Suppression of electrical conductivity and switching of conduction mechanisms in ‘stoichiometric’ (Na 0.5 Bi 0.5 TiO 3 ) 1 (cid:2) x (BiAlO 3 ) x (0 r x r 0.08) solid solutions

(Na


Introduction
Sodium bismuth titanate, Na 0.5 Bi 0.5 TiO 3 (NBT), is considered a promising lead-free piezoelectric material to replace lead zirconate titanate (PZT) because of its high Curie temperature (T c B 325 1C), relatively high remnant polarization (P r = 38 mC cm À2 ) and piezoelectric constant (d 33 = 73 pC N À1 ). [1][2][3] NBT was first reported in the 1960s and has been receiving increasing attention in recent years driven by the surge in developing lead-free materials. 4 One major drawback of NBT as a piezoelectric/dielectric material can be its high electrical conductivity which leads to high dielectric loss (tan d) and leakage currents at elevated temperatures. 1 Many studies have been carried out to modify the electrical properties of NBT by forming solid solutions with other perovskites, [5][6][7][8][9][10][11][12][13] among which the NBT-BiAlO 3 system has been reported to present excellent ferroelectric and piezoelectric properties compared with NBT. 12,13 BiAlO 3 (BA) is a relatively new lead-free ferroelectric material with a high T c . [14][15][16] Its large ferroelectric polarization and piezoelectricity were first predicted using density functional theory reported by Baettig et al. 14 and later confirmed by experiments. 15,16 BiAlO 3 has a rhombohedral perovskite-type structure at room temperature with Al 3+ on an octahedral site. It has a T c 4 520 1C, d 33 = 28 pC N À1 , and P r = 9.5 mC cm À2 at room temperature which increases to 26.7 mC cm À2 at 225 1C. 15 BiAlO 3 can only be prepared under high pressure (e.g., 6 GPa), and it decomposes around 550 1C; however, it can be partially stabilized by forming solid solutions with other perovskite materials such as BaTiO 3 17 and NBT 12,13,18,19 to modify the structure and properties of the host.
(NBT) 1Àx (BA) x solid solutions have been studied by several researchers. Yu and Ye 12 reported that the NBT-BA system can remain single phase up to x = 0.08. They found that incorporation of BA into NBT enhanced P r and d 33 , decreased E c and significantly reduced the dielectric loss at elevated temperatures. Watanabe et al. 18 also reported a solid solution limit of 8% for BA in NBT and an increased d 33 with increasing x. Ullah et al. 13 reported optimised ferroelectric and piezoelectric properties at x = 0.05 and a rhombohedral to pseudocubic phase transition at x = 0.075. Manotham et al. 19 compared the properties of (NBT) 0.94 (BA) 0.06 ceramics prepared by two-step sintering and conventional sintering. Peng et al. 20 combined the results from dielectric measurements and transmission electron microscopy to suggest the co-existence of ferroelectric and anti-ferroelectric phases in (NBT) 0.92 (BA) 0.08 ceramics. The above studies focus mainly on the improvement of the ferroelectric/piezoelectric properties of NBT by BA incorporation. There is little information about the effect of BA on the electrical conductivity and conduction mechanism of NBT, which are critical to the dielectric loss and leakage current of NBT. [21][22][23] Our previous studies have shown that NBT displays a variety of electrical behaviour. [21][22][23][24] The nominally stoichiometric NBT (nominal Na 0.5 Bi 0.5 TiO 3 ; NB 0.50 T) presents high conductivity with an oxide-ion transport number t ion B 0.9 at 600-800 1C. As t ion is the fraction of the total current carried by oxygen ions, such a high t ion suggests that the electrical conduction is dominated by oxygen ions. The predominance of oxide-ion conduction (as opposed to sodium ion or electronic conduction) in NB 0.50 T has been further confirmed by 18 O tracer diffusion measurements. The high oxide-ion conductivity in NB 0.50 T is attributed to oxygen vacancies generated through low levels of Bi 2 O 3 loss during ceramic processing according to the Kroger-Vink equation, as well as the high oxygen ion mobility associated with highly polarized Bi 3+ ions and weak Bi-O bonds. 25 26 The predominant electronic conduction in NB 0.51 T is confirmed by a t ion o 0.1 at 600-800 1C. Later work shows that a further increase in the initial Bi-excess content (for example, Na 0.5 Bi 0.52 TiO 3.03 ; NB 0.52 T) can reintroduce oxide-ion conductivity into NBT. NB 0.52 T shows a mixed conduction behaviour with comparable contributions from oxide-ion conduction and electronic conduction showing a t ion close to 0.5, which is possibly linked to a change in the Bi-content in the NBT main phase or a space charge effect because of the presence of a Bi-rich secondary phase. 23 Mixed ionic-electronic conduction followed by low levels of electronic conduction and therefore an excellent high temperature dielectric behaviour was also observed for Nb-doped NBT. This study was based on Nb-replacing Ti on the B-sites with incorporation of excess oxygen 'filling' the oxygen vacancies associated with Bi 2 O 3 loss during processing. 23 Based on the magnitude of bulk conductivity, s b and t ion values, we concluded that undoped NBT and Nb-doped NBT can exhibit three types of electrical behaviour: type I, predominant oxide-ion conduction, high s b , t ion B 0.9; type II, mixed ionic-electronic conduction, intermediate s b , t ion B 0.5; type III, predominant electronic conduction, low s b , t ion o 0.1. These three types of electrical behaviour can be clearly distinguished from the tan d-T relationship (measured at 1 MHz). Type I NBT shows a sharp rise of tan d with increasing temperature and tan d exceeds 0.2 at B350 1C. In contrast, type III presents low tan d in a wide temperature range (o0.02 from 300 to 600 1C), making it an excellent hightemperature dielectric material. In between types I and III, type II shows low tan d in a narrow temperature range and a steep rise above B500 1C to exceed 0.1 at 600 1C.
The above findings not only reveal the electrical conduction mechanisms of NBT but also show the flexibility in tailoring the properties of NBT for various applications such as piezoelectric/ dielectric devices, oxide-ion conductors and mixed ionicelectronic conductors. Here, the electrical conductivity and conduction mechanism of (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions were studied by impedance spectroscopy and electromotive force measurements. The purpose is not only to investigate the effect of BA on the electrical conductivity of NBT, but also to further understand the factors that control the oxide-ion conduction in NBT to tailor its electrical properties. The results show that BA incorporation decreases the electrical conductivity of NBT and changes the conduction mechanism from predominantly oxygen-ion conduction to mixed ionic-electronic conduction and then to predominantly electronic conduction with increasing BA content. The suppressed conductivity and changes in conduction mechanisms significantly reduce the dielectric loss at elevated temperatures to make NBT an excellent high-temperature dielectric material. This study provides an alternative approach to fine-tune the electrical properties of NBT as opposed to manipulating the A-site Na/Bi non-stoichiometry in undoped materials or by B-site Nb donor doping.
Experimental (Na 0.5 Bi 0.5 TiO 3 ) 1Àx (BiAlO 3 ) x (0 r x r 0.08) solid solutions were prepared by a solid-state reaction method using Na 2 CO 3 (99.5%, Fisher chemical, UK), Bi 2 O 3 (99.9%, Acros Organics, USA), TiO 2 (99.9%, Sigma Aldrich, UK) and Al 2 O 3 (99.95%, Alfa Aesar, UK) as starting materials. Prior to weighing, the raw powders were dried overnight at 300 1C for Na 2 CO 3 and Bi 2 O 3 , 800 1C for TiO 2 and 900 1C for Al 2 O 3 . Appropriate amounts of each precursor were weighed and mixed thoroughly in iso-propanol using yttria-stabilised zirconia grinding media for 6 h. The mixture was dried at 85 1C overnight, sieved and calcined at 850 1C for 2 h. The resultant powder was subjected to a second round of ball milling, drying, sieving and calcined at 900 1C for 2 h. After a third round of milling, drying and sieving, the final powder was compacted into pellets by uni-axial cold pressing followed by isostatic pressing at 200 MPa. Pellets were embedded in sacrificial powder of the same composition and sintered at 1175 1C for 2 h in air. For pure NBT, powder was calcined at 800 1C twice and the pellet was sintered at 1150 1C. After sintering, pellets were ground on SiC sand paper to remove the sacrificial powder. Pellets of B0.85 cm in diameter and B0.15 cm in thickness were used for impedance and LCR measurements.
Ceramic density was measured by the Archimedes' method and compared to the theoretical X-ray density. Phase purity was examined by X-ray diffraction on crushed pellets using a highresolution STOE STADI-P diffractometer (STOE & Cie GmbH, Darmstadt, Germany) operating with CuKa 1 radiation with a linear position-sensitive detector. Before measurements, the crushed pellets were annealed at 400 1C for 4 h to eliminate any residual stress caused by crushing and grinding. Structural refinement was carried out for reflections in the range of 201 r 2y r 801 using EXPGUI. 27,28 Ceramic microstructures were observed by scanning electron microscopy on thermally-etched surfaces using a Philips XL30 SEM. Compositions were obtained by energy-dispersive X-ray spectroscopy (EDS) on carbon-coated polished surfaces (without thermal etching). Raman spectroscopy measurements were carried out using a 514 nm Ar laser line in a Renishaw inVia Raman microscope.
Electrical properties of the pellets were obtained from ac impedance spectroscopy using an Agilent E4980A impedance analyser (Agilent Technologies Inc, Palo Alto, CA; frequency range 1 MHz to 20 Hz) and/or a Solartron 1260 system (Solartron Analytical, UK; frequency range 1 MHz to 0.1 Hz). Before measurements, Au paste was painted to cover both surfaces of the pellets and then fired at 800 1C for 2 h to serve as electrodes. Measurements were carried out in flowing N 2 , air and O 2 from 400 to 800 1C at increments of 50 1C. The equilibrium time between each measurement was 30 minutes. Equivalent circuit fitting was performed using ZView software (Scribner Associates, Inc, Southern Pines, NC). Dielectric properties were measured using an LCR meter (Agilent E4980 Precision LCR Meter, Agilent Technologies) with an applied ac voltage of 100 mV. Data points were collected every 60 s from room temperature (RT) to 800 1C using a non-inductively wound tube furnace at a ramping rate of 1 1C min À1 . Oxygen-ion transport number measurements were performed using a ProboStat system (NorECs Norwegian Electro Ceramics AS, Oslo, Norway). A sample of B1.7 cm in diameter and B0.2 cm in thickness was sealed onto an YSZ tube using a commercial glass frit. Before that, Pt electrodes of B1.0 cm in diameter were coated onto the centre of the pellet surfaces and fired at 900 1C for 2 h. An oxygen partial pressure ( pO 2 ) difference was created across the ceramic by flowing N 2 into the YSZ tube and leaving the outside of the ceramic in air. The pO 2 difference was monitored by measuring the voltage across the inner and outer electrodes using the YSZ tube. The voltage was measured using a Keithley 182 sensitive digital voltmeter. More details of transport number measurements can be found in ref. 21.

Results
Phase, composition and microstructure (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions are phase-pure based on XRD patterns (Fig. 1a). An expanded view of the 2y range between 38 and 421 shows the superlattice reflection of a rhombohedral structure for all compositions (Fig. 1b). The structure could be refined to a rhombohedral cell (space group R3c; Fig. 1c). The pseudo-cubic cell volume decreases with increasing x (Fig. 1d). The relative density of sintered ceramics was 495%, as listed in Table 1.
Although these samples are phase-pure based on the XRD patterns, SEM micrographs of polished surfaces for x = 0.07 and 0.08 showed the presence of small amounts of an Al-rich secondary phase ( Fig. 2a and b). EDS analysis of the solid solutions shows that the atomic fractions of the A-site (Na, Bi) cations are close to their nominal values (Fig. 2c); the atomic fractions of Al 3+ on the B-site slightly deviate from their nominal values for x = 0.07 and 0.08 because of the presence of the Al-rich secondary phase (Fig. 2d).
A typical SEM micrograph of a thermally-etched surface of a solid solution is shown in Fig. 3a. Average grain sizes of the solid solutions decrease with increasing x from B10 mm for x = 0.01 to B1.5 mm for x = 0.08. Undoped NBT has smaller grains compared to x = 0.01 and 0.02, which may be due to the lower sintering temperature (1150 1C) compared to 1175 1C for the solid solutions.

Raman spectroscopy
Room-temperature Raman spectra of (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions are shown in Fig. 4a. The spectrum of NBT is where k is the force constant and m is the reduced mass based on the harmonic oscillator approximation. The ionic radius of Al 3+ (0.535 Å, 6-fold co-ordination) is smaller than that of Ti 4+ (0.605 Å, 6-fold co-ordination), resulting in a shorter bond length and thus a higher force constant k. 33 The relative atomic mass of Al (26.98) is also lower than Ti (47.87). Because of the smaller ionic size and atomic mass of Al, the Ti-O band shifts to a higher frequency with increasing x. The TiO 6 octahedral bands are dominated by vibrations involving mainly oxygen displacement, and thus are expected to be unaffected by the mass of the cations. The shift to a higher frequency of these bands is due to an increased force constant k caused by the smaller ionic size of Al 3+ . Raman spectra further confirm the formation of NBT-BA solid solutions, and the Ti-O band shift to high frequency gives evidence that Al 3+ goes to the Ti-site of NBT as desired.

Electrical properties
Complex impedance plane (Z*) plots of (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions measured at 600 1C are shown in Fig. 5a-c. The Z* plot for NBT shows three well-resolved arcs (inset of Fig. 5a), from high to low frequency, corresponding to responses from bulk, grain boundary and electrode effects, respectively. This is consistent with our previous report. 21,23 For the NBT-BA solid solutions, the Z* plots show the following evolution with increasing BA concentration: (1) the magnitude of impedance, for both the bulk and grain boundary regions, increases with increasing x; (2) the two responses from the bulk and grain boundaries become less well-resolved with increasing x (0.01 r x r 0.05) and eventually merge into a single arc for x Z 0.06. The associated capacitance of the single arc is B7 Â 10 À11 F cm À1 , corresponding to a relative permittivity (e r ) of B800, which agrees with the value for paraelectric NBT materials at this temperature. Therefore, the single arc in the Z* plots for x Z 0.06 represents the bulk response. The decreasing resolution for the two arcs on the Z*   plots for 0.01 r x r 0.05 is attributed to the closer time constant (t) for the bulk and the grain boundary components with increasing x. The impedance data are also presented as M 00 -log f spectroscopic plots (Fig. 5d). M is the electric modulus and its complex form is defined as M* = joC 0 Z*, where o is the angular frequency, C 0 is the capacitance of an empty cell and Z* is the complex impedance. For easy comparison, M 00 (the imaginary component of M*) was normalized to its peak maximum and it shows a systematic peak shift to a lower frequency with increasing x. The M 00 peak position, f max = 1/(2pRC), is an intrinsic property of a material. As C does not show significant change with composition, a peak shift to a lower frequency indicates a decrease in conductivity (and therefore an increase in resistance). For 0 r x r 0.02, the relatively well-resolved impedance spectra were fitted by an equivalent circuit of three seriesconnected R-CPE elements to obtain the resistances R b , R gb and R tot (R tot = R b + R gb ). For 0.03 r x r 0.08, the bulk resistance was calculated from the M 00 peak frequency and peak maximum, and the total resistance was obtained from the Z 0 intercept on Z* plots. This is to avoid large errors from equivalent circuit fitting due to the less well-resolved impedance responses from the bulk and grain boundary components. R b and R tot were converted to s b (= 1/R b ) and s tot (= 1/R tot ) and presented in Arrhenius plots (Fig. 6), where systematic decreases of s b and s tot with increasing x can be observed.
Activation energies (E a ) for s b and s tot are listed in Table 2. For s b , there is a notable change in the activation energy (E a ) with increasing x from {1 eV for 0 r x r 0.02, B1.2 eV for x = 0.04, 0.05 and to 41.6 eV for 0.06 r x r 0.08. E a for s tot also increases with x from B0.9 eV for x = 0, 1.3-1.5 eV for 0.01 r x r 0.05 to 41.6 eV for 0.06 r x r 0.08. Fig. 7 shows the impedance spectra measured in flowing nitrogen, air and oxygen for selected compositions showing the effect of pO 2 . For x = 0.01, the bulk response does not change with pO 2 , as shown in the inset of Fig. 7a and the overlapping peaks in the M 00 -log f spectroscopic plots (Fig. 7b). This suggests that bulk conduction is dominated by ionic species. The grain boundary impedance is dependent on pO 2 : it is the lowest in N 2 and the highest in O 2 , indicating the presence of n-type electronic conduction. It is also noteworthy to mention that the lowfrequency electrode spike is most prominent in N 2 and least prominent in O 2 , suggesting the presence of oxide-ion conduction. For x = 0.06, the Z* plots show the smallest single arc in N 2 and the largest arc in O 2 (Fig. 7c), and the M 00 -log f spectroscopic plots show a peak shift towards high frequency in N 2 (Fig. 7d). The low-frequency electrode spike is still present in N 2 , as shown in the inset of Fig. 7c. The pO 2 -dependent impedance and the low frequency spike suggest a mixed ionic-electronic conduction mechanism. The conducting species are electrons and oxygen ions. For x = 0.07, the Z* and M 00 -log f plots show a similar pO 2 -dependence as x = 0.06; however, the low-frequency electrode spike is less apparent (inset of Fig. 7e). This suggests that the bulk conduction is dominated by an n-type electronic conduction mechanism.
Oxygen-ion transport number, t ion , at 600 1C for selected compositions of x is shown in Fig. 8. t ion drops from 40.9 for NBT (x = 0), to 0.4-0.8 for 0.02 r x r 0.06 and to o0.1 for x = 0.07.   This agrees with the information extracted from Fig. 7. According to the classification proposed in our previous study, 23 the electrical conduction of NBT-BA solid solutions also displays three types of behaviour: type I: t ion 4 0.85, predominantly oxide-ion conduction; type II, 0.15 r t ion r 0.85, mixed ionic-electronic conduction; type III, t ion o 0.15, electronic conduction. Incorporation of BA into NBT is an alternative approach to tune the electrical conduction mechanism and conductivity of NBT-based materials as opposed to solely manipulating the A-site nonstoichiometry (Na/Bi ratio) or the B-site Nb doping. 23

Dielectric properties
The permittivity-temperature (e r -T) profiles for selected compositions of the NBT-BA solid solutions are shown in Fig. 9a. The permittivity maximum decreases slightly with increasing x, from B3000 for NBT to B2700 for x = 0.07. The temperature where permittivity shows its maximum, T m , also decreases with increasing x from B325 1C for NBT to B290 1C for x = 0.07. Incorporation of BA into NBT has a much more significant effect on the dielectric loss-temperature profile (Fig. 9b). NBT (x = 0) shows a sharp rise of tan d with increasing temperature and tan d exceeds 0.2 at B350 1C. In contrast, x = 0.07 exhibits very low tan d over a wide temperature range (o0.02 from 300 to 700 1C). Compositions in between x = 0 and 0.07 show low tan d in a narrower temperature range and a steep rise above B600 1C, exceeding 0.1 at 650 1C.

Discussion
The electrical conductivity of (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions decreases with increasing x and the conduction mechanism changes from predominantly oxygen-ion conduction via mixed ionic-electronic conduction to predominantly electronic conduction with a continuous drop of t ion from 40.9 for x = 0 to o0.1 for x = 0.07. Incorporation of BA into NBT suppresses the oxide-ion conduction in NBT and makes it an excellent high-temperature dielectric material. Possible reasons for the suppressed oxide-ion conduction are discussed below. For a single type of charge carrier, the electrical conductivity is determined by s = cÁqÁm, where c, q and m are the concentration, charge and mobility of the charge carriers, respectively. As the oxide-ion conduction is suppressed by BA incorporation,   there is either a decrease in the concentration and/or a decrease in the mobility of the oxygen vacancies.
The oxide-ion conductivity of NBT originates from the oxygen vacancies generated through a small amount of Bi 2 O 3 -loss during ceramic processing as described in eqn (1). Our previous study 24 showed that 0.5-1% donor (Nb) doping on the B-site of NBT can fill up the oxygen vacancies and significantly decrease the electrical conductivity. Therefore, the oxygen vacancy concentration in NBT is estimated to be in the range of 0.25-0.5%, corresponding to a Bi 2 O 3 -loss of 0.17-0.33%. Such a small loss of Bi 2 O 3 is ''accidental'' and therefore difficult to control in a reproducible manner. 24 With BA incorporation into NBT, the defect chemistry can be described by the following Kroger-Vink equation: where we have used the subscript A to denote the disorder of the Na and Bi ions on the A-site of the NBT lattice. Incorporation of BA into NBT does not induce any additional oxygen vacancies or create any additional oxygen ions and can therefore be considered as a 'stoichiometric' doping mechanism. Oxygen vacancies in the NBT-BA solid solutions are only generated by Bi 2 O 3 -loss during ceramic processing. Consequently, the oxygen vacancy concentration in the solid solution is not completely controllable and should therefore occur at a randomly low level, which is very unlikely to result in a systematic decrease of conductivity with increasing x. Therefore, a significant change in the oxygen vacancy concentration, if there is any, is not the dominant factor for the suppressed oxide-ion conduction in the NBT-BA solid solutions. It is more reasonable therefore to attribute the suppressed oxide-ion conduction on BA incorporation to the increased trapping of the residual oxygen vacancies, as discussed below.

Average structures
From general structural considerations, oxide-ion conductivity in a perovskite is often predicted by the following four empirical parameters: (1) Goldschmidt tolerance factor, t: 34 where r A and r B are the average ionic sizes of the A-and B-site cation(s) (12-and 6-fold co-ordination, respectively); r O is the ionic size of the oxygen ion (6-fold co-ordination, r O = 1.40 Å).
(2) The lattice free volume, V sf : 35 where V and V ion are the volume of the unit cell and the volume of each constituent ion, respectively. V can be estimated by 36 where where r A * is the ionic radius of the A-site cation in an 8-fold co-ordination (not 12).
(3) The critical radius, r C , defined by Kilner and Brook: 36 where a 0 is the pseudo cubic lattice parameter.
(4) The average metal-oxygen bond energy, E b , derived via a Born-Haber cycle: 37 where DH A m O n and DH B m O n are the heats of formation of the A m O n and B m O n oxides, respectively. DH A and DH B are the heats of sublimation of the metals A and B, respectively, and D O 2 is the oxygen dissociation energy. The tolerance factor, t, describes the lattice distortion in the perovskite structure. A small t represents large lattice distortion and thus is detrimental to oxide-ion conduction. 38 The specific free volume, V sf , describes the free space inside a unit cell and a large V sf is beneficial for the migration of oxygen ions. Hayashi et al. 35 summarized the electrical conductivity data from literature and found an optimum t of 0.96 to obtain the maximum conductivity in perovskites. They attributed the maximized conductivity to a compromise between t and V sf . The critical radius, r C , describes the saddle point formed by two A-site and one B-site cations. The larger the r C , the easier it is for the oxygen ions to pass through the saddle point. The average metal-oxygen bond energy, E b , was found to have a linear relationship with the activation energy for oxygen migration: the smaller the absolute E b , the lower the activation energy. 37 The values of these four parameters of the NBT-BA solid solutions were calculated and are listed in Table 3. Thermodynamic data of the corresponding oxides and metals used to calculate E b were obtained from ref. 39. With increasing BA content, V sf , and r C decrease while t and the absolute value of E b increase. These are all detrimental to oxide-ion conduction in perovskites. However, it should be noted that the change of these parameters with increasing x is quite small. Such a small Table 3 Tolerance factor t, specific free volume V sf , critical radius r C and average metal-oxygen bond energy E b of (NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions change in the average structure is unlikely to result in such a dramatic change in conductivity.

Local structure
Compared to the average structure, the local structure has a more significant impact on the oxygen ion diffusion in NBT, as revealed by first-principles calculations. [40][41][42] These calculations showed the lowest energy barriers for oxygen ion migration occur in saddle points between Bi-Bi-Ti ions (0.22 eV), whereas higher barriers are observed for Na-Bi-Ti (0.6-0.85 eV) and Na-Na-Ti (1.0-1.3 eV) saddle points. Experimentally there is no evidence for the long-range ordering of the A-site cations in NBT, and therefore the Na-Bi-Ti saddle points are considered as the rate-limiting step in the overall oxygen ion migration in NBT. For the NBT-BA solid solution, there is no evidence for the ordering of the A-site cations with BA incorporation: no additional XRD peaks or sharpening of Raman peaks were observed. Instead, the peak width of the B135 cm À1 band (Na-O vibration) increases with increasing x, as shown in Fig. 10. Consequently, the Na-Bi-Ti(Al) saddle points are considered to dominate the energy barrier for oxygen ion migration. As Al 3+ is much smaller than Ti 4+ and its polarizability is much smaller, i.e. a Al = 0.79 Å 3 43 compared to a Ti = 2.93 Å 3 , 43 it is more difficult for oxygen ions to pass through the Na-Bi-Al saddle point. With increasing x, the number of Na-Bi-Al saddle points increases and therefore the oxygen ion mobility is decreased. However, as the polarizability of Bi 3+ (6.12 Å 3 43 ) is much higher than Ti 4+ and Al 3+ , local deformation at the saddle point when an oxygen ion is passing through should come mainly from Bi 3+ . The low polarizability of Al 3+ may not be the determining factor for the suppressed conductivity.
To further understand the importance of the ionic radius and polarizability of the B-site ''dopant'', (NBT) 1Àx (BiGaO 3 ) x (BG, x = 0.02, 0.04, 0.06 and 0.08) solid solutions were prepared. NBT-BG shows a very similar behaviour as that of NBT-BA: the bulk conductivity also decreased with increasing x (unpublished results). Ga 3+ has a comparable size (0.62 Å, 6-fold co-ordination) to Ti 4+ , indicating that the ionic size is not a critical factor.
The decreased mobility of charge carriers can originate from trapping of oxygen vacancies. As also revealed in ref. 41 and is listed in Table 4. When the BA content is low, i.e., x = 0.01, to trap 0.5% V O , 50% of the B-sites must be occupied by Al 3+ , which is much higher than the actual Al 3+ occupancy (1%).  (Table 4). Therefore, trapping of V O is a more important factor for the suppressed oxide-ion conduction in the NBT-BA solid solution. Although recent density-functional-theory (DFT) calculations 44 suggest that the association of Mg 00 Ti and V O in Mg-doped NBT is significant only at a low temperature range (i.e., o400 1C), it is possible that Al 0 Ti has a stronger ability to trap V O as the Al-O binding strength (B502 kJ mol À1 45 ) is significantly higher than that of Mg-O (358 kJ mol À1 45 ), and therefore the Al 0 Ti À V O À Á complex can be stable at higher temperatures.
Pinning of the oxygen vacancies by grain boundaries may be another possibility and/or an additional factor that contributes to the reduced mobility of the oxygen vacancies in the ceramics.   Fig. 3b shows the decrease in grain size with increasing x, therefore the number of grain boundary increases with increasing x and consequently a higher chance to pin the oxygen vacancies. Grain boundaries have much more complicated defect chemistry than the bulk and therefore need further investigation.

Na/Bi ratio
Our previous studies 22,23 show that the electrical conductivity and bulk conduction mechanisms of NBT are highly sensitive to low levels of the A-site nonstoichiometry. When Na/Bi Z 1, i.e., Na-rich or Bi-deficient, NBT is predominantly an oxide-ion conductor with high s b (41.0 Â 10 À3 S cm À1 at 600 1C); when Na/Bi o 1, i.e., Bi-rich or Na-deficient, NBT exhibits predominantly electronic conduction with very low s b (B2.0 Â 10 À6 S cm À1 at 600 1C). As shown in Fig. 11, a dramatic change in the bulk conductivity of around three orders of magnitude is observed at the vicinity of Na/Bi = 1 at 600 1C due to this switch in the conduction mechanism. The bulk conductivity of the NBT-BA solid solution also shows a dependence on the Na/Bi ratio (Fig. 11). In contrast to the sharp change observed for undoped NBT, a continuous drop of conductivity with decreasing Na/Bi ratio is observed, which is attributed primarily to the change of oxygen vacancy mobility. This result indicates that a Bi-rich, A-site environment is not necessarily good for the oxide-ion conduction even though the polarizability of Bi 3+ is high. Trapping of the oxygen vacancies by B-site acceptor-type dopants plays a more important role in the oxide-ion conduction of the NBT-based material, even at high temperatures.

Conclusions
(NBT) 1Àx (BA) x (0 r x r 0.08) solid solutions are prepared by a solid-state reaction and their electrical properties studied by ac impedance spectroscopy and electromotive force transport number measurements. Incorporation of BA decreases the electrical conductivity of NBT and changes the conduction mechanism with increasing x from predominantly oxide-ion conduction (type I) to mixed ionic-electronic conduction (type II) and finally to predominantly electronic conduction (type III). The suppression of oxide-ion conductivity significantly reduces the dielectric loss at elevated temperatures and consequently transforms the NBT-BA solid solution higher end members into excellent hightemperature dielectric materials. The suppressed oxide-ion conduction with increasing BA content is attributed mainly to a decrease in oxygen vacancy mobility associated with Al acceptor trapping. Although we cannot rule out the influence of grain boundaries as a source of trapping centres, the close correlation between the expected oxygen vacancy concentration and the level of BA doping (see Table 4 for details) provides compelling evidence for an alternative approach to fine-tune the electrical conductivity and conduction mechanism of NBT, viz. the trapping of oxygen vacancies using B-site acceptor dopants (i.e. Al 3+ ) as opposed to the filling of oxygen vacancies using B-site donor dopants (i.e. Nb 5+ ). This study not only presents an alternative approach to fine-tune the electrical conductivity and conduction mechanism of NBT, but also reveals the importance of local structures, especially defect association, on the oxide-ion conduction mechanisms in NBT-based materials.