Effect of the incorporation of BiFeO3 on the structural, electrical and magnetic properties of the lead-free Bi0.5Na0.5TiO3

Powders of the system (1–x)Bi0.5Na0.5TiO3–xBiFeO3 (x = 0, 0.02, 0.08, 0.10) are synthesized by the combustion reaction method. The crystal structure and the particle size of Bi0.5Na0.5TiO3 are modified by the incorporation of BiFeO3, as can be seen from the infrared spectroscopy and X-ray diffraction results. The inclusion of iron and the increase in the molar percentage of bismuth in the BNT matrix generate new bonds with a different force constant. The structural analysis showed that the addition of BFO to the BNT does not induce any structural phase transition, preserving the rhombohedral symmetry of the Bi0.5Na0.5TiO3 system. The electrical measurements show that the incorporation of iron increases the conductivity of the system generated by an increase in the concentration of oxygen vacancies; alternatively, the addition of 10% of BiFeO3 generates ferrimagnetic behavior reflected in the magnetic hysteresis curves obtained at room temperature.


Introduction
One of the promising approaches to create new materials is the combination of different physical properties in a material to increase its functionality. The coupling between the parameters of magnetic and ferroelectric order can lead to magnetoelectric effects, in which magnetization may

Materials and methods
Bismuth nitrate (Bi(NO 3 ) 3 RA-Chemicals-98%), sodium nitrate (Na(NO 3 ) 3 Aldrich-98%), titanium tetrabutoxide (TBT Across-99%) and iron nitrate (Fe(NO 3 ) 3 Aldrich-97%) were used for the synthesis of the BNT-xBFO system (x = 0, 0.05, 0.08, 0.10, 0.20). Urea (CON 2 H 4 Merck-99.5%) and glycine (C 2 H 5 NO 2 Merck-98%) were used as fuels in a 50:50 ratio. First, each precursor was dissolved in water and/or nitric acid (HNO 3 ), until obtaining a transparent solution that indicates the non-formation of precipitates; also, the fuels were diluted in water until dissolution. The resultant solution was then evaporated and dried at approximately 200 ℃ on a hot plate under continuous stirring at ~300 rpm until the majority of the solvent is removed. This mixture was then heated in muffle furnace at a temperature of 600 ℃. Evaporation occurs which is followed by combustion. The resultant product consists of foamy flakes which are macerated in an agate mortar and the obtained powder is then calcined at a temperature of 800 ℃ for 4 h; in the Figure 1 we show a schema of the synthesis method. The ceramic powders were characterized by infrared spectroscopy with fourier transform using a SHIMADZU IR Affinity-FT infrared Spectrophotometer 4000-225 cm −1 . For the qualitative and semi quantitative analysis, the deconvolution of the bands took place using the Fityk 0.9.2 software [18]. The phase formation was investigated by X-ray diffraction (X'pert PRO PANalytical) equipped with Cu Kα (λ = 1.5418 Å) a wide range of Bragg angles 2θ (20°-80°) at scanning rate of 0.02° per minute. GSAS program [19] was used to analyze the phases in the diffractogram and to know their crystallographic characteristics. A vibrating sample magnetometer (VSM, the Quantum Design VersaLab Instrument) was used for magnetization measurements as a function of the magnetic field. X-ray profile analysis is a simple and powerful tool for estimating crystallite size and lattice deformation [20][21][22]. The Williamson-Hall analysis (W-H) is a simple method where the deconvolution of the diffraction profile width is induced by both the size of the crystallite and the deformation, considering the peak width as a function of 2 [23]. In this study, the W-H analysis was used to estimate the crystallite size and the deformation of the lattice. The ceramic powders were processed by the slip casting method to obtain green ceramic pieces that were subsequently sintered. The ceramic processing may undergo three stages: obtaining the slip, obtaining the pellets, and sintering. To obtain the slip, it was necessary to perform the calculation of solids and liquids from Eq 1 that relates the densities and concentrations of BNT, distilled water and the optimum density of the slip containing the oxide. Substituting the respective values in Eq 1, Eq 2 is obtained. From the calculations, taking into account that the total concentration must be equal to 1 (Eq 3), we obtain the quantity of solids and liquids necessary to stabilize the particles in suspension in the presence of a deflocculant, as seen in Eqs 4 and 5. In this process, a change occurs in the surface electrical charge of the particles, causing an increase in the repulsive forces avoiding the attraction between them [24]. Literature reports an ideal density value of 2.1 g/cm 3 [25] to guarantee a stable slip containing an oxide.
Pellets of 10 mm diameter were prepared by slip casting. An appropriate amount of slip is deposited in a mold and is left at rest for 3 h, where it acquires enough mechanical resistance to remove them from the mold. The highest density was obtained by sintering the pellets at 1120 ℃ for 2 h, finding a density of 5.81 g/cm 3 (96% of the theoretical density). The two circle surfaces of sintered ceramics were polished, coated with silver paster as the electrode and fired at 500 ℃ for 30 min. The dielectric properties measures were achieved with an impedance gain/phase analyzer SI 1260 (Solartron Analytical). Figure 2 shows the FTIR spectra of ceramic powders of the BNT-xBFO system. Three regions can be distinguished in the spectra: (i) a band located around 3500 cm −1 (R1) associated to the mode of flexion of the water molecule of the environment; (ii) between 1300 and 1700 cm −1 (R2) bands associated with vibrational modes of adsorbed C-O, of the CO 2 of air [26]; (iii) between 1100 and 470 cm −1 (R3), there are bands corresponding to functional groups associated with metal-oxygen bonds and may point to the BNT-xBFO system formation.

Results and discussion
The spectra in R3 interval was analyzed in more detail by means of the deconvolution process ( Figure 3). Figure 3a shows the deconvolution of the spectrum corresponding to the pure BNT sample where bands related to the Ti-O bond within the [TiO 6 ] octahedron are at 560, 585 and 637 cm −1 ; these bands are characteristics of the formation of perovskite [27,28]. There is also a band around ~862 cm −1 that belongs to the Bi-O bond [29] and a band around ~769 cm −1 that is associated with the stretching mode of the Bi-O bond in [BiO 3 ] [30,31]. The vibrational modes of Na 2 O are below 400 cm −1 , so characterization by Raman spectroscopy is required to identify this functional group. For x = 0.05 (Figure 3b), the shift to a greater wave number of the bands belonging to the Ti-O bond is evident. The bands belonging to the Bi-O bond undergo a displacement at ~785 cm −1 and ~852 cm −1 .
Additionally, three new bands appear: one around ~526 cm −1 associated with the Bi-O bond within the BiO 6 [32] octahedron; a second band at ~546 cm −1 that belongs to the stretching mode of the Fe-O bond in the octahedral FeO 6 [32] and a third band around ~727 cm −1 corresponding to the stretching mode of the Bi-O bond in BiO 3 [30,31].  For x = 0.08 (Figure 3c), the bands associated with the vibrations of the TiO 6 octahedron move to ~561 cm −1 , ~618 cm −1 and ~684 cm −1 while the bands of the Bi-O bonds undergo a displacement towards ~778 cm −1 , ~857 cm −1 . Furthermore, there are two new bands: one around ~506 cm −1 associated with the twisting mode of the Bi-O bond in the bismuthate group (BiO 3 ) [33] and another one ~949 cm −1 related to the stretching mode of the Bi-O [34]. For x = 0.10, the bands do not experience a significant change (Figure 3d).
When BFO is incorporated into the structure of the BNT, the Fe occupies the site of the Ti since the ionic radii of Fe is closer to the ionic radii of Ti (r Fe 3+ = 0.65 Å, r Ti 4+ = 0.61 Å, both in coordination 6 [35]) than the radii of Bi and Na (r Bi 3+ ~ 1.38 Å, r Na 1+ = 1.39 Å, both in coordination 12 [36]). Increasing the concentration of BFO, the displacement of the bands may be due to: (i) the variation in the electronegativity difference of the new bonds, which is proportional to the strength of the bond, an indirect measure of the resistance of the molecule to be deformed [37]. For example, the Ti-O bond has an electronegativity difference of 2.0, that is greater than that of the Fe-O bond (1.7), which makes the vibration frequencies of the TiO 6 octahedra different; (ii) the incorporation of BFO makes the percentage of bismuth higher than that of Na, while iron ions are incorporated in the titanium sites; the difference of atomic masses between Bi (208.98 g/mol), Na (22.98 g/mol), Ti (47.90 g/mol) and Fe (55.84 g/mol) causes a change in the frequency of vibration, related to the reduced mass of the system by the relation , where k is the force constant of the bonds and μ the reduced mass. Figure 4 shows the X-ray diffraction patterns. For x = 0, it is observed that the system crystallizes in a major phase related to the Bi 0.5 Na 0.5 TiO 3 system, with rhombohedral symmetry with space group R3c at room temperature and lattice parameters a = b = 5.4902 Å and c = 13.4859 Å, according to the CIF (Crystallographic Information File) number 2103295 [38,39]. In all the diffractograms, it is observed, that the majority crystalline phase corresponds to the perovskite structure of the Bi 0.5 Na 0.5 TiO 3 system. In general, the addition of BFO to the BNT does not induce any structural phase transition, preserving the rhombohedral symmetry, in agreement with previously reported results [40]. The Goldschmidt tolerance factor t is an indicator of the stability and distortion of the perovskite structure ABO 3 [41], allowing to predict the symmetry of the structure based on the ratio of the ionic radius, √ where R A , R B and R O are the ionic radii of the cations A, B and oxygen, respectively. For t = 1 the symmetry is cubic. When t decreases the structure becomes distorted; values of t ˂ 1 imply the compression of the B-O bonds and the elongation of the A-O bonds: the structure tends to twist the octahedrons to relieve the tensions caused by the mismatch in the sizes of the cations. When t > 1, the opposite occurs, the B-O bonds are lengthened and the A-O bonds are compressed and the hexagonal symmetry is stabilized [42,43]. The tolerance factor calculated for the BNT is t  0.98 indicating that it is a distorted perovskite, in agreement with the values reported in the literature [44,45].
The Figure 5 shows the behavior of t for the different compositions of the BNT-xBFO system, it is observed that the tolerance factor decreases with the increase of x, due to a structural distortion. A detail analysis of the diffractograms by means of the program GSAS helped us to confirm this hypothesis. The XRD patterns of the sample were analyzed by employing the Rietveld refinement method with the help of GSAS software. The Table 1 shows the lattice parameters, volume, crystallite size and deformation obtained from the Rietveld refinement for all compositions studied, and in the Figure 6 are shown two XRD spectra and Rietveld analysis, (x = 0.00, 0.20). It is seen that the volume of the cell increases due to the increase of the lattice parameters with the increase of BFO, as reported in the literature [46].

•• and
(iii) the difference in electronegativity that determines the percentage of covalence and/or ionicity, which affects the length of the bonds that are part of the crystal structure. For most fittings, except for x = 0.08, low values of  2 (<2) are obtained, signaling a good refinement. Generally, changes in the microstructure of a sample affect the intensity and the width of the Xray diffraction peaks. Improving the Scherrer formalism, Williamson and Hall identified that the grain size and lattice strain are two main sources of X-ray diffraction peak broadening at certain room temperature [48]. According to Scherrer's method for the size of nanoparticles, the Scherrer's crystalline size, D, is given by the Eq 6 [49]: cos (6) where K is the shape factor (0.9), β D is the peak width due to the crystallite size, is the wavelength of Cu-k α radiation and is the diffraction angle. In order to understand the peak broadening with lattice strains, various peaks in the XRD pattern were used. The Stokes and Wilson formula given in Eq 7 was used to calculate the strain induced broadening of the Bragg's diffraction peak [50]: One can rewrite Eq 6 as Eq 8: where β hkl is the total width at the average intensity (FWHM) [51,52]. A plot of 4 and is shown in Figure 8. Using a linear fit to the data, the crystalline size was estimated from the y-intercept, and the strain , from the slope of the fit. Eq 8 represents the uniform deformation model considering the isotropic nature of the crystal, where the strain was assumed to be uniform in all crystallographic directions. The Table 1 shows the values of and D for each concentration. When the BFO concentration increases, the crystallite size increases from 43.08 nm (x = 0) to 139.19 nm (x = 0.20),  also increases from 0.01 for x = 0 to 0.09 for x = 0.20.  In order to study the effect of BFO on the magnetic response of the BNT, in Figure 9 we show the magnetization curves vs. magnetic field (M-H) at room temperature (300 K) between −30 and 30 kOe. The sample doped with 5% BFO exhibits a paramagnetic behavior (Figure 9a), like pure BNT, indicating that this percentage is not enough to modify its magnetic behavior. When increasing the doping to 10% (Figure 9b), it is observed a small cycle of hysteresis characteristic of a ferrimagnetic response, with a coercive field of 152.5 kOe and a remanent magnetization of 5.63 × 10 −5 emu/g. The Figure 9c shows the magnetic behavior of the system for 20% BFO; the increase in BFO enhances the magnetic response, increasing the values of both, the remanent magnetization and the magnetization at the maximum magnetic field (since none magnetic measures were carried out until saturation, we introduce the M Hmax parameter as the one corresponding to the magnetization of the sample at the maximum magnetic field. This parameter allows us to analyze the magnetic order obtained); according to the above, we get a greater magnetic order and a greater "magnetic memory" in the system. Contrary to the increase of the remanent magnetization the coercive field decreases, which can be explained by the presence of spurious phases in the BNT-xBFO. As expected, the M-H relationship for the BNT-BFO system is highly dependent on the composition. It is also expected a stronger magnetic behavior at low temperatures since the thermal randomness effect tends to break the magnetic order. To observe this behavior, the sample doped with 10% BFO was subjected to a magnetic field at 50 K, 200 K and 300 K, as is shown in the Figure 10. It is seen that both the remanent magnetization and the M Hmax increase with the decrease of temperature, evidencing higher magnetic ordering and higher magnetic memory in response to decreased thermal randomness effect. However, the coercive field decrease can be explained by the "competition" between the two magnetic behaviors (paramagnetism-antiferromagnetism) that results in a weak ferrimagnetism: the concentration of BFO is not enough to provide the magnetic order that compensates the low thermal effect by decreasing the temperature; as it is known, paramagnetism is temperature dependent (M  T −1 ): at lower T, it is easier to obtain a magnetic response for low applied fields.  Figure 11 shows the typical evolution of the dielectric permittivity versus temperature for different frequencies and for different BNT-xBFO compositions. For x = 0 two anomalies are observed in the dielectric constant: a hump around 198 ℃ where the dielectric constant is frequency dependent and a diffuse maximum near 326 ℃, almost frequency independent, these results were consistent with previous studies [53][54][55]. The hump may be related to a phase coexistence, where the long-range ferroelectric domains breaking down into polar nanoregions (PNRs) at and above the T FD [56]. The diffuse peak could be related to a transition from an orthorhombic non-polar phase to a tetragonal non-polar phase [57]. It has been reported an additional dielectric anomaly between 520-540 ℃, although not measured in this study, associated with a phase transition from tetragonal to cubic [38]. The dependence of the dielectric constant with the frequency disappears at T FD ~ 262 ℃. The hump at 198 ℃ is only observed for pure BNT and for the lowest dopant content (x = 0.02). The sudden increase in permittivity at high temperature relates to the increase in electrical conductivity; however, it is observed that this phenomenon appears at lower temperatures as the BFO content increases. Some authors suggest that the increase in conductivity in the solid solution is related to an increase in the concentration of oxygen vacancies induced by the reduction of Fe 3+ in Fe 2+ , the concentration of iron increases as x increases [54]. In BNT, the abnormality of permittivity is associated with ferroelectric relaxor behavior [58]; and this type of behavior should disappear with increasing BFO content. However, the frequency-dependent anomaly, better observed in dielectric loss curves (tan), remains for all compositions. For x = 0, the location of a maximum around 200 ℃ is associated with a nonpolar phase, while the polar character drops sharply at the phase coexistence temperature. In this respect, studies carried out on the system BNT-xBFO report that for x < 0.5 the temperature at which the hump appears corresponds to the depolarization temperature [54]. It has been reported that for BFO rich compounds, the conductivity is due to oxygen vacancies and these can play a key role in the relaxation phenomenon [59]; in fact, the mechanism of relaxation linked to oxygen vacancies is present in all compositions, but its contribution increases when the amount of Fe increases.

Conclusions
The combustion reaction method allowed the synthesis of BNT-xBFO perovskite for all concentrations; the molecular homogeneity achieved in this method favors the formation of the desired phase. According to FTIR results, when x is increased, there is a displacement of the bands associated with the vibrations of the TiO 6 octahedron and new bands appear related to the twisting mode of the Bi-O bond and the stretching mode of the Fe-O bond. The addition of BFO to the BNT system maintains the rhombohedral symmetry and the crystallite size increases, however there is no phase transition in the compositions studied. The antiferromagnetic behavior of the BFO contributes to the magnetic order of the BNT (paramagnetic) giving place to a magnetic hysteresis loop with a ferrimagnetic response for x = 0.10. For x = 0.20; the remanent magnetization and the magnetization at the maximum magnetic field are higher, instead the coercive field is lower, as can be seen from the hysteresis magnetic loops at different temperatures. In the permittivity curves as a function of the temperature, there is an increase in conductivity due to the incorporation of iron in the crystalline structure, and it is seen a relaxor behavior for all compositions.