Technology (via Grant No. SP/S2/M43/99) andpartly by Department of Atomic Energy (via Grant No.2002/37/32/BRNS), Government of India.

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