Comprehensive Characterization of Bi_1.34Fe_0.66Nb_1.34O_6.35 Ceramics: Structural, Morphological, Electrical, and Magnetic Properties

Abstract

Recent research in solid-state physics and materials engineering focuses on the development of new dielectric materials, with bismuth-based pyrochlores being already extensively applied in communications technology for their excellent dielectric properties and relatively low sintering temperatures. Herein, the structural, morphological, electrical, and magnetic properties of Bi_1.34Fe_0.66Nb_1.34O_6.35 ceramic, prepared by the sol–gel method and sintered at 500 °C, are investigated. The Rietveld refinement of the XRD pattern showed a cubic phase belonging to the space group Fd-3m and a crystallite size of 42 nm. Transmission electron microscopy further confirmed the crystallite size and the homogeneous distribution of Bi, Fe, Nb, and O elements, as evidenced by high-angle annular dark field imaging and STEM-EDX mapping. The morphology of the sample, assessed by scanning electron microscopy, is characterized by submicron-sized spherical particles. Dielectric spectroscopic studies revealed that the dielectric properties, strongly influenced by frequency and temperature, indicate the material’s potential for energy storage due to lower dielectric loss compared to the dielectric constant. The observed relaxation phenomena, confirmed through variations in dielectric loss and loss tangent, highlight the influence of grain boundaries and temperature on electron hopping and charge carrier dynamics. Using SQUID magnetometry, we identified two distinct magnetic phases. The primary phase, corresponding to the Bi_1.34Fe_0.66Nb_1.34O_6.35 ceramic, exhibits an antiferromagnetic behavior below its Néel temperature at around 8.8 K. A secondary high-Curie temperature ferrimagnetic phase, likely vestigial maghemite and/or magnetite, was also detected, indicating an estimated fraction below 0.02 wt.%.

1. Introduction

Pyrochlores are complex metal oxides with a general formula of A₂B₂O₇, where the A site typically consists of metals, such as Ca, Sr, Sn, Pb, Bi, Y, La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, and Lu, and the B site consists of metals such as Sn, Ti, Nb, Ta, Zr, Hf, Ru, and Ce. The A site cation generally has an oxidation state of +2 or +3 and is coordinated by eight oxygen atoms, while the B site cation has a corresponding oxidation state of +5 or +4, being surrounded by six oxygen atoms [1,2].

Pyrochlores exhibit a wide range of chemical compositions, resulting in a diverse array of unique properties that are valuable for various technological applications. They are widely used in both active and passive electronic components, including switching devices, thermistors, thick-film resistors, and screen printing materials. Additionally, they have also gained recognition as promising candidates for temperature-stable, low-loss, high-permittivity dielectric applications [2,3,4,5].

Bismuth niobate and bismuth titanate cubic pyrochlore phases have attracted significant attention due to their unique crystal chemistry, earning them the label of “misplaced-displacive” pyrochlores [6,7]. Their combination of high dielectric constants and low dielectric losses across a broad frequency range near room temperature, along with their relatively low sintering temperatures, opens up various opportunities for practical applications of these materials [6,8,9].

Cann et al. [8] conducted a dielectric characterization of ten different bismuth-based pyrochlores (Bi₂Zn_2/3Nb_4/3O₇, Bi₂Zn_2/3Ta_4/3O₇, Bi₂Mg_2/3Nb_4/3O₇, Bi₂Mg_2/3Ta_4/3O₇, Bi₂Ni_2/3Ta_4/3O₇, Bi₂ScNbO₇, Bi₂ScTaO₇, Bi₂InNbO₇, Bi₂InTaO₇, and Bi₂Cu_2/3Nb_4/3O₇,), which were prepared using the solid-state reaction method. This procedure involved calcination at 700–800 °C, followed by sintering at 950–1100 °C. At room temperature and a frequency of 1 MHz, the Bi₂Cu_2/3Nb_4/3O₇ exhibited the highest dielectric constant, 250, with a loss tangent of 0.08. The lowest loss tangent, 0.001, was observed for Bi₂Zn_2/3Ta_4/3O₇, Bi₂Mg_2/3Ta_4/3O₇, and Bi₂Ni_2/3Nb_4/3O₇, which had dielectric constants of 67, 80 and 122, respectively.

Somphon et al. [4] studied the bismuth-based pyrochlores Bi₂FeNbO₇ and Bi₂InNbO₇, which were synthesized using the solid-state reaction method with annealing temperatures of 1000 °C and 1100 °C, respectively.

When measured at a frequency of 1 MHz at room temperature, the dielectric constant of Bi₂FeNbO₇ was found to be 100, with a loss tangent of 0.007. For Bi₂InNbO₇, the corresponding values were 133 and 0.002, respectively.

Huang et al. [10] performed the dielectric characterization of Bi_(1.5−x)Nd_xMgNb_1.5O₇ (x = 0–0.6), prepared by the solid-state reaction method and sintered at temperatures between 1000 and 1100 °C. For the pure bismuth-based pyrochlore, a dielectric constant of 170 and a loss tangent of ≈10⁻³ were reported at room temperature and a frequency of 1 MHz.

Bi_1.34Fe_0.66Nb_1.34 was prepared by the solid-state reaction method and sintered at 1000 °C by Mowri et al. [11]. At a frequency of 1 MHz and room temperature, the authors reported a dielectric constant of 28 and a loss tangent of 0.15.

Both stoichiometric and non-stoichiometric pyrochlores can exhibit interesting dielectric behavior, a feature that is not exclusive to pyrochlores or their dielectric properties. For example, both stoichiometric and non-stoichiometric NdMnO₃ display a variety of remarkable physical and chemical properties [12]. Additionally, the Sm_0.55(Sr_0.5Ca_0.5)_0.45MnO₃ manganite shows potential for applications in the fields of magnetic refrigeration and spintronics [13].

In this study, Bi_1.34Fe_0.66Nb_1.34O_6.35 powders were prepared using the sol–gel method and sintered at 500 °C. The structural analysis was carried out through X-ray diffraction and scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy, while the morphological characteristics were examined using scanning electron microscopy. The complex permittivity was measured over a frequency range of 100 Hz to 1 MHz, as a function of temperature, using the impedance spectroscopy technique, and the magnetic properties were inspected with a Quantum Design MPMS3 superconducting quantum interference device magnetometer.

Dielectric analysis revealed that the sample maintains a stable dielectric constant and low loss tangent across a broad frequency range, indicating its potential for energy storage applications. While other bismuth-based pyrochlores may show superior dielectric properties within the studied temperature and frequency ranges, the relatively low sintering temperature used in this study offers a distinct advantage for various technological applications, particularly in the development of cofired dielectric components.

2. Materials and Methods

2.1. Materials

The starting materials used for the synthesis of Bi_1.34Fe_0.66Nb_1.34O_6.35 were bismuth (III) nitrate pentahydrate, Bi(NO₃)₃·5H₂O (98%, Sigma-Aldrich, St. Louis, MO, USA), iron (III) nitrate nonahydrate, Fe(NO₃)₃·9H₂O (98%, Mateck, Juelich, Germany), niobium (V) chloride, NbCl₅ (99%, Merck, Kenilworth, NJ, USA), citric acid, C₆H₈O₇ (99%, Sigma-Aldrich), ethylene glycol, C₂H₆O₂ (99%, Sigma-Aldrich), and hydrogen peroxide, H₂O₂ (Sigma-Aldrich). Deionized water was self-produced by the ultra-pure water equipment.

2.2. Sol–Gel Process

The studied samples were synthesized by the sol–gel method using the citrate route. Bi(NO₃)₃·5H₂O, NbCl₅, and Fe(NO₃)₃·9H₂O were used as raw materials in the stoichiometric ratio of 0.75:1.00:0.25 and were previously dissolved in a small amount of hydrogen peroxide (3% v/v). Citric acid and ethylene glycol were added as a chelating agent and reaction medium, respectively. To promote solubility and increase viscosity, the suspension was stirred for 168 h. After that, it was dried at 300 °C for 60 h to evaporate the solvent and calcine the organic material present. Finally, the obtained mixture was ground into a fine powder, which was isostatically pressed, at a pressure of 325 GPa, into circular pellets using a hydraulic press and sintered at 500 °C for 4 h at a heating rate of 5 °C/minute in an air atmosphere.

2.3. Characterization Techniques

The structural characterization by X-ray diffraction (XRD) was performed using an Empyrean diffractometer (CuKα radiation, λ = 1.54060 Å) at 45 kV and 40 mA, in a Bragg–Brentano parafocusing optics configuration. The step counting method was applied with a step size of 0.02° and a time per step of 1 s, covering a 2θ angle range of 10–60°.

The transmission electron microscopy (TEM) specimen was prepared by dropcasting a suspension of the ground powder and ethanol onto a holey carbon TEM grid. STEM characterization was performed using a probe-side aberration-corrected FEI Titan Themis S/TEM with a 200 kV, 150 pA electron beam. Both bright field and high-angle annular dark field (HAADF) detectors were used to identify the particles as crystalline and to characterize their morphology and size. Energy dispersive X-ray (EDX) spectrum imaging was acquired in parallel. The relative intensities of the bismuth, iron, niobium, and oxygen characteristic edges were used to map the distribution of these elements across the particles.

The morphology of the sintered sample surface was analyzed by the scanning electron microscopy (SEM) technique using TESCAN-Vega III equipment with an accelerating beam voltage of 25 kV. To enhance the conductivity of the sample, a carbon deposition was applied on its surface.

For the electrical characterization, silver conducting paste was applied to the opposite sides of the pellets. Measurements were performed in a helium atmosphere, to eliminate moisture and improve heat transfer, in the frequency range of 100 Hz to 1 MHz, using a precision impedance analyzer (Agilent 4294A, Agilent, Santa Clara, CA, USA) in the Cp-Rp configuration, with the temperature varying between 200 and 330 K.

The real (ε′) and imaginary (ε″) parts of permittivity and the loss tangent, tan δ were calculated using the following relations [14]:

$${\epsilon }^{\prime }={\displaystyle \frac{d}{A}}{\displaystyle \frac{C_p}{{\epsilon }_0}}$$

(1)

$${\epsilon }^{″}={\displaystyle \frac{d}{A}}{\displaystyle \frac{1}{\omega {R_p\epsilon }_0}}$$

(2)

$$\tan \delta ={\displaystyle \frac{{\epsilon }^{″}}{{\epsilon }^{\prime }}}$$

(3)

where C_p and R_p are the measured capacitance and resistance, respectively, ω is the angular frequency, d is the sample thickness, A is the electrode area, and ε₀ is the vacuum permittivity (8.8542 × 10⁻¹² F/m).

The magnetic properties were inspected with a Quantum Design MPMS3 superconducting quantum interference device (SQUID) magnetometer. Field dependent magnetization curves were measured at 5, 300 and 380 K with applied fields ranging from −70 to 70 kOe. To correct sample geometry and offset effects we used the “geometry-independent moment correction” (GIMC) method described in [15].

Temperature dependent magnetic measurements were performed using field cooled (FC) methodologies, during sample heating from 5 to 380 K, applying a 1000 Oe magnetic field.

3. Results

3.1. Stuctural Characterization

Figure 1 shows the XRD patterns of the as-synthesized sample, as well as the stick patterns for the standard reference ICDD 00-052-1774 [16]. All the diffraction peaks are indexed and in agreement with those of pure cubic Bi_1.34Fe_0.66Nb_1.34O_6.35. From the diffraction peaks of the Bi_1.34Fe_0.66Nb_1.34O_6.35 sample, and using the software PROFEX (version 5.0.1) [17], the cell parameters and the crystallite size were estimated, with a goodness of fit of 2.10, and are presented in

Table 1. Cell parameters and crystallite size.

		Sample	Reference [16]	Reference [18]
Cell parameters	a = b = c (Å) V (Å3) α = β = γ	10.509 1160.6 90.0°	10.4998 1157.56 90.0°	10.494 1155.65 90.0°
Crystallite size	D (nm)	42.4413	__________	__________

. These results are well aligned with the reference data, also depicted in the same table.

Figure 2a shows a high-angle annular dark field (HAADF) image of the sample, with Figure 2b corresponding to the enlarged section highlighted in green. Figure 2c–f presents the STEM-EDX mapping analysis of the same enlarged region, revealing the homogeneous distribution of Bi, Fe, Nb, and O elements on the surface of the particles. All the mentioned elements appear to be co-located throughout the particles, indicating that they are part of a common compound. Furthermore, no impurities were detected.

These findings align well with the results obtained from the XRD analysis that was conducted earlier, demonstrating a high degree of consistency between the elemental distribution observed in the STEM-EDX mapping and the crystalline structure identified through XRD.

The elemental ratio of Bi:Fe:Nb:O was determined by analyzing the section highlighted in yellow in the HAADF image depicted in Figure 2a. Quantitative analysis using the Cliff–Lorimer method on EDX peak intensities yielded the ratio 2.1:1.0:2.8:12.6.

This observed ratio shows some discrepancy, particularly in the case of the Nb and O elements, when compared to the stoichiometric ratio expected from the crystalline structure identified by XRD analysis, which is 2.0:1.0:2.0:9.6. This difference can be attributed to the overlap of peaks from lighter and heavier elements, such as Nb/Bi and O/Fe, which can lead to an overestimation of the atomic concentration of the lighter elements [19,20].

STEM analysis was used to further examine the crystallite size. Figure 3 displays the STEM bright field micrographs of the powders, while the crystallite size distribution is shown in Figure 4.

The crystallite size was measured using ImageJ (Version 1.54g) software. Three different particle size measurements were taken from each one along the long, medium, and short axes, and the average particle size was calculated based on these three measurements.

The average crystallite size obtained was 41.02 nm, which once again shows good agreement with the results previously obtained from the XRD measurements.

3.2. Morphological Characterization

The surface morphology of the sintered sample was analyzed by scanning electron microscopy. The micrography (Figure 5a) shows visible porosity and a non-homogeneously grain distribution, exhibiting a spherical habit and also with some agglomeration, which is in accordance with the reported in literature [18]. The porosity of the sample can be attributed to the heat treatment temperature, which may not have been sufficient to produce a fully densified sample. Nevertheless, as reported by [18] the pure phase of Bi_1.34Fe_0.66Nb_1.34O_6.35 is obtained at 600 °C, while Bi_1.33Fe_0.052Nb_1.24Fe_1.04O_7-δ is formed at 650 °C, meaning that the heat promotes the accommodation of the additional iron ions into the lattice.

ImageJ (Version 1.54g) software was used to determine the grain size distribution (Figure 5b), achieving a grain size average of (313 ± 43) nm.

3.3. Electrical Characterization

Through dielectric spectroscopic studies, it is possible to access information about the structure, grain, grain boundary, transport properties, and charge storage capabilities of a dielectric material [21,22].

The dielectric permittivity is represented by ε = ε′ − jε″, where the first term, the real part or dielectric constant, describes the stored energy, and the second term, the imaginary part or dielectric loss, describes the dissipated energy [23].

The dielectric properties are strongly dependent on several factors, including chemical composition, preparation method, etc. [21,24].

Figure 6a shows the variation of the dielectric constant as a function of frequency and temperature for the sintered sample. It can be seen that ε′ initially decreases more sharply in the low-frequency region; however, at high frequencies, this decrease becomes smoother, approaching a frequency-independent behavior.

The dielectric dispersion curve can be understood based on the Maxwell–Wagner model for the homogeneous double structure, in agreement with Koop’s phenomenological theory. According to this model, the dielectric structure is composed of a well-conducting layer of grains followed by a poorly-conducting layer of grain boundaries, with the grain boundaries being more effective at lower frequencies, and the grains at higher frequencies [23,24].

The high value of the dielectric constant comes from the space charge polarization produced at the grain boundary. The polarization mechanism involves the exchange of electrons between ions of the same element, which are present in more than one valence state and are distributed randomly over crystallographically equivalent lattice sites. During this exchange mechanism, the electrons have to pass through the grains and grain boundaries of the dielectric medium. For instance, in the low-frequency region, the high resistance of the grain boundary causes electrons to accumulate there and produce space charge polarization. Hence, due to the grain boundary effect, the dielectric constant decreases rapidly. On the other hand, at high frequencies, the grains come into action, and the hopping of electrons cannot follow the high-frequency AC field, thus resulting in a decrease of polarization. Any species contributing to polarizability is found to lag behind the applied field at higher frequencies. Consequently, the dielectric constant decreases, as does its frequency dependence [23,24,25,26].

It is also observable that, for the same frequency, the dielectric constant increases with the rise in temperature. With increasing temperature, electron hopping is activated due to lattice vibrations, which leads to an increase in ε′. The number of charge carriers starts to increase with rising temperature and accumulates at grain boundaries, enhancing both interfacial and space-charge polarization. Consequently, we obtain a larger value of ε′ at higher temperatures [27].

The frequency dependence of the dielectric loss is depicted in Figure 6b. The higher value of ε″ at lower frequencies may be due to contributions from both conduction and relaxation. As the frequency increases, conduction losses start to decrease. Therefore, the lower value of ε″ at higher frequencies is mainly due to relaxation losses [27].

At higher frequencies, particularly at higher temperatures, a noticeable inflection can be seen, as illustrated in the inset, suggesting the presence of a relaxation phenomenon.

Figure 6c shows the frequency dependence of tan δ, indicating that, in the frequency and temperature range studied, the loss tangent values are less than one. This means that the dielectric loss is lower than the dielectric constant. Consequently, the energy dissipated is less than the stored energy, demonstrating the material’s potential for energy storage applications.

At 1 MHz and room temperature, the calculated dielectric constant and loss tangent are 65 and 0.27, respectively. The loss tangent can also be used to characterize the dielectric loss of a material, since it behaves like the imaginary part of the permittivity [28]. In Figure 6c, the peaks observed, which occur when the jumping frequency of the localized electric charge carrier is approximately equal to that of the externally applied AC electric field [23], confirm the existence of a relaxation mechanism.

The peak position, as the inflection position in the dielectric loss plot, moves to higher frequencies with the temperature increase, indicating the presence of an activation process in the relaxation mechanism [29].

The peak location can be represented by the relaxation time, which is defined as the inverse angular frequency at the maximum of the curve. For instance, τ_ε″ denotes the relaxation time at which ε″ reaches its maximum. Similarly, τ_{tan δ} can be defined. Thus, these two relaxation times can be considered, since they describe the same relaxation process from different perspectives [28].

In the loss tangent representation, the relaxation time can be calculated from the frequency of the peak, which can be directly extracted from the graphical representation, given that the peaks are well-defined. For the dielectric loss representation, the data were fitted using software developed in MATLAB (version R2014a), part of which is presented in Ref. [30].

Since the aforementioned relaxation process is thermally activated, the activation energy, Ea, can be calculated from the values of the maximum frequencies, f_max, in each curve as a function of temperature by fitting the experimental data to an Arrhenius equation [31,32]:

$$f_{max}=f_0{e}^{-{\displaystyle \frac{E_a}{k_{B}T}}}$$

(4)

where f_max is the peak frequency at temperature T, f₀ is a pre-exponential factor and k_B is the Boltzmann constant.

The logarithmic representation of the maximum frequency versus the inverse temperature allows the calculation of the activation energy [30].

Figure 7a presents the logarithm of the relaxation frequency versus the inverse temperature along with the activation energy values. As expected, the activation energy values are very similar, since they describe the same relaxation mechanism.

Figure 7b shows the relaxation time of each representation at corresponding temperatures, showing that, as stated by [28], τ_ε″ > τ_{tan δ}.

3.4. Magnetic Properties

Figure 8 shows the temperature dependent magnetic properties of a Bi_1.34Fe_0.66Nb_1.34O_6.35 powder sample, presented in the form of the linear magnetic susceptibility defined by Equation (5):

$$\chi \left(T\right)={\displaystyle \frac{M\left(T\right)}{H}}$$

(5)

where M(T) is the magnetization as a function of temperature and H is the applied magnetic field.

It is possible to see that the sample exhibits a profile consistent with a paramagnetic Curie-like curve, although it is vertically shifted. This shift suggests the presence of an additional high-Curie temperature phase, which exhibits minimal variation within this temperature range, resulting in a vertical shift. This spurious phase is likely a vestigial iron oxide, detectable only in the magnetization curves. Since the sample remains mostly paramagnetic at most temperatures, even a minimal contribution from a magnetically ordered phase stands out against the near-zero magnetization of the paramagnetic phase. To test this hypothesis, we fitted the magnetic susceptibility curve from Figure 7 to the following mean field-based expression [33,34,35]:

$$\chi \left(T\right)={\displaystyle \frac{C}{T-{\Theta }_p}}+M_0{\left[1-\mathrm{s}{\tau }^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}-(1-s){\tau }^{{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\right]}^{\beta }$$

(6)

The first term of Equation (6) fits the paramagnetic contribution to the magnetic susceptibility curve using the Curie–Weiss law, where $C$ represents the Curie constant and ${\Theta }_p$ is the critical temperature. The second term models the vestigial iron oxide contribution through a polynomial function, as proposed by Kuz’min et al. [35,36]. In this model, $M_0$ serves as a scaling factor for magnetization, $\tau ={\displaystyle \raisebox{1ex}{$T$}\!\left/ \!\raisebox{-1ex}{$T_C$}\right.}$, $T_C$ is the Curie temperature of the ferrimagnetic iron oxide, $\beta$ is the critical exponent, here set to $\beta =0.369$, corresponding to the 3D Heisenberg model, and $s$ is a dimensionless parameter that defines the curve’s shape and is constrained within the range $0<\mathrm{s}<5/2$. The results of the mean field fit are presented in

Table 2. Fitted parameters of Equation (6) for the linear magnetic susceptibility and specific magnetization.

Fit Parameter	$\mathit{\chi }\left(\mathit{T}\right)$$\mathit{fit} \left(\frac{\mathit{e}\mathit{m}\mathit{u}}{\mathit{g}.\mathit{O}\mathit{e}}\right)$	$\mathit{M}\left(\mathit{T}\right)$$\mathit{fit} \left(\frac{\mathit{e}\mathit{m}\mathit{u}}{\mathit{g}}\right)$
$C$	$\left(1.303\pm 0.008\right)\times {10}^{-3} {\displaystyle \frac{emu . T}{g .Oe}}$	$\left(1.303\pm 0.008\right) {\displaystyle \frac{emu . T}{g}}$
${\Theta }_p$	$\left(-8.8\pm 0.1\right) \mathrm{K}$
$M_0$	$\left(3.72\pm 0.09\right)\times {10}^{-6} {\displaystyle \frac{emu}{g.Oe}}$	$\left(3.72\pm 0.09\right)\times {10}^{-3} {\displaystyle \frac{emu}{g}}$
$T_C$	$\left(610\pm 19\right) \mathrm{K}$
s	$2.5\pm 0.1$
$\beta$	$0.369$
$R^2$	$0.99902$

.

From the results presented in Table 2, we observe that the obtained $T_C$ for the vestigial iron oxide is 610 ± 19 K. This does not match the $T_C$ of bulk magnetite (Fe₃O₄) or maghemite (γ-Fe₂O₃), which are $T_C\approx 858$ and $950 \mathrm{K}$, respectively, and are the simpler and the most likely spurious ferrimagnetic iron oxide secondary phases [37,38,39,40]. However, recent studies report that the $T_C$ of magnetite and maghemite can vary significantly with particle size, dropping to as low as $T_C\approx 600$ and $545 \mathrm{K}$ for nanoparticles of 10 nm and 5 nm, respectively [41,42]. These reported values agree well with the $T_C$ obtained in our fit, thereby supporting our findings. In fact, assuming the spurious magnetic phase corresponds to maghemite (the ferrimagnetic phase with lower saturation, which would result in the largest detected amount), we can estimate its weight percentage. Using maghemite’s saturation magnetization ($M_s\approx 80 \mathrm{e}\mathrm{m}\mathrm{u}/\mathrm{g}$) and knowing that 1000 Oe is relatively close to saturation conditions (conservatively assuming that it reaches ${\displaystyle \frac{1}{4}}{\mathrm{M}}_{\mathrm{s}}$) [33,34], this translates to approximately 0.02 wt.%, which is well below the detection limits of XRD or EDS analysis. For these amounts of spurious iron oxides, it can be assumed that they exist as nanoscopic segregations, supporting the hypothesis that our residual iron oxides are magnetite or maghemite spurious phases. Due to their nanoscale dimensions, these phases would exhibit lower Curie temperatures, as reported by Nikiforov et al. [41,42].

The obtained critical temperature, ${\Theta }_p\approx -8.8 \mathrm{K}$, confirms that the sample remains paramagnetic across most of the measurement range, transitioning to an antiferromagnetic state with a Néel temperature of $T_N\approx 8.8 \mathrm{K}$ near the lower measurement limit.

Figure 9 further supports these findings. The field-dependent magnetization curves at 300 K and 380 K exhibit mostly linear behavior with a slight vertical shift due to the vestigial iron oxide contribution, raising the coercive field, $H_{\mathrm{C}}$, from the expected null value to $H_{\mathrm{C}}\approx 9 Oe$. The 5 K curve, below the $T_N$, shows a paramagnetic Brillouin-like curve combined with an asymmetric, left-shifted $H_{\mathrm{C}}$,. This exchange bias-like effect is typical at the interface between antiferromagnetic and ferro/ferrimagnetic materials. In this case, it can be attributed to the interfaces between the antiferromagnetic Bi_1.34Fe_0.66Nb_1.34O_6.35 phase and the ferrimagnetic spurious nanoscopic iron oxide segregations.

4. Conclusions

Bi_1.34Fe_0.66Nb_1.34O_6.35 pyrochlore was successfully prepared by the sol–gel method at a relatively low sintering temperature. Structural characterization revealed a consistent and well-defined cubic crystalline structure, with XRD analysis confirming that the cell parameters are in good agreement with standard reference data, indicating the successful synthesis of the desired phase. STEM-EDX mapping further supported these findings by showing a homogeneous distribution of the constituent chemical elements.

The morphology of the sample is characterized by submicron-sized spherical particles and with visible porosity, which may be attributed to the low sintering temperature.

Dielectric studies demonstrated that the sample possesses a relatively stable dielectric constant and low loss tangent across a wide range of frequencies, making it suitable for potential energy storage applications. Although other bismuth-based pyrochlores may exhibit more favorable dielectric properties within the analyzed frequency and temperature ranges, the low sintering temperature employed in this study could be advantageous for various technological applications, particularly in cofired dielectric components.

Magnetic analysis confirms the high purity of Bi_1.34Fe_0.66Nb_1.34O_6.35, which exhibits paramagnetic behavior over most of the measured range. This near-zero magnetization allowed us to detect a vestigial magnetic phase. Using a mean-field approach, the model fit results indicate a Néel temperature of around 8.8 K for the main phase (which is antiferromagnetic below $T_N$) and ferrimagnetic properties for the vestigial phase, compatible with less than 0.02 wt.% of a ferrimagnetic iron oxide with a $T_C\approx 610 \mathrm{K}$.

Although dielectric properties are highly sensitive to chemical composition, the presence of 0.02 wt.% maghemite and/or magnetite has a negligible influence on the dielectric behavior of Bi_1.34Fe_0.66Nb_1.34O_6.35.