Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion

Avadhut Manage; Balachandra G. Hegde; Shidaling Matteppanavar

doi:doi:10.11648/j.ajn.20261002.12

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Structural, Morphological, Magnetic, and Electrical Properties of ZrFe_2−xBi_xO₅ Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion

Avadhut Manage

, Balachandra G. Hegde^*

, Shidaling Matteppanavar

Published in American Journal of Nanosciences (Volume 10, Issue 2)

Received: 1 June 2026 Accepted: 10 June 2026 Published: 26 June 2026

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Abstract

ZrFe_2−xBi_xO₅ (x = 0, 0.25, 0.50, 0.75, 1.00) nanoparticles were synthesized using Sol-gel auto-combustion method and their structural, morphological, magnetic, and frequency-dependent electrical properties were systematically characterized at room temperature. X-ray diffraction analysis confirms single phase monoclinic C2/c formation for every composition, the principal interplanar spacing increases linearly from 2.9503 Å to 3.0034 Å, crystallite size decreases from 32.1 to 16.7 nm, and dislocation density grows nearly four times as x advances to unity. Scanning electron microscopy reveals a progressive transition from large, irregularly agglomerated grains to a finer, more densely packed nanoparticulate microstructure. All M-H loops measured over ±10 kOe identify soft ferromagnetic, multi-domain behavior (S < 0.5 throughout); saturation magnetization plummets from 16.46 to 1.67 emu g⁻¹ while the coercive field rises from 102.24 to 182.22 G. Impedance measurements (100 Hz - 10 MHz) show that bulk resistance increases ten times over the substitution range, Nyquist plots fit to a two element equivalent circuit of two CPE-resistor pairs in series, and the extracted grain and grain-boundary resistances rise monotonically with x, establishing that Bi³⁺ incorporation progressively depletes the Fe³⁺/Fe²⁺ charge carrier pool. The dielectric constant follows Maxwell-Wagner-Sillars behavior and decreases with both frequency and Bi content, while AC conductivity spectra display a characteristic dual-peak pattern attributed to space-charge polarization at grain boundaries at low frequency and grain-interior Fe hopping at high frequency, both peaks diminishes with increasing Bi content. The correlated structure-property picture presented here establishes the Bi-substituted ZrFe₂O₅ system as a candidate for compositionally tunable soft-magnetic and dielectric applications.

Published in	American Journal of Nanosciences (Volume 10, Issue 2)
DOI	10.11648/j.ajn.20261002.12
Page(s)	52-63
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

ZrFe_2−xBi_xO₅, AB₂O₅, Sol-gel Auto-combustion, Soft Ferromagnetism, Non Debye Relaxation, Maxwell-Wagner Polarization, Complex AC Conductivity

1. Introduction

The interplay of structural, magnetic, and dielectric degrees of freedom in complex transition-metal oxides has become one of the most fertile areas of contemporary material science research, driven equally by fundamental curiosity and by the demand for multifunctional ceramics in next-generation spintronics, high-frequency communication, magnetic hyperthermia, and energy-storage technologies

[1-4]

. Within this broad landscape, compounds of the general formula AB₂O₅ attract growing attention because the structural versatility of their cation sublattice-accommodating diverse A and B occupants while retaining the characteristic 3: 5 cation-to-oxygen stoichiometry translates directly into a correspondingly rich portfolio of tunable properties

[5-10]

. Pseudobrookite TiFe₂O₅, karrooite MgTi₂O₅, and the orthorhombic multiferroic TbMn₂O₅ illustrate distinct manifestations of this structural flexibility

[7-10]

Zirconium iron oxide in the 1: 2: 5 stoichiometry (ZrFe₂O₅) occupies a structurally distinctive niche within the AB₂O₅ family. Its monoclinic C2/c crystal structure seats Zr⁴⁺ in an eight-coordinated polyhedron alongside two inequivalent Fe³⁺ sites in distorted octahedral environments, a connectivity that sustains frustrated spin pathways and active Fe³⁺/Fe²⁺ charge-transfer channels

[11]

. Prior investigations have established that ZrFe₂O₅ nanoparticles display significant photocatalytic and Fenton-type reactivities and soft ferromagnetic behavior whose intensity depends sensitively on the synthesis protocol and annealing history

[12-15]

. The related compound ZrFe₂O₄ has attracted parallel interest as a magnetic nano catalyst for organic synthesis and photodegradation applications

[16, 17]

. Systematic investigations of the AC impedance and dielectric response of pure and Ni-doped ZrFe₂O₅ were reported in our prior study

[11]

, which revealed non-Debye relaxation and characteristic dual-peak AC conductivity spectra, and provided the structural and compositional baseline for the present work.

Chemical substitution at the B (iron) site is the most direct route to modify the magnetic exchange network and electrical transport properties of ZrFe₂O₅ while preserving the host crystal structure. In our earlier investigation

[11]

, Ni²⁺ doping (up to x = 0.05) produced modest but measurable changes in lattice parameters, grain morphology, saturation magnetization, and dielectric relaxation dynamics, attributable to the moderate size mismatch (δr/r ≈ 7%) between Ni²⁺ (0.69 Å) and Fe³⁺ (0.645 Å). Extending the approach to Bi³⁺ substitution (r = 1.03 Å

[18]

) magnifies this mismatch to nearly 60% and introduces three additional physical effects absent in the Ni-doped system: (i) far greater lattice strain per dopant unit, enabling structural tuning over a wider single-phase composition range; (ii) a stereochemical active 6s² lone pair that distorts local oxygen coordination and creates anisotropic dielectric response

[19]

; and (iii) a completely spin-inactive substituent that quantitatively dilutes the iron magnetic sublattice without contributing any compensating moment unlike Ni²⁺ (2 μ_B). These features make Bi³⁺ a uniquely informative probe of the structural property relationships in this system.

The sol-gel auto-combustion synthesis route exploited here combines the stoichiometric homogeneity of wet-chemical precursor mixing with the rapid exothermic ignition that produces finely divided, phase-pure powders at relatively low processing temperatures, circumventing the coarse microstructures and impurity phases typical of high-temperature solid-state reactions

[20, 21]

. No comprehensive study of Bi-substituted ZrFe₂O₅ spanning the full x = 0-1.00 range, and covering XRD, SEM, magnetic hysteresis, complex impedance, dielectric, and AC conductivity properties simultaneously, appears in the published literature. The present paper addresses this gap.

2. Synthesis and Experimental Techniques

Nanocrystalline ZrFe_2−xBi_xO₅ (x = 0, 0.25, 0.50, 0.75, 1.00) were prepared by the sol-gel auto-combustion method using citric acid as the organic fuel

[20, 21]

. Analytical reagent grade ferric nitrate [Fe(NO₃)₃·9H₂O], bismuth nitrate [Bi(NO₃)₃·5H₂O], zirconyl nitrate [ZrO(NO₃)₂·3H₂O], and citric acid (C₆H₈O₇) were dissolved in deionized water maintaining an oxidizer-to-fuel molar ratio of 1: 1. The solution was heated with continuous stirring at 80 °C until a viscous, amber gel formed; raising the temperature to 120 °C induced spontaneous ignition, producing a voluminous ashy precursor within seconds. The product was collected, ground in an agate mortar, and calcined and sintered at 500 °C for 5 h to eliminate organic residues and forming pure phase.

Room-temperature PXRD patterns were recorded on a diffractometer using Cu K_α radiation (λ = 1.5406 Å) over 2θ = 10-90°. Surface morphology and elemental composition were examined by scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy. Magnetic hysteresis loops were recorded at 300 K on a home-built vibrating sample magnetometer (VSM)

[22]

over ±10 kOe. For electrical measurements, sintered powders were mixed with 6 wt% poly(vinyl alcohol) binder, uniaxially pressed into 8 mm-diameter pellets at 50 kg cm⁻², heated at 500 °C for 5 h, and contact-coated with silver paste cured at 100 °C for 30 min. Frequency-dependent impedance, dielectric, and AC conductivity data were acquired on a Wayne Kerr 6500B impedance analyzer at 300 K over 100 Hz to 10 MHz.

3. Results and Discussion

3.1. X-ray Diffraction Analysis

Every reflection in the parent compound indexes on a monoclinic unit cell, space group C2/c (No. 15), consistent with the polyhedral framework comprising Zr⁴⁺ in eight-coordination and two inequivalent Fe³⁺ sites in distorted octahedra

[11, 23, 24]

. No secondary-phase reflections attributable to ZrO₂, Fe₂O₃, or Bi₂O₃ were detected, confirming single-phase formation across the entire substitution range. The dominant reflection near 30° (2θ) shifts monotonically to 29.72° as x rises to 1.00, while the associated interplanar spacing expands from 2.9503 Å to 3.0034 Å, a linear variation that obeys Vegard’s law

[25, 26]

with a coefficient of determination R² = 0.9994. The driving force is the ionic-size mismatch between Fe³⁺ (r = 0.645 Å) and Bi³⁺ (r = 1.03 Å) in six-fold coordination

[18]

, a nearly 60% discrepancy that dilates the surrounding oxygen polyhedra at each Bi site, in accordance with Bragg’s law

[27]

Download: Download full-size image

Figure 1. Room temperature PXRD patterns of ZrFe₂−xBixO₅ compositions.

Crystallite size D was evaluated from the Scherrer relation

[28]

. D contracts from 32.1 nm (x = 0) to 16.7 nm (x = 1.00), a 48% reduction, following the established trend of crystallite suppression under large-ion doping

[29]

. Williamson-Hall (W-H) plots

[30]

(β cosθ vs. 4 sinθ) provide the micro-strain ε from the gradient and confirm that all broadening trends are tensile: ε rises from 0.93 × 10⁻³ to 1.81 × 10⁻³. Dislocation density

ρ

[31]

climbs nearly four times from 3.08 to 11.34 × 10¹³ m⁻². No superlattice satellites appeared, confirming random Bi³⁺ distribution within the detection limit of the diffraction experiment. All derived parameters are given in Table 1.

Table 1. XRD-derived structural and microstructural parameters for ZrFe_2−xBi_xO₅compositions.

Composition (x)	2θ (°)	Interplanar Spacing d (Å)	Crystalline Size D (nm)	Micro-Strain (W-H) ε (10−3)	Dislocation Density $ρ = \frac{1}{D^{2}}$ (1013 m−2)
0	30.27	2.9503	32.1	0.93	3.08
0.25	30.13	2.9636	27.5	1.14	4.20
0.50	29.99	2.9768	23.8	1.36	5.59
0.75	29.86	2.9901	20.1	1.58	7.83
1.00	29.72	3.0034	16.7	1.81	11.34

3.2. Surface Morphology and EDAX

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Figure 2. SEM images of ZrFe_2−xBi_xO₅ at (a) x = 0, (b) 0.25, (c) 0.50, (d) 0.75, (e) 1.00.

SEM images reveal a clear and progressive response of surface morphology to Bi substitution. The undoped parent compound (Figure 2a) shows large, irregularly shaped, angular grain clusters separated by conspicuous inter-grain voids. The comparatively broad particle size distribution and high porosity are consistent with the large crystallite size (32.1 nm) and low dislocation density (ρ = 3.08 × 10¹³ m⁻²) documented in Table 1; scattered bright protrusions are attributable to topographic secondary-electron contrast enhancement at surface asperities rather than chemical inhomogeneity

[32]

As x increases from 0.25 to 1.00 (Figures 2b-2e), the microstructure evolves markedly toward a finer, more densely packed assembly. For x = 0.25 and 0.50, grains appear polygonal facets, inter-grain contact area grows with multi-domain grains, each encompassing several coherently scattering XRD crystallite domains. For x = 0.75 and 1.00, grain boundaries are sharply defined and porosity diminishes markedly. The grain-size with Bi content mirrors the crystallite refinement in Table 1 and is attributed to the elevated elastic energy around oversized Bi³⁺ centres impeding grain-boundary migration, an effect analogous to Zener pinning

[33, 34]

. EDAX analysis (Table 2) confirms Zr, Fe, Bi, and O in stoichiometric proportions without extraneous peaks, establishing phase purity consistent with the XRD data.

Table 2. EDAX elemental atomic percentages for ZrFe_2−xBi_xO₅ compositions.

Composition (x)	Atomic%
Composition (x)	Zr	Fe	Bi	O
0	10.54 ± 0.6	23.02 ± 1.04	0	66.44 ± 3.05
0.25	10.58 ± 0.7	20.12 ± 0.8	3.04 ± 0.3	66.26 ± 3.08
0.50	10.56 ± 0.5	17.27 ± 0.6	5.77 ± 0.5	66.40 ± 3.02
0.75	10.59 ± 0.8	14.35 ± 0.3	8.86 ± 0.6	66.20 ± 3.11
1.00	10.53 ± 0.6	11.53 ± 0.3	11.01 ± 0.7	66.93 ± 3.15

3.3. Magnetic Properties

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Figure 3. Room-temperature M-H loops of ZrFe_2−xBi_xO₅ compositions.

Room-temperature M-H loops recorded over ±10 kOe (Figure 3) are open and relatively narrow for every composition, the characteristic signature of soft ferromagnetic behaviour. The squareness ratio S ranges from 0.165 (x = 0) to 0.252 (x = 1.00), comfortably below the 0.5 threshold that the Stoner-Wohlfarth model

[35]

identifies with single-domain particles. Such S values indicate a multi-domain ferromagnetic ground state

[36, 37]

in which reversal is governed by Bloch-wall displacement rather than coherent spin rotation, consistent with the SEM-derived apparent grain diameters of 45-90 nm that comfortably exceed the single-domain radius for iron-oxide-class ceramics

[36]

. All derived magnetic parameters are collected in Table 3.

M_s falls from 16.46 emu g⁻¹ at x = 0 to 1.67 emu g⁻¹ at x = 1.00, a 90% suppression. Comparison with our previous investigation

[11]

is instructive: over x = 0-0.05, Ni²⁺ doping reduced M_s by only ~31%. The disparity directly reflects the magnetic valence contrast between the two dopants Ni²⁺ (d⁸, 2 μ_B) partially maintains the sublattice moment, whereas Bi³⁺ (6s², 0 μ_B) contributes no spin and simultaneously severs Fe-O-Fe superexchange bridges

[38, 39]

. Magnetic moment per formula unit

n_{B}

was calculated using following formula n_B

[40, 41]

n_{B} = \frac{Molecular Weig h t X M_{s}}{5585}

(1)

n_{B}

drops from 0.834 μ_B to 0.130 μ_B across the series. A marginal non-monotonic bump between x = 0.25 (0.527 μ_B) and x = 0.50 (0.565 μ_B) is a molecular-weight artefact, the formula weight increases by nearly 38 g mol⁻¹ in this step while M_s barely changes and carries no independent physical significance

[42]

H_c climbs monotonically from 102.24 G (x = 0) to 182.22 G (x = 1.00), a 78% overall gain that contrasts sharply with the near-constant coercive field (~100-103 G) in the Ni-doped system

[11]

. Three independent mechanisms, each corroborated by XRD or SEM data, drive this coercivity increase. (i) Grain-boundary pinning: the denser grain-boundary network in finer-grained samples (Section 3.2) multiplies Bloch-wall pinning sites

[36, 37]

. (ii) Magnetoelastic coupling to lattice microstrain: the doubling of ε (Table 1) creates local anisotropy gradients that resist domain-wall motion

[43, 44]

. (iii) The stereochemically active Bi³⁺ 6s² lone pair induces off-centre oxygen displacements

[19]

that lower local symmetry and scatter walls. The disproportionate H_c jump between x = 0.75 (133.1 G) and x = 1.00 (182.22 G) is consistent with the lone-pair effect becoming percolative once Bi³⁺ is the majority B-site occupant.

Table 3. Room Temperature Magnetic parameters for ZrFe_2−xBi_xO₅ compositions.

Composition (x)	Saturation Magnetiszaton $M_{s}$ (emu g⁻¹)	Remanent Magnetization $M_{r}$ (emu g⁻¹)	Coercive Field $H_{c}$ (Gauss)	Squareness Ratio $S = \frac{M_{r}}{M_{s}}$	Magnetic Moment $n_{B} (μ_{B})$
0	16.46	2.71	102.24	0.1646	0.834
0.25	9.17	1.88	106.23	0.2050	0.527
0.50	8.78	1.56	125.20	0.1777	0.565
0.75	4.35	0.85	133.10	0.1954	0.310
1.00	1.67	0.42	182.22	0.2515	0.130

3.4. Impedance Properties

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Figure 4. Real part of impedance Z′ versus frequency for ZrFe_2−xBi_xO₅ compositions.

The real component of impedance Z′ (Figure 4) is high at 100 Hz and decreases steadily with frequency for all compositions, all curves converging near zero above nearly 10⁵ Hz. The magnitude at 100 Hz rises from nearly 0.8 MΩ (x = 0) to ~10.5 MΩ (x = 1.00), with intermediate compositions taking values of nearly 3.0, 6.0, and 8.0 MΩ. Within the Maxwell-Wagner-Koops microstructural model

[45-47]

, the high Z′ at low frequency reflects the dominant role of highly resistive grain boundaries, while the convergence to low values at high frequency indicates that charge carriers interact principally with the more conductive grain interiors. Bi³⁺ incorporation reduces the concentration of mobile Fe³⁺/Fe²⁺ hopping pairs, simultaneously raising grain-bulk and grain-boundary resistance. Nickel doping in our prior study

[11]

showed the same qualitative trend but with far smaller magnitudes, consistent with the much lower substitution levels used (x ≤ 0.05) and Ni²⁺ being only weakly hole-forming at the Fe site.

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Figure 5. Imaginary part of impedance Z′′ versus frequency for ZrFe_2−xBi_xO₅ compositions.

The imaginary part Z″ (Figure 5) follows an analogous monotonic decay from large values at 100 Hz toward zero at high frequency, with the amplitude hierarchy x = 1.00 > 0.75 > 0.50 > 0.25 > 0 at any given low frequency. The absence of a resolved Z″ maximum within the measurement window (100 Hz-10 MHz) for x ≥ 0.50 indicates that the predominant relaxation frequency lies below 100 Hz, i.e., the grain-boundary arc is too large to be fully captured in the accessible frequency range. This is a direct consequence of the large R_gb values documented in the equivalent-circuit fitting. The combined Z′ and Z″ behaviour is characteristic of non-Debye type relaxation

[48, 49]

, arising from a distribution of relaxation times across grain-boundary regions of varying thickness, composition, and local Bi³⁺ enrichment.

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Figure 6. Nyquist plots (Z″ vs Z′) for ZrFe_2−xBi_xO₅ compositions with equivalent circuit.

Complex impedance Nyquist plots for all compositions are shown in Figure 6. For x = 0, the arc spans an extremely small impedance range compare to doped one and lies almost entirely within the noise floor of the plot, consistent with the high AC conductivity of this composition. For x = 0.25, a partially resolved, depressed semicircular arc is discernible. At x ≥ 0.50, the data trace large-radius arcs whose low-frequency limbs fall outside the measurement window (100 Hz), so only the ascending portions are captured. The depression of all arcs below the real axis confirms non-Debye type relaxation

[49, 50]

, arising from a distribution of relaxation times rather than a single exponential process.

All data were fitted to the equivalent circuit (R_g||CPE_g) + (R_gb||CPE_gb), where two parallel constant phase element and resistor units are connected in series, with the grain element (R_g||CPE_g) dominating at high frequency and the grain-boundary element (R_gb||CPE_gb) at low frequency

[47, 50, 51]

. All fitted parameters are tabulated in Table 4.

Table 4. Equivalent circuit parameters from Nyquist plot fitting for ZrFe_2−xBi_xO₅ compositions.

Composition x	Grain Resistance Rg (Ω)	Grain CPE Qg (F)	Grain CPE Phase Exponent ng	Grain Boundary Resistance Rgb (Ω)	Grain Boundary CPE Qgb (F)	Gran Boundary CPE Phase Exponent ngb	Chi Square Value χ2
0	6.03×10⁵	3.55×10^-¹¹	0.9079	1.28×10⁶	2.02×10^-⁷	0.3912	6.63× 10^-4
0.25	1.78×10⁶	1.43×10^-¹⁰	0.7907	4.37×10⁶	2.61×10^-⁹	0.7711	6.32× 10^-³
0.50	3.24×10⁶	3.87×10^-¹⁰	0.7600	6.48×10⁶	1.93×10^-¹⁰	0.7923	1.15× 10^-²
0.75	5.16×10⁶	6.94×10^-¹⁰	0.7441	9.37×10⁶	1.14×10^-¹⁰	0.8136	1.82× 10^-²
1.00	7.82×10⁶	1.12×10^-⁹	0.7218	1.36×10⁷	6.87×10^-¹¹	0.8312	2.55× 10^-²

Trends in Table 4 are evident that both R_g and R_gb increase monotonically from x = 0 through x = 1.00 (R_g: 6.03 × 10⁵ to 7.82 × 10⁶ Ω; R_gb: 1.28 × 10⁶ to 1.36 × 10⁷ Ω), confirming that Bi³⁺ incorporation progressively impedes charge transport in both microstructural regions. The CPE coefficient Q_g rises steadily from 3.55 × 10⁻¹¹ to 1.12 × 10⁻⁹ F, consistent with the increase in grain-boundary-to-volume ratio documented by SEM, that is smaller grains = higher specific grain capacitance. Conversely, Q_gb decreases by approximately three order of magnitude across the series (2.02 × 10⁻⁷ to 6.87 × 10⁻¹¹ F), reflecting the progressive reduction in grain-boundary capacitance as the boundary regions become more resistive and the charge accumulation is depleted. The grain phase exponent n_g decreases gradually (0.908→0.722) while n_gb increases (0.391→0.831), indicating that grain-interior relaxation becomes more heterogeneous while grain-boundary behaviour approaches that of a more idealised Debye-like capacitor with increasing Bi content, a trend reported for Bi-containing ferrite composites as well

[42, 52]

. For all compositions R_gb > R_g and Q_gb > Q_g, a well-established hallmark of polycrystalline ionic oxides where grain boundaries offer a higher energy barrier than bulk grains

[47, 50, 51]

3.5. Dielectric Properties

The dielectric constant ε′ and dielectric loss ε″ are determined from the measured capacitance C and dissipation factor tan δ

[53, 54]

ε^{'} = \frac{Cd}{ε_{0} A}

(2)

ε^{″} = ε^{'} \tan δ

(3)

where d is pellet thickness, A the electrode area, and ε₀ the permittivity of free space. At 100 Hz, ε′ spans nearly two decades across the series: from nearly 5 × 10⁴ for ZrFe₂O₅ to nearly 10³ for x = 1.00 (Figure 7). By 10 MHz all curves converge to ε′ values in the range 10-30, where only intrinsic lattice polarization mechanisms contribute. The high low-frequency ε′ and its steep frequency dependence are the textbook signature of Maxwell-Wagner-Sillars (MWS) space-charge polarization

[45-47]

: at low frequencies, charge carriers accumulate at resistive grain boundaries on a timescale exceeding the field period, generating giant effective permittivities; at high frequencies, carriers cannot follow the rapidly alternating field and ε′ plateaus near its intrinsic value. Bi substitution reduces ε′ because the Verwey-type

[55]

Fe³⁺↔Fe²⁺ electron hopping that generates the mobile space charge is progressively diluted as Bi³⁺ occupies Fe sites, in direct analogy to the behaviour documented for Ni²⁺ doping in our prior study

[11]

and for Bi³⁺-bearing spinel ferrites in the wider literature

[42, 52, 56]

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Figure 7. Dielectric constant ε′ vs frequency of ZrFe_2−xBi_xO₅ compositions.

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Figure 8. Loss tangent tanδ vs frequency of ZrFe_2−xBi_xO₅ compositions.

The dielectric loss ε″ (Figure 8) follows the same monotonically decreasing frequency dependence and scales proportionally with ε′ at each composition, as expected when ohmic conduction losses dominate at low frequencies. At high frequencies ε″ drops toward intrinsic polarization loss values and Bi doping reduces ε″ across the full frequency window, confirming suppression of conduction-driven polarization.

The loss tangent tanδ (Figure 9) begins at nearly 8-9 at 100 Hz for ZrFe₂O₅ and decreases to nearly 1-1.5 for x ≥ 0.50. A broad shoulder centred near 10³-10⁴ Hz for the x = 0 and 0.25 compositions signals a dielectric relaxation process; the absence of a sharp, symmetric Debye-type peak is the hallmark of non-Debye relaxation

[48, 57]

, arising from a distribution of relaxation times across grain-boundary regions of heterogeneous thickness and local composition. This shoulder attenuates and shifts with increasing Bi content as Fe hopping pairs become fewer

[11, 55, 56]

. Above 10⁶ Hz, tanδ drops sharply for all compositions, indicating that polarization mechanisms can no longer track the rapidly alternating field. The progressive suppression of tanδ with x suggests enhanced dielectric stability, analogous to the behaviour of Bi-doped nickel-cobalt ferrites

[52, 58]

and Ni-doped copper ferrite

[59]

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Figure 9. Dielectric loss ε′′ vs frequency of ZrFe_2−xBi_xO₅ compositions.

3.6. AC Conductivity

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Figure 10. AC Conductivity vs frequency of ZrFe_2−xBi_xO₅ compositions.

The AC conductivity was calculated from

[54, 60]

σ_{ac} = 2 πf ε_{0} ε^{'} \tan δ

(4)

Figure 10 presents the σ_ac spectra. The most revealing feature is the characteristic dual-peak structure prominently visible in the x = 0 (black) curve: a low-frequency peak at nearly 100-200 Hz (σ_ac ≈ 2 × 10⁻³ S m⁻¹), a conductivity minimum near 5 × 10³ Hz, and a second peak near 3 × 10⁶ Hz (σ_ac ≈ 3 × 10⁻³ S m⁻¹). This same fingerprint was documented in the Ni-doped analogue

[11]

and is interpreted within an established framework. The low-frequency peak arises when the external field frequency matches the characteristic relaxation rate for space-charge accumulation at grain boundaries, including the resonance condition for Fe³⁺→Fe²⁺ carrier hopping across those boundaries; the intermediate conductivity minimum represents the DC-like plateau where neither boundary hopping nor grain-interior processes are resonant; and the high-frequency peak is assigned to short-range, localised Fe³⁺/Fe²⁺ hopping within grain interiors, generating transient dipoles that relax at the grain characteristic frequency

[11, 55, 60]

For x = 0.25, both peaks persist at lower amplitudes (nearly1.5 × 10⁻⁴ and nearly 1.5 × 10⁻³ S m⁻¹ for the low- and high-frequency peaks, respectively). From x ≥ 0.50, the low-frequency peak is no longer resolvable: the grain-boundary hopping carrier density is too dilute to sustain a measurable resonance, and only the high-frequency grain-interior peak remains, its amplitude decreasing from nearly 5 × 10⁻⁴ S m⁻¹ (x = 0.50) to nearly 3 × 10⁻⁴ S m⁻¹ (x = 0.75). The slight uptick at x = 1.00 (nearly 8 × 10⁻⁴ S m⁻¹) may reflect the onset of percolating Bi-enriched interfacial pathways identified in the SEM micrographs. The universal power-law behaviour σ_ac

\propto

ω^s (Jonscher’s law

[48]

) is broadly obeyed in the intermediate frequency plateau, providing an empirical signature of hopping-type conduction in disordered oxide systems

[48, 60]

4. Conclusion

A comprehensive sol-gel auto-combustion study of ZrFe_2−xBi_xO₅ (x = 0-1.00) has produced a self-consistent picture linking crystal structure, grain morphology, magnetic response, and broadband electrical behaviour across the full substitution range. Structurally, Bi³⁺ incorporation within the monoclinic C2/c framework obeys Vegard’s law (R² = 0.9994), expanding the lattice by 1.80% while halving the crystallite size and nearly quadrupling the dislocation density. These XRD-derived changes manifest directly in the SEM microstructures progressive grain refinement, sharpening of grain boundaries, and appearance of Bi-enriched triple-junction inclusions all consistent with size-mismatch driven grain-boundary pinning. Magnetically, the complete spin inactivity of Bi³⁺ drives a 90% collapse of saturation magnetisation while the coercive field rises 78% through three concurrent mechanisms: denser grain-boundary Bloch-wall pinning, magnetoelastic coupling to the doubled lattice microstrain, and local anisotropy from the Bi³⁺ 6s² lone pair. Complex impedance analysis reveals that both grain and grain-boundary resistances increase monotonically from x = 0 to 1.00 (nearly 10 times at 100 Hz), fitted by a two-element CPE equivalent circuit whose parameters evolve in a physically interpretable fashion. Dielectric permittivity decreases with both frequency and Bi content satisfying the Maxwell-Wagner-Sillars framework, and AC conductivity spectra exhibit a dual-peak nature whose progressive attenuation with x quantitatively shows the depletion of Fe³⁺/Fe²⁺ hopping carriers. All these results demonstrate that Bi³⁺ substitution in ZrFe₂O₅ provides a wide and experimentally accessible compositional arrangement for simultaneously tuning soft-magnetic coercivity, dielectric permittivity, and electrical resistance, establishing this system as a promising platform for multifunctional nanoceramics.

Abbreviations

XRD	X-Ray Diffraction
PXRDD	Powder X-Ray Diffraction
SEM	Scanning Electron Microscopy
EDAX	Energy Dispersive X-ray Analysis
VSM	Vibrating Sample Magnetometer
AC	Alternating Current
CPE	Constant Phase Element
MWS	Maxwell–Wagner–Sillars
W-H	Williamson–Hall

Acknowledgments

AM and SM acknowledge the Vision Group on Science and Technology for sanctioning the project under the "Center of Excellence in Science, Engineering and Medicine" (CESEM GRD No 852) Government of Karnataka. SM also, thanks to UGC-DAE Consortium of Scientific Research letter/Order No. 2021-22/03/587 dated 30/03/2022 for the financial support.

Author Contributions

Avadhut Manage: Data curation, Validation, Visualization, Writing – original draft, Writing – review & editing

Balachandra G. Hegde: Conceptualization, Methodology, Project administration, Resources, Supervision, Validation, Writing – review & editing

Shidaling Matteppanavar: Formal Analysis, Investigation, Resources, Validation, Supervision, Writing – review & editing

Conflicts of Interest

Authors don’t have any conflict of interest.

References

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Manage, A., Hegde, B. G., Matteppanavar, S. (2026). Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. American Journal of Nanosciences, 10(2), 52-63. https://doi.org/10.11648/j.ajn.20261002.12

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Manage, A.; Hegde, B. G.; Matteppanavar, S. Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. Am. J. Nanosci. 2026, 10(2), 52-63. doi: 10.11648/j.ajn.20261002.12

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Manage A, Hegde BG, Matteppanavar S. Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. Am J Nanosci. 2026;10(2):52-63. doi: 10.11648/j.ajn.20261002.12

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@article{10.11648/j.ajn.20261002.12,
  author = {Avadhut Manage and Balachandra G. Hegde and Shidaling Matteppanavar},
  title = {Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion},
  journal = {American Journal of Nanosciences},
  volume = {10},
  number = {2},
  pages = {52-63},
  doi = {10.11648/j.ajn.20261002.12},
  url = {https://doi.org/10.11648/j.ajn.20261002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajn.20261002.12},
  abstract = {ZrFe2−xBixO5 (x = 0, 0.25, 0.50, 0.75, 1.00) nanoparticles were synthesized using Sol-gel auto-combustion method and their structural, morphological, magnetic, and frequency-dependent electrical properties were systematically characterized at room temperature. X-ray diffraction analysis confirms single phase monoclinic C2/c formation for every composition, the principal interplanar spacing increases linearly from 2.9503 Å to 3.0034 Å, crystallite size decreases from 32.1 to 16.7 nm, and dislocation density grows nearly four times as x advances to unity. Scanning electron microscopy reveals a progressive transition from large, irregularly agglomerated grains to a finer, more densely packed nanoparticulate microstructure. All M-H loops measured over ±10 kOe identify soft ferromagnetic, multi-domain behavior (S −1 while the coercive field rises from 102.24 to 182.22 G. Impedance measurements (100 Hz - 10 MHz) show that bulk resistance increases ten times over the substitution range, Nyquist plots fit to a two element equivalent circuit of two CPE-resistor pairs in series, and the extracted grain and grain-boundary resistances rise monotonically with x, establishing that Bi3+ incorporation progressively depletes the Fe3+/Fe2+ charge carrier pool. The dielectric constant follows Maxwell-Wagner-Sillars behavior and decreases with both frequency and Bi content, while AC conductivity spectra display a characteristic dual-peak pattern attributed to space-charge polarization at grain boundaries at low frequency and grain-interior Fe hopping at high frequency, both peaks diminishes with increasing Bi content. The correlated structure-property picture presented here establishes the Bi-substituted ZrFe2O5 system as a candidate for compositionally tunable soft-magnetic and dielectric applications.},
 year = {2026}
}

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TY  - JOUR
T1  - Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion
AU  - Avadhut Manage
AU  - Balachandra G. Hegde
AU  - Shidaling Matteppanavar
Y1  - 2026/06/26
PY  - 2026
N1  - https://doi.org/10.11648/j.ajn.20261002.12
DO  - 10.11648/j.ajn.20261002.12
T2  - American Journal of Nanosciences
JF  - American Journal of Nanosciences
JO  - American Journal of Nanosciences
SP  - 52
EP  - 63
PB  - Science Publishing Group
SN  - 2575-4858
UR  - https://doi.org/10.11648/j.ajn.20261002.12
AB  - ZrFe2−xBixO5 (x = 0, 0.25, 0.50, 0.75, 1.00) nanoparticles were synthesized using Sol-gel auto-combustion method and their structural, morphological, magnetic, and frequency-dependent electrical properties were systematically characterized at room temperature. X-ray diffraction analysis confirms single phase monoclinic C2/c formation for every composition, the principal interplanar spacing increases linearly from 2.9503 Å to 3.0034 Å, crystallite size decreases from 32.1 to 16.7 nm, and dislocation density grows nearly four times as x advances to unity. Scanning electron microscopy reveals a progressive transition from large, irregularly agglomerated grains to a finer, more densely packed nanoparticulate microstructure. All M-H loops measured over ±10 kOe identify soft ferromagnetic, multi-domain behavior (S −1 while the coercive field rises from 102.24 to 182.22 G. Impedance measurements (100 Hz - 10 MHz) show that bulk resistance increases ten times over the substitution range, Nyquist plots fit to a two element equivalent circuit of two CPE-resistor pairs in series, and the extracted grain and grain-boundary resistances rise monotonically with x, establishing that Bi3+ incorporation progressively depletes the Fe3+/Fe2+ charge carrier pool. The dielectric constant follows Maxwell-Wagner-Sillars behavior and decreases with both frequency and Bi content, while AC conductivity spectra display a characteristic dual-peak pattern attributed to space-charge polarization at grain boundaries at low frequency and grain-interior Fe hopping at high frequency, both peaks diminishes with increasing Bi content. The correlated structure-property picture presented here establishes the Bi-substituted ZrFe2O5 system as a candidate for compositionally tunable soft-magnetic and dielectric applications.
VL  - 10
IS  - 2
ER  -

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Author Information

Avadhut Manage

Department of Physics, Rani Channamma University, Belagavi, India

http://orcid.org/0009-0000-3460-4863
Balachandra G. Hegde

Department of Physics, Rani Channamma University, Belagavi, India

Contact Email

http://orcid.org/0000-0003-0478-5223
Shidaling Matteppanavar

Department of Physics, KLE Society’s Basavaprabhu Kore Arts Science and Commerce College, Chikodi, India

http://orcid.org/0000-0002-4317-7637

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Manage, A., Hegde, B. G., Matteppanavar, S. (2026). Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. American Journal of Nanosciences, 10(2), 52-63. https://doi.org/10.11648/j.ajn.20261002.12

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ACS Style

Manage, A.; Hegde, B. G.; Matteppanavar, S. Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. Am. J. Nanosci. 2026, 10(2), 52-63. doi: 10.11648/j.ajn.20261002.12

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AMA Style

Manage A, Hegde BG, Matteppanavar S. Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion. Am J Nanosci. 2026;10(2):52-63. doi: 10.11648/j.ajn.20261002.12

Copy | Download

@article{10.11648/j.ajn.20261002.12,
  author = {Avadhut Manage and Balachandra G. Hegde and Shidaling Matteppanavar},
  title = {Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion},
  journal = {American Journal of Nanosciences},
  volume = {10},
  number = {2},
  pages = {52-63},
  doi = {10.11648/j.ajn.20261002.12},
  url = {https://doi.org/10.11648/j.ajn.20261002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajn.20261002.12},
  abstract = {ZrFe2−xBixO5 (x = 0, 0.25, 0.50, 0.75, 1.00) nanoparticles were synthesized using Sol-gel auto-combustion method and their structural, morphological, magnetic, and frequency-dependent electrical properties were systematically characterized at room temperature. X-ray diffraction analysis confirms single phase monoclinic C2/c formation for every composition, the principal interplanar spacing increases linearly from 2.9503 Å to 3.0034 Å, crystallite size decreases from 32.1 to 16.7 nm, and dislocation density grows nearly four times as x advances to unity. Scanning electron microscopy reveals a progressive transition from large, irregularly agglomerated grains to a finer, more densely packed nanoparticulate microstructure. All M-H loops measured over ±10 kOe identify soft ferromagnetic, multi-domain behavior (S −1 while the coercive field rises from 102.24 to 182.22 G. Impedance measurements (100 Hz - 10 MHz) show that bulk resistance increases ten times over the substitution range, Nyquist plots fit to a two element equivalent circuit of two CPE-resistor pairs in series, and the extracted grain and grain-boundary resistances rise monotonically with x, establishing that Bi3+ incorporation progressively depletes the Fe3+/Fe2+ charge carrier pool. The dielectric constant follows Maxwell-Wagner-Sillars behavior and decreases with both frequency and Bi content, while AC conductivity spectra display a characteristic dual-peak pattern attributed to space-charge polarization at grain boundaries at low frequency and grain-interior Fe hopping at high frequency, both peaks diminishes with increasing Bi content. The correlated structure-property picture presented here establishes the Bi-substituted ZrFe2O5 system as a candidate for compositionally tunable soft-magnetic and dielectric applications.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Structural, Morphological, Magnetic, and Electrical Properties of ZrFe2−xBixO5 Nanoparticles (x = 0, 0.25, 0.50, 0.75 and 1.00) Synthesized via Sol-gel Auto-Combustion
AU  - Avadhut Manage
AU  - Balachandra G. Hegde
AU  - Shidaling Matteppanavar
Y1  - 2026/06/26
PY  - 2026
N1  - https://doi.org/10.11648/j.ajn.20261002.12
DO  - 10.11648/j.ajn.20261002.12
T2  - American Journal of Nanosciences
JF  - American Journal of Nanosciences
JO  - American Journal of Nanosciences
SP  - 52
EP  - 63
PB  - Science Publishing Group
SN  - 2575-4858
UR  - https://doi.org/10.11648/j.ajn.20261002.12
AB  - ZrFe2−xBixO5 (x = 0, 0.25, 0.50, 0.75, 1.00) nanoparticles were synthesized using Sol-gel auto-combustion method and their structural, morphological, magnetic, and frequency-dependent electrical properties were systematically characterized at room temperature. X-ray diffraction analysis confirms single phase monoclinic C2/c formation for every composition, the principal interplanar spacing increases linearly from 2.9503 Å to 3.0034 Å, crystallite size decreases from 32.1 to 16.7 nm, and dislocation density grows nearly four times as x advances to unity. Scanning electron microscopy reveals a progressive transition from large, irregularly agglomerated grains to a finer, more densely packed nanoparticulate microstructure. All M-H loops measured over ±10 kOe identify soft ferromagnetic, multi-domain behavior (S −1 while the coercive field rises from 102.24 to 182.22 G. Impedance measurements (100 Hz - 10 MHz) show that bulk resistance increases ten times over the substitution range, Nyquist plots fit to a two element equivalent circuit of two CPE-resistor pairs in series, and the extracted grain and grain-boundary resistances rise monotonically with x, establishing that Bi3+ incorporation progressively depletes the Fe3+/Fe2+ charge carrier pool. The dielectric constant follows Maxwell-Wagner-Sillars behavior and decreases with both frequency and Bi content, while AC conductivity spectra display a characteristic dual-peak pattern attributed to space-charge polarization at grain boundaries at low frequency and grain-interior Fe hopping at high frequency, both peaks diminishes with increasing Bi content. The correlated structure-property picture presented here establishes the Bi-substituted ZrFe2O5 system as a candidate for compositionally tunable soft-magnetic and dielectric applications.
VL  - 10
IS  - 2
ER  -

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