Nanoparticles of BNTF were prepared through egg-white method. The starting materials Bi(NO₃)₃·5H₂O, Nd(NO₃)₃·6H₂O, TiCl₃, and FeCl₃ were mixed together in proper stoichiometric proportions. Extracted egg white (60 ml), dissolved in 40 ml of double distilled water through vigorous stirring, was added to the metal mixture at room temperature. After constant stirring for 30 min, the resultant sol–gel was evaporated at 80°C until a dry precursor was obtained. The dried precursor was sintered at 700°C for 10 h. The final material obtained was ground for 1 h using mortar and pestle.

The powder samples obtained were characterized for structural phase and nanosize formation using PANalytical X'Pert Pro X-ray diffractometer (The Netherlands) with Cu Kα (λ = 1.54 Å) in the range of 20° to 80° with a sweeping rate of 2°/min.

The microstructural and morphological analysis of the samples were carried out using a field emission scanning electron microscope (FESEM, JSM 7600 F, JEOL Ltd., Akishima, Tokyo, Japan) and field emission transmission electron microscope (HRTEM, JEOL 2010 F, JEOL Ltd.) with the energy dispersive X-ray (EDX) facility attached.

For electrical measurements, a fixed amount of powder sample was taken, and a few drops of PVA were added to it. The mixture was left over night, dried at room temperature, and pressed into disc-shaped pellets (12 mm × 12 mm) with the help of hydraulic press. The pallets were heated at 500°C for 1 h, and silver paste coating was applied on opposite flat faces of the pallets to make parallel plate capacitor geometry. The dielectric measurements were performed in the frequency range 1 kHz to 1 MHz using Wayne Kerr 6500B impedance analyzer (Wayne Kerr Electronics Ltd., Woburn, MA, USA). The polarization versus electric field hysteresis measurements were carried out at 1 kV/cm field using P-E loop tracer of Marine India, New Delhi, India. Room temperature magnetic hysteresis measurements were carried out using Lake Shore VSM (Lake Shore Croyotronics Inc., OH, USA) with a field of 20 kOe.

The powder samples of BNTF were characterized for structural and phase analysis through X-ray diffraction shown in Figure 1. The XRD patterns for annealed samples reveal the characteristic well-crystallized pattern with a few signatures of secondary phase corresponding to pure Bi₄Ti₃O₁₂ compound and alpha-Fe₂O₃. Figure 2 shows the EDX pattern of the pure sample confirming the chemical formation of the polycrystalline BNTF nanoparticles. Figure 3a,b shows the FE-SEM microstructure of the fracture surfaces of pristine and 5% doped Nd sample. Interestingly, with Nd doping, the densification is promoted in the grown nanoparticles. Figure 4a shows the FE-TEM micrograph with inset showing the average grain size plot and selective area electron diffraction pattern for the composition x = 0.0. The micrograph shows irregular-shaped highly agglomerated nanoparticles with an average grain size of 50 nm for the composition x = 0.05. The average crystallite sizes calculated through FE-TEM show a broad size distribution from 50 to 72 nm as shown in Figure 5. A high crystalline order is observed in the grown nanoparticles. Figure 4b shows lattice pattern for the composition x = 0.05 with inset showing the d spacing value of 0.240 Å. The d value obtained collaborated well with the value obtained from X-ray diffraction pattern.

The high resistivity and low dielectric loss (tanδ ≈ 1.6 at 42 Hz at RT) in Nd-substituted specimens allowed the dielectric constant (ϵ′) to be determined, as shown in Figure 6. The room temperature dielectric constant was found 515 at 1 kHz maximum for 5% Nd concentration. The obtained dielectric constant is higher than the values of thin films (≈107) 15 16 and Nb-doped BiFeO₃ ceramics 17 reported earlier. Both the dielectric constant and loss tangent (Figure 7) are found to decrease rapidly in low-frequency region and show frequency independent response above 22 kHz. These variations can be explained in the light of space charge polarization as discussed by Maxwell 18 and Wagner 19 and is in good agreement with Koop's phenomenological theory 20 . At low frequencies, the space charges are able to follow the frequency of the applied field, while at high frequencies, they may not have time to build up and undergo relaxation. The low loss values at higher frequencies show potential applications of these materials in high-frequency microwave devices. Moreover, the dielectric loss factor also depends on a number of factors, such as stoichiometry and structural homogeneity, which in turn, depend upon the composition and sintering temperature of the samples 21 . The room temperature resistivity measurements as a function of composition x are presented in Figure 8. It is seen that the resistivity of the samples increases with the increasing percentage Nd doping. The behavior may be attributed to the decreasing number of the conduction ions.

The ferroelectric hysteresis loop measurement is always hampered by the high leakage current. Because of low resistivity of the samples, it is difficult to apply high electric fields to the bulk samples. The ferroelectric polarization hysteresis loops at room temperature for Nd-doped Bi_{4 − x} FeTi₃O₁₂ samples measured under an applied field (E) of about 10 kV/cm are presented in Figure 9. The loops are not really saturated and represent a partial reversal of the polarization almost elliptical-shaped 22 23 . The P _r and E _c values of the BNTF nanoparticles as a function of Nd composition are shown in Figure 10. The remanence polarization, P _r increases first and then decreases with an increasing vaue of x. The highest value of P _r = 0.110 μC/cm² and a relatively low coercive field (E _c) of 7.918 kV/cm were observed for 5% Nd concentration. Similar behavior in E _c is also observed where it increases first and then follows a decreasing trend with increasing Nd content 24 25 . The remnant polarization of the samples is not too high. It is well known that most magnetic materials usually have high electrical conductivity. Thus, few multiferrioc materials could exhibit the ferroelectric response properly. It is very critical for magnetic materials with high insulating resistivity to posses both ferroelectric and ferromagnetic properties simultaneously. Otherwise, an applied electric field would cause an increase in current for conducting samples rather than inducing electrical polarization.

Figure 11 shows the magnetization versus magnetic field (M H) hysteresis loops for the BNTF nanoparticles at room temperature for the maximum applied field (H) of 20 kOe. It is seen that all the samples show intrinsic antiferromagnetism and a weak ferromagnetism with a maximum value of remnant magnetization (M _r) of 0.00107 emu/gm for sample x = 0.05. Various authors have reported earlier similar results 24 25 26 . The M _r value decreases with increasing Nd doping percentage. The substitution of Nd at Bi site may lead to the effective suppression of the spiral spin structure of BNTF, resulting in the appearance of magnetization. In order to verify and evaluate further the source of magnetism in the grown nanoparticles, room temperature Mossbauer spectroscopy measurements were tried on the present samples, but due to low percentage of Fe⁵⁷ in the pure and doped samples, no clear Mossbauer peaks were observed.