Variable-range-hopping conduction and polaron dielectric relaxation in Cu and Nb co-doped BaTiO3

Accepted Manuscript Variable-range-hopping conduction and polaron dielectric relaxation in Cu and Nb codoped BaTiO3 Junwei Liu, Qiaoli Liu, Wenjun Wang, Yue Liang, Dayong Lu, Pinwen Zhu PII:

S0022-3697(18)32012-2

DOI:

https://doi.org/10.1016/j.jpcs.2018.12.036

Reference:

PCS 8852

To appear in:

Journal of Physics and Chemistry of Solids

Received Date: 29 July 2018 Revised Date:

28 December 2018

Accepted Date: 29 December 2018

Please cite this article as: J. Liu, Q. Liu, W. Wang, Y. Liang, D. Lu, P. Zhu, Variable-range-hopping conduction and polaron dielectric relaxation in Cu and Nb co-doped BaTiO3, Journal of Physics and Chemistry of Solids (2019), doi: https://doi.org/10.1016/j.jpcs.2018.12.036. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Variable-range-hopping conduction and polaron dielectric relaxation in Cu and Nb co-doped BaTiO3 Junwei Liu1,2, Qiaoli Liu2, Wenjun Wang2, Yue Liang2, Dayong Lu2,*, Pinwen Zhu1,* 1

State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun

130012, China Research Center for Materials Science and Engineering, Jilin Institute of Chemical Technology,

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2

Jilin 132022, China

Pinwen Zhu Prof.; Ph.D.;

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Corresponding authors： ：

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We declare under our ethical responsibility that this paper is original and is not being considered for publication elsewhere, and that all authors have seen and approved the manuscript.

Tel: +86 15948393088; fax: +86 431 85168881

Dayong Lu Prof.; Ph.D.;

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[email protected]

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E-mail address: [email protected]

Tel: +86 13578509271

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E-mail address: [email protected]

ABSTRACT

BaTi0.7(Cu0.1Nb0.2)O3 ceramic was prepared using a solid-state method and its structure, valence states, conduction mechanism and dielectric properties were investigated in detail. A fine-grained microstructure and a distorted pseudo-cubic perovskite structure were confirmed by scanning electron microscopy, X-ray diffraction analysis and Raman spectroscopy. X-ray photoelectron spectroscopy analysis suggested that Cu in BaTi0.7(Cu0.1Nb0.2)O3 was polyvalent but the valence states of Ti and Nb were invariable. Mott’s variable-range-hopping (VRH) conduction was

ACCEPTED MANUSCRIPT observed. The two colossal dielectric constant plateaus in low- and high-temperature ranges were ascribed to the electrode and grain boundary responses, respectively. The VRH model described the low-temperature relaxation well, indicating that the dielectric relaxation was a polaron relaxation rather than Maxwell–Wagner type. Both grain and grain boundary resistances were well

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fitted by the VRH model, suggesting that the VRH mechanism was tenable in both grain and grain boundaries. The electron paramagnetic resonance signal was ascribed to Cu ions, and the linewidth showed a linear relationship with T−1/4, corresponding to the charge transfer between different valence via Cu+-O-Cu2+ and Cu2+-O-Cu3+ paths. The hopping of carriers was also

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responsible for the conduction and polaron dielectric relaxations.

Keywords: Cu and Nb co-doped BaTiO3; Variable-range-hopping conduction; Dielectric relaxation;

1.

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Electron paramagnetic resonance.

Introduction

Recently, the colossal dielectric constant (CDC) behavior and dielectric relaxations in transition-metal-containing complex perovskites A(B′1/2B″1/2)O3 and A(B′1/3B″2/3)O3 (A = Pb, Ba,

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Sr, Ca; B′ = Fe, Co, Ni, Cu, Mg; B″ = Nb, Ta, Sb, etc.) have been extensively researched [1–4]. These compounds and ATiO3 have typical perovskite structures, and the ionic radii of B′ and B″ cations are similar to that of Ti. Therefore, A(B′1/2B″1/2)O3, A(B′1/3B″2/3)O3 and BaTiO3/SrTiO3 are

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expected to form solid solutions. Several studies on the CDC behavior and dielectric relaxations of these solid solutions have been reported in recent years [5–10], but the mechanisms involved

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remain unclear. Lemanov et al. studied the dielectric relaxations in SrTiO3–SrMg1/3Nb2/3O3 and SrTiO3–SrSc1/2Ta1/2O3 solid solutions, and suggested that local charge compensation was responsible for the relaxation [5]. The high dielectric constant of BaTi0.85(Fe1/2Nb1/2)0.15O3 ceramic was attributed to space-charge carriers polarization by Abdelkafi et al., and the dielectric relaxation and inner grain conductivity showed the same Arrhenius behavior [6]. When the Fe and Nb doping content was high, a CDC plateau caused by the interfacial layer was also observed [7]. Zhao et al. studied BaTi0.9 (Ni1/2W1/2)0.1O3 and found that CDC behavior only existed in samples with larger grain size, and concluded that the dielectric abnormities were mainly attributable to the domain boundary effect [8]. However, Wang et al. and Zhou et al. pointed out that the relaxations in BaTi1−x(Fe0.5Nb0.5)xO3 and BaTi1−x(Co0.5Nb0.5)xO3 were related to the hopping of charge carriers,

ACCEPTED MANUSCRIPT which is an intrinsic effect of the mixed-valent structure [9,10]. Apart from the CDC phenomenon and dielectric relaxations, structural distortion and cation disorder in the above solid solutions have also been observed. Heterogeneous distribution of B-site ions and distortion of the octahedron were confirmed by Raman spectroscopy [11,12]. However,

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despite the effort devoted to interpret the origins of CDC behavior, the lattice-distortion effects on electrical conduction, polarization and dielectric relaxations in these compounds are still undetermined. It is well known that lattice distortion and cation disorder will lead to the localization of charge carriers and the formation of small polarons [13]. Charge hopping between

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these localized states is responsible for conductivity and polarization [14]. Recently, Maurya and coworkers carried out intensive research on low-content Cu and Nb co-doped BaTiO3 ceramics

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and films, which exhibited low dielectric loss and high piezoelectric response with low coercive field, high remanent polarization and excellent switching and hysteresis behavior [12,15–19]. With the assistance of high energy X-ray diffraction (XRD) and Raman spectroscopy, the local structure distortions were found to play a major role in the piezoelectric response [12]. It is well known that Cu2+ in octahedral coordination presents a doubly degenerate ground state

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eg. According to the Jahn–Teller (JT) theorem, the eg state is coupled with the vibrational modes, thereby removing electronic degeneracy and causing a distortion in the octahedral cluster site [20]. Thus, Cu doping would result in a more distorted and disordered structure than Fe, Co or Ni. In

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the event of increased structural distortion, Mott’s variable-range-hopping (VRH) of small polarons sets in at low temperature [21]. However, until now the electrical transport and dielectric

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properties of Cu and Nb co-doped BaTiO3 have not been clearly understood. Therefore, the influence of local structural distortion on the polarization and dielectric relaxation in Cu and Nb co-doped BaTiO3 is worthy of study. In this work, BaTiO3 ceramic with a high level of Cu and Nb doping was prepared using a solid-state reaction method. The CDC behavior and relaxations were observed by broadband impedance spectroscopy. The VRH mechanism was found to depict well the dc conductivity and dielectric relaxation frequencies. The hopping between localized charges due to the distorted lattice played an important role in the origins of electrical conduction, polarization and dielectric relaxation.

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Experimental

2.1. Preparation of (Cu, Nb) co-doped BaTiO3 ceramic The BaTi0.7(Cu0.1Nb0.2)O3 (BTCN) ceramic was prepared by the conventional solid-state reaction method. Starting materials (BaCO3, TiO2, CuO and Nb2O5) with high purity (≥99.9%)

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were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). The reagents were weighted according to their stoichiometry and were calcined at 1373 K for 5 h. The calcined powder was milled again and then pressed into 2-mm-thick pellets with a diameter of 12 mm at 200 MPa. Finally, these pellets were sintered at 1573 K for 12 h in air and cooled at a rate of 100

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K h−1. 2.2. Characterization

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The room-temperature crystal structure of BTCN was identified by XRD (Cu Kα radiation, DX-2700, Dandong, China) with a scanning step size of 0.02° and counting time of 3 s. Rietveld refinement for XRD data was performed using the GSAS-EXPGUI program package [22,23]. The morphology of the ceramic was examined by scanning electron microscope (SEM) (EVO MA10, Zeiss, Germany). Raman spectra using Nd:YAG laser (532 nm) were recorded at different

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temperatures (XploRA, Horiba Jobin Yvon, France). X-ray photoelectron spectroscopy (XPS) measurements were carried out to study the valence states of cations on a Thermo ESCALAB 250Xi spectrometer with Al Kα radiation. The measurement curves of XPS data were fitted by a

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mixed Gaussian–Lorentzian function and a Shirley-type background subtraction was used. The dielectric properties of BTCN were measured on a broadband dielectric spectrometer (Concept 41,

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Novocontrol Technologies, Germany) in a temperature range of 173−473 K and a frequency range of 1 Hz–10 MHz. The dielectric constant (ε), ac conductivity (σac) and impedance (Z) were used to analyze the conductivity and relaxation behavior. On both sides of the ceramic, Ag paste was fired at 573 K for 15 min and used as an electrode. To clarify the electrode effects on dielectric properties, a sample with sputtered gold electrodes was also prepared for comparison. Electron paramagnetic resonance (EPR) measurements were carried out with an X-band (≈ 9.4 GHz) spectrometer (A300, Bruker, Germany) at 173−473 K, and the powder weight for the EPR measurement was 10 mg. The gyromagnetic constant (g) was calculated using hν = gµ0H, where h is the Planck constant, µ0 is the Bohr magneton, H is magnitude of the magnetic field and ν is frequency of the microwave source.

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3.

Results and discussion

3.1. Microstructure and phase analysis by SEM, XRD and Raman spectroscopy A fine microstructure was observed in the SEM micrograph (Fig. 1). The relative density,

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defined by the ratio of measured density to theoretical density, was 90%. The ceramic had a bimodal microstructure consisting of a few larger grains of size 2 µm and many fine grains of less than 1 µm. As discussed in the following sections, Cu and Nb doping caused lattice distortion, which prohibited growth of the grain and resulted in the fine grains of BTCN.

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The room-temperature XRD pattern and Rietveld analysis results are presented in Fig. 2. The pattern was identifiable as a single cubic perovskite phase with space group Pm-3m (no. 221), and

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there was no secondary phase observable within the resolution limit of the XRD equipment, confirming the successful incorporation of Cu and Nb in the BaTiO3 lattice. Since the ionic radii of Cu and Nb are close to Ti4+ (0.61 Å), it is reasonable to assume that Cu and Nb ions had completely entered the BaTiO3 lattice. The refined cell lattice parameters a = b = c = 4.035(7) Å were slightly larger than that of pure BaTiO3 (a = 4.031 Å) due to the larger ion radii of Cu and

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Nb. The pattern factor Rp, weighted factor Rwp and the expected factor χ2 were 6.6%, 9.1% and 2.39, respectively, showing good agreement between the calculated and the experimental data. As a sensitive tool for detecting the local structure and dynamic symmetry, Raman spectroscopy

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is widely used to determine the phase transition and site occupancy of dopants in BaTiO3 [24–26]. There is no first-order Raman mode in an ideal cubic BaTiO3 structure, while 18 long-wavelength first-order Raman active modes exist in the tetragonal phase with C4v symmetry [27]. The

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tetragonal phase is usually characterized by sharp Raman bands at ~170 and 306 cm−1, and asymmetric broader bands at ~270, 520 and 720 cm−1 [28]. The 270, 520 and 720 cm−1 bands, also known as second-order modes, can also be observed in the cubic paraelectric phase, but are much broader and more symmetrical than those in the tetragonal phase. These three bands are usually attributed

to

the

disorder

of

Ti

displacements

in

the

TiO6

octahedron

[26,27].

Temperature-dependent Raman spectra of BTCN for 100–1200 cm−1 are shown in Fig. 3. Although the XRD refinement result showed a well-defined Pm-3m cubic phase, the Raman spectra were very different from the undoped cubic-BaTiO3 [26]. Three peaks at around 158, 205 and 502 cm−1 can be attributed to A1(TO) modes, and the intensity at 502 cm−1 increased with

ACCEPTED MANUSCRIPT decreasing temperature. These modes suggest a deviation from the perfect cubic structure; however, the characteristic E(TO2) peak of tetragonal phase at 304 cm−1 exhibited only a broad shoulder and was difficult to resolve even at 123 K. The weak 304 cm−1 peak and the similar Raman spectra in the temperature range 123−473 K indicated that BTCN possessed a

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pseudo-cubic phase without any phase transition in the temperature range of 123−473 K. A new peak emerged at 113 cm−1 and can be assigned to an F2g mode caused by the motion of Ba2+ ions against the oxygen octahedron [29]. Because Cu and Nb ions have larger ionic radii than Ti, the substitution of Cu and Nb on Ti sites gives rise to elastic distortion of the surrounding octahedra.

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Furthermore, the 4d Nb5+ ions are more covalently bounded to oxygen than 3d transition ions, resulting in a strong off-centered axially perturbed octahedral crystal field [30]. The JT ion Cu2+ is

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another source of structure distortion. We suppose that these effects led to the emergence of the 113 cm−1 mode. Alternatively, the distortion of the octahedra themselves also resulted in new Raman modes in a high-wavenumber region around 800 cm−1 (Fig. 3). Two strong modes of BTCN at around 721 and 775 cm−1 were assigned to the A1g breathing-like mode, which is related to the asymmetry of the octahedra due to the dissimilar ions [26,31]. This two-mode-like behavior

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in Raman spectra was also observed in Pb(Mg1/3Nb2/3)O3-PbTiO3 solid solution and heavily Fe and Nb co-doped BaTiO3 ceramics [11,32]. As pointed out by Chaabane et al. and Zhang et al., the A1g mode is strongly affected by the heterogeneous distribution of B-site ions. Instead of the

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displacement of Ti4+, the local ion rich regions, i.e. compositional fluctuation, play an important role in the two-mode-like behavior [11,32]. Maurya et al. recently observed the splitting of

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high-frequency modes in (1-x)BaTiO3-xA(Cu1/3Nb2/3)O3 (A = Sr, Ca, Ba) solid solutions even when x was only a few percent [12]. However, the A1g peak became asymmetric and exhibited splitting only with high Fe and Nb content in Ba[(Fe1/2Nb1/2)1-xTix]O3 compounds [11]. These results suggest Cu ions have more significant effects on the distortion of octahedra than Fe ions, which may be ascribed to the JT effect of Cu2+. The lower 721 cm−1 mode may correspond to the Ti–O stretching mode, whereas the higher 775 cm−1 peak is related to the dopants [11,12]. Based on the above discussion, we conclude that although the XRD result indicated a cubic phase of BTCN, the local structure was highly distorted. However, this distortion was a local effect and did not destroy the cubic symmetry. The disorder distribution of Cu and Nb ions and the local structural distortion on the one hand result in localized nano-polar regions that impart a high

ACCEPTED MANUSCRIPT piezoelectric response [12] and, on the other hand, lead to localization of charge carriers and force small polaron movement through tunneling or hopping mechanisms [33].

3.2. XPS spectra analysis

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It is well known that oxygen vacancies are unavoidable in perovskite oxides under high-temperature sintering conditions and low partial oxygen pressure. The ionization of the oxygen vacancies creates conducting electrons that can be captured by transition-metal cations [34,35]. Therefore, the mixed-valent structure of transition-metal cations widely exists, and has

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been found to be crucial for the physical and chemical properties of perovskite oxides [36]. Chen et al. also considered that the CDC is associated with the mixed-valent structure [37]. Thus, before

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discussing the conduction and dielectric relaxation mechanisms of BTCN, we performed XPS measurement to investigate the valence states of transition-metal cations. Fig. 4 displays the XPS spectra of Cu 2p, Ti 2p, and Nb 3d core levels of BTCN. The 2p3/2 peak of Cu was asymmetrical and could be split into three peaks with positions at the binding energy values of 931.8, 932.9 and 934.3 eV, and assigned to Cu+, Cu2+ and Cu3+, respectively [38,39].

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The ratio of Cu+:Cu2+:Cu3+ was 0.30:0.46:0.24. The Ti 2p3/2 signal is shown in Fig. 4(b). Only one peak at 458.2 eV was obtained and was identified as Ti4+. For the Nb 3d3/2, 5/2 spectrum in Fig. 4(c), the fitting result suggests that the valence state of Nb was pentavalent, and no other valence state

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existed, similar to published results [40].

The XPS spectra showed that Cu were polyvalent ions, but valences of Ti and Nb ions were invariable. The number of Cu+ was larger than Cu3+. To maintain the charge balance, the surplus

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Cu+ could be compensated by the oxygen vacancies. This result suggests Cu and Nb doping could inhibit the reduction of Ti4+, as also observed by Zhang et al. in BaTi0.8(Ni0.1Nb0.1)O3 [41]. However, a mixed-valent Ti3+/Ti4+ structure was also observed by the same research group in BaTi0.6(Co0.2Nb0.2)O3 [10]. The valence-state evolution of Ti in such oxides is still unclear and needs further investigation. In summary, the mixed-valent structure of Cu was shown to exist in BTCN, but Ti and Nb showed a single oxidation state. The polyvalent cations with different ionic radii, together with the JT Cu2+, would enhance the lattice distortion.

ACCEPTED MANUSCRIPT 3.3. VRH conduction Fig. 5(a) shows the frequency dependence of the real part of conductivity σ′ond low temperatures for BTCN. The conductivity showed a plateau at low frequencies and increased rapidly to another plateau at high frequencies. In each plateau the conductivity increased slowly

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with frequency. For inhomogeneous structures containing grain and grain boundaries, low-frequency conductivity is usually ascribed to the grain-boundary effect, while the conductivity of high frequencies is related to the bulk contribution [42]. The high-frequency behavior of σ′ could be described by the universal dielectric response (UDR) model proposed by

σ′ = σdc + σ0f s

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Jonscher [43]: (1)

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where σdc is dc bulk conductivity, σ0 and s are constants and f is the experimental frequency. The fitted values of σdc according to Eq. (1) are shown in Fig. 5(b). The σdc increased with an increase in temperature, indicating a thermally-activated conduction of the semiconductor. The parameter s was found to be between 0.5 and 0.6 depending on temperature. We first fitted the σdc data using the Arrhenius law for nearest-neighbor hopping (NNH):

(2)

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σdc = σ1exp(−Ea/kBT)

where σ1 is the pre-exponential factor, Ea is activation energy for the carrier hopping, kB is the Boltzmann constant and T is absolute temperature. The Arrhenius law describes σdc well above

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233 K, and the linear fit yields Ea = 0.22 eV. However, the experimental data did not follow the Arrhenius law and deviated from a straight line at low temperatures, therefore the NNH

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mechanism can be excluded at low temperature. Mott first pointed out that the VRH process sets in at low temperatures [44]. According to the VRH model, the hopping conduction of charge carriers is then used to fit the experimental data of BTCN: σdc = σ2exp[−(T0/T)1/4]

(3)

where σ2 is the pre-exponential factor and T0 is the parameter related to the density of localized states at the Fermi level and decay length of the localized wave function. Fig. 5(b) also shows the plot of logσdc versus T−1/4 and the fitting result. The experimental data exhibited a good straight line, indicating that σdc obeyed the VRH conduction mechanism. The value of T0 = 4.45 × 108 K was in good agreement with reported values for some perovskite structure materials [45,46]. The T0 is given by T0 = 24/[πkBN(EF)ξ3], where N(EF) is the density of localized states at the

ACCEPTED MANUSCRIPT Fermi level and ξ is the decay length of the localized wave function. For ξ ≈ a = 4.035 Å, the distance between neighboring B (Ti, Cu and Nb) site ions, we obtained N(EF) = 3.02 × 1018 eV−1·cm−3. The hopping energy W for localized carriers is given by W = 0.25kBT0 1/4T 3/4

(4)

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The hopping energy W was 0.15 eV at 173 K, and W increased to 0.27 eV monotonically when T increased to 373 K. These values are similar to those disordered materials in which electronic transport occurs by means of hopping between localized states [14,47].

According to Mott’s VRH mechanism, W is also expressed by W = 3/[4πR3N(EF)], where R is

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the hopping length and given by R = ξ1/4[8πN(EF)kBT]1/4 [44]. The estimated R was 4.34 nm at 173 K and decreased to 3.88 nm when temperature increased to 273 K. The R values were almost 10

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times larger than the lattice constant, which justifies the VRH transport in the system. The VRH conduction behavior is usually observed in amorphous materials via “states in the gap” which are attributed to the lattice disorder [47]. The VRH phenomenon, therefore, suggests that the BTCN ceramic was highly disordered, consistent with our Raman analysis. The mixed-valent Cu and JT ion Cu2+ induced a more distorted lattice, which acted as a potential well causing the

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self-trapping of the charge carrier. The quasiparticle, originating from electron–phonon coupling of the charge carrier and its self-induced distortion, is known as a polaron [48,49]. The mixed-valent structure of Cu forms Cu+-O-Cu2+ and Cu2+-O-Cu3+, which provide a path for

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polaron hopping under a dc field [42,50]. The localized charges, associated with the highly disordered structure, were responsible for the VRH behavior in BTCN. Therefore, we assume that

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the VRH behavior mainly originated from the effect of Cu doping.

3.4. General dielectric responses Fig. 6 shows the frequency dependence of the real and imaginary parts of the dielectric constant (ε′ and ε″) and loss (tan δ) at various temperatures. Below room temperature, the CDC (ε′ ≈ 104) was observed at low frequencies and decreased rapidly to a low plateau (~300−400). Dielectric relaxation peaks in ε″ and tan δ emerged with the decrease in the dielectric constant [R1 in Fig. 6(c)]. The peak position of tan δ shifted to high frequencies with increasing temperature, suggesting a thermally-activated relaxation behavior. For higher temperatures, a new dielectric constant plateau (105−106) appeared at low frequency, indicating another polarization mechanism

ACCEPTED MANUSCRIPT giving rise to ε′ values. Another set of dielectric relaxation (R2) peaks was also observed in tan δ and the peaks were almost concealed by the dispersion of tan δ. The sharp increase in ε″ and tan δ at low frequencies and high temperatures can be attributed to the dc electrical conductivity and/or sample–electrode interface [51], which are usually dominant at high temperature and low

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frequency. Considering the dc conduction, the complex dielectric constant ε* can be expressed:

ε* = ε′∞ +

εs′ − ε′∞ σ′ −i 1 + iωτ ω

(5)

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where ω is the angular frequency, ε′s and ε′∞ are the static- and high-frequency dielectric constant, σ′ is ohmic conductivity and τ is relaxation time. Eq. (5) gives the so called Maxwell–Wagner

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(MW) polarization and relaxation, which often occurs in heterogeneous systems [52]. According to the widely accepted internal barrier layer capacitor model, which is based on MW polarization, the CDC phenomenon is related to the electrically inhomogeneous structure of the sample. The CDC at low frequencies is attributed to the grain boundary and/or domain boundary barrier layer with high resistance, while the low dielectric constant plateau at high frequencies is associated

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with high-conduction grain [53,54]. However, there is still dispute over the polarization mechanism of low frequencies. Lunkenheimer et al. suggested that CDC might originate from a MW-type contribution from depletion layers at the grain boundaries, or at the interface between

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sample and contacts [55]. The domains within the grain have also been found to play an important role in CDC materials [56–58]. When there is a mismatch between the Fermi level of the

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composite and the work function of the electrode, the electrode effect is notable [59]. Depending on the kind of electrode and the interface state of the ceramic, an additional high dielectric constant plateau, i.e. electrode polarization, can be observed [60]. Therefore, the origins of the polarization of BTCN should be clarified first before further discussion. The inhomogeneous electrical structure is depicted well by the impedance complex plane plot of Z″ versus Z′ (Z′ and Z″ are the real and imaginary parts of the complex impedance Z*). The dielectric responses of the grain interiors, grain boundaries and sample–electrode contacts can be identified from the impedance complex plane plot [61]. A semicircle in the complex impedance plane plots represents an electric homogeneous structure. The impedance complex plane plots for BTCN at selected temperatures are presented in Fig. 7. Below room temperature the impedance

ACCEPTED MANUSCRIPT spectra consisted of two semicircles, a small semicircle at high frequencies and a large one at low frequencies [Fig. 7(a)]. With an increase in temperature, a new semicircle emerged [Fig. 7(b)], indicating three dielectric responses in BTCN at high temperatures. Schönhals and Kremer pointed out that electrode polarization set in when the slope of the plot of logε″−logf is larger than

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−1 [62], as seen in Fig. 6(b). Therefore, the high dielectric constant plateau at low frequencies in the high-temperature range may be related to the electrode effect. To prove this speculation, samples with sputtered Au and Ag paste electrodes were prepared and the impedance complex plane plots at 473 K are shown in Fig. 8. The semicircle radius at low frequencies with the Au

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electrode was larger than that of the Ag electrode sample, whereas the intermediate frequency and the high-frequency semicircles remained unchanged. This result indicates that the low-frequency

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semicircle was associated with the electrode effect. The difference between samples with Au and Ag electrodes is mainly ascribed to the different work function of the electrode materials [60]. Thus the intermediate and high-frequency semicircles of BTCN were associated with grain boundary and bulk responses.

For inhomogeneous structures, the impedance data are often modeled by an equivalent circuit

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consisting of two or more parallel RC elements connected in serial. For BTCN, the dielectric responses consist of grain and grain boundary contributions at low temperature, thus the equivalent circuit contained two RC elements, as illustrated in the inset of Fig. 7(a). The complex

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impedance in this condition may be expressed by the following equations:

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Z' =

Z * = Z '− iZ ''

Rg

1 + (ωRg Cg )

2

+

(6)

Rgb 1 + (ωRgbCgb )2

(7)

and

 ω Rg C g   ωRgb C gb  Z'' = Rg  + Rgb  2  2  1 + (ωRg C g )  1 + (ωRgb C gb ) 

(8)

where Rg and Rgb are resistances for the grain and grain boundary, respectively, and Cg and Cgb are the corresponding capacitances. The electrode contribution was notable at high temperatures and the equivalent circuit would contain three RC elements, as shown in the inset of Fig. 7(b), where Re and Ce are the resistances and capacitances of the electrode components, respectively. To further study the bulk and interfacial behavior, we performed measurements on BTCN with

ACCEPTED MANUSCRIPT Ag paste electrodes under different dc bias voltages at 293 and 473 K, and the results are shown in Fig. 9. The application of a dc bias remarkably suppressed the electrode polarization, but the bulk and grain boundary dielectric constant were not affected [Fig. 9(a)]. In the complex plane plot of Z* in Fig 9(b), the low-frequency semicircle of electrode response almost disappeared at 5 V,

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whereas the intermediate and high-frequency semicircles were unaffected. These results mean the Schottky barriers formed at sample–electrode interfaces were easier to destroy than grain boundary and bulk.

The dependence on bias showed the non-ohmic property of sample–electrode interface. Chung

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et al. pointed out that the barrier at the grain boundary is responsible for the non-ohmic property. The increase in the width of the depletion layer at the grain boundary with an applied dc bias may

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explain the decrease in the dielectric constant [63]. The non-ohmic property of grain boundaries has been widely observed in CaCu3Ti4O12 (CCTO) and other perovskite structures in past years [64–66]. However, there were many more grain boundaries in fine-grained than in coarse-grained samples, so the electric field across each grain boundary was smaller in fine-grained than in coarse-grained samples. Therefore, the semicircle related to the grain boundary was

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bias-independent [67]. This effect is more significant when the electrode contribution is large [68]. For BTCN, the average grain size was less than 1 µm, thus the bias-independent grain boundary

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semicircle may be ascribed to the small grain size, consistent with the results of Adams et al. [67].

3.5. Origin of the dielectric relaxations

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In semiconducting materials, the hopping of localized charge carriers not only produces conductivity but also gives rise to dipolar polarization [69]. The UDR model describes well the frequency-dependent response caused by localized carrier hopping. As previously mentioned, the conductivity of BTCN at low temperatures was depicted well by the UDR model. According to the UDR model, the dielectric response of the localized carriers can be calculated [43]: ε′ = tan(sπ/2)σ0f s−1/ε0

(9)

where f is frequency, σ0 and s are constants, and ε0 is the dielectric permittivity of free space. The above equation can be rewritten: log(fε′) = log(A(T)) + slogf

(10)

where A(T) = tan(sπ/2)σ0/ε0 is a temperature-dependent constant. Eq. (10) suggests that a straight

ACCEPTED MANUSCRIPT line with a slope s will be obtained in the plot of log(fε′) vs logf. Fig. 10(a) shows the plots at low temperatures. Straight lines were observed across a wide range of frequencies with the same slopes, and the data deviated from a straight line at intermediate frequencies as the relaxation process occurred. The fitted values of s for 173 K at low and high frequencies were 0.86 and 0.99,

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respectively. This result suggests that the dielectric relaxation was related to the localized charge carriers [69]. The linear behavior almost vanished above room temperature [Fig. 10(b)], which is ascribed to the new relaxation process and the delocalization of carriers at high temperature.

We further analyzed the temperature dependence of dielectric relaxations (Fig. 6). For

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relaxation R1, the loss peaks fmax moved toward higher frequencies with increasing temperature, indicating a thermally-activated-relaxation process [Fig. 6(c)]. As shown in Fig. 11, the data

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obeyed the Arrhenius law only at high temperatures: fmax = f0exp(−Ea/kBT)

(11)

where Ea is the activation energy and f0 is the pre-exponential factor. The calculated values for f0 and Ea were 9.12 × 107 Hz and 0.25 eV, respectively. Deviation from Arrhenius behavior was also observed in other perovskite materials such as CCTO [42] and LaFe0.9Ni0.1O3 [70]. According to

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Mott, the NNH process dominates the hopping of localized carriers in a high temperature range and obeys the Arrhenius law, whereas the VRH process is valid at low temperatures [44]. Zhang and Tang [42] reported a polaron relaxation in CCTO and found that the following VRH-like relation fitted the data better:

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fmax = f1exp[−(T1/T)1/4]

(12)

where f1 and T1 are constants. Fig. 11 also shows the fitting result of experimental data according

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to Eq. (12). The f1 and T1 were determined to be 2.51 × 1019 Hz and 5.02 × 108 K from the linear fit, which agree with the reported results [68,71]. The value of T1 was comparable to that of T0 in Eq. (3). Zhang and Tang showed an approximate linear relation between f1 and σdc in CCTO, suggesting that both the electrical conduction and polarization originate from localized carriers [42]. Our results strongly suggest that the dielectric behavior was related to the conductivity, and that relaxation at high frequencies was a dipolar-type relaxation. To get a better understanding of the inhomogeneous structure, we used ZView software to fit our impedance data based on the equivalent circuits in Fig. 7 and Eqs (6−8). The values of the resistances for grain and grain boundary, Rg and Rgb, were extracted (Fig. 12). Both Rg and Rgb

ACCEPTED MANUSCRIPT decreased with the increase in temperature, indicating the semiconducting behavior of the sample. Both Rg and Rgb were fitted well by the VRH model: Rg, gb = Rg0, gb0exp[(T2/T)1/4]

(13)

where Rg0, gb0 are pre-exponential factors. The T2 values for Rg and Rgb were 5.02 × 108 K and 3.80

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× 108 K. T2 for Rg had the same value as T1 in Eq. (12), indicating that the relaxation R1 was related to bulk distribution while the relaxation R2 was related to the grain boundary response based on the above analysis. In Eq. (5) the relaxation time τ (τ = 1/fmax) can be calculated based on

τ=

Rg R gb (Cg + Cgb ) Rg + Rgb

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the equivalent circuit [52]:

(14)

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In most cases, Rgb >> Rg and Cgb >> Cg, and relaxation time can be rewritten as τ ≈ RgCgb. Because Cgb usually has a weak dependence on temperature, τ thus exhibits a linear relationship with Rg, which could explain the similar behavior of the grain conduction and dielectric relaxation processes. These results suggest that both the conduction and relaxation processes obey the same VRH mechanism, which originates from the hopping of localized charge carriers.

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It is worth noting that VRH conduction and polaron relaxations were not observed in other perovskite ceramics such as BaTi0.85(Fe1/2Nb1/2)0.15O3 and BaTi0.9(Ni1/2W1/2)0.1O3 [5,6,8]. This phenomenon may be ascribed to the highly distorted structure of BTCN, which was shown in

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Raman spectra. Although transition-metal ions and Nb/W/Ta co-doped BaTiO3 or SrTiO3 also have a distorted structure due to the mismatch of ionic radii, NNH conduction rather than VRH

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indicates that the localization of carriers in such compositions is weaker than that of BTCN. It was found that both Rg and Rgb obeyed the VRH mechanism, implying both the grain and grain boundaries of BTCN were highly disordered. The VRH processes in grain and grain boundaries were also reported by other authors [72–74]. We attributed the VRH process in BTCN to the existence of Cu ions. As discussed above, Cu2+ ions are JT-active cations, and led to additional distortion of the lattice. The localized defect states, which originated from the distorted structure, were responsible for the VRH conduction. The charge transfer between different valence states was also responsible for the polarization and dielectric relaxation. The local crystal field around Cu2+ is important for understanding the localized distortions and defect structure [12]. We performed further EPR measurement, which is a powerful tool for

ACCEPTED MANUSCRIPT studying the Cu2+ ions and the local structure, to study the effects of Cu ions. The Cu2+ ions have unfilled d-orbitals (3d9) with an electron spin S = 1/2, which can be represented by a spin Hamiltonian H = µBB·g·S – µngnB·I + S·A·I

(15)

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where gn is the nuclear g factor and µB, µn and B are the Bohr, nuclear magnetons and the external field, respectively. The variation of the first-derivative EPR spectra with temperature for BTCN is shown in Fig. 13(a). A single broad and symmetric signal with a Lorentzian line shape was observed, and the resonance field was almost independent of temperature with g ≈ 1.982−1.987,

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while the linewidths and intensities were sensitive to temperature. The EPR signal for Ti3+ (3d1) showed that defect centers at g = 1.9599 [35] were absent, consistent with our XPS results and

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published literature [41]. Maurya et al. observed a axial symmetrical EPR spectrum with gx = gy = 2.01 and gz = 2.302 in lightly Cu and Nb co-doped BaTiO3 [12]. In our case, the observed spectrum could be assigned to the Cu2+ signal [75], and the high concentration of Cu2+ ions and the isotropic polycrystalline structure were responsible for the broad signal, thus the hyperfine structure in EPR could not be observed. The average g value was smaller than Maurya’s result,

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which may be ascribable to the Cu+, Cu2+ and Cu3+ interaction as mentioned. Due to the high concentration of Cu ions and the compositional fluctuation, the Cu+-O-Cu2+ and Cu2+-O-Cu3+ dipoles were easily formed. When electrons transferred from different valence via Cu+-O-Cu2+ and

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Cu2+-O-Cu3+, the EPR signal of Cu2+ was also affected. Mixed-valent-related EPR signals are common in manganese perovskite oxides, and the broadening of the EPR linewidth under the

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bottleneck effect is usually followed by the adiabatic small polaron hopping model in perovskite manganite oxides [76]. Fig. 13(b) shows the temperature dependence of the peak-to-peak EPR linewidth ∆Hpp. There was a linear relationship between ∆Hpp and T−1/4, similar to the behavior of conductivity and dielectric relaxation. Phan et al. pointed out that the broadening of EPR spectra as temperature increased was related to the hopping rate of charge carriers in manganite oxides [77], which also seems applicable for interpreting the dynamical behavior of EPR linewidth in BTCN. Based on the above discussion, we propose that mixed-valent Cu ions played an important role in the VRH conduction and polaron dielectric relaxation. To verify this, we prepared BaTi0.7(Mg0.1Nb0.2)O3 ceramic (BTMN for short) with the same stoichiometry as BTCN for

ACCEPTED MANUSCRIPT comparison. The BTMN had a structure identical to that of BTCN, and no impurity phase was observed in the XRD pattern, indicating that Mg and Nb ions were completely incorporated into the BaTiO3 lattice. The comparison of dielectric constant between BTCN and BTMN is shown in Fig. 14. The BTMN had a low dielectric constant of ≈ 102, much lower than that of BTCN.

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Because the ionic radius of Mg2+ (0.72 Å) is nearly equal to those of Cu+, Cu2+ and Cu3+, the huge difference in the dielectric constant between BTCN and BTMN suggests that the CDC behavior in BTCN was due to the mixed-valent Cu ions.

Conclusions

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4.

In summary, fine-grain BTCN with cubic structure was prepared and its dc conductivity was

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found to obey the Mott’s VRH mechanism. The VRH mechanism indicates that carriers were localized, which is related to the distorted and disorder structure as revealed by Raman spectra. The dielectric responses were ascribed to the contributions of bulk and grain boundary activity at low temperatures, and the electrode effect took place at high temperatures. Dielectric relaxation at high frequencies was a polaron relaxation rather than MW relaxation and could be depicted by the

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VRH model. Based on EPR analysis, we proposed that mixed-valent Cu ions were responsible for the CDC and the VRH conduction. Acknowledgments

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The authors wish to acknowledge financial support of the National Natural Science Foundations of China (21271084) and of Jilin Province (20160101290JC) and Changbai Mountain Scholar

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Fig. 1. SEM micrograph of BaTi0.7(Cu0.1Nb0.2)O3 (BTCN).

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Fig. 10. Log(fε') vs. logf plots at selected temperatures.

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Fig. 11. The NNH and VRH plots for the relaxation frequencies of tan δ. Symbols are the experimental data and solid straight lines are fitting results.

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Fig. 12. Fitting of the resistances of grain and grain boundary by VRH model.

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Fig. 13. (a) Variation of EPR spectra of BTCN vs. temperature; (b) log(∆Hpp) vs. T-1/4 plot and linear fitting result.

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Fig. 14. Frequency dependence of dielectric constant for BaTi0.7(Cu0.1Nb0.2)O3 and BaTi0.7(Mg0.1Nb0.2)O3.

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Fig. 2. XRD pattern (symbols) with Rietveld refinement (solid line) for BTCN polycrystalline powder.

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Fig. 3. Temperature-dependent Raman spectra of BTCN.

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Fig. 4. XPS spectra of (a) Cu 2p3/2, (b) Ti 2p3/2 and (c) Nb 3d3/2, 5/2 for BTCN.

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Fig. 5. (a) Frequency dependent conductivity σ' at different temperatures. Symbols are experimental data, lines are fitting results according to UDR model. (b) Fitting results of σdc using NNH and VRH models. Symbols are σdc extracted from (a) and lines are fitting results.

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Fig. 6. Frequency dependence of (a) ε', (b) ε" and (c) tan δ at various temperatures for BTCN.

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Fig. 7. Impedance complex plane plot (Z*) for BTCN at 273 K (a) and 373 K (b). Insets show the enlarged view of high-frequency-range data and the equivalent RC circuits. Solid lines are fitted curves by ZView software.

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Fig. 8. Z* Plots with different electrodes at 473 K.

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Fig. 9. Influence of dc bias on ε' (a) and Z* (b) at 293 K and 473 K.

ACCEPTED MANUSCRIPT Figure Captions Fig. 1. SEM micrograph of BaTi0.7(Cu0.1Nb0.2)O3 (BTCN). Fig. 2. XRD pattern (symbols) with Rietveld refinement (solid line) for BTCN polycrystalline powder.

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Fig. 3. Temperature-dependent Raman spectra of BTCN. Fig. 4. XPS spectra of (a) Cu 2p3/2, (b) Ti 2p3/2 and (c) Nb 3d3/2, 5/2 for BTCN.

Fig. 5. (a) Frequency dependent conductivity σ at different temperatures. Symbols are experimental data, lines are fitting results according to the UDR model. (b) Fitting results of σdc

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using NNH and VRH models. Symbols are σdc extracted from (a) and lines are fitting results.

Fig. 6. Frequency dependence of (a) ε′, (b) ε″ and (c) tan δ at various temperatures for BTCN.

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Fig. 7. Impedance complex plane plot (Z*) for BTCN at 273 K (a) and 373 K (b). Insets show the enlarged view of high-frequency-range data and the equivalent RC circuits. Solid lines are fitted curves by ZView software.

Fig. 8. Z* Plots with different electrodes at 473 K.

Fig. 9. Influence of dc bias on ε′ (a) and Z* (b) at 293 K and 473 K.

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Fig. 10. Log(fεʹ) vs. logf plots at selected temperatures.

Fig. 11. The NNH and VRH plots for the relaxation frequencies of tan δ. Symbols are the experimental data and solid straight lines are fitting results. Fig. 12. Fitting of the resistances of grain and grain boundary by VRH model.

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Fig. 13. (a) Variation of EPR spectra of BTCN vs temperature; (b) log(∆Hpp) vs T−1/4 plot and

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linear fitting result.

Fig. 14. Frequency dependence of dielectric constant for BaTi0.7(Cu0.1Nb0.2)O3 and BaTi0.7(Mg0.1Nb0.2)O3.

ACCEPTED MANUSCRIPT Highlights 1. VRH conduction and polaron relaxation exist in pseudo-cubic BaTi0.7(Cu0.1Nb0.2)O3. 2. Grain boundary and electrode are responsible for colossal dielectric plateaus. 3. Mixed valence of Cu was confirmed by XPS.

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4. Jahn–Teller-active Cu2+ and charge transfer are decisive to the properties.