3Cu3Ti4O12 ceramic

Materials Research Bulletin 88 (2017) 320–329

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Dielectric relaxation behavior and mechanism of Y2/3Cu3Ti4O12 ceramic Jianming Denga , Laijun Liua,* , Xiaojun Suna , Saisai Liua , Tianxiang Yana , Liang Fanga , Brahim Elouadib a Key Laboratory of Nonferrous Materials and New Processing Technology, Ministry of Education, College of Materials Science and Engineering, Guangxi Universities Key Laboratory of Non-ferrous Metal Oxide Electronic Functional Materials and Devices, Guilin University of Technology, Guilin 541004, PR China b Laboratory of Chemical Analysis Elaboration and Materials, Engineering (LEACIM), Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 01, France

A R T I C L E I N F O

Article history: Received 29 July 2016 Received in revised form 10 November 2016 Accepted 8 January 2017 Available online 9 January 2017 Keywords: Y2/3Cu3Ti4O12 Ceramics Scaling behavior Polaron hopping Dielectric relaxation

A B S T R A C T

Y2/3Cu3Ti4O12 (YCTO) ceramics were sintered in air (YCTO-air) and pure O2 atmosphere (YCTO-O2), respectively. It was found that the permittivity and dielectric loss of YCTO-O2 were decreased drastically in low frequency. The frequency dependent impedance (Z00 ) and modulus (M00 ) spectra of YCTO-air and YCTO-O2 show a thermal activated process. The scaling behavior of both Z00 and M00 spectra further suggest that the distribution of relaxation times is temperature independent. The Cole–Cole plot in impedance formalism shows that electrical response of the samples originates from both grains and grainboundaries. Conductivity (s 0 ) spectra follow Universal Dielectric Repose law. The short-range translation hopping assisted by small polaron hopping mechanisms for YCTO-O2. Moreover, the scaling behavior of s 0 spectra further confirms that the distribution of local electrical response time is temperature independent. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction The search for new high performance dielectric materials, exhibiting good temperature and frequency stability, colossal permittivity (er > 1000) as well as sufficiently low dielectric loss, continues to arouse considerable interest motivated by their myriad device miniaturization and high-energy-density storage applications [1–3]. The compounds in the ACu3(Ti, Ru)4O12 (A = Bi2/ 3, Y2/3, La2/3, Pr2/3) system crystallize as cubic perovskite-related structures in space-group Im-3 [4], as shown in Fig. 1. Recently, Y2/ 3Cu3Ti4O12 (YCTO) ceramics, as a member of the ACu3Ti4O12 compounds, have been reported to exhibit a giant dielectric permittivity (er > 10,000) with a relatively low dielectric loss (0.033 at 1 kHz) and a good temperature stability [5]. However, a systematic understanding on the electrical properties of the ACu3Ti4O12 compounds is still lacking up to now. Impedance spectroscopy has been widely used in the last two decades, being a powerful technique to study the dielectric behavior and analyze the microstructure-property relationship

* Corresponding author. E-mail address: [email protected] (L. Liu). http://dx.doi.org/10.1016/j.materresbull.2017.01.005 0025-5408/© 2017 Elsevier Ltd. All rights reserved.

of polycrystalline ceramic materials [6–9]. Impedance spectroscopy study of the Pr2/3Cu3Ti4O12 have been widely carried out [10]. The dielectric relaxation of the Bi2/3Cu3Ti4O12, La2/ 3Cu3Ti4O12 and W-doped CaCu3Ti4O12 ceramics are found to be greatly affected by the Maxwell-Wagner effect [11–14]. It is suggested that the grain boundary or electrode interface play important roles on the high dielectric response. For most perovskite oxides, such as SrTiO3, BaTiO3, K0.5Na0.5NbO3, oxygen vacancy will be created at high temperature due to low partial pressure of oxygen during sintering [15–17]. However, the grain boundaries of the oxides can be re-oxidized during cooling. Consequently, the conductivity and capacitance between grains and grain boundaries are different, which results in MaxwellWagner effect or positive temperature coefficient resistance in these oxides. Up to now, the relationship between dielectric relaxation mechanism and microstructure (grains and grain boundaries) in complex perovskite oxides, such as ACu3Ti4O12 has not been well understood, which is both physically interesting and technically important. In this work, Y2/3Cu3Ti4O12 (YCTO) ceramic was sintered in air and pure O2 atmosphere to create different microstructure morphologies and oxygen-vacancy concentrations. The impedance, modulus, and alternate current (ac) conductivity properties

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Fig. 2. XRD patterns of the YCTO-air and YCTO-O2 (a) 2u from 10 to 80 and (b) 2u from 47 to 65 .

fired at 650  C for 30 min. The dependence of the dielectric permittivity on temperature was measured with precision impedance analyzer (Agilent 4294A, USA) in a temperature range from 329 to 409 K. Fig. 1. Crystal structure of the compounds in ACu3Ti4O12 system. For A = Bi2/3, Y2/3, La2/3, and Pr2/3, 1/3 of A sites are vacant. The Ti atoms sit at the center of the TiO6 octahedra.

of the YCTO have been investigated as a function of the frequency (40–106 Hz) and temperature (329–409 K). 2. Experimental procedure The YCTO ceramics were prepared by solid-state reactions. The starting materials, high purity Y2O3 (99.99%), TiO2 (99.99%) and CuO (99%) were mixed according to the stoichiometric YCTO composition. After ball-milled in alcohol for 24 h, the slurry was dried, then calcined in a closed environment at 930  C for 2 h in air. The calcined powder was ball-milled and dried again to obtain homogeneous powder. Pellets with 12 mm in diameter and about 1.10 mm in thickness were uniaxially pressed at 350 MPa using 5% PVA binder. Slow heating at 550  C for 2 h burned out the binder. These pellets were sintered at 1020  C in air and in O2 (99.99% purity) for 10 h, respectively, and then cooled to room temperature in furnace. Crystal structures of the YCTO ceramics were identified by X-ray diffraction (XRD, PANalytical X’Pert PRO) using Cu Ka radiation (l = 1.5406 Å) in the range of 2u = 10–80 . The surface microstructure of the samples was examined using a field emission scanning electron microscope (FE-SEM, Model S4800, Hitachi, Japan). Composition analysis was performed using energy-dispersive spectroscopy (EDS, IE 350; INCA, Oxford, U.K). Silver paste electrodes were formed at the two surfaces of the samples and

3. Results and discussion XRD patterns of the YCTO-air and YCTO-O2 are shown in Fig. 2a. A cubic symmetry is detected without any secondary phase. The pattern is identical to the YCTO-air and no systematic variation of the lattice parameter is observed. A careful examination of the XRD patterns reveals that the diffraction peaks of the YCTO-O2 shift toward high angle, evident from the enlarged view of the peaks (400) and (422) shown in Fig. 2b. Lattice parameters calculated from the XRD patterns using Cohen’s least mean square method, which are 7.387(7) and 7.386(4) Å for the YCTO-air and YCTO-O2, respectively. These values are comparable to the values reported in the literature, i.e., 7.393 Å for CaCu3Ti4O12 (CCTO) [18], 7.371 Å for YCTO [19] and 7.3797 Å for Na0.5Y0.5Cu3Ti4O12 (NYCTO) [20]. The decrease in lattice parameter with the Y3+ concentration might be attributed to the different ionic radii between the Ca2+ and Y3+ at 6fold coordinate are 0.102 and 0.090 nm, respectively. Slight difference of the lattice parameters between YCTO by this work and Na0.5Y0.5Cu3Ti4O12 due to similar ionic radii between the Na+ and Y3+. However, the lattice constants are not in agreement with literature value of YCTO. This discrepancy may be due to a possible sites electivity of Y3+ ions on Cu and Ti sites in the unit cell. Fig. 3 shows the scanning electron micrograph of the samples. Two kinds of microstructure morphology and size distribution can be found. The bigger grains show good crystallization and perfect cubic-like appearance, which have the same size in both YCTO-air and YCTO-O2. The smaller ones include clear growth steps on their

Fig. 3. The scanning electron micrograph of the YCTO-air (a) and YCTO-O2 (b).

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surface. It suggests that the latter could coarsen and ripen into the former. As shown in Fig. 3b, the sample sintered in O2 atmosphere has fewer pores, which implies it is more compact. The density value of sample sintered in pure O2 atmosphere reaches about 5.48 g/cm3, and the other sample sintered in air is 5.41 g/cm3. Compared with the morphology of YCTO-air, both number and size of uncured grains is much less in that of YCTO-O2, indicating oxygen increases the coarsening velocity of uncured grains. In order to confirm the composition of the uncured grains in YCTO-O2, back scattered electron micrograph (BSEM) image and

energy dispersive spectrometer (EDS) analysis were carried out, as shown in Fig. 4. The smaller grain is marked as “A” while the large grains marked as “B”. Grain “A” shows much light contrast compared with grain “B”, suggesting they have different stoichiometry. According to the EDS analysis, the grain “A” is Cu-rich phase. It is known that a small amount of CuO can act as a sintering aid for various ceramics (e.g., BaTiO3-based ceramics) to promote the grain growth and ceramic densification due to its low melting point and liquid-phase effect [21], which is in agreement with the results obtained in Fig. 3. The CuO segregation effect is considered to play very important roles in the formation of the insulating grain boundaries and has a significant influence on dielectric permittivity due to the evaporation of CuO phase at high temperature [22]. A small amount of oxygen loss from the lattice during sintering may be generate the electronic charge carriers [23]. While the ratio of Y: Cu:Ti:O of “B” region is approximate 2/3:3:4:12, which was consistent with the composition of the Y2/3Cu3Ti4O12 stoichiometry. Both YCTO-air and YCTO-O2 show quite high dielectric permittivity, as shown in Fig. 5, for the frequency dependence of (a) the real part e0 and (b) loss tangent and (c) the imaginary part e00 of the complex permittivity of two kinds of YCTO samples sintered in different atmospheres, at room temperature. The solid curves are the best fits to Eqs. (4) and (5) for e0 (a) and e00 (c), respectively. However, a great difference occurs at low frequency <105 Hz, e0 and the loss tangent (tan d) were decreased in YCTO-O2, e.g., the dielectric permittivity of the YCTO-air is 50,000 while it is 8000 for YCTO-O2 at 1 kHz, which are higher than that of the CCTO [24] and NYCTO [20] in Table 1. These features were associated with the oxygen vacancy concentration at grain boundaries. A decrease in low-frequency tan d was caused by enhancement of grain boundaries resistance, which was due to filling oxygen vacancies at grain boundaries [25]. With increasing frequency, the dielectric permittivity of the samples decreased slowly between 1 kHz and 1 MHz, while the dielectric permittivity decreased drastically when frequency was higher than 2 MHz, corresponding to a peak of dielectric loss. Similar to other ACu3Ti4O12 oxides [26–28], the two samples could have the same relaxation behavior associated with grain response. In CCTO ceramics, the complex dielectric permittivity may primarily be attributed to interfacial polarization at grain boundaries [9]. Interestingly, two dielectric relaxation processes occurred at low frequency, which were attributed to grain boundary responses. Consequently, the difference on dielectric response at low frequency originates from grain boundaries. To analysis dielectric dispersion of YCTO, we used the Cole–Cole relaxation equation in Fig. 5a and c. Previous dielectric dispersion model where it is assumed that the effect of the electrical conduction is ignored [29],

e ¼ e1 þ

es  e1

1 þ ðivt Þ1a

ð1Þ

where es is the static permittivity, e1 is the permittivity at very high frequencies, v is the angular frequency, t is the mean relaxation time, and a is the Cole–Cole parameter. A contribution term by the electrical conduction is generally added to the relaxation equation when the electrical conductivity is not ignored, as shown in Eq. (2),

e ¼ e1 þ

Fig. 4. BSEM images (a) and EDS analysis (b) and (c) of the YCTO-O2.

es  e1 s j s 1a e 0v 1 þ ðivt Þ

ð2Þ

where s(0 < s < 1) is a constant and s  (s  ¼ s 1 þ js 2 ) is the complex conductivity. Where s1 is the free charge carrier and s2 is the conductivity due to the space charges. This relationship shows that the conductivity may have contributions to the real and imaginary part of the permittivity. Similar models including the

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Fig. 5. Frequency dependence of (a) the real part e0 and (b) loss tangent and (c) the imaginary part e00 of the complex permittivity of two kinds of YCTO samples sintered in different atmospheres, at room temperature (300 K). The solid curves are the best fits to Eqs. (4) and (5) for e0 (a) and e00 (c), respectively.

complex conductivity were proposed by Kang et al. [30] to analyze the dielectric dispersion in ionic conductors. In such materials, the free carrier localization at defect sites and interfaces imaginary conductivity can make large contribution to the real part of the dielectric permittivity. This is the physical model that will be used in the following analysis [31]. The complex permittivity may be decomposed into real and imaginary parts, i.e.,

e ¼ e0  ie00

ð3Þ

e ¼ e1 þ

i h ðes  e1 Þ 1 þ ðvt Þ1a sinðap=2Þ

times t Z are calculated using the relation, t Z ¼ 1=2pf m , where t Z Z

Z fm

are the dielectric relaxation times and is peak frequency of Z00 . The relaxation time at various temperatures are obtained and plotted as a function of the reciprocal temperature is shown in Fig. 6c. It should be noted that the relaxation times t Z can be well fitted with the Arrhenius relation t Z ¼ t Z0 expðEZt =kB TÞ, where t Z0 is the pre-exponential factor, kB and T are Boltzmann constant and

where 0

temperature, indicating the electrical response belongs to thermal activated process. This is possibly due to the presence of space charge at the grain boundaries [32–34]. The dielectric relaxation

s2

þ 1 þ 2ðvt Þ1a sinðap=2Þ þ ðvt Þ22a e0 vs

ð4Þ

and   ðvt Þ cos ap s1 e00 ¼ ðes  e1 Þ þ ap 2 1a sin 2 þ ðvt Þ22a e0 vs 1 þ 2ðvt Þ 1a

ð5Þ

Analysis of our experimental data was carried out on the basis of Eqs. (4) and (5). Typical fitting results are shown in Fig. 5a and c for YCTO. It is seen that the experimental data are well fitted to this model. Fig. 6 shows frequency dependence of imaginary part of impedance (Z00 ) at various temperatures. Strong loss peaks appears in the measured frequency range in both YCTO-air and YCTO-O2, as shown in Fig. 6a and b, respectively. The loss peak moves to higher frequency with a sharp fall in intensity with increasing Table 1 The e0 (at 1 kHz at room temperature), activation energy for dielectric relaxation (Ea), activation energy for conduction inside grain (Eg) and grain boundary (Egb) for ceramic samples. Samples

e0

Ea (eV)

Eg (eV)

Egb (eV)

YCTO-air (this work) YCTO-O2 (this work) CCTO [18,24] NYCTO [20,32] YCTO [19,33]

55470 8066 5439 11038 7835

0.586 0.485 0.096 0.163 1.200

0.453 0.361 0.082 – –

0.513 0.495 0.692 0.639 0.690

absolute temperature, respectively, and EZt is the activation energy. By fitting the Arrhenius plot of relaxation time against temperatures, the activation energy of the samples can be figured out (Fig. 6c), in which the activation energy EZt of 0.586 eV for YCTO-air and that of 0.485 eV for YCTO-O2. These values are comparable to reported values of CCTO [18,24], NYCTO [20,35] and YCTO [19,36] for the activation energy of dielectric relaxation as shown in Table 1. In addition, the full width at half maxima calculated from the impedance loss spectra (Z00 vs log f) are greater than 1.144 decades (ideal Debye relaxation). The non-Debye relaxation feature might be cause by an inherent nonexponential process such as the nonuniformities in the material microstructure [37,38]. Furthermore, the Z00 values for all temperatures also merge together at high frequency. It suggests that a possible release of space charges at the grain boundaries. The above impedance spectra confirms that the polydispersive nature for the dielectric relaxation of the YCTO samples. In order to investigate whether the distribution of relaxation times is temperature dependent or not, we plotted the Z00 (v, T) data in scaled coordinates, i.e., Z00 (v, T)/Z00 max and log(v/vmax), where v is the angular frequency, T is absolute temperature and vmax corresponds to the frequency of the loss peak. If entire the impedance loss data are collapsed into one master curve, it suggests that the distribution of relaxation times is temperature independent [39]. Electric impedance spectra of YCTO-air and YCTO-O2, corresponding to Fig. 6d and e, respectively, have been shown in a scaled coordinate. All peaks indeed overlap into one

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master curve at different temperatures. It suggests that the dynamic processes of the charges occurring at different time scales exhibit the same activation energy and that the distribution of the relaxation times is temperature independent. The Cole–Cole plots of YCTO-air and YCTO-O2 are shown in Fig. 7a and b, respectively. There are three dielectric relaxations according to the plots. The large arc is attributed to two grain boundary responses, while the non-zero intercept at high frequency (106 Hz) associates with grain response (inset of Fig. 7a and b), which are well consistent with the above results in Fig. 5. The resistances of both grain and grain boundary decrease with an increase of temperature. In order to further analyze the impedance data and establish the correlation between microstructure and electrical properties, we used an equivalent circuit based on the brick-layer model [40,41] as shown schematically in Fig. 7c. In this circuit, (Rg, Cg) represents the resistance and capacitance of grains, respectively. (Rgb, Cgb) and (Rgb*, Cgb*) represent the resistance and capacitance of grain boundaries, respectively, CPE stands for a constant phase element, indicating the departure from ideal Debye-type model. CPE is the modified capacitance of the sample with an admittance YCPE = A0(jv)n, where A0 and n are frequency independent parameters which usually depend on temperature, v is the angular frequency v = 2pf pffiffiffiffiffiffiffi and j = 1, A0 determines the magnitude of the dispersion and n (0  n  1) is a dispersion parameter. Normally, n = 0 describes an ideal resistor, while n = 1 is an ideal capacitor [40]. Therefore, the

equivalent circuit can be expressed as: Z  ¼ Z 0  jZ 00 ¼

1 R1 g þ jvC g

þ

1 n R1 gb þ jvC gb þ A0 ðjvÞ

ð6Þ

The fitted value of n of CPE is in the range of 0.38–0.60 and increases with increasing temperature. The fitted the Arrhenius plot of sample resistance against temperatures, as shown in Fig. 7d. The fitting results indeed display that Rgb is higher than Rg. The difference between Rgb and Rg will lead to the piling up of space charges at the grain boundaries and producing polarization (Maxwell-Wagner effect) [42,43]. Fig. 7d and e show that both Rg and Rgb also obey the Arrhenius relaxation R ¼ R0 expðEZ =kB TÞ, where R is the resistance of the ceramic sample, R0 is the prefactor and EZ is the activation energy. By fitting the Arrhenius plot of ceramic resistances against temperatures, the activation energy of the samples can be figured out (Fig. 7), in which the activation energy of grain are 0.453 eV and 0.361 eV for YCTO-air and YCTOO2, respectively. Slight difference of the activation energy between them indicates they could be attributed to the same physical mechanism (hopping of oxygen vacancies, electrons and holes) [44]. However, the activation energy of grain boundary for the samples YCTO-air and YCTO-O2 are 0.513 eV and 0.495 eV, respectively as shown in Table 1. Slight difference of the activation energy between them indicates they could be attributed to the same physical mechanism (hopping of oxygen vacancies, electrons and holes). In the previous discussion, the dielectric relaxation has

Fig. 6. Frequency dependent Z00 at different temperatures of (a) the YCTO-air and (b) the YCTO-O2 (c) the temperature dependence of the relaxation times of the YCTO-air and YCTO-O2, scaling behaviors of Z00 spectra of (d) the YCTO-air and (e) the YCTO-O2.

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been investigated in the complex impedance Z*. In order to distinguish the microscopic processes responsible for localized dielectric relaxations and the long-range conduction, we analyzed the complex impedance (Z*) and electrical modulus (M*). The electrical modulus of the equivalent circuit in Fig. 7c is M* = jvC0Z*, pffiffiffiffiffiffiffi where v is the angular frequency v = 2pf and j = 1. C0 = e0S/d is the empty cell capacitance, where S is the sample area and d is the sample thickness. The electric modulus is especially useful for analyzing electrical relaxation processes whose measurement is compromised by high capacitance effects [45,46]. The maximum values of M00 are proportional to the reciprocals of the associated capacitance. The capacitance related to observed M00 max strongly depended on temperature as shown in Fig. 8. The electric modulus can be expressed as the Fourier transform of a relaxation function wðtÞ [47] 2 3   Z1 df dt5 ð7Þ M ¼ M1 41  expðvtÞ  dt 0

where the function wðtÞ is the time evolution of the electric field within the materials and is usually taken as the KohlrauschWilliams-Watts function [48] h i ð8Þ fðtÞ ¼ exp ðt=t m Þb where tm is the conductivity relaxation time and the exponent b(0  b1) indicates the deviation from Debye-type relaxation. The value of b could be determined by fitting the experimental data in the above equations [49], but it is desirable to reduce the

325

number of adjustable parameters while fitting the experimental data. Keeping this point in view, the electric modulus behavior of the present glass system is rationalized by invoking the modified KWW function suggested by Bergman. The imaginary part of the electric modulus M00 can be defined as [50] M00 ¼

h

ð1  bÞ þ 1þbb

M00max

bðvmax =vÞ þ ðv=vmax Þb

i

ð9Þ

where M00 max is the peak value of M00 , and vmax is the corresponding frequency. The theoretical fit of Eq. (9) to the experimental data is shown in Fig. 8a as the solid lines. It is seen that the experimental data are well fitted to this model. The Arrhenius plot (ln(fmax) versus 1000/T) shown in the inset of Fig. 8a. The activation energy for YCTO-air is 0.583 eV. In the imaginary modulus spectra versus frequency, the frequency region below peak maximum (lowfrequency) determines the range in which charge carriers are mobile over long distances. At the frequency above peak maximum (high-frequency), the carriers are confined to potential wells, being mobile over short distances. The full width at half maxima calculated from the modulus loss spectra (M00 vs log f) are greater than 1.144 decades, indicating the deviation from Debye-type relaxation and a distribution of relaxation times, which agreed with the Z00 plots. As shown in Fig. 8c, the dielectric relaxation times t M are calculated using the relation, t M ¼ 1=2pf m , where tM M

M fm

is the dielectric relaxation time and is peak frequency of M00 . The M relaxation times t are obtained and plotted as a function of the reciprocal temperature which can be well fitted with the Arrhenius

Fig. 7. Temperature dependence of grain and grain boundary conductivity, (a), (d) for the YCTO-air, and (b), (e) for the YCTO-O2. The inset in (a) and (b) shows an expanded view of the high frequency data close to the origin. (c) equivalent circuit based on the bricklayer model for the impedance spectra.

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M M relation t M ¼ t M 0 expðEt =kB TÞ, where t 0 is the pre-exponential factor, kB and T are Boltzmann constant and absolute temperature,

respectively, and EM t is the activation energy. The corresponding activation energy EM t of YCTO-air is 0.523 eV and that of YCTO-O2 is

0.424 eV are deviated from that from EZt , which indicates that they have the different relaxation mechanism. However, conduction process may be attributed to the same type of charge carriers. This is consistent with the previous results in Fig. 7d. The YCTO-O2 shows similar relaxation properties but with decreased peak frequencies, as shown in Fig. 8b. The M00 (w, T) were plotted in scaled coordinates in Fig. 8d and e, corresponding to YCTO-air and YCTO-O2, respectively. The perfect overlap of the curves for all the different temperatures into a single master curve. The overlapping spectra show that the relaxation dynamics almost stay unchanged with the measurement temperature. Therefore, the scaling behavior for all samples suggests the same dielectric relaxation and conduction mechanisms are involved in these samples regardless of varied temperatures. The slight deviation in YCTO-air at higher frequency implies another relaxation process occurs. The high-temperature curves are not complete due to our instrument limit. Fig. 9 shows the frequency dependence of the ac conductivity (s 0 ) of the YCTO-O2 measured at different temperatures. The ac conductivity s 0 can be calculated by s 0 = Z0 d/[(Z0 )2 + (Z00 )2]S, where the real and imaginary part of the electric impedance Z' and Z00 , respectively, d and S are the thickness and electrode area of sample, respectively. Extrapolation of this part toward lower frequency gives s dc [51]. Fig. 9a shows that both the length and the

magnitude of frequency independent (dc) conductivity plateau increase with increasing temperature. The curves tend to flatten with increasing temperature, especially in the low frequency regions, suggesting dc conduction behavior. The frequency independent plateau in the 1–100 kHz range indicates relaxation of the bulk conduction, while at lower frequency there is a strong frequency dependence associated with the dispersion toward relaxation of the grain boundary. The experiment conductivity data were fitted to the universal power law [52]

s 0 ðf Þ ¼ s dc þ s 0 f s

ð10Þ

where s dc is the dc bulk conductivity, f is the frequency, s dc is a constant, and 0  s  1.The s0fs term is an empirical expression representing the transport properties of polarons, electrons, and ions. The temperature variation of s dc thus obtained follows the Arrhenius law given by:   E s dc ¼ s 0 exp  con ð11Þ kB T Where s0 is the preexponential factor, kB is the Boltzmann constant, T is absolute temperature, and Econ is the dc conduction activation energy. Econ was calculated for the YCTO-O2 at different frequencies from the slopes of straight lines obtained from lns dc  1000/T plot in Fig. 9b. As shown in Fig. 9b, the dc activation energy Econ calculated from least-squares-fit to the data points is 0.514 eV, which is consistent with that from impedance spectra. This further reveals that the conduction behavior and relaxation process should be attributed to the same electric entities. When the conductivity axis is scaled with respect to s dc, a perfectly superimposed master

Fig. 8. Frequency dependent M00 at different temperatures of (a) the YCTO-air and (b) the YCTO-O2 (c) the temperature dependence of the relaxation times of the YCTO-air and YCTO-O2, scaling behaviors of M00 spectra of (d) the YCTO-air and (e) the YCTO-O2. The solid lines are the theoretical fits using Eq. (9) in the text. Inset shows the Arrhenius relation of fmax vs 1000/T of the YCTO-air.

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Fig. 9. (a) Real part of the ac conductivity s 0 at different temperatures of the YCTO-O2, the temperature dependence of the (b) dc conductivity s dc obtained from fitting universal power law to the ac conductivity (c) Crossover regime of the conductivity master curves of YCTO-O2 at various temperatures.

curve for the conductivity spectra is obtained, as shown in Fig. 9c. This result implies that the relaxation mechanism is temperature independent under conductivity formalism. A detail analysis of the scaled data reveals that scaling law [53,54] is exactly valid only at high values of f/(s dc T x), while deviations occur in the crossover dc regime from dc to dispersive conductivity. This is seen more clearly when the crossover regime is replotted at higher resolution, see Fig. 9c. Obviously, with increasing temperature, the curvature of the master curves in the log–log representation increases. Therefore, the extension of the crossover regime on the frequency scale increasing temperature. This suggests that in the crossover regime, the ion transport

mechanism depends on temperature, while the transport mechanism is universal at shorter time scales. In Fig. 10, the variations of the normalized parameter Z00 /Z00 max and M00 /M00 max as a function of logarithmic frequency measured for (a) YCTO-air and (b) YCTO-O2 at 369 K are shown. It was observed that the frequency gap (Df) between Z00 /Z00 max and M00 /M00 max peaks is significantly decreased by sintering in O2. In general, the overlapping of peaks of Z00 /Z00 max and M00 /M00 max is an evidence of a long range conductivity [55]. However, for the present system, they do not overlap in two kinds of samples, suggesting the components from localized relaxation. In this case, the decreased Df values by sintering in O2 indicate that the conduction process becomes less

Fig. 10. Frequency dependence of normalized peaks, Z00 /Z00 max and M00 /M00 max for (a) YCTO-air and (b) YCTO-O2 at 369 K.

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localized when grains or grain boundaries re-oxidation [28]. In order to mobilize the localized electron, the assistance of lattice oscillation should be required. In the circumstance, electrons are considered not only to move by themselves but also by hopping motion activated by lattice oscillation. That is to say, the conduction mechanism is considered as the short-range translation hopping of small polaron between localized states. The magnitude of the activation energy in Fig. 9b suggests that the carrier transport is due to the hopping conduction. 4. Conclusions The impedance spectroscopy of polycrystalline YCTO ceramics was investigated as a function of temperatures from 329 to 409 K. The frequency dependent impedance (Z00 ) and modulus (M00 ) spectra show that for YCTO-air and YCTO-O2, the electrical responses of YCTO are thermal activated. The scaling behavior of Z00 and M00 spectra further suggest that the distribution of relaxation times is temperature independent. The complex impedance plots show that the electric response of YCTO is contributed by both grains and grain-boundaries. The frequency dependent conductivity (s 0 ) spectra follow the universal power law. The fitting results of s 0 spectra show that the short-range translation hopping assisted by small polaron hopping mechanisms for YCTO-O2. Moreover, the scaling behavior of s 0 spectra further confirms that the distribution of local electrical response times is temperature independent. The YCTO-O2 shows similar thermally activated electrical responses and scaling behaviors as well. Acknowledgments This work was financially supported by the Natural Science Foundation of China (Grant Nos. 51002036, 11264010, 21061004 and 50962004), and by the Natural Science Foundation of Guangxi (Grant No. BA053007). References [1] C.C. Homes, T. Vogt, S.M. Shapiro, S. Wakimoto, A.P. Ramirez, Optical response of high-dielectric-constant perovskite-related oxide, Science 293 (2001) 673– 676. [2] S. Krohns, P. Lunkenheimer, S. Meissner, A. Reller, B. Gleich, A. Rathgeber, T. Gaugler, H.U. Buhl, D.C. Sinclair, A. Loidl, The route to resource-efficient novel materials, Nat. Mater. 10 (2011) 899–901. [3] L.J. Liu, H.Q. Fan, P.Y. Fang, L. Jin, Electrical heterogeneity in CaCu3Ti4O12 ceramics fabricated by sol–gel method, Solid State Commun. 142 (2007) 573– 576. [4] M.A. Subramanian, A.W. Sleight, ACu3Ti4O12 and ACu3Ru4O12 perovskites: high dielectric constants and valence degeneracy, Solid State Sci. 4 (2002) 347–351. [5] P.F. Liang, Z.P. Yang, X.L. Chao, Z.H. Liu, Giant dielectric constant and good temperature stability in Y2/3Cu3Ti4O12 ceramics, J. Am. Ceram. Soc. 95 (2012) 2218–2225. [6] A. Srivastava, A. Garg, F.D. Morrison, Impedance spectroscopy studies on polycrystalline BiFeO3 thin films on Pt/Si substrates, J. Appl. Phys. 105 (2009) 054103. [7] L.J. Liu, H.Q. Fan, X.L. Chen, P.Y. Fang, Electrical properties and microstructural characteristics of nonstoichiometric CaCu3xTi4O12 ceramics, J. Alloy Compd. 469 (2009) 529–534. [8] L.J. Liu, H.Q. Fan, P.Y. Fang, X.L. Chen, Sol–gel derived CaCu3Ti4O12 ceramics: synthesis, characterization and electrical properties, Mater. Res. Bull. 43 (2008) 1800–1807. [9] R. Schmidt, M.C. Stennett, N.C. Hyatt, J. Pokorny, J. Prado-Gonjal, M. Li, D.C. Sinclair, Effects of sintering temperature on the internal barrier layer capacitor (IBLC) structure in CaCu3Ti4O12 (CCTO) ceramics, J. Eur. Ceram. Soc. 32 (2012) 3313–3323. [10] A. Dittl, S. Krohns, J. Sebald, On the magnetism of Ln2/3Cu3Ti4O12 (Ln = lanthanide), Eur. Phys. J. B 79 (2011) 391–400. [11] D. Szwagierczak, Dielectric behavior of Bi2/3Cu3Ti4O12 ceramic and thick films, J. Electroceram. 23 (2009) 56–61. [12] J.J. Liu, C.G. Duan, W.G. Yin, W.N. Mei, R.W. Smith, J.R. Hardy, Large dielectric constant and Maxwell-Wagner relaxation in Bi2/3Cu3Ti4O12, Phys. Rev. B 70 (2004) 144106.

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