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Ionic conductivity and electrical relaxation of nanocrystalline scandia-stabilized c-zirconia using complex impedance analysis
ARTICLE IN PRESS
Physica B 403 (2008) 2298–2305 www.elsevier.com/locate/physb
Ionic conductivity and electrical relaxation of nanocrystalline scandia-stabilized c-zirconia using complex impedance analysis Ashok Kumar, I. Manna Department of Metallurgy and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India Received 13 June 2007; received in revised form 5 December 2007; accepted 7 December 2007
Abstract A solid solution of 8 mol% of scandia-stabilized cubic-zirconia (8ScSZ) has been prepared by co-precipitation technique. The synthesized powder has an average crystallite size 40 nm, surface area of 8.49 m2/g, and agglomerated particle size of 150 nm. The activation energy of 8ScSZ has been calculated from impedance loss spectra; electrical modulus spectra are in the range of 0.90–1.30 eV. The frequency and temperature-dependent conductivities and impedance were measured in range of 50 Hz–1 MHz and 300–900 K, respectively. Complex impedance spectra, complex modulus formalism and complex conductivity spectra have been carefully analyzed in order to separate the grain, grain boundary and electrode–electrolyte effects. Analysis of ac impedance data using complex impedance indicates a typical negative temperature coefficient of resistance (NTCR) behavior of the materials. The intrinsic conductivity is mainly due to hopping of mobile ions among the available localized site. Relaxation time obtained from complex conductivity spectra are matched well with the impedance loss and modulus loss spectra. Impedance analysis suggests the presence of temperature-dependent electrical relaxation process in the material. r 2008 Elsevier B.V. All rights reserved. PACS: 07.50.e; 66.10.Ed; 73.61.Tm; 73.90.+f Keywords: Ionic conduction; Impedance spectroscopy; Dielectric relaxation; Electrolyte material
1. Introduction Much interest has been paid in recent years to study of the effects of rare earth doping on zirconia. It has been seen that scandia-stabilized zirconia (49 mol%) provides high conductivity in the intermediate temperature range [1]. Although it has the highest ionic conductivity of all the zirconia-based materials, however, it is difficult to stabilize the high conductivity in the high-temperature region (4500 1C). This material is well known as an oxygen ion conductor at elevated temperature and is used as an important material in gas sensor and in solid oxide fuel cell [2–7]. In order to understand complete electrical conduction mechanism, it is essential to distinguish the grain, grain boundary and electrode–electrolyte effects in the Corresponding author. Tel.: +91 787 751 4210; fax: +91 787 764 2571.
E-mail addresses: [email protected] (A. Kumar), [email protected] (I. Manna). 0921-4526/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.12.009
material matrix at that particular temperature and frequency domain. The electrical conductivity and dielectric properties of the materials depend strongly on the particle size, the dopant concentration, the phase present, temperature and applied frequency, which have been investigated thoroughly with the help of ac impedance spectroscopy (IS) [8]. It is generally accepted that mobile oxygen ions are bound at temperature below 400 1C and then gradually become mobile at elevated temperature [9]. Badwal et al. has studied the stability of dopant concentration on ternary system (Y2O3–Sc2O3–ZrO2, 8 and 9 mol%) [6,7]. Mizutani et al. have investigated that the 8 mol% Sc2O3–ZrO2 (also 8YSZ) showed a significant decrease in electrical conductivity by annealing at high temperature. However, the hightemperature annealing of 11-mol% Sc2O3–ZrO2 (11ScSZ) showed good stability over 5000 h [10,11]. Jones and Ingel developed scandia-stabilized ZrO2 ceramics which are useful to protect the turbine blades and engine pistons
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[12]. Novel synthesis method and microstructure-property relation of 8ScSZ were employed by Lee et al. [13] and Nomura et al. [14], respectively, who observed the decrease in conductivity due to local ordering of tetragonal structure in cubic matrix. The purpose of this research is, therefore, to explore the utility of different mechanism to explain the frequency and temperature dependence of the ionic conductivity of 8ScSZ and explore the particle size effects on its electrical conductivity.
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surface area of the investigated material. Particle size has been calculated with the help surface area measured from BET. The impedance measurements were carried out at an input signal level of 1.5 V in the temperature range of 35–600 1C using a computer-controlled impedance analyzer (HIOKI LCR Hi TESTER, Model 3532-50) in the frequency range of 100 Hz–1 MHz. 3. Results and discussion 3.1. Microstructural studies
2. Experimental technique In the present work, the Sc2O3–ZrO2-mixed oxides have been prepared by the co-precipitation method using as precursor salts ZrOCl2 8H2O, and Sc2O3 with the purpose of observing the influence of the scandia precursor salt in the Sc2O3–ZrO2 system. Moreover, the effect of some preparation conditions, such as drying, thermal aging, pH control, and aging along precipitation, was also investigated. The starting materials used to make green pellets are commercially available ZrOCl2 8H2O (Loba Chemie Pvt. Ltd., Mumbai; purity 99.5%) and Sc2O3 (Alfa Aesar; purity 99.9%). In order to prepare the powder mixtures, ZrOCl2 8H2O is dissolved in distilled water at room temperature. Sc2O3 is dissolved in dilute HCl and then is heated until it gives a clear solution. Five percent NH4OH solution is prepared. Solution of dopant and zirconia are mixed in a beaker and then mixed with NH4OH solution. After the precipitation, the precipitate is separated, rinsed with distilled water and dried. The co-precipitated powder is then calcined at 850 1C. The calcined powder so obtained was cold-pressed into cylindrical pellets of diameter 10 mm and thickness 1–2 mm with polyvinyl alcohol (PVA) as the binder using a hydraulic press at a pressure of 300 MPa. The pellets were then sintered in an air atmosphere at 1400 1C for 2–3 h and then polished with fine emery paper to make their faces flat and parallel. The pellets were finally coated with conductive silver paint and fired at 400 1C for 2 h before carrying out impedance measurements. X-ray diffraction (XRD) studies of the materials were carried out at room temperature in the Bragg angle range 201p2yp801 at a scan speed of 21/min by an X-ray diffractometer (Miniflex, Rikagu, Japan) using Cu Ka radiation (l ¼ 1.5418 A˚). Slow scan XRD (0.51/min) has been carried out in the diffraction plane 220 and 210 to check the splitting in Braggs peaks. We measured the density of sintered pellets with an Archimedes method. Scanning electron micrographs of the materials were taken with high-resolution scanning electron microscope (SEM; JOEL-JSM, model 5800F) to study the surface morphology/microstructure of the sample pellets. The pellets were gold-coated prior to being scanned under high-resolution field emission gun of SEM. The gold coating was carried out under argon (Ar) atmosphere at a vacuum level of 102 Torr. BET has been carried out to calculate the
The XRD patterns (Fig. 1) comprises of sharp diffraction peaks of varying intensity which are different from those of precursor materials, confirms the formation of 8ScSZ. The peaks have been successfully indexed using standard computer software (POWDMULT) [15]. A preliminary structural analysis indicates that the system under investigation has a cubic crystal structure. The lattice parameters as evaluated using the software were refined by the least square refinement method. The calculated values are in well agreement with the structural data as reported in JCPDS file (301468). XRD of sintered powder is used to evaluate the theoretical density of the material and compared with its bulk (measured) density (96%). No traces of any extra peaks due to constituent oxides were found, suggesting that the compound is having a singlephase cubic structure. Slow scan (rate of 0.011/s) in the range of (2 0 0) and (2 2 0) plane was done for both the samples. It has been observed from the slow scan XRD that there is no splitting in the XRD peaks in the crystal plane (2 0 0) and (2 2 0) which suggests the cubic nature of prepared compounds. Table 1 provides microstructural details of 8ScSZ under present investigation. 3.2. Complex impedance analysis Fig. 2 shows the Nyquist plot of 8ScSZ. The bulk impedance properties of the material exhibit only up to 300 1C; after this temperature, both grain and grain boundary resistance appears. The net values of impedance decrease with increase in temperature. It indicates semiconducting nature, i.e. negative temperature coefficient of resistance (NTCR) of the materials. Above 400 1C, impedance spectra show the electrode–electrolyte resistance in the material. The bulk resistance (grain) plays prominent role in the conductivity behavior of the materials. This property is well-matched with the particle size calculated from the XRD/SEM/BET analysis of the material. At elevated temperature, the grain effects move out the experimental frequency window and grain boundaries influence come into the frequency spectrum. The grain boundary resistances decrease with increase in temperature. The grain boundary becomes more conducting at elevated temperatures, which enhance the O2 ions conduction through the grain boundary and increase overall O2 ions conduction in the electrolyte. The type
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8SSZ calcined at 850°C (111)
7000
6000
∗ +
2000
1000
+
8SSZ as coprecipitate
∗
∗
∗
∗
(400)
(311)
3000
(222)
(220)
4000
(200)
Intensity (a.u)
5000
+ Sc2O3 ∗ ZrO2
+
0 20
40
60
80
Braggs angle (2θ) Fig. 1. X-ray diffraction patterns of 8ScSZ at room temperature.
Table 1 Microstructure parameters of 8ScSZ nanocystalline powder Crystal system Unit cell parameter (A˚) Unit cell volume (A˚3) Experimental (XRD) density (g/cm3) Bulk (measured) density (g/cm3) Density after sintering (g/cm3) % Porosity before sintering % Porosity after sintering Surface area (m2/g) Particle size (nm) Grain size (mm) Crystallite size (nm)
Cubic a ¼ 5.092 132.03 5.69 2.894 5.4572 49 6 8.49 150 3 40
of presentation generally allows a clear separation of the different processes in ionic conducting samples [16]. Fig. 3 shows the impedance loss spectra of 8ScSZ. The curves showed the broad and asymmetric peaks above 300 1C. Maximum inflection points are observed. Both characteristics are a function of temperature and frequency. In the investigated temperature range, two inflections are identified. The inflections due to grain properties of the materials are vanished at the higher temperature range. The first inflection is shown at low frequency (1–10 kHz), while the second one is observed at around (X10 kHz) above 300 1C. However, at temperature X400 1C, only a single unique peak is observed in the highfrequency region (X10 kHz). Below 300 1C, the first response peak at low frequency is correlated to the grain boundary contribution, while the second one is correlated
with the grain effects. In addition, the curve shapes suggest that there are two types of relaxation with most frequent value at very similar frequency. Moreover, the impedance value decreases with increasing temperature and the relaxation frequency is shifted towards higher frequency side with increasing temperature. The phenomenon is wellmatched with the microstructure and complex impedance (Nyquist) plot of the related materials. The relaxation times are calculated from the peak frequency of Z00 and M00 spectroscopic plots with the help of following relation: 2pf max RC ¼ omax RC ¼ 1.
(1)
The RC product for each peak is a fundamental parameter, which is the inverse value of fmax. This is because the RC product is usually independent of the geometrical factor of the material. The activation energy calculated from relaxation times is well-matched with the activation energy calculated from the dc and ac conductivity, as given in Table 2. IS is a versatile tool to observe the microstructure property relation. It provides the clear information about the frequency-dependent and frequency-independent conduction from the bulk (grain), grain boundary and electrode–electrolyte effects or due to space charge effects. This feature of IS is unique compare to other process (twoprobes and four-probes dc conductivity measurements) reported in literature. 3.3. Complex modulus formalism Master modulus formalism is one of the best fundamental tools to investigate the in-situ ionic conduction of
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14
325°C
400°C
200 12 10
Z``(KΩ)
150
8 100
6 4
50 2 0
0 0
50
100
150
2
200
4
6
8
10
12
3.0 450°C
500°C
0.35
2.5 0.30
Z``(KΩ)
2.0
0.25 0.20
1.5
0.15 1.0 0.10 0.5
0.05 0.00
0.0 1.0
1.5
2.0
2.5 Z`(KΩ)
3.0
3.5
4.0
0.15
0.20
0.25
0.30
0.35 0.40 Z`(KΩ)
0.45
0.50
0.55
Fig. 2. Complex impedance spectrum (Nyquist plots) of 8ScSZ at various temperatures.
materials [17]. The modulus representation suppresses the unwanted effects of extrinsic relaxation often used in the analysis of dynamic conductivities of ionically conducting glasses. Although the physical meaning of this type of representation is still controversially discussed [18,19], the dielectric modulus is frequently used in the analysis of dielectric data of ionic conductors [20,21]. Fig. 4(a) shows the loss spectra of the master modulus curves. These spectra exhibit single relaxation phenomena occurring in the materials. The relaxation frequency shifted towards higher frequency side with increase in temperature. At elevated temperature and high-frequency region, the M00 tends to become M 1 , which indicates the mobility of charge ions from short range to long range. It also indicates the influence of grain boundaries and electrode–electrolyte blocking relaxations are effectively suppressed for the modulus data. On the other hand, we can say that due to large dynamic range and the strong temperature dependence of ionic conducting materials, its relaxation time is not affected by the grain boundaries. It is interesting to note that for a large number of experimentally observed spectra of ionically conducting materials, the
frequency of the modulus peak lies in the transition region from dc to ac conductivity. Master modulus curve (Fig. 4(b)) indicates the single semicircular arc for 8ScSZ. The arc length decreases with increase in temperature. The entire single arc overlapped each other for any temperature. This overlapping of arc for each temperature indicates the single-phase formation of the compounds. The observation of single semicircular arc in electric modulus spectra indicates the almost-same-magnitude of grain and grain boundary capacitance. We also point out that grain boundary resistance becomes more conducting than grain boundary capacitance at elevated temperature. The absence of two inflexion points in these spectra indicates the in-situ O2 ions conduction of the materials through conducting grain boundary. 3.4. ac and dc conductivity and relaxation time The temperature dependence of bulk ac conductivity is represented in Fig. 5(a) at 10 and 100 kHz. Fig. 5(a) indicates that the ac conductivity of the investigated material increase with increase in temperature. It can be
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60 55 50
Z2400 Z2425
2.0
325°C 350°C
45
1.5
Z`` (KΩ)
40 35 1.0
30 25 20
0.5
15 10 0.0
5 0 0.1
1
10
100
1000
0.1
1
10
100
1000
10 100 Frequency (kHz)
1000
0.40 0.07
450°C 500°C
0.35
525°C 550°C
0.06 0.30 0.05
Z`` (KΩ)
0.25
0.04
0.20
0.03
0.15 0.10
0.02
0.05
0.01
0.00
0.00 0.1
1
10 100 Frequency (kHz)
1000
0.1
1
Fig. 3. Impedance loss spectra of 8ScSZ as function of frequency over a wide range of temperatures.
Table 2 ac and dc conductivity, and activation energy calculated from dc conductivity and relaxation time of 8ScSZ nanocystalline powder Temperature (K)
625 690 720
Relaxation time Ea (eV)
Dc Ea (eV)
ScSZ sdc (S/cm)
sac (S/cm)
Grain
Grain boundary
Grain (Z00 )
Grain boundary
s00
M00
1.01 105 8.05 105 3.33 104
1.02 105 9.3 105 2.3 104
1.16
1.22
1.21
1.14
1.24
1.14
distinguished in two regions: (1) nonlinear region below 300 1C and (2) linear region above 300 1C. Nonlinear region well obey the Mott-type electrical conduction in the materials. In the linear region, the materials well behave and the Arrhenius-type thermally activated transport of charge carriers is governed by the following relation: Ea sac ¼ As0 exp , (2) kT
where A, Ea and k represent the pre-exponential factor, activation energy of the mobile charge carriers and Boltzmann constant, respectively. The activation energy evaluated in these regions (Ea ¼ 1.1–1.2 eV) are well enough for O2 ions conduction in the material. The variation of ac conductivity of 8ScSZ as a function of frequency at higher temperatures is shown in Fig. 5(b). The ac conductivity of the system depends on the dielectric properties and sample capacitance of the material.
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0.1
325°C 350°C 400°C 450°C 500°C 550°C
0.008
1E-3 1E-4 σac (Scm-1)
0.006 M``
1E-3
0.01 σac (Scm)-1
0.010
0.004
0.002
1E-6
1E-7 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 -1
1E-7
1000/T (°K)
Ea(10 kHz) = 1.1 ev Ea(100 kHz) = 1.2 ev σac 10kHz
1E-10 1
10 100 Frequency (kHz)
1E-5
1E-6
1E-9 0.000
1E-4
1E-5
1E-8
0.1
2303
σac 100kHz
1E-11
1000
1.0
1.5
2.0
2.5
3.0
3.5
1000/T (°K)-1
0.025
0.020
325°C 350°C 400°C 450°C 500°C 550°C
350°C 400°C 450°C 500°C 550°C
1E-3
M``
σac (Scm-1)
0.015
0.010
1E-4
1E-5
0.005 1E-6
0.000 0.000
0.005
0.010 M`
0.015
0.020
0.025
Fig. 4. (a) Complex modulus formalism of 8ScSZ at various temperatures. (b) Modulus loss spectra 8ScSZ as a function of frequency.
The pattern of variation for 8ScSZ indicates strong conductivity dispersion in the low-frequency region. This behavior may be attributed to the presence of space charge in the material. The modification of the conductivity spectrum with rise in temperature has characterized by a low-frequency dispersion followed by a high-frequency plateau region at elevated temperatures. Low-frequency conductivity dispersion has been attributed to be due to the contribution of space charge whereas high-frequency plateau may be related to contribution of O2 ions conduction. The doping of rare earths changes the crystal structure matrix of the zirconia. The substitution of Zr4+ by Sc3+ causes the formation of oxygen ion vacancies (equal to half the amount of Sc3+ ions) to maintain the electrical neutrality. These O2 vacancies are mobile at the elevated temperature and give rise to oxygen ionic conductivity. The defects formation reaction in Sc2O3-doped ZrO2 can be written in Kroger and Vink
0.1
1
10 100 Frequency (kHz)
1000
Fig. 5. (a) Ac conductivity plots of 8ScSZ as a function of temperature. (b) Ac conductivity plots of 8ScSZ as a function of frequency.
notation [22]. 0
x Sc2 O3 ¼ 2ScZr þ V 0 þ 3O0 .
(3) 0
Due to columbic and elastic attractive forces between ScZr and V 0 , we can postulate the existence of two associates 0 0 ScZr þ V , (4) 0 ¼ ScZr V0 and 0 0 x ScZr þ V . 0 ¼ 2ScZr V0
(5)
At lower temperature, association is almost complete. At 0 higher temperature, the complex dissociate into ScZr and V0 . The conductivity can be explained by the following equation: s ¼ qmV 0 ,
(6)
where m is mobility of the charged ions, q the effective charge and V 0 the concentration of oxygen ion vacancies.
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This behavior of ac conductivity spectrum is governed by Jonscher’s universal power law: sac ¼ sdc+Aon, where A is a thermally activated constant depending upon temperature [23,24]. The frequency at which change in slope of the pattern occurs is known as hopping frequency (op). These results suggest that electrical conduction in the material takes place via hopping mechanism. Concerning the linear region at high frequencies, it has been previously observed in different materials and proposed to be a universal feature in ionic conductor [25]. Fig. 6(i) shows that the dc conductivity of 8ScSZ increases linearly with increase in temperature. Activation energy calculated from the Arrhenius plots are wellmatched with the activation energy calculated from the relaxation time of different electrical mechanism. The value of dc conductivity is 0.002 S/cm, which is better than the earlier reported values at 525 1C. This enhancement in dc
0.01 RG RGB
1E-3 Ea=1.16 ev for grain Ea=1.22 ev for grain boundary
σdc (scm-1)
1E-4
conductivity may be due the smaller particle size of the 8ScSZ. Fig. 6(ii) shows the typical variation of relaxation time (t) as a function of temperature for c-zirconia. It indicates that the relaxation time is pretty small at higher temperatures in comparison to that at lower temperatures. The inverse of frequency region (omax), where the impedance loss spectra (Z00 ), electric modulus spectra (M00 ) and imaginary part of electrical conductivity spectra shows a maximum loss in the characterizing material is called its relaxation time which is derived from Eq. (1). The activation energy calculated from relaxation spectra matched well with activation energy of ac and dc conductivity in the same temperature region (Table 2). The relaxation time basically gives an estimate of the dynamics of the electrical relaxation process occurring in the material. Higher the value of t, slower is the electrical relaxation process and vice versa. The results obtained in the present studies indicate, therefore, that the rate of electrical conduction would be high at higher temperature. The relaxation time for conducting ions becomes more prominent for grain boundary conduction than that of the grain at elevated temperature. The activation energy calculated from relaxation time graph well-matched with ac and dc conductivity of the materials.
1E-5
3.5. Complex conductivity formalism 1E-6 1E-7 1E-8 1E-9 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 103/T (°K)-1
Fig. 7 shows the imaginary part of conductivity of the 8ScSZ. The plot indicates the frequency dispersion in lowfrequency domain whereas complete merger in the highfrequency region (o400 1C). This phenomenon indicates the occurrence of grain boundary relaxation in the sample [26], which is seen in the complex impedance plot in Fig. 3. The plot shows the characteristic frequency which is shifted towards the high-frequency region with increase in
350°C
Ea (g)=1.21 eV
1E-3
400°C
1E-3
Ea (gb)=1.14 eV Ea (σ``)=1.24 eV
450°C
Ea (M``)=1.14 eV
500°C 550°C
1E-4 σ``
τ (second)
1E-4
1E-5
1E-5 1E-6 1E-6 1E-7 1.2
1.3
1.4
1.5 103/T
1.6
1.7
1.8
1.9
(°K)
Fig. 6. (i) Dc conductivity plots of 8ScSZ (for both grain and grain boundary) as a function of temperature. (ii) Relaxation time graphs of 8ScSZ form different conduction mechanism.
1E-7 0.1
1
10 100 Frequency (kHz)
1000
Fig. 7. Frequency dependence conductivity s00 (u) of 8ScSZ as a function of frequency at different temperature.
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temperature. Frequency-independent conductivity has been found at elevated temperature (4400 1C) and high frequency region (4100 kHz) which is the special feature of ionic conductor [27,28]. At temperature above 400 1C the grain boundary effects modified this plateau in two different frequency-independent (dc conductivity) regions on both side of grain boundary relaxation. The lowfrequency part reflects the properties of low-conducting regions between the grains whereas high-frequency values give the intrinsic conductivity of mobile ion. Activation energy calculated from this admittance graph matched well with impedance loss spectra. Interestingly, our data on conductivity relaxation show Arrhenius behavior for the relaxation time. The nature of conductivity relaxation in ionic conductors has a complexity beyond the expectations from the crystalline translational order. In fast ionic conductors, crystalline in nature, the number of available sites exceeds the number of mobile ions and they cannot be unambiguously arranged in an optimized manner; in this sense, ionic conductors are said to be characterized by positional disorder [29]. 4. Conclusion We have prepared the nanocrystalline ionically conducting 8ScSZ using co-precipitation technique. Its electrical properties have been investigated through various tools of IS. It has been found that 8ScSZ shows grain, grain boundary and electrode–electrolyte effect in the impedance spectra whereas absence of grain boundary and electrode–electrolyte effects in the master modulus formalism. Absence of grain boundary in master modulus formalism indicates the very little role of the grain boundary capacitance. The frequency-dependent conductivities and dielectric permittivity were measured, which reveals two relaxations in the documented spectra. The grain (bulk) and grain boundary conductivity are calculated from the complex impedance spectra and compared with the published data. The frequency-dependent conductivity are well-described in terms of universal dielectric response. The temperature dependence of relaxation time is calculated from impedance loss spectra, modulus loss spectra, conductivity spectra and activation energy calculated from all these mechanisms are matched well with each other. It can be concluded that ac and dc conductivity in the material matrix are governed by the same microscopical mechanism. Both ac and dc conductivity follows Arrhenius-type thermally activated conduction above 400 1C. Complex conductivity spectra showed the typical ionic conduction through electrolyte.
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Acknowledgments This investigation was supported by Human Resource Development (HRD) with financial aid from the Council of Scientific and Industrial Research (CSIR), New Delhi. Authors also gratefully acknowledge the supports of Prof. R.N.P. Choudhary, Physics Department (Ferroelectric Lab), IIT Kharagpur. References [1] F. Boulc’h, E. Djurado, Solid State Ionics 157 (2003) 335. [2] D.S. Lee, W.S. Kim, S.H. Choi, J. Kim, H.W. Lee, J.H. Lee, Solid State Ionics 176 (2005) 33. [3] K. Huang, R.S. Tichy, J.B. Goodenough, J. Am. Chem. Soc. 81 (1998) 2565. [4] P. Huang, A. Petric, J. Electrochem. Soc. 143 (1996) 1644. [5] K. Nomura, S. Tanase, Solid State Ionics 98 (1997) 229. [6] S.P.S. Badwal, F.T. Ciacchi, D. Milosevic, Solid State Ionics 136 (2000) 91. [7] S.P.S. Badwal, K. Foger, Mater. Forum 21 (1997) 187. [8] J.R. Macdonald, W.B. Johnson, in: J.R. Macdonald (Ed.), Impedance Spectroscopy, Wiley, New York, 1987, p. 1. [9] M.J. Bannister, P.F. Skilton, J. Mater. Sci. Lett. 2 (1983) 561. [10] Y. Mizutani, M. Kawai, K. Nomura, Y. Nakamura, O. Yamamoto, Jpn. Proc. Electrochem. Soc. 40 (1997) 196. [11] Y. Mizutani, M. Kawai, K. Nomura, Y. Nakamura, O. Yamamoto, Jpn. Proc. Electrochem. Soc. 95 (1995) 301. [12] L.R. Jones, P.R. Ingel, US Patent no. PAT-APPL-7-199 815, 1988, p. 24. [13] D. Lee, I. Lee, Y. Jeon, R. Song, Solid State Ionics 176 (2005) 1021. [14] K. Nomura, Y. Mizutani, M. Kawai, Y. Nakamura, O. Yamamoto, Solid State Ionics 132 (2000) 235. [15] POWDMULT: An Interactive Powder Diffraction Data Interpretation and Indexing Program, Version 2.1, E. Wu School of Physical Sciences, Flinder University of South Australia, Bradford Park, SA, Australia. [16] D. Ravaine, J.L. Souquet, P. Hagenmuller, W.V. Gool, Solid Electrolytes, Academic Press, New York, 1978, p. 277. [17] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171. [18] C.T. Moynihan, J. Non-Cryst. Solids 172 (1994) 1385. [19] S.R. Elliott, J. Non-Cryst. Solids 170 (1994) 97. [20] K.C. Sobha, K.J. Rao, Solid State Ionics 81 (1995) 145. [21] J.M. Bobe, J.M. Reau, J. Senegas, M. Poulain, Solid State Ionics 82 (1995) 39. [22] S. Sen, R.N.P. Choudhary, A. Tarafdar, P. Pramanik, J. Appl. Phys. 99 (2006) 124114. [23] A.K. Jonscher, Nature 267 (1977) 673. [24] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983. [25] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [26] S.P.S. Badwal, Appl. Phys. A 50 (1990) 449. [27] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [28] O. Kanert, J. Steinert, H. Jain, K.L. Ngai, J. Non-Cryst. Solids 130 (1991) 1001. [29] K. Funke, Prog. Solid State Chem. 22 (1993) 111.
Physica B 403 (2008) 2298–2305 www.elsevier.com/locate/physb
Ionic conductivity and electrical relaxation of nanocrystalline scandia-stabilized c-zirconia using complex impedance analysis Ashok Kumar, I. Manna Department of Metallurgy and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India Received 13 June 2007; received in revised form 5 December 2007; accepted 7 December 2007
Abstract A solid solution of 8 mol% of scandia-stabilized cubic-zirconia (8ScSZ) has been prepared by co-precipitation technique. The synthesized powder has an average crystallite size 40 nm, surface area of 8.49 m2/g, and agglomerated particle size of 150 nm. The activation energy of 8ScSZ has been calculated from impedance loss spectra; electrical modulus spectra are in the range of 0.90–1.30 eV. The frequency and temperature-dependent conductivities and impedance were measured in range of 50 Hz–1 MHz and 300–900 K, respectively. Complex impedance spectra, complex modulus formalism and complex conductivity spectra have been carefully analyzed in order to separate the grain, grain boundary and electrode–electrolyte effects. Analysis of ac impedance data using complex impedance indicates a typical negative temperature coefficient of resistance (NTCR) behavior of the materials. The intrinsic conductivity is mainly due to hopping of mobile ions among the available localized site. Relaxation time obtained from complex conductivity spectra are matched well with the impedance loss and modulus loss spectra. Impedance analysis suggests the presence of temperature-dependent electrical relaxation process in the material. r 2008 Elsevier B.V. All rights reserved. PACS: 07.50.e; 66.10.Ed; 73.61.Tm; 73.90.+f Keywords: Ionic conduction; Impedance spectroscopy; Dielectric relaxation; Electrolyte material
1. Introduction Much interest has been paid in recent years to study of the effects of rare earth doping on zirconia. It has been seen that scandia-stabilized zirconia (49 mol%) provides high conductivity in the intermediate temperature range [1]. Although it has the highest ionic conductivity of all the zirconia-based materials, however, it is difficult to stabilize the high conductivity in the high-temperature region (4500 1C). This material is well known as an oxygen ion conductor at elevated temperature and is used as an important material in gas sensor and in solid oxide fuel cell [2–7]. In order to understand complete electrical conduction mechanism, it is essential to distinguish the grain, grain boundary and electrode–electrolyte effects in the Corresponding author. Tel.: +91 787 751 4210; fax: +91 787 764 2571.
E-mail addresses: [email protected] (A. Kumar), [email protected] (I. Manna). 0921-4526/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.12.009
material matrix at that particular temperature and frequency domain. The electrical conductivity and dielectric properties of the materials depend strongly on the particle size, the dopant concentration, the phase present, temperature and applied frequency, which have been investigated thoroughly with the help of ac impedance spectroscopy (IS) [8]. It is generally accepted that mobile oxygen ions are bound at temperature below 400 1C and then gradually become mobile at elevated temperature [9]. Badwal et al. has studied the stability of dopant concentration on ternary system (Y2O3–Sc2O3–ZrO2, 8 and 9 mol%) [6,7]. Mizutani et al. have investigated that the 8 mol% Sc2O3–ZrO2 (also 8YSZ) showed a significant decrease in electrical conductivity by annealing at high temperature. However, the hightemperature annealing of 11-mol% Sc2O3–ZrO2 (11ScSZ) showed good stability over 5000 h [10,11]. Jones and Ingel developed scandia-stabilized ZrO2 ceramics which are useful to protect the turbine blades and engine pistons
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[12]. Novel synthesis method and microstructure-property relation of 8ScSZ were employed by Lee et al. [13] and Nomura et al. [14], respectively, who observed the decrease in conductivity due to local ordering of tetragonal structure in cubic matrix. The purpose of this research is, therefore, to explore the utility of different mechanism to explain the frequency and temperature dependence of the ionic conductivity of 8ScSZ and explore the particle size effects on its electrical conductivity.
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surface area of the investigated material. Particle size has been calculated with the help surface area measured from BET. The impedance measurements were carried out at an input signal level of 1.5 V in the temperature range of 35–600 1C using a computer-controlled impedance analyzer (HIOKI LCR Hi TESTER, Model 3532-50) in the frequency range of 100 Hz–1 MHz. 3. Results and discussion 3.1. Microstructural studies
2. Experimental technique In the present work, the Sc2O3–ZrO2-mixed oxides have been prepared by the co-precipitation method using as precursor salts ZrOCl2 8H2O, and Sc2O3 with the purpose of observing the influence of the scandia precursor salt in the Sc2O3–ZrO2 system. Moreover, the effect of some preparation conditions, such as drying, thermal aging, pH control, and aging along precipitation, was also investigated. The starting materials used to make green pellets are commercially available ZrOCl2 8H2O (Loba Chemie Pvt. Ltd., Mumbai; purity 99.5%) and Sc2O3 (Alfa Aesar; purity 99.9%). In order to prepare the powder mixtures, ZrOCl2 8H2O is dissolved in distilled water at room temperature. Sc2O3 is dissolved in dilute HCl and then is heated until it gives a clear solution. Five percent NH4OH solution is prepared. Solution of dopant and zirconia are mixed in a beaker and then mixed with NH4OH solution. After the precipitation, the precipitate is separated, rinsed with distilled water and dried. The co-precipitated powder is then calcined at 850 1C. The calcined powder so obtained was cold-pressed into cylindrical pellets of diameter 10 mm and thickness 1–2 mm with polyvinyl alcohol (PVA) as the binder using a hydraulic press at a pressure of 300 MPa. The pellets were then sintered in an air atmosphere at 1400 1C for 2–3 h and then polished with fine emery paper to make their faces flat and parallel. The pellets were finally coated with conductive silver paint and fired at 400 1C for 2 h before carrying out impedance measurements. X-ray diffraction (XRD) studies of the materials were carried out at room temperature in the Bragg angle range 201p2yp801 at a scan speed of 21/min by an X-ray diffractometer (Miniflex, Rikagu, Japan) using Cu Ka radiation (l ¼ 1.5418 A˚). Slow scan XRD (0.51/min) has been carried out in the diffraction plane 220 and 210 to check the splitting in Braggs peaks. We measured the density of sintered pellets with an Archimedes method. Scanning electron micrographs of the materials were taken with high-resolution scanning electron microscope (SEM; JOEL-JSM, model 5800F) to study the surface morphology/microstructure of the sample pellets. The pellets were gold-coated prior to being scanned under high-resolution field emission gun of SEM. The gold coating was carried out under argon (Ar) atmosphere at a vacuum level of 102 Torr. BET has been carried out to calculate the
The XRD patterns (Fig. 1) comprises of sharp diffraction peaks of varying intensity which are different from those of precursor materials, confirms the formation of 8ScSZ. The peaks have been successfully indexed using standard computer software (POWDMULT) [15]. A preliminary structural analysis indicates that the system under investigation has a cubic crystal structure. The lattice parameters as evaluated using the software were refined by the least square refinement method. The calculated values are in well agreement with the structural data as reported in JCPDS file (301468). XRD of sintered powder is used to evaluate the theoretical density of the material and compared with its bulk (measured) density (96%). No traces of any extra peaks due to constituent oxides were found, suggesting that the compound is having a singlephase cubic structure. Slow scan (rate of 0.011/s) in the range of (2 0 0) and (2 2 0) plane was done for both the samples. It has been observed from the slow scan XRD that there is no splitting in the XRD peaks in the crystal plane (2 0 0) and (2 2 0) which suggests the cubic nature of prepared compounds. Table 1 provides microstructural details of 8ScSZ under present investigation. 3.2. Complex impedance analysis Fig. 2 shows the Nyquist plot of 8ScSZ. The bulk impedance properties of the material exhibit only up to 300 1C; after this temperature, both grain and grain boundary resistance appears. The net values of impedance decrease with increase in temperature. It indicates semiconducting nature, i.e. negative temperature coefficient of resistance (NTCR) of the materials. Above 400 1C, impedance spectra show the electrode–electrolyte resistance in the material. The bulk resistance (grain) plays prominent role in the conductivity behavior of the materials. This property is well-matched with the particle size calculated from the XRD/SEM/BET analysis of the material. At elevated temperature, the grain effects move out the experimental frequency window and grain boundaries influence come into the frequency spectrum. The grain boundary resistances decrease with increase in temperature. The grain boundary becomes more conducting at elevated temperatures, which enhance the O2 ions conduction through the grain boundary and increase overall O2 ions conduction in the electrolyte. The type
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8SSZ calcined at 850°C (111)
7000
6000
∗ +
2000
1000
+
8SSZ as coprecipitate
∗
∗
∗
∗
(400)
(311)
3000
(222)
(220)
4000
(200)
Intensity (a.u)
5000
+ Sc2O3 ∗ ZrO2
+
0 20
40
60
80
Braggs angle (2θ) Fig. 1. X-ray diffraction patterns of 8ScSZ at room temperature.
Table 1 Microstructure parameters of 8ScSZ nanocystalline powder Crystal system Unit cell parameter (A˚) Unit cell volume (A˚3) Experimental (XRD) density (g/cm3) Bulk (measured) density (g/cm3) Density after sintering (g/cm3) % Porosity before sintering % Porosity after sintering Surface area (m2/g) Particle size (nm) Grain size (mm) Crystallite size (nm)
Cubic a ¼ 5.092 132.03 5.69 2.894 5.4572 49 6 8.49 150 3 40
of presentation generally allows a clear separation of the different processes in ionic conducting samples [16]. Fig. 3 shows the impedance loss spectra of 8ScSZ. The curves showed the broad and asymmetric peaks above 300 1C. Maximum inflection points are observed. Both characteristics are a function of temperature and frequency. In the investigated temperature range, two inflections are identified. The inflections due to grain properties of the materials are vanished at the higher temperature range. The first inflection is shown at low frequency (1–10 kHz), while the second one is observed at around (X10 kHz) above 300 1C. However, at temperature X400 1C, only a single unique peak is observed in the highfrequency region (X10 kHz). Below 300 1C, the first response peak at low frequency is correlated to the grain boundary contribution, while the second one is correlated
with the grain effects. In addition, the curve shapes suggest that there are two types of relaxation with most frequent value at very similar frequency. Moreover, the impedance value decreases with increasing temperature and the relaxation frequency is shifted towards higher frequency side with increasing temperature. The phenomenon is wellmatched with the microstructure and complex impedance (Nyquist) plot of the related materials. The relaxation times are calculated from the peak frequency of Z00 and M00 spectroscopic plots with the help of following relation: 2pf max RC ¼ omax RC ¼ 1.
(1)
The RC product for each peak is a fundamental parameter, which is the inverse value of fmax. This is because the RC product is usually independent of the geometrical factor of the material. The activation energy calculated from relaxation times is well-matched with the activation energy calculated from the dc and ac conductivity, as given in Table 2. IS is a versatile tool to observe the microstructure property relation. It provides the clear information about the frequency-dependent and frequency-independent conduction from the bulk (grain), grain boundary and electrode–electrolyte effects or due to space charge effects. This feature of IS is unique compare to other process (twoprobes and four-probes dc conductivity measurements) reported in literature. 3.3. Complex modulus formalism Master modulus formalism is one of the best fundamental tools to investigate the in-situ ionic conduction of
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14
325°C
400°C
200 12 10
Z``(KΩ)
150
8 100
6 4
50 2 0
0 0
50
100
150
2
200
4
6
8
10
12
3.0 450°C
500°C
0.35
2.5 0.30
Z``(KΩ)
2.0
0.25 0.20
1.5
0.15 1.0 0.10 0.5
0.05 0.00
0.0 1.0
1.5
2.0
2.5 Z`(KΩ)
3.0
3.5
4.0
0.15
0.20
0.25
0.30
0.35 0.40 Z`(KΩ)
0.45
0.50
0.55
Fig. 2. Complex impedance spectrum (Nyquist plots) of 8ScSZ at various temperatures.
materials [17]. The modulus representation suppresses the unwanted effects of extrinsic relaxation often used in the analysis of dynamic conductivities of ionically conducting glasses. Although the physical meaning of this type of representation is still controversially discussed [18,19], the dielectric modulus is frequently used in the analysis of dielectric data of ionic conductors [20,21]. Fig. 4(a) shows the loss spectra of the master modulus curves. These spectra exhibit single relaxation phenomena occurring in the materials. The relaxation frequency shifted towards higher frequency side with increase in temperature. At elevated temperature and high-frequency region, the M00 tends to become M 1 , which indicates the mobility of charge ions from short range to long range. It also indicates the influence of grain boundaries and electrode–electrolyte blocking relaxations are effectively suppressed for the modulus data. On the other hand, we can say that due to large dynamic range and the strong temperature dependence of ionic conducting materials, its relaxation time is not affected by the grain boundaries. It is interesting to note that for a large number of experimentally observed spectra of ionically conducting materials, the
frequency of the modulus peak lies in the transition region from dc to ac conductivity. Master modulus curve (Fig. 4(b)) indicates the single semicircular arc for 8ScSZ. The arc length decreases with increase in temperature. The entire single arc overlapped each other for any temperature. This overlapping of arc for each temperature indicates the single-phase formation of the compounds. The observation of single semicircular arc in electric modulus spectra indicates the almost-same-magnitude of grain and grain boundary capacitance. We also point out that grain boundary resistance becomes more conducting than grain boundary capacitance at elevated temperature. The absence of two inflexion points in these spectra indicates the in-situ O2 ions conduction of the materials through conducting grain boundary. 3.4. ac and dc conductivity and relaxation time The temperature dependence of bulk ac conductivity is represented in Fig. 5(a) at 10 and 100 kHz. Fig. 5(a) indicates that the ac conductivity of the investigated material increase with increase in temperature. It can be
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60 55 50
Z2400 Z2425
2.0
325°C 350°C
45
1.5
Z`` (KΩ)
40 35 1.0
30 25 20
0.5
15 10 0.0
5 0 0.1
1
10
100
1000
0.1
1
10
100
1000
10 100 Frequency (kHz)
1000
0.40 0.07
450°C 500°C
0.35
525°C 550°C
0.06 0.30 0.05
Z`` (KΩ)
0.25
0.04
0.20
0.03
0.15 0.10
0.02
0.05
0.01
0.00
0.00 0.1
1
10 100 Frequency (kHz)
1000
0.1
1
Fig. 3. Impedance loss spectra of 8ScSZ as function of frequency over a wide range of temperatures.
Table 2 ac and dc conductivity, and activation energy calculated from dc conductivity and relaxation time of 8ScSZ nanocystalline powder Temperature (K)
625 690 720
Relaxation time Ea (eV)
Dc Ea (eV)
ScSZ sdc (S/cm)
sac (S/cm)
Grain
Grain boundary
Grain (Z00 )
Grain boundary
s00
M00
1.01 105 8.05 105 3.33 104
1.02 105 9.3 105 2.3 104
1.16
1.22
1.21
1.14
1.24
1.14
distinguished in two regions: (1) nonlinear region below 300 1C and (2) linear region above 300 1C. Nonlinear region well obey the Mott-type electrical conduction in the materials. In the linear region, the materials well behave and the Arrhenius-type thermally activated transport of charge carriers is governed by the following relation: Ea sac ¼ As0 exp , (2) kT
where A, Ea and k represent the pre-exponential factor, activation energy of the mobile charge carriers and Boltzmann constant, respectively. The activation energy evaluated in these regions (Ea ¼ 1.1–1.2 eV) are well enough for O2 ions conduction in the material. The variation of ac conductivity of 8ScSZ as a function of frequency at higher temperatures is shown in Fig. 5(b). The ac conductivity of the system depends on the dielectric properties and sample capacitance of the material.
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0.1
325°C 350°C 400°C 450°C 500°C 550°C
0.008
1E-3 1E-4 σac (Scm-1)
0.006 M``
1E-3
0.01 σac (Scm)-1
0.010
0.004
0.002
1E-6
1E-7 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 -1
1E-7
1000/T (°K)
Ea(10 kHz) = 1.1 ev Ea(100 kHz) = 1.2 ev σac 10kHz
1E-10 1
10 100 Frequency (kHz)
1E-5
1E-6
1E-9 0.000
1E-4
1E-5
1E-8
0.1
2303
σac 100kHz
1E-11
1000
1.0
1.5
2.0
2.5
3.0
3.5
1000/T (°K)-1
0.025
0.020
325°C 350°C 400°C 450°C 500°C 550°C
350°C 400°C 450°C 500°C 550°C
1E-3
M``
σac (Scm-1)
0.015
0.010
1E-4
1E-5
0.005 1E-6
0.000 0.000
0.005
0.010 M`
0.015
0.020
0.025
Fig. 4. (a) Complex modulus formalism of 8ScSZ at various temperatures. (b) Modulus loss spectra 8ScSZ as a function of frequency.
The pattern of variation for 8ScSZ indicates strong conductivity dispersion in the low-frequency region. This behavior may be attributed to the presence of space charge in the material. The modification of the conductivity spectrum with rise in temperature has characterized by a low-frequency dispersion followed by a high-frequency plateau region at elevated temperatures. Low-frequency conductivity dispersion has been attributed to be due to the contribution of space charge whereas high-frequency plateau may be related to contribution of O2 ions conduction. The doping of rare earths changes the crystal structure matrix of the zirconia. The substitution of Zr4+ by Sc3+ causes the formation of oxygen ion vacancies (equal to half the amount of Sc3+ ions) to maintain the electrical neutrality. These O2 vacancies are mobile at the elevated temperature and give rise to oxygen ionic conductivity. The defects formation reaction in Sc2O3-doped ZrO2 can be written in Kroger and Vink
0.1
1
10 100 Frequency (kHz)
1000
Fig. 5. (a) Ac conductivity plots of 8ScSZ as a function of temperature. (b) Ac conductivity plots of 8ScSZ as a function of frequency.
notation [22]. 0
x Sc2 O3 ¼ 2ScZr þ V 0 þ 3O0 .
(3) 0
Due to columbic and elastic attractive forces between ScZr and V 0 , we can postulate the existence of two associates 0 0 ScZr þ V , (4) 0 ¼ ScZr V0 and 0 0 x ScZr þ V . 0 ¼ 2ScZr V0
(5)
At lower temperature, association is almost complete. At 0 higher temperature, the complex dissociate into ScZr and V0 . The conductivity can be explained by the following equation: s ¼ qmV 0 ,
(6)
where m is mobility of the charged ions, q the effective charge and V 0 the concentration of oxygen ion vacancies.
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This behavior of ac conductivity spectrum is governed by Jonscher’s universal power law: sac ¼ sdc+Aon, where A is a thermally activated constant depending upon temperature [23,24]. The frequency at which change in slope of the pattern occurs is known as hopping frequency (op). These results suggest that electrical conduction in the material takes place via hopping mechanism. Concerning the linear region at high frequencies, it has been previously observed in different materials and proposed to be a universal feature in ionic conductor [25]. Fig. 6(i) shows that the dc conductivity of 8ScSZ increases linearly with increase in temperature. Activation energy calculated from the Arrhenius plots are wellmatched with the activation energy calculated from the relaxation time of different electrical mechanism. The value of dc conductivity is 0.002 S/cm, which is better than the earlier reported values at 525 1C. This enhancement in dc
0.01 RG RGB
1E-3 Ea=1.16 ev for grain Ea=1.22 ev for grain boundary
σdc (scm-1)
1E-4
conductivity may be due the smaller particle size of the 8ScSZ. Fig. 6(ii) shows the typical variation of relaxation time (t) as a function of temperature for c-zirconia. It indicates that the relaxation time is pretty small at higher temperatures in comparison to that at lower temperatures. The inverse of frequency region (omax), where the impedance loss spectra (Z00 ), electric modulus spectra (M00 ) and imaginary part of electrical conductivity spectra shows a maximum loss in the characterizing material is called its relaxation time which is derived from Eq. (1). The activation energy calculated from relaxation spectra matched well with activation energy of ac and dc conductivity in the same temperature region (Table 2). The relaxation time basically gives an estimate of the dynamics of the electrical relaxation process occurring in the material. Higher the value of t, slower is the electrical relaxation process and vice versa. The results obtained in the present studies indicate, therefore, that the rate of electrical conduction would be high at higher temperature. The relaxation time for conducting ions becomes more prominent for grain boundary conduction than that of the grain at elevated temperature. The activation energy calculated from relaxation time graph well-matched with ac and dc conductivity of the materials.
1E-5
3.5. Complex conductivity formalism 1E-6 1E-7 1E-8 1E-9 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 103/T (°K)-1
Fig. 7 shows the imaginary part of conductivity of the 8ScSZ. The plot indicates the frequency dispersion in lowfrequency domain whereas complete merger in the highfrequency region (o400 1C). This phenomenon indicates the occurrence of grain boundary relaxation in the sample [26], which is seen in the complex impedance plot in Fig. 3. The plot shows the characteristic frequency which is shifted towards the high-frequency region with increase in
350°C
Ea (g)=1.21 eV
1E-3
400°C
1E-3
Ea (gb)=1.14 eV Ea (σ``)=1.24 eV
450°C
Ea (M``)=1.14 eV
500°C 550°C
1E-4 σ``
τ (second)
1E-4
1E-5
1E-5 1E-6 1E-6 1E-7 1.2
1.3
1.4
1.5 103/T
1.6
1.7
1.8
1.9
(°K)
Fig. 6. (i) Dc conductivity plots of 8ScSZ (for both grain and grain boundary) as a function of temperature. (ii) Relaxation time graphs of 8ScSZ form different conduction mechanism.
1E-7 0.1
1
10 100 Frequency (kHz)
1000
Fig. 7. Frequency dependence conductivity s00 (u) of 8ScSZ as a function of frequency at different temperature.
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temperature. Frequency-independent conductivity has been found at elevated temperature (4400 1C) and high frequency region (4100 kHz) which is the special feature of ionic conductor [27,28]. At temperature above 400 1C the grain boundary effects modified this plateau in two different frequency-independent (dc conductivity) regions on both side of grain boundary relaxation. The lowfrequency part reflects the properties of low-conducting regions between the grains whereas high-frequency values give the intrinsic conductivity of mobile ion. Activation energy calculated from this admittance graph matched well with impedance loss spectra. Interestingly, our data on conductivity relaxation show Arrhenius behavior for the relaxation time. The nature of conductivity relaxation in ionic conductors has a complexity beyond the expectations from the crystalline translational order. In fast ionic conductors, crystalline in nature, the number of available sites exceeds the number of mobile ions and they cannot be unambiguously arranged in an optimized manner; in this sense, ionic conductors are said to be characterized by positional disorder [29]. 4. Conclusion We have prepared the nanocrystalline ionically conducting 8ScSZ using co-precipitation technique. Its electrical properties have been investigated through various tools of IS. It has been found that 8ScSZ shows grain, grain boundary and electrode–electrolyte effect in the impedance spectra whereas absence of grain boundary and electrode–electrolyte effects in the master modulus formalism. Absence of grain boundary in master modulus formalism indicates the very little role of the grain boundary capacitance. The frequency-dependent conductivities and dielectric permittivity were measured, which reveals two relaxations in the documented spectra. The grain (bulk) and grain boundary conductivity are calculated from the complex impedance spectra and compared with the published data. The frequency-dependent conductivity are well-described in terms of universal dielectric response. The temperature dependence of relaxation time is calculated from impedance loss spectra, modulus loss spectra, conductivity spectra and activation energy calculated from all these mechanisms are matched well with each other. It can be concluded that ac and dc conductivity in the material matrix are governed by the same microscopical mechanism. Both ac and dc conductivity follows Arrhenius-type thermally activated conduction above 400 1C. Complex conductivity spectra showed the typical ionic conduction through electrolyte.
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Acknowledgments This investigation was supported by Human Resource Development (HRD) with financial aid from the Council of Scientific and Industrial Research (CSIR), New Delhi. Authors also gratefully acknowledge the supports of Prof. R.N.P. Choudhary, Physics Department (Ferroelectric Lab), IIT Kharagpur. References [1] F. Boulc’h, E. Djurado, Solid State Ionics 157 (2003) 335. [2] D.S. Lee, W.S. Kim, S.H. Choi, J. Kim, H.W. Lee, J.H. Lee, Solid State Ionics 176 (2005) 33. [3] K. Huang, R.S. Tichy, J.B. Goodenough, J. Am. Chem. Soc. 81 (1998) 2565. [4] P. Huang, A. Petric, J. Electrochem. Soc. 143 (1996) 1644. [5] K. Nomura, S. Tanase, Solid State Ionics 98 (1997) 229. [6] S.P.S. Badwal, F.T. Ciacchi, D. Milosevic, Solid State Ionics 136 (2000) 91. [7] S.P.S. Badwal, K. Foger, Mater. Forum 21 (1997) 187. [8] J.R. Macdonald, W.B. Johnson, in: J.R. Macdonald (Ed.), Impedance Spectroscopy, Wiley, New York, 1987, p. 1. [9] M.J. Bannister, P.F. Skilton, J. Mater. Sci. Lett. 2 (1983) 561. [10] Y. Mizutani, M. Kawai, K. Nomura, Y. Nakamura, O. Yamamoto, Jpn. Proc. Electrochem. Soc. 40 (1997) 196. [11] Y. Mizutani, M. Kawai, K. Nomura, Y. Nakamura, O. Yamamoto, Jpn. Proc. Electrochem. Soc. 95 (1995) 301. [12] L.R. Jones, P.R. Ingel, US Patent no. PAT-APPL-7-199 815, 1988, p. 24. [13] D. Lee, I. Lee, Y. Jeon, R. Song, Solid State Ionics 176 (2005) 1021. [14] K. Nomura, Y. Mizutani, M. Kawai, Y. Nakamura, O. Yamamoto, Solid State Ionics 132 (2000) 235. [15] POWDMULT: An Interactive Powder Diffraction Data Interpretation and Indexing Program, Version 2.1, E. Wu School of Physical Sciences, Flinder University of South Australia, Bradford Park, SA, Australia. [16] D. Ravaine, J.L. Souquet, P. Hagenmuller, W.V. Gool, Solid Electrolytes, Academic Press, New York, 1978, p. 277. [17] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171. [18] C.T. Moynihan, J. Non-Cryst. Solids 172 (1994) 1385. [19] S.R. Elliott, J. Non-Cryst. Solids 170 (1994) 97. [20] K.C. Sobha, K.J. Rao, Solid State Ionics 81 (1995) 145. [21] J.M. Bobe, J.M. Reau, J. Senegas, M. Poulain, Solid State Ionics 82 (1995) 39. [22] S. Sen, R.N.P. Choudhary, A. Tarafdar, P. Pramanik, J. Appl. Phys. 99 (2006) 124114. [23] A.K. Jonscher, Nature 267 (1977) 673. [24] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983. [25] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [26] S.P.S. Badwal, Appl. Phys. A 50 (1990) 449. [27] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [28] O. Kanert, J. Steinert, H. Jain, K.L. Ngai, J. Non-Cryst. Solids 130 (1991) 1001. [29] K. Funke, Prog. Solid State Chem. 22 (1993) 111.