Bismuth ferrite (BFO) nanostructures and thin films have gained attraction as suitable candidates for energy storage and energy conversion due to their high energy storage efficiency, temperature stability and low dielectric loss. Electrical properties of such multiferroic materials are tailored by ferroelectric and ferromagnetic constituents and have opened up amazing avenues in electrochemical supercapacitor and photovoltaic applications. Dopants play a significant role in optimizing the magnetic and dielectric properties of such materials owing to suitable applications. This review highlights the scientific advancements reported in BFO nanostructures for energy applications by optimizing their magnetic and dielectric properties. This paper starts with a brief introduction of BFO and a discussion on the effects of various dopants by different synthesis techniques, and their effects on the magnetic and dielectric properties are also portrayed. Eventually, this review summarizes the various doping effects, which paves way for future research on this multiferroic material.Bismuth ferrite (BFO) nanostructures and thin films have gained attraction as suitable candidates for energy storage and energy conversion due to their high energy storage efficiency, temperature stability and low dielectric loss. Electrical properties of such multiferroic materials are tailored by ferroelectric and ferromagnetic constituents and have opened up amazing avenues in electrochemical supercapacitor and photovoltaic applications. Dopants play a significant role in optimizing the magnetic and dielectric properties of such materials owing to suitable applications. This review highlights the scientific advancements reported in BFO nanostructures for energy applications by optimizing their magnetic and dielectric properties. This paper starts with a brief introduction of BFO and a discussion on the effects of various dopants by different synthesis techniques, and their effects on the magnetic and dielectric properties are also portrayed. Eventually, this review summarizes the various doping effects, which paves way for future research on this multiferroic material.

The dielectric and pyroelectric performances of 91.5Na0.5Bi0.5TiO3–8.5K0.5Bi0.5TiO3 lead-free single crystal were investigated. The depolarization temperature of the crystal is about 153 ∘C. Among the , , and crystallographic orientations, the -oriented crystal possesses the highest pyroelectric coefficient and the largest figures of merit, and the values of p, Fv, and Fdare 5.63×10−4 C/m2 •K, 0.06 m2/C, and 21.5 μPa−1/2 for the -oriented crystal at room temperature. The Fdand Fvexhibit weak frequency dependence in the range of 100–300 Hz. With the increase of the temperature, the value of pincreases, while the value of Fv decreases from 18 ∘C to 103 ∘C.The dielectric and pyroelectric performances of 91.5Na0.5Bi0.5TiO3–8.5K0.5Bi0.5TiO3 lead-free single crystal were investigated. The depolarization temperature of the crystal is about 153 ∘C. Among the , , and crystallographic orientations, the -oriented crystal possesses the highest pyroelectric coefficient and the largest figures of merit, and the values of p, Fv, and Fdare 5.63×10−4 C/m2 •K, 0.06 m2/C, and 21.5 μPa−1/2 for the -oriented crystal at room temperature. The Fdand Fvexhibit weak frequency dependence in the range of 100–300 Hz. With the increase of the temperature, the value of pincreases, while the value of Fv decreases from 18 ∘C to 103 ∘C.

Ba0.85Ca0.15(Ti1−xZrx)O3(BCTZ) ceramics with x= 0.05, 0.10, 0.15, 0.20, 0.25, 0.30 were prepared by the solid-state reaction method. Calcination of the powders was carried out at 1100 ∘C for 4 h and the green pellets were sintered at 1400 ∘C for 2 h. X-ray diffraction patterns of the sintered pellets showed tetragonal splitting up to x= 0.10 while the mixture of the rhombohedral/cubic phase appeared at higher ZrO2 concentrations. Maximum piezoelectric charge constant d33= 510 pC/N and strain (S= 0.103%) were measured for BCT doped by 0.10 mol ZrO2. Dielectric constant, remnant polarization and saturation polarization also found maxima for this composition. The Curie temperature (TC) of the compositions decreased with increase in ZrO2 concentration and reached 98 ∘C, 87 ∘C and 36 ∘C at x= 0.05, 0.10, 0.15 mol, respectively. The remaining compositions have TC below the room temperature; therefore, they can be used for subzero/cryogenic applications. The scanning electron microscopy study revealed an increase in grain size with increase in ZrO2 concentration and confirmed the complete solubility of ZrO2 in the crystal lattice. Overall, low ZrO2-doped BCT compositions with high d33 could be suitable for low temperature (∘C) applications.Ba0.85Ca0.15(Ti1−xZrx)O3(BCTZ) ceramics with x= 0.05, 0.10, 0.15, 0.20, 0.25, 0.30 were prepared by the solid-state reaction method. Calcination of the powders was carried out at 1100 ∘C for 4 h and the green pellets were sintered at 1400 ∘C for 2 h. X-ray diffraction patterns of the sintered pellets showed tetragonal splitting up to x= 0.10 while the mixture of the rhombohedral/cubic phase appeared at higher ZrO2 concentrations. Maximum piezoelectric charge constant d33= 510 pC/N and strain (S= 0.103%) were measured for BCT doped by 0.10 mol ZrO2. Dielectric constant, remnant polarization and saturation polarization also found maxima for this composition. The Curie temperature (TC) of the compositions decreased with increase in ZrO2 concentration and reached 98 ∘C, 87 ∘C and 36 ∘C at x= 0.05, 0.10, 0.15 mol, respectively. The remaining compositions have TC below the room temperature; therefore, they can be used for subzero/cryogenic applications. The scanning electron microscopy study revealed an increase in grain size with increase in ZrO2 concentration and confirmed the complete solubility of ZrO2 in the crystal lattice. Overall, low ZrO2-doped BCT compositions with high d33 could be suitable for low temperature (∘C) applications.

Frequency-dependent dielectric constant, dielectric loss, AC conductivity values and complex impedance spectra of V2O5-added Ni–Co–Zn ferrites (Ni0.62Co0.03Zn0.35Fe2O4+xV2O5, where x= 0, 0.5, 1 and 1.5 wt.%) have been investigated at room temperature. The dielectric properties of the samples follow the Maxwell–Wagner polarization model. An inverse relationship was found between dielectric constant and AC electrical resistivity for all the samples. The dielectric constants decreased with the addition of V2O5, while the electrical resistivities of V2O5-added Ni–Co–Zn ferrites are found to be larger than that of pure Ni–Co–Zn ferrite. The AC conductivity was reduced with the addition of V2O5to Ni–Co–Zn ferrite at lower-frequency region. However, AC conductivity shows a sharp increase at higher-frequency region, which could be attributed to the enhancement of electron hopping between the Fe2+ and Fe3+ ions in the ferrite matrix due to the activity of the grains. The complex impedance spectroscopy results through Cole–Cole/Nyquist plot have demonstrated a single semicircular arc. It indicates that conduction mechanism takes place predominantly through the grain/bulk property, which could be ascribed to the larger grain size of V2O5-added Ni–Co–Zn ferrites.Frequency-dependent dielectric constant, dielectric loss, AC conductivity values and complex impedance spectra of V2O5-added Ni–Co–Zn ferrites (Ni0.62Co0.03Zn0.35Fe2O4+xV2O5, where x= 0, 0.5, 1 and 1.5 wt.%) have been investigated at room temperature. The dielectric properties of the samples follow the Maxwell–Wagner polarization model. An inverse relationship was found between dielectric constant and AC electrical resistivity for all the samples. The dielectric constants decreased with the addition of V2O5, while the electrical resistivities of V2O5-added Ni–Co–Zn ferrites are found to be larger than that of pure Ni–Co–Zn ferrite. The AC conductivity was reduced with the addition of V2O5to Ni–Co–Zn ferrite at lower-frequency region. However, AC conductivity shows a sharp increase at higher-frequency region, which could be attributed to the enhancement of electron hopping between the Fe2+ and Fe3+ ions in the ferrite matrix due to the activity of the grains. The complex impedance spectroscopy results through Cole–Cole/Nyquist plot have demonstrated a single semicircular arc. It indicates that conduction mechanism takes place predominantly through the grain/bulk property, which could be ascribed to the larger grain size of V2O5-added Ni–Co–Zn ferrites.

The U-type hexaferrites (Ba1−3xLa2x)4Co2Fe36O60 (x= 0, 0.05, 0.10, 0.15, 0.20, 0.25) have been synthesized by auto-combustion method. The work involves the study of structural, microstructural, dielectric, magnetic and magneto-dielectric properties of the prepared materials. The structural analysis has been done by X-ray diffraction technique along with Le Bail refinement which confirmed the pure hexagonal phase for all the samples. The microstructural analysis has been carried out by field-emission scanning electron microscopy. The vibrating sample magnetometer is used to measure the magnetic properties. The sample with a composition of x= 0.15 has shown the maximum magnetization of approximately 73.31 emu/g with the remnant magnetization of 38.89 emu/g and coercive field of 1.77 kOe at room temperature. Moreover, the same sample has delivered the maximum magneto-dielectric response of about 54.18% at 1.5-T field.The U-type hexaferrites (Ba1−3xLa2x)4Co2Fe36O60 (x= 0, 0.05, 0.10, 0.15, 0.20, 0.25) have been synthesized by auto-combustion method. The work involves the study of structural, microstructural, dielectric, magnetic and magneto-dielectric properties of the prepared materials. The structural analysis has been done by X-ray diffraction technique along with Le Bail refinement which confirmed the pure hexagonal phase for all the samples. The microstructural analysis has been carried out by field-emission scanning electron microscopy. The vibrating sample magnetometer is used to measure the magnetic properties. The sample with a composition of x= 0.15 has shown the maximum magnetization of approximately 73.31 emu/g with the remnant magnetization of 38.89 emu/g and coercive field of 1.77 kOe at room temperature. Moreover, the same sample has delivered the maximum magneto-dielectric response of about 54.18% at 1.5-T field.

Monophasic and polycrystalline double perovskite Eu2CoMnO6 has been synthesized, and its structural characterization, frequency and temperature-dependent dielectric relaxation have been studied. Observed thermally activated dielectric relaxation was explained using the empirical Havriliak–Negami (HN) dielectric relaxation function with an estimated activation energy E∼ 0.22 eV and attempt frequency f0∼ 2.46 × 109 Hz. The frequency-dependent AC conductivity data, over a wide range of temperature (100–325 K), followed the empirical universal power law behavior (∼fn, n is the constant exponent) showing two different frequency exponents, respectively, in the high- and low-temperature regions. The high-temperature (> 275 K) conductivity data followed the continuous time random walk (CTRW) approximation model proposed by Dyre. However, this model failed to reproduce the observed conductivity spectra in the low-temperature side ( 200 K). Interestingly, both the high- and low-temperatures’ conductivity data can be scaled to the master curve with suitably chosen scaling parameters.Monophasic and polycrystalline double perovskite Eu2CoMnO6 has been synthesized, and its structural characterization, frequency and temperature-dependent dielectric relaxation have been studied. Observed thermally activated dielectric relaxation was explained using the empirical Havriliak–Negami (HN) dielectric relaxation function with an estimated activation energy E∼ 0.22 eV and attempt frequency f0∼ 2.46 × 109 Hz. The frequency-dependent AC conductivity data, over a wide range of temperature (100–325 K), followed the empirical universal power law behavior (∼fn, n is the constant exponent) showing two different frequency exponents, respectively, in the high- and low-temperature regions. The high-temperature (> 275 K) conductivity data followed the continuous time random walk (CTRW) approximation model proposed by Dyre. However, this model failed to reproduce the observed conductivity spectra in the low-temperature side ( 200 K). Interestingly, both the high- and low-temperatures’ conductivity data can be scaled to the master curve with suitably chosen scaling parameters.

Spinel ferrite Ni0.08Mn0.90Zn0.02Fe2O4 was prepared by a conventional ceramic process followed by sintering at three different temperatures (1050∘ C, 1100∘ C and 1150∘ C). X-ray diffraction (XRD) investigations stated the single-phase cubic spinel structure and the FTIR spectra revealed two prominent bands within the wavenumber region from 600 cm−1 to 400 cm−1. Surface morphology showed highly crystalline grain development with sizes ranging from 0.27 μm to 0.88 μm. The magnetic hysteresis curve at ambient temperature revealed a significant effect of sintering temperature on both coercivity (Hc) and saturation magnetization (Ms). Temperature caused a decrease in DC electrical resistivity, while the electron transport increased, suggesting the semiconducting nature of all samples and that they well followed the Arrhenius law from which their activation energies were determined. The values of Curie temperature (Tc) and activation energy were influenced by the sintering temperature. Frequency-dependent dielectric behavior (100 Hz–1 MHz) was also analyzed, which may be interpreted by the Maxwell–Wagner-type polarization. The UV–vis–NIR reflectance curve was analyzed to calculate the bandgap of ferrites, which showed a decreasing trend with increasing sintering temperature.Spinel ferrite Ni0.08Mn0.90Zn0.02Fe2O4 was prepared by a conventional ceramic process followed by sintering at three different temperatures (1050∘ C, 1100∘ C and 1150∘ C). X-ray diffraction (XRD) investigations stated the single-phase cubic spinel structure and the FTIR spectra revealed two prominent bands within the wavenumber region from 600 cm−1 to 400 cm−1. Surface morphology showed highly crystalline grain development with sizes ranging from 0.27 μm to 0.88 μm. The magnetic hysteresis curve at ambient temperature revealed a significant effect of sintering temperature on both coercivity (Hc) and saturation magnetization (Ms). Temperature caused a decrease in DC electrical resistivity, while the electron transport increased, suggesting the semiconducting nature of all samples and that they well followed the Arrhenius law from which their activation energies were determined. The values of Curie temperature (Tc) and activation energy were influenced by the sintering temperature. Frequency-dependent dielectric behavior (100 Hz–1 MHz) was also analyzed, which may be interpreted by the Maxwell–Wagner-type polarization. The UV–vis–NIR reflectance curve was analyzed to calculate the bandgap of ferrites, which showed a decreasing trend with increasing sintering temperature.

Photocatalytic degradation kinetics of Jurlewicz–Weron–Stanislavsky (JWS) type has been identified. Experimental data are taken from previous published works, and fitted with the JWS relaxation function as well as that of the Havriliak–Negami (HN) model. All experimental data can fit with either model fairly good. From the fitting parameters, the Jonscher indices are calculated and Jonscher diagram is plotted for the chemical kinetics of photocatalytic degradations. This work suggests that material parameters of photocatalysts can be well defined in the sense of fractional calculus.Photocatalytic degradation kinetics of Jurlewicz–Weron–Stanislavsky (JWS) type has been identified. Experimental data are taken from previous published works, and fitted with the JWS relaxation function as well as that of the Havriliak–Negami (HN) model. All experimental data can fit with either model fairly good. From the fitting parameters, the Jonscher indices are calculated and Jonscher diagram is plotted for the chemical kinetics of photocatalytic degradations. This work suggests that material parameters of photocatalysts can be well defined in the sense of fractional calculus.