Impedance spectroscopy of V2O5–Bi2O3–BaTiO3 glass–ceramics

Solid State Sciences 26 (2013) 72e82

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Impedance spectroscopy of V2O5eBi2O3eBaTiO3 glasseceramics Aref M. Al-syadi a, b, El Sayed Yousef a, c, *, M.M. El-Desoky a, d, M.S. Al-Assiri a, e a

Physics Dept., Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia Physics Dept., Faculty of Education in AL-Nadirah, Ibb University, Yemen c Physics Dept., Faculty of Science, Al Azhar University, Assiut Branch, Assiut, Egypt d Physics Dept., Faculty of Science, Suez University, Suez, Egypt e Physics Dept., College of Science and Arts, Najran University, Najran, Saudi Arabia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 August 2013 Received in revised form 28 September 2013 Accepted 8 October 2013 Available online 15 October 2013

The glasses within composition as: (80
x)V2O5/20Bi2O3/xBaTiO3 with x ¼ 2.5, 5, 7.5 and 10 mol% have been prepared. The glass transition (Tg) increases with increasing BaTiO3 content. Synthesized glasses ceramic containing BaTi4O9, Ba3TiV4O15 nanoparticles of the order of 25e35 nm and 30e46 nm, respectively were estimated using XRD. The dielectric properties over wide ranges of frequencies and temperatures were investigated as a function of BaTiO3 content by impedance spectroscopy measurements. The hopping frequency, uh, dielectric constant, ε0 , activation energies for the DC conduction, Es, the relaxation process, Ec, and stretched exponential parameter b of the glasses samples have been estimated. The, uh, b, decrease from 51.63 to 0.31  106 (s
1), 0.84 to 0.79 with increasing BaTiO3 respectively. Otherwise, the Es, increase from 0.279 to 0.306 eV with increasing BaTiO3. The value of dielectric constant equal 9.5$103 for the 2.5BaTiO3/77.5V2O5/20Bi2O3 glasses-ceramic at 330 K for 1 KHz which is ten times larger than that of same glasses composition. Finally the relaxation properties of the investigated glasses are presented in the electric modulus formalism, where the relaxation time and the respective activation energy were determined. Published by Elsevier Masson SAS.

Keywords: Vanadate glasses Dielectric properties Activation energy

1. Introduction Vanadium pentoxide (V2O5) is known as a semiconducting material, its based compounds is of interest view because of their relative high electrical conductivity, thermal stability, glass formation range compared to other transition-metal oxide glasses [1], and their possible applications such as electrical threshold and memory switching as well as optical switching devices. Several studies have been carried out on the local structure of pure V2O5 glass [2e4], in which some complicated VO4, VO5 and VO6 polyhedra have already been proposed as the local structural units. Navabi et al. [3] have discussed the coordination number on the basis of IR spectroscopy, EXAFS and XANES at the vanadium K-edge, and solid-state NMR measurements, showing that vanadium exhibits both four- and five-fold coordinations. They concluded that the ratio of VO4 to VO5 depends mainly on experimental parameters such as the temperature, quenching rate or the partial pressure of water.

* Corresponding author. Physics Dept., Faculty of Science, Al Azhar University, Assiut Branch, Assiut, Egypt. Tel.: þ20 9662418217; fax: þ20 482528888. E-mail address: [email protected] (E.S. Yousef). 1293-2558/$ e see front matter Published by Elsevier Masson SAS. http://dx.doi.org/10.1016/j.solidstatesciences.2013.10.002

The vanadium glasses containing V4þ / V5þ þ e takes place between two vanadium ions which the charge transfer is usually termed small polaron hopping (SPH) [5,6]. The electrical conductivity for such glasses depends strongly upon the local interaction of an electron with its surroundings and distance between vanadium ions [7,8]. The dielectric and ferroelectric properties of BaTiO3 are known to correlate with size of the modifier ions in the glass structure, their field strengths and the composition of the glass, and the technological trend toward decreasing dimensions makes it of interest to examine this correlation when sizes are at the nanoscale [9,10]. Hence, the connection between the position of bismuth ion in volatile BaTiO3 glass network and the electrical properties of these glasses is expected to be quite interesting. Though considerable studies on electrical properties along of some BaTiO3-based glasses are available in literature, majority of these studies are devoted to BaTiO3-based glasses and further they are mainly concentrated on dc conductivity studies [11]. The purpose of this work was to correlate the dielectric properties of glass ceramics to the annealing temperature of the prepared glasses by formation nanocrystalline phase to increasing dielectric constant. Moreover, we studied the influence of BaTiO3 on the dielectric properties of V2O5eBi2O3 glass and its glasse

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

ceramics from a systematic study of impedance spectroscopy measurements in the frequency range 20 Hze1 MHz and in the 310e340 K temperature range.

at α = 15 K/min

The glass systems (80
x)V2O5/20Bi2O3/xBaTiO3 with x ¼ 2.5, 5, 7.5 and 10 mol%, were prepared by mixing specified weights of Barium Titanium oxide (BaTiO3, purity 99%, Alfa Aesar), Bismuth oxide, (Bi2O3, purity 99.9%, SigmaeAldrich), Vanadium oxide (V2O5, purity 98%, SigmaeAldrich). Samples A, B, C, and D have the composition of 77.5V2O5/20Bi2O3/2.5BaTiO3, 75V2O5/20Bi2O3/ 5BaTiO3, 72.5V2O5/20Bi2O3/7.5BaTiO3 and 70V2O5/20Bi2O3/ 10BaTiO3 respectively. The powder mixture was heated in a silica crucible at 1050  C for 15 min. The melt was then poured on a thick copper block and immediately quenched by pressing with another similar copper block. Following this procedure we obtained bulk glass of about 2.0 mm in thickness, the sample was transferred to an annealing furnace and kept for 2 h at 250  C. Then, the furnace was switched off, and the glass sample was allowed to cool. The glasseceramics were prepared by crystallization of the abovementioned glasses by heating in air at crystallization temperature Tc for two hours. The densities, r, of the glassy samples were measured by a helium pycnometer (AccuPyc 1330 Pycnometer) with an accuracy of 0.0003%. The thermal behavior was investigated using differential scanning calorimetric (Shimadzu DSC 50). The powdered samples (z15 mg) were placed into covered aluminum crucibles and the DSC curves were recorded between 300 and 800 K at temperature rate 15 K min
1. The samples were examined by X-ray diffraction (Siemens D 6000) using CuKa radiation at 40 kV in the 2q range from 10 to 80 . Transmission electron microscope (TEM), JEOL JEM 200CX studies was carried out on the as-quenched and heated treated (at different temperature) samples to confirm their amorphous and crystalline nature. Complex impedance spectroscopy measurements were taken of 1.5 mm thick samples obtained from the initial rectangular with silver past was evenly applied on both sides of the sample for better electrical contact. The sample was then held between two spring loaded electrodes. The impedance jZ*j, the phase angle q and the capacitance C were measured with Agilent 4284A Precision LCR meter in the 20 Hze1 MHz frequency range from 310 to 340 K.

<−−− Δ Q −−−>

Exo

sample D

sample C

sample B

Indo

2. Experiments

73

sample A

100

200

300

400

0

Temperature in C Fig. 1. DSC thermogram for BaTiO3$V2O5$Bi2O3 glasses.

the prepared glasses are summarized in Table 1. The densities of the prepared glasses are of special importance; they are strongly affected by the respective structure. Also, the molar volume is of high interest, because it is directly related to the spatial distributions of the oxygen in the glass network. Table 1 summarizes the values of densities, r, and molar volumes, Vm, as a function of the BaTiO3 concentration. Here, the density increased from 4.173 to 4.412 g cm
3 while increasing the BaTiO3 concentration from 2.5 to 10 mol% (the V2O5 concentration decreased from 77.5 to 70 mol%). The molar volume decreased from 56.53 to 55.26 cm3 mol
1 with increasing BaTiO3 and decreasing of V2O5 concentration. The increase of density and the decrease in the molar volume can be attributed to the higher mean atomic weight of the glasses with higher BaTiO3 concentrations. The structure of prepared glasses can be studied using the concept of the oxygen packing density (O.p.d) which is the fractional filling of space by ions within the glass. This concept takes into account the O.p.d was estimated by using following equation;

3. Results and discussion 3.1. Density, molar volume, oxygen packing density and DSC

Table 1 Composition, density, molar volume, oxygen packing density and glass transition temperature of prepared glasses. Sample name

Sample Sample Sample Sample

Glass composition (mol%)

A B C D

V2O5

Bi2O3

BaTiO3

77.5 75 72.5 70

20 20 20 20

2.5 5 7.5 10

Density (g/cm3)

Molar volume (cm3/mol)

O.p.d

Tg ( C) at 15 K/min

4.173 4.251 4.346 4.412

56.53 56.17 55.81 55.26

80.49 80.11 79.73 79.61

259 267 275 282

Sample A

Intensity (a.u)

The glasses prepared in the glass system 77.5V2O5/20Bi2O3/ 2.5BaTiO3 (sample A), 75V2O5/20Bi2O3/5BaTiO3 (sample B), 72.5V2O5/20Bi2O3/7.5BaTiO3 (sample C) and 70V2O5/20Bi2O3/ 10BaTiO3 (sample D), respectively. Compositions, densities, molar volume, oxygen packing density and glass transition temperature of

Sample B

Sample C

Sample D

0

20

40

60

2 θ (Degree) Fig. 2. XRD of BaTiO3$V2O5$Bi2O3 glasses.

80

100

74

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

°BaTi 4O9 Δ Ba3TiV4O15

° Δ

°

Δ

° °

°

°

0 at 280 C

0 sample B at 305 C

° ° sample C at 310

Δ

Intensity (a.u)

°

°

Δ

5

Δ

° °

Δ

°

° ° sample A

Δ

°

°

°°

Δ Δ

°

Δ

°

° °

0 C

0 sample D at 320 C

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

2θ (degree) Fig. 3. XRD of BaTiO3$V2O5$Bi2O3 glasseceramics.

O:p:d ¼

1000  r  Oi Mi

(1)

where Oi is number of oxygen atoms in the composition. The O.p.d value of prepared samples decreases from 80.49 to 79.62 g atom liter
1 with increasing BaTiO3 content. Here, Ti4þ ions combine with Ba3þ ions to improve the connectivity of the network and consist of the non-bridging oxygens, but might also be affected by an increase in the bond lengths, i.e. the interatomic distances between the respective atoms. This leads to decrease of oxygen packing density with increasing BaTiO3 content. The DSC thermogram for glass samples at heating rate a ¼ 15 K min
1 are shown in Fig. 1.The shapes of all the curves are similar and confirm the glassy nature of all the glasses. The exothermic peaks corresponding to crystallization temperature (Tp) are observed in the temperature range 320e380  C. The endothermic dips corresponding to the glass transition (Tg) are observed at the temperature range 286e324  C. The Tg increases with increasing BaTiO3 content, suggesting that the present glass system decreases the contribution of the non-bridging oxygen (NBO). From DSC studies, increasing of Tg can be interpreted as increasing of the rigidity of the glass matrix. This leads to the cross link density of the network for prepared glasses increased with increasing BaTiO3.

Fig. 4. a, b, c, d and e: TEM micrographs of annealed (a) sample A at 280  C/2 h, (b) sample B at 305  C/2 h, (c) sample C at 310  C/2 h, and (d) sample D at 320  C/2 h and (e) High resolution lattice image of sample C at 310  C/2 h.

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

Therefore the increase in Tg indicates that the network structure is becoming more strong due to the substitution of V2O5 by BaTiO3.

3.2. XRD and TEM Fig. 2 shows X-ray diffraction patterns (XRD) of the quenched glasses samples A, B, C and D. The patterns of these samples do not show any sharp peaks caused by crystalline phases. Fig. 3 shows XRD patterns of thermally treated samples with composition sample A, B, C and D. The patterns were collected for prepared glasses after heat treated of the samples A, B, C and D tempered for 2 h, at 380, 305, 310 and 320  C, respectively. Samples A, B, C and D distinct major concentration lines attributed to BaTi4O9 (JCPDS-file no: 00-034-0070) and minor contribution to phase Ba3TiV4O15 (JCPDS-00-036-1488) are observed. The phases formed during tempering depend upon the conditions applied as shown in Fig. 3. Increasing temperatures led to a full decreasing width at half maximum of all XRD lines attributed to BaTi4O9 and Ba3TiV4O15. In the principle two effects may contribute to XRD-line broadening firstly internal stress and secondly size of crystallites of phase form in sample. Therefore the XRD line broadening should predominantly be caused by small particle size. Average size of crystallites was approximated from the widths of diffraction peaks by using the Scherrer’s formula d ¼ Gl=Bcos q where d, the mean crystallite size; G z 1, l, the wave-length of the radiation used (¼0.154 nm for CuKa); B, the full width at half maximum and q, the Bragg angle. Depending on the tempering condition crystallite sizes of phase BaTi4O9 calculated are in range from 25 to 35 nm and the mean

3.3. AC conductivity formalism The frequency dependent ac conductivity is found to follow the Jonscher’s power law [12]:

sac ðuÞ ¼ sDC þ Aun

1200

Cb

b Glass sample B

3000

310 K 320 K 330 K 340 K

310 K 320 K 330 K 340 K

2500

ρ '' (Ω . m)

1000

Rb

800

600

2000

1500

400

1000

200

500

0

0

0

200

400

600

800

1000

1200

1400

0

500

1000

ρ ' (Ω . m)

Glass sample C

d

40000

310 K 320 K 330 K 340 K

2000

2500

3000

3000

2000

Glass sample D 310 K 320 K 330 K 340 K

30000

ρ '' (Ω . m)

4000

1500

ρ ' (Ω . m)

c 5000

ρ '' (Ω . m)

(2)

where, sDC, and, sac, are the dc and ac conductivities of the glass sample, A is the constant and n is the frequency exponent. Ac conductivity is determined by the complex impedance analysis, which gives perfect semicircle with its center on the real axis. Figs. 5 and 6 show the impedance plot at different temperature

3500

Glass sample A

ρ '' (Ω . m)

average size of second phase Ba3TiV4O5 calculated is in rage 30e 46 nm. The transmission electron micrograph (TEM) for heat treated samples A, B, C and D were shown in Fig. 4(a)e(d). It clearly demonstrates the distribution of fine spherical crystallites in the prepared glass matrix. We note that, the crystallites density (number of crystallites per unit volume) is larger in sample D than in sample A (see Fig. 4(d)). That means the increase in BaTiO3 concentration from 2.5 to 10 mol% increases the crystal growth velocity. The mean average size of second phase Ba3TiV4O5 was calculated and it is in range of 30e46 nm. Which is in the same range as that obtained by XRD analyses. A high resolution image of the sample D is shown in Fig. 4(d), the fringe spacing, which is around ¼ 2.8  A. That are assigned to the planes (0 2 1), (0 3 1), (0 0 2), (1 3 2) and (2 3 1). The corresponding d values 4.75, 3.84, 3.15, 2.17 and 1.7  A.

a

1400

75

20000

10000 1000

0

0

0

1000

2000

3000

ρ ' (Ω . m)

4000

5000

0

10000

20000

ρ ' (Ω . m)

Fig. 5. Complex plane plots of the resistivity at selected temperatures for prepared glasses.

30000

40000

3500

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A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

a

3500

glasses ceramic B

Cb

310 K 320 K 330 K 340 K

2500

Cg

4000

ρ '' (Ω . m)

3000

ρ '' (Ω . m)

b

5000

glasses-ceramic A

2000

Rb

Rg

1500

310 K 320 K 330 K 340 K

3000

2000

1000 1000 500

0

0 0

500

1000

1500

2000

2500

3000

0

3500

1000

2000

ρ' (Ω . m)

c

7000

glasses ceramic C

6000

310 K 320 K 330 K 340 K

ρ '' (Ω . m)

5000

4000

5000

d

16000

glasses ceramic D

14000

310 K 320 K 330 K 340 K

12000

ρ '' (Ω . m)

8000

3000

ρ' (Ω . m)

4000

10000

8000

3000

6000

2000

4000

1000

2000

0

0 0

2000

4000

6000

8000

0

2000

4000

6000

ρ' (Ω . m)

8000

10000

12000

14000

16000

ρ' (Ω . m)

Fig. 6. Complex plane plots of the resistivity at selected temperatures for glasses ceramic.

obtained for prepared glasses and their glasseceramics, respectively. Fig. 5 shows one semicircle as clear and another very small semicircle obtained in the prepared glasses. This is indicated the impedance may be contribution by both bulk and grain boundary. By contrast, two clear semicircles were observed in glass ceramics, one at higher and other at lower frequency range. In glass samples at low frequency, semicircle is a characteristic of interfacial impedance while at high frequency the semicircle is a parallel combination of bulk capacitance (Cb) and bulk resistance (Rb) of the material. From the impedance plot, it can be observed that with the increase in temperature, the intercept of arc on the real axis shifts towards the origin means that the bulk resistance of the sample decreases with increase of temperature and consequently conductivity increases. A. Mogus-Millankovic et al. [13] studied the dielectric on LiIeAgIeB2O3 doped by MnO. They estimated the spectrum of these glasses cantinas one semicircle and inclined spur at low frequency. The semicircle arc corresponds to the bulk conduction whereas the spur is the electrode polarization. Fig. 7(a) and (b) shows the frequency response of the conductivity at different temperatures 310, 320, 330 and 340 K of prepared glasses sample C and its glasseceramic respectively. The conductivity shows a dispersion, as the frequency is increased which shifts to higher frequencies with the increase in temperature. The frequency response of the other glass samples compositions also behaved similarly. We have studied the dynamics of charge carriers in the glasses under consideration in the framework of the AlmondeWest formula [14],




sðuÞ ¼ sDC 1 þ



u uh

n  0
(3)

where, uh, is the hopping frequency of the charge carriers and, n, is the dimensionless frequency exponent. In this presentation, the real part of the frequency dependent conductivity s0 (u) is expressed by Eq. (3) and the frequency exponent is calculated from the slope of the plot log (s0 (u)
sDC) vs. log u, which is a straight line. The value of, n, at 330 K for all the samples is shown in (Table 1). The hopping frequency (uh) is calculated by the expression, uh ¼ ðsDC =AÞn and the dependence of hopping frequency shows Arrhenius behavior. In the present studies of prepared glasses and glasseceramic samples both the hopping frequency and dc conductivity are thermally activated indicating that they are originating from the ion migration. The activation energy calculated from the conductivity relaxation time matches well with the activation energy of conduction process due to small polaron. This indicates that the ions in these glasses and glasseceramics also have to overcome the same barrier while conductivity by hopping as well as when relaxing. Moreover, we have scaled the conductivity spectra by a scaling process [15]. In this scaling process, the ac conductivity is scaled by sDC, and the frequency axis is scaled by the crossover frequency uh, which is expected to be more appropriate for scaling the conductivity spectra of ionic conductors. Since it dependence of the conductivity spectra on structure and the possible changes of the hopping distance experienced by the mobile ions. Fig. 8(a) and (b) shows the perfect overlap of the spectra at different temperatures for glass and glasseceramic (sample C)

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

-2.9

Glasses sample C

0.4

77

glasses sample C

-3.0

310 K 320 K 330 K 340 K

-3.1

0.2

log(σ '/ σ DC)

log σ '

-3.2

310 K 320 K 330 K 340 K

0.3

-3.3 -3.4

0.1

0.0

-3.5 -3.6

-0.1

-3.7

-0.2 1

2

3

4

5

-5

6

-4

-3

-2

-1

0

1

log (ω/ ω h)

log f (Hz)

a Glasses ceramic C -3.0

glasses ceramic C

0.3

310 K 320 K 330 K 340 K

0.2 0.1

log(σ '/ σ DC)

-3.2

log σ '

0.4

310 K 320 K 330 K 340 K

-3.4

0.0 -0.1 -0.2

-3.6

-0.3

-3.8

-0.4 -0.5 -5

-4.0 1

2

3

4

5

6

log f (Hz)

Fig. 7. a): Conductivity spectra at different temperatures for (glasses sample C). b): Conductivity spectra at different temperatures for (glasses ceramic C).

indicate that it obeys the timeetemperature superposition principle. Herein, this implies that the relaxation dynamics of charge carriers in the present glass is independent of temperature. It is clear from Table 2 that the conductivity decreases with the increase of the BaTiO3 content. The decrease value of electrical conductivity are similar to those for SrTiO3eV2O5ePbO2 and BaTiO3eV2O5 glasses [16e18]. This change in conductivity may help to detect the structural changes as a consequence of increasing BaTiO3 and decreasing V2O5 content. In the V2O5eBi2O3eBaTiO3 system of our present investigation, the BaTiO3 addition decreased the conductivity. Generally, it is known that the addition of BaTiO3 to glass decreases the conductivity as a result of decreasing non-bridging oxygen (NBO) cations [16,17]. This may decrease the open structure, through which the charge carriers can move with lower mobility. Also, Table 2 presents variation in conductivity with BaTiO3 content at a fixed temperature (330 K) of glasses and corresponding glasseceramic nano-composites. It is interesting to note that these corresponding glasseceramic nano-composites show high conductivity compared to the samples in glassy phase. The enhancement of conductivity of these corresponding glasse ceramic nano-composites is considered to be due to the presence of

-4

-3

-2

-1

0

1

log (ω/ ω h)

b Fig. 8. a): Plot of log (s/sdc) vs. log (u/uh) for (glasses sample C). b): Plot of log (s/sdc) vs. log (u/uh) for (glasses ceramic C).

nanocrystals with an average grain size of 20e46 nm as reported in TEM and XRD results. Such remarkable increases in conductivity have been reported in other SrTiO3eV2O5ePbO2 and BaTiO3eV2O5 glasses. On the other hand, the improvement of electrical conductivity of glasseceramic nano-composites system under study can be explained in the following way. The most important for electronic conduction in the glasses of the BaTiO3eV2O5eBi2O3 system with high amount of V2O5 is the spatial distribution of V4þ and V5þ ions which are centers of hopping for electrons. In the initial glass, there is a random distribution of such centers. The annealing at temperatures close to crystallization temperature leads to formation of nanocrystallites of V2O5 embedded in the glass matrix. Since the average size of these grains is small about 20e46 nm, the interface between crystalline and amorphous phases is very extensively ramified and strongly influences overall electrical properties of the nanomaterial as reported in TEM and XRD. In particular, it may contain the improved concentration of V4þ and V5þ centers dispersed on the surface of V2O5 crystallites. However, this enhancement of electrical conductivity can be attributed to (i) an increasing of concentration of V4þeV5þ pairs (a possible reason of this increase between surfaces of nanocrystallites and glassy phase) and (ii) formation of defective, well-conducting regions along the glassecrystallites interfaces.

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Table 2 Ac conductivity parameters, hopping frequency, uh, and dielectric constant, ε0 , of the prepared glasses and glasses ceramic samples at 330 K.

Glasses samples

Glasses-ceramic samples

Sample name

sDC  10
4 (U m)
1

A

Glasses Glasses Glasses Glasses Glasses Glasses Glasses Glasses

15.4 8.40 3.91 0.57 16.41 7.48 3.85 1.74

3.03 5.19 1.03 2.67 6.65 9.19 9.13 1.34

sample A sample B sample C sample D ceramic A ceramic B ceramic C ceramic D

ε0 at 1 KHz

0.74 1.00 0.95 0.42 0.84 0.95 0.96 0.93

51.63 17.01 8.00 0.31 39.07 19.81 8.10 4.01

10.4 9.46 2.85 2.68 9.5 3.7 1.01 0.4

       

102 102 102 102 103 103 103 103

-7

-8

i h BðtÞ ¼ exp
ðt=sc Þb

sDC ¼ s0 expð
Es =kTÞ

(4)

where s0 is the pre-exponential factor, Es the activation energy and k is Boltzmann’s constant. The activation energies for the electrical conduction, calculated from Eq. (4), are listed in Table 3. In the modulus formalism [19] an electric modulus M* is defined as the inverse of the complex dielectric permittivity ε*.

M* ¼

1 ε*

¼

2

¼ MN 41


ε’
jε} jεj2

ZN

¼ M’ þ jM}

3   df dt 5 expð
jutÞ
dt

(5)

0

where M0 and M00 are the real and imaginary part of the complex modulus M* and MN is the high frequency value of M0 where MN ¼ 1/εN0 . The function F(t) gives the time evolution of the electric field with in the materials. Fig. 10(a) and (b) shows the variation of imaginary part of complex modulus M* with different temperatures of glass sample C and its glasseceramic C. The obtained plots are asymmetric with respect to peak maxima and the peaks are considerably broader on both sides of the maxima than would be predicted by the ideal Debye behavior. The shape of the spectrum remains constant but the frequency of the modulus maximum, Mmax00 shifts to higher frequency side with increase in temperature. The peak heights at different temperatures are nearly

-5

glasses sample A glasses sample B glasses Sample C glasses Sample D

-6

-1

-1

10
9 10
11 10
10 10
7 10
10 10
11 10
11 10
10

uh  106 (s
1)

the same. The constancy of the height of the modulus plot suggests the invariance of the dielectric constant and distribution of relaxation times with temperature [20]. The region to the left of the peak is where the charge carriers are mobile over long distances while the region to the right is where they are spatially confined to the potential wells. The full width half-maximum (FWHM) was found to be almost constant with change in temperature. Fig. 11(a) and (b) shows the real part of modulus spectrum of sample C and glasses ceramic C at different temperature. At lower frequencies, M0 approaches to zero indicating that the electrode polarization makes a negligible contribution to M* and the dispersion is mainly due to conductivity relaxation [21]. Where the higher temperature, M0 levels off at frequencies higher than that of those at lower temperatures because the relaxation processes are spread over a range of frequencies. A master plots of the modulus isotherms are shown in Fig. 12(a) and (b) for glass samples and glasseceramics, respectively, where the frequency axis is scaled by the peak frequency fmax and M0 (or M00 ) is scaled by MN (or Mmax). The perfect overlap of all the curves on a single master curve for all the temperatures indicates that the dynamical processes are temperature independent. The scaled spectra of M00 for different compositions at a fixed temperature are shown in Fig. 13(a) and (b) for glasses and glasse ceramics, respectively. It can be seen that the spectra for different compositions also merge on a single master curve, which implies that the conductivity relaxation is independent of the glass and glasseceramic composition. A remarkable characteristic of this type of data representation is that a direct comparative analysis can be performed for each branch of curves M00 /Mmax00 vs. log f/fmax. In the same way, any type of dispersion phenomenon can be easily detected. The scaling of the frequency by fmax parameter gives a distribution of M00 /Mmax00 values considering logarithmic representation at around log f/fmax ¼ 1. At frequency above this value, some degree of dispersion can be observed depending on the glass formulation and temperature of measurement. The normalized modulus plot is non-symmetric in agreement with the non-exponential behavior of the electrical function, which is well described by the KohlrauscheWilliameWatts (KWW) exponential function [22,23].

Fig. 9 shows the relation between the electrical conductivity versus temperature of prepared glasses can be described well by the Arrhenius relation:

ln σ DC (Ω .m )

       

n

-9

-10

2.90

2.95

3.00

3.05

3.10

3.15

3.20

3.25

-1

1000/T (K ) Fig. 9. Temperature dependence of the DC electrical conductivity for glasses samples.

0
(6)

where s and b are the conductivity relaxation time and Kohlrausch exponent is less than one for most practical solid electrolyte. The smaller is the value of b, the larger is the deviation of the relaxation with respect to Debye type relaxation. The value of b can be evaluated by knowing the width at half height of the M00 /Mmax00 plot (b ¼ 1.14/FWHM) value. The b values obtained for different samples are shown in (Table 2). According to Ngai et al. [24], the b parameter gives the extent to which the mobile ions couple during the conduction processes. The concept of the cooperative motions in a glass is issued from the universal behavior discussed by Jonscher

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

Glasses ceramic samples

Ec (eV)

b

Es (eV)

Ec (eV)

B

0.279 0.281 0.285 0.306

0.268 0.268 0.274 0.275

0.84 0.81 0.80 0.79

0.278 0.278 0.280 0.293

0.275 0.299 0.294 0.31

0.87 0.87 0.87 0.86

[25]. It means that jump of a mobile ion in a glass and glasse ceramic may not be treated as an isolated event i.e., when the ion jumps from one equilibrium position to another it causes a time dependent movement of other charge carriers in the surroundings, which leads to additional relaxation of the applied field. Therefore, it results the smaller value of b to a more extended cooperative motion between the charge carriers. The non-exponential parameter b obtained from the modulus formalism and the frequency exponent parameter n obtained from the power law model represents the interaction between the charge carriers. Ngai [26] has

Glasses sample C

16 14

310 K 320 K 330 K 340 K

M " × 10

8 3 6 2 4 1

2

0

0

0.4

0.4

0.2

0.2

0.0

0.0

-4

-3

-2

-1

0

1

2

log f/f max

a

glasses ceramic C

1.0

1.0

310 K 320 K 330 K 340 K

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0

-5

-4

-3

-2

-1

0

1

2

log f/f max

b Fig. 11. a, b): Plots of M0 /MN00 and M00 /Mmax00 at different temperatures for glasses sample C and corresponding glasses ceramic.

-2

-1 0

1

2

3

4

5

6

7

log f (Hz)

a 5

12

glasses ceramic C 10

310 K 320 K 330 K 340 K

8

-3

6 2 4 1

2

0

0

0

1

2

3

4

5

6

-3

3

M' ×10

4

M " ×10

0.6

10

-3

4

12

M' × 10-3

5

0.8

0.6

-5

M " /M "max

7

1.0

310 K 320 K 330 K 340 K

M'/M'α

Es (eV) Sample Sample Sample Sample

M "/M "max

Glass samples

6

Glasses sample C

0.8

Sample name

A B C D

1.0

M'/M'α

Table 3 Values or the activation energies for the DC conduction, Es, and the relaxation process, Ec, and stretched exponential parameter b for different compositions of the prepared glasses and glasses ceramic.

79

7

log f (Hz)

b Fig. 10. a, b): Frequency dependence of the real part, M0 (f), and imaginary part, M00 (f), of the electric modulus at different temperatures for prepared glasses and corresponding glasses ceramic.

proposed that a correlation exists between n and b namely n ¼ 1
b. However, we have not found such a relation for the present glasses. The fact that the shape of the modulus spectra is influenced by the values of the high frequency dielectric constant is documented [27]. In contrast, the conductivity takes into account the high frequency region of the conductivity spectra. The plot of frequency corresponding to Mmax00 i.e., log fmax vs. 1000/T for all prepared glasses and glasseceramics are shown Fig. 13(a) and (b). The plot obeys the Arrhenius nature and the activation energy calculated from the modulus spectrum is also comparable (Table 3) to the values obtained from the impedance spectrum. The near value of activation energy of both impedance and modulus spectrum suggests that transport of ions in the present system is by a hopping polaron mechanism. The carriers such as electrons or holes are present in a polar crystal, the atoms in its space are polarized and displaced producing a local lattice displaced producing a local lattice distortion [28]. The quasiparticle formed by the electron and its self induced distortion is called a small polaron if the range of the lattice distortion is of the order of the lattice constant [12]. In the transition metal oxides, it is generally accepted that charge carriers create small polaron [29]. Polaron migration can be described by the distortion of the lattice deformation along a one dimensional on the Born surface [28].

80

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

glasses sample A glasses sample B glasses sample C glasses sample D

1.0

0.8

glasses sample A glasses sample B glasses sample C glasses sample D

14.5 14.0 13.5

ln fmax (Hz)

M "/M "max

13.0

0.6

0.4

12.5 12.0 11.5

0.2

11.0 10.5

0.0 10.0

-5

-4

-3

-2

-1

0

1

2.90

2

2.95

3.00

3.20

3.25

a 14.0

glasses ceramic A glasses ceramic B glasses ceramic C glasses ceramic D

glasses ceramic A glasses ceramic B glasses ceramic C glasses ceramic D

13.5 13.0

ln fmax (Hz)

M "/M "max

3.15

1000/T (K )

a

0.8

3.10 -1

log (f/fmax)

1.0

3.05

0.6

0.4

12.5 12.0 11.5 11.0

0.2 10.5

0.0

10.0 2.90

-5

-4

-3

-2

-1

0

1

2

2.95

3.00

3.05

3.10

3.15

3.20

3.25

-1

1000/T (K )

b

log (f/fmax)

b

Fig. 13. a, b): The log fmax vs. 1000/T plot for prepared glasses and glasses ceramic.

Fig. 12. a, b): Plots of M0 /MN0 and M00 /Mmax00 at 330 K for different prepared glasses and glasses ceramic.

3.4. Dielectric properties The dielectric permittivity was calculated from the impedance data using the relation:

ε* ðuÞ ¼ 1=j2pfC0 Z * ðuÞ

(7)

where C0 is the vacuum capacitance of the sample holder and electrode arrangement. Fig. 14(a) and (b) shows the representative frequency dependence of the real part of the dielectric permittivity, ε0 (f), at different temperatures for glass sample C and glassesceramic C respectively. In these figures the ε0 (f) approaches a limiting constant value of εN0 , at high frequencies. Also, decreasing frequency ε0 (f) increases the space charge polarization at the sampleeelectrode interface. It is noted that the similar behavior of ε0 (f) was also observed for the other prepared glass and glasseceramics compositions. The temperature dependence of the dielectric constant for the investigated glass and glasseceramic in the 310e340 K temperature range, is represented in Fig. 14(a) and (b) at selected frequencies. The increase in dielectric constant of the samples with the increase in temperature is usually associated with the decrease in bond energies [30e32]. When the temperature increases two

effects on the dipolar polarization may occur; (i) it weakens the intermolecular forces and hence enhances the orientational vibration, (ii) it increases the thermal agitation and hence strongly disturbs the orientational vibrations. The dielectric constant becomes larger at lower frequencies and at higher temperatures, which is normal in oxide glasses and, is not an indication for spontaneous polarization [32]. This may be due to the fact that as the frequency increases, the polarizability contribution from ionic and orientation sources decreases and finally disappears due to the inertia of the ions. Moreover, The relaxation phenomena in dielectric materials were associated with a frequency dependent on the orientation polarization. At low frequency, the permanent dipoles along the field and contribute fully to the total polarization of the dielectric. Otherwise, the dielectric permittivity can become negligible at higher frequency; the variation in the field is too rapid for the dipoles to align themselves [13,28,33]. The value of the dielectric constant decreases from 10.43  102 to 2.68  102 for glass samples and decreases from 95  102 to 3.59  102 for annealed glass samples at 1 kHz and 330 K with the variation of BaTiO3 content from 2.5 to 10 mol%, as shown in Fig. 15. We conclude that herein the dielectric constant value for present glass ceramic contained in nanocrystallite phase are found to be very high comparable to be that of bulk BaTiO3 [34], BaOeTiO2e SiO2 glass ceramic [35] and BaOePbOeTiO2eB2O3eAl2O glasses

A.M. Al-syadi et al. / Solid State Sciences 26 (2013) 72e82

glasses sample C

3

4.5x10

310 K 320 K 330 K 340 K

3

4.0x10

3

Dielectric Constant

3.5x10

3

3.0x10

3

2.5x10

3

2.0x10

3

1.5x10

3

1.0x10

2

5.0x10

0.0 1

2

3

4

5

6

81

ceramics [36]. The high dielectric constant of these glasses ceramic is considered to be due to the present of nanocrystals BaTi4O9 and Ba3TiV4O15 embedded in the glass ceramic matrix. The dielectric constants was measured in the gigahertz range correlate as well with literature values for BaTi4O9 [37,38]. We can conclude that, these phases may cause more probable to increase polarization of the glass ceramic matrix. Furthermore because of highly dielectric constant these glass ceramic indicate the possibility of their use as capacitor material. Finally, the decreasing in value of the dielectric constant with increasing of frequency can be attributed to addition of BaTiO3 decreases the dielectric constant as a result of decreasing nonbridging oxygen (NBO) cations. This may decrease the open structure, through which the dipole in sample can move with lower mobility. 4. Conclusions

log f (Hz)

a

4

4.5x10

glasses ceramic C

310 K 320 K 330 K 340 K

4

4.0x10

4

Dielectric constant

3.5x10

4

3.0x10

4

2.5x10

4

2.0x10

4

1.5x10

4

The incorporation of BaTiO3 into the binary glasses in the system V2O5eBi2O3 leads to decrease dielectric constant from 10.4  102 to 2.68  102. Otherwise incorporation of nanocrystallites particles into present glasses leads to increase the dielectric constant. The activation energies for the electrical conduction, Es for present glasses are higher than that of corresponding glasses ceramic. By contrast both the EC and b for glasses are lower than of corresponding glasses ceramic. In addition, an analysis of the relaxation behavior of the investigated glasses and glasses ceramic by electric modulus shows slight deviation from ideal Debye relaxation, where the relaxation process was found to be independent of temperature.

1.0x10

Acknowledgments

3

5.0x10

0.0 1

2

3

4

5

This research has been supported by the Long-Term Comprehensive National Plan for Science, Technology and Innovation in Kingdom of Saudi Arabia (Grant no. 08-NAN 1467)

6

log f (Hz)

b

References

Fig. 14. a, b): The real dielectric permittivity spectra at different temperatures for glasses sample C and glasses ceramic C.

[5] [6] [7] [8]

At 330 K for 1KHz

glasses ceramic A

4

1.0x10

[1] [2] [3] [4]

[9]

3

2.0x10

0.0

[12] [13]

glas ses ceramic D

3

glasses ceramic C

glasses sample A

Dielectric Constant

3

6.0x10

4.0x10

[10] [11]

glasses ceramic B

3

8.0x10

[14] [15] [16] [17]

glasses sample B glasses sample C 2

3

4

5

6

7

glasses sample D 8

9

10

[18] 11

BaTiO3 (mol%) Fig. 15. Composition dependence of the dielectric constant measured at 1 KHz and 330 K for prepared glasses and glasses ceramic.

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