Structure and electrical conductivity relaxation studiesof Nb2O5-doped B2O3–Bi2O3–LiF glasses

M. H. Shaaban

Received: 24 January 2012 / Accepted: 5 April 2012 / Published online: 1 May 2012

� Springer Science+Business Media, LLC 2012

Abstract Glasses with composition (70 - x) B2O3�15Bi2O3�15LiF�xNb2O5 with x = 0–1.0 mol% were prepared by

conventional glass-melting technique. The molar volume

Vm values decrease and the glass transition temperatures Tg

increase with increase of Nb2O5 content up to 0.2 mol%,

which indicates that Nb5? ions act as a glass former.

Beyond 0.2 mol% Nb2O5 the Vm increases and the Tg

decreases, which suggests that Nb5? ions act as a glass

modifier. The FTIR spectra suggest that Nb5? ions are

incorporated into the glass network as NbO6 octahedra,

substituting BO4 groups. The temperature dependence of

the dc conductivity follows the Greaves variable range

hopping model below 454 K, and follows the small polaron

hopping model at temperatures [454 K. rdc, rac conduc-

tivity and dielectric constant (e) decrease and activation

energy for dc conduction DEdc which increases with

increasing Nb2O5 content up to 0.2 mol%, whereas rdc, rac

and (e) increase and DEdc decreases with increasing Nb2O5

content beyond 0.2 mol%. The impedance spectroscopy

shows a single semicircle or arcs which indicate only the

ionic conduction mechanism. The electric modulus for-

malism indicates that the conductivity relaxation is

occurring at different frequencies exhibit temperature-

independent dynamical process. The (FWHM) of the nor-

malized modulus increases with increase in Nb2O5 content

suggesting that the distribution of relaxation times is

associated with the charge carriers Li? or F- ions in the

glass network.

Introduction

Borate glasses containing Bi2O3 have received significant

attention for optical applications because of their special

properties such as high refractive index, IR transmitting,

and high non-linear optical susceptibility [1, 2]. Also,

niobium borate glasses have high chemical resistance,

surface hardness, high refractive indices, excellent trans-

parency in the visible-IR region, and intense UV absorp-

tion, which give then a promising application as nonlinear

photonic materials [3]. B2O3 is a common glass former.

The structure of vitreous B2O3 glasses consists of a random

network of boroxyl rings and BO3 triangles connected by

B–O–B linkages [4].The addition of a network modifier in

borate glasses could induce the conversion of the triangular

BO3 structural units to BO4 tetrahedral with a coordination

number four [5]. Bi2O3 is a conditional glass former, par-

ticipates in the glass structure with two possible coordi-

nation, [BiO3] pyramidal and [BiO6] octahedral units [6].

Previous studies of the introduction of Nb2O5 in alkali or

alkali earth borate glasses [7–9] revealed that the Nb5? ions

are incorporated into the glass network as NbO6 octahedral,

substituting BO4 groups and giving rise to non-bridging

oxygens (NBOs). These studies indicated that with increase

in Nb2O5 concentration in glass, changes in the glass

properties are observed e.g., (i) a decrease in the glass

transition temperature; (ii) An increase in the density and

the molar volume; (iii) Decrease in the optical band gap

energy (Eg); and (iv) An increase in the dc conductivity.

These results revealed the increase in the number of NBO

sites and reviled also that Nb2O5 acts as a network

modifier.

The ac conductivity measurements are widely used to

study ionic dynamics in glasses of different composition.

The ac data are usually analyzed in terms of conductivity

M. H. Shaaban (&)

Department of Chemistry, Faculty of Science,

Tanta University, Tanta, Egypt

e-mail: mhani55@hotmail.com

123

J Mater Sci (2012) 47:5823–5832

DOI 10.1007/s10853-012-6482-3

relaxations [10]. In electronic and ionic conducting glasses,

hopping of charge carriers is the principal mechanism of

relaxation. Thus the frequency dependence of the ac con-

ductivity provides important information about ion trans-

port mechanism in solid electrolytes [11]. Glasses

containing Li? ion had considerable applications in high

energy density batteries and sensors [12]. Glasses con-

taining network modifier such as Li? ions are ionic con-

ductors [13]. Introduction of LiF has been known to

decrease the electrical conductivity of the glass. This

behavior was attributed to the formation of local columbic

traps of F- ions which impede Li? ion motion [14].

Previous studies in fluoride and bismuthate glasses

containing LiF [12] concluded that the electrical conduc-

tivity results from mixed contribution of the positively

charged Li? ions and the F- ions, which may act as

impurity and/or as terminal non-bridging halide ion.

Previous studies on Nb2O5-containing glass were carried

out on glasses containing more than 1 mol% Nb2O5 at

least. There are no reports on the electrical properties of

borate glasses containing less than 1 mol% Nb2O5. Hence,

in this work, the ac conductivity of (70 - x)B2O3�15Bi2O3�15LiF�xNb2O5 with x = 0–1.0 mol% glasses was

studied as a function of frequency and temperature to

investigate the effect of Nb2O5 content on the conduction

and relaxation mechanism in such glasses.

Experimental

Glass preparation

The (70 - x) B2O3�15Bi2O3�15LiF�xNb2O5 glasses with

x = 0, 0.1, 0.2, 0.4,0. 5, 0.6, 0.8, and 1.0 mol% were

prepared by melting the appropriate mixtures of Analar

grade Bi2O3, H3BO3, LiF, and Nb2O5. The mixtures were

melted in alumina crucibles at 950 �C for 30–40 min. The

glass melts were stirred occasionally with an alumina rod

to achieve good homogeneity. The highly viscous melt was

cast into a cylindrically shaped split mold of mild steel

plate. A coin-shaped samples of thickness about 2–3 mm

were formed of 10-mm diameter The glass produced was

annealed at 400 �C in another furnace for 1 h after which

the furnace was switched off and the glass was allowed to

cool gradually in situ for 24 h.

Glass characterization

The X-ray diffraction technique was used to confirm the

glassy nature of the prepared compositions, using a XRD-

6000 Shimadzu diffractometer, equipped with a mono-

chromator of graphite for the Cu–K radiation (=1.54 A) at

room temperature. The featureless nature of these patterns

(not shown) confirms that all prepared samples are amor-

phous. The XRD patterns (not shown) did not reveal dif-

fraction peaks. These confirm the amorphous nature of the

present glasses.

Physical properties

The density measurements of the samples were carried out

at room temperature, by the Archimedes method with

xylene as an immersion liquid. The density was calculated

according to the equation:

q ¼ W1= W1 þW2ð Þð Þ � 0:86 ð1Þ

where q is the density of the sample, W1 the weight of the

sample in air, W2 the weight of the sample in xylene, and

0.86 is the density of xylene. The molar volume, Vm, is

determined as

Vm ¼ Mi=q ð2Þ

Mi is the average molecular weight.

Differential thermal analysis (DTA) was performed

using a Shimadzu XD-30 thermal analyzer. A heating rate

of 5 �C min-1 was used to determine the glass transition

temperature.

FTIR spectroscopy

The IR transmission spectra of glass samples were recorded

at room temperature, by KBr pellet technique on Shimadzu

FTIR-8001 PC spectrophotometer in the range 400–

4000 cm-1.

Ac and dc conductivity measurements

The glass samples were polished by usual techniques to a

thickness about 2 mm. Each sample was coated with col-

loidal silver paste on both sides. The samples were heated

at 100 �C for 2 h to insure the good adherence between the

electrode and the sample surfaces. The constructed cell for

the electrical measurements consists of a silica tube sur-

rounded by nickel chrome wire as a heater. A (chromel–

alumel) thermocouple (inside the tube) was used for

temperature measurement. The ac conductivity was mea-

sured by applying the complex impedance technique. A

constant ac voltage (Vr.m.s = 1 V) was applied to the

sample. The current passes through the sample were

determined by measuring the potential difference across an

ohmic resistor connected in series to the sample using a

lock-in amplifier (Stanford Research System SR510). The

lock-in amplifier simultaneously measures the voltage

across the resistor and the phase difference / between this

voltage and the applied voltage on the sample. Since the

voltage drop on the ohmic resistance is in phase with the

5824 J Mater Sci (2012) 47:5823–5832

123

current I, it can be assumed that / is the phase angle

between the voltage drops on the sample and the current

I passing through it. The ac conductivity rac, the dielectric

constant e\, the imaginary part of permittivity e\\, and the

real and imaginary parts of the electric modulus M* were

calculated by a computer program (Microsoft office Excel

2007). To overcome the effect of humidity, the electrical

conductivity was measured under vacuum. The measure-

ments were acquired at different temperatures from 300 K

up to 607 K. Furthermore, the dc conductivity was mea-

sured by applying a constant voltage (10 V) and measuring

the current, then applying Ohm’s Law. The current was

measured using Keithley Electrometer type 617.

Results and discussion

Density, molar volume, and glass transition temperature

The density of the studied glasses (Table 1) increases with

increasing Nb2O5 content. The increase in the density can

be related to the replacement of B2O3 by Nb2O5 of a

greater molecular mass. Table 1 shows also that the molar

volume Vm values decrease and the glass transition tem-

perature Tg values increase with the initial replacement of

B2O3 by Nb2O5 up to 0.2 mol% Nb2O5. However, with

further increase of Nb2O5 content, an increase in the Vm

values and decrease in the Tg values are noticed. The

decrease in Vm and increase in Tg values at such low Nb2O5

content (up to 0.2 mol%) may indicate that the Nb2O5

placed in substitutional positions in the glass network, i.e.,

it acts as a glass former [15, 16]. The increase in Vm and

decrease in Tg values with further increase of Nb2O5 (for

x [ 0.2 mol%), could be explained assuming that the

Nb2O5 (NbO6 octahedral) groups replace the BO4 tetra-

hedral groups producing NBOs, which form a more open

structure [7, 9].

FTIR spectral studies

The effects of Nb2O5 content on the FTIR spectra of

(70 - x) B2O3.15Bi2O3.15LiF.xNb2O5 glasses are shown

in Fig. 1 which reveals the following:

(1) A sharp band around 700 cm-1 due to the bending

vibration of B–O–B linkages of BO3 units [17].

(2) IR band in region around 800–1200 cm-1 can be

attributed to B–O stretching vibration of borate

tetrahedral (BO4) unit [18].The shoulder around

840 cm-1 is related to the symmetrical stretching

vibration of the Bi–O bonds in the [BiO3] groups [19].

Table 1 Composition, average molecular weight (Mi), density (q), molar volume (Vm), and glass transition temperature (Tg) of xNb2O5

(x = 0–1.0 mol%)

Glass number (x = Nb2O5%) Average molecular

weight (Mi)

Density

g/cm3 (q)

Molecular

volume (Vm)

Glass transition

temperature (K) (Tg)

1 0.0 122.516 4.280 28.625 728

2 0.1 122.714 4.292 28.591 730

3 0.2 122.911 4.305 28.550 731

4 0.4 123.304 4.309 28.615 726

5 0.5 123.500 4.311 28.634 723

6 0.6 123.696 4.315 28.662 721

7 0.8 124.088 4.321 28.727 718

8 1.0 124.481 4.324 28.803 714

Fig. 1 The FTIR spectra of (70 - x) B2O3�15Bi2O3�15LiF�xNb2O5

glasses

J Mater Sci (2012) 47:5823–5832 5825

123

(3) A peak is observed in the region between 1200 and

1600 cm-1 and is attributed to the B–O stretching

vibration of BO3 units [20]. The shoulder around

1234 cm-1 found in this glass system is assigned to

the B–O stretching vibrations of (BO3) units with

non-bridging oxygen atoms [17, 21]. This shoulder

becomes more observed as the content of Nb2O5

increases, as revealed in Fig. 1. This result indicates

that the number of non-bridging oxygen atoms

increases with increase in the content of Nb2O5.

(4) A broad band 3200–3600 cm-1 is obtained in all the

glasses, which is attributed to hydroxyl or water

groups [22].

FTIR spectra revealed that the intensity of the vibration

due to (BO4) unit is observed to decrease, whereas the

intensity of the band due to (BO3) units increases at the

expense of (BO4) structural units with increasing Nb2O5

content. Since the bands of BO4 unit are positioned in the

same region as those of the NbO6, it is difficult to distin-

guish the vibration bands of NbO6 [23]. Accordingly, the

observed change in molar volume Vm and Tg values (Sec-

tion ‘‘Density, molar volume, and glass transition temper-

ature’’) is indirectly supporting the introduction of NbO6

groups. The NbO6 octahedral is the preferred form of Nb5?

[24].The results obtained from FTIR spectra suggest that

Nb5? ions are incorporated into the glass network as NbO6

octahedral, substituting BO4 group, with increasing number

of NBO atoms [7].

Dc conductivity

The temperature dependence of the dc conductivity, inthe

temperature range (300–607 K), for the glass system (70 - x)

B2O3.15Bi2O3.15LiF.xNb2O5 with x = 0–1.0 mol% is

shown in Fig. 2. This figure illustrates a linear temperature

dependence of the dc conductivity at high temperatures

[454 K, whereas in the low temperature region below 454 K

a non-linear dependence of dc conductivity was observed.

This behavior is in agreement with that reported for different

borate glasses [25, 26], and is attributed to the change of

conduction model from small polaron hopping (SPH) model

at high temperature to Greaves variable range hopping (VRH)

at low temperature [27]. At low temperatures, where the

polaron binding energy is small and the static disorder energy

of the system plays the dominant role in the conduction

mechanism, Mott [27] has proposed that polarons may hop

preferentially beyond nearest neighbors. The conductivity

according to VRH model is given by:

½r ¼ roexp �A=T1=4� �

ð3Þ

where A ¼ 2:06 a3=kN Efð Þ� �1=4 ð4Þ

roT ¼ e2=2 8pð Þ1=2n o

mph N Efð Þ =a k T½ �1=2 ð5Þ

where mph is the phonon frequency, A is constant, a is the

electron wave function decay constant, e is the electron

charge, and N (Ef) is the density of state at the Fermi level.

A plot of log rdc versus T-1/4 should be linear as revealed

from Eq. 3. Figure 3 represents a linear relation between

log rdc and T-1/4 at low temperatures. The observed line-

arity suggested the validity of the VRH model for the

conduction mechanism at such low temperatures [28].

According to SPH, the electrical conductivity at high

temperatures [454 K (non-adiabatic regime) is expressed

as

r ¼ ro exp DEdc=k Tð Þ ð6Þ

1.6 2.0 2.4 2.8 3.2-15

-14

-13

-12

-11

-10

-9

-8

Logσ

dc (

Ω-1cm

-1)

T-1(1000/K)

x=0.0% x=0.1% x=0.2% x=0.4% x=0.5% x=0.6% x=0.8% x=1.0%

Fig. 2 The relation between Log rdc conductivity and 1000/T for

glass samples as a function of Nb2O5 content (x = Nb2O5 mol%)

0.220 0.225 0.230 0.235 0.240 0.245-14

-13

-12

-11

-10

Logσ

dc (

Ω-1cm

-1)

T-1/4(K-1/4)

x=0.0% x=0.1% x=0.2% x=0.4% x=0.5% x=0.6% x=0.8% x=1.0%

Fig. 3 Log rdc conductivity and Log rac conductivity at 100 kHz

versus Nb2O5 content at 300 K

5826 J Mater Sci (2012) 47:5823–5832

123

where ro is the constant for a given glass, k is the Boltz-

mann constant, and DEdc is the activation energy for dc

conduction. The values of DEdc and ro were evaluated by

least-square fitting of the experimental data. DEdc values

are given in Table 2. Figure 4 represents the variation of dc

conductivity as a function of Nb2O5 content. This figure

indicates that the dc conductivity decreases and reaches a

minimum value for glasses containing 0.2 mol% Nb2O5.

However, the activation energy for dc conduction DEdc

behavior shows a reverse behavior with increasing Nb2O5

content (Table 2). The gradual decrease in the dc con-

ductivity and increase in the activation energy (up to

0.2 mol% Nb2O5) reveal a decrease in the mobility of the

charge carriers which could be attributed to the fact that the

Nb2O5 occupy preferentially substitutional positions in

the glass network. In other words, Nb5? ions act as a glass

former and accordingly decrease the electrical conductivity

[15, 16].

Figure 2 reveals also an obvious increase in dc con-

ductivity and decrease in dc activation energy with

increasing Nb2O5 content beyond 0.2 mol%. This can be

explained by taking into consideration that as the Nb2O5

content in glass increase, the number of NBO ions

increases and thereby the glass network is weakened,

making ion displacement easier causing an increase in

the dc electrical conductivity [7, 9]. This result supports the

conclusion obtained from the observed change in the molar

volume values with the change of Nb2O5 content in the

studied glasses. The observed increase in dc conductivity

with increase in temperature (Fig. 2) reveals the semicon-

ducting nature of the present glass samples. The linearity

between the conductivity and the activation energy (Fig. 5)

suggests that (i) hopping is adiabatic, which indicates that

the activation energy is temperature-independent in this

temperature range [21]. (ii) The conductivity enhancement

is directly related to the increasing mobility of the charge

carriers, mainly due to monovalent lithium and or fluoride

ions. Previous studies [29] revealed that the ionic

conduction mechanism is attributed to the mobility of

lithium ions. Thus, the increase in the concentration of

Nb2O5 increases the modifying action of Nb?5 ions, which

creates easy paths for the movement of the charge carriers

(Li? and or F ions), which in turn increase the dc con-

ductivity and decreases the activation energy for dc

conduction.

Ac conductivity

The frequency dependence of the ac conductivity in glass

containing Nb2O5 at different temperatures is represented

in Fig. 6 (for sample containing 0. 6 mol% Nb2O5). At

room temperature, the ac conductivity shows linear fre-

quency dependence. However, at higher temperatures, the

ac conductivity exhibits two distinct regimes: (i) the low

frequency plateau corresponds to frequency independent ac

conductivity, rdc, and (ii) high frequency dispersion regime

(ac conductivity frequency dependent). The frequency-

independent plateau at low frequency region is attributed to

Table 2 The calculated values of dc conductivity, ac conductivity and frequency exponents at room temperature, activation energy DEdc, and

activation energy for the conductivity relaxation DEs of xNb2O5 (x = 0–1.0 mol%)

Glass number (x = Nb2O5%) Logdc (300 K) (X-1 cm-1) Lograc (300 K) (X-1 cm-1) s value at (300) K DEdc (eV) DEs (eV)

1 0 -13.25 -9.21 0.932 0.832 0.851

2 0.1 -13.43 -9.35 0.940 0.897 0.891

3 0.2 -14.08 -9.42 0.922 0.916 0.910

4 0.4 -12.78 -9.14 0.904 0.823 0.813

5 0.5 -12.12 -8.81 0.887 0.790 0.786

6 0.6 -11.90 -8.66 0.864 0.744 0.736

7 0.8 -11.48 -8.54 0.854 0.712 0.704

8 1.0 -11.01 -8.43 0.822 0.669 0.662

0.0 0.2 0.4 0.6 0.8 1.0

-14

-13

-12

-11

-10

-9

-8

Log(

cond

uctiv

ity)

( Ω-1cm

-1)

Nb2O

5mol%

dc conductivity ac conductivity at100kHz

Fig. 4 The relation between Log rdc conductivity and T1/4 for glass

samples as a function of Nb2O5 content t (x = Nb2O5 mol%)

J Mater Sci (2012) 47:5823–5832 5827

123

the long-range translational motion of ions contributing to

dc conductivity rdc. Figure 6 reveals that the switch over of

the frequency independent region to frequency-dependent

region at higher frequencies, shifts to higher frequencies

with increasing temperature. This behavior implies the

onset of conductivity relaxation. The strong frequency

dispersion of the ac conductivity is because the inhomo-

geneities in the glasses may be of a microscopic scale in

nature with the distribution of relaxation processes through

distribution of energy barriers [30]. The temperature and

frequency dependences of the ac conductivity for other

glass compositions are qualitatively similar. The conduc-

tivity dispersion is well described by the Jonscher’s who

referred to it as universal dynamic response (UDR) [31].

r xð Þ ¼ ro þ A xs ð7Þ

where ro is the dc conductivity, rac = A xs, A is a constant

and s is the power law exponent. The values of the

exponent s, for all samples determined to be in the range

0.93 and 0.64. The s values are almost less than unity and

decrease with increasing temperature. The numerical values

of s at room temperature are in the range 0.82 \ s \ 0.93

(Table 2). Many reports evolving hopping models give

values of s in the range from 0.6 to 1[32, 33]. The correlated

barrier hopping model (CBH) proposed by Elliot [34],

indicated that the exponent s is frequency and temperature

dependent, with s values increasing toward unity as tem-

perature decreased. The data obtained from Table 2 and

Fig. 6 clearly shows that the CBH model seems to be the

appropriate theory for the AC conductivity in the studied

glasses. The exponent s is a measure of the degree of inter-

action with the environment. Generally the parameter s may

depend on the glass composition and the limit of measure-

ment temperature [35]. Sidebottom concluded that the

exponent s depends upon the dimensionality of the local

conduction space and its value decreases with decreasing

dimensionality [36]. According to these conclusions, the

observed decrease in the value of s with increasing Nb2O5

content could be explained by the fact that, the addition of

Nb2O5 promote the formation of a high number of non-

bridging oxygen atoms which induce disruption in the

diborate units [37].

Dielectric constant

Figure 7a represents the variation of dielectric constant (e\)

values with frequency in glass containing 0.6 mol% Nb2O5

at different temperatures. It can be noticed that the

dielectric constant values increase with increasing tem-

perature, which could be explained by taking into account

that at high temperatures the intermolecular forces are

weakening and hence enhances the orientational vibration.

Thus, at high temperatures, the jump frequency of the

charge carrier becomes large and comparable with the

frequency of the applied field. An increase in dielectric

constant (e\) values at higher temperatures is more pro-

nounced at lower frequencies (Fig. 7a). This could be

explained considering that at low frequencies the charge

carriers hop easily out of the sites with low free energy.

This leads to a net polarization and gives an increase in the

dielectric constant values. However, at high frequencies,

the charge carriers will no longer be able to rotate suffi-

ciently rapidly, so their oscillation will begin to lay behind

this field resulting in a decrease of dielectric constant

values (up to 0.2 mol%) [38].

Figure 7b illustrates that for low concentration of

Nb2O5, the values of dielectric constant seem to decrease

up to Nb2O5 content of 0.2 mol%. Beyond this concen-

tration, the dielectric constant increases. This behavior

could be explained in the light of the conclusion made by

Bergo et al. [15]. For low concentrations of B0.2 % Nb2O5,

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

-14.0

-13.5

-13.0

-12.5

-12.0

-11.5

Log(

σ dc)(

Ω-1cm

-1)

ΔE (eV)

B

Fig. 5 Effect of activation energy on Log rdc conductivity at

T = 300 K for different glass

1 2 3 4 5

-12

-11

-10

-9

-8

-7

Log

σ ac (

Ω-1cm

-1)

Log f (Hz)

300K 337K 377K 417K 460K 495K 528K 572K 607K

Fig. 6 Variation of Log rac versus Log frequency for glass

containing Nb2O5 = 0.6 mol% at various temperatures

5828 J Mater Sci (2012) 47:5823–5832

123

Nb5? ions occupy substitutional positions in the glass

network, reinforcing the covalent bonds between the Nb

ions and the glass former. This in turn reduces the polari-

zation and therefore reducing the dielectric constant (e). An

increase in the dielectric constant values is observed with

increase in Nb2O5 content beyond 0.2 mol%. As men-

tioned before, the increase in Nb2O5 content, which acts as

glass modifier, increases in the number of non-bridging

oxygen (NBOs) sites. This, leads to weaken the glass

network and create pathways suitable for migration of free

ions that build up space charge, [36]. The development of

the space charge polarization increases the dielectric con-

stant values (Fig. 7b).

Impedance spectroscopy

Impedance spectroscopy is a well-established method for

characterizing the dielectric behavior of a material. The Z\

versus Z\\ plot (Fig. 8a, b), shows semicircles and semi-

arcs. The centers of which are under the x-axis, which

indicates the existence of a distribution of relaxation times

[39]. This reveals that the associated relaxation of ions is

non-Debye in nature and the dielectric response is related

to the bulk effect of the glass matrix. Similar results have

been obtained for all other samples under investigation.

Figure 8a, b reveal that all depressed semicircles or arcs

shift to higher frequencies along with a reduction in their

size with increasing temperature and increasing Nb2O5

concentration in the glass, indicating that some structural

changes in the present glass samples take place with the

addition of Nb2O5 [40]. All glass samples (at different

temperatures) show a single semicircle or arcs (Fig. 8a, b),

which indicates the single conduction mechanism that

would be predominantly ionic [41].These results are sup-

ported by Singh [19] conclusions in Li2O–B2O3–Bi2O3

glasses containing less than 25 mol% of Bi2O3, only BiO6

units are in micro molecular chains and accordingly the

glass has an ionic electrical conductivity.

The electric modulus formalism

The advantage feature of the electric modulus formalism is

that it provides a quantitative description of the observed

electrical relaxation behavior in ion conducting materials

[42]. In addition, the electrode polarization effects are

minimized since the electrical modulus peak, M00, is shifted

toward higher frequency [43]. The dielectric modulus is

defined in terms of the reciprocal of the complex relative

permittivity e* [44]:

10

15

20

25

30

35

40

45

50

55(a)

Die

lect

ric c

onst

ant (

ε)

Logf (f)

300K 337K 377K 417K 460K 495K 528K 572K 607K

1 2 3 4 5 1 2 3 4 5

4

6

8

10

12

14

16(b)

Die

lect

ric c

onst

ant (

ε )

Log (f)

x=0.0% x=0.1% x=0.2% x=0.4% x=0.5% x=0.6% X=0.8% x=1.0%

Fig. 7 Dielectric constant (e)as function of frequency. a For

sample 6 at different

temperatures. b For different

Nb2O5 content

(x = Nb2O5 mol%)

0

50

100

150

200

250

(b)

Z// (

Ω)

Z/ (Ω )

400K 440K 490K 550K 606K

0 20 40 60 80 1000 50 100 150 200 250 300

0

50

100

150

200

250

(a)

Z// (

Ω)

Z / (Ω)

480K 520K 570K 610K

Fig. 8 Impedance spectra of

glass at various temperatures.

a containing 0.0 mol% Nb2O5

(base glass). b Containing

1.0 mol% Nb2O5

J Mater Sci (2012) 47:5823–5832 5829

123

M� ¼ 1= e� ¼ M0 þ j M00 ð8Þ

where M0 and M00 are the real and imaginary parts of the

complex modulus M*. Figure 9 shows the frequency

(angular) dependence of real (M0) and imaginary (M00) parts

of complex electric modulus at various temperatures for the

glass containing 0.8 mol% Nb2O5. The frequency depen-

dence of electric modulus for the other glass compositions

is qualitatively similar. It is observed from Fig. 9, that the

low frequency value of M0 is zero indicating the ease of

migration of ions which suggests negligible or absent

electrode polarization phenomenon [45]. As the frequency

of the applied electric field increases, M0 shows a disper-

sion that tends to attain a maximum asymptotic value M0 at

high frequency.

The normalized imaginary parts parameters M00/M00max

show an asymmetric peak at each temperature within the

dispersion region of M0 as represented in Fig. 10. The

dielectric modulus peak, M00max, shifts to higher frequen-

cies with increase of the temperature. fm is the character-

istic frequency corresponding to M00max. Such asymmetric

peak (Fig. 10) describes two regions, (i) the low frequency

region fm determines the range in which charge carriers are

mobile over long distances and is associated with hopping

conduction. (ii) High frequency region fm, the carriers are

spatially confined to potential wells, being mobile on short

distances making only localized motion within the wells.

The maximum of modulus spectra M00max shifts toward the

higher frequencies with increase in temperature. This

behavior suggests that the spectral intensity of the dielec-

tric relaxation is activated thermally in which hopping

process of charge carriers are taking place [46]. Also,

shifting of the peak frequencies in the forward direction

with temperature implies that the relaxation time decreases

with increase in temperature. The peak frequency fm is

typically correlated to the average conductivity relaxation

time or most probable ion relaxation time s. from the

condition xcs = 1, where xc = 2p fm [45]. The values of

log s of the various compositions when plotted as a func-

tion of reciprocal temperature 1/T, were found to follows

linear Arrhenius relation:

s ¼ soexpðDEs=k TÞ ð9Þ

where so is the pre-exponential factor and DEs is the

activation energy for the conductivity relaxation. The

activation energy values DEs, calculated from the slope of

such linear relation are listed in Table 2. The DEdc values

determined from dc conductivity plot (Fig. 2) and the DEs

values are very close to each other for each composition, as

observed in Table 2. This indicates that the ions have to

overcome the same barrier while conducting as well as

when relaxing [47].

Figure 11a, b represent the normalized plots of mod-

ulus isotherms for the base and 0.8 Nb2O5 glass samples,

0.00

0.02

0.04

0.06

0.08

(a)

M' (

ω)

450K 491K 525K 561K 607K

1 2 3 4 5

log f (Hz)

1 2 3 4 5

0.00

0.01

0.02

0.03

0.04

(b)

M''(

ω)

log f (Hz)

450K 491K 525K 561K 607K

Fig. 9 Frequency dependence

of a the real part (M0) and

b imaginary part of the electric

modulus M00 for glass

containing 0.8 mol% Nb2O5 at

various temperatures

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

M"/

M" m

ax

Log(f) (Hz)

450K 491K 525K 561K 607K

Fig. 10 Frequency dependence of the imaginary part of electrical

modulus, M// for 0.8 mol% Nb2O5 glass at different temperatures

5830 J Mater Sci (2012) 47:5823–5832

123

where the frequency axis is scaled by peak frequency fmand M00 axis is scaled by M00max at different temperatures.

All curves are overlapped on a single master curve indi-

cating that the conductivity relaxation is occurring at

different frequencies exhibiting a temperature-independent

dynamical process. The scaling of the frequency by fmparameter gives a distribution of M00/M00max values con-

sidering logarithmic representation at around log f/fm = 1.

At frequency range above this value, some degree of

dispersion can be observed depending on the glass for-

mulation and temperature of measurement. Considering

previous assumptions, it is possible to hypothesize the

existence of a distribution of potential wells, in which the

carriers are trapped. This is consistent with the non-Debye

frequency dependence shown in Fig. 8 [29, 35]. The full

width at half maximum (FWHM) of the normalized

modulus plots, as observed in Fig. 11a, b, increases with

increase in Nb2O5 content. This behavior suggests that the

distribution of relaxation times is associated with the

increase in charge carriers Li? ion relaxation process in

the glass network. Hence, the breadth of the electrical

relaxation peak is a sensitive function of the concentration

of mobile charge carriers [11].

Conclusions

The density of the studied glasses (Table 1) increases with

increasing Nb2O5 content.

The molar volume Vm values decrease, whereas the

glass transition temperatures Tg increase with increasing

Nb2O5 (up to x = 0.2 mol%), which indicate that Nb5?

ion acts as a glass former. With increase of Nb2O5

content(x = [0.2 mol%), the Vm increases and the Tg

decreases, which suggests that Nb5? ion acts as glass

modifier.

The FTIR spectra suggest that Nb5? ions are incorpo-

rated into the glass network as NbO6 octahedra, substitut-

ing BO4 groups.

The temperature dependence of the dc conductivity

follows the Greaves VRH model below 454 K, and follow

the SPH model at temperatures [454 K.

The rdc and rac conductivity and the dielectric constant

(e) decrease, whereas the activation energy for dc con-

duction DEdc increases with increase of Nb2O5 (x = up to

0.2 mol%). On the other hand rdc, rac and (e\) increase and

DEdc decreases with increasing Nb2O5 content (x [ 0.2

mol%), which support the results obtained from physical

properties.

The impedance spectroscopy shows a single semicircle

or arcs, which indicates the single conduction mechanism

that would be predominantly ionic conductivity.

The normalized plots of modulus isotherms curves are

overlapped on a single master curve indicating that the

conductivity relaxation occurs at different frequencies and

exhibits a temperature-independent dynamical process.

The FWHM of the normalized modulus plots increases

with increase of Nb2O5 content suggesting that the dis-

tribution of relaxation times is associated with increase in

the charge carriers Li? ion relaxation process in the glass

network.

Acknowledgements The authors wish to thank Prof. M. K.

El-Nimer, physics Department, Faculty of Science, Tanta University

for allowing us to carry out the experimental work ac measurements

electrical conductivity and for fruitful discussions.

0.0

0.2

0.4

0.6

0.8

1.0

(a)

M"/

M" m

ax

Log(f/fm)

450K 491K 525K 561K 607K

-2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

0.0

0.2

0.4

0.6

0.8

1.0

(b)

M"/

M" m

ax

Log(f/fm)

450K 491K 525K 561K 607K

Fig. 11 Normalized plots of

dielectric modulus versus

normalized frequency at various

temperatures. a For 0.0 mol%

Nb2O5 (base glass). b for

0.8 mol% Nb2O5

J Mater Sci (2012) 47:5823–5832 5831

123

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