- Email: [email protected]
Dielectric behavior and impedance spectroscopy of bismuth iron phosphate glasses
Journal of Non-Crystalline Solids 351 (2005) 3235–3245 www.elsevier.com/locate/jnoncrysol
Dielectric behavior and impedance spectroscopy of bismuth iron phosphate glasses A. Mogusˇ-Milankovic´ a
a,*
, A. Sˇantic´ a, V. Licˇina a, D.E. Day
b
Rud-er Bosˇkovic´ Institute, Department of Physics, Division of Materials Physics, 10000 Zagreb, Croatia b University of Missouri-Rolla, Materials Research Center, Rolla, MO 65401, USA Received 31 January 2005; received in revised form 3 August 2005
Abstract The electrical and dielectrical properties of Bi2O3–Fe2O3–P2O5 glasses were measured by impedance spectroscopy in the frequency range from 0.01 Hz to 4 MHz and over the temperature range from 303 to 473 K. It was shown that the dc conductivity strongly depends on the Fe2O3 content and Fe(II)/Fetot ratio. With increasing Fe(II) ion content from 17% to 34% in the bismuth-free 39.4Fe2O3– 59.6P2O5 and 9.8Bi2O3–31.7Fe2O3–58.5P2O5 glasses, the dc conductivity increases. On the other hand, the decrease in dc conductivity for the glasses with 18.9 mol% Bi2O3 is attributed to the decrease in Fe2O3 content from 31.7 to 23.5 mol%, which indicates that the conductivity for these glasses depends on Fe2O3 content. The conductivity for these glasses is independent of the Bi2O3 content and arises mainly from polaron hopping between Fe(II) and Fe(III) ions suggesting an electronic conduction. The evolution of the complex permittivity as a function of frequency and temperature was investigated. At low frequency the dispersion was investigated in terms of dielectric loss. The thermal activated relaxation mechanism dominates the observed relaxation behavior. The relationship between relaxation parameters and electrical conductivity indicates the electronic conductivity controlled by polaron hopping between iron ions. The Raman spectra show that the addition of up to 18.9 mol% of Bi2O3 does not produce any changes in the glass structure which consists predominantly of pyrophosphate units. 2005 Elsevier B.V. All rights reserved.
1. Introduction Binary iron phosphate glasses are electronically conducting glasses with polaronic conduction mechanism [1–3]. In these glasses, iron ions exist in two valence states and the electrical conduction occurs by hopping of polaron from Fe(II) to Fe(III). In hopping process, the electron disorders its surroundings, by moving its neighboring atoms from their equilibrium positions causing structural defects in the glass network named small polarons. Hence, small polarons are charge carriers trapped by self-induced lattice distortions which transport consists of phonon-assisted hopping.
*
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 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.08.011
It was also reported that the glasses containing bismuth oxide exhibit the high refractive index, IR transmission and non-linear optical susceptibilities [4,5]. The large polarizability of bismuth in oxide glasses makes them suitable for optical devices and environmental guidelines. However, bismuth oxide is not a traditional glass former and cannot form glass by itself. In the presence of strong polarizing cations, Bi(III) ions can reduce its coordination number from six to three and the glass networks may consist of both [BiO6] highly distorted octahedral and [BiO3] pyramidal units [6,7]. Because of its dual role, as modifier with [BiO6] octahedral and as glass former with [BiO3] pyramidal units, bismuth ions may influence the electrical properties of glasses. It was found [8] that dielectric properties of ZnF2–Bi2O3–TeO2 glasses strongly depend on Bi2O3 content and structural coordination of Bi(III) ions. When Bi2O3 is present in smaller concentration, up to 12 mol%, bismuth mainly occupies the octahedral positions
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3236
and acts as a modifier, whereas, for higher concentrations takes the network forming positions with BiO3 pyramidal units. Consequently, the decrease in the dielectric constant and tan d beyond 12 mol% of Bi2O3 suggests a decrease in the distortion of glass network due to the network forming positions of bismuth ions. Gosh et al. studied the electrical properties of binary bismuth glasses containing different transition metal oxides such as CuO [9,10], V2O5 [11,12] and Fe2O3 [13]. Their results indicate that the electrical conduction in these glasses occurs by the small polaron hopping between transition metal ions in different valence states. It was found that the dielectric properties of these glasses are best explained by dipolar relaxation model with distribution of relaxation times. High value of the dielectric constant observed in these glasses has been attributed to the influence of the high polarizability of the Bi(III) ions to the relaxing dipoles which are formed between two valence states of transition metal ions. Although, much work has been done on the electrical properties of unconventional binary bismuth glasses, not much information is available on influence of Bi2O3 on structure and electrical properties of well-characterized iron phosphate glasses [14,15]. The purpose of the present paper is to study conduction mechanisms of the different glass composition and the effect of unconventional network former Bi2O3 on the electrical properties of bismuth iron phosphate glasses over a wide temperature and frequency range. The electrical properties of iron phosphate glasses containing various amount of Bi2O3 have been investigated by impedance spectroscopy. It was known from the previous results [16] that the iron oxide forms stable glass with Bi2O3. Therefore, it was of interest to investigate the effect of replacing Fe2O3 with Bi2O3 on glass structure. Raman spectroscopy was used to study the modes and the nature of the bonds between metal and its surrounding oxygen atoms within glass network. 2. Experimental procedure The Bi2O3–Fe2O3–P2O5 glasses were prepared from appropriate mixtures of reagent grade NH4H2PO4, Fe2O3, Bi2O3 and melted between 1273 K and 1373 K for
2 h in air in high purity alumina crucibles. The melt was quenched in air by pouring it into a steel mould to form rectangular bars (1 · 1 · 5 cm3), which were annealed for 2 h at 723 K. Chemical analysis was performed by Scanning Electron Microscopy, SEM, equipped with EDS detector (Vega TS 5136 Tescan) to find exact composition of the glasses. The disc of each glass was analyzed at six different positions and the mean composition is given in Table 1. 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 cm3. The Raman spectra of glasses 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-glancing angle. The recorded Raman spectra were deconvoluted using a symmetric Gaussian function. The structural units in phosphate network were classified according to their connectivities by Qn notation, where n represents the number of bridging oxygen atoms per PO4 tetrahedron (n = 0–3). 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 s1. The Mo¨ssbauer absorbers of approximate thickness 140 mg cm2 were prepared using 125 lm powders. The Mo¨ssbauer spectra were fitted with broadened paramagnetic Lorentzian doublets. 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. Electrical properties were obtained by measuring complex impedance using an impedance analyzer over a wide frequency range from 0.01 Hz to 4 MHz and in temperature range from 303 to 473 K. The temperature was controlled to ±3 K. The complex impedance data, Z*(x), were plotted in the Nyquist representation form, a typical
Table 1 Composition and selected properties of the bismuth iron phosphate glasses Sample code
F40 B3 B10 B20 a b
Glass composition determined by EDS (mol%)
Molar ratio
Bi2O3
Fe2O3
P2O5
O/Pa
(Fe + Bi)/Pa
0 3.3 9.8 18.9
39.4 38.5 31.7 23.5
59.6 58.2 58.5 57.6
3.49 3.58 3.56 3.60
– 0.72 0.71 0.74
Molar ratios of O/P and (Fe + Bi)/P were calculated from the glass compositions. Fe(II)/Fetot ratio was calculated from the Mo¨ssbauer results.
Fe(II)/Fetotb (±0.03%)
D (g cm3) (±0.02 g cm3)
˚) RFe–Fe (A (±0.5%)
0.17 0.33 0.32 0.34
3.02 3.30 3.76 4.31
2.99 2.92 2.98 3.15
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
complex plane plot represented by imaginary part Z00 (x) vs. real part Z 0 (x) for each temperature. A point of this curve represents a given measurements of Z 0 (x) and Z00 (x), at a specific angular frequency x (x = 2pf). The experimental impedance spectra were fitted using complex non-linear least square (CNLLSQ) fitting procedure. This procedure works in an environment for equivalent electrical circuits and it is based on the fitting of experimental diagram. The average distance between the iron ions, RFeFe, was calculated using relation: RFe–Fe ¼ ð4pN =3Þ1=3 ;
ð1Þ
where N is the concentration of total iron (both Fe(II) and Fe(III) ions) per unit volume, calculated from the glass composition and measured density. If the iron ions are not uniformly distributed, the actual distance may be different from the R value calculated from Eq. (1). The estimated errors in the density and average distance between the iron ions were estimated as ±0.5%. 3. Results 3.1. Raman spectra The Raman spectra for the Bi2O3 free (F40) and Bi2O3– Fe2O3–P2O5 glasses (B3, B10, B20) are shown in Fig. 1. The band assignments for the bismuth-free, F40, glass are characteristic of pyrophosphate Q1 structure with most prominent bands at 1074 and 748 cm1 related to the symmetric stretching mode of non-bridging (PO2)sym and bridging (P–O–P)sym oxygen atoms, respectively [14,15]. Some barely detectable bands at 1215 and 620 cm1 are attributed to the non-bridging, (PO2)sym, and bridging oxygen atoms (P–O–P)sym in Q2 phosphate tetrahedra. The shoulder at 940 cm1 suggests the presence of Q0 phosphate units. Low frequency bands at 400 cm1 are as-
252 164
Relative intensity
1074 558 435 620
940 1215
748
B10 B3 F40 1400
signed to the bending mode of the phosphate polyhedra with iron as a modifier. This spectrum suggests that the binary iron phosphate glass with 39.4 mol% of Fe2O3 consists predominantly of pyrophosphate (P2O7)4 groups along with a small amount of metaphosphate chains of (PO3) groups and isolated orthophosphate (PO4)3 groups. The Raman spectra of the Bi2O3–Fe2O3–P2O5 glasses (B3, B10 and B20) differ slightly from the spectrum of the bismuth-free glass (F40). The Raman bands due to the pyrophosphate groups are still dominant, along with some traces of metaphosphate and orthophosphate groups. However, some new bands appear in the lower wave number region (<600 cm1) of Raman spectra. With increasing Bi2O3 content up to 18.9 mol%, the bands at about 164, 252, 435 and 558 cm1 grow in intensity. This spectral region in the Raman spectra can be attributed to the bismuth unit vibrations [7,17]. It was assumed that in these glasses Bi2O3 exists mostly as [BiO6] units, where the Bi atoms are located in octahedral sites. The two strongest bands at 164 and 252 cm1 are related to the vibrations of heavy metal cations, which clearly evidences the presence of Bi(III) ions in the glass network. Some barely detectable bands at 435 and 558 cm1 are attributed to the stretching mode of the bridging oxygen atoms, (Bi–O–Bi), in the highly distorted [BiO6] octahedral units. The band at about 620 cm1 is related to both the stretching mode of nonbridging oxygen atoms, (Bi–O) in [BiO6] units as well as to the non-bridging oxygen atoms in metaphosphate chains. It is well known that the phosphate structure is strongly influenced by the overall O/P ratio [15]. The average phosphate chain length becomes progressively shorter as the O/ P ratio increases. With increasing O/P ratio from 3.0 to 3.5 the phosphate structure changes from methaphosphate chains, Q2 to pyrophosphate, Q1, based units. Generally, for glasses with O/P ratio >3.5 the network structure contains Q1 pyrophosphate and Q0 isolated orthophosphate units. For the glasses in the present study the O/P ratio was maintained constant at 3.5 and the structure is dominated by pyrophosphate, Q1 units. However, the addition of Bi2O3 to iron phosphate glasses causes an increase in the intensity of the Raman bands attributed to the bismuth units in the glass network. 3.2. Electrical conductivity
B20
1600
3237
1200
1000
800
600
400
200
0
-1
Raman shift (cm ) Fig. 1. The Raman spectra of the bismuth iron phosphate glasses.
The conductivity spectroscopy is a well established method for characterizing the hopping dynamics of polaron. For the analysis and interpretation of the obtained data, the electrical conductivity can be described by means of equivalent circuit or frequency-dependent conductivity spectra. Fig. 2 shows the impedance spectra at 363, 393 and 423 K and their corresponding electrical equivalent circuits for the B20 glass. The impedance spectrum at each temper-
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3238
120
B20
ments (CPEs) rather than ordinary capacitors in equivalent circuits. The CPE is an empirical impedance function of the type:
R
100
a
80 Z"/MΩ
Z CPE ¼ AðjxÞ ;
CPE
60
363 K
40 20
393 K 423 K
0 0
20
40
60 Z'/MΩ
80
100
120
Fig. 2. Complex impedance plots for the B20 glass at various temperatures and corresponding equivalent electrical circuit.
ature consists of single well-shaped semicircle related to bulk effects, which is characteristic for electronic conductors [18]. No residual semicircle at low frequencies attributed to contact or electrode effects has been noticed, probably due to the fact that samples were finely polished and electroded by sputtering. Similar results have been obtained for all glasses in the present study. The impedance spectra from Fig. 2 can be interpreted by means of equivalent circuit where each impedance semicircle can be represented by resistor, R, and capacitor, C in parallel (parallel RC element) [19]. 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, R, of the sample. However, experimental data show depressed semicircle with the center below the real axis, which is the reason for using constant-phase ele-
ð2Þ
where A and a are constants. There are two reasons for such non-ideal behavior: heterogeneous property of system and presence of a distribution in relaxation times within the bulk response and distortion by other relaxation such as electrode polarization effect. Experimental impedance data were fitted using complex non-linear least square procedure and an excellent agreement between experimental (scatter) and theoretical curve (line) was obtained. Equivalent circuit modeling gives three parameters at each temperature: bulk resistance, R, and two parameters for CPEs, A and a. Fitting results for all glasses at two temperatures are listed in Table 2. The CPE parameters, A and a, are constant over the temperature range. The values of bulk resistance, R, for the single semicircle together with electrode dimensions, (S is the electrode area and d is the sample thickness) were used to determine the dc conductivity, rdc of the glasses, rdc = (d/S)/R, see Table 3. It should be noted that the complex impedance plot in the wide frequency range was single semicircle for all glasses indicating a single conductivity process for all glasses in the present study. Fig. 3 shows the frequency dependence of the real part of the conductivity, r 0 (x), for the B20 glass at different temperature. The spectra display the typical shape found for electronically conducting glasses [20]. At low frequency the conductivity is independent of frequency and identical to dc conductivity, rdc, of glass, whereas, at higher frequency exhibits dispersion in power law fashion. The values of rdc obtained from low frequency plateau are equal to rdc calculated from equivalent circuit modeling, Table
Table 2 Fitting parameters of impedance spectra at 303 and 423 K for bismuth iron phosphate glasses Sample code
R (X) at 303 K (±0.5%)
R (X) at 423 K (±0.5%)
A at 303 K (±0.5%)
A at 423 K (±0.5%)
a at 303 K (±0.5%)
a at 423 K (±0.5%)
F40 B3 B10 B20
1.00 · 1010 5.19 · 108 4.83 · 108 2.65 · 109
1.95 · 107 2.08 · 106 2.00 · 106 9.45 · 106
7.62 · 1012 1.09 · 1011 1.53 · 1011 1.53 · 1011
2.34 · 1011 3.09 · 1011 3.73 · 1011 3.22 · 1011
0.84 0.85 0.85 0.85
0.83 0.83 0.85 0.86
The equivalent circuit shown in Fig. 2 was used for numerical fitting.
Table 3 DC conductivity, rdc, and activation energies, Edc, EZ 00 , EM 00 for the bismuth iron phosphate glasses Sample code
rdc (X m)1 at 303 K obtained from conductivity plateau (±0.5%)
rdc (X m)1 at 303 K obtained from equivalent circuit modeling (±0.5%)
Edc (kJ mol1) (±0.5%)
EZ 00 (kJ mol1) (±0.5%)
EM 00 (kJ mol1) (±0.5%)
F40 B3 B10 B20
3.49 · 109 8.28 · 108 6.75 · 108 9.85 · 109
3.10 · 109 8.40 · 108 6.78 · 108 9.73 · 109
57.5 50.7 50.4 51.9
57.5 50.7 50.5 52.0
57.5 50.7 50.6 51.9
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
-3
B20
473 K -5
log σdc (Ωm)-1
log σ (ω) (Ωm)-1
-4 423 K 393 K 363 K 333 K
-6 -7
-5 -6 -7 -8
303 K
-8
-9
-9 -1
0
1
2 3 log f (Hz)
4
5
6
7
2.4
2.8 1000/T
Fig. 3. Frequency dependence of the conductivity, r(x), at temperatures shown for the B20 glass.
3. The dc conductivity of these glasses exhibits an Arrhenius-type temperature dependence. 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 [2]: mph e2 Cð1 CÞ expð2aRÞ expðW =kT Þ; kTR
2.0
ð3Þ
3.6
to those of Edc calculated from Arrhenius-type dependence of the dc conductivity. The dependence of dc conductivity, rdc, at 303 K and activation energy for dc conductivity, Edc, upon the Bi2O3 content for all glasses is shown in Fig. 5. Bismuthfree glass has the lowest value of rdc, 3.10 · 109 (X m)1. For glasses containing 3.3 and 9.8 mol% Bi2O3, the rdc increases for one order of magnitude and has almost equal value for both glasses, 8.40 · 108 and 6.78 · 108 (X m)1, respectively. However, with increasing Bi2O3 up to 18.9 mol%, the rdc decreases to 9.73 · 109 (X m)1. Similarly, Edc decreases significantly to the constant value for the glasses containing 3.3 and 9.8 mol%
-6.5
-6.0 -6.5
0.36
Fe(II)/Fetot
-7.0
0.32
-7.5
0.28 0.24
-8.0
σdc at 303 K
-8.5
0.20
58
0.16
-9.0 20
25 30 35 mol% Fe2O3
40
56
σdc at 303 K
-7.5
54 52
-8.0
Edc (kJmol-1)
-7.0
Fe(II)/Fetot
where mph is the phonon frequency, C is the fraction of reduced transition metal ion, (Fe(II)/Fetot), R is the average spacing between transition metal ions, 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. (3) describes a non-adiabatic regime of small polaron hopping. In MottÕs 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 [2,21]. In this temperature region the jump of an electron (polaron) occurs between nearest neighbors with activation energy 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. (3) are constant, the dependence of the dc conductivity on temperature can be compared with the Arrhenius equation rdc = r0 exp(Edc/kT) where rdc is the dc conductivity, r0 is the pre-exponent, Edc is the activation energy for the dc conductivity, k is the Boltzmann constant and T is the temperature (K). According to this equation, activation energy for dc conductivity, Edc, can be calculated from the slope of log rdc vs. 1/T curves as shown in Fig. 4. The values for rdc at 303 K and Edc for each glass are given in Table 3. It should be noted that the calculated values are identical
3.2
(K)-1
Fig. 4. Temperature dependence of the dc conductivity, rdc, for the bismuth iron phosphate glasses. See Table 3 for the dc activation energy, Edc, calculated from the slope log rdc vs. 1/T.
log σdc (Ωm)-1
-2
r¼
F40 B3 B10 B20
-4
-3
log σdc (Ωm)-1
-2
3239
50
-8.5
Edc
-9.0
48 0
5
10 15 mol% Bi2O3
20
Fig. 5. The dependence of the dc conductivity, rdc, at 303 K and activation energy for dc conductivity, Edc, upon the Bi2O3 content in the bismuth iron phosphate glasses. Inset: dc conductivity, rdc, at 303 K and Fe(II)/Fetot ratio as a function of Fe2O3 content. Lines are drawn connecting data symbols of each kind.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
Bi2O3, whereas, slightly increases for glass containing 18.9 mol%. Going further in the interpretation of these results, the dependences of the rdc and Fe(II)/Fetot ratio upon Fe2O3 content is shown in the inset in Fig. 5. With increasing Fe2O3 content from 23.5 to 38.5 mol% the rdc increases, whereas for glass with 39.4 mol% Fe2O3 the rdc unexpectedly decreases. An other factor that affects the dc conductivity is the concentration of Fe(II) ions determined from the Mo¨ssbauer spectra for each glass. 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. So, the Fe(II)/Fetot ratio is important for the electrical conductivity of these glasses. Since the ratio Fe(II)/Fetot has the lowest value, 0.17, consequently the concentration of polarons is the smallest in bismuth-free glass. Comparing relative amount of Fe(II) ions in bismuthfree glass to those with bismuth iron phosphate glasses, an increase in Fe(II) ion concentration from 17% to 34% is observed. The increase in Fe(II) ion concentration from 17% to 33% for F40 and B3 glass, respectively, results in an increase in dc conductivity and decrease in activation energy. On the other hand, the Fe(II) ion concentration for B3, B10 and B20 glasses remains almost constant at 33%. Since the dc conductivity is associated with the migration of polaron between Fe(II) and Fe(III) ions with the distribution in hopping distances it seems that the decrease in Fe2O3 content from 39.4 to 23.5 mol% increases the distance between Fe ions, RFeFe, see Table 1. Such an increase in RFeFe diminishes the probability of electron hopping and reduces the possibility for formation of polarons. Clearly, a decrease in the chance for electron hopping from Fe(II) to Fe(III) sites decreases the concentration of polarons and consequently decreases dc conductivity for one order of magnitude in B20 glass. 3.3. Dielectric properties The complex permittivity e*(x) = 1/(jxC0Z*) can be expressed as a complex number: e ðxÞ ¼ e0 ðxÞ je00 ðxÞ;
ð4Þ
where e 0 (x) and e00 (x) are the real and imaginary parts of the complex permittivity.
8
B20
303 K 333 K 363 K 393 K 423 K 473 K
Electrode polarization
7 6 log ε'(ω)
3240
5 4 ε'∞(ω)
3 2 1 -2
-1
0
1
2
3
4
5
6
log f (Hz) Fig. 6. Frequency dependence of the real part of electrical permittivity, e 0 (x), for the B20 glass at various temperatures. The increase in e 0 (x) at low frequencies is caused by electrode polarization.
The frequency dependence of the real part of the complex permittivity, e 0 (x), for B20 glass is shown in Fig. 6. The dielectric permittivity, e 0 (x), measured at 333 K and 1 kHz for the present glasses is given in Table 4. At higher frequency, e 0 (x) approaches a constant value, 0 e1 ðxÞ, which probably results from rapid polarization processes occurring in the glasses [21]. With decreasing frequency, e 0 (x) increases due to electrode polarization arising usually from space charge accumulation at the glass-electrode interface. The increase in e 0 (x) occurs at higher temperatures and is more pronounced at lower frequency. The factor, which means the phase difference due to the loss of energy within the sample at a particular frequency is the loss factor tangent, tan d = e00 /e 0 . The frequency dependence of tan d at different temperatures for B20 glass is shown in Fig. 7(a). The maximum in the tan d peak shifts to higher frequency with increasing temperature. It should be noted that the dielectric loss peak is positioned at low frequency region, where the conductivity is dominated by dc conductivity. Generally, the dielectric losses at high frequency are much lower than those occurring at low frequencies. This kind of dependence of tan d on frequency is typically associated with losses by conduction. Consequently, the tan d for glasses with higher electrical conductivity, B3 and B10, is higher than for the F40 and B20 glasses.
Table 4 Real part of the dielectric permittivity, e 0 (x), relaxation time, sr, characteristic frequencies, foZ 00 and foM 00 , characteristic relaxation times, soZ 00 and soM 00 , non-adiabatic terms, 2aR, calculated from soZ 00 and soM 00 , for the bismuth iron phosphate glasses Sample code
e0 ðxÞ at 1 kHz, 333 K (±0.5%)
sr (s) at 333 K (±0.5%)
foZ 00 (Hz) (±0.5%)
foM 00 (Hz) (±0.5%)
soZ 00 (s) (±0.5%)
soM 00 (s) (±0.5%)
2aR from soZ 00 (±0.5%)
2aR from soM 00 (±0.5%)
F40 B3 B10 B20
11.4 18.9 20.4 18.0
4.19 · 103 2.25 · 104 3.20 · 104 2.39 · 103
2.35 · 1010 3.35 · 1010 2.36 · 1010 5.40 · 109
4.49 · 1010 6.99 · 1010 4.46 · 1010 9.57 · 109
6.79 · 1012 4.75 · 1012 6.75 · 1012 2.95 · 1011
3.55 · 1012 2.28 · 1012 3.57 · 1012 1.66 · 1011
4.22 3.86 4.21 5.69
3.57 3.13 3.58 5.11
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245 140
(a) B20
303 K 333 K 363 K 393 K 423 K 473 K
120 100
tan δ
80 60 40 20 0 -2
-1
0
1
0.03
2 3 log f (Hz)
4
5
6
303 K 333 K 363 K 393 K 423 K 473 K
f= 1/(2 πτσ)
(b) B20
7
M"
0.02
0.01
0.00 -2
-1
0
1
2 3 log f (Hz)
4
5
6
7
Fig. 7. Frequency dependence of the loss tangent, tan d (a) and the imaginary part of electrical modulus, M00 (b) for B20 glass at temperatures shown.
An alternative formalism particularly suitable to detect bulk effects and electrode polarization as an apparent conductivity relaxation times, sr [22,23], is the dielectric modulus model. The dielectric modulus is defined as M* = 1/e*, where e* is the complex permittivity,
0
0 2
00 2
00
0 2
3241
It is clear, that at any chosen temperature, sr for B3 and B10 glasses exhibits lower values, whereas sr for F40 and B20 glasses is almost one order of magnitude higher. The relaxation times, sr, for the glasses measured at 333 K, are shown in Table 4. The temperature dependence of the maximum M00 , indicates a linear relationship within the temperature and frequency range measured. The plot of the relaxation frequency, fM 00 ¼ 1=ð2psr Þ versus 1/T is represented by an Arrhenius equation, fM 00 ¼ foM 00 expðEM 00 =kT Þ, where EM 00 is the activation energy for the electrical relaxation. The activation energy, EM 00 , determined from the slope of the log fM 00 vs. 1/T for these glasses is given in Table 3 and shown in Fig. 9 for B20 glass. The activation energy values for the electrical modulus, EM 00 , and for dc conductivity, Edc, are almost identical, suggesting a hopping mechanism for all glasses [25]. The conduction mechanism for the present glasses is due to the polaron hopping based on electron carriers. However, it should be mentioned that the electrical behavior for polaronic mechanism with frequency and temperature is very similar to the ionic ones. Going further in the description of experimental data the variation of normalized parameters M 00 =M 00max and Z 00 =Z 00max as a function of logarithmic frequency measured at 363 K for B20 glass are shown in Fig. 8. Comparison with the impedance, electrical modulus and loss factor data allow the determination of bulk response in terms of localized, i.e. defect relaxation or non-localized conduction, i.e. ionic or electronic conductivity [22]. The Debye model is related to an ideal frequency response of localized relaxation. In reality the non-localized process is dominated at low frequencies. In the absence of interfacial effects, the non-localized conductivity is known as the dc conductivity. Thus, the high dielectric loss, tan d, is usually accompanied by rising e 0 (x) at low frequencies. Such behavior is found for the present glasses and showed in Fig. 6. However, it should be noted that the
1.0
Z" M"
00 2
M ¼ 1=e ¼ e =ððe Þ þ ðe Þ Þ þ je =ððe Þ þ ðe Þ Þ ð5Þ
Fig. 7(b) shows the imaginary part of the electrical modulus, M00 as a function of frequency for B20 glass at different temperatures. The maximum in the M00 peak shifts to higher frequency with increasing temperature. The frequency region below peak maximum M00 determines the range in which charge carriers are mobile on long distances. At frequency above peak maximum M00 , the carriers are confined to potential wells, being mobile on short distances. The M00 shows a maximum at a characteristic frequency, which is equal to the relaxation frequency fM 00 . The relaxation time, sr, can be extracted from the position of the M00 maximum where fM 00 ¼ 1=ð2psr Þ [24], as shown in Fig. 7(b).
0.8 Normalized peak
¼ M 0 þ jM 00 .
B20 363 K
0.6 0.4 0.2 0.0 -2
-1
0
1
2 3 log f (Hz)
4
5
6
7
Fig. 8. Frequency dependence of normalized peaks, Z 00 =Z 00max , and M 00 =M 00max for B20 glass at 363 K.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3242
localized relaxation process has much smaller values of e 0 (x) and sr than the non-localized one. Therefore, the position of the peak in the tan d/tan dmax curve is shifted to a lower frequency region in relation to the M 00 =M 00max and Z 00 =Z 00max peaks. According to Figs. 7(a) and 8, the three peaks that describe a priori the same relaxation process [21] are in accordance with the following order proposed elsewhere [22]. stan d > sZ P sM ; where s is the relaxation time and the subscripts represent the loss tangent, tan d, complex function Z*(x) and M*(x). Through these representations, it is possible to determine the type of dielectric response by inspection of the magnitude of overlapping between the peaks of both parameters Z00 (x) and M00 (x) [22]. The overlapping peak position of M 00 =M 00max and Z 00 =Z 00max curves is evidence of delocalized or long-range relaxation [22]. However, for the present glasses the M 00 =M 00max and Z 00 =Z 00max peaks do not completely overlap but are very close suggesting the components from both long-range and localized relaxation. This is supported by the complete complex impedance plot exhibited in Fig. 2. The plot of the relaxation frequency maximum, log fZ 00 , derived from Z00 (x) as a function of reciprocal temperature 1/T is shown in Fig. 9 for B20 glass. The data are represented by Arrhenius relation: fZ 00 ¼ foZ 00 expðEZ 00 =kT Þ, where EZ 00 is the activation energy for the conduction derived from Z00 (x) function and foZ 00 is the pre-exponential factor or characteristic relaxation frequency constant. Almost identical values for EZ 00 and EM 00 are observed on entire temperature range being equal to 52.0 and 51.9 kJ mol1, respectively. The slight difference observed between EZ 00 and EM 00 values suggests experimental features indicating that both
5 B20
4
EM" = 51.9 kJmol-1
fZ"
log f (Hz)
fM"
3
values are almost same. In addition, the magnitude of the activation energy suggests that the carrier transport is due to the hopping conduction. According to the Fig. 9 the values of the intrinsic relaxation times show that ones exhibit a short time. The characteristic relaxation frequencies calculated from the plot log f vs. 1/T for B20 glass are equal to foZ 00 ¼ 5:40 109 Hz and foM 00 ¼ 9:57 109 Hz being associated to the parameters soZ 00 ¼ 2:95 1011 s and soM 00 ¼ 1:66 1011 s, respectively. These values belong to superior limit of one to unequivocal assignment of polarization mechanism as being a lattice phenomenon, a typical phenomenon identified at around 1012 Hz. The parameters derived from Fig. 9 are addressed to the electrical behavior involving electronic process. The values of characteristic relaxation times can be correlated to the presence of space charge accumulated probably at the glass-electrode interface. The characteristic relaxation frequencies foZ 00 and foM 00 , along with the characteristic relaxation times soZ 00 and soM 00 , for all glasses investigated are given in Table 4. 4. Discussion The Raman bands due to the heavy metal oxides such as Bi2O3, can be classified into four regions: (1) low wave number modes (<100 cm1), (2) heavy metal ion vibrations (70–160 cm1), (3) bridged anion modes (300–600 cm1) and non-bridging anion modes at higher wave numbers [7,17]. The Raman spectra for the present glasses show bands associated to the least three regions suggesting that Bi2O3 takes part in the formation of the glass network. Raman spectrum for the bismuth-free glass consists of predominantly pyrophosphate, Q1, structure with traces of metaphosphate, Q2, and orthophosphate, Q0 units. With increasing Bi2O3 content from 3.3 to 18.9 mol%, there are no changes in the pyrophosphate glass network since the O/P ratio was maintained constant at 3.5, Table 1. However, the addition of Bi2O3 to iron phosphate glasses causes an increase in the intensity of the Raman bands attributed to the highly distorted [BiO]6 octahedral units in glass structure. The strong bands appeared at lower frequencies at 164 and 252 cm1, Fig. 1, are due to the vibrations of Bi(III) ions incorporated into glass network, which suggests glass forming character of bismuth ions. 4.1. Electrical properties
2 EZ" = 52.0 kJmol-1
1 0 2.0
2.4
2.8 1000/T
3.2
3.6
(K)-1
Fig. 9. Temperature dependence of the relaxation frequencies, fM 00 and fZ 00 , for the B20 glass. See Table 3 for the activation energies, EZ 00 , EM 00 , calculated from the slope log f vs. 1/T.
The increase initially and than decrease in the dc conductivity, rdc, and decrease in activation energy, Edc, for these glasses is related to the decrease in the Fe2O3 content from 39.4 to 23.5 mol% as Bi2O3 content increases from 0 to 18.9 mol%. Such behavior suggests that the conductivity depends strongly on Fe2O3 content. It has been previously reported [9] that in iron phosphate glasses the rdc is electronic and depends strongly upon distance between iron ions, RFeFe. The reduction in Fe2O3 content increases distances between iron ions. So, assuming that the conductiv-
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
ity is due to the electron hopping from Fe(II) to Fe(III) then with increasing RFeFe from 2.92 for B3 glass to ˚ for B20 glass it is reasonable to expect a decrease 3.15 A in the dc conductivity. The dc conductivity, also depends on the concentration of Fe(II) ions in these glasses. The ratio Fe(II)/Fetot is determined from the Mo¨ssbauer spectra and is listed in Table 1 for each glass in the present study. The increase in Fe(II) ion concentration from 17% to 33% for F40 to B3 glass, respectively, results in an increase in dc conductivity and decrease in activation energy for these glasses. However, for B3, B10 and B20 glasses, Fe(II) ion concentration remains almost constant at 33%. Assuming that the dc conductivity is due to migration of polaron between Fe(II) and Fe(III) ions with the distribution in hopping distances, it seems that the decrease in Fe2O3 content and increase in distance RFeFe reduces the possibility of polaron formation. Consequently, a decrease in the concentration of polarons in B20 glass results in a decreased dc conductivity. These results agree with the studies [1,2,26] where ratio Fe(II)/Fetot, Fe2O3 content and distance between iron ions were found the important factors for electrical conductivity of these glasses. 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 where 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 [26]. Therefore, the reorientation of such dipoles gives rise to characteristic frequency dependent features of the complex permittivity, e*(x) = e 0 (x) je00 (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. In order to mobilize the localized electron, in polaron conductive glasses, the aid of lattice oscillation is required. In these circumstances electrons are considered not to move by themselves but by hopping motion activated by lattice oscillation. Thus, in temperature region measured at T > H/2, where H is the Debye temperature, the conduction is considered as phonon-assisted hopping of small polaron between localized states [2,21]. It should be mentioned that the electron, which creates a polaron is the same electron that later separates from its neighborhood by hopping motion producing conduction at lower frequency. Therefore, in electron conducting glasses polarization and conduction are integrated into a single continuous process [21].
3243
For all glasses investigated, the increase in e 0 (x) and e (x) with decreasing frequency, is attributed to the conductivity r(x), which is directly related to an increase in mobility of localized charge carriers. The B3 and B10 glasses show highest dc conductivity, which indicates the highest polaron concentration. This improves easier movement of space charge carriers responsible for electrode polarization at low frequency. At the same time, at lower frequency, an increase in the magnitude of e 0 (x) is caused by dipolar effects. 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 [27]. Similarly, the observed dielectric loss, tan d, is due to two main contributions. The first is related to the thermal activated relaxation of freely rotating dipoles in which the thermal energy is only type of excitation. A second part at higher temperature, which increases with temperature is due to electrical conduction with hopping motion from Fe(II) to Fe(III). The frequency dependence of tan d at different temperature exhibited in Fig. 7(a) for B20 glass shows an increase of the loss magnitude at low frequency whereas at high frequency the loss magnitudes are much lower. Taking into account that the tan d represents the conduction loss, the peak position can give further insight on the conduction mechanism. The increase in dielectric loss, tan d, positioned at very low frequency for the present glasses, is related to the increase in e 0 (x) at low frequency, Figs. 6 and 7(a). The conductivity relaxation model, where a dielectric modulus is defined by M*(x) = 1/e*(x), can provide information about the relaxation mechanism [24]. According to the earlier discussion two apparent relaxation regions appeared, the low frequency region, being associated with the hopping conduction and higher region being associated with the relaxation polarization process. In the case that the data are presented in electrical modulus representation the effect of electrode polarization, observed for all glasses measured, can be avoided since the electrical modulus peaks, M00 , are shifted toward higher frequency. The relaxation times, sr, as calculated from the frequency at the M00 maximum, shown in Fig. 7(b) and listed in Table 4 are thermally activated with the following respective activation energy EM 00 . From Table 4 it is clear that the relaxation times, sr, for the B3 and B10 glasses are much smaller due to a smaller EM 00 and Edc and consequently, a higher conductivity, r(x). For the B20 and F40 glasses the relaxation times, sr, become higher with decreasing Fe2O3 content and Fe(II) concentration, respectively, which causes lower conductivity in these glasses. It was previously mentioned that by combining imaginary modulus with imaginary impedance it is possible to distinguish the localized (relaxation defects) from nonlocalized conduction (electronic or ionic conductivity) pro00
3244
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
cesses within the bulk of glasses. For all glasses investigated a very close maximum position of M 00 =M 00max and Z 00 =Z 00max peaks, represented for B20 glass in Fig. 8, suggests both localized and long-range conductivity. In addition, such a overlapping illustrates that the dynamic process occurring at different frequencies exhibits the same thermal activation energy and existence of a single carriers. Therefore, both peaks, M 00 =M 00max and Z 00 =Z 00max , describe the same relaxation process. As already mentioned, the temperature dependence of the relaxation times for these glasses is a process thermally activated following Arrhenius law. The activation energies, EM 00 and EZ 00 , observed on the temperature range measured for B20 glass are equals to 51.9 and 52.0 kJ mol1, respectively. The characteristic relaxation frequencies for B20 glass, foZ 00 ¼ 5:40 109 Hz and foM 00 ¼ 9:57 109 Hz, are related to the parameters soZ 00 ¼ 2:95 1011 s and soM 00 ¼ 1:66 1011 s. It can be noticed that the characteristic relaxation frequencies for all glasses in the present study appear to be much lower than the expected value of the optical phonon frequency (1013 Hz). Such deviation could be explained by non-adiabatic approximation of phonon assisted quantum mechanical tunneling. There are two different conductivity mechanisms for relaxation process: temperature dependent classical activation of carrier over a potential barrier spreading two sites with activation energy, W (s = s0 exp (W/kT)) and temperature independent quantum mechanical tunneling of a carrier through the potential barrier between the sites separated by a distance R (s0 = sph exp(2aR)). As pointed out before, activation energies for relaxation process, EM 00 and EZ 00 , in Table 2, are in excellent agreement with activation energy for dc conductivity, Edc. According to Mott [2,3], if the main conductivity mechanism is in adiabatic regime than the tunneling term exp(2aR) is negligible (exp(2aR) 1). Consequently, characteristic relaxation time, s0, is equal to optical phonon relaxation time, sph. On the contrary, in a case of non-adiabatic regime electronic frequency is much higher than the average phonon frequency and tunneling term cannot be neglected. Values for characteristic relaxation frequencies, soZ 00 and soM 00 , given in Table 4 indicate that although thermal activated relaxation mechanism dominates the observed relaxation behavior, the non-adiabatic term should not be ignored on studying the relaxation phenomena. Furthermore, non-adiabatic contributions, 2aR, for all glasses under study are given in Table 4. It should be noted that the values for non-adiabatic contribution could be obtained form dc conductivity measurements and are consistent with those for similar glasses [28]. For the F40, B3 and B10 glasses this contribution is almost constant at 4, but for B20 glass is slightly higher, 5.69. This result suggests that the probability of quantum tunneling is smallest for B20 glass. The reason for that could be the smallest concentration of polarons in this glass due to the smallest Fe2O3 content. Thus, the relationship between relaxation parameters and electrical conductivity indicates electronic conductivity
controlled by polaron hopping from Fe(II) to Fe(III) ions in these glasses. 5. Conclusion The changes in the electrical properties of Bi2O3–Fe2O3– P2O5 glasses, show that electrical conductivity is independent of Bi2O3 content and that main conduction mechanism is small polaron hopping between Fe(II) and Fe(III) sites. Therefore, electrical conductivity in these glasses is strongly controlled with polaron concentrations which depend upon Fe2O3 content and Fe(II)/Fetot ratio. The dielectric properties, such as e 0 (x) and e00 (x) and their variations with frequency and temperature, indicate a dispersion at frequency lower than 1 kHz, due to the increase in electrode polarization. The relaxation observed on the M00 (x) or Z00 (x) functions is correlated to both localized and long-range conduction. The overlapping of the M00 (x) or Z00 (x) peaks suggests the same activation energy and existence of a single carrier that are related to the same relaxation processes. The dielectric loss, tan d, for these glasses is due to electrical conduction with hopping motion between Fe(II) and Fe(III) ions. The Raman spectra indicate that all glasses consist of predominantly pyrophosphate units. With addition of Bi2O3 content up to 18.9 mol% an increase in the Raman bands attributed to the distorted [BiO]6 octahedral units in glass structure suggests that the Bi(III) ions are incorporated in the glass network. References [1] L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91. [2] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [3] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [4] J.C. Lapp, W.H. Dumbaugh, M.L. Powley, Riv. Staz. Sper. Vetro. 1 (1989) 91. [5] D.W. Hall, M.A. Newhause, N.F. Borrelli, W.H. Dumbaugh, L.A. Weidman, Phys. Lett. 54 (1989) 1293. [6] S. Hazra, S. Mandal, A. Ghosh, Phys. Rev. B 56 (1997) 13. [7] L. Baia, R. Stefan, W. Kiefer, J. Popp, S. Simon, J. Non-Cryst. Solids 303 (2002) 379. [8] D.K. Durga, N. Veeraiah, Bull. Mater. Sci. 24 (2001) 421. [9] S. Hazra, A. Ghosh, J. Phys. Condens. Matter 9 (1997) 3981. [10] S. Hazra, A. Ghosh, J. Appl. Phys. 84 (1998) 987. [11] A. Ghosh, J. Appl. Phys. 65 (1989) 227. [12] A. Ghosh, J. Appl. Phys. 65 (1988) 2652. [13] A. Ghosh, J. Appl. Phys. 66 (1989) 2425. [14] A. Mogusˇ-Milankovic´, B. Pivac, K. Furic´, D.E. Day, Phys. Chem. Glasses 38 (1997) 74. [15] A. Mogusˇ-Milankovic´, M. Rajic´, A. Drasˇner, R. Trojko, D.E. Day, Phys. Chem. Glasses 39 (1998) 70. [16] B.K. Chaudhuri, K. Chaudhuri, K.K. Som, J. Phys. Chem. Solids 50 (1989) 1137. [17] L. Baia, T. Iliescu, S. Simon, W. Kiefer, J. Molecul. Struct. 599 (2001) 9. [18] J.E. Gabarczyk, M. Wasinciouk, P. Machowski, W. Jakubowski, Solid State Ionics 119 (1999) 9. [19] J.R. Macdonald (Ed.), Impedance Spectroscopy, Wiley, New York, 1987. [20] A. Mogusˇ-Milankovic´, A. Sˇantic´, M. Karabulut, D.E. Day, J. NonCryst. Solids 330 (2003) 128.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245 [21] D.L. Sidebottom, B. Roling, K. Funke, Phys. Rev. B 63 (2000) 024301-1. [22] R. Gerhardt, J. Phys. Chem. Solids 55 (1994) 1491. [23] F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynhan, J. Phys. Chem. 78 (1974) 639. [24] P.B. Macedo, C.T. Moynhan, R. Bose, Phys. Chem. Glasses 13 (1972) 171.
3245
[25] J.M. Re´au, X.Y. Jun, J. Sevegas, Ch.Z. Deit, M. Polain, Solid State Ionics 95 (1997) 191. [26] A. Mogusˇ-Milankovic´, D.E. Day, J. Non-Cryst. Solids 162 (1993) 275. [27] S.R. Elliot, Adv. Phys. 36 (1987) 135. [28] L. Murawski, R.J. Barczyn´ski, D. Samatowicz, Solid State Ionics 157 (2003) 293.
Dielectric behavior and impedance spectroscopy of bismuth iron phosphate glasses A. Mogusˇ-Milankovic´ a
a,*
, A. Sˇantic´ a, V. Licˇina a, D.E. Day
b
Rud-er Bosˇkovic´ Institute, Department of Physics, Division of Materials Physics, 10000 Zagreb, Croatia b University of Missouri-Rolla, Materials Research Center, Rolla, MO 65401, USA Received 31 January 2005; received in revised form 3 August 2005
Abstract The electrical and dielectrical properties of Bi2O3–Fe2O3–P2O5 glasses were measured by impedance spectroscopy in the frequency range from 0.01 Hz to 4 MHz and over the temperature range from 303 to 473 K. It was shown that the dc conductivity strongly depends on the Fe2O3 content and Fe(II)/Fetot ratio. With increasing Fe(II) ion content from 17% to 34% in the bismuth-free 39.4Fe2O3– 59.6P2O5 and 9.8Bi2O3–31.7Fe2O3–58.5P2O5 glasses, the dc conductivity increases. On the other hand, the decrease in dc conductivity for the glasses with 18.9 mol% Bi2O3 is attributed to the decrease in Fe2O3 content from 31.7 to 23.5 mol%, which indicates that the conductivity for these glasses depends on Fe2O3 content. The conductivity for these glasses is independent of the Bi2O3 content and arises mainly from polaron hopping between Fe(II) and Fe(III) ions suggesting an electronic conduction. The evolution of the complex permittivity as a function of frequency and temperature was investigated. At low frequency the dispersion was investigated in terms of dielectric loss. The thermal activated relaxation mechanism dominates the observed relaxation behavior. The relationship between relaxation parameters and electrical conductivity indicates the electronic conductivity controlled by polaron hopping between iron ions. The Raman spectra show that the addition of up to 18.9 mol% of Bi2O3 does not produce any changes in the glass structure which consists predominantly of pyrophosphate units. 2005 Elsevier B.V. All rights reserved.
1. Introduction Binary iron phosphate glasses are electronically conducting glasses with polaronic conduction mechanism [1–3]. In these glasses, iron ions exist in two valence states and the electrical conduction occurs by hopping of polaron from Fe(II) to Fe(III). In hopping process, the electron disorders its surroundings, by moving its neighboring atoms from their equilibrium positions causing structural defects in the glass network named small polarons. Hence, small polarons are charge carriers trapped by self-induced lattice distortions which transport consists of phonon-assisted hopping.
*
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 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.08.011
It was also reported that the glasses containing bismuth oxide exhibit the high refractive index, IR transmission and non-linear optical susceptibilities [4,5]. The large polarizability of bismuth in oxide glasses makes them suitable for optical devices and environmental guidelines. However, bismuth oxide is not a traditional glass former and cannot form glass by itself. In the presence of strong polarizing cations, Bi(III) ions can reduce its coordination number from six to three and the glass networks may consist of both [BiO6] highly distorted octahedral and [BiO3] pyramidal units [6,7]. Because of its dual role, as modifier with [BiO6] octahedral and as glass former with [BiO3] pyramidal units, bismuth ions may influence the electrical properties of glasses. It was found [8] that dielectric properties of ZnF2–Bi2O3–TeO2 glasses strongly depend on Bi2O3 content and structural coordination of Bi(III) ions. When Bi2O3 is present in smaller concentration, up to 12 mol%, bismuth mainly occupies the octahedral positions
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3236
and acts as a modifier, whereas, for higher concentrations takes the network forming positions with BiO3 pyramidal units. Consequently, the decrease in the dielectric constant and tan d beyond 12 mol% of Bi2O3 suggests a decrease in the distortion of glass network due to the network forming positions of bismuth ions. Gosh et al. studied the electrical properties of binary bismuth glasses containing different transition metal oxides such as CuO [9,10], V2O5 [11,12] and Fe2O3 [13]. Their results indicate that the electrical conduction in these glasses occurs by the small polaron hopping between transition metal ions in different valence states. It was found that the dielectric properties of these glasses are best explained by dipolar relaxation model with distribution of relaxation times. High value of the dielectric constant observed in these glasses has been attributed to the influence of the high polarizability of the Bi(III) ions to the relaxing dipoles which are formed between two valence states of transition metal ions. Although, much work has been done on the electrical properties of unconventional binary bismuth glasses, not much information is available on influence of Bi2O3 on structure and electrical properties of well-characterized iron phosphate glasses [14,15]. The purpose of the present paper is to study conduction mechanisms of the different glass composition and the effect of unconventional network former Bi2O3 on the electrical properties of bismuth iron phosphate glasses over a wide temperature and frequency range. The electrical properties of iron phosphate glasses containing various amount of Bi2O3 have been investigated by impedance spectroscopy. It was known from the previous results [16] that the iron oxide forms stable glass with Bi2O3. Therefore, it was of interest to investigate the effect of replacing Fe2O3 with Bi2O3 on glass structure. Raman spectroscopy was used to study the modes and the nature of the bonds between metal and its surrounding oxygen atoms within glass network. 2. Experimental procedure The Bi2O3–Fe2O3–P2O5 glasses were prepared from appropriate mixtures of reagent grade NH4H2PO4, Fe2O3, Bi2O3 and melted between 1273 K and 1373 K for
2 h in air in high purity alumina crucibles. The melt was quenched in air by pouring it into a steel mould to form rectangular bars (1 · 1 · 5 cm3), which were annealed for 2 h at 723 K. Chemical analysis was performed by Scanning Electron Microscopy, SEM, equipped with EDS detector (Vega TS 5136 Tescan) to find exact composition of the glasses. The disc of each glass was analyzed at six different positions and the mean composition is given in Table 1. 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 cm3. The Raman spectra of glasses 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-glancing angle. The recorded Raman spectra were deconvoluted using a symmetric Gaussian function. The structural units in phosphate network were classified according to their connectivities by Qn notation, where n represents the number of bridging oxygen atoms per PO4 tetrahedron (n = 0–3). 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 s1. The Mo¨ssbauer absorbers of approximate thickness 140 mg cm2 were prepared using 125 lm powders. The Mo¨ssbauer spectra were fitted with broadened paramagnetic Lorentzian doublets. 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. Electrical properties were obtained by measuring complex impedance using an impedance analyzer over a wide frequency range from 0.01 Hz to 4 MHz and in temperature range from 303 to 473 K. The temperature was controlled to ±3 K. The complex impedance data, Z*(x), were plotted in the Nyquist representation form, a typical
Table 1 Composition and selected properties of the bismuth iron phosphate glasses Sample code
F40 B3 B10 B20 a b
Glass composition determined by EDS (mol%)
Molar ratio
Bi2O3
Fe2O3
P2O5
O/Pa
(Fe + Bi)/Pa
0 3.3 9.8 18.9
39.4 38.5 31.7 23.5
59.6 58.2 58.5 57.6
3.49 3.58 3.56 3.60
– 0.72 0.71 0.74
Molar ratios of O/P and (Fe + Bi)/P were calculated from the glass compositions. Fe(II)/Fetot ratio was calculated from the Mo¨ssbauer results.
Fe(II)/Fetotb (±0.03%)
D (g cm3) (±0.02 g cm3)
˚) RFe–Fe (A (±0.5%)
0.17 0.33 0.32 0.34
3.02 3.30 3.76 4.31
2.99 2.92 2.98 3.15
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
complex plane plot represented by imaginary part Z00 (x) vs. real part Z 0 (x) for each temperature. A point of this curve represents a given measurements of Z 0 (x) and Z00 (x), at a specific angular frequency x (x = 2pf). The experimental impedance spectra were fitted using complex non-linear least square (CNLLSQ) fitting procedure. This procedure works in an environment for equivalent electrical circuits and it is based on the fitting of experimental diagram. The average distance between the iron ions, RFeFe, was calculated using relation: RFe–Fe ¼ ð4pN =3Þ1=3 ;
ð1Þ
where N is the concentration of total iron (both Fe(II) and Fe(III) ions) per unit volume, calculated from the glass composition and measured density. If the iron ions are not uniformly distributed, the actual distance may be different from the R value calculated from Eq. (1). The estimated errors in the density and average distance between the iron ions were estimated as ±0.5%. 3. Results 3.1. Raman spectra The Raman spectra for the Bi2O3 free (F40) and Bi2O3– Fe2O3–P2O5 glasses (B3, B10, B20) are shown in Fig. 1. The band assignments for the bismuth-free, F40, glass are characteristic of pyrophosphate Q1 structure with most prominent bands at 1074 and 748 cm1 related to the symmetric stretching mode of non-bridging (PO2)sym and bridging (P–O–P)sym oxygen atoms, respectively [14,15]. Some barely detectable bands at 1215 and 620 cm1 are attributed to the non-bridging, (PO2)sym, and bridging oxygen atoms (P–O–P)sym in Q2 phosphate tetrahedra. The shoulder at 940 cm1 suggests the presence of Q0 phosphate units. Low frequency bands at 400 cm1 are as-
252 164
Relative intensity
1074 558 435 620
940 1215
748
B10 B3 F40 1400
signed to the bending mode of the phosphate polyhedra with iron as a modifier. This spectrum suggests that the binary iron phosphate glass with 39.4 mol% of Fe2O3 consists predominantly of pyrophosphate (P2O7)4 groups along with a small amount of metaphosphate chains of (PO3) groups and isolated orthophosphate (PO4)3 groups. The Raman spectra of the Bi2O3–Fe2O3–P2O5 glasses (B3, B10 and B20) differ slightly from the spectrum of the bismuth-free glass (F40). The Raman bands due to the pyrophosphate groups are still dominant, along with some traces of metaphosphate and orthophosphate groups. However, some new bands appear in the lower wave number region (<600 cm1) of Raman spectra. With increasing Bi2O3 content up to 18.9 mol%, the bands at about 164, 252, 435 and 558 cm1 grow in intensity. This spectral region in the Raman spectra can be attributed to the bismuth unit vibrations [7,17]. It was assumed that in these glasses Bi2O3 exists mostly as [BiO6] units, where the Bi atoms are located in octahedral sites. The two strongest bands at 164 and 252 cm1 are related to the vibrations of heavy metal cations, which clearly evidences the presence of Bi(III) ions in the glass network. Some barely detectable bands at 435 and 558 cm1 are attributed to the stretching mode of the bridging oxygen atoms, (Bi–O–Bi), in the highly distorted [BiO6] octahedral units. The band at about 620 cm1 is related to both the stretching mode of nonbridging oxygen atoms, (Bi–O) in [BiO6] units as well as to the non-bridging oxygen atoms in metaphosphate chains. It is well known that the phosphate structure is strongly influenced by the overall O/P ratio [15]. The average phosphate chain length becomes progressively shorter as the O/ P ratio increases. With increasing O/P ratio from 3.0 to 3.5 the phosphate structure changes from methaphosphate chains, Q2 to pyrophosphate, Q1, based units. Generally, for glasses with O/P ratio >3.5 the network structure contains Q1 pyrophosphate and Q0 isolated orthophosphate units. For the glasses in the present study the O/P ratio was maintained constant at 3.5 and the structure is dominated by pyrophosphate, Q1 units. However, the addition of Bi2O3 to iron phosphate glasses causes an increase in the intensity of the Raman bands attributed to the bismuth units in the glass network. 3.2. Electrical conductivity
B20
1600
3237
1200
1000
800
600
400
200
0
-1
Raman shift (cm ) Fig. 1. The Raman spectra of the bismuth iron phosphate glasses.
The conductivity spectroscopy is a well established method for characterizing the hopping dynamics of polaron. For the analysis and interpretation of the obtained data, the electrical conductivity can be described by means of equivalent circuit or frequency-dependent conductivity spectra. Fig. 2 shows the impedance spectra at 363, 393 and 423 K and their corresponding electrical equivalent circuits for the B20 glass. The impedance spectrum at each temper-
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3238
120
B20
ments (CPEs) rather than ordinary capacitors in equivalent circuits. The CPE is an empirical impedance function of the type:
R
100
a
80 Z"/MΩ
Z CPE ¼ AðjxÞ ;
CPE
60
363 K
40 20
393 K 423 K
0 0
20
40
60 Z'/MΩ
80
100
120
Fig. 2. Complex impedance plots for the B20 glass at various temperatures and corresponding equivalent electrical circuit.
ature consists of single well-shaped semicircle related to bulk effects, which is characteristic for electronic conductors [18]. No residual semicircle at low frequencies attributed to contact or electrode effects has been noticed, probably due to the fact that samples were finely polished and electroded by sputtering. Similar results have been obtained for all glasses in the present study. The impedance spectra from Fig. 2 can be interpreted by means of equivalent circuit where each impedance semicircle can be represented by resistor, R, and capacitor, C in parallel (parallel RC element) [19]. 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, R, of the sample. However, experimental data show depressed semicircle with the center below the real axis, which is the reason for using constant-phase ele-
ð2Þ
where A and a are constants. There are two reasons for such non-ideal behavior: heterogeneous property of system and presence of a distribution in relaxation times within the bulk response and distortion by other relaxation such as electrode polarization effect. Experimental impedance data were fitted using complex non-linear least square procedure and an excellent agreement between experimental (scatter) and theoretical curve (line) was obtained. Equivalent circuit modeling gives three parameters at each temperature: bulk resistance, R, and two parameters for CPEs, A and a. Fitting results for all glasses at two temperatures are listed in Table 2. The CPE parameters, A and a, are constant over the temperature range. The values of bulk resistance, R, for the single semicircle together with electrode dimensions, (S is the electrode area and d is the sample thickness) were used to determine the dc conductivity, rdc of the glasses, rdc = (d/S)/R, see Table 3. It should be noted that the complex impedance plot in the wide frequency range was single semicircle for all glasses indicating a single conductivity process for all glasses in the present study. Fig. 3 shows the frequency dependence of the real part of the conductivity, r 0 (x), for the B20 glass at different temperature. The spectra display the typical shape found for electronically conducting glasses [20]. At low frequency the conductivity is independent of frequency and identical to dc conductivity, rdc, of glass, whereas, at higher frequency exhibits dispersion in power law fashion. The values of rdc obtained from low frequency plateau are equal to rdc calculated from equivalent circuit modeling, Table
Table 2 Fitting parameters of impedance spectra at 303 and 423 K for bismuth iron phosphate glasses Sample code
R (X) at 303 K (±0.5%)
R (X) at 423 K (±0.5%)
A at 303 K (±0.5%)
A at 423 K (±0.5%)
a at 303 K (±0.5%)
a at 423 K (±0.5%)
F40 B3 B10 B20
1.00 · 1010 5.19 · 108 4.83 · 108 2.65 · 109
1.95 · 107 2.08 · 106 2.00 · 106 9.45 · 106
7.62 · 1012 1.09 · 1011 1.53 · 1011 1.53 · 1011
2.34 · 1011 3.09 · 1011 3.73 · 1011 3.22 · 1011
0.84 0.85 0.85 0.85
0.83 0.83 0.85 0.86
The equivalent circuit shown in Fig. 2 was used for numerical fitting.
Table 3 DC conductivity, rdc, and activation energies, Edc, EZ 00 , EM 00 for the bismuth iron phosphate glasses Sample code
rdc (X m)1 at 303 K obtained from conductivity plateau (±0.5%)
rdc (X m)1 at 303 K obtained from equivalent circuit modeling (±0.5%)
Edc (kJ mol1) (±0.5%)
EZ 00 (kJ mol1) (±0.5%)
EM 00 (kJ mol1) (±0.5%)
F40 B3 B10 B20
3.49 · 109 8.28 · 108 6.75 · 108 9.85 · 109
3.10 · 109 8.40 · 108 6.78 · 108 9.73 · 109
57.5 50.7 50.4 51.9
57.5 50.7 50.5 52.0
57.5 50.7 50.6 51.9
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
-3
B20
473 K -5
log σdc (Ωm)-1
log σ (ω) (Ωm)-1
-4 423 K 393 K 363 K 333 K
-6 -7
-5 -6 -7 -8
303 K
-8
-9
-9 -1
0
1
2 3 log f (Hz)
4
5
6
7
2.4
2.8 1000/T
Fig. 3. Frequency dependence of the conductivity, r(x), at temperatures shown for the B20 glass.
3. The dc conductivity of these glasses exhibits an Arrhenius-type temperature dependence. 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 [2]: mph e2 Cð1 CÞ expð2aRÞ expðW =kT Þ; kTR
2.0
ð3Þ
3.6
to those of Edc calculated from Arrhenius-type dependence of the dc conductivity. The dependence of dc conductivity, rdc, at 303 K and activation energy for dc conductivity, Edc, upon the Bi2O3 content for all glasses is shown in Fig. 5. Bismuthfree glass has the lowest value of rdc, 3.10 · 109 (X m)1. For glasses containing 3.3 and 9.8 mol% Bi2O3, the rdc increases for one order of magnitude and has almost equal value for both glasses, 8.40 · 108 and 6.78 · 108 (X m)1, respectively. However, with increasing Bi2O3 up to 18.9 mol%, the rdc decreases to 9.73 · 109 (X m)1. Similarly, Edc decreases significantly to the constant value for the glasses containing 3.3 and 9.8 mol%
-6.5
-6.0 -6.5
0.36
Fe(II)/Fetot
-7.0
0.32
-7.5
0.28 0.24
-8.0
σdc at 303 K
-8.5
0.20
58
0.16
-9.0 20
25 30 35 mol% Fe2O3
40
56
σdc at 303 K
-7.5
54 52
-8.0
Edc (kJmol-1)
-7.0
Fe(II)/Fetot
where mph is the phonon frequency, C is the fraction of reduced transition metal ion, (Fe(II)/Fetot), R is the average spacing between transition metal ions, 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. (3) describes a non-adiabatic regime of small polaron hopping. In MottÕs 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 [2,21]. In this temperature region the jump of an electron (polaron) occurs between nearest neighbors with activation energy 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. (3) are constant, the dependence of the dc conductivity on temperature can be compared with the Arrhenius equation rdc = r0 exp(Edc/kT) where rdc is the dc conductivity, r0 is the pre-exponent, Edc is the activation energy for the dc conductivity, k is the Boltzmann constant and T is the temperature (K). According to this equation, activation energy for dc conductivity, Edc, can be calculated from the slope of log rdc vs. 1/T curves as shown in Fig. 4. The values for rdc at 303 K and Edc for each glass are given in Table 3. It should be noted that the calculated values are identical
3.2
(K)-1
Fig. 4. Temperature dependence of the dc conductivity, rdc, for the bismuth iron phosphate glasses. See Table 3 for the dc activation energy, Edc, calculated from the slope log rdc vs. 1/T.
log σdc (Ωm)-1
-2
r¼
F40 B3 B10 B20
-4
-3
log σdc (Ωm)-1
-2
3239
50
-8.5
Edc
-9.0
48 0
5
10 15 mol% Bi2O3
20
Fig. 5. The dependence of the dc conductivity, rdc, at 303 K and activation energy for dc conductivity, Edc, upon the Bi2O3 content in the bismuth iron phosphate glasses. Inset: dc conductivity, rdc, at 303 K and Fe(II)/Fetot ratio as a function of Fe2O3 content. Lines are drawn connecting data symbols of each kind.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
Bi2O3, whereas, slightly increases for glass containing 18.9 mol%. Going further in the interpretation of these results, the dependences of the rdc and Fe(II)/Fetot ratio upon Fe2O3 content is shown in the inset in Fig. 5. With increasing Fe2O3 content from 23.5 to 38.5 mol% the rdc increases, whereas for glass with 39.4 mol% Fe2O3 the rdc unexpectedly decreases. An other factor that affects the dc conductivity is the concentration of Fe(II) ions determined from the Mo¨ssbauer spectra for each glass. 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. So, the Fe(II)/Fetot ratio is important for the electrical conductivity of these glasses. Since the ratio Fe(II)/Fetot has the lowest value, 0.17, consequently the concentration of polarons is the smallest in bismuth-free glass. Comparing relative amount of Fe(II) ions in bismuthfree glass to those with bismuth iron phosphate glasses, an increase in Fe(II) ion concentration from 17% to 34% is observed. The increase in Fe(II) ion concentration from 17% to 33% for F40 and B3 glass, respectively, results in an increase in dc conductivity and decrease in activation energy. On the other hand, the Fe(II) ion concentration for B3, B10 and B20 glasses remains almost constant at 33%. Since the dc conductivity is associated with the migration of polaron between Fe(II) and Fe(III) ions with the distribution in hopping distances it seems that the decrease in Fe2O3 content from 39.4 to 23.5 mol% increases the distance between Fe ions, RFeFe, see Table 1. Such an increase in RFeFe diminishes the probability of electron hopping and reduces the possibility for formation of polarons. Clearly, a decrease in the chance for electron hopping from Fe(II) to Fe(III) sites decreases the concentration of polarons and consequently decreases dc conductivity for one order of magnitude in B20 glass. 3.3. Dielectric properties The complex permittivity e*(x) = 1/(jxC0Z*) can be expressed as a complex number: e ðxÞ ¼ e0 ðxÞ je00 ðxÞ;
ð4Þ
where e 0 (x) and e00 (x) are the real and imaginary parts of the complex permittivity.
8
B20
303 K 333 K 363 K 393 K 423 K 473 K
Electrode polarization
7 6 log ε'(ω)
3240
5 4 ε'∞(ω)
3 2 1 -2
-1
0
1
2
3
4
5
6
log f (Hz) Fig. 6. Frequency dependence of the real part of electrical permittivity, e 0 (x), for the B20 glass at various temperatures. The increase in e 0 (x) at low frequencies is caused by electrode polarization.
The frequency dependence of the real part of the complex permittivity, e 0 (x), for B20 glass is shown in Fig. 6. The dielectric permittivity, e 0 (x), measured at 333 K and 1 kHz for the present glasses is given in Table 4. At higher frequency, e 0 (x) approaches a constant value, 0 e1 ðxÞ, which probably results from rapid polarization processes occurring in the glasses [21]. With decreasing frequency, e 0 (x) increases due to electrode polarization arising usually from space charge accumulation at the glass-electrode interface. The increase in e 0 (x) occurs at higher temperatures and is more pronounced at lower frequency. The factor, which means the phase difference due to the loss of energy within the sample at a particular frequency is the loss factor tangent, tan d = e00 /e 0 . The frequency dependence of tan d at different temperatures for B20 glass is shown in Fig. 7(a). The maximum in the tan d peak shifts to higher frequency with increasing temperature. It should be noted that the dielectric loss peak is positioned at low frequency region, where the conductivity is dominated by dc conductivity. Generally, the dielectric losses at high frequency are much lower than those occurring at low frequencies. This kind of dependence of tan d on frequency is typically associated with losses by conduction. Consequently, the tan d for glasses with higher electrical conductivity, B3 and B10, is higher than for the F40 and B20 glasses.
Table 4 Real part of the dielectric permittivity, e 0 (x), relaxation time, sr, characteristic frequencies, foZ 00 and foM 00 , characteristic relaxation times, soZ 00 and soM 00 , non-adiabatic terms, 2aR, calculated from soZ 00 and soM 00 , for the bismuth iron phosphate glasses Sample code
e0 ðxÞ at 1 kHz, 333 K (±0.5%)
sr (s) at 333 K (±0.5%)
foZ 00 (Hz) (±0.5%)
foM 00 (Hz) (±0.5%)
soZ 00 (s) (±0.5%)
soM 00 (s) (±0.5%)
2aR from soZ 00 (±0.5%)
2aR from soM 00 (±0.5%)
F40 B3 B10 B20
11.4 18.9 20.4 18.0
4.19 · 103 2.25 · 104 3.20 · 104 2.39 · 103
2.35 · 1010 3.35 · 1010 2.36 · 1010 5.40 · 109
4.49 · 1010 6.99 · 1010 4.46 · 1010 9.57 · 109
6.79 · 1012 4.75 · 1012 6.75 · 1012 2.95 · 1011
3.55 · 1012 2.28 · 1012 3.57 · 1012 1.66 · 1011
4.22 3.86 4.21 5.69
3.57 3.13 3.58 5.11
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245 140
(a) B20
303 K 333 K 363 K 393 K 423 K 473 K
120 100
tan δ
80 60 40 20 0 -2
-1
0
1
0.03
2 3 log f (Hz)
4
5
6
303 K 333 K 363 K 393 K 423 K 473 K
f= 1/(2 πτσ)
(b) B20
7
M"
0.02
0.01
0.00 -2
-1
0
1
2 3 log f (Hz)
4
5
6
7
Fig. 7. Frequency dependence of the loss tangent, tan d (a) and the imaginary part of electrical modulus, M00 (b) for B20 glass at temperatures shown.
An alternative formalism particularly suitable to detect bulk effects and electrode polarization as an apparent conductivity relaxation times, sr [22,23], is the dielectric modulus model. The dielectric modulus is defined as M* = 1/e*, where e* is the complex permittivity,
0
0 2
00 2
00
0 2
3241
It is clear, that at any chosen temperature, sr for B3 and B10 glasses exhibits lower values, whereas sr for F40 and B20 glasses is almost one order of magnitude higher. The relaxation times, sr, for the glasses measured at 333 K, are shown in Table 4. The temperature dependence of the maximum M00 , indicates a linear relationship within the temperature and frequency range measured. The plot of the relaxation frequency, fM 00 ¼ 1=ð2psr Þ versus 1/T is represented by an Arrhenius equation, fM 00 ¼ foM 00 expðEM 00 =kT Þ, where EM 00 is the activation energy for the electrical relaxation. The activation energy, EM 00 , determined from the slope of the log fM 00 vs. 1/T for these glasses is given in Table 3 and shown in Fig. 9 for B20 glass. The activation energy values for the electrical modulus, EM 00 , and for dc conductivity, Edc, are almost identical, suggesting a hopping mechanism for all glasses [25]. The conduction mechanism for the present glasses is due to the polaron hopping based on electron carriers. However, it should be mentioned that the electrical behavior for polaronic mechanism with frequency and temperature is very similar to the ionic ones. Going further in the description of experimental data the variation of normalized parameters M 00 =M 00max and Z 00 =Z 00max as a function of logarithmic frequency measured at 363 K for B20 glass are shown in Fig. 8. Comparison with the impedance, electrical modulus and loss factor data allow the determination of bulk response in terms of localized, i.e. defect relaxation or non-localized conduction, i.e. ionic or electronic conductivity [22]. The Debye model is related to an ideal frequency response of localized relaxation. In reality the non-localized process is dominated at low frequencies. In the absence of interfacial effects, the non-localized conductivity is known as the dc conductivity. Thus, the high dielectric loss, tan d, is usually accompanied by rising e 0 (x) at low frequencies. Such behavior is found for the present glasses and showed in Fig. 6. However, it should be noted that the
1.0
Z" M"
00 2
M ¼ 1=e ¼ e =ððe Þ þ ðe Þ Þ þ je =ððe Þ þ ðe Þ Þ ð5Þ
Fig. 7(b) shows the imaginary part of the electrical modulus, M00 as a function of frequency for B20 glass at different temperatures. The maximum in the M00 peak shifts to higher frequency with increasing temperature. The frequency region below peak maximum M00 determines the range in which charge carriers are mobile on long distances. At frequency above peak maximum M00 , the carriers are confined to potential wells, being mobile on short distances. The M00 shows a maximum at a characteristic frequency, which is equal to the relaxation frequency fM 00 . The relaxation time, sr, can be extracted from the position of the M00 maximum where fM 00 ¼ 1=ð2psr Þ [24], as shown in Fig. 7(b).
0.8 Normalized peak
¼ M 0 þ jM 00 .
B20 363 K
0.6 0.4 0.2 0.0 -2
-1
0
1
2 3 log f (Hz)
4
5
6
7
Fig. 8. Frequency dependence of normalized peaks, Z 00 =Z 00max , and M 00 =M 00max for B20 glass at 363 K.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
3242
localized relaxation process has much smaller values of e 0 (x) and sr than the non-localized one. Therefore, the position of the peak in the tan d/tan dmax curve is shifted to a lower frequency region in relation to the M 00 =M 00max and Z 00 =Z 00max peaks. According to Figs. 7(a) and 8, the three peaks that describe a priori the same relaxation process [21] are in accordance with the following order proposed elsewhere [22]. stan d > sZ P sM ; where s is the relaxation time and the subscripts represent the loss tangent, tan d, complex function Z*(x) and M*(x). Through these representations, it is possible to determine the type of dielectric response by inspection of the magnitude of overlapping between the peaks of both parameters Z00 (x) and M00 (x) [22]. The overlapping peak position of M 00 =M 00max and Z 00 =Z 00max curves is evidence of delocalized or long-range relaxation [22]. However, for the present glasses the M 00 =M 00max and Z 00 =Z 00max peaks do not completely overlap but are very close suggesting the components from both long-range and localized relaxation. This is supported by the complete complex impedance plot exhibited in Fig. 2. The plot of the relaxation frequency maximum, log fZ 00 , derived from Z00 (x) as a function of reciprocal temperature 1/T is shown in Fig. 9 for B20 glass. The data are represented by Arrhenius relation: fZ 00 ¼ foZ 00 expðEZ 00 =kT Þ, where EZ 00 is the activation energy for the conduction derived from Z00 (x) function and foZ 00 is the pre-exponential factor or characteristic relaxation frequency constant. Almost identical values for EZ 00 and EM 00 are observed on entire temperature range being equal to 52.0 and 51.9 kJ mol1, respectively. The slight difference observed between EZ 00 and EM 00 values suggests experimental features indicating that both
5 B20
4
EM" = 51.9 kJmol-1
fZ"
log f (Hz)
fM"
3
values are almost same. In addition, the magnitude of the activation energy suggests that the carrier transport is due to the hopping conduction. According to the Fig. 9 the values of the intrinsic relaxation times show that ones exhibit a short time. The characteristic relaxation frequencies calculated from the plot log f vs. 1/T for B20 glass are equal to foZ 00 ¼ 5:40 109 Hz and foM 00 ¼ 9:57 109 Hz being associated to the parameters soZ 00 ¼ 2:95 1011 s and soM 00 ¼ 1:66 1011 s, respectively. These values belong to superior limit of one to unequivocal assignment of polarization mechanism as being a lattice phenomenon, a typical phenomenon identified at around 1012 Hz. The parameters derived from Fig. 9 are addressed to the electrical behavior involving electronic process. The values of characteristic relaxation times can be correlated to the presence of space charge accumulated probably at the glass-electrode interface. The characteristic relaxation frequencies foZ 00 and foM 00 , along with the characteristic relaxation times soZ 00 and soM 00 , for all glasses investigated are given in Table 4. 4. Discussion The Raman bands due to the heavy metal oxides such as Bi2O3, can be classified into four regions: (1) low wave number modes (<100 cm1), (2) heavy metal ion vibrations (70–160 cm1), (3) bridged anion modes (300–600 cm1) and non-bridging anion modes at higher wave numbers [7,17]. The Raman spectra for the present glasses show bands associated to the least three regions suggesting that Bi2O3 takes part in the formation of the glass network. Raman spectrum for the bismuth-free glass consists of predominantly pyrophosphate, Q1, structure with traces of metaphosphate, Q2, and orthophosphate, Q0 units. With increasing Bi2O3 content from 3.3 to 18.9 mol%, there are no changes in the pyrophosphate glass network since the O/P ratio was maintained constant at 3.5, Table 1. However, the addition of Bi2O3 to iron phosphate glasses causes an increase in the intensity of the Raman bands attributed to the highly distorted [BiO]6 octahedral units in glass structure. The strong bands appeared at lower frequencies at 164 and 252 cm1, Fig. 1, are due to the vibrations of Bi(III) ions incorporated into glass network, which suggests glass forming character of bismuth ions. 4.1. Electrical properties
2 EZ" = 52.0 kJmol-1
1 0 2.0
2.4
2.8 1000/T
3.2
3.6
(K)-1
Fig. 9. Temperature dependence of the relaxation frequencies, fM 00 and fZ 00 , for the B20 glass. See Table 3 for the activation energies, EZ 00 , EM 00 , calculated from the slope log f vs. 1/T.
The increase initially and than decrease in the dc conductivity, rdc, and decrease in activation energy, Edc, for these glasses is related to the decrease in the Fe2O3 content from 39.4 to 23.5 mol% as Bi2O3 content increases from 0 to 18.9 mol%. Such behavior suggests that the conductivity depends strongly on Fe2O3 content. It has been previously reported [9] that in iron phosphate glasses the rdc is electronic and depends strongly upon distance between iron ions, RFeFe. The reduction in Fe2O3 content increases distances between iron ions. So, assuming that the conductiv-
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
ity is due to the electron hopping from Fe(II) to Fe(III) then with increasing RFeFe from 2.92 for B3 glass to ˚ for B20 glass it is reasonable to expect a decrease 3.15 A in the dc conductivity. The dc conductivity, also depends on the concentration of Fe(II) ions in these glasses. The ratio Fe(II)/Fetot is determined from the Mo¨ssbauer spectra and is listed in Table 1 for each glass in the present study. The increase in Fe(II) ion concentration from 17% to 33% for F40 to B3 glass, respectively, results in an increase in dc conductivity and decrease in activation energy for these glasses. However, for B3, B10 and B20 glasses, Fe(II) ion concentration remains almost constant at 33%. Assuming that the dc conductivity is due to migration of polaron between Fe(II) and Fe(III) ions with the distribution in hopping distances, it seems that the decrease in Fe2O3 content and increase in distance RFeFe reduces the possibility of polaron formation. Consequently, a decrease in the concentration of polarons in B20 glass results in a decreased dc conductivity. These results agree with the studies [1,2,26] where ratio Fe(II)/Fetot, Fe2O3 content and distance between iron ions were found the important factors for electrical conductivity of these glasses. 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 where 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 [26]. Therefore, the reorientation of such dipoles gives rise to characteristic frequency dependent features of the complex permittivity, e*(x) = e 0 (x) je00 (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. In order to mobilize the localized electron, in polaron conductive glasses, the aid of lattice oscillation is required. In these circumstances electrons are considered not to move by themselves but by hopping motion activated by lattice oscillation. Thus, in temperature region measured at T > H/2, where H is the Debye temperature, the conduction is considered as phonon-assisted hopping of small polaron between localized states [2,21]. It should be mentioned that the electron, which creates a polaron is the same electron that later separates from its neighborhood by hopping motion producing conduction at lower frequency. Therefore, in electron conducting glasses polarization and conduction are integrated into a single continuous process [21].
3243
For all glasses investigated, the increase in e 0 (x) and e (x) with decreasing frequency, is attributed to the conductivity r(x), which is directly related to an increase in mobility of localized charge carriers. The B3 and B10 glasses show highest dc conductivity, which indicates the highest polaron concentration. This improves easier movement of space charge carriers responsible for electrode polarization at low frequency. At the same time, at lower frequency, an increase in the magnitude of e 0 (x) is caused by dipolar effects. 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 [27]. Similarly, the observed dielectric loss, tan d, is due to two main contributions. The first is related to the thermal activated relaxation of freely rotating dipoles in which the thermal energy is only type of excitation. A second part at higher temperature, which increases with temperature is due to electrical conduction with hopping motion from Fe(II) to Fe(III). The frequency dependence of tan d at different temperature exhibited in Fig. 7(a) for B20 glass shows an increase of the loss magnitude at low frequency whereas at high frequency the loss magnitudes are much lower. Taking into account that the tan d represents the conduction loss, the peak position can give further insight on the conduction mechanism. The increase in dielectric loss, tan d, positioned at very low frequency for the present glasses, is related to the increase in e 0 (x) at low frequency, Figs. 6 and 7(a). The conductivity relaxation model, where a dielectric modulus is defined by M*(x) = 1/e*(x), can provide information about the relaxation mechanism [24]. According to the earlier discussion two apparent relaxation regions appeared, the low frequency region, being associated with the hopping conduction and higher region being associated with the relaxation polarization process. In the case that the data are presented in electrical modulus representation the effect of electrode polarization, observed for all glasses measured, can be avoided since the electrical modulus peaks, M00 , are shifted toward higher frequency. The relaxation times, sr, as calculated from the frequency at the M00 maximum, shown in Fig. 7(b) and listed in Table 4 are thermally activated with the following respective activation energy EM 00 . From Table 4 it is clear that the relaxation times, sr, for the B3 and B10 glasses are much smaller due to a smaller EM 00 and Edc and consequently, a higher conductivity, r(x). For the B20 and F40 glasses the relaxation times, sr, become higher with decreasing Fe2O3 content and Fe(II) concentration, respectively, which causes lower conductivity in these glasses. It was previously mentioned that by combining imaginary modulus with imaginary impedance it is possible to distinguish the localized (relaxation defects) from nonlocalized conduction (electronic or ionic conductivity) pro00
3244
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245
cesses within the bulk of glasses. For all glasses investigated a very close maximum position of M 00 =M 00max and Z 00 =Z 00max peaks, represented for B20 glass in Fig. 8, suggests both localized and long-range conductivity. In addition, such a overlapping illustrates that the dynamic process occurring at different frequencies exhibits the same thermal activation energy and existence of a single carriers. Therefore, both peaks, M 00 =M 00max and Z 00 =Z 00max , describe the same relaxation process. As already mentioned, the temperature dependence of the relaxation times for these glasses is a process thermally activated following Arrhenius law. The activation energies, EM 00 and EZ 00 , observed on the temperature range measured for B20 glass are equals to 51.9 and 52.0 kJ mol1, respectively. The characteristic relaxation frequencies for B20 glass, foZ 00 ¼ 5:40 109 Hz and foM 00 ¼ 9:57 109 Hz, are related to the parameters soZ 00 ¼ 2:95 1011 s and soM 00 ¼ 1:66 1011 s. It can be noticed that the characteristic relaxation frequencies for all glasses in the present study appear to be much lower than the expected value of the optical phonon frequency (1013 Hz). Such deviation could be explained by non-adiabatic approximation of phonon assisted quantum mechanical tunneling. There are two different conductivity mechanisms for relaxation process: temperature dependent classical activation of carrier over a potential barrier spreading two sites with activation energy, W (s = s0 exp (W/kT)) and temperature independent quantum mechanical tunneling of a carrier through the potential barrier between the sites separated by a distance R (s0 = sph exp(2aR)). As pointed out before, activation energies for relaxation process, EM 00 and EZ 00 , in Table 2, are in excellent agreement with activation energy for dc conductivity, Edc. According to Mott [2,3], if the main conductivity mechanism is in adiabatic regime than the tunneling term exp(2aR) is negligible (exp(2aR) 1). Consequently, characteristic relaxation time, s0, is equal to optical phonon relaxation time, sph. On the contrary, in a case of non-adiabatic regime electronic frequency is much higher than the average phonon frequency and tunneling term cannot be neglected. Values for characteristic relaxation frequencies, soZ 00 and soM 00 , given in Table 4 indicate that although thermal activated relaxation mechanism dominates the observed relaxation behavior, the non-adiabatic term should not be ignored on studying the relaxation phenomena. Furthermore, non-adiabatic contributions, 2aR, for all glasses under study are given in Table 4. It should be noted that the values for non-adiabatic contribution could be obtained form dc conductivity measurements and are consistent with those for similar glasses [28]. For the F40, B3 and B10 glasses this contribution is almost constant at 4, but for B20 glass is slightly higher, 5.69. This result suggests that the probability of quantum tunneling is smallest for B20 glass. The reason for that could be the smallest concentration of polarons in this glass due to the smallest Fe2O3 content. Thus, the relationship between relaxation parameters and electrical conductivity indicates electronic conductivity
controlled by polaron hopping from Fe(II) to Fe(III) ions in these glasses. 5. Conclusion The changes in the electrical properties of Bi2O3–Fe2O3– P2O5 glasses, show that electrical conductivity is independent of Bi2O3 content and that main conduction mechanism is small polaron hopping between Fe(II) and Fe(III) sites. Therefore, electrical conductivity in these glasses is strongly controlled with polaron concentrations which depend upon Fe2O3 content and Fe(II)/Fetot ratio. The dielectric properties, such as e 0 (x) and e00 (x) and their variations with frequency and temperature, indicate a dispersion at frequency lower than 1 kHz, due to the increase in electrode polarization. The relaxation observed on the M00 (x) or Z00 (x) functions is correlated to both localized and long-range conduction. The overlapping of the M00 (x) or Z00 (x) peaks suggests the same activation energy and existence of a single carrier that are related to the same relaxation processes. The dielectric loss, tan d, for these glasses is due to electrical conduction with hopping motion between Fe(II) and Fe(III) ions. The Raman spectra indicate that all glasses consist of predominantly pyrophosphate units. With addition of Bi2O3 content up to 18.9 mol% an increase in the Raman bands attributed to the distorted [BiO]6 octahedral units in glass structure suggests that the Bi(III) ions are incorporated in the glass network. References [1] L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91. [2] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [3] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [4] J.C. Lapp, W.H. Dumbaugh, M.L. Powley, Riv. Staz. Sper. Vetro. 1 (1989) 91. [5] D.W. Hall, M.A. Newhause, N.F. Borrelli, W.H. Dumbaugh, L.A. Weidman, Phys. Lett. 54 (1989) 1293. [6] S. Hazra, S. Mandal, A. Ghosh, Phys. Rev. B 56 (1997) 13. [7] L. Baia, R. Stefan, W. Kiefer, J. Popp, S. Simon, J. Non-Cryst. Solids 303 (2002) 379. [8] D.K. Durga, N. Veeraiah, Bull. Mater. Sci. 24 (2001) 421. [9] S. Hazra, A. Ghosh, J. Phys. Condens. Matter 9 (1997) 3981. [10] S. Hazra, A. Ghosh, J. Appl. Phys. 84 (1998) 987. [11] A. Ghosh, J. Appl. Phys. 65 (1989) 227. [12] A. Ghosh, J. Appl. Phys. 65 (1988) 2652. [13] A. Ghosh, J. Appl. Phys. 66 (1989) 2425. [14] A. Mogusˇ-Milankovic´, B. Pivac, K. Furic´, D.E. Day, Phys. Chem. Glasses 38 (1997) 74. [15] A. Mogusˇ-Milankovic´, M. Rajic´, A. Drasˇner, R. Trojko, D.E. Day, Phys. Chem. Glasses 39 (1998) 70. [16] B.K. Chaudhuri, K. Chaudhuri, K.K. Som, J. Phys. Chem. Solids 50 (1989) 1137. [17] L. Baia, T. Iliescu, S. Simon, W. Kiefer, J. Molecul. Struct. 599 (2001) 9. [18] J.E. Gabarczyk, M. Wasinciouk, P. Machowski, W. Jakubowski, Solid State Ionics 119 (1999) 9. [19] J.R. Macdonald (Ed.), Impedance Spectroscopy, Wiley, New York, 1987. [20] A. Mogusˇ-Milankovic´, A. Sˇantic´, M. Karabulut, D.E. Day, J. NonCryst. Solids 330 (2003) 128.
A. Mogusˇ-Milankovic´ et al. / Journal of Non-Crystalline Solids 351 (2005) 3235–3245 [21] D.L. Sidebottom, B. Roling, K. Funke, Phys. Rev. B 63 (2000) 024301-1. [22] R. Gerhardt, J. Phys. Chem. Solids 55 (1994) 1491. [23] F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynhan, J. Phys. Chem. 78 (1974) 639. [24] P.B. Macedo, C.T. Moynhan, R. Bose, Phys. Chem. Glasses 13 (1972) 171.
3245
[25] J.M. Re´au, X.Y. Jun, J. Sevegas, Ch.Z. Deit, M. Polain, Solid State Ionics 95 (1997) 191. [26] A. Mogusˇ-Milankovic´, D.E. Day, J. Non-Cryst. Solids 162 (1993) 275. [27] S.R. Elliot, Adv. Phys. 36 (1987) 135. [28] L. Murawski, R.J. Barczyn´ski, D. Samatowicz, Solid State Ionics 157 (2003) 293.