Colossal permittivity and dielectric relaxations in (La0.5Nb0.5)xTi1-xO2 ceramics

Journal of Alloys and Compounds 768 (2018) 368e376

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Colossal permittivity and dielectric relaxations in (La0.5Nb0.5)xTi1-xO2 ceramics Baochun Guo, Peng Liu*, Xiulei Cui, Yuechan Song College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 March 2018 Received in revised form 19 July 2018 Accepted 21 July 2018 Available online 25 July 2018

A series of LaþNb co-doped TiO2 (La0.5Nb0.5)xTi1-xO2 (0.25%  x  5%) ceramics were prepared using a solid-state reaction method. Colossal permittivity (CP) (εʹ > 104) and low dielectric loss (tand < 0.05) were obtained when the ceramics were sintered at 1673 K in an N2 atmosphere and annealed at 1073e1173 K in air. A pure rutile phase was achieved when x ¼ 0.25% and secondary phase La2TiO5 was detected when x  0.5%. The optimum dielectric performance of εʹ > 104 and tand < 0.05 within 1 Hze2 MHz and 25 e350 K was obtained for x ¼ 0.5%. Three types of dielectric relaxations were observed through the dielectric-temperature spectrum: electron-pinned defect-dipoles (EPDD) polarization, electron hopping, and MaxwelleWagner polarization. The CP (> 25 K at 1 kHz) was primarily related to EPDD polarization. The high activation energy of the grain boundary (Egb ¼ 1.98 eV) is one of the reasons for the low tand in this study. © 2018 Elsevier B.V. All rights reserved.

Keywords: Grain boundaries Dielectric properties TiO2 Capacitors

1. Introduction The colossal permittivity (CP) of dielectric materials has been extensively investigated in recent years because of the increasingly high-performance requirements for capacitive devices used in high-energy density storage and microelectronics applications. Many dielectric materials that exhibit unusually high dielectric permittivities above 103 without any detectable ferroelectric phase transitions, such as doped NiO [1], CaCu3Ti4O12(CCTO) [2] and AFe1/ 2B1/2O3 (A ¼ Ba, Sr and Ca; B]Nb, Ta and Sb) [3] have been studied. However several severe problems have still not been resolved, thereby preventing the wide application of these materials and hindering further advances in device performance. These problems include the high dielectric loss (tand) and strong dependence of dielectric properties on temperature and frequency [4,5]. A new CP material of co-doped TiO2 has been extensively investigated in recent years owing to its excellent electrical properties: the (Nb, In) co-doped TiO2 ceramics are characterized by εr > 104 and tand  0.05 within of frequency range of 20 Hze2 MHz at 80 Ke450 K [6,7]. The novel co-doped TiO2 system provides insights for studying a CP material with low tand. CP co-doped TiO2 ceramics, such as the TiO2 co-doped with

* Corresponding author. E-mail address: [email protected] (P. Liu). https://doi.org/10.1016/j.jallcom.2018.07.248 0925-8388/© 2018 Elsevier B.V. All rights reserved.

different trivalent element (In, Y, Yb, Er, Ga or Al) with pentavalent Nb/Ta or divalent element (Mg, Ca, or Zn) with Nb/Ta or even ZrþNb, have been extensively studied [8e20]. These studies indicated that the co-doped TiO2 with CP is easy to obtain, but the low tand <0.05 in the frequency range of 20 Hze2 MHz is difficult to achieve [6,8,15,18,21,22]. Generally, in (A3þB5þ)xTi4þ1-xO2 type ceramics, the electrons can be introduced by Nb5þ. By doping the A3þ ion, the electrons were confined within complex defect clusters  3þ 3þ 4þ (A3þ or B5þ (C ¼ A3þ, Ti3þ, or Ti4þ)) into TiO2 lattice, 2 Vo Ti 2 Ti CTi so co-doped TiO2 ceramic/film/single crystal with CP and low tand properties were obtained due the presence of electron-pinned defect-dipoles (EPDD) polarization [6,12,22,23]. However, further studies indicated that many additional factors such as electron hopping or internal barrier layer capacitor (IBLC) polarization contribute to the dielectric response in those co-doped TiO2 ceramics over a broad frequency and temperature ranges in addition to EPPD polarization [8,24e27]. As a typical oxide of co-doped TiO2, oxygen vacancies are easily produced during the sintering process, so the oxygen vacancy hopping effect on dielectric properties cannot be ignored [28]. The conventional method is to choose elements with similar ionic radii to form a solid-solution. For the (In0.5Nb0.5)xTi1-xO2 ceramics, The radius of In3þ (RIn3þ ¼ 0.094 nm, CN ¼ 6) is considerably larger than Ti4þ (RTi4þ ¼ 0.0745 nm, CN ¼ 6) [29], yet the pure solid-solution rutile was achieved at doping level x ¼ 0.1 due to the combination effect of Nb and In, while the solid solubility limit was

B. Guo et al. / Journal of Alloys and Compounds 768 (2018) 368e376

only x ¼ 0.01 for InxTi1-xO2 ceramics [6]. This phenomenon enlightens us to use much bigger ion to dope into TiO2 with Nb. Some studies have indicated that the CP mechanisms in co-doped TiO2 are closely related to the size of doped trivalent ion [12,30e33]. The dielectric properties of the ion Bi (RBi3þ ¼ 0.117 nm, CN ¼ 6) with Nb co-doped TiO2 have been researched and the low tand is obtained due to Bi ions which are doped into the TiO2 lattice and the formation of the Bi1.74Ti2O6.624 phase [34]. Good dielectric performance in (La0.5Nb0.5)0.3Ti0.7O2 ceramics was thought to be caused by the formation of a segregation structure [33]. The much bigger trivalent element radius compared to that of Ti4þ often leads to lattice mismatch, causing the second phase to establish the dense grain-boundary structure. In this study, we chose the very big and stable La3þ (RLa3þ ¼ 0.1172 nm, CN ¼ 6) as the acceptor and Nb5þ as the donor co-doped into TiO2. The (La0.5Nb0.5)xTi1-xO2 (x ¼ 0.25%e 5%) ceramics were investigated. By adjusting the sintering and annealing processes, excellent dielectric properties (εʹ > 104 and tand  0.05 within 1 Hze2 MHz) were obtained. The structures, elements distribution, dielectric relaxations in the temperature range of 15 Ke425 K, and impedance characteristics were investigated in detail. 2. Experimental The (La0.5Nb0.5)xTi1-xO2 ceramics samples were prepared by a solid-state reaction method. The starting materials used in this work were high-purity TiO2 (rutile, 99.99%), Nb2O5 (99.99%), and La2O3 (99.99%). Those powders were accurately weighed according to the compositions (La0.5Nb0.5)xTi1-xO2 (x ¼ 0.25%, 0.5%, 1.5%, 2.5%, 3.5%, and 5.0%), La0.5%Ti99.5%O2 (TiO2-La), Nb0.5%Ti99.5%O2 (TiO2-Nb) and then ball-mixed for 12 h with ethanol as the medium. After the ball-milling, the powders, incorporating a 5 wt% polyvinyl alcohol (PVA) binder solution, were pressed into disks with a diameter of 10 mm and thickness of 1.2e1.5 mm at a uniaxial pressure of 200 MPa, Then, the disks were put in the tube furnace. The closed tube furnace is connected to the flow gas controller (MKS 247D, Four Channel Power Supply/Readout, USA), which is used to control the pressures of mixed gas. The mixed gases are O2 (gas purity:

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99.999%) and N2 (gas purity: 99.999%), respectively. The samples were debound for 2 h at 773 K and sintered at 1623e1723 K for 10 h in the different atmosphere at a flow rate of 160 ml/min; finally, all sintered samples were polished to 0.6 mm in thickness and annealed at 923e1473 K for different times in air. The heating rate was set at 3 K/min and the cooling rate was 3 K/min until the temperature decreased to 773 K, then the samples cooled inside the furnace to room temperature (RT). The parallel surfaces of the samples were coated using silver at 923 K for 30 min for the characterization of their electrical properties. X-ray diffraction (XRD) was performed on a Rigaku D/Max 2250 diffraction-meter (Japan) with Cu ka radiation (40 kV and 100 mA). The data were measured using the continuously-scan mode at a speed of 8 /min, and the data for refining measured with a slow scanning speed of 0.01 /second. Surface, cross-section morphologies and elements distribution information were collected using field emission scanning electron microscopy (FEI Nova Nano-SEM 450). Dielectric dispersion was studied by the combination of an impedance analyzer Agilent 4991A in the frequency range of 2 MHze3 GHz, Agilent E4980A with the frequency range of 20 Hze2MHz and alpha-A high-performance frequency analyzer in the frequency range of 103 Hze1 MHz, respectively. The dielectric properties as a function of temperature were measured using an Agilent E4980A with a temperature controller vibration sample magnetometer (VSM, CFM-8T, Cryogenic Ltd, England) ranging from 15 to 250 K. A Novocontrol broadband dielectric spectrometer was used with an alpha-A high-performance frequency analyzer (BDS40, Germany) over the temperature range of 123 Ke425 K. The margin of error for the permittivity (20 Hze2 MHz) at RT between two different temperature-variation measurement-systems was below 5%. 3. Results and discussion The dielectric properties of LaþNb co-doped rutile TiO2 ceramics with respect to the sintering and annealing conditions are summarized in Table 1. For x ¼ 0.5%, the ceramics with εʹ over 104

Table 1 The dielectric properties for LaþNb co-doped rutile TiO2 ceramics with respect to the sintering and annealing conditions. component

x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% x ¼ 0.5% La0.5%Ti99.5%O2 Nb0.5%Ti99.5%O2 x ¼ 0.25% x ¼ 1.5% x ¼ 2.5% x ¼ 3.5% x ¼ 5.0% a

Prepared process

Dielectric properties

Sintering atmosphere

Sintering temperature(K)

Annealed temperature(K)

Annealed times(hours)

εʹ tand (@1 kHz) (@1 kHz)

Frequency range (εʹ > 8000&tand < 0.05)

N2 flow air 0.10a 0.25a 0.50a N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2

1673 1673 1673 1673 1673 1623 1723 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673 1673

No No No No No No No 923 1073 1123 1173 1273 1473 1123 1123 1123 1123 1123 1123 1123 1123 1123 1123

0 0 0 0 0 0 0 2 2 2 2 2 2 0.5 1 10 2 2 2 2 2 2 2

24450 1060 260 130 110 33340 21560 11360 17430 12010 13960 2087 1590 24920 23570 11000 300 21000 650 9150 11010 10860 26780

        573 Hz- 273 kHz 1 Hz- 2 MHz 1 Hz-2 MHz   75 kHz-467 kHz 659 Hz- 1 MHz 1 Hz 2 MHz    1Hz-30 kHZ 1 Hz-187 kHZ 1 Hz-62 kHz 42 Hz-324 kHz

The mix gases were O2 and N2, controlled oxygen partial pressure at 0.1, 0.25, and 0.50.

0.13 0.14 0.11 0.075 0.097 0.13 1.0 1.5 0.007 0.018 0.049 0.14 0.25 0.10 0.047 0.019 0.019 0.74 0.038 0.013 0.021 0.025 0.017

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were obtained while sintering at N2 atmosphere; when the ceramics were sintered in the flowing air or mixture gas, the εʹ dropped dramatically. Meanwhile, the high εʹ was accompanied by a high tand. The dielectric properties of N2-sintered x ¼ 0.5% ceramics annealed at different times and temperatures show that εʹ > 104 and tand < 0.05 over broad frequencies could be achieved through appropriate annealing conditions, that is, annealing at the temperature of 1073 Ke1173 K for 2e10 h. Therefore the LaþNb codoped TiO2 ceramics with different doping contents (x ¼ 0.25%e5%) were sintered at 1673 K in N2 atmospheres and annealed at 1123 K for 2 h. The frequency dependence of the dielectric properties for those ceramics is shown in Fig. 1. The permittivity (at 1 kHz) increased with doping level x, as observed in TiO2 ceramics codoped with In þ Nb [6], Ga þ Nb [12], or Al þ Nb [13]. The relatively stable CP values greater than 104 accompanied by a relatively low tand <0.05 at 1 kHz were obtained at doping level x ¼ 0.5%e 5.0%. The ultra-high tand at low frequencies (<100 Hz) for x ¼ 5.0%

Fig. 1. The frequency dependence of dielectric properties for (La0.5Nb0.5)xTi1-xO2 (0.25%  x  5%) ceramics sintering at 1673 K N2 atmosphere and annealed at 1123 K in air for 2 h.

may be related to the large leakage current or strong MaxwelleWagner effect. For x ¼ 0.5, the ceramic shows ε0 > 104 and tand < 0.05 within a frequency range of 1 Hze2 MHz. Fig. 2(a) shows the XRD patterns of (La0.5Nb0.5)xTi1-xO2 (x ¼ 0.25%e5.0%) ceramic powders and that of pure rutile TiO2 to confirm the phase structure. For all the samples, the main rutile TiO2 (PDF#99-0090) phase was observed and perfectly indexed based on a tetragonal structure. A secondary phase of La2TiO5 (PDF#54-0179) appeared in the ceramics for x ¼ 0.5%e5.0%. Fine scan XRD patterns in the 2q range of 26.8e27.8 for x ¼ 0.25%e5.0% samples are shown in Fig. 2(a) inset. As the composition of x increased from 0.25% to 5.0%, the (110) peak gradually shifted to lower diffraction angles. The XRD patterns of pure TiO2, TiO2-Nb, TiO2-La, and x ¼ 0.5% sample were presented in Fig. 2(b), the position of (110) peak located at 27.49 , 27.48 , 27.42 and 27.40 , respectively. Compared with TiO2 and TiO2-Nb, the (110) peak for the x ¼ 0.5% sample shifted toward to lower angles implying that the crystal lattices of the co-doped TiO2 had been enlarged. Since the average radius of Nb5þ(RNb5þ ¼ 0.078 nm, CN ¼ 6) and La3þ ions is larger than that of Ti4þ, Nb5þ and La3þ ions on the Ti4þ sites will cause an increase in the interplanar spacing of the (110) plane (Fig. 2(a) inset). At the same doping level, the lower angle of (110) obtained for TiO2-La than pure TiO2, and for (La0.5Nb0.5)0.5%Ti99.5%O2 than TiO2-Nb can confirm that the La has been in TiO2 lattice. Rietveld refinement was performed (Fig. 2(c)) on the powder XRD data using the software MAUD and the fitting result reveals that the x ¼ 0.5% ceramics possessed a rutile structure (space group, p42/ mnm). The lattice parameters and relative densities are summarized in Table 2. The ceramic had larger lattice parameters and unit cell volume than pure TiO2 due to the dopants incorporated into the lattice. The very weak second phase could be detected in the fine scan XRD pattern (see Fig. 2(c) inset), and ILa2TiO5/ITiO2 ¼ 0.021% where ILa2TiO5 and ITiO2 are the integrated intensities of the strongest diffraction peaks of La2TiO5 and TiO2 phases, respectively. The relative weight percent of the La2TiO5 phase was 0.072 wt% in the mixed samples which determined by the XRD reference intensity ratio (RIR) method [35], so for the x ¼ 0.5% sample, 88.5% of the doped La element was incorporated into the TiO2 lattice and 11.5% was used in the formation of second phase La2TiO5. Surface SEM micrographs of sintered (La0.5Nb0.5)xTi1-xO2 ceramics with different x values are shown in Fig. 3(aef). As shown in Fig. 3(a), the denser microstructure with a uniform grain size of

Fig. 2. (a) The XRD patterns of (La0.5Nb0.5)xTi1-xO2 (x ¼ 0.25%e5%) ceramics powder with the XRD peaks of rutile TiO2 to confirm the phase structure and inset show fine scan XRD patterns in the 2q range of 26.8e27.8 for x ¼ 0.25%e5.0%. (b) XRD patterns of pure TiO2, TiO2-Nb, TiO2-La and x ¼ 0.5% sample (c) Rietveld refinement for x ¼ 0.5% XRD pattern.

B. Guo et al. / Journal of Alloys and Compounds 768 (2018) 368e376 Table 2 Rietveld refinement lattices properties and relative density of x ¼ 0.5% and TiO2 ceramics.

TiO2 x ¼ 0.5%

a(b) (Å)

c (Å)

cell volume (Å3)

Relative density(%)

4.593(3) 4.597(1)

2.959(2) 2.963(2)

62.434(4) 62.621(7)

95.9 94.4

20 mm was obtained for x ¼ 0.25%. When x ranged from 0.5% to 5%, a secondary phase clearly appeared on the surface and the average grain size decreased from 18.2 mm to 7.3 mm. The secondary phase was characterized by using an energy dispersive spectrometer (EDS). Fig. 3(f) shows the EDS detected at locations A and B for x ¼ 0.5 ceramic surface. The results showed that La is rich in location A on the bright grains, and Ti is rich in location B on the dark grains. The results are in good agreement with the XRD observations that TiO2 and La2TiO5 phases coexist in the sintered body.

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Cross-section SEM micrographs for x ¼ 0.5% sample in Fig. 3(g) show that the La and Nb elements are homogeneously dispersed in the TiO2 ceramic. Combined with the results of XRD data, it was determined that for x ¼ 0.5% ceramic, some La element formed secondary phase La2TiO5 and some incorporated into the TiO2 lattice. The dependence of the dielectric properties on temperatures within a 10e420 K range for the x ¼ 0.5% ceramic at various frequencies(100 Hz, 1 kHz, 10 kHz) is shown in Fig. 4. Breakpoints appeared around 230 K because of using different measured instruments. The inset gives the difference for the measured εʹ (at 1 kHz) data using two dielectric analyzers in the overlap temperature (150 Ke250 K). The deviation was about 5% around 230 K in this experiment. Across the full dielectric spectrum, stable CP (εʹ > 104) and low dielectric loss (tand < 0.05) were obtained within measured temperatures 25e350 K. Several sets of relaxation peaks observed in the tand curves were denoted as R1, R2, R3 and R4. For a

Fig. 3. (aef) Surface SEM micrographs sintered ceramics with different x values (g) cross-section SEM micrographs for x ¼ 0.5% and (h) EDS detected at locations A and B for x ¼ 0.5 ceramics surface.

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of oxygen vacancies at such low temperatures and it may be a result of activating/freezing electrons in the defect-dipoles [6,37]. The relaxation behavior cannot be fitted well using only a single Arrhenius type nearest-neighbor-hopping model (eq. (1)) in the temperature range of 25e150 K. Zhao [25] argued that this relaxation in CP co-doped TiO2 ceramics is related to polaron relaxation, and the Mott's VRH-like relation should fit the data better [38]:

f ¼ f0 expðT0 =TP Þ1=4 ;

(2)

where f0 is the eigenfrequency and T0 is a constant related to the activation energy. The plot of lnf versus 1/T1/4 p is shown Fig. 5(b) inset and quite good linear behavior is obtained. For x ¼ 0.5% ceramic, the La3þ can induce oxygen vacancies for charge compensation as follows:

(3)

Fig. 4. The dependence of the dielectric properties on temperatures within the 10 Ke420 K range for the x ¼ 0.5% ceramic at various frequencies (100 Hz, 1 kHz, 10 kHz).

clear description, εʹ and εʹʹ at different fixed frequencies as a function as temperature are shown in Fig. 5(aeb). The step-like features were accompanied by broad relaxation peaks, and the εʹʹ peak position monotonously shifted toward higher frequencies with increasing temperature, indicating a thermally activated dynamic. Therefore, the relaxation parameters can be calculated according to the Arrhenius law as follows [36]:

f ¼ f0 expðEa =Kb TÞ;

(1)

where f is frequency at the peak maximum of ε00 , f0 is a constant, Kb is the Boltzmann constant, and Ea is the activation energy. The Ea-R1 values of the dielectric relaxations R1 (see Fig. 5(a) inset) were obtained from the slopes of the fitted straight lines. The activation energy of R1 (Ea-R1 ¼ 0.0125 eV) is far smaller than the typical grain activation energy, so it cannot be attributed to the motion/hopping

The extra electrons can be induced when the Nb5þ occupies the position of Ti4þ as shown below:

(4)

Ti4þ þ e/Ti3þ The complex clusters among LaTi0 , NbTi, TiTi0 , and V o as well as  0 0 LaTi0 /NbTi, LaTi0 /NbTi)LaTi0 , LaTi0 /V o )TiTi , NbTi/TiTi , and TiTi0 /V o )TiTi will be formed in the samples, thus R1 is related to the EPDD polarization, and R2 is related to a variable range hopping mechanism and is attributed to the contribution of Ti3þ ions that have not yet formed a cluster with La3þ ions [12,25,34]. Relaxation peaks R3 and R4 were located at high temperature (>273 K) and low frequency (<1 kHz), so the electrical modulus (M*) was chosen to analyze those two relaxation processes. M* is one of the effective methods to understand the electrical process where the low-frequency electrode polarization effects are

Fig. 5. εʹ and εʹʹ at different fixed frequencies as a function as temperatures (a) 15 Ke50 K, (b) 25 Ke150 K; The insets shows the Arrhenius fitting plots and Mott's VRH fitting.

B. Guo et al. / Journal of Alloys and Compounds 768 (2018) 368e376

suppressed [27,39]. M* was calculated as follows:

.  00 ε02 þ ε 2 .  00 00 00 ε02 þ ε 2 M ¼ε

M 0 ¼ ε0

M *2 ¼ M 02 þ M

00

2

(5)

;

where Mʹ and Mʹʹ are the real and imaginary parts of the complex modulus. The frequency dependences of Mʹ and Mʹʹ at different temperatures for x ¼ 0.5% are shown in Fig. 6 (a, b). Using the Arrhenius law (eq. (1)), R3 with an activation energy of Ea7 R3 ¼ 0.39 eV appeared at 273e393 K with f0 ¼ 5.0  10 Hz, and R4 with an activation energy of Ea-R4 ¼ 1.93 eV appeared 403e438 K with f0 ¼ 6.0  1024 Hz. The values of tand (tandmax ¼ 0.024) peak for R3 occurred at 43 Hz (see Fig. 1) at room temperature. Similarly, tand peaks have been observed in InþNb co-doped TiO2 ceramics at about 100 Hz in previous studies [8,40]. The Ea-R3 ¼ 0.39 eV is comparable with the energy of oxygen vacancy at the grain boundaries in various titanium oxides and many studies have confirmed that this behavior attributed to MaxwelleWagneretype polarization [27,41]. In a study by Han et al. [41], similar dielectric relaxations to R3, R4 were observed in microcrystalline InþNb codoped TiO2 ceramics, and were determined to be caused by the grain and the grain boundary with energies of 0.48(2) eV and 0.65(7) eV, respectively. In our study, a much higher Ea-R4 related to grain boundary was obtained. In Table 1, dielectric properties are remarkably enhanced for x ¼ 0.5% by the annealing process, so the complex impedance plane plots of ceramics annealed at different temperatures are revealed in Fig. 7(a). An expanded view of the high frequency data close to the origin is given in the inset. The higher frequency response corresponding to the x-intercept is attributed to the contribution of grains, and the large semicircular arc in the lower frequency range is attributed to the insulating grain boundaries. Thus, the values of grain resistance (Rg) and grainboundary resistance (Rgb) obtained from Fig. 7(a) are presented in Table 3. Compared with the values of Rgb for the as-sintered sample, those of the ceramics annealed at 1123 K increased from 106 to 1011 U cm, an increase of almost five orders of magnitude, whereas the Rg values were nearly unchanged. The annealing treatment in the air decreased the number density of oxygen vacancies and thus strongly affected the

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resistivity of grainboundary [8]. However, as the annealing temperature was increased to 1473 K, the Rg obviously increased to 105 U cm because of the transformation of Ti3þ to Ti4þ at high temperature. The impedance complex plane (Z*) plot of the x ¼ 0.5% ceramic as-sintered and annealed samples at various temperatures are shown in Fig. 7(b and c). The curves bent toward the abscissa to form a semi-circular arc, and the radii of the semi-circular arcs became smaller, indicating smaller values of Rgb at higher temperatures. This electrical response was therefore thermally activated. The Rg values calculated from the nonzero intercept, shifted very slightly with changing temperatures from 293 to 423 K, and it was difficult to calculate the conduction activation energy inside the grains (Fig. 7(c) inset). The activation energy for the thermally activated hopping process in the grain boundary was obtained by fitting the DC conductivity data with the Arrhenius equation:



sgb T ¼ s0 exp

 Egb ; Kb T

(6)

where s0 is a constant value, sgb (sgb ¼ 1/Rgb) is the grain boundary conductivity, and Egb is the activation energy for conduction across the grain boundary. The grain boundary activation energy for assintered sample is Es-gb ¼ 0.25 eV and annealed sample is EAgb ¼ 1.98 eV. The dielectric and impendence properties of some typical CP (A(4-5y)/3By)1-xTixO2 ceramics are summarized in Table 3. The impendence analysis shows that the CP co-doped TiO2 ceramics were composed of semiconducting grains and insulating grain boundary with grain boundary activation energy of 0.2e1.0 eV. The value of EA-gb was much higher than that of codoped TiO2 reported by others [40,42e47], the higher value of EAgb means that more electrons were blocked in the grain boundaries, which was one of the reasons for the low tand in this study. The broad frequency (103 to 109 Hz) dependence of dielectric properties and a summary of the different dielectric relaxations that contributed to permittivity for x ¼ 0.5% ceramics at RT is shown in Fig. 8. Different polarizations can contribute to dielectric properties in different temperature/frequency ranges. Dielectrictemperature spectrum showed that the permittivity dramatically increased by almost two orders of magnitude, from 102 to 104 (ε0 ¼ 360 at 17 K and ε0 ¼ 10030 at 45 K at 1 MHz, see Fig. 5(a)), and

Fig. 6. Mʹ and Mʹʹ at different fixed temperatures as a function as frequencies for R3, R4. The insets show the Arrhenius fitting plots.

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Fig. 7. (a) Complex plane impedance plots of ceramics annealed at different temperatures, Inset shows expanded the view of high frequency data. Impedance analysis for x ¼ 0.5% measured at various temperatures: (b) as-sintered, (c) annealed samples. The insets show Arrhenius fitting plot of the conductivity of grain boundary; (c) Inset shows expanded view of high frequency data measured at different temperatures.

remained stable until the measured temperature up to 425 K because of the EPDD polarization. Dielectric-frequency spectrum revealed that the εʹ > 104 obtained in the frequency range (<10 MHz) and the εʹ abrupt dropped from 104 to 232 as the test frequency range from 10 MHz to 3 GHz. Dielectric relaxations of R2, R3 and R4 weakly contributed to εʹ but had a significant effect on tand. A rough calculation of the contribution for different dielectric mechanism could be given. At 1 kHz, the εʹ (T ¼ 25 K) ¼ 12229, εʹ (T ¼ 120 K) ¼ 12917 and εʹ (T ¼ 293 K) ¼ 15209, so the contribution to εʹ for EPDD, electron hopping, MaxwelleWagner polarization at RT were about 80.4%, 4.6%, 15.0%, respectably. The CP in (La0.5Nb0.5)0.5%Ti99.5%O2 ceramic was primarily related to EPDD polarization.

In this study, despite the use of a different acceptor and sintering process, the (La0.5Nb0.5)0.5%Ti99.5%O2 ceramic exhibited dielectric properties comparable to (In0.5Nb0.5)0.5%Ti99.5%O2 ceramics [6]. The dielectric-temperature spectrum shows that in addition to EPPD polarization, the redundant dielectric relaxations occurred. It was difficult to effectively eliminate the R2, R3 and R4 relaxations without sacrificing CP properties in this study. Therefore, there is an ongoing need to find a proper strategy to form EPDD polarization without introducing redundant polarizations in co-doped TiO2 ceramics.

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Table 3 Dielectric and impedance properties for some typical co-doped colossal permittivity TiO2 ceramics and (La0.5Nb0.5)xTi1-xO2 in this work. samples

(In0.5Nb0.5)0.01Ti0.99O2 (Y0.5Nb0.5)0.02Ti0.98O2 (In0.5Nb0.5)0.015Ti0.985O2 (Sc0.5Nb0.5)0.1Ti0.9O2 (Ta0.5Sm0.5)0.02Ti0.98O2 (Ga0.5Ta0.5)0.025Ti0.975O2 Al0.03Nb0.03Ti0.97O2 (TL0.5Nb0.5)0.015Ti0.985O2 x ¼ 0.5% as-sintered x ¼ 0.5% annealed 1123 K x ¼ 0.5% annealed 1473 K

Dielectric properties(1 kHz,RT)

Impedance(at RT)

εr

tanq

Rg(U cm)

Rgb(U cm)

ERgb(eV)

Ref.

10000 65500 42376 1000e10000 23000 5500e35000 40000 14750 24650 12010 1640

0.01 0.22 0.06 0.016e0.035 0.11 0.017e0.079 0.1 0.037 0.13 0.018 0.25

17.5 15(U)@ 453 K 10e20 e 2.7(U)@433 K z35@423 K e 96 17 15 1.3E5

1.6E9 2938(U)@ 453 K e e 8005(U)@ 433 K 1.2E6@423 K e 8.4E9 1.1E6 1.0E11 8.2E10

e 0.289 0.717 0.66e0.95 0.301 0.909 0.69 0.86 0.25 1.98 e

[8] [9] [40] [43] [44] [45] [46] [47] this work this work this work

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Fig. 8. The broad frequency (103 to 109 Hz) dependence of dielectric properties and the contribution of electron-pinned defect-dipoles polarization, electron hopping, MaxwelleWagner polarization to εʹ and εʹʹ at RT for x ¼ 0.5% ceramic.

4. Conclusions LaþNb co-doped TiO2 ((La0.5Nb0.5)xTi1-xO2 (0.25%  x  5%)) ceramics were prepared by a solid-state reaction method. CP and low tand were obtained when the ceramics were sintered in an N2 atmosphere and annealed at 1073 Ke1173 K in air. A pure rutile phase was achieved as x ¼ 0.25% and secondary phase La2TiO5 was detected when x  0.5%. For x ¼ 0.5%, the optimum dielectric performance of εʹ > 104 and tand < 0.05 over a frequency range of 1 Hze2 MHz and 25e350 K was obtained. Through the dielectrictemperature spectrum, three kinds of dielectric relaxations were observed: EPDD, electron hopping and MaxwelleWagner polarization. The CP (>25 K at 1 kHz) was primarily related to EPDD polarization. The grain boundary resistance was greatly enhanced by the annealing process and the high activation energy of grain boundary was one of the reasons for the low tand in this study. Conflict of interest The authors declare that they have no conflict of interest.

Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 51572162), and the Fundamental Research Funds for the Central Universities (GK201604006, 2016CBZ007).

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