Materials Research Bulletin 45 (2010) 1533–1536

Mixed cation effect in xR2O–(40 � x)Na2O–50B2O3–10Bi2O3 (R = Li, K) glasses

Syed Rahman, Shashidhar Bale *, R. Vijaya Kumar, N. Srinivasa Rao

Department of Physics, Osmania University, Hyderabad, Andhra Pradesh 500007, India

A R T I C L E I N F O

Article history:

Received 3 July 2009

Received in revised form 30 March 2010

Accepted 2 June 2010

Available online 10 June 2010

Keywords:

A. Amorphous materials

A. Glasses

C. Differential scanning calorimetry

D. Ionic conductivity

A B S T R A C T

Mass density, glass transition temperature and ionic conductivity are measured in xLi2O–(40 � x)Na2O–

50B2O3–10Bi2O3 and xK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass systems with 0 � x � 40 mol%. The

strength of the mixed alkali effect in Tg, dc electrical conductivity and activation energy has been

determined in each glass system. The magnitudes of the mixed alkali effect in Tg for the mixed Li/Na glass

system are much smaller than those in the mixed K/Na glasses. The impact of mixed alkali effect on dc

electrical conductivity in mixed Li/Na glass system is more pronounced than in the K/Na glass system.

The results are explained based on dynamic structure model.

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1. Introduction

When two types of alkali ions are introduced into a glassynetwork, a phenomenon known as mixed alkali effect (MAE) isobserved. It represents the non-linear variations in many physicalproperties associated with the alkali ion movement and structuralproperties, when one type of alkali ion in an alkali glass is graduallyreplaced by another, while total alkali content in the glass beingconstant [1,2]. The most evident manifestation of this effect hasbeen observed in DC electrical conductivity as a function ofcomposition where a deep minima is observed in the intermediatemixing ratio of alkali ions [3,4]. Another prominent MAE isobserved in the activation energy exhibiting a maximum as therelative composition is changed [5]. Interestingly other ‘‘dynam-ical’’ properties such as internal friction, viscosity, glass transition,expansion coefficient also exhibit a more or less pronounceddeviation. On the other hand, static properties like density appearto be linear [6]. In recent years MAE was found in mixed crystals[7], cation and anion conducting glasses [8,9] and also for glassescontaining two glass formers [10]. Recently, Chakradhar et al. [11]and Srinivasa Rao et al. [12,13] studied the EPR and opticalabsorption spectra of iron and copper doped mixed alkali glasses.

The strength of the MAE depends on many factors [1,6,14–18],e.g., temperature, total alkali content, the size and mass differenceof the involved alkali ions, etc. It has also been reported [19–22]that the magnitude of the MAE increases with the difference in sizeor mass of the involved alkali ions.

* Corresponding author. Tel.: +91 40 27222552; fax: +91 40 27222552.

E-mail address: sss_bale@yahoo.co.in (S. Bale).

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doi:10.1016/j.materresbull.2010.06.004

Different models for MAE have been proposed in the literatureand are compiled in several reviews [1,2,6]. These models assumeeither large structural modification induced by mixing mobilespecies of different sizes or specific interaction between thesedissimilar mobile species. Greaves et al. [23] in EXAFS studyindicated that the environment of the mobile cations in glasses iswell determined by the type of cation that creates the site itoccupies. Based on these results, Bunde et al. [24,25] proposed anew model for ionic migration in glasses, called the DynamicStructural Model (DSM). The main idea of the DSM model is theexistence of mismatches between the different types of sitesdesignated by cations in the glass. Ion migration is associated witha ‘‘memory effect’’ of the sites previously occupied, which leads tothe creation of ionic pathways. Hunt [26] applied the theory ofpercolative transport to the MAE and predicted a disappearance ofmixed alkali effect when temperature is raised. Recently Imre et al.[27] proposed a definition, independent component glass (ICG) andsub-network diffusion concept (SDC) to explain the mixed alkalieffect.

The aim of this paper is to study the essence of mixed alkalieffect in two mixed alkali glass systems xR2O–(40 � x)Na2O–50B2O3–10Bi2O3 with R = Li, K and 0 � x � 40 mol%. The values of x

were adjusted so that the compositional parameter defined asRLi = Li2O/(Li2O + Na2O) and RK = K2O/(K2O + Na2O) takes thevalues 0, 0.2, 0.4, 0.6, 0.8 and 1.

2. Experimental

2.1. Glass preparation

Two series of glasses having the molar formula xR2O–(40� x)Na2O–50B2O3–10Bi2O3 with R = Li, K and 0 � x � 40 mol%

Table 1Density r, molar volume Vm, oxygen packing density O, ionic concentrations N, inter-ionic distance (R) and glass transition temperature for xLi2O–(40� x)Na2O–50B2O3–

10Bi2O3 and yK2O–(40� y)Na2O–50B2O3–10Bi2O3 glass systems.

Glass composition r (g/cm3) (�0.01) Vm (cm3/mol) (�0.1) O (g-atm/l) NR (�1021/cm3) NT (�1021/cm3) R (A) Tg (8C) (�0.1)

Li(K) Na

x = 0 3.62 28.6 76.9 0 16.8 16.8 3.90 441.1

x = 08 3.34 26.5 82.8 3.6 14.5 18.1 3.80 425.0

x = 016 4.06 24.0 91.9 8.0 12.1 20.1 3.67 406.9

x = 024 4.03 23.5 93.7 12.3 18.2 30.5 3.20 403.1

x = 032 3.76 22.2 99.1 17.4 4.3 21.7 3.58 413.7

x = 040 3.54 28.9 76.1 16.7 0 16.7 3.91 416.5

y = 00 3.62 28.2 77.8 0 17.1 17.1 3.88 441.1

y = 08 3.16 33.2 66.3 2.9 11.6 14.5 4.90 350.0

y = 016 4.08 26.3 83.5 7.3 10.9 18.2 3.80 334.2

y = 024 3.76 29.3 75.1 9.9 6.6 16.5 3.92 330.0

y = 032 3.44 32.7 67.2 11.8 2.9 14.7 4.08 337.6

y = 040 2.82 40.8 53.8 11.8 0 11.8 4.39 349.2

[(Fig._1)TD$FIG]

Fig. 1. Compositional dependent glass transition temperature of xLi2O–

(40 � x)Na2O–50B2O3–10Bi2O3 and xK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glasses.

S. Rahman et al. / Materials Research Bulletin 45 (2010) 1533–15361534

have been prepared by melt quench technique. The chemicalcompositions of the studied glass samples are shown in Table 1.Li2CO3, Na2CO3, K2CO3 (all GR grade, Merck), boric acid (GRgrade) and Bi2O3 (99.8% purity) were mixed together inthe required proportion and melted in porcelain crucibles inan electrical furnace maintained at temperature rangingbetween 1000 and 1150 8C according to the composition.The melt was swirled to ensure homogeneity. The bubble freemelt is quickly cast in a stainless steel mould kept at 200 8C andpressed with another steel disc maintained at the sametemperature. All the samples were then annealed at 200 8Cfor about 12 h. The absence of any Bragg peaks in X-raydiffraction pattern confirmed that the glasses are amorphousand homogeneous. The glass composition mentioned is thenominal glass composition. The actual composition wascalculated from the exact masses of the components in theglass batch, assuming that the glass composition does notchange during melting.

2.2. Density

Density (r) measurements were carried out using Archimedesmethod with xylene (0.86 g/cm3) as an immersion liquid at roomtemperature. Molar volume (Vm), oxygen packing density (O),alkali ion concentrations (NR) and inter ionic distance (R) werecalculated and are presented in Table 1.

2.3. Glass transition temperature

The thermal behavior of the glass samples was investigatedusing a differential scanning calorimeter (Du Pont 1090).Glass samples in form of powder weighing about 15 mg weresealed in copper pans and were scanned through their meltingtemperatures with a heating rate of 10 8C/min. During all runsthe sample chamber was purged with dry nitrogen. Thetransition temperatures of the glass samples are presented inTable 1.

2.4. DC electrical conductivity

Parallel glass discs of thickness around 1.5 mm and diameter12 mm were polished for DC electrical conductivity measure-ments. The flat surfaces of the glass samples were paintedwith silver paste. The current through the sample wasmeasured by using a Keithley 616 digital electrometer. Theelectrical conductivity was measured as a function of tempera-ture.

3. Results and discussion

3.1. Density and glass transition temperature

The measured densities (r) of the lithium sodium borobis-muthate and potassium sodium borobismuthate glasses are listedin Table 1. The mass density varies in a non-linear way with theincrease in compositional parameter. For glasses containing40 mol% of alkali content, density follows the order Na > Li > K.The molar volume, oxygen packing density and inter ionic distancefor mixed alkali borobismuthate glasses are presented in Table 1.

The glass transition temperature Tg as a function of glasscomposition is shown in Fig. 1 for both quaternary glass systems.From the above figure it is clear that the glass transitiontemperature exhibit a negative deviation from linearity. Forglasses containing 40 mol% of alkali content, Tg follows the orderNa > Li > K. The strength of the mixed alkali effect in Tg can bedefined as [28]

DTg ¼ Tg;lin � Tg;min (1)

where DTg and Tg,min represent the strength of the mixed alkalieffect in Tg and the minimum value, respectively. Tg,lin isdetermined at the composition which corresponds to Tg,min andit is obtained by the linear interpolation between the glasstransition temperature of the two end members. The magnitudesof the mixed alkali effect in Tg calculated by Eq. (1) for the mixed Li/

[(Fig._2)TD$FIG]

Fig. 2. Arrhenius plots of dc conductivity for the xLi2O–(40 � x)Na2O–50B2O3–

10Bi2O3 glass system.

[(Fig._4)TD$FIG]

Fig. 4. Isothermal conductivity plots of xLi2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass

system at 150, 200 and 250 8C as a function of compositional parameter.

S. Rahman et al. / Materials Research Bulletin 45 (2010) 1533–1536 1535

Na and K/Na glasses are 23 and 56 8C, respectively. The magnitudeof the MAE in glass transition temperature in the mixed Li/Na glasssystem is much smaller than those in the mixed K/Na glass system,which coincides with studies of other mixed alkali glass systems[1,19,21,22,28–30].

3.2. DC conductivity

DC electrical conductivity was measured as a function oftemperature ranging from 100 8C to below the glass transitiontemperature of the respective glass. Figs. 2 and 3 show the DCconductivity plots of xLi2O–(40 � x)Na2O–50B2O3–10Bi2O3 andxK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass samples, respectively.It is observed that the conductivity plots are linear in log scale. Theelectrical conductivity of the glass follows the Arrhenius relation

s ¼ so exp�Ea

kT

� �(2)

where Ea is the activation energy, k is the Boltzmann’s constant, T isthe absolute temperature and so is the temperature dependentpre-exponential factor.

[(Fig._3)TD$FIG]

Fig. 3. Arrhenius plots of dc conductivity for the xK2O–(40 � x)Na2O–50B2O3–

10Bi2O3 glass system.

The isothermal plots of electrical conductivity against thecompositional parameter are shown in Figs. 4 and 5. The abovegraphs clearly shows that the minimum in conductivity wasobserved at RLi = RK = 0.4 a distinct feature of the mixed alkalieffect.

The magnitude of MAE in dc conductivity expressed in(V cm)�1 at constant temperature can be defined as

Dlog10ðsdcÞ ¼ log10ðsdc;linÞ � log10ðsdc;minÞ (3)

where log10(sdc,min) represents the minimum experimentalvalue of log10(sdc). The value of log10(sdc,lin) is obtained from thelinear interpolation between the experimentally determinedlogarithmic conductivity of the end members, at the compositionwhich corresponds to log10(sdc,min). The calculated values ofDlog10(sdc) at 150 8C by Eq. (3) for the mixed Li/Na and K/Na glasssystems are 2.10 and 1.55, respectively. However, here it issurprisingly found that in the mixed K/Na glass system themagnitude of the mixed alkali effect in log10(sdc) is smaller thanthat in the mixed Li/Na glass system even though the sizedifference between Na+ and K+ is larger than that between Li+ andNa+.

Figs. 4 and 5 show that the MAE in the logarithm of dcconductivity for the two glass systems becomes less pronounced asthe temperature is increased. The calculated values of Dlog10(sdc)for xLi2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass system are found to[(Fig._5)TD$FIG]

Fig. 5. Isothermal conductivity plots of xK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass

system at 150, 200 and 250 8C as a function of compositional parameter.

[(Fig._6)TD$FIG]

Fig. 6. Composition dependent activation energy of xLi2O–(40 � x)Na2O–50B2O3–

10Bi2O3 and xK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glasses.

S. Rahman et al. / Materials Research Bulletin 45 (2010) 1533–15361536

be 2.1, 1.75 and 1.55 at 150, 200 and 250 8C, respectively. For xK2O–(40 � x)Na2O–50B2O3–10Bi2O3 glass systems the calculated valuesof Dlog10(sdc) are found to be 1.55, 1.37 and 1.02. The similarbehavior has been found for other glass systems [14,31].

The activation energy for electrical conduction is determinedfrom the slopes of the conductivity plots. The compositionaldependant activation energies of the two glass systems are shownin Fig. 6. The activation energy exhibits a maximum as one type ofalkali ion is gradually replaced by another, a distinct feature of theMAE. Analogous to the definitions given above, the strength of theMAE in activation energy can be defined as

DEa ¼ Ea;max � Ea;lin (4)

Here Ea,max represents the maximum value of activation energy.Ea,lin is determined at the composition which corresponds to Ea,max

and it is obtained by a linear interpolation between the activationenergies of the two end members. The calculated values of DEa byusing Eq. (4) for mixed Li/Na and K/Na glasses are 0.17 and 0.28 eV,respectively. The MAE in activation energy in the mixed Li/Na glasssystem is much weaker than that in the K/Na glass system.

The mixed alkali effect observed in Figs. 4–6 can be understoodon the basis of structural model (SM) proposed by Swenson and hisco-workers [32–35], of which the essential ideas are shortlysummarized in the following.

The structure model is constructed directly from experimentalstructural data of mixed alkali glasses, and by applying the bond-valence method to reverse Monte Carlo simulations. The modelsuggests that the two types of alkali ions in mixed alkali glasses arerandomly mixed and tend to attain the same local structuralenvironment as in the single alkali glasses. The two types of alkaliions have distinctly different low dimensional conduction path-ways. This results in a large energy mismatch for ions jumpingbetween dissimilar alkali sites [36]. The mixed alkali effect ismainly due to large mismatch between the local potentials of site Aand the induced potential of ion B, as reflected by a high activationenergy for ion jumps to dissimilar sites, viz., the ion A tends toblock the pathways for B ions and vice versa. Various recentmolecular dynamic simulations [37,38] have independentlyconfirmed that the large energy mismatch is basically independentof compositions.

When analyzed in terms of the structural model, the Li+ and Na+

ions in the mixed Li/Na glasses are taken to be randomly mixed in all

the conduction pathways. This random mixing, coupled with themismatch, results in highly effective blocking of Li+ pathways by Na+

ions, and vice versa. This blocking considerably reduces the longrange mobility of both Li+ and Na+ ions in comparison to thecorresponding single component Li and Na glasses. These effectsresult in a lower dc conductivity and a higher activation energy formixed Li/Na glasses relative to their corresponding single compo-nent Li and Na glasses, producing the mixed alkali effect shown inFigs. 4 and 6. MAE’s impact on the dc conductivity in K/Na glass is lesspronounced than in the mixed Li/Na glass system. Furthermore theMAE’s impact on the activation energy in K/Na glass is morepronounced than in the mixed Li/Na glass system. Similarobservations were found in other mixed alkali glass system [28].

4. Conclusions

In this paper, density, glass transition temperature and dcconductivity of two mixed alkali borobismuthate glass systems arereported. The mass density varies non-linearly with the glasscomposition. The strength of the mixed alkali effect in Tg and inactivation energy in the mixed Li/Na glass system is lesspronounced than in the mixed K/Na glass system. This is attributedto the smaller degree of energy mismatch in the mixed Li/Naglasses than in the mixed K/Na glass system. However, it issurprisingly found that the mixed alkali effect in the dcconductivity in the mixed Li/Na glass system is higher than inthe mixed K/Na glass system.

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