Temperature dependent conductivity of Bi4Ti3O12 ceramics induced by Sr dopants

Bi4Ti3O12 is an important lead-free ferroelectric material. Doping modification of Bi4Ti3O12 has attracted great attention to improving its performances. In this work, the effect of Sr dopants on the microstructure, dielectric, and conductivity of Bi4Ti3O12 ceramic was investigated by XRD, SEM, and AC impedance spectroscopy. Substitution of 1 at% Sr for Bi decreased the grain size, suppressed the dielectric dispersion of Bi4Ti3O12 ceramic at room temperature, and resulted in different effects on the conductivity of grains and grain boundaries. The conductivity of grains in Bi4Ti3O12 ceramic was increased by the small amount of Sr dopants in the whole experimental temperature range. While the grain boundaries of 1 at% Sr-doped Bi4Ti3O12 exhibited lower conductivity than pure Bi4Ti3O12 below ~380 °C and higher conductivity above ~380 °C. The experimental phenomena were interpreted in term of compensating defects for Sr dopants.


Introduction 
Bismuth-based layer-structured ferroelectrics (BLSF) known as Aurivillius compounds are generally represented by a formula (A n-1 B n O 3n+1 ) 2-(Bi 2 O 2 ) 2+ , where A denotes mono-, di-, or trivalent cations or a mixture of those at the 12-coordinated site, B stands for tri-, tetra-, or pentavalent cations at the 6coordinated site, and n indicates the number of perovskite units [1,2]. Its crystal structure is built up by perovskite blocks (A n-1 B n O 3n+1 ) 2and fluorite structure layers (Bi 2 O 2 ) 2+ alternatively stacking up along the pseudo-tetragonal c-axis. Aurivillius compounds have Aurivillius compounds have not been systematically investigated.
The leakage of BIT is believed to be closely related to the oxygen vacancies induced by the evaporation of Bi at the sintering temperature. The Sr-O bond has the higher bond energy (454 kJ/mol) than the Bi-O bond (343 kJ/mol) [17], so it is expectable that the Sr doping maybe suppress the evaporation of Bi to decrease the leakage. Meanwhile, the aliovalent Sr 2+ substitution for Bi 3+ can work as acceptors to compensate for the electrons from the ionization of oxygen vacancies, which would further inhibit the leakage of BIT. Therefore, it is necessary to experimentally investigate the effect of Sr dopants on the conduction of BIT.
In this work, Sr-doped Bi 4 Ti 3 O 12 (SBIT) samples were prepared by conventional solid-state reaction. The effect of small amount of Sr dopants on dielectric properties and electrical conduction of BIT was studied by AC impedance spectroscopy because the impedance analysis is a powerful technique to distinguish the different contributions of microstructural components (i.e., grains, grain boundaries, and electrode interfaces) to the conduction of materials. The experiments provided some referential results for modification of BIT related materials.

Experiment
Sr-doped BIT ceramics with nominal compositions of (Bi 1-x ,Sr x ) 4 Ti 3 O 12-2x (SBIT, x = 0, 0.01, 0.02, 0.05) were synthesized by conventional solid-state reaction method, which are denoted as BIT, 1%Sr, 2%Sr, and 5%Sr, respectively. For comparison, a SrBi 8 Ti 7 O 27 sample was also prepared. Stoichiometric amounts of Bi 2 O 3 , TiO 2 , and SrCO 3 with purity > 99.9% were thoroughly mixed in ethanol medium in an agate mortar. The mixed raw material was initially pre-calcined at 780 ℃ for 3 h in air and calcined at 850 ℃ for 3 h in air. The obtained powders were ground and uniaxially pressed into pellets with thickness of 1 mm and diameter of 12 mm. The pressed pellets were sintered at 1100 ℃ for 2 h in air. X-ray powder diffraction (XRD, Cu Kα, X'pert Pro, PANalytical B.V., Almelo, Netherlands) technique was used to identify the phase constituent of the sintered samples. The microstructure of the sintered pellets was observed by using a scanning electron microscope (SEM, HITACHI S-4800, Hitachi Ltd., Tokyo, Japan). For dielectric measurement, both sides of the pellets were polished smooth and parallel, and coated by silver paint. The pasted pellets were heated at 620 ℃ for 15 min. The dielectric and impedance responses were measured using impedance analyzer (impedance analyzer, WK6510B, Wayne Kerr, UK) in the frequency range from 50 Hz to 10 MHz from room temperature to 720 ℃. The polarization-electric field (P-E) loop measurement was performed using an aixACT TF 2000 analyzer. The measurement was performed by applying to the samples single sinusoidal waveforms of 100 Hz. During the measurements, the samples were immersed in silicone oil.

1 Phase identification and microstructure
Phase identification of prepared SBIT samples was performed by XRD as shown in Fig. 1  . The enlarged parts of XRD patterns clearly show that the single peaks at ~16.2° and ~30° in the samples of x = 0 and 0.01 become two peaks in the sample of x = 0.05, evidencing the existence of two Aurivillius phases. For the sample of x = 0.02, the peak at ~16.2° has a tail on the high angle side, suggesting the possible existence of a minor phase. In addition, a small amount of Bi-rich oxide (Bi 20 TiO 32 ) is observed in the samples of x = 0.05 and SrBi 8 Ti 7 O 27 , which is evidenced by the weak peak at ~28°. The XRD patterns of x = 0, 0.01, and 0.02 are well indexed with the monoclinic structure B2cb. The lattice parameters are obtained by fitting the XRD patterns with the Fullprof software [18] and plotted in Figs. 1(b) and 1(c). It is found that the unit cell volume expands with increasing the Sr content. The volume expansion of Sr-doped BIT may be caused by the substitution of Sr 2+ ions which has larger size (r = 1.26 Å, coordination number CN = 8) than Bi 3+ ions (r = 1.17 Å, CN = 8) [19]. The results demonstrate that the Sr 2+ cations are incorporated into the lattice structure of BIT. The lattice parameters of the 2%Sr sample do not follow the linear expansion relation of the BIT and 1%Sr samples, in consistent with the observation of minor second phase in the 2%Sr sample. The solubility of Sr in (Bi 1x Sr x ) 4 Ti 3 O 12 is less than 0.02 according to the experimental results.  [20,21]. The depression of dielectric dispersion by Sr doping suggests that Sr dopants decrease the number of activated space charges in samples at RT. At 250 ℃, the dielectric relaxation is clearly observed in the samples. The relaxation frequency of BIT is lower than those of 1%Sr and 2%Sr samples as marked by arrows in Fig. 3(b). The r   value of the 1%Sr sample is less than that of BIT at low frequency but larger at high frequency. At 450 ℃, the r   value of 1%Sr sample is larger than that of BIT approximately in all frequency range. The log r   vs. logf plots of the samples show a linear relation at low frequency with slope nearly equal to 1 as shown in Fig. 3(c), which suggests the dominance of DC conductivity in the corresponding frequency. The temperature spectra of r   in Fig. 3 [11,22], confirming that the dielectric anomalies correspond to the ferroelectric transition. It indicates that the Sr dopants decrease T c of BIT. Figure 2 shows the SEM images of the samples. All the ceramics are composed of plate-like grains, which is a typical characteristic of layer-structured compounds. It is found that the undoped BIT ceramic has the largest grain size with the length from 5 to 10 μm and the thickness about 2 μm on average, and the Sr doping significantly decreases the grain size. The 1%Sr sample has the smallest grain size with the length of 1-2.5 μm and the thickness of ~0.7 μm. With increasing the Sr content, the grain size of doped samples becomes larger.

2 Dielectric and impedance analysis
Frequency dependence of real part ( r   ) and imaginary part ( r   ) of complex relative permittivity at various temperatures is displayed in Fig. 3. At room temperature (RT), the BIT sample shows more intensive dielectric dispersion than the Sr-containing samples at low The decrease of T c induced by Sr dopants can be reasonably understood considering the possible effects of Sr dopants on the crystal structure of Bi 4 Ti 3 O 12 . It is believed that the T c of Aurivillius compounds is closely related with the perovskite tolerance factor ( where r A , r B , and r O are the average effective ionic radii of the A and B cations and oxygen anion in ABO 3 perovskite compounds, respectively) [23]. A smaller value of τ (for the case of τ < 1) indicates heavier structural distortion, consequently increasing the T c of Aurivillius compounds [23]. The larger size of Sr 2+ ions increases the τ value of perovskite units, which should result in the decrease of T c . In addition, Sr dopants can weaken the covalent hybridization of the Bi 6s and O 2s/p orbits which is believed to result in the ferroelectric distortion of Bi-containing perovskite compounds [24]. Therefore, the decrease of T c in Sr-doped samples with respect to the undoped sample is reasonable.
To clarify the conduction characteristics and understand the dielectric differences between BIT and 1%Srdoped BIT at different temperatures, the impedance analysis was carried out. Figure 4 shows the Nyquist plots of complex impedance ( Z  vs. Z  ) of BIT and 1%Sr samples at several characteristic temperatures. At 50 ℃, impedance curve of 1%Sr is closer to the imaginary axis than that of BIT, indicating higher resistivity of 1%Sr than that of BIT. With increasing temperature, the curves gradually bend toward the real axis, which indicates the decrease of resistivity with temperature. At 110 ℃, a relaxation semicircular arc is clearly observed in the 1%Sr sample. Increasing temperature to 190 ℃, the BIT sample also exhibits a relaxation arc at high frequency. It is known that the intercept of the impedance semicircular arc on the real axis marks out the resistance of the corresponding microstructural components, such as grains, grain boundaries, and electrode interfaces [25]. Therefore, the resistance of the high-frequency microstructural component of the 1%Sr sample is lower than that of the BIT sample as shown in Fig. 4(c). However, the slope of the curve of BIT at low frequency is less than that of the 1%Sr sample, indicating that the 1%Sr sample is more resistive than the BIT sample at 190 ℃. The Nyquist diagrams at 250 ℃ reflect the similar properties as those at 190 ℃ except that the curves bend closer to the real axis, namely the resistances become lower. At 310 ℃, nearly whole semicircular arcs at low frequencies are observed as well as the highfrequency arcs, showing the corresponding resistance of the 1%Sr sample is close to that of BIT. As temperature rises up to 450 ℃ , the whole lowfrequency semicircular arcs are obtained. Both the low-frequency and high-frequency resistances of the 1%Sr sample are lower than those of BIT. The critical temperature at which the resistances of two samples are nearly equal is about 380 ℃ as shown in Fig. S1 in the Electronic Supplementary Material (ESM). An equivalent circuit containing a series combination of two parallel (QR) circuit elements gives a good fitting of the complex impedances as shown in Fig. 4 where R is the resistance and Q is the constant phase element (CPE). The high-frequency and low-frequency impedance arcs are attributed to the contributions from grains and grain boundaries respectively, which are determined by the capacitance criterion, C hf < C lf , based on the fact that the much thinner boundaries result in much larger capacitance (C) of grain boundaries than that of grains. To obtain a more intuitive comparison of C hf and C lf , the frequency dependence of electric modulus ( * M ) is plotted. Figure 5 [26,27], so the low-frequency peaks of M  correspond to more capacitive components than the high-frequency peaks. Therefore, the two relaxations are distinguished: the low-frequency one originates from grain boundaries and the high-frequency one results from grains. The BIT sample has lower relaxation frequencies than the 1%Sr sample, in consistent with the dielectric data displayed in Fig. 3.
The electrical properties of microstructural components are qualitatively assessed according to the dielectric and impedance analysis. For both samples of BIT and 1%Sr, the resistances are dominated by grain boundaries as evidenced by the much larger diameters of the impedance semicircular arcs at low frequencies than those at high frequencies as shown in Fig. 4. Doping Sr in BIT dramatically decreases the resistivity of grains (i.e., the compound), however, brings about different effects on the resistance of grain boundaries depending on temperature. The resistance of grain boundaries of the 1%Sr sample is larger than that of the BIT sample below ~380 ℃, and changes to be lower above ~380 ℃ as shown in Fig. S1 in the ESM.
To understand the temperature dependent conductivities of the samples, the kinetic analysis of conduction is performed. Figure 6 shows the frequency dependence of AC conductivity (σ ac ) which is calculated from the dielectric data using the relation σ ac = ωε 0 ε″, where ω is angular frequency and ε 0 is the permittivity of free space. It is observed that the AC conductivity of the ceramics increases with increasing temperature. The frequency independent plateau (region I) is observed at low frequency and high temperature, indicating the dominance of DC conductivity in the region I, which is consistent with the linear region with slope ~1 in Fig. 3(c). With increasing frequency, σ ac changes to frequency dependent as the frequency is beyond a certain value due to the capacitance impedance contribution. Comparing with the log Z f   and log M f   plots in Fig. 5, the frequencies when σ ac departs from the linear region in Fig. 6 are consistent with the low-frequency relaxation frequencies in Fig. 5, indicating the departure of σ ac from DC dominance is caused by the capacitance impedance contribution    can withstand about 100 kV voltage. However, the 1%Sr and 2%Sr doped ceramics can only bear a voltage of ~80 kV because the Sr dopants increase the conductivity of grains as discussed below. The 5%Sr sample exhibits a plump loop, which may be attributed to the mixed microstructure of large leakage Sr-doped phase and insulated SrBi 8 Ti 7 O 27 phase. The mixed microstructure forms a complicated capacitance structure, leading to the plump loop but not from the intrinsic ferroelectric polarization. It should be noted that the BIT ceramic displays a necking P-E loop, which may result from pinning by defects, probably acceptoroxygen-vacancy defect complexes [28].

Discussion
The impedance analysis indicates that the resistance of grain boundaries is higher than that of grains in the prepared ceramics. This phenomenon would be caused by the re-oxidation of grain boundaries during cooling from sintering temperature. It is generally accepted that the dielectric properties and conduction behaviors of perovskite-related oxides are closely related to the oxygen vacancies [29,30]. Our previous work of oxidation/reduction annealing on BIT-based ceramics also confirms the above conclusion [31]. It is believed that the oxygen vacancies are induced by the evaporation of Bi at sintering temperature [32]. The ionization of oxygen vacancies creates electrons and charged oxygen vacancies with the Kroger-Vink notation [33]: , (1) where and are the single and doubleionized oxygen vacancies, respectively. The long-range migrations of these oxygen-vacancy-related carriers result in conduction, and the localized reorientation hopping of these carries contributes to the polarization and dielectric relaxations. During cooling down from sintering temperature, the samples are re-oxidized, but the re-oxidation takes place mainly at grain boundaries because the oxidation is controlled by oxygen diffusion [34]. Therefore, the grain boundaries of the prepared ceramics are more resistive than grains.
In this work, the 1%Sr dopants suppress the lowtemperature conduction of BIT while increase the high-temperature conduction, and lead to different effects on the conduction of grains and grain boundaries. To understand these phenomena, it requires an insight to the mechanism of conduction. The conduction activation energy of BIT and Sr-doped samples at high temperatures is ranging from 0.91 to 1.01 eV, close to the reported values of charged oxygen vacancies in perovskite oxides [33,[35][36][37][38]. Paladino [35] reported that the activation energy for diffusion of the doubleionized oxygen vacancies in SrTiO 3 crystal is 0.98 eV. The conduction activation energies for doubly ionized oxygen vacancies in (Sr 1-1.5x ,Bi x )TiO 3 is 0.99-1.12eV [36]. Waser et al. [37] reported that the conduction activation energy of oxygen vacancy is 1.005-1.093 eV in Fe-doped SrTiO 3 . This is a good agreement with the experimental results of the conduction activation energy (0.91-1.01 eV) obtained in the present paper. Hereby, the conduction above 270 ℃ for the 1%Sr sample and above 310 ℃ for BIT very likely arises from the movement of •• O V . The activation energy of conduction at low temperature is 0.54-0.56 eV. The low-temperature conduction could be attributed to the thermally activated electrons from the second-ionization of oxygen vacancies as suggested by Ang et al. [36]. In their work, the Bi-doped SrTiO 3 ceramics showed the conduction activation energies from 0.59 to 0.78 eV associated with the second-ionization of oxygen vacancies. Therefore, the different conduction mechanisms would exist in the experimental samples depending on temperature, the long-range motion of the doubleionized oxygen vacancies provides dominant contribution to conduction at high temperature, i.e., above ~270 ℃ for the 1%Sr sample and above ~310 ℃ for BIT; below these temperatures, the conduction mainly originates from the motion of electrons created by the ionization of oxygen vacancies.
ac a E The impedance analysis in Fig. 4 indicates that the 1%Sr dopants dramatically increase the conductivities of grains of BIT ceramics, while suppress the conductivities of grain boundaries as the temperature below ~380 ℃ and enhance the electrical conduction of grain boundaries above ~380 ℃. These microstructurerelated conduction behaviors are interpreted in term of the compensating effect of Sr dopants. The aliovalent Sr 2+ dopants preferentially substitute Bi 3+ in BIT because the interstitial occupancy would not be favourable due to the large ionic size of Sr 2+ [39]. To keep the charge neutrality, the incorporation of Sr can lead to the following defect reaction [40]: (2) 4 [17]. In the experimental samples, the decrease of oxygen vacancies due to the suppression of Bi evaporation is apparently weaker than the inducing of oxygen vacancies by reaction (2) according to the experimental fact that the 1%Sr sample has more conductive grains than BIT. It is believed that there would be more oxygen vacancies in grains of 1%Sr sample than in BIT, which results in the higher conductivity of grains in the 1%Sr sample. During cooling down from the sintering temperature, the re-oxidation reaction eliminates partially oxygen vacancies and produces holes, but mainly at grain boundaries [34]: Combining equations (2) and (3), the Sr dopants work as acceptors to provide holes at grain boundaries: The holes created by reaction (4) will compensate for the electrons resulting from the ionization of oxygen vacancies. This could be the main reason for the higher resistivity of Sr-doped samples than that of BIT at low temperature, where the conduction of samples originates from electronic carriers. The reaction (4) implies that the amount of oxygen vacancies in grain boundaries of the Sr-doped samples is less than that of BIT at low temperature since the Sr dopants provide the lattice oxygen ( O O ). When the temperature rises up to the range where the conduction is dominated by the motion of charged oxygen vacancies ( ), the reaction (2) would take effect and induce more oxygen vacancies in grain boundaries. This results in that the conductivity of the 1%Sr sample gradually exceeds that of BIT as shown in Fig.  4 and Fig. 7. The experimental results support well the above deduction. The other Sr-doped samples show the similar temperature dependence of conduction with the 1%Sr sample, but the conductivity is lower because they are two phase samples and the SrBi 8 Ti 7 O 27 ceramic is highly resistive. O V 

Conclusions
Bi 4 Ti 3 O 12 ceramics doped with small amount Sr ions were synthesized by conventional solid-state reaction route and investigated by temperature dependent AC impedance spectroscopy. The small amount of Sr dopants decreased grain size and suppressed the ferroelectric phase transition temperature. The impedance analysis indicated that the resistance of the prepared ceramics was controlled by grain boundary. The grain boundaries of 1 at% Sr-doped Bi 4 Ti 3 O 12 were more resistive than pure Bi 4 Ti 3 O 12 below ~380 while ℃ more conductive above ~380 . The substitution of Sr ℃ for Bi would increase the number of intracrystalline oxygen vacancies resulting in higher intracrystalline conductivity. At low temperature, the Sr dopants play the hole-doping effect in grain boundaries and consequently result in higher resistance of Sr-doped samples than that of pure BIT. At high temperature, the Sr dopants induce more oxygen vacancies in grain boundaries to cause the higher conductivity of the 1%Sr sample than that of pure BIT. The present results provide useful information for designing and/or modifying the properties of Bi 4 Ti 3 O 12 related ceramics.