# Influence of the La3+, Eu3+, and Er3+ Doping on Structural, Optical, and Electrical Properties of BiFeO3 Nanoparticles Synthesized by Microwave-Assisted Solution Combustion Method

Authors: Angelika Wrzesinska; Alexander Khort; Izabela Bobowska; Adam Busiakiewicz; Aleksandra Wypych-Puszkarz
Journal: Journal of Nanomaterials
 (2019)

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## Abstract

In this study, nanocrystalline (18–28 nm) perovskite-like bismuth ferrite rare earth-doped powders (Bi0.9RE0.1FeO3, where RE = La (BLaFO), Eu (BEuFO), and Er (BErFO)) were obtained by microwave-assisted modification of solution combustion synthesis (SCS). The influence of high load La3+, Eu3+, and Er3+ doping on structural, optical, and electrical properties of BiFeO3 was investigated. It was found that rare earth doping along with fast phase formation and quenching significantly distorts the crystal cells of the obtained materials, which results in the formation of mixed rhombohedral- (R3c-) orthorhombic (Pbnm) crystal structures with decreased lengths of Bi-O and Fe-O bonds along with a decreasing radius size of doping ions. This promotes reduction of the optical band gap energy and suppression of ionic polarization at high frequencies and results in enhanced dielectric permittivity of the materials at 1 MHz.


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## Body

## 1. Introduction

Bismuth ferrite BiFeO3 (BFO) is a multiferroic material, which combines ferroelectricity and ferromagnetism in the same phase and has attracted great attention due to its potential applications in multifunctional devices, such as data storage systems, spintronics, and microelectronics [1–4]. Among a few known single-phase multiferroics, BFO is distinguished by its high temperature electrical and magnetic ordering (i.e., Curie temperature TC=810–830°C [5] and Neel temperature TN=370°C [6]). Because of these features and good optical properties [7, 8], pure and doped BFO are considered highly promising candidates for practical applications in next-generation smart materials.At room temperature, BFO has a rhombohedral distorted perovskite structure with the R3c space group [9]. This structure can be obtained from a cubic parent perovskite by rotations of the oxygen octahedra around the 111c direction and displacements of Bi3+ and Fe3+ cations along the same c direction. Fe3+ ions are in the distorted oxygen octahedra, while Bi3+ ions, occupying the dodecahedral positions, are strongly shifted from the central position towards one of Fe3+ ions due to the lone pair effect [10, 11]. At around 825°C, BFO has a strong first-order transition from a rhombohedral to an orthorhombic structure (Pbnm symmetry) with attendant unit cell shrinks [5, 12].Recently, much attention has been paid to understand the effect of chemical composition [13–16], pressure [17, 18], temperature of the synthesis, and annealing [19, 20] on crystal structure and physical properties of BFO-based nanopowders. A number of studies reported strong dependence of BFO electromagnetic properties from its nanoscale structure [21, 22]. For example, high-resolution neutron diffraction studies have shown that the magnetic order of BFO is antiferromagnetic with G-type cycloid spin configuration with a period of 62 nm [23, 24]. Magnetization exhibits higher values with a decrease of particle sizes, which is correlated to the higher suppression of its spin cycloid incommensurate to particle size. In addition, RE-ion (RE rare earth ion) doping is an easy way to enhance ferroelectric [25–27] and optical properties of BFO-based materials (increase dielectric constant, decrease optical band gap, etc.), which is crucially required for the creation of a new type of functional materials for application in multiple devices [28, 29]. Doping by RE-ions gives a great possibility to control physical properties of BFO-based materials by varying their nanoscale structure, and due to this feature, it is a subject of numerous ongoing and future studies.Numerous synthesis techniques, such as hydrothermal, coprecipitation, molten-salt, thermal decomposition, and sol-gel [30–35], have been developed to obtain doped and neat BFO nanoparticles. Among them, a variety of modified solution combustion methods have several advantages: low initialization temperature, fast kinetics of reaction, and homogeneous powder with very fine particles [36–38]. In this paper, we studied the effect of high load RE doping on structure, phase composition, and electrical and optical properties of BFO nanomaterials, prepared by microwave-assisted modification of solution combustion synthesis (SCS) aiming the creation of ferroelectric nanomaterial with enhanced properties for photocatalysis and photovoltaic devices. Microwave heating ensures a homogeneous increase of temperature in the reagent mixture and preparation of the uniform precursor for a combustion step of synthesis. These cause fast-phase formation and significantly affect crystal structure and properties of the materials.


## 2. Experimental

### 2.1. Synthesis Procedure

All used chemicals had analytical purity and were purchased from Speckhimteh Ltd. (Russia). Perovskite-like structured bismuth ferrites, i.e., neat (BFO) and rare earth-doped (Bi0.9RE0.1FeO3, where RE = La (BLaFO), Eu (BEuFO), and Er (BErFO)) powders were synthesized by microwave-assisted modification of SCS using stoichiometric mixtures of metal nitrates (oxidizer) with fuel (reducer). Bismuth(III)-nitrate pentahydrate (Bi(NO3)3⋅5H2O) and iron(III)-nitrate nonahydrate (Fe(NO3)3⋅9H2O) were used as the main raw materials. Lanthanum(III)-nitrate hexahydrate (La(NO3)3⋅6H2O), europium(III)-nitrate hexahydrate (Eu(NO3)3⋅6H2O), and erbium(III)-nitrate hexahydrate (Er(NO3)3⋅6H2O) were chosen as the sources of RE doping ions. Citric acid (CA) was used as a fuel component. The combustion reactions take place according to the scheme suggested in:
(1)3‐xBiNO33+xRENO33+3FeNO33+5φC6H8O7+22.5φ−1O2⟶3Bi1‐xRExFeO3+30φCO2+9N2+20φH2OThe parameterφ, the fuel to oxidizer ratio, is defined such that φ=1 corresponds to a stoichiometric oxygen concentration, meaning that the initial mixture does not require atmospheric oxygen for complete oxidation of the fuel, while φ>1 (<1) implies fuel-rich (or lean) conditions. In the case of φ>1, the protective atmosphere is formed from the oxidation products of the fuel.For all experiments, the ratioφ between the fuel and the oxidizer was kept constant and equal to 1.25. According to our preliminary research, the chosen fuel to oxidizer ratio provides optimal conditions for the preparation of highly dispersed BFO nanoparticles with a minimal content of secondary phases.All the samples were synthesized by the microwave-assisted SCS method, applied earlier for metallic nanopowder synthesis [39–41]. In general, bismuth(III)-nitrate pentahydrate with 2% excess and CA were dissolved in a minimum volume of acidic aqueous solution in order to prevent bismuth subnitrate precipitation. Iron(III)-nitrate nonahydrate was dissolved in a minimum amount of twice distilled water. Then these solutions were mixed together and rapidly dried in a microwave oven (800 W, 2.450 GHz—maximal working parameters of our oven) until gel formation, and then foam was formed. Microwave heating causes rapid water evaporation from a bulk of solutions and very fast production of large quantity of steam; then foam formation occurs that is preferred for self-combustion synthesis. The foam was ignited and burnt in thermal explosion mode in a preheated 300°C muffle furnace, leading to the formation of a brown fluffy powder. The obtained powder was grinded and annealed in air at 650°C for 30 min with rapid heating and cooling by means of quenching. After annealing, the obtained powders were grinded one more time.


### 2.2. Characterization

X-ray diffraction (XRD) measurements in the Bragg–Brentano reflection geometry were done at room temperature (21°C) using a PANalytical X’Pert Pro MPD diffractometer with copper CuKα radiation (λ=1.5406Å). Diffractograms were recorded with a 0.0167o step at an exposure time of 20 s. The powder samples were spun during measurements to decrease preferred orientation effects. The phase analysis was performed by a comparison of peak positions and relative intensities of obtained XRD data with standard reference materials from the International Centre for Diffraction Data (JCPDS) powder diffraction (PDF-2 ver. 2009) database. The obtained diffraction data were refined using the Rietveld method in the PANalytical High Score Plus software package. The pseudo-Voigt function was used for the peak profile refinement.The average crystallite size of obtained samples was calculated using the Scherrer formula:(2)D=kλβcosθ,where D is the mean size of the crystallite, k is a dimensionless shape factor (with a typical value of 0.9), λ is the X-ray wavelength, β is the line broadening at the half of the maximum intensity, and θ is the Bragg angle (in degrees).Raman investigations were performed using a JobinYvon T64000 triple-grating Raman spectrometer equipped with an Olympus BX40 confocal microscope. The Argon laser withλ=514.5nm wavelength was used for sample excitation. Acquisition time was 400 s for each spectrum.Absorption FT-IR spectra were measured by a Thermo Scientific Nicolet iS50 Infrared Spectrometer. Spectra were recorded in a far infrared range (FIR) of 300–600 cm-1 using the attenuated total reflection (ATR) accessory with a diamond crystal.The morphology of the samples was studied using scanning electron microscopy (SEM) with a Vega 5135 MM Tescan instrument equipped with secondary electron and backscattered electron detectors and an Oxford Instruments Link 300 ISIS system for energy dispersive X-ray (EDX) microanalysis.The reflectance measurements of pelleted samples were carried out by UV-Vis-NIR spectrometry (Varian Inc., Carry 5000 spectrometer), using an integrating sphere. The scans were conducted in a 350–700 nm range.The dielectric response measurements were carried out using a Novocontrol GmbH Concept 40 broadband dielectric spectrometer equipped with a Quatro Cryosystem in the frequency range of10–1÷106Hz. For measurements, all synthesized powders were hydraulically pressed with a pressing force of 4000 kg for 5 min to form pellets (diameter ~13 mm and high ~0.9 mm). To improve the contact between the sample and external electrodes during measurements, 150 nm thick gold electrodes were deposited on both sides of the pellets. Before measurements, all pelleted samples were dried at 90°C in a vacuum to eliminate the influence of the humidity.


## 2.1. Synthesis Procedure

All used chemicals had analytical purity and were purchased from Speckhimteh Ltd. (Russia). Perovskite-like structured bismuth ferrites, i.e., neat (BFO) and rare earth-doped (Bi0.9RE0.1FeO3, where RE = La (BLaFO), Eu (BEuFO), and Er (BErFO)) powders were synthesized by microwave-assisted modification of SCS using stoichiometric mixtures of metal nitrates (oxidizer) with fuel (reducer). Bismuth(III)-nitrate pentahydrate (Bi(NO3)3⋅5H2O) and iron(III)-nitrate nonahydrate (Fe(NO3)3⋅9H2O) were used as the main raw materials. Lanthanum(III)-nitrate hexahydrate (La(NO3)3⋅6H2O), europium(III)-nitrate hexahydrate (Eu(NO3)3⋅6H2O), and erbium(III)-nitrate hexahydrate (Er(NO3)3⋅6H2O) were chosen as the sources of RE doping ions. Citric acid (CA) was used as a fuel component. The combustion reactions take place according to the scheme suggested in:
(1)3‐xBiNO33+xRENO33+3FeNO33+5φC6H8O7+22.5φ−1O2⟶3Bi1‐xRExFeO3+30φCO2+9N2+20φH2OThe parameterφ, the fuel to oxidizer ratio, is defined such that φ=1 corresponds to a stoichiometric oxygen concentration, meaning that the initial mixture does not require atmospheric oxygen for complete oxidation of the fuel, while φ>1 (<1) implies fuel-rich (or lean) conditions. In the case of φ>1, the protective atmosphere is formed from the oxidation products of the fuel.For all experiments, the ratioφ between the fuel and the oxidizer was kept constant and equal to 1.25. According to our preliminary research, the chosen fuel to oxidizer ratio provides optimal conditions for the preparation of highly dispersed BFO nanoparticles with a minimal content of secondary phases.All the samples were synthesized by the microwave-assisted SCS method, applied earlier for metallic nanopowder synthesis [39–41]. In general, bismuth(III)-nitrate pentahydrate with 2% excess and CA were dissolved in a minimum volume of acidic aqueous solution in order to prevent bismuth subnitrate precipitation. Iron(III)-nitrate nonahydrate was dissolved in a minimum amount of twice distilled water. Then these solutions were mixed together and rapidly dried in a microwave oven (800 W, 2.450 GHz—maximal working parameters of our oven) until gel formation, and then foam was formed. Microwave heating causes rapid water evaporation from a bulk of solutions and very fast production of large quantity of steam; then foam formation occurs that is preferred for self-combustion synthesis. The foam was ignited and burnt in thermal explosion mode in a preheated 300°C muffle furnace, leading to the formation of a brown fluffy powder. The obtained powder was grinded and annealed in air at 650°C for 30 min with rapid heating and cooling by means of quenching. After annealing, the obtained powders were grinded one more time.


## 2.2. Characterization

X-ray diffraction (XRD) measurements in the Bragg–Brentano reflection geometry were done at room temperature (21°C) using a PANalytical X’Pert Pro MPD diffractometer with copper CuKα radiation (λ=1.5406Å). Diffractograms were recorded with a 0.0167o step at an exposure time of 20 s. The powder samples were spun during measurements to decrease preferred orientation effects. The phase analysis was performed by a comparison of peak positions and relative intensities of obtained XRD data with standard reference materials from the International Centre for Diffraction Data (JCPDS) powder diffraction (PDF-2 ver. 2009) database. The obtained diffraction data were refined using the Rietveld method in the PANalytical High Score Plus software package. The pseudo-Voigt function was used for the peak profile refinement.The average crystallite size of obtained samples was calculated using the Scherrer formula:(2)D=kλβcosθ,where D is the mean size of the crystallite, k is a dimensionless shape factor (with a typical value of 0.9), λ is the X-ray wavelength, β is the line broadening at the half of the maximum intensity, and θ is the Bragg angle (in degrees).Raman investigations were performed using a JobinYvon T64000 triple-grating Raman spectrometer equipped with an Olympus BX40 confocal microscope. The Argon laser withλ=514.5nm wavelength was used for sample excitation. Acquisition time was 400 s for each spectrum.Absorption FT-IR spectra were measured by a Thermo Scientific Nicolet iS50 Infrared Spectrometer. Spectra were recorded in a far infrared range (FIR) of 300–600 cm-1 using the attenuated total reflection (ATR) accessory with a diamond crystal.The morphology of the samples was studied using scanning electron microscopy (SEM) with a Vega 5135 MM Tescan instrument equipped with secondary electron and backscattered electron detectors and an Oxford Instruments Link 300 ISIS system for energy dispersive X-ray (EDX) microanalysis.The reflectance measurements of pelleted samples were carried out by UV-Vis-NIR spectrometry (Varian Inc., Carry 5000 spectrometer), using an integrating sphere. The scans were conducted in a 350–700 nm range.The dielectric response measurements were carried out using a Novocontrol GmbH Concept 40 broadband dielectric spectrometer equipped with a Quatro Cryosystem in the frequency range of10–1÷106Hz. For measurements, all synthesized powders were hydraulically pressed with a pressing force of 4000 kg for 5 min to form pellets (diameter ~13 mm and high ~0.9 mm). To improve the contact between the sample and external electrodes during measurements, 150 nm thick gold electrodes were deposited on both sides of the pellets. Before measurements, all pelleted samples were dried at 90°C in a vacuum to eliminate the influence of the humidity.


## 3. Results and Discussion

Figures1(a) and 1(b) illustrate SEM micrographs at a magnification of ×10k and EDX spectra of all the samples. The neat BFO sample is characterized by homogenous spherical crystalline aggregates with an average size varying from 100 nm to 500 nm. The sample BEuFO has less regular shape of grains; however, the mean size is lower than that for BFO. The BLaFO and BErFO samples are distinguished by heterogeneous morphology composed of fine grains and flaky particles of a micrometer size. The results of EDX analysis confirm the presence of rare earth elements in the doped samples. The quantitative data presented in the tables (Figure 1(b)) indicate the approximate element ratio that is in agreement with an expected amount of doping, i.e., Bi0.9RE0.1FeO3.Figure 1
(a) SEM images at a magnification of ×10k and (b) EDX spectra with results of elemental analysis of BFO, BLaFO, BEuFO, and BErFO samples. (SEM images and corresponding EDX data are placed in one row.)
(a)
(b)XRD patterns of BFO, BLaFO, BEuFO, and BErFO samples are presented in Figure2. The main crystalline phase in all samples is BiFeO3 with a distorted perovskite structure. In addition, diffraction peaks of secondary phases, such as Bi2Fe4O9, α-Bi2O3, and β-Bi2O3, were indexed. The presence of the secondary phases could be due to the local heterogeneity of the high-temperature combustion process of a foamed precursor [42]. After the precursor starts to combust, temperature locally reaches very high values. As bismuth is inclined to sublimation, it can evaporate from hotter regions and condense on colder surfaces, creating a local concentration gradient. Moreover, no additional diffraction peaks related to secondary RE-based phases have been observed, implying good solubility of high load RE ions in the BFO crystal lattice.Figure 2
Results of XRD analysis of BFO, BLaFO, BEuFO, and BErFO samples: (a) Rietveld refined XRD patterns and (b) enlarged view of the diffraction peaks around 32° 2θ range with doublet peaks (104) and (110), simulated with Lorenz function, showing peak shift and splitting.
(a)
(b)Figure2(b) shows the enlarged view of the doublet peaks corresponding to the (104) and (110) planes around 2θ ~32°. According to the literature data [43, 44], RE doping leads to a slight shift of both peaks to higher 2θ values, which could even merge into a single peak due to partial phase transition from a rhombohedral (R3c) to an orthorhombic (Pbnm) structure. The main reason of such peaks’ shift is the substitution of Bi3+ by smaller size RE ions, which reduces cell parameters. The partial structural transition can produce a distortion of the FeO6 octahedron due to the changes in the Fe–O bond length and O–Fe–O bond angles, affecting the electrical properties of BiFeO3. In our case, Bi3+ is substituted by close in size La3+ and smaller Eu3+ and Er3+ ions (rionBi3+=1.03Å, rionLa3+=1.03Å, rionEu3+=0.95Å, and rionEr3+=0.89Å, respectively).Calculated Rietveld refined XRD parameters for all synthesized materials are summarized in Table1. The BFO and BLaFO samples have quite similar unite cell parameters. Due to close ionic radii, substitution of Bi3+ by La3+ ions in the BFO crystal structure does not strongly affect the positions of (104) and (110) peaks. At the same time, it can be noticed that the (110) peak of the BFO sample is significantly smaller than the (104) peak, unlike the peaks of the BLaFO sample. The ratio of the areas of the (104) peak to the (110) peak for BFO is 2.731, which is much higher than that for BLFO (0.522). In this case, a higher ratio of the peak areas indicates a higher degree of R3c to Pbnm structure transition. We suppose that the La doping did not significantly affect the perovskite structure. At the same time, the structure of the undoped sample was slightly changed due to the partial “freezing” of the high-temperature phase shift as a result of fast phase formation during combustion reaction and follow-up quenching.Table 1
Rietveld refined XRD parameters for neat and doped BFO.
Samples
BFO
BLaFO
BEuFO
BErFO
Parameters
Space group
R3c
R3c
R3c
R3c
Pbnm
a (Å)
5.584
5.583
5.570
5.593
5.538
b (Å)
5.584
5.583
5.570
5.593
5.594
c (Å)
13.853
13.853
13.654
13.384
7.843
Volume (Å3)
374.07
373.99
366.96
362.61
242.96
Content of the main phase (wt.%)
91.2
90.3
90.5
90.2
Content of Bi2Fe4O9 (wt.%)
4.1
4.3
2.8
7.6
Content of Bi2O3 (wt.%)
4.7
5.4
6.7
2.2
Rp
6.01
5.18
5.64
6.21
Rw
8.10
6.39
6.80
7.38
Goodness of fit
0.74
1.05
1.12
2.01In the case of the Eu-doped sample, the shrinkage of all cell parameters is clearly seen. Both (104) and (110) peaks are shifted to higher 2θ angles of 32.09° and 32.23°, respectively (Figure 2(b)). It can be also noticed that the (110) peak is almost suppressed and merged with the (104) peak (ratio of the peaks’ areas is 8.803). This clearly indicates a very high degree of rhombohedral to orthorhombic structure transition.In the BErFO sample, two separate perovskite BiFeO3 crystal phases (low-temperature R3c and high-temperature Pbnm) were found. Positions of (104) and (110) peaks of the R3c phase are shifted to 31.89° and 32.28°, respectively, and their areas’ ratio is 1.158, which indicates a low degree of structural transition. Obviously, due to the high difference in the ionic radii of Bi3+ and Er3+ (~14%), the effect of Er doping on the perovskite structure of bismuth ferrite is so significant that the structure distortion promotes the appearance of the two separate phases. Such a combination of phases, apparently, is more energy-efficient at room temperature than only one highly distorted structure.In all cases, the observed merging of the peaks indicates rhombohedral to orthorhombic phase transition, high enough to affect electrical and optical properties of BFO-based materials.The average crystallite sizes were calculated for the main peak (110) of all the samples and found to be about 17 nm for the neat BFO sample and 28 nm, 18 nm, and 18 nm for BLaFO, BEuFO, and BErFO samples, respectively. The observed decrease in size is typical for RE-doped materials [43, 44]. However, crystalline sizes of the materials, prepared by our modified method, are quite lower in the comparison of grain sizes of bismuth ferrites synthesized by other methods. It could be due to the application of intense microwave drying, which provides formation of homogenous foams with high surface areas. The foams promote follow-up fast SCS reaction, which starts at low temperature practically simultaneously in the whole reacting volume and ends in a very short time (~5–10 s). This excludes necessity of long time high-temperature calcination to remove traces of a fuel and prevents intense growth of crystalline sizes. Moreover, fast SCS in an explosion mode along with postsynthesis heat treatment with follow-up quenching could be another reason of mixed phase formation in RE-doped bismuth ferrites with highly distorted crystal cells.The Raman spectra of neat and doped BFO samples are shown in Figure3. Raman spectroscopy is sensitive to the change in the crystal structure of the investigated materials; thus, this technique allows better understanding of the structural modifications induced by the substitution of Bi3+ by lanthanide ions. Obtained results are in good agreement with literature-reported spectra of rhombohedral BFO [42, 45, 46]. Based on a group theory, neat BFO with a rhombohedral lattice system (R3c space group) is characterized by 13 Raman active modes represented by Г=4A1+9E. In the present research, BFO peaks at 139 cm-1, 211 cm-1, 273 cm-1, and 445 cm-1 were assigned to A1 modes. E-type Raman modes were observed at 121 cm-1, 312 cm-1, 375 cm-1, and 386 cm-1. The low-frequency A1 and some of E (TO) modes are assigned to the Bi-O bonds, while E (TO) modes, which appear in a higher Raman shift region, are attributed to Fe–O bonds [47]. With the decrease of doping ionic radii, one can observe band movement to the higher Raman shift positions which is connected with decreasing of the Bi-O bond length [48]. The variation in the vibrational modes of doped samples in comparison to neat BFO is clearly visible. The observed peak shift and broadening accompanied with the variation of their intensity clearly show structural transition that was substantiated by the XRD study.Figure 3
Raman scattering spectra of neat and RE-doped BFO nanomaterials in the range of 80-500 cm-1.FTIR spectra recorded in the range of 300–600 cm-1 in the absorbance mode for all synthesized materials are shown in Figure 4. There are typical band characteristics of metal oxygen bonds. Two strong absorption peaks observed near 436 cm-1 and 536 cm-1 were assigned to the Fe–O bending and stretching vibrations in the FeO6 octahedral groups in the BFO perovskite structure, respectively [49, 50]. Two other weak peaks around 380 cm-1 and 477 cm-1 are due to the presence of Bi–O bonds in BiO6 octahedra along with the FeO6 group [51–53]. In addition, in the case of the BErFO sample, the peak split is observed around 536 cm-1, which indicates the presence of two separate perovskite phases in this sample.Figure 4
FTIR spectra of neat and RE-doped BFO nanopowders in the range of 300-600 cm-1.In addition, FTIR spectra reveal the softening of vibration modes in a row of BLaFO–BFO–BEuFO–BErFO, which is due to the concomitant structural R3c–Pbnm phase transitions as confirmed by the XRD analysis. However, no significant shift of absorption bands in doped samples was observed, due to 10 mol% doping by RE elements, which is in good agreement with literature data [49].Figure5 shows the absorbance vs. wavelength plot of neat and doped samples derived from diffuse reflectance data. The strong band at 450–600 nm is attributed to a metal-metal transition, and the weak peak at ~700 nm is assigned to the crystal field transition.Figure 5
UV-Vis absorption spectra of neat and doped BFO nanomaterials in the range 350-700 cm-1.The Kubelka-Munk function was used to calculate the optical absorption coefficient (α) from the reflectance data as follows:
(3)a=1−R22R,where R is the measured reflected light. Band gap values for all samples can be determined using the formula:
(4)αhv=Bhv−Egn,where hν is the incident photon energy, α is the absorption coefficient, B is the absorption edge width parameter, Eg is the band gap, and n is the exponent dependent on direct and indirect transition across the band gap.Extrapolation of the linear region of theαhν2 vs. E (eV) plot to the intersection with the x-axis provides accurate determination of the optical band gap energy (Eg) values (linear extrapolation of the Tauc method) (Figure 6). For BFO material, determined optical band gap energy corresponds to the energy difference between the top of the O 2p valence band and bottom of the Fe 3d conduction band [54]. The obtained Eg value for BFO is 2.02 eV and is in good agreement with previously reported values being in a range of ca. 1.8–2.8 eV [55–57]. The lower band gap energy value could be explained by the smaller size of crystallites of obtained BFO as reported in the literature [42, 54, 58, 59]. The substitution of Bi3+ by RE ions in BFO determined a noticeable decrease in the optical band gap energy to 1.96, 1.93, and 1.94 eV for BLaFO, BEuFO, and BErFO, respectively, which are lower than those previously reported [54–60]. There might be several explanations of the observed reduced band gap in the doped BFO samples. As it was mentioned before, crystalline size reduction can cause decreased optical band gap energy. Besides, the bond lengths directly effect on electron bandwidth (W) and, hence, band gap of the obtained materials. The band gap reduction in doped BFO samples is possible due to lattice contractions, resulting from reducing of Fe-O and Fe-O-Fe bond lengths [7, 54, 60, 61]. As reported elsewhere [54, 60], W has an inverse dependence from Fe-O bond length and Eg is connected to W as Eg=Δ–W, where Δ is the charge transfer energy. Thus, decreasing Fe-O bond length with the incorporation of rare earth ions into BFO structure may considerably increase W values and, consequently, reduce Eg. To sum up, optical measurements showed the reduction of band gap with rare earth ion doping, which increases the absorption capability of the obtained materials in visible range and, in turn, broadens their possible applications in photocatalysis and photovoltaic devices.Figure 6
α
h
ν
2 vs. photon energy, hν, plot to calculate band gap energy of the neat and doped BFO samples.To investigate the dielectric properties of neat and doped BFO samples, broadband dielectric spectroscopy was applied. Figures7 and 8 show variation of the real part of dielectric permittivity (ε′) and loss tangent (tan δ) as the function of frequency in the range of 0.7 Hz–6.5 MHz at 30°C.Figure 7
Frequency dependence of real-part dielectric permittivity at 30°C of neat and codoped BFO materials. The insert shows the enlarged view of the dielectric permittivity curves in the frequency range of1⋅105÷3⋅106 Hz.Figure 8
Frequency dependence of loss tangent at 30°C of neat and codoped BFO materials. The insert shows the enlarged view of the loss tangent curves in the frequency range of1⋅105÷3⋅106 Hz.The dispersive behavior is observed for all the samples in the whole frequency range for bothε′ and tan δ representations. The dielectric permittivity dispersion is associated with four fundamental different mechanisms of polarization, and each of them dominates at different frequencies. At lower frequencies, dipolar and interfacial polarization plays an important role in the dielectric behavior of BFO materials, whereas at higher frequencies, the main contribution in ε′ is due to the electronic and ionic polarizations [62]. As dielectric media consists of poorly conductive grain boundaries and well conductive crystallites, a space charge polarization occurs at low frequencies as an effect of the heterogeneity of the material structure that subsequently increases dielectric permittivity values. As frequency increases, an additional contribution becomes dominant due to electrons hopping between Fe3+ and Fe2+ ions at FeO6 octahedra sites [24, 60]. The latter is connected with dipole rotation in the field direction. The influence of polarization and its relaxation on ε′ becomes less perceptible as frequencies increase because of inertia of charge movement. A further frequency increase leads to the decrease of dielectric permittivity, which finally becomes frequency-independent [43]. Similar to the optical properties, the electric properties of synthesized nanomaterials have been found to be greatly influenced by the structural changes as a result of doping and features of the synthesis process. The dielectric value as well as dielectric dispersion increases in a row of BLaFO–BErFO–BFO–BEuFO, which is in good agreement with the polarization theory and structure of obtained samples revealed by XRD, Raman, and FTIR data. At low frequencies, ε′ values are mostly influenced by the amount of hopping electrons between Fe3+ and Fe2+ ions, which is the highest in the Eu-doped sample due to a highly distorted perovskite crystal structure. Obviously, the polarization through this mechanism should be higher when the greater difference in the dimensions of the ionic radii between Bi3+ and RE3+ ions is observed. However, this rule does not work when energy stabilization occurs through formation of two phases due to very high distortion of crystal structure (BErFO sample in this work). In this case, one of these phases is paraelectric and does not contribute much to a value of dielectric permittivity and dispersion. On the other hand, BFO has a high enough distorted structure due to fast phase formation and quenching to show a high value of permittivity and dielectric dispersion.At higher frequencies, the contribution of dipole polarization and interfacial polarization decreases, as well as reduction ofε′, becomes less significant for all samples. Nevertheless, it could be noticed that frequencies higher than ~105 Hz correlation of permittivity values switch to the opposite side (i.e., the highest ε′ value for La-doped and neat BFO and the lowest one for BEuFO). At 1.15 MHz frequency, the real part of the dielectric permittivity was 41, 38, 34, and 36 for BLaFO, BFO, BEuFO, and BErFO, respectively. We suppose that the main reason of this switch is due to the suppression of ionic polarization of the distorted perovskite crystal structure at high frequencies. This assumption is confirmed by tan δ data. At low frequencies, tan δ is affected by dipole polarization and changes in a similar order like ε′ representation for all investigated samples. At about 105 Hz, there is an obvious abrupt change in gradient of loss tangent curves of BLaFO, which indicates change in polarization mechanism, as dipole polarization becomes negligible and ionic polarization does not affect dielectric loss. On the other hand, a very slight change in the gradient of tan δ for BFO, BEuFO, and BErFO samples is observed. Thus, ionic polarization is suppressed considerably for neat and Eu- and Er-doped samples due to a high degree of distortion of their structure while less suppressed for the BLaFO sample. This suppression might be caused by the change of Fe–O length bond, which obstructs ionic polarization, and by the decrease of the amount of oxygen vacancies.Other factors influencing theε′ and tan δ values are grain sizes and sample morphology, i.e., polydispersity of grain’s size [63]. We suppose that lower grain sizes promote dipole mobility at high frequencies through the change of the amount of domain boundaries. However, low concentration of secondary phases did not significantly affect dielectric behavior in all investigated samples.


## 4. Conclusions

In this study, we investigated the effect of high load La3+, Eu3+, and Er3+ doping on structural, optical, and electrical properties of nanocrystalline BiFeO3 obtained by microwave-assisted modification of solution combustion synthesis. The combination of features of our modified SCS method and high load of RE doping results in significant distortion of crystalline cells of the obtained bismuth ferrite nanopowders with follow-up formation of mixed rhombohedral-orthorhombic crystal structures, which was confirmed by the results of XRD, Raman spectrometry, and FTIR analysis. The highest degree of distortion of crystalline parameters was found in Eu-doped samples. At the same time, high load Er doping led to the formation of doped bismuth ferrite in two polymorph structures, as a result of energy relaxation. It was found that the observed cell distortion as well as the decrease of crystalline sizes affects optical and electrical properties of the BFO-based materials. The optical band gap energy was decreased from 2.02 eV to 1.96-1.93 eV for neat BFO and RE-doped samples, respectively, that makes obtained materials promising candidates for photocatalytic and photovoltaic devices. Performed studies showed that microwave-assisted solution combustion synthesis is a favorable method to prepare a broad variety of neat and doped nanomaterials. Such method allows us a fast and efficient way to adjust properties of nanomaterials by its doping.



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