Mixed ion–polaron transport in Na2O–PbO–Fe2O3–P2O5 glasses

Journal of Non-Crystalline Solids 342 (2004) 97–109 www.elsevier.com/locate/jnoncrysol

Mixed ion–polaron transport in Na2O–PbO–Fe2O3–P2O5 glasses A. Mogusˇ-Milankovic´ a b

a,*

, A. Sˇantic´ a, S.T. Reis b, K. Furic´ a, D.E. Day

b

Department of Physics, Ruder  Bosˇkovic´ Institute, Bijenicˇka c.54, 10000 Zagreb, Croatia Graduate Center for Materials Research, University of Missouri-Rolla, MO 65409, USA Received 1 January 2004

Abstract The electrical and dielectric properties of the xNa2O Æ (100
x) Æ [28.3PbO Æ 28.7Fe2O3 Æ 43.0P2O5] (0 6 x 6 30) glasses were measured by impedance spectroscopy in the frequency range from 0.01 Hz to 3 MHz and the temperature range from 303 to 473 K. The conductivity for glasses containing 615 mol% Na2O is predominantly electronic and is controlled by electron hopping between Fe(II) and Fe(III) ions. In these glasses the sodium ions have such a low mobility, caused by ion–polaron interaction, that they make no detectable contribution to the total conductivity. For Na2O contents >15 mol%, the conductivity increases significantly due to an increase in the sodium ion mobility. The increasing concentration of sodium ions, increases the degree of disorder in the glass network, with an increase in the number of non-bridging oxygens. This in turn enhances the pathways suitable for migration of the sodium ions responsible for an increase in the ionic conductivity. The dielectric properties, such as e 0 (x) and e00 (x), and their variation with frequency and temperature indicates an increase in electrode polarization, which reduces the dipolar relaxation effects. The structural changes in these glasses have been investigated by Raman and IR spectroscopy. The Raman spectra show that with increasing Na2O content there is corresponding reduction in number of the Q1 phosphate units and an increase in non-bridging oxygens as more Q0 phosphate units are formed in the glass network. The decrease in glass temperature, Tg and glass density, D, is due to the lower degree of cross-bonding between the sodium and non-bridging oxygens in Q0 phosphate units resulting in a weakening of the glass network.
2004 Elsevier B.V. All rights reserved.

1. Introduction Phosphate glasses have several technological advantages over conventional silicate and borate glasses due to their superior physical properties such as high thermal expansion coefficient, low melting and softening temperatures and high ultra-violet transmission [1–4]. The binary iron phosphate glasses have gained attention as candidates for immobilizing certain types of highlevel nuclear wastes (HLW) because of their good chemical durability. The exceptionally high chemical durability of these glasses is believed to be due to the *

Corresponding author. Tel.: +385 1 4561 149; fax: +385 1 4680 114. E-mail address: [email protected] (A. Mogusˇ-Milankovic´). 0022-3093/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.07.012

more hydration resistant Fe–O–P bonds that replace more easily hydrated P–O–P bonds present in common phosphate glasses [5–7]. Recently, lead–iron phosphate glasses waste forms obtained by adding PbO to an iron phosphate glass, have been reinvestigated because their chemical durability is comparable to borosilicate waste glasses [8,9]. Reis et al. [8] found that the chemical durability of a 43.3PbO–13.7Fe2O3–43P2O5 glass (mol%) is comparable to the best binary iron phosphate glass with an approximate composition of 40Fe2O3–60P2O5. They reported that the replacement of Fe–O–P for Pb–O–P bonds does not affect the chemical durability when the O/P ratio was 3.5. The specific applications of these glasses are the challenge for the investigation of their structure–properties

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A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

relationships. However, there have been only a few studies of their structural and electrical properties [10–12]. Iron phosphate glasses behave as typical semiconductors, where the electrical conduction is thermally activated polaron hopping from Fe(II) to neighboring Fe(III) sites with an activation energy in the range 51– 70 kJ mol
1 [11,13]. On the other hand, the conductivity of alkali containing iron phosphate glasses consists of a mixed electronic and ionic conduction. The ionic conduction should be proportional to the concentration and mobility of the alkali ions while the electronic conduction is described by the hopping theory [14]. Ideally, the motion of the alkali ions and electrons are independent of each other. However, Bazan et al. [15] have reported a coupling of ion and electron transport processes that is caused by the electrostatic interaction between mobile ions and electrons (polarons). This effect, designated as the ion–polaron effect (IPE), is responsible for a decrease in the effective mobility and decrease in electrical conductivity in mixed ionic–electronic conductors. It causes a slowing of both electronic and ionic motions due to coulombic attraction between the oppositely charged ions and polarons. This effect is most pronounced when the concentration of both types of charge carriers is comparable. For the glasses, where one of the components, either ions or polarons, strongly dominates, the IPE effect disappears. However, it was found [16] that the dc conductivity for mixed sodium and potassium, iron phosphate glasses was independent of the Na/K ratio and there was no evidence of the mixed alkali effect. The sodium and potassium ions have such a low mobility in both, single and mixed alkali iron phosphate glasses that they make no detectable contribution to the total conductivity that is electronic in origin. A gradual change in the electrical conductivity with composition, lead to understanding the interdependence between the electronic and ionic components of the total conductivity in mixed electronic–ionic conductors. In a previous paper [17] the effect of Fe2O3 content on the conductivity and crystallization tendency in the glass system PbO–Fe2O3–P2O5 was investigated. It was shown that the electronic conduction in these glasses depends not only on the Fe(II)/Fetot ratio, but also on easy pathways for electron hopping in a non-disrupted pyrophosphate network. The Raman spectra of crystallized compositions indicate a much lower degree of crosslinking since more non-bridging oxygen ions are present in the network. Despite the significant increase in the Fe2O3 content and Fe(II) concentration there is a considerable weakening of the interaction between the Fe sites. The decrease in conductivity, seen in impedance spectra is caused by discontinuities in the conduction pathways as a result of the disruption and inhomogeneity in the crystalline network where two or more crystalline phases are formed.

The aim of the present work was to study the structural modifications and changes in the character of the electrical conductivity in the Na2O–PbO–Fe2O3–P2O5 glasses using Raman, IR, Mo¨ssbauer and impedance spectroscopy. Attention was paid to the relation between the type of conductivity, mixed electronic–ionic, predominantly ionic or mainly electronic and the shape of impedance spectra. The electronic component of the electrical conduction in these glasses is due to the iron ions being in two valence states as Fe(II) and Fe(III) and acting as a center for electron hopping. The presence of a glass modifier Na2O is responsible for the ionic part of the electrical conduction. However, little is known about the relationship between structure and electrical transport in Na2O–PbO–Fe2O3–P2O5 glasses that exhibit a mixed ionic–electronic conduction with predominance of ionic or electronic depending on their composition. These glasses were additionally characterized by DTA and chemical durability tests.

2. Experimental 2.1. Preparation and melting of glass samples Glasses of the composition xNa2O Æ (100
x) Æ [28.3PbO Æ 28.7Fe2O3 Æ 43.0P2O5] (0 6 x 6 30) (in mol%) were prepared by conventional melting and quenching. The glasses were melted between 1373 and 1473 K for 2 h in air in high purity alumina crucibles. The melt was quenched in air by pouring it into a 1 · 1 · 5 cm3 steel mold. The samples were transferred to a furnace and annealed at 723 K for 3 h. In this series of glasses the (Fe + Pb)/P ratio was fixed at 1.0, whereas, the molar O/P ratio increases from 3.83 to 4.33 with increasing Na2O content. 2.2. Density, DTA and chemical durability The density of each glass was measured at room temperature by the Archimedes method using water as the buoyancy liquid. The estimated error is ±0.02 g cm
3. The DTA measurements were performed in flowing nitrogen at a heating rate of 10 K min
1 using a Perkin Elmer instrument. The estimated error in glass transition (Tg) and crystallization temperature (Tc) is ±2 K. The chemical durability of glassy and crystallized samples was evaluated from the weight loss of samples (1 · 1 · 1 cm3) immersed in distilled water at 363 K for 2–32 days. The samples were polished to a 600 grit finish with SiC paper, cleaned with acetone and suspended in glass flasks containing 100 mL of distilled water at 363 K. Duplicate measurements were made for each glass and the average dissolution rate (DR), normalized to the surface area and the corrosion time, was calculated from the weight loss.

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99

the experimental data and sample dimensions. All the experimental data at a given temperature is contained in G(x) and C(x) where G is the conductance, C is the capacitance and x (=2pf) is the angular frequency. The conductivity, r(x), and relative permittivity, e(x), were calculated from the impedance measurements using the equation, r(x) = Gd/S, and e(x) = Cd/e0S where S and d are the sample area and thickness, respectively, and e0 is the permittivity of free space [18].

2.3. Mo¨ssbauer, IR and Raman spectra The Mo¨ssbauer spectra were measured at room temperature on a spectrometer (ASA 600), which utilized a room temperature 50 mCi cobalt-57 source embedded in a rhodium matrix. The spectrometer was calibrated at 296 K with a-iron foil and the line width of the a-iron spectrum was 0.27 mm s
1. The Mo¨ssbauer absorbers of approximate thickness 140 mg cm
2 were prepared using 125 lm powders. The Mo¨ssbauer spectra were fit with broadened paramagnetic Lorentzian doublets. The infrared spectra (IR) were measured between 500 and 1500 cm
1 using a Bruker Optic FTIR Interferometer Equinox 55. Samples were prepared as pellets by pressing a mixture of glass and anhydrous KBr powder. The spectrum of pure KBr was subtracted from each glass spectrum to correct for the background. Raman spectra of each glass were obtained using 200 mW of 514.5 nm light from a coherent argon-ion laser model (Innova 100) and were recorded with a computerized triple monochromator Dilor model Z 24. A 90 scattering geometry was used with the sample oriented at a near-grazing angle. The complex shape of the experimentally recorded Raman bands was analyzed using a least-square fitting procedure assuming a Gaussian shape for all bands.

3. Results 3.1. DTA, density and chemical durability The composition and selected properties of each glass are shown in Table 1. Fig. 1 shows the DTA patterns for these Na2O–PbO– Fe2O3–P2O5 glasses. As shown by small endothermic peaks the glass transition temperature, Tg, range between 777 and 794 K. The temperature of the exothermic crystallization peaks decrease from 869 to 822 K with increasing Na2O content. For the glasses B1, B2 and B3 the exothermic peaks at about 869 and 852 K are probably due to the crystallization of pyrophosphate structures as indicated by Raman spectroscopy, Fig. 3(a). Similar exothermic peaks, attributed to the crystallization of Fe3(P2O7)2 [19], were observed between 860 and 920 K in the DTA patterns for a binary iron phosphate glass (40Fe2O3–60P2O5) and lead–iron phosphate glasses [17]. Based upon the Raman and IR spectra of the B4 and B5 glasses in Fig. 3, the exothermic peaks at 822 K probably corresponds to the crystallization of an orthophosphate. The crystallization tendency for this series of glasses increases with increasing Na2O content and molar O/P ratio, which increases from 3.89 to 4.33 for the B1 and B5 glasses, respectively. The density of the glasses, see Table 1, decreases from 4.4 to 3.9 g cm
3 with increasing Na2O content as a result of a weakening of cross-linking within glass network.

2.4. Electrical measurements Samples for electrical property measurements were cut from annealed bars and polished with 600 grit polishing paper. Gold electrodes, 6 or 7 mm in diameter, were evaporated onto both sides of 1 mm thick discs cut from the glass bars. The samples were stored in a dessicator until the electrical conductivity was measured. The real and imaginary parts of the complex impedance were measured from 303 to 473 K using an impedance analyzer over a frequency range of 0.01 Hz to 3 MHz. The temperature was controlled to ±3 K. Calculation of r(x) and e(x) was performed separately using

Table 1 Batch composition and selected properties for the xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses Sample code

B0 B1 B2 B3 B4 B5 a b c

Composition (mol%)

Molar ratio

Na2O

Fe2O3

PbO

P2O5

O/Pc

(Fe + Pb)/Pc

– 5.0 10.0 15.0 20.0 30.0

28.7 27.3 25.8 24.1 22.6 19.8

28.3 26.9 25.5 24.4 23.0 20.1

43.0 40.9 38.7 36.6 34.4 30.1

3.83 3.89 3.96 4.04 4.12 4.33

1.0 1.0 1.0 1.0 1.0 1.0

Fe2+/Fetot (±0.03%)a

log DR at 363 Kb

Tg (±2 K)

Tc (±2 K)

D (g cm
3) (±0.02 g cm
3)

˚) RFe–Fe (A (±0.5%)

0.27 0.32 0.31 0.31 0.30 0.27


8.4
8.1
8.1
7.5
7.2
5.5

804 791 794 – 777 –

946 869 813/859 852/891 822 822

4.4 4.4 4.4 4.2 4.2 3.9

2.93 2.98 3.03 3.15 3.22 3.45

Fe2+/Fetot ratio calculated from the Mo¨ssbauer spectra. Dissolution rates (g/cm2 min) for glass samples measured from the weight loss experiments in distilled water at 363 K for 32 days. Molar ratios of O/P and (Fe + Pb)/P calculated from the batch compositions.

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100

Tg

the dissolution rate increased with increasing Na2O content, but most of the glasses still had a DR comparable to window glass, excluding B5. For the B3, B4 and B5 glasses, whose O/P ratio exceeds 4.0, the DR increases due to the increase in non-bridging oxygens, NBO, in the orthophosphate structure, which may have an adverse effect on the chemical durability [9].

B5

822

822

∆T

EXO

B4

ENDO

777

852

891

3.2. Raman and IR spectra B3

859

B2

869

B1

794

791

680 720 760 800 840 880 920 960 Temperature (K) Fig. 1. Differential thermal analysis (DTA) curves for xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (5 6 x 6 30) glasses.

The dissolution rate, DR, of each glass, as measured from the weight loss in distilled water at 363 K up to 32 days, is given in Table 1 and Fig. 2. For the B0 (sodium-free), B1 and B2 glasses, the dissolution rate is almost constant for a given immersion time. The dissolution rates of the B3 and B4 glasses gradually increased from log(DR)
8.1 to log(DR)
7.2 as the Na2O content increases, whereas, for glass B5 containing 20 mol% Na2O increased to log(DR)
5.5. It should be noted that

2 days 4 days 8 days 16 days 32 days

log DR (g/cm 2 min) at 363 K

-4 xNa2 O-(100-x)[28.3PbO-28.7Fe2O3 - 43.0P2 O5 ]

-5 0 ≤ x ≤ 30 -6 -7 Window glass

-8 -9

-10 0

5

10

15 20 mol% Na2 O

25

30

Fig. 2. Dissolution rate (DR) for xNa2O Æ (100
x)[28.3PbO– 28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses as a function of the Na2O content after immersion in distilled water at 363 K for 2, 4, 8, 16, 32 days.

The Raman and IR spectra for Na2O–PbO–Fe2O3– P2O5 glasses are shown in Fig. 3(a) and (b) while the assignment of the Raman and IR bands are given in Table 2. The Raman spectra for the sodium-free, B0, glass is characteristic of pyrophosphate Q1 structure with the most prominent bands at 1052 and 743 cm
1 related to the symmetric stretching mode of non-bridging (PO2)sym and bridging (P–O–P)sym oxygen atoms, respectively. Some barely detectable bands at 1195 and 627 cm
1 are attributed to the non-bridging, (PO2)sym, and bridging oxygen atoms (P–O–P)sym in Q2 phosphate tetrahedra. The shoulder at 938 cm
1 suggests the presence of Q0 phosphate units. The frequency of this band, assigned to the symmetric stretching mode of non-bridging oxygen in orthophosphate groups, agrees with the value of 945 cm
1 for sodium orthophosphates reported by Nelson et al. [20]. The spectra for the B1 and B2 glasses are almost identical with the spectrum for the B0 glass showing bands that correspond to Q1 phosphate groups. It is well known that with increasing O/P ratio from 3.5 to 4.0 the phosphate structure changes from Q1 to Q0 units [10,19]. Since with increasing Na2O there is a corresponding increase in the O/P ratio from 4.04 to 4.33 for the B3 and B5 glasses, respectively, it is reasonable to expect an increase in the number of orthophosphate, Q0, units in the glass structure. The Raman spectrum for the B5 glass consists of two dominant bands at 989 and 443 cm
1 attributed to the isolated (PO4)3
units in a Q0 structure while the band at 742 cm
1 related to the bridging P–O–P bond completely disappeared. Thus, these changes in the Raman spectra for the B5 glass confirm some bond breaking in the pyrophosphate, (P2O7)4
units which results in an increase in the number of NBO with the addition of Na2O. However, barely detectable bands at 1139 and 621 cm
1 associated with the non-bridging, (PO2)sym, and bridging oxygen atoms (P–O–P)sym in Q2 phosphate tetrahedra along with band at 1295 cm
1 attributed the stretching mode of the terminal P@O bond suggests that some metaphosphate units are present in the network of the B5 glass. Similar changes in the IR spectra for these glasses are seen in the frequency range between 400 and 1500 cm
1.

B5

νs P-O-P in Q1 3δ (P3O9) ring δ O-P=O δ O-P-O

2-

νs P=O 2 νas (PO2) in Q

νas (PO3) terminal in Q νas (PO4)3- in Q0 νas P-O-P in Q1

0

δ O-P-O in Q

2

νs P-O-P in Q

1

νs P-O-P in Q

2

-

νs P=O

101

1

νs (PO2) in Q 421 νs (P2O7) , (PO3) in Q 30 νs (PO4) in Q

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

B5

Trasmittance (%)

Relative intensity

B4

B4

B3

B3

B2

B2 B1

B1 B0

(a)

1400 1200 1000 800 600 400 200

(b) 1400

Raman shift (cm-1)

1200

1000

800

600

-1

Wavenumber (cm )

Fig. 3. The Raman (a) and IR (b) spectra of xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses.

Table 2 Raman and IR assignments for the xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses Raman bands (cm
1) 443 <566 619–627 737–743 938–989 1014–1057 1099–1139 1296

Assignment of the Raman bands 0

d O–P–O in Q units d of phosphate chains ms P–O–P in Q2 units ms P–O–P in Q1 units ms (PO4)3
in Q0 units ms (P2O7)4
, (PO3)2
in Q1 units ms (PO2)
in Q2 units ms P@O

It should be mentioned that the IR spectra are dominated by intense bands related to the asymmetric, whereas, the Raman spectra are mostly dominated by bands related to the symmetric stretches. For the B1 glass, the main IR bands in Fig. 3(b) at 1047, 928, 752 and 537 cm
1 are assigned to the asymmetric stretch of the (PO3)2
terminal groups, asymmetric and symmetric modes of P–O–P bonds and bending mode of O–P–O bonds in the Q1 structure, respectively [21]. The intensity of the bands at 928 and 752 cm
1 tends to decrease and eventually disappear with increasing Na2O content in the B3, B4 and B5 glasses. On the other hand, the intensity of the band at 982 cm
1 related to the (PO4)3
group in the Q0 structure in-

IR bands (cm
1)

Assignment of the IR bands

534–544 571–578 613–625 748–752 928 982 1030–1047 1177 1259

d O–P–O d O–P@O d of (P3O9)3
metaphosphate rings ms P–O–P in Q1 units mas P–O–P in Q1 units mas (PO4)3
in Q0 units mas (PO3)2
terminal in Q1 units mas (PO2)
in Q2 units ms P@O

creases with increasing Na2O content, indicating an increase in the number of NBO due to depolymerization of the glass network. The IR spectra of the B4 and B5 glass contain bands at 1177 and 625 cm
1 associated with the (PO3)
groups in Q2 and bending mode in (P3O9)3
metaphosphate rings, respectively [21]. 3.3. Electrical measurements Fig. 4(a) and (b) show the impedance spectra at 393, 423 and 473 K and their corresponding electric equivalent circuits for the B2 and B4 glasses. The spectrum for the B2 glass contains one semicircle related to bulk effects at each temperature, which is characteristic for

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

102

(a) B2

6

Re

Z"/MΩ

CPE g 393 K

4

2

423 K 473 K

0 0

2

4

6

8

10

12

Z’/MΩ 6 Re

(b) B4

CPEdl Ri

4 Z"/MΩ

CPEg 393 K

2 423 K 473 K

0 0

2

4

6 Z’/MΩ

8

10

12

Fig. 4. Complex impedance plots at various temperatures and their corresponding equivalent electric circuits for the B2 (a) and B4 (b) glass.

electronic conductors [22]. Each semicircle can be represented by single parallel RC element in equivalent circuit. Ideally, such semicircular arc passes through the origin of complex plot and gives a low frequency intercept on the real axis corresponding to the resistance, Re, of the sample. However, experimental data show depressed semicircle with the center below the real axis, which is the reason for using constant phase elements (CPEs) rather than ordinary capacitors in equivalent circuits. The CPE is an empirical impedance function of the type: Z CPE ¼ AðjxÞ
a ;

ð1Þ

where A and a are constants. The barely visible beginning of residual semicircle at low frequencies is attributed to electrode effects. This assignment was confirmed by the fact that this part of the spectrum was much smaller for finely polished samples with sputtered electrodes.

The impedance plot for the B4 glass consists of high frequency depressed semicircle and low-frequency spur that is typical for ionic conductors. An impedance plot with the same shape was observed for the B5 glass. The elements of the appropriate equivalent circuit (part of the circuit drawn with solid line) are Ri, CPEdl and CPEg where Ri is the resistance due to ionic conduction of glass and CPEdl and CPEg correspond to the constant phase elements representing double layer and geometric capacitance of the system, respectively. It should be noted that the spectrum for the mixed ionic–electronic conductors consist of two separated semicircles (equivalent circuit consists of both parts drawn with solid and dashed lines). For obtaining the low frequency semicircle, the impedance should be measured at much lower frequency (10
5 Hz) than that in the present paper. The frequency dependence of the total conductivity, r(x) at various temperatures for the B2 glass is shown in Fig. 5(a). It should be noted that r(x) is nearly independent of frequency at low frequency, while becoming strongly dependent at higher frequency. The transition point, between these two regions is shifted toward higher frequency with increasing temperature. At low frequency, the conductivity is the dc conductivity, rdc. At the high frequency the conductivity obeys a powerlaw, rac(x) = Axs, where A is a temperature dependent constant and s is a power. Thus, the total conductivity can be given as, r(x) = rdc + Axs. The values for rac(x) were derived by subtracting rdc from the total measured conductivity, r(x), at different temperatures. The dependence of r(x), rac(x), and rdc upon reciprocal temperature for the B2 glass is shown in Fig. 5(b). At higher temperature, rac(x) is temperature dependent and approaches rdc. The temperature where rdc equals the measured total conductivity r(x), increases with increasing frequency. The values of the exponent s calculated from the slopes log rac(x) versus log f at different temperatures for the B1, B2 and B3 glasses lie in the range of 0.60 6 s 6 0.83 which is consistent with the s parameter values that Murawski et al. [23] reported for different iron phosphate glasses. Table 4 gives the s parameter values at 303 and 363 K for the Na2O– PbO–Fe2O3–P2O5 glasses. For the glasses of higher Na2O content, B4 and B5, the values for s are in the range of 0.36 6 s 6 0.61. It is also noteworthy that the s parameter depends upon the temperature (decreases with increasing temperature and dc conductivity). The temperature dependence of the electronic conductivity for amorphous semiconductors containing transition metal ions, such as Fe(II) and Fe(III), is usually expressed by the Austin–Mott equation [14]: r¼

mel e2 Cð1
CÞ expð
2aRÞ expð
W =kT Þ; kTR

ð2Þ

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

(a) B2

-2

log σ (ω) (Ωm)-1

-3

473 K 423 K

-4

393 K 363 K

-5

333 K -6

303 K

-7 -2

-1

0

1

2

3

4

5

6

7

log f (Hz)

-2 (b) B2 -3

log σ (ω) (Ωm)-1

106 Hz -4

σdc -5

105 Hz σ (ω)

104 Hz

σac(ω)

103 Hz

-6 -7

σdc

2.0

σac (ω) 2.4

σ (ω) 2.8

1000/T (K)

3.2

3.6

-1

Fig. 5. Frequency dependence of the conductivity at the temperatures shown for the B2 glass (a) and temperature dependence of the dc and ac conductivity for the B2 glass for several different frequencies (b). Lines are drawn connecting data symbols of each type. See Table 2 and Table 3 for the dc and ac activation energies, Edc and Eac, calculated from the slope of the plots log rdc and log rac(x) versus 1/T.

where C is the fraction of reduced transition metal ion (Fe(II)/Fetot), R is the average spacing between transi-

103

tion metal ions (R = (1/N)1/3), a is the tunneling factor (ratio of the wave function decay), e is the electronic charge, k is the Boltzmann constant, T is absolute temperature and W is the activation energy for the hopping conduction. Eq. (2) describes a non-adiabatic regime of small polaron hopping. In Motts theory, the mechanism of electron transport in amorphous semiconductors depends on temperature. In the high temperature region (T > H/2), where H is the Debye temperature, the conduction mechanism is considered as phonon-assisted hopping of small polaron (SPH) between localized states [14,24]. In this temperature region the jump of an electron (polaron) occurs between nearest neighbors with W = Wh + Wd/ 2. Wh is the polaron hopping energy and Wd is the energy difference between two neighboring ions. Since W and R in Eq. (2) are constant, the dependence of the dc conductivity on temperature can be compared with the Arrhenius equation rdc = r0exp(
Edc/ kBT) where rdc is the dc conductivity, r0 is the pre-exponent, Edc is the activation energy for the dc conductivity, kB is the Boltzmann constant and T is the temperature (K). The electrical parameters of the Arrhenius-like dependence of the dc conductivity and Edc observed at temperatures from 303 to 473 K are summarized in Table 3. The rac(x) conductivity that remains after subtracting rdc is also temperature dependent. The activation energy, Eac, was determined from the slope of log rac(x) versus 1/T for each frequency and is listed in Table 4. It should be noted that for frequencies <100 Hz, the activation energy, Eac, equals the activation energy for dc conductivity, Edc, whereas, at higher frequencies (1 kHz–1 MHz) Eac is significantly smaller than Edc. Using the Austin–Mott model [14,24] of small polaron hopping (SPH) in the high temperature region, (above H/2), from 303 to 473 K, it is possible to determine a transport mechanism for the present glasses. It was mentioned earlier that the dc conductivity–temperature relationship for SPH in the non-adiabatic region obeyed Eq. (2) as shown in Fig. 6. For each glass, the

Table 3 DC conductivity, rdc, activation energies, Edc, W, EM, pre-exponent, r0, relaxation time, sr, and real part of dielectric permittivity, e 0 (x), for the xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses Sample code

rdc (X m)
1 at 303 K (±0.5%)

Edca (kJ mol
1) (±0.5%)

log (r0/(X m)
1)a (±0.5%)

W b (kJ mol
1) (±0.5%)

log (r0/(X m)
1)b (±0.5%)

EMc (kJ mol
1) (±0.5%)

sr (s) at 333 K (±0.5%)

e 0 (x) at 103 Hz, 303 K (±0.5%)

B0 B1 B2 B3 B4 B5

4.38 · 10
7 5.11 · 10
7 3.48 · 10
7 5.41 · 10
7 2.77 · 10
6 3.29 · 10
4

47.7 47.9 48.8 47.7 44.7 35.1

1.79 1.91 1.89 1.89 2.15 2.57

50.8 51.1 51.8 50.8 47.9 37.9

4.79 4.93 4.90 4.89 5.17 5.56

47.9 48.1 48.8 47.9 43.4 –

6.52 · 10
5 1.84 · 10
6 6.52 · 10
5 7.92 · 10
5 1.10 · 10
5 1.28 · 10
7

25.9 24.6 23.0 36.4 116.1 2161.6

a b c

Electrical parameters calculated from Arrhenius equation. Electrical parameters calculated from Austin–Mott equation. Activation energy, EM, calculated using electrical modulus formalism.

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

104

Table 4 AC conductivity, rac(x), activation energies, Eac, at different frequencies and parameter s at 303 and 363 K for the xNa2O Æ (100
x)[28.3PbO– 28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses Sample code

rac(x) (X m)
1 at 103 Hz, 303 K (±0.5%)

Eac (kJ mol
1) at 103 Hz (±0.5%)

Eac (kJ mol
1) at 104 Hz (±0.5%)

Eac (kJ mol
1) at 105 Hz (±0.5%)

Eac (kJ mol
1) at 106 Hz (±0.5%)

s at 303 K (±0.5%)

s at 363 K (±0.5%)

B0 B1 B2 B3 B4 B5

2.77 · 10
7 2.67 · 10
7 2.00 · 10
7 2.97 · 10
7 3.19 · 10
6 1.11 · 10
4

21.7 20.3 14.9 13.9 35.6 30.9

19.2 16.3 14.1 13.3 29.4 23.4

15.8 13.6 13.6 12.7 21.7 21.2

4.4 4.7 4.4 3.4 10.3 21.4

0.70 0.68 0.75 0.83 0.61 0.49

0.60 0.60 0.74 0.77 0.45 0.36

1

-1

log σdc T (Ωm) K

0

B0 B1 B2 B3 B4 B5

-1 -2 -3 -4 -5 2.0

2.4

2.8 1000/T (K)

3.2

3.6

-1

Fig. 6. Temperature dependence of the dc conductivity, rdc, for the xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5](0 6 x 6 30) glasses. See Table 2 for activation energy, W, calculated from the slope log(rdcT) versus 1/T.

FeII / (FeII+FeIII)

0.32

-4

0.30 -5 0.28 -6

0.26

-2 0.24

log σdc (Ω m)-1

-3

60

dc at 303 K 0

5

10 15 20 mol% Na2 O

25

30

-7

55

W

-4

50

-5

45

-1

1 Hz

FeII/(FeII+FeIII)

W (kJmol )

2

-3

0.34

log σdc (Ωm)-1

calculated values for the activation energy, W, from Eq. (2) are reported in Table 3. The calculated values are almost identical to those of Edc calculated from the Arrhenius-like dependence of the dc conductivity, Table 3. Fig. 7 shows the dependence of rdc and W upon the addition of Na2O. For the glasses containing up to 15 mol% Na2O, rdc and W are almost constant, for the B4 glass containing 20 mol% Na2O, rdc increases slightly, whereas, for the B5 glass with 30 mol% Na2O, rdc increases nearly two orders of magnitude. It can be also seen from the inset in Fig. 7 that the small change in Fe(II)/Fetot ratio (0.31) parallels the small change in rdc, varying from 5.41 · 10
7 to 3.48 · 10
7 (X m)
1. However, despite the decrease in the Fe(II)/ Fetot ratio for the B5 glass, rdc significantly increases. This suggests that the small polaron charge transport mechanism is dominant in the glasses with up to 15 mol% Na2O, whereas, the conductivity for glasses with 30 mol% Na2O is caused by mobile sodium ions.

σdc at 303 K

-6

40

-7

35 0

5

10

15

20

25

30

mol% Na2O Fig. 7. The dependence of the dc conductivity, rdc, at 303 K and activation energy, W, upon the Na2O content in the xNa2O Æ (100
x)[28.3PbO–28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses. Inset: dc conductivity, rdc, at 303 K and FeII/(FeII + FeIII) ratio as a function of Na2O content. Lines are drawn connecting data symbols of each kind.

3.3.1. Dielectric properties The temperature dependence of the real e 0 (x), and imaginary part of the dielectric permittivity e00 (x), on frequency for the B4 glass is shown in Fig. 8(a) and (b). The e 0 (x) and e00 (x) gradually increase as the temperature increases. All the glasses in the present study show the same behavior. The dielectric permittivity, e 0 (x), measured at 303 K and 1 kHz for the present glasses is given in Table 3. At higher frequency, e 0 (x) approaches a constant value, e01 ðxÞ, which probably results from rapid polarization processes occurring in the glasses [24]. With decreasing frequency, e 0 (x) increases due to electrode polarization arising usually from space charge accumulation at the glass–electrode interface. For the present glasses, e 0 (x) and e00 (x) increases with increasing Na2O content. The temperature dependence

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

105

100 Hz

(a) B1

2

2x10

1 kHz

ε ’(ω)

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 2

1x10

10 kHz 100 kHz 1 MHz 0 300

330

360

390

420

450

480

510

T (K)

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

5

2x10

ε ’(ω)

100 Hz

(b) B5

5

3x10

5

1x10

1 kHz 10 kHz 100 kHz

0 1 MHz

300

330

360

390

T(K)

Fig. 9. Temperature dependence of e 0 (x) for the B1 (a) and B5 (b) glasses at different frequencies. Fig. 8. Frequency dependence of e 0 (x) (a) and e00 (x) (b) for the B4 glass at various temperatures. The increase in e 0 (x) at low frequencies is caused by electrode polarization.

of e 0 (x) at different frequencies for glasses B1 and B5 is shown in Fig. 9(a) and (b). The considerable increase in e 0 (x) occurs at higher temperatures and is more pronounced at lower frequency. The variation of e 0 (x) with the Na2O concentration as a function of the temperature at 1 kHz is given in Fig. 10(a). For all but the B4 and B5 glasses, e 0 (x) varies only slightly from 23.0 to 36.4, whereas, it increases significantly to over 2.2 · 103, measured at 303 K and 1 kHz, for the B5 glass, Table 3. The factor, which measures the phase difference due to the loss of energy within a sample at a particular frequency is the loss factor tangent, tan d = e00 /e 0 . The temperature dependence of tan d at 100 kHz for all the present glasses is shown in Fig. 10(b). The tan d for B0, B1, B2 and B3 glasses, measured at temperatures up to 393 K, is constant whereas at higher temperature it increases significantly. On the other hand, the loss factor for the B5 glass is much higher than for the glasses con-

taining less Na2O. However, the temperature variation of the loss tangent, tan d, did not exhibit any relaxation peak. Because of the absence of a well-defined loss peak, it is difficult to use conventional methods for estimating the relaxation frequency, f, and the nature of the dispersion, characterized by a distribution of relaxation times. An approach that may be used for analyzing the data is the dielectric modulus model, defined by Macedo et al. [34]. The dielectric modulus is defined as M* = 1/e*, where e* is the complex permittivity, M  ¼ 1=e ¼ e0 =ðe0 Þ2 þ ðe00 Þ2 þ ie00 =ðe0 Þ2 þ ðe00 Þ2 ¼ M 0 þ iM 00 :

ð3Þ

In this case, the effects of electrode polarization can be avoided since the electrical modulus peaks, M00 , are shifted toward higher frequency. Thus, two apparent relaxation regions appear, the lower frequency region being associated with the conduction process (hopping) and the higher frequency region being associated

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

106

B0 B1 B2 B3 B4 B5

4

1.5x10

(a)

1 kHz B5

ε '(ω)

4

1.0x10

3

5.0x10

B4 B0 - B3

0.0

300

330

360

390

420

450

480

T (K) 4.0

3.0 2.5

tan δ

(b)

B0 100 kHz B1 B2 B3 B4 B5

3.5

Fig. 11. Frequency dependence of the electrical modulus, M00 , for B1 glass at temperatures shown.

4. Discussion

2.0 1.5 1.0 0.5 0.0 300

330

360

390

420

450

480

T (K) Fig. 10. Temperature dependence of e 0 (x) at 1 kHz (a) and loss tangent, tan d, at 100 kHz (b) for the xNa2O Æ (100
x)[28.3PbO– 28.7Fe2O3–43.0P2O5] (0 6 x 6 30) glasses.

with the relaxation polarization processes. In the case, that the data are presented in electrical modulus representation [24] the effect of conductivity may be suppressed. For all glasses investigated, the temperature dependence of the imaginary part of the electrical modulus M00 , at different frequencies was used to calculate the activation energy, EM, and relaxation times, sr. The maximum in the M00 peak shifts to higher temperature with increasing frequency. M00 shows a maximum at a characteristic frequency, which is equal to the relaxation frequency f. The relaxation time, sr, can be extracted from the position of the M00 maximum where f = 1/(2psr) [34], as shown in Fig. 11. The relaxation times, sr, for the glasses measured at 333 K are shown in Table 3. It is clear, that at any chosen temperature, sr decreases for glasses containing >30 mol% Na2O, whereas, sr increases in glasses containing up to 15 mol% Na2O. The activation energy values for the electrical modulus, EM, and for the dc conductivity, Edc, are almost identical.

The basic phosphate network in the B0, B1 and B2 glasses are the pyrophosphate, Q1 units since the Raman spectra contained the most intense band at 1052 and 743 cm
1, Fig. 3(a) and the IR spectra showed a broad band centered at 1047 cm
1, Fig. 3(b). However, the phosphate network also contains some metaphosphate, Q2 and orthophosphate, Q0 units, Table 2. For glasses B3, B4 and B5 whose O/P ratio exceeds 4.0, the disappearance of the band at 743 cm
1 indicates that the addition of Na2O depolymerizes the bridging, P–O–P, oxygens present in the Q1 to form isolated Q0 phosphate units. Similarly, a formation of Q0 units along with increase in the number of NBOs was found in IR spectra, Fig. 3(b). The observed Q0 phosphate units along with a low concentration of Q2 groups indicated a more random configuration of BO and NBO atoms that is reflected in glass stability. It is known that the Tg and glass density, D, decreases with decreasing bond strength and cross-linking in phosphate glasses [6,16]. The data in Table 1 and Fig. 1 show that for the present glasses, the Tg and D decrease with increasing Na2O content. The decrease in Tg and D for the B3, B4 and B5 glasses is due to the lower degree of crossbonding between the sodium ions and NBO in orthophosphate units. Therefore, the resulting increase in structural depolymerization for these glasses is responsible for the decrease in Tg and D. Since iron phosphate glasses have been identified as a possible candidate for immobilizing nuclear waste due to their excellent chemical durability [3,5,9] it was of interest to investigate the dissolution rate for these glasses. It was previously reported [6,8,9] that the O/P ratio is an important factor affecting the chemical durability. Glasses with an O/P ratio <4.04 whose composi-

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

tion is close to the Q1 phosphate structure, have smallest dissolution rate (highest chemical durability) with log DR of
8.1 at 363 K. This good chemical durability is consistent with the stronger bonding in these sodium lead–iron phosphate glasses that contain predominantly pyrophosphate Q1 units. However, glasses have a lower chemical durability (higher dissolution rate) with a Na2O content up to 30 mol% and O/P > 4.04. The phosphate network of these glasses contains predominantly Q0 phosphate units suggesting a larger number of NBOs and some metaphosphate Q2 units. It is generally accepted that the improved chemical durability in iron and lead–iron phosphate glasses is attributed to the replacement of easily hydrated P–O–P bonds by more chemically resistant Fe–O–P bonds with increasing iron content [3,5,6,8,9,16]. Since the Fe2O3 content decreases from 24.1 to 19.8 mol% as the Na2O content increases from 15 to 30 mol% for the B3, B4 and B5 glasses, respectively, it is reasonable to expect a lower chemical durability. However, the overall chemical durability for these glasses is comparable to soda lime window glass. 4.1. Electrical properties In interpreting the electrical properties of the Na2O– PbO–Fe2O3–P2O5 glasses, it should be noted that there are a few important factors affecting electrical conductivity. It is well known that the iron phosphate glasses are electronically conducting glasses where the polaronic conduction takes place by an electron hopping from Fe(II) to Fe(III) ions. Thus, the Fe(II)/Fetot ratio, the total Fe2O3 content and the distance between the Fe ions are important to the electrical conductivity of these glasses. Also, in alkali containing iron phosphate glasses, different processes can contribute to the electrical conduction at different temperatures. In general, ionic conduction is due to the motion of alkali ions so the electrical conductivity is expected to be proportional to the concentration of the alkali ions. Fig. 7 and Table 3 show that the dc conductivity, rdc, and activation energy, W, for the Na2O–PbO–Fe2O3– P2O5 glasses containing up to 20 mol% Na2O is almost constant. In spite of the increase in sodium content, the rdc does not increase. Thus, unlike the typical mixed electronic–ionic conductive glasses, the sodium ions in these glasses have a lower mobility. Bazan et al. [15] propose a likely explanation, which assumes that the mobile electrons or polarons are attracted to the oppositely positive charged sodium ions and move together as neutral entities. Such a migration does not involve any net displacement of electric charge, so, this process does not contribute to rdc. It should be noted that the ratio Fe(II)/Fetot determined by Mo¨ssbauer analysis, varies only slightly from 0.27 to 0.32 for the glasses investi-

107

gated, thus, the concentration of polarons should be approximately the same in each glass. This is consistent with the previous results [16,25] that polaron hopping mainly determines the conductivity in Na2O–Fe2O3– P2O5 glasses containing less than 20 mol% Na2O. Accordingly, the single semicircle indicates a single conductivity mechanism for the B0, B1, B2 and B3 glasses, Fig. 4(a). On the other hand, when a higher concentration of sodium ions is present, the movement of the free cations exceeds the movement of the free polarons and the ionic conductivity increases at Na2O contents >20 mol%. The predominance of the ionic component of the electrical conductivity in the B4 and B5 glasses produces the low-frequency spurs in the impedance plot, Fig. 4(b). Such a feature indicates the blocking of the mobile ionic charge carriers (Na+) at the Au electrodes. This indicates that the electrons have a minor role in the transport of electrical charge in glasses whose Na2O content is >20 mol%. According to the Raman spectra in Fig. 3(a), there is corresponding decrease in the number of Q1 phosphate units with increasing Na2O content. As the P–O–P bonds, present in Q1 phosphate units are broken, nonbridging oxygens appear close to the neighboring sodium cations that enhances the pathways suitable for migration of sodium ions resulting in an increase of ionic conductivity. The decrease in activation energy, Edc, for the B4 and B5 glasses is in accordance with the increase in dc conductivity, rdc, Table 3. The activation energy for the ac conductivity, Eac is almost identical to the activation energy for dc conductivity, Edc, at frequencies below 100 Hz, whereas, at higher frequencies, 1 kHz, Eac is significantly lower than Edc for the B0, B1, B2 and B3 glasses. For the B4 and especially the B5 glasses, the measured Eac values at 1 kHz are close to Edc suggesting an increase in the ionic component of the conductivity. In the ion conducting glasses, it was found that the dc conductivity, rdc, depends on the concentration of mobile ions, x, in a power-law fashion [26]. This means that the mobility, which is proportional to rdc / x, increases with x according to a power-law. However, a power-law is not valid for glasses where polaronic conductivity dominates [27], for example, for glasses containing up to 15 mol% Na2O, which exhibit ion–polaron interaction. Thus, the total conductivity, rtot(x), is given by rtot(x) = rdc + Axs. Since in the low frequency range, the conductivity refers to the dc conductivity and at high frequency the conductivity obeys the power-law relation, the ac conductivity is expressed as rac(x) = rtot(x)
rdc = Axs. The values for s calculated at 303 and 363 K, Table 4, lie in the range 0.60 6 s 6 0.83 for glasses of Na2O content 615 mol%. This confirms polaron hopping between Fe(II) to Fe(III) ions [28]. For glasses of higher Na2O content, >15 mol%, the

108

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values for s are smaller, in the range 0.36 6 s 6 0.61, suggesting the domination of ionic conduction. It should be noted that the model [29] based on classical hopping of electrons over a barrier predict a decrease in the exponent s with increasing temperature, which is consistent with the data in Table 4. Generally, at lower temperatures, the classical hopping of electrons is the dominant conduction mechanism in glasses containing transition metal ions [30]. On the other hand, at higher temperatures, where the ac conductivity approaches the dc conductivity, it makes no sense to determine the exponent, s [31]. Thus, the experimental data are then discussed in terms of the dielectric relaxation model. For all the glasses investigated, the increase in dielectric permittivity, e 0 (x), at low frequency is attributed to electrode polarization. Such an increase can be also associated with structural changes occurring in the glass network. With increasing Na2O content, there is corresponding increase in non-bridging oxygens as more Q0 phosphate units are formed in the glass. Consequently, the decrease in glass transformation temperature, Tg and glass density, D, is due to the lower degree of cross-bonding between sodium and NBO in Q0 phosphate units so that the glass network is weakened. Thus, the addition of Na2O weakens the glass network and creates pathways suitable for sodium ion migration that causes a space charge build up and an increase in the dielectric parameters, e 0 (x), e00 (x) and tan d for glasses with 20 and 30 mol% Na2O, Figs. 8–10 and Table 3. Relaxation phenomena in dielectric materials are associated with a frequency dependent orientational polarization. At low frequency, the permanent dipoles align themselves along the field and contribute fully to the total polarization of the dielectric. At higher frequency, the variation in the field is too rapid for the dipoles to align themselves, so their contribution to the polarization and hence, to dielectric permittivity can become negligible. Therefore, the dielectric permittivity, e 0 (x) decreases with increasing frequency. For glasses containing 615 mol% Na2O, when polaronic conductivity is dominant, it is assumed that the electrons interact strongly with the network to form small polarons. These polarons can form positively and negatively charge defects, which act as dipoles in glass [32]. Therefore, the reorientation of such dipoles gives rise to characteristic frequency dependent features of the complex permittivity, e*(x) = e 0 (x)
ie00 (x), where e00 (x) passes through a maximum at a frequency which is temperature dependent and whose inverse is associated with the time required for the dipoles to reorient. Since the permittivity loss, e00 (x) is related to the ac conductivity and the frequency and is calculated from the relation e00 (x) = rac(x)/xe0, then rac(x) is defined as rac(x) = r(x)
rdc. Thus, when dipoles are present, the dc conductivity should be subtracted from the measured conductivity

to treat the resulting permittivity as a relaxation process. Since at low frequencies, however, the conductivity is dominated by the dc conductivity, valuable information can be extracted from the permittivity loss spectra. Also, at frequencies near the relaxation peak, the permittivity loss current is usually much smaller than the conduction current [33]. This makes it difficult to observe the dielectric relaxation spectra. Some problems arose in calculating the loss factor tangent, tan d, and the permittivity loss, e00 (x) for present glasses. The dc conductivity, rdc, for glasses containing up to 15 mol% Na2O is smaller, which indicates a smaller number of dipoles in the glass network. This reduces the space charge that is responsible for electrode polarization at low frequency. Also, the dipoles formed between two different iron valence states act as a relaxing species, which have a distribution of relaxation times, the width of which changes with the distribution of sites. It is generally assumed that a Debye-type dielectric response with a distribution of relaxation times is responsible for electrical conduction [29]. Thus, the absence of a peak in tan d for glasses with 615 mol% Na2O, is related to the smaller values of e 0 (x) and e00 (x) at a given frequency which gives rise to smaller specific dielectric losses. Also, the values for tan d, at 100 kHz, were the same over the temperature range from 303 to 423 K, for the B0, B1, B2 and B3 glasses, Fig. 10. This indicates a low degree of freedom for dipoles to orient in the field direction. A different situation was found for the B4 and B5 glasses. As mentioned earlier, an increase in concentration of sodium ions increases the degree of disorder in the glass with increasing NBO, which in turn enhances the pathways suitable for sodium ion migration. Thus, a weaker glass increases the space charge polarization, leading to an increase in the dielectric parameters shown in Figs. 9 and 10. Since the polarization and conduction are integrated into a single, continuous process [24] the increase in e 0 (x) and e00 (x) is attributed to the conductivity, r(x) which is directly related to an increase in mobility of the charge carriers. Therefore, the e 0 (x) values are expected to be larger and consequently, electrode polarization becomes larger for the B4 and B5 glasses because movement of the charge carriers becomes easier with increasing Na2O content. Similarly, the loss tangent, tan d, shows a considerable increase at 100 kHz and is more pronounced at higher temperatures for the B5 glass, Fig. 10(b). Furthermore, the dc conductivity for the B4 and B5 glasses increases two orders of magnitude, Table 3, compared with the glasses of lower Na2O content. Such an increase in dc conductivity is related to the formation of dipoles formed between the positively charged sodium ions and the negatively charged NBO in Q0 phosphate units. Consequently, high number of dipoles results in an increase of the concentration of space charges accumulated at glass–electrode interface. This

A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 342 (2004) 97–109

leads to the conclusion that electrode polarization masks the low frequency permittivity and prevents any permittivity loss peak from being observed. The conductivity relaxation model, where a dielectric modulus is defined by M*(x) = 1/e*(x), can provide information about the relaxation mechanism in the absence of a well-defined dielectric loss peak [34]. The relaxation times, sr, as calculated from the frequency at the M00 maximum, shown in Fig. 11 and listed in Table 3 are thermally activated with the following respective activation energy Edc. From Table 3 it is clear that the relaxation time, sr, for the B5 glass is much smaller due to a smaller Edc, W and EM and consequently, a higher conductivity, r(x). For glasses containing 615 mol% Na2O, the relaxation times, sr, are larger as the ion–polaron interaction becomes effective and lower the conductivity in these glasses. 5. Conclusion The changes in the structural and electrical properties for the xNa2O Æ (100
x) Æ [28.3PbO Æ 28.7Fe2O3 Æ 43.0P2O5] (0 6 x 6 30) glasses, show that with increasing Na2O content there is corresponding decrease in number of Q1 phosphate units and an increase in the non-bridging oxygens as more Q0 phosphate units are formed in the glass. The resulting increase in structural depolymerization for these glasses is responsible for the decrease in Tg and D due to the lower degree of cross-bonding between the sodium and non-bridging ions in Q0 phosphate units. The nearly constant dc conductivity and activation energy for glasses containing 615 mol% Na2O is attributed to an ion–polaron interaction which is responsible for the low mobility of the sodium ions that make no detectable contribution to the total conductivity. With increasing Na2O content, up to 30 mol%, the total conductivity increases which is directly related to an increase in the mobility of the sodium ions. An increase in the number of non-bridging oxygens that appear in the neighborhood of the sodium ions is responsible for an increase in the ionic conductivity. The dielectric properties, such as e 0 (x) and e00 (x) and their variation with frequency and temperature, indicate an increase in electrode polarization, which reduces the dipolar relaxation effects. Acknowledgment This work was supported by the International Atomic Energy Agency (IAEA-Vienna) under Research Contact No. 10638/R.

109

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