Sol-Gel Synthesis, Structural Characterization and Microwave Dielectric Properties of Bismuth Niobate Modified by Iron Inclusion

Abstract

The current progress in communication technologies is leading to extensive studies on the development of miniaturized electronic devices with high electromagnetic performances, reliability, and low cost. Contributing to this purpose, the development and study of new materials, with promising electric properties in radio and microwave ranges, have been subject of our research in particular niobate-based materials. Bismuth niobate, BiNbO4, is a low-firing ceramic that has been studied for a variety of applications in the microelectronic industry. In this work, the microwave dielectric characterization of (Bi1−x Fex )NbO4 (0.00 ≤ x ≤ 1.00) samples, prepared by the sol-gel method and heat treated at specific temperatures, is performed and related with their structure and morphology. The structural data were obtained by X-ray diffraction and Raman spectroscopy and the morphology by scanning electron microscopy. The dielectric characterization in the microwave region was made using the small perturbation theory, with a resonant cavity operating in TE105 mode, at the frequency of 2.7 GHz. The results show that the sol-gel method has the advantage of allowing the formation of α-BiNbO4 phase at lower temperatures when compared with conventional preparation methods, and that the inclusion of iron inhibits the formation of low- and high-temperature β-BiNbO4 phases.

1. Introduction: state of the art

In the modern communication systems, where microwave frequencies are used, wireless equipment are indispensable [1]. Therefore, the development of smaller, faster, and multifunctional equipment, with high electromagnetic performances and reliability, is an important technological challenge [2]. Since this goal can be achieved using ceramics technology, in the last decades a lot of research has been devoted to the improvement of dielectric ceramic materials that can be sintered at low temperature [3].

Bismuth oxides are recognized as low temperature-cofired ceramics (LTCC) and are considered promising materials for applications in the microelectronic industry [4]. In particular, bismuth niobate, BiNbO₄, has been studied to be used as resonators and filters in satellite and mobile communication systems [5].

The sintering temperatures of these microwave dielectrics cannot be high, since they need to cofire with low-loss conductors and low melting point electrodes, such as copper, silver, and gold [6]. Moreover, it is desirable that these ceramics have a high dielectric constant (ε′), a low dielectric loss (ε”), and a small coefficient of resonant frequency (τ_f) in the microwave range [7].

Bismuth niobate exists in two polymorph structures, an orthorhombic (α) phase (space group P_nna) and a triclinic (β) phase (space group P₁).

Figure 1 shows the crystal structures of (a) α-BiNbO₄ and (b) β-BiNbO₄. There are four formula units in the unit cell in both structures. The α structure consists of layers of vertex-sharing NbO₆ octahedra, which is normal to the c plane, with the Bi³⁺ positioned on the sites between these layers. The β phase presents pseudo layers of [Bi₂O₂] units connected with each other and surrounded by sheets of formula [NbO₄]n along the bc plane, in which the NbO₆ octahedra are joined at four vertices so that the two free oxygen atoms are in c axis. The Bi atoms hold these sheets together and are coordinated to eight oxygen atoms in the form of a much more distorted square antiprism. Summing up, the structure of α phase could be thought to be composed of two bismuth layers and two separated NbO₆ octahedral layers with different distortions. β-BiNbO₄ is composed of two bismuth layers and two joined octahedron layers [8, 9].

Figure 1.

Schematic illustrations of crystal structures of (a) α-BiNbO₄ and (b) β-BiNbO₄.

According to previous studies, the transition of low temperature β-BiNbO₄ to α-BiNbO₄ occurs at temperatures between 600 and 750°C, with the opposite, and supposed irreversible, transition occurring at 1020/1050°C [10, 11]. In 2007, Zhou et al. [8] reported the transformation from high temperature β-BiNbO₄ to α-BiNbO₄ in bulk samples; however, this transition is still considered irreversible in powder samples.

BiNbO₄ ceramics can have low sintering temperature; however, they are difficult to densify without sintering aids [5]. The first attempt to improve the bismuth niobate properties was developed by Kagata et al. [12] in 1992. They used V₂O₅ and CuO as additives, with the purpose of densifying the ceramic materials without compromising their dielectric properties. Since then, in order to obtain higher densification, better dielectric properties, and reduce the sintering temperature, various attempts have been undertaken to improve the bismuth niobate properties as a microwave dielectric ceramic [4]. Besides the addition of different oxides, such as CuO [6], ZnO [13], V₂O₅ [14, 15], PbO, Bi₂O₃ [16], and Fe₂O₃ [17], several researchers tried to improve bismuth niobate properties through the substitution of bismuth for metals or lanthanides. In order to accomplish this task, (Bi_1−xR_x)NbO₄ compositions were developed and studied, where R represents different metals, such as Fe [18] or Pb [19], and different lanthanides, such as Ce, Nd, Dy, Er, La, Sm, Ta, Gd, and La [20–25].

The solid-state reaction has been the most common method to process bismuth niobate [1, 7, 8], which means its benefits and drawbacks are already documented in the literature. BiNbO₄ powders prepared by solid-state reaction result in high crystallinity, but not always in pure and homogeneous phases, because some metastable phases can be obtained under the same conditions [25]. This method may cause other problems such as large grain growth, segregation of components, and loss of stoichiometry due to the volatilization of bismuth at a high temperature [10].

The wet-chemical techniques, such as co-precipitation, alkoxide and citrate sol-gel methods, and flux method, were found to present several advantages: nanosize particles, high reactivity, very good homogeneity in composition, and lower energy consumption, because they operate in mild temperatures. However, in these methods, metastable phases can also be formed [1, 7, 10].

Co-precipitation is considered one of the most successful techniques for the synthesis of ultrafine ceramic powders, having narrow particle size distribution. It is a less time-consuming method, since that can avoid complex steps such as refluxing of alkoxides. Nonetheless, an important drawback of co-precipitation is that all the cations should have similar solubility product [7, 10, 26].

The flux method is an alternative process that uses low-temperature liquid-phase reaction. According to previous studies, the BiNbO₄ prepared by the flux method exhibits higher crystallinity than that obtained by solid-state reaction; however, the successful application of this method depends on a large number of factors, like eutectic temperatures and solubility of solid components in the eutectic melts. Besides that, the decrease of the sintering temperature is not always achieved, since a proper combination of material/dopant is needed. In some cases, the mechanical separation between product and flux can be difficult [27, 28].

The sol-gel method, through citrate route, is considered a simple way to obtain stable precursors and stoichiometric fine powders which have been employed in the production of various oxides. This method is considered promising for achieving high homogeneity, since the formation of citrate complexes allows mixing the component cations in an atomic scale, thus they can immediately react with each other at relatively low temperatures [10, 13, 25].

In this work, the microwave dielectric properties of (Bi_1−xFe_x)NbO₄ (0.00 ≤ x ≤ 1.00) samples, prepared by sol-gel method, through the citrate route, and heat-treated at specific temperatures, are studied. Since it is recognized that the behavior of functional materials is intrinsically linked to their structures [29], a structural characterization of the obtained samples was performed, using X-ray diffraction (XRD). Furthermore, to verify the structure consistency between low- and high-temperature β-BiNbO₄, and to better understand the phase transition process, the Raman spectroscopy was performed [10].

Since it is recognized that the dielectric properties can be related with density, porosity, and grain boundaries [20], the density of the samples was measured, using Archimedes method, and the morphology data was obtained by scanning electron microscopy (SEM).

2. Case study

2.1. Samples preparation

(Bi_1−xFe_x)NbO₄ powders were prepared by the sol-gel method. Bismuth nitrate (Bi(NO₃)₃⋅5H₂O), niobium chloride (NbCl₅), iron nitrate (Fe(NO₃).9H₂O), were used as starting materials and citric acid and ethylene glycol as chelating agent and reaction medium, respectively. All reagents used in the whole procedure were of analytical grade. The starting materials, with purities >99.9%, were supplied by Mateck and Merk and the chelating agent and reaction medium by Sigma-Aldrich. Bismuth nitrate, niobium chloride, and iron nitrate solutions were prepared in minor amounts of hydrogen peroxide (3%, V/V), combined in the corresponding molar ratio, and then added to citric acid and ethylene glycol. The obtained mixtures were stirred, to promote the solubility, until clear colloidal suspensions were obtained.

The obtained solutions were dried to evaporate the solvent: the solution of the reference sample, x = 0.00, was dried at 400°C, for 48 h; the solutions with 0.25 < x < 0.75 were dried at 300°C, for 60 h; the solution with x = 1.0 was dried at 300°C, for 24 h. Subsequently, the obtained powders were thermally analyzed by differential thermal analysis (DTA), performed in a Linseis Apparatus type L92/095, in the temperature range of 20–1200°C, with a heating rate of 5 and 10°C/min, using Al₂O₃ as reference. Finally, the dry powders were pressed into cylinders and heat-treated, according to the DTA results, at temperatures between 500 and 1200°C, using a dwell time of 4 h, with a heating rate of 5°C/min.

2.2. Experimental methods

The structural characterization was performed using X-ray diffraction (XRD). The patterns data was obtained on a X’Pert MPD Philips diffractometer and on an Empyrean diffractometer (CuK α radiation, λ = 1.54060 Å) at 45 kV and 40 mA, in a Bragg–Brentano parafocusing optics configuration. The step counting method was used, with a step of 0.02° and a time per step of 1 s, with a 2θ angle range of 10–60°.

Raman spectroscopy measurements were performed at room temperature, in backscattering geometry, with a 441.6 nm laser line using a HR-800-UV Jobin Yvon Horiba spectrometer. A microscope objective focused the exciting light onto the sample.

The ceramics bulk density was measured using the Archimedes method in reference to water.

The morphology of the sintered samples was analyzed by scanning electron microscopy (SEM), using a TESCAN-Vega III. The samples were covered with carbon before microscopic observation.

The measurement of the complex permittivity was made using the small perturbation theory, with a cavity operating in TE₁₀₅ mode, at resonant frequency of 2.7 GHz. These measurements were made using a HP 8753D coupled to the cavity resonator.

Microwave resonant cavities have been used for evaluating the dielectric properties of geometrically defined samples, when the cavity is calibrated with dimensionally identical sample of known permittivity.

For a given cavity and a sample of regular shape and well-defined dimensions, it is possible to determine the permittivity of the material. The permittivity values of a sample can be obtained through the changes in the resonant frequency, Δf, and in the inverse of the quality factor Δ(1/Q) of the resonant cavity, when introducing a sample in the cavity, where the electric field is maximal [30–33].

The shift in the resonant frequency of the cavity, Δf, can be related to the real part of the complex permittivity, ε′, whereas the change in the inverse of the quality factor of the cavity, Δ(1/Q), can be related with the imaginary part, ε”.

Considering only the first-order perturbation in the electric field caused by the sample [30–33], we obtain

${\epsilon }^{\prime }=K\frac{\text{Δ}f}{f_0}\frac{V}{v}+1$E1

${\epsilon }^{″}=\frac{K}{2}\text{Δ}\left(\frac{1}{Q}\right)\frac{V}{v}$E2

where K is a constant related to the depolarization factor, which depends upon the geometric parameters, v and V are the volumes of the sample and the cavity, respectively, and f₀ is the resonance frequency of the cavity. Using a sample of known permittivity, in our case polytetrafluorethylene (PTFE), we can determine the constant K.

2.3. Results and discussion

2.3.1. DTA

The DTA data of the powders with x = 0.00 (BiNbO₄) and x = 1.00 (FeNbO₄) are shown in Figure 2. In Figure 2(a), one can see the occurrence of three exothermic peaks, at 649, 1043, and 1129°C. Figure 2(b) shows four endothermic phenomena at 391, 708, 881, and 1151°C. The peak that occurs at 391°C is due to the decomposition of residual organic compounds that were not released during the drying process.

Figure 2.

(a) DTA of BiNbO₄ powder, x = 0.00, heated at the rate of 10°C/min; (b) DTA of FeNbO₄ powder, x = 1.00, heated at the rate of 5°C/min.

The powders with 0.25 ≤ x ≤ 0.75 were also thermally analyzed. When x = 0.25, three exothermic phenomena were identified, centered at 519, 637, and 1054°C. With x = 0.50, we can highlight once again three exothermic peaks, at 489, 556, and 637°C. The powder with x = 0.75 shows two exothermic peaks at 485 and 1157°C.

The heat treatments were made in agreement with these results, as shown in Table 1.

	Treatment temperatures (°C)
x	500	650	800	850	1000	1050	1100	1150	1200
0.00	×	×	–	×	_	×	_	×	a
0.25	×	×	×	–	–	–	×	_	_
0.50	×	×	×	–	–	–	×	_	_
0.75	×	×	×	–	–	–	×	–	–
1.00	×	×	–	×	×	–	–	–	×

Table 1.

Heat treatments performed in the cylindrical samples.

^a

The heat treatment performed at 1200°C promoted the fusion of the powders.

2.3.2. XRD pattern analysis

Figure 3 shows the X-ray diffraction patterns of (Bi_1−xFe_x)NbO₄ powders, for x = 0.00, Figure 3(a), and x = 1.00, Figure 3(b).

Figure 3.

X-ray diffraction patterns of (Bi_1−xFe_x)NbO₄ samples for (a) x = 0.00 and (b) x = 1.00.

Analyzing the diffraction patterns shown in Figure 3(a), for the powders treated at 500°C, there are two secondary phases Bi₂O₃ and BiOCl, and the beginning of the β and α phases formation. The sample treated at 650°C is a combination of α- and β-BiNbO₄ phases, with the secondary phase BiOCl still present. After the treatment of the samples at 850°C, the X-ray diffraction pattern shows the formation of pure orthorhombic BiNbO₄ and, with a further temperature increase, this phase is converted to triclinic BiNbO₄. For the highest treatment temperature, the volatile nature of Bi³⁺ ions, at elevated temperatures, promotes the formation of a non-stoichiometric phase of bismuth niobate, Bi_3.54Nb_7.09O_22.7.

Therefore, the DTA exothermic band centered at 649°C can be due to the formation of α-BiNbO₄, and the exothermic reaction occurring at 1043°C can be attributed to the conversion of α-BiNbO₄ to β-BiNbO₄. The thermal treatment at 1200°C promoted the fusion of the samples; consequently, there is no exact information about the exothermic phenomenon at 1181°C. However, the formation of a non-stoichiometric phase, due to the volatile nature of bismuth [3], is predictable.

In Figure 3(b), it is observed the formation of monoclinic FeNbO₄, even at the lowest heat-treatment temperature. For the treatment temperatures from 500 to 1000°C, one additional phase was detected, Fe₂O₃, with a content equal or inferior at 5%. For the 1200°C heat treatment, single-phase FeNbO₄ sample was obtained. Therefore, the DTA exothermic phenomena appearing at 747°C can be related with an improvement of the crystallization process of FeNbO₄ and the phenomena visible at 1151°C can be attributed to the decomposition of the Fe₂O₃, and consequent formation of FeNbO₄, with the niobium still present in the amorphous form. The increase of the amplitude and decrease of the half-width of the obtained XRD peaks, and of the Raman bands, shows that the increase of the heat treatment temperature promotes an increase of the crystallinity.

The samples with 0.25 ≤ x ≤ 0.75 were also characterized using X-ray diffraction, with the diffraction patterns shown in Figure 4 and the present phases identified in Table 2. Besides the expected phases like α-BiNbO₄ and FeNbO₄, there was the formation of two non-stoichiometric phases, Bi_1.34Fe_0.66Nb_1.34O_6.35 and Bi_1.721Fe_1.056Nb_1.134O₇, where the substitution of Bi³⁺ for Fe³⁺ ions was successful, and five more secondary phases. The absence of β-BiNbO₄ in the samples treated at 1100°C was unexpected, since the transition of α- to β-BiNbO₄ occurs, according to previous works, at 1020/1050°C [10, 11], and happened in the host sample at 1043°C.

	HT 500	HT 650	HT 800	HT 1100
x = 0.25	Bi1.34Fe0.66Nb1.34O6.35	α-BiNbO4; Bi1.34Fe0.66Nb1.34O6.35	α-BiNbO4; FeNbO4; Bi2O3	Bi1.721Fe1.056Nb1.134O7; BiFeO3
x = 0.50	Bi1.34Fe0.66Nb1.34O6.35	α-BiNbO4; Bi1.34Fe0.66Nb1.34O6.35	Bi1.721Fe1.056Nb1.134O7; FeNbO4	Bi1.721Fe1.056Nb1.134O7; FeNbO4
x = 0.75	Bi15NbO25; Fe2O3; Fe0.33Nb0.67O2	FeNbO4; Bi2O3	FeNbO4; Bi2O3	FeNbO4; Bi15NbO25

Table 2.

Identification of the crystalline phases of (Bi_1−xFe_x)NbO₄ samples for 0.25 ≤ x ≤ 0.75.

Figure 4.

X-ray diffraction patterns of (Bi_1−xFe_x)NbO₄ samples for 0.25 ≤ x ≤ 0.75.

Confronting the X-ray diffraction data with the DTA, it is possible to assume that for the samples with x = 0.25 and 0.50, the exothermic peaks can be related with the formation of the Bi_1.34Fe_0.66Nb_1.34O_6.35, α-BiNbO₄, and Bi_1.721Fe_1.056Nb_1.134O₇ phases, respectively. Since these three peaks are dislocated for lower temperatures in the sample with x = 0.50, it means that the energy required for these phase transformations decreases with the increase of the amount of iron. Considering the sample with x = 0.75, the peak occurring at 485°C can be assigned to the formation of Bi₁₅NbO₂₅ and the one centered at 1157°C should be related to a non-stoichiometric phase formation.

In the present study, one can conclude that the sol-gel method has the advantage of forming the orthorhombic BiNbO₄ phase at even lower temperatures, since the sample with x = 0.00, treated at 500°C, presents already the α phase, and that the inclusion of iron inhibits the formation of low- and high-temperature triclinic bismuth niobate.

2.3.3. Raman spectroscopy analysis

The Raman spectroscopy data of (Bi_1−xFe_x)NbO₄ powders, for x = 0.00 and x = 1.00, are presented in Figure 5.

Figure 5.

Raman spectra of (Bi_1−xFe_x)NbO₄ samples for (a) x = 0.00 and (b) x = 1.00.

In Figure 5(a), we can see that the Raman spectrum of the sample treated at 850°C, pure orthorhombic BiNbO₄, is less complex than the spectra were the triclinic BiNbO₄ is present. This result was expected since the lowered symmetry of the triclinic phase produces more Raman active modes [10]. The samples treated at 500, 650, 1050, and 1150°C possess peaks at 102, 450, and 687 cm⁻¹ attributed to the vibration modes of β-BiNbO₄. This means that both low and high temperature β-BiNbO₄ have identical vibration modes. In the sample treated at 850°C, where only α-BiNbO₄ was detected, these peaks are absent. Furthermore, the peaks at 139 and 199 cm⁻¹ are distinctive of the orthorhombic BiNbO₄, which explains their absence in the spectra of the samples treated at 1050 and 1150°C. All the peaks present in these two samples are attributed to triclinic BiNbO₄ [10, 34]. No vibration that can be assigned to non-stoichiometric phase Bi_3.54Nb_7.09O_22.7 was detected.

In the spectra presented in Figure 5(b), all the detected bands are attributed vibrations of the base units of the monoclinic FeNbO₄ phase. The Nb─O stretching bands were observed at 276, 394, 597, and 818 cm⁻¹, and the bands visible at 365 and 467 cm⁻¹ are exclusively for the monoclinic FeNbO₄ [35–38]. With the increase of the temperature, it can be seen a better definition of bands, which is consistent with the increase of the crystallinity of the samples.

The Raman spectroscopy data of (Bi_1−xFe_x)NbO₄ powders, with 0.25 ≤ x ≤ 0.75, are presented in Figure 6. Regardless of the x value, the obtained data shows that the crystallinity increases with the temperature.

Figure 6.

Raman spectra of (Bi_1−xFe_x)NbO₄ samples for (a) x = 0.25, (b) x = 0.50, and (c) x = 0.75.

In the samples with x = 0.25 treated at 650 and 850°C and x = 0.50 treated at 650°C, the peak occurring at 200 cm⁻¹ is distinctive of the orthorhombic BiNbO₄. On the other hand, the peaks visible at 224, 276, 304, 365, 394, 467, 501, 597, and 817 can be assigned to FeNbO₄.

2.3.4. Density

The bulk density values of (Bi_1−xFe_x)NbO₄ ceramics, for x = 0.00 and x = 1.00, in reference to water versus treatment temperature are shown in Figure 7.

Figure 7.

Bulk density of (Bi_1−xFe_x)NbO₄ samples for x = 0.00 and x = 1.00.

The bulk density increase with the treatment temperature increase is clearly visible for both the series of samples, and it allows to predict that porosity decreases at higher treatment temperatures.

The theoretical density of β-BiNbO₄ ceramic (7.5 g/cm³) is higher than that of α-BiNbO₄ ceramic (7.345 g/cm³) [21, 22]. Thus, and considering the samples with x = 0.00, the increase of bulk density of BiNbO₄ ceramics from 850 to 1050°C can be due to the orthorhombic-triclinic phase transformation of BiNbO₄. According to the literature, it is very difficult to densify the ceramics above 85% of theoretical density without sintering additives [24]. However, in the sample treated at 1150°C, the density is 85.3% of the theoretical density and that was slightly above the pointed level.

Considering now the samples with x = 1.00, and knowing that the theoretical density of FeNbO₄ ceramic is 5.40 g/cm³ [39], we can determine that for the highest heat treatment, the only one where pure FeNbO₄ was formed, the density is 92.6% of the theoretical density.

For the remaining samples, the evolution of the bulk density values with the treatment temperature is shown in Figure 8. In this case, we can see the same trend for this set of samples. The bulk density increases when the treatment temperature increases for 650°C, decreases for the treatment at 800°C, reaching a minimum value, and increases again with the higher treatment temperature. Regardless of the heat treatment, the samples with higher bulk density are the ones with x = 0.50.

Figure 8.

Bulk density of (Bi_1−xFe_x)NbO₄ samples for x = 0.25, x = 0.50, and x = 0.75.

2.3.5. Morphological characterization

In Figure 9, SEM micrographs of the samples with x = 0.25 and 0.50, treated at 650°C, are shown. In these samples, where the same phases were identified, we can see particles with spherical shape and diameter of 0.2 μm. Increasing the amount of iron, a decrease in porosity is detectable, a result that is coherent with the increase in density, previously analyzed.

Figure 9.

SEM micrographs of the samples with x = 0.25 and x = 0.50, treated at 650°C.

2.3.6. Microwave dielectric properties

In Figure 10 is presented the transmission results obtained with the 2.7 GHz cavity, for the cases of the cavity only with the sample holder, with the sample holder filled with PTFE and filled with the samples with 0.25 ≤ x ≤ 0.75, treated at 650°C. The expected shift in the resonant frequency of the cavity, Δf, is observed.

Figure 10.

Transmission of the unperturbed and perturbed 2.7 GHz cavity, for 0.25 ≤ x ≤ 0.75 (Bi_1−xFe_x)NbO₄ samples, treated at 650°C.

Since this shift, Δf, can be related to the real part of the complex permittivity, ε′, it is expected that the sample with x = 0.75 presents the lowest ε′, followed by the sample with x = 0.25 and finally the sample with x = 0.50, with the highest dielectric constant of this series of samples. This prediction will be confirmed later.

Figure 11 shows the real and the imaginary parts of the complex permittivity at 2.7 GHz, as function of the treatment temperatures, for the samples with x = 0.00 and x = 1.00.

For the samples with x = 0.00, Figure 11(a) shows that ε′ values increase with the treatment temperature. The same trend was previously seen for the bulk density, suggesting that the dielectric constant increase with temperature is due to the density increase. With the exception of the sample treated at 500°C, where BiNbO₄ presence is still reduced, the dielectric losses also show the same evolution, increasing with the treatment temperature.

Figure 11.

Calculated ε′ and ε” of (Bi_1−xFe_x)NbO₄ samples for (a) x = 0.00 and(b) x = 1.00, at room temperature.

Figure 11(b) shows that for the samples with x = 1.00, the dielectric constant and the dielectric losses follow the same trend.

In Figure 12, it is presented the dielectric constant for the samples with 0.25 ≤ x ≤ 0.75, as function of the treatment temperatures. Once more, the experimental data suggests that the increase of the bulk density is determinant for the increase of the dielectric constant. Nevertheless, the samples treated at 1100°C, besides the higher ε′ values, also show the higher losses.

Figure 12.

Calculated ε′ for 0.25 ≤ x ≤ 0.75 (Bi_1−xFe_x)NbO₄ samples, at room temperature.

Table 3 resumes the calculated ε′ and ε” for the different samples.

x		HT 500	HT 650	HT 800	HT 850	HT 1000	HT 1050	HT 1100	HT 1150	HT 1200
0.00	ε′	4.03	4.94	–	5.42	–	6.97	–	7.81	–
	ε”	0.62	0.01	–	0.05	–	0.11	–	0.28	–
0.25	ε′	4.24	3.74	3.65	–	–	–	10.66	–	–
	ε”	0.08	0.06	0.07	–	–	–	0.22	–	–
0.50	ε′	3.81	3.81	5.59	–	–	–	11.15	–	–
	ε”	0.09	0.09	0.15	–	–	–	0.35	–	–
0.75	ε′	2.83	2.37	3.57	–	–	–	15.91	–	–
	ε”	0.08	0.03	0.15	–	–	–	2.59	–	–
1.00	ε′	4.63	4.10	–	3.43	3.55	–	–	–	4.76
	ε”	0.27	0.25	–	0.19	0.34	–	–	–	0.42

Table 3.

Calculated ε′ and ε” for different samples.

2.4. Conclusion

We can conclude that the (Bi_1−xFe_x)NbO₄ ceramic powders were prepared successfully by the sol-gel method.

For x = 0.00, this method allows the formation of orthorhombic BiNbO₄ at lower temperatures than other preparation techniques. Both α and β phases can be stable in different temperature regions, below 850 and above 1050°C, respectively.

Furthermore, the density of the obtained samples was very promising, since no additives were used in the host samples.

The substitution of bismuth by iron was successful, since the two non-stoichiometric phases, Bi_1.34Fe_0.66Nb_1.34O_6.35 and Bi_1.721Fe_1.056Nb_1.134O₇, were obtained. Moreover, one can conclude that the inclusion of iron inhibits the formation of low- and high-temperature triclinic bismuth niobate.

Concerning the dielectric characterization, the small perturbation technique proved to be very practical for dielectric measurements on ceramic materials, featuring important advantages, as the easy sample preparation, the absence of measurement contacts, and the simplicity of the calculations.

The dielectric study revealed that, for x = 0.00, the dielectric constant increases with the increase of the sintering temperature, with the dielectric losses showing the same trend.

With the inclusion of iron, the highest ε′ values were obtained for the highest treatment temperature; however, only the samples with x = 0.25 and 0.50 showed ε” acceptable values.