Tailoring the functional properties of BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites via ceramic route for advanced electronic and energy applications

The increasing global demand and transition to sustainable energy technologies solutions has accelerated the development for novel functional materials that combine high energy storage efficiency, environmental compatibility, and high-frequency electronics applications. In this regard, ferrites particularly barium-based hexaferrites, have well-suited as highly promising candidates for these applications duo to their unique combination of magnetic and dielectric properties, thermal and chemical stability, and resistance to corrosion. These characteristics render them highly suitable highly suitable employed in a wide range of advanced applications, such as magnetic data storage, microwave devices, high-frequency transformers, electromagnetic interference shielding, high-performance electronic components [1,2,3,– 4]. Within the class of ferrites, W-type barium hexaferrites are distinguished by their high magnetocrystalline anisotropy and favorable dielectric behavior, making them especially attractive for electronic and energy applications. Their physical and functional characteristics can be further finely tuned through ionic substitution, particularly by introducing suitable dopants, which directly influences their microstructure and physical performance. The substitution of divalent ions such as zinc (Zn²⁺) has garnered special attention due to its ability to enhance AC conductivity and dielectric properties by promoting charge carrier mobility and reducing hopping barriers between Fe²⁺ and Fe³⁺ ions [5,6,– 7]. Zn²⁺ incorporation has shown potential for reducing dielectric losses, improving AC conductivity thereby improving the energy efficiency and performance of ferrites in capacitive and high-frequency applications [8, 9]. This enhancement positions these materials as viable candidates for clean energy storage systems and sustainable electronic technologies.

Extensive studies have examined the impact of various divalent and trivalent ion substitutions in ferrite systems. Zn²⁺ doping, in particular, has been shown to enhance dielectric constant, increase grain size, improve optical properties, and improve AC conductivity by reducing grain boundary resistance [10,11,12, – 13]. Many studies focus exclusively on either structural or optical properties, with limited emphasis on the simultaneous analysis of dielectric and electrical performance [14,15, – 16]. Furthermore, the role of Zn²⁺ in BaNi₂Fe₁₆O₂₇ ferrites across a wide compositional range has not been extensively investigated. The impact of traditional synthesis methods, such as the ceramic route, on phase stability and microstructural control has also been underexplored.

Recent developments in the field have introduced novel dopants and synthesis strategies that expand the functional range of ferrites. For instance, studies investigated the structure-property relationships in Zn-substituted CoFe₂O₄, linking ionic radius variations with shifts in AC conductivity and polarization mechanisms [17].further explored how cationic redistribution across tetrahedral and octahedral sites directly affects electrical hopping mechanisms, reinforcing the role of ion location in tuning performance metrics [18]. Similarly, advancements in synthesis techniques, including sol-gel methods, derived nanocomposites to enhance the dielectric constant of ferrites for capacitor applications [19]. Additionally, recent work highlights the significance of crystallite size, grain boundary structure, and site occupancy in dictating dielectric and magnetic responses [20,21,22,23, – 24]. also Zn²⁺ tends to occupy tetrahedral sites, attributed to its ionic radius and site preference theory, which plays a critical role in enhancing electrical characteristics while preserving magnetic integrity [25, 26].

Despite these insights, the understanding of Zn²⁺ effects across a broad compositional range (0 ≤ x ≤ 2.0) in BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites remains insufficient.

This study aims to address these gaps by investigating the effect of Zn²⁺ incorporation (0 ≤ x ≤ 2.0) on the structural, dielectric, and AC conductivity properties of BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites synthesized via the conventional ceramic method. Characterization techniques such as X-ray diffraction (XRD), dielectric measurements, and AC conductivity analysis are employed to evaluate composition-microstructure-property relationships. Special emphasis is placed on optimizing Zn²⁺ content for improved dielectric performance and reduced energy losses.

By providing a comprehensive understanding of Zn²⁺ substitution in W-type ferrites and validating the effectiveness of a scalable synthesis method, this research contributes to the advancement of ferrite-based materials for use in capacitors, high-frequency transformers, and clean energy storage devices. The findings demonstrate that controlled Zn²⁺ doping can significantly enhance material performance, making these ferrites viable for next-generation energy and electronic technologies.

Characterization is performed using X-ray diffraction (XRD), dielectric spectroscopy, and impedance analysis to elucidate the phase composition, grain morphology, and frequency-dependent electrical behavior. The results demonstrate that controlled Zn²⁺ substitution markedly improves the performance of W-type ferrites, making them excellent candidates for integration into capacitors, RF devices, and energy storage systems. Moreover, the use of a scalable, cost-effective ceramic route underlines the industrial relevance of this work, enabling the design of next-generation ferrite materials for sustainable electronic and power technologies.

The samples in the present study were prepared using a well-established ceramic technique. In this context, high-purity barium carbonate (BaCO₃ purity 99%,), zinc oxide (ZnO purity 99%,), nickel oxide (NiO purity 99.9%,), and ferric oxide (Fe₂O₃ purity 99%,) from Aldrich Chemical Company Inc., were mixed in an appropriate proportion by considering molecular weight ratios for different compositions as listed in Table 1. This is how the desired compound was formed using the following chemical reaction:

BaCO₃+(2 − x) NiO + xZnO + 8Fe₂O₃→BaNi(2-x) ZnxFe₁₆O₂₇+CO₂↑.

Each sample had to be first ground manually by an agate mortar two hours in total; then, each sample underwent an additional four-hour grinding in a Mechanical Grinder. The resulting mixture was then pre-sintered in air at 950 °C ± 5 °C for six hours and subsequently allowed to cool gradually to room temperature. Afterwards, samples were reground for five hours until a finer powder was obtained. The corresponding powder was then compacted into disc-shaped pellets (1.4 cm diameter and 0.3–0.6 cm thick) at a pressure of 10 tons/cm² for electrical property measurements. First, the disks were sintered at 1100 °C ± 5 °C for four hours, followed by furnace cooling to room temperature. To ensure proper electrical contact, the disk surfaces were polished to achieve smoothness, after which a thin coating of silver paste was applied.

The XRD analysis of the ferrites prepared in the present work has been done in order to determine the structure of the crystalline phase and phase purity by using a Shimadzu EDX-720. The used radiation was Cu Kα, with λ = 1.54018 Å. The instrument was set to 40 kV and 20 mA, while the diffraction patterns within the 2θ angular range between 5° and 75° were recorded, in steps of 0.04°, scanning speed 0.02°/sec. Samples were then mounted in an aluminum sample holder, 35 × 50 mm², sample size 20 × 18 mm². The AC electrical and dielectric properties were characterized across a temperature range from room temperature to 500 °C and within a frequency span of 1 Hz to 10⁵ Hz, employing the complex impedance technique with a Lock-in amplifier (Stanford SR 510, USA) and the two-probe measurement method. Disk-shaped pellets were prepared with a diameter of 1 cm and 0.2–0.3 cm thick. Silver paste was applied to ensure proper electrical contact for the measurement. Inductance measurements were performed at selected frequency across a temperature range extending from room temperature to 500 °C.

The XRD pattern of the BaNi_₂₋ₓZnₓFe₁₆O₂₇ nanoparticles corresponding to x = 0, 0.4, 0.8, 1.2, 1.6, 2.0 are shown in Fig. 1, which confirm that all the diffraction peaks are indexed and matched with the standard JCPDS#54–0097, confirming the formation of single-phase W-type hexaferrite structure [14]. No extra peaks were detected that may indicate the substitution of Zn²⁺ for Ni²⁺ ions. The diffraction peaks of hexaferrite appear at 2θ values of 30.22°, 31.88°, 32.29°, 34.45°, 35.50°, 36.90°, 55.21°, and 57.59°, representing the crystallographic planes at (110, 112, 1010, 116, 202, 204, 2110, 2016, and 220). Thus, it confirms that the synthesized materials had a hexagonal geometry with space group P63/mmc (194). The replacement of Ni²⁺ ions with Zn²⁺ ions led to a noticeable shift of the diffraction peaks toward lower angles, a result that was further supported by the increase of lattices parameters. 2. The observed behavior can be linked to the relatively greater ionic radius of Zn²⁺ in comparison with Ni²⁺ [16].

XRD, pattern of BaNi_2−xZn_xFe₁₆O₂₇ ferrite samples with varying Zn²⁺ concentrations (x = 0.0, 0.4, 0.8, 1.2, 1.6, and 2) with the standard JCPD card No. 00-54-0097

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The lattice parameters a and c were calculated by applying a crystallographic formula (Eq. 1) that correlates the interplanar distance (d) with the Miller indices (h, k, l) [15].

This equation helps determine the structural dimensions of the unit cell. As the concentration of Zn increased, a noticeable rise in both a and c was observed, attributed to the larger ionic radius of Zn²⁺, which promotes lattice expansion. This structural change was evidenced by a systematic shift in XRD peaks toward lower 2θ angles. Additionally, the unit cell volume exhibited a linear increase with higher Zn content doping, consistent with the incorporation of Zn²⁺ into the crystal lattice, as computed using Eq. (2). These results are summarized in Table 2. The observed c/a ratio ranging between 5.33 and 5.55, confirms the stability of the hexagonal W-type ferrite phase [27]. Further structural and physical parameters including bulk density, X-ray density ρ_x, ρ_m, porosity percent %P, and specific surface area (S) were calculated using Eqs. (3–6) in accordance with previously established methods respectively [27].

Increasing the Zn concentration reduced X-ray density and porosity, due to the higher molecular mass of doped Zn with respect to Ni. With this decrease in X-ray density comes its inverse relation with increasing cell volume. On the other hand, bulk density increased for higher Zn contents due to high density of Zn (8.96 g/cm³) with respect to Ni (8.9 g/cm³). A further contribution to this variation must be ascribed to the different specific gravities of NiO and ZnO, namely 6.72 g/cm³ and 5.60 g/cm³, respectively, which contribute to a decrease in porosity and an improvement in the magnetic properties of the material. The crystallite size average was calculated using the Scherrer equation, Eq. 6, that provided values within the range from 35 to 37 nm, confirming the samples as monocrystalline. An anomaly was, however, observed at x = 0.4, where crystallite size slightly reduced to 35.18 nm before increasing gradually to 36.7 nm at x = 2. This confirms that in-deed Ni acts as a crystallite inhibitor, as reported by literature [14]. Increased crystallite dimensions reduce grain boundary density, and therefore, grain boundary pinning of magnetic walls, and in consequence, coercivity and improving µ_i. It also promotes easier motion of charge carriers, with reduced dielectric loss and increased AC conductance [28]. Ferrimagnetic materials with crystallite size < 50 nm have been known to reduce signal-to-noise ratios in applications such as high-density recording and microwaves [29, 30]; thus, the prepared samples could be auspicious candidates for microwave technology.

Generally, all results are in consistent with standard powder diffraction data of (PDF#54–0097) for Barium Nickel Iron Oxide Ba Ni₂ Fe₁₆ O₂₇, and (JCPDS,54-1868) for Barium Zinc Iron Oxide Ba Zn₂ Fe₁₆ O₂₇.

To determine the cation distribution in BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites, X-ray diffraction (XRD) data were analyzed by comparing intensity ratios from the experimental and theoretical patterns. The analysis was conducted using the Bertaut method [31], which estimates cation occupancy by evaluating the relative intensities of specific reflections. This technique involves the proportionality of the observed and calculated intensity ratios for two reflections, as expressed by:

Here, I^Obs and I^Calc denote the observed and calculated intensities for the given (hkl) planes, respectively.

Table 3. presents the refined cation distributions and corresponding inversion degrees (δ) for all synthesized BaNi₂₋ₓZnₓFe₁₆O₂₇ samples. It is well established that Zn²⁺ ions preferentially occupy the A (tetrahedral) sites replacing Fe³⁺, which migrates to octahedral. The site occupancy refinement further confirmed that Ni²⁺ ions favor the B (octahedral) sites, and Fe³⁺ ions can occupy both sites depending on local charge balance and ionic radii. As the Zn content increases, a corresponding substitution of Ni ions occurs [17, 18]. This results in the migration of Fe²⁺ ions from tetrahedral to octahedral positions, thereby increasing the population of Fe ions at the B sites. The cation distribution analysis showed that Zn²⁺ preferentially occupies the tetrahedral sites, replacing Fe³⁺, which migrates to octahedral sites. The substitution of Zn²⁺ alters the balance of A (tetrahedral) and B (octahedral) site interactions, leading to a weakening of the superexchange interactions between Fe³⁺(A)–O–Fe³⁺(B), which is reflected in the observed decrease in the Curie temperature and the enhancement in dielectric performance.

This redistribution of cations is reflected in the observed increase in the degree of inversion (δ), which quantifies the ratio of Fe ions occupying tetrahedral versus octahedral positions. The rising δ values with Zn doping suggest an increasing structural distortion and modification of magnetic exchange interactions, which may influence the material’s overall magnetic and dielectric behavior.

The variation in σ_ac conductivity of prepared samples ferrites was evaluated at different selected frequency and temperatures, as shown in Fig. 2(a–f). At all compositions and temperatures, σ_ac exhibits a typical dispersion pattern distinguished by independent behaviour at lower frequencies, after that gradually increase in conductivity with increasing frequency. This behavior aligns with that of disordered semiconductors and is consistent with previous findings in ferrite systems [30]. At low frequencies, AC conductivity remains nearly constant due to the dominant influence of grain boundaries, which act as insulating barriers and hinder charge transport. As the frequency of the applied alternating field increases, the capacitive reactance of the grain boundaries diminishes, allowing charge carriers to respond more rapidly to the alternating electric field. This transition results in enhanced hopping between localized Fe³⁺ and Fe²⁺ states at octahedral sites, contributing to the observed increase in AC conductivity [4]. This behavior of conductivity variation with respect to frequency is very similar to the corresponding reported systems already published in the literature. Zn²⁺ has an electronegativity of 1.66, closer to that of Ni²⁺, which is 1.91, while Fe³⁺ holds an electronegativity of 1.83 and Ba²⁺ is way lower at 0.89. This structure allows electrons to flow, thus with an increase in Zn doping, there is a rise in charge carrier density, polarizability of the material, dielectric constant, and conductivity [24]. This behavior is characteristic of semiconductors and is particularly useful in applications such as microwave-absorbing composites and electronic components designed for efficient microwave conduction with minimal power loss. These findings are consistent with previously published works on hexaferrites for similar applications [27]. The frequency-dependent behavior is effectively interpreted through the Maxwell–Wagner polarization mechanism, with enhanced charge transport resulting from the reduced electron hopping between Fe³⁺ and Fe²⁺ ions. The introduction of Zn²⁺ ions diminished the electron hopping activity between Fe³⁺ and Fe²⁺ cations, leading to decreased dielectric loss and improved AC conductivity. This enhancement in conductivity is critical for energy storage applications, as it enables more efficient charging and discharging processes, thus making these materials highly suitable for use in high-frequency devices such as oscillators and power amplifiers [32]. At high frequencies, conduction is dominated by the grains, while at low frequencies, the grain boundaries exert greater control over carrier movement. To further understand the conduction mechanism, The AC conductivity data were analyzed using Jonscher’s universal power law, expressed as :

Here, ‘A’ are the temperature-dependent functions, ‘ω’ is the angular frequency, and ‘s’ corresponds to the frequency exponent (0 < s < 1), indicative of the charge transport dynamics. the frequency exponent (s) was derived linear fitting of log(σ_ac) vs. log(f) Fig. 2(a–f) within the frequency range where Jonscher’s law holds. As shown in Fig. 3(a–f), and Table 4. the exponent s increases with temperature for all compositions, suggesting a thermally activated transport mechanism, which describes the peculiarity of amorphous semiconductors [33].

(a-f), The variation in σ_ac conductivity versus logarithm frequency and temperatures for BaNi_2-xZn_xFe₁₆O₂₇ (at selected concentration as; x = 0.00, 0.40, 0.80, 1.20, 1.60, and 2.00)

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Figure 3, illustrates how the frequency exponent (s) varies with temperature and its implication for conductivity in these materials. All samples show an increase in ‘s’ values with rising in temperature supports the Small Polaron Hopping (SPH) model [34], where charge transport occurs via thermally assisted hopping of localized polaron between adjacent Fe²⁺ and Fe³⁺ ions. The increase in s with temperature reflects the enhanced mobility of charge carriers and the increasing contribution of localized hopping to AC conductivity [34]. This Synergy between these two theories would suggest that optimization of a ferrite-based material could be carried out for better performance of the current devices and possibly even extended toward new applications.

Additionally, these materials, hold promise for application for energy storage and conversion in variable environmental conditions. The enhancement in conductivity with higher Zn²⁺ content is associated with both conduction and ion exchange mechanisms. Additionally, this improvement has been linked to these mechanisms as reported by [35]. Moreover, the combination of small crystallite size and large surface area, along with the favorable dielectric properties has rendered BaNi₂₋ₓZnₓFe₁₆O₂₇ nanoparticles (x = 0.0, 0.4, 0.8, 1.2, 1.6, and 2.0) highly suitable as electrode materials for flexible supercapacitors applications. The crystallite size, ranging between 35 and 37 nm, and the expanded surface area facilitate rapid ion diffusion and minimize scattering at grain boundaries. Typically, larger crystallite sizes generally contribute to lower grain boundary density, thereby reducing charge scattering and improving electrical conductivity. Moreover, the electronegativity values of the constituent ions (Zn²⁺: 1.66, Ni²⁺: 1.91, Fe³⁺: 1.83, Ba²⁺: 0.89) indicate that Zn²⁺ substitution causes moderate lattice distortion and increases charge carrier concentration. This, in turn, enhances polarizability, dielectric constant, and electrical conductivity [27]. Furthermore, the observed enhances in conductivity with Zn²⁺ content is linked to both increased carrier concentration and the improvement of ion exchange pathways [38]. These combined attributes, alongside the superior dielectric performance, position Zn²⁺-doped BaNi₂Fe₁₆O₂₇ as a suitable candidate for use in flexible supercapacitors electrodes and energy storage applications. Similar effects of crystallite size on conductivity and supercapacitors performance has been similarly reported in literature [36, 37]. In the future, these materials could potentially be integrated with an energy harvesting system like solar cells, to create multifunctional devices capable of both energy generation and storage. The standard errors associated with the Jonscher’s power-law fitting parameters (A and s) offer valuable insight into the quality and consistency of the model fitting across varying temperatures and doping concentrations. As observed in Table 4, the standard error in parameter A (logarithmic pre-exponential factor) decreases steadily with increasing temperature for all compositions, indicating improved confidence in the estimation of A at elevated thermal conditions.

Similarly, the standard error in the s-exponent is generally higher at lower temperatures, especially in undoped or lightly doped samples. As temperature increases, these standard errors systematically decline, suggesting that the conduction mechanism becomes more thermally activated and predictable. The observed reduction in standard errors with temperature and doping concentration supports the reliability of the fitted parameters and validates the applicability of Jonscher’s universal law in describing AC conduction in BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites. The high adjusted R-square values (> 0.85–0.99) across all samples further confirm the robustness of the fitting procedure.

(a-f), Variation of Jonscher’s power law for pre-exponential factor A, and frequency exponent s, parameters versus temperature for BaNi_2−xZn_xFe₁₆O₂₇ compositions

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Figure 4(a-f), and Table 3 illustrate the frequency-dependent behavior of the real part dielectric constant (ε′) acrosse variious temperatures. The measurements were done on the BaNi_₂-xZnₓFe₁₆O₂₇ system for the entire composition samples (x = 0.0 to 2.0), in the temperature range from 300 K to 350 K and in the frequency range from 1 Hz to 10⁵ Hz.

Generally, the trend represented is that, ε′ is relatively high at lower temperatures and frequencies but decreases with increasing temperature or frequency. An exception is noted in the x = 0 sample, which exhibits high-temperature dielectric behavior different from the usual ferrites, with abnormal variations behavior in the dielectric constant against frequency, marked by the appearance of dielectric relaxation peaks. As zinc substitution increase, these relaxation peaks shift toward lower temperatures, indicating an interrelation between composition and thermal response.

Additionally, the peaks shift towered higher frequencies with raising temperature, suggesting thermally activated charge carrier dynamics—a characteristic behavior commonly reported in ferrite materials, which is ascribed to the enhanced hopping of charge carriers between Fe²⁺ and Fe³⁺ ions at the octahedral sites [4, 25]. The shift of the relaxation peak to higher frequencies with temperature increase is attributed to enhanced charge carrier hopping between Fe²⁺ and Fe³⁺ ions at octahedral sites.

This trend follows well-documented behavior in ferrites, where increasing temperature facilitates electron exchange between Fe²⁺ and Fe³⁺, thereby increasing polarization and dielectric constant values. However, beyond a peak value, hole transfer mechanisms become dominant, reducing polarization and leading to a decline in ε′. This suggests that dipole relaxation effects, influenced by structural modifications due to Zn substitution, play a crucial role in governing dielectric properties. Interestingly, the relaxation peak shift was independent of zinc concentration beyond x = 0.4, suggesting that beyond a certain substitution level, charge carrier localization effects dominate. However, in the present work, the relaxation peak shift was independent of zinc concentration or magnetization and directly proportional to sample temperature. The inset shows the shifting of the maximum dielectric constant, ε′ max, to the lower frequency side, qualitatively following the behavior of charge carriers of the material. This behavior can be interpreted based on the assumption that the mechanism of dielectric polarization analogous to that of electrical conduction. As temperature increased, electron exchange between Fe²⁺ and Fe³⁺ ions became more effective, leading to a rise in the dielectric constant. Therefore, with the rises of thermal energy, electron transfers increased and showed the peaks in the dielectric constant. The hole transfer mechanisms dominated beyond this peak value, reducing the polarization capacity of the system, hence falling the value of the dielectric constant. Such a low-temperature trapping of dipoles in ferrites in less favorable orientation usually results in poor dielectric properties. As the temperature increases, the dipoles become mobile and align better along the field, and ε′ increases. This trend follows what has already been observed in other ferrite materials and probably arises from increased orientation and molecular rearrangement with increased thermal energy. In the case of dielectric materials, usually, molecular arrangements are entirely stabilized by static forces between dipoles, and when the temperature is increased, such forces weaken, allowing more dipoles to move into lower energy positions, therefore increasing ε′ [2]. Whereas ε′ basically reflects the capacitive storage capabilities of the material, ε′′ will be dominated by the conduction processes and therefore quantifies the energy losses within the system.

The dielectric properties of hexaferrites also depended on frequency, confirming the electron-hopping model of conduction-that is, the higher dielectric constant at lower frequencies was found with a change in the valence states of Fe³⁺ and Fe²⁺ ions. Substitution of some Ni²⁺ ions by Zn²⁺ ions introduces an extra charge in the ferrite structure that reduces Fe³⁺ to Fe²⁺. The decrease in dielectric constant with frequency confirms the electron-hopping conduction model, where high dielectric constant values at lower frequencies correspond to valence state changes of Fe³⁺ and Fe²⁺ ions. Zn²⁺ substitution introduces additional charges into the ferrite lattice, reducing Fe³⁺ to Fe²⁺ and leading to increased dielectric constant values. However, at higher frequencies, charge carriers are unable to follow the rapidly oscillating electric field, leading to reduced polarization. Overall, this analysis provides valuable insight into the interplay between temperature, composition, and dielectric relaxation in ferrites. Understanding these mechanisms is crucial for optimizing these materials for high-frequency and capacitive applications, in alignment with previous reports [38, 39].

(a-f), Variation of the real permittivity (ε′) of BaNi_2−xZn_xFe₁₆O₂₇ ferrite at different selected frequency and temperatures

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The frequency-dependent behavior of the dielectric loss (ε”) follows a pattern similar to that of the real dielectric constant (ε′), as depicted in Fig. 5. Dielectric loss represents the energy dissipated within the dielectric material, and in ferrite systems, it generally diminishes as the frequency increases. Again, several mechanisms explain this phenomenon at various frequency ranges.

The dielectric loss is relatively high at low frequencies, which can be attributed to ion migration. During this frequency range, ion migration takes the lead in the dielectric response. More resistance at the grain boundary requires more energy for electron exchange between Fe³⁺ and Fe²⁺ ions, thereby resulting in the highest energy dissipation. This phenomenon has been reported to be fairly common in ferrite materials; hence, in view of these facts, the grain boundary effects become responsible for dielectric loss at low frequencies [24]. The dominating mechanisms of dielectric loss change with increased frequency. Energy dissipation is minimal around the moderate frequency due to dominance by ion jumping with less ion migration. Such damping of dielectric loss is considered linked to improved polarization activated by dipole moments. Research work by Islam et al. evidence that dielectric loss is at a minimum when ion jumping is in dominance without much ion migration [40].

In ferrite systems, the dielectric loss typically decreases with increasing frequency. At low frequencies, the dominant mechanism is ion migration, wherein charge carriers traverse long distances across grains or boundaries, leading to significant energy dissipation. However, as frequency increases, the time available for long-range ion movement decreases. In this regime, localized ion hopping (or ion jumping) between adjacent Fe²⁺ and Fe³⁺ sites becomes dominant. This process, while still contributing to polarization, involves less energy loss compared to migration. Consequently, the dielectric loss diminishes, consistent with earlier reports on ferrites [24, 40]. This frequency-driven shift from migration to hopping results in improved dipolar response and lower tanδ values.

At higher frequencies, the dielectric loss is dominated by ion vibrations, and hence, a further decrease in ε” is observed. In this regards, it agrees with the Jonscher’s universal dielectric response, which expects lower dielectric loss at high frequency. Similar to many other ferrites, BaNi_₂₋ₓZnₓFe₁₆O₂₇ ferrite also exhibits lower energy dissipation at high frequencies due to enhanced resistivity across the grain. As the applied frequency increases, the energy that promotes electron exchange between Fe³⁺ and Fe²⁺ ions decreases, and hence, the energy loss is minimized [18].

These results are in agreement with the conventional mechanisms in ferrite materials: grain boundary effects within low frequencies and reduced conduction losses within higher frequencies [18]. The results further establish the effectiveness of Zn substitution in ferrites toward the improvement in performance for energy storage and renewable energy systems operating at high frequencies with low dielectric loss. The dielectric loss is further reduced as the Zn doping concentration increases. This is because Zn substitution reduces oxygen vacancies, leading to improved lattice stability and decreased dielectric loss. The BaZn₂Fe₁₆O₂₇ composition exhibited the lowest dielectric loss, highlighting its potential as a strong candidate for high-frequency applications, such as microwave and radio frequency communication tools. Overall, the dependence of dielectric loss on both frequency and temperature provides insights into optimizing these materials for high-frequency and microwave applications, ensuring energy efficiency and minimal signal attenuation in practical applications.

Variation of the imaginary permittivity (ε”) of BaNi_2−xZn_xFe₁₆O₂₇ ferrite at different selected frequency and temperatures

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Tangent of dielectric loss, tanδ, basically refers to the energy dissipated as heat when there is an applied electric field in any material. Thus, it takes place with insulating materials that do not let electric current flow through them but can store electrical energy. These ceramics are very common as dielectrics in different capacitors, where they store and release energy at needs. It will also define the amount of energy lost as heat on account of the material’s resistivity since no direct current flows through an insulator [18]. Low dielectric loss or tanδ suggests that the material does not heat up at all, whatever the frequency. Material tanδ that stays fairly constant over an excellent range of frequency would suggest that energy efficiency is retained even under a wide variation in operating frequencies.

Figure 6, illustrates how the tangent loss varies with temperature and frequency for BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites. It was found that dielectric losses are higher at lower frequencies, primarily due to the elevated resistivity at the grain boundaries, which demands more energy for electron exchange between Zn²⁺ ↔ Zn³⁺ and Fe³⁺ ↔ Fe²⁺ ions. These results are consistent with Koops’ phenomenological theory, which attributes the significant dielectric loss at low frequencies to the dominant role of grain boundary effects. As the frequency rises further, with increased frequency, the role of the grain boundaries becomes weaker and more significant, the dominance of grains with lower resistivity reduces the energy dissipation; thus, the dielectric loss decreases. Braun’s model also explained such behavior, considering conductive grains and less conductive grain boundaries. The two most important contributors, based on Koop’s theory, are: (1) electron hopping and (2) charged defect dipoles [33]. Generally, electron hopping is more prominent in lower frequencies versus charged defect dipoles in higher frequencies. Since the dipoles participate in that high-frequency polarization that cannot relax efficiently in an electric field, they do indeed respond more efficiently to reduce the dielectric loss.

Further, impurities and crystal imperfections involve losses in ferrites. The dielectric loss in the present study decreases with an increase of frequency at lower temperatures and does not show any pronounced peak. However, on further increasing the temperature, the ohmic losses dominating at low frequencies decrease more rapidly compared to those on the higher frequency side [32]. This indicates that the grains of the material become more active as the temperature increases, as has also been seen by other workers. The temperature dependence of dielectric loss reflects the increase in efficiency of the electronic conduction mechanism at elevated temperatures. The dielectric behavior observed in BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites can also be interpreted based on the Koop’s and Maxwell–Wagner models, which describe the frequency and temperature dependence of dielectric loss [26]. Koop’s model provides a phenomenological description of ferrites as comprising well-conducting grains separated by resistive grain boundaries, where low-frequency dielectric loss is attributed to space charge accumulation at boundaries. As temperature rises, the grain conductivity improves, resulting in reduced ohmic losses, as reflected in our data. Meanwhile, the Maxwell–Wagner model accounts for interfacial polarization in heterogeneous media with alternating conductive and resistive layers. At higher frequencies, the inability of dipoles to keep pace with the electric field leads to suppressed interfacial polarization and hence lower dielectric loss. These models collectively explain the observed reduction in tanδ with increasing frequency and Zn doping [41]. The BaZn₂Fe₁₆O₂₇ samples show extremely low leakage current, and the dielectric loss decreases with the rise in frequency and dopant concentration. The weakest tanδ found in BaZn₂Fe₁₆O₂₇ may be because of the reduced number of oxygen vacancies in the material. As illustrated in Fig. 6; Table 4, the dielectric loss (tanδ) exhibits a clear inverse relationship with both frequency and Zn doping concentration. At lower frequencies, charge carriers have sufficient time to respond to the applied electric field, resulting in enhanced polarization and higher energy dissipation. However, with increasing frequency, dipoles fail to realign rapidly, reducing polarization and consequently minimizing dielectric loss. Additionally, higher Zn content contributes to a decrease in oxygen vacancies and improves lattice stability, further suppressing dielectric losses. These combined effects render the BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites highly suitable for radio-frequency and microwave applications, where minimal energy dissipation is crucial. In devices such as radio-frequency oscillators, power amplifiers, and communication modules, low tanδ implies minimal energy dissipration as heat, thereby reducing thermal management requirements and extending device longevity. Moreover, a lower dielectric loss enhances signal fidelity and minimizes attenuation, which is crucial for maintaining performance in high-frequency electronic circuits. The extremely low tanδ observed in BaZn₂Fe₁₆O₂₇ makes it a highly promising material for such energy-sensitive and frequency-dependent technologies (Table 5).

(a-f), Variation of tangent loss (tan δ)of BaNi2-xZnxFe16O27 ferrite at different selected frequency and temperatures

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6.1 Permeability (µ_i)

(a) Temperature dependence of permeability (µ_i)

Figure 7, presents the variation in initial magnetic permeability (µi) with temperature for the BaNi₂₋ₓZnₓFe₁₆O₂₇ samples. As is characteristic of W-type ferrites, µi decreases progressively with increasing temperature until the Curie temperature (Tc) is reached, beyond which magnetic ordering collapses. This decline is attributed to reduced magnetic anisotropy and the thermal agitation of magnetic domains [35]. The incorporation of Zn²⁺ ions influences the µi–temperature behavior by modulating magnetic interactions and thermal stability, with doped samples displaying lower Tc values due to weaker A–B site exchange interactions.

The data in Fig. 7 show that the initial magnetic permeability (µi) increases with Zn substitution, reaching a maximum at x = 1.0, beyond which the increase becomes marginal. This trend reflects the enhanced domain wall mobility resulting from larger crystallite sizes, as supported by Fig. 8. Concurrently, a gradual decline in Curie temperature (Tc) is observed with increasing Zn content, indicating a weakening of magnetic exchange interactions. Figure 8 further reveals that crystallite size and lattice parameter ‘a’ increase monotonically with Zn²⁺ doping, suggesting lattice expansion and microstructural coarsening. These combined structural and magnetic trends confirm the effectiveness of Zn²⁺ substitution in tailoring the magnetic performance of BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites.

(b) Crystallite size, structure, and magnetic implications

“Figure 8 correlates the impact of Zn²⁺ substitution on crystallite size and crystal structure with magnetic performance. Zn²⁺ doping increases the crystallite size, which reduces grain boundary pinning and enhances magnetic domain wall mobility, leading to higher µi. This behavior is consistent with the Globus relation, where µi is proportional to the square of the grain size and saturation magnetization [41]. Structural analysis reveals that Zn²⁺ ions preferentially occupy tetrahedral (A) sites, displacing Fe³⁺ ions into octahedral (B) sites. This site preference can be attributed to the ionic radius and electronic configuration of of Zn²⁺. With an ionic radius of approximately 0.60 Å (tetrahedral), Zn²⁺ exhibits minimal crystal field stabilization and favors low-field tetrahedral environments. This substitution disrupts the strong Fe³⁺ (A)–Fe³⁺ (B) superexchange interactions, leading to a reeducation in magnetic coupling and curi temperature. Such redistribution also contributes to lattice expansion and altered magnetic anisotropy, consistent with observed structural and magnetic changes. Additionally, the observed increase in lattice parameter ‘a’ with Zn content expands interionic spacing, further diminishing magnetic coupling. These findings emphasize the role of Zn²⁺ in tailoring both microstructural and magnetic characteristics of W-type ferrites.

These structural modifications, coupled with the enhanced permeability and tuned magnetic transition temperature, highlight the significant role of Zn²⁺ substitution in optimizing BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites for integration into advanced magnetic and electronic devices such as high-frequency transformers, inductors, magnetic temperature switches, and –thermal sensitive magnetic sensors.

Initial permeability with temperature

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Variation of initial permeability (µ_i) and Curie temperature (T_c) as a function of Zn²⁺ content in BaNi_2-xZnₓFe₁₆O₂₇ ferrites

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This study investigated the structural, electrical conductivity, and permittivity properties of Zn-incorporated at BaNi₂₋ₓZnₓFe₁₆O₂₇ ferrites, were explored to assess their potential for use in renewable energy storage systems and high-frequency electronic applications.

XRD confirmed a single W-type hexaferrite structure, with the absence of any additional peaks confirming the material’s purity. The crystal size, measured between 35 and 37 nm, supports its suitability for high-frequency and microwave applications. The established dielectric behavior is a notable improvement in the AC conductivity and dielectric constant upon zinc substitution. The rise in the dielectric constant is attributed to increased lattice expansion and increased polarization caused by Zn²⁺ and is equally attributed to a fall in dielectric loss. The Maxwell-Wagner theory rationalized trends and attributed grain boundary resistance in observed frequency-dependent behavior. The AC conductivity values observed had a rise in frequency and temperature and confirmed the Small Polaron Hopping (SPH) theory for conduction. The behavior is in line with zinc substituted ferrites having good electrical traits for use in energy storage systems and high performance capacitors. Magnetally, zinc ion substitution affected some key features such as saturation magnetization and coercivity. The loss in magnetic anisotropy upon zinc ion incorporation produced lower coercivity but improved initial permeability (µ_i) and thereby suited them for application in regulated magnetic behavior-based processes such as electromagnetic shielding and transformers for application at high-frequency.

Optimized BaNi_2−xZnₓFe₁₆O₂₇ formulations exhibit better stability and no loss at high-frequency conditions and are thus suitable for use in oscillators, power amplifier circuits, and in RF networks for communications. Moreover, increased energy efficiency and lower current leakage position them as good candidates for use in advanced energy and electrical systems.

The substitution of Zn²⁺ alters the balance of A (tetrahedral) and B (octahedral) site interactions, leading to a weakening of the superexchange interactions between Fe³⁺(A)–O–Fe³⁺(B), which is reflected in the observed decrease in the Curie temperature and the enhancement in dielectric performance. Generally, these results are indicative of the extensive impact of Zn²⁺ substitution in altering structure, dielectric, and magnetic properties of BaNi_2−xZnₓFe₁₆O₂₇ ferrites. Synthesis should be optimized and followed up with further electrochemical research in future research to validate performance in actual energy storage and energy transformation processes. In addition, supplementation of these ferrites in energy harvesters such as solar cells could provide opportunities for multifunctional energy solutions.