Synergistic Grain Refinement and Insulating Phase Formation via Zr⁴⁺ Doping for Low-Loss Colossal Permittivity in (In,Nb) Codoped TiO₂ Ceramics

Abstract

Colossal permittivity (In,Nb) codoped TiO₂ ceramics are promising for microelectronic applications but suffer from high low-frequency dielectric loss primarily due to leakage currents across grain boundaries. This work demonstrates that Zr⁴⁺ doping at Ti-sites in (In_0.5N_b0.5)_0.05Ti_0.95O₂ effectively mitigates this issue. A series of (In_0.5N_b0.5)_0.05Ti_0.95‑xZr _x O₂ (x = 0–0.20) ceramics were synthesized via solid-state reaction. Zr⁴⁺ incorporation refines grain size from ∼56.1 μm (undoped) to ∼2.5 μm (x = 0.20) and promotes the precipitation of an insulating ZrTiO₄ secondary phase at grain boundaries for compositions with x ≥ 0.10. These microstructural modifications synergistically enhance the grain boundary resistance, which peaks at 10.50 × 10⁶ Ω·cm for the x = 0.10 composition, nearly an order of magnitude higher than the undoped ceramic. Consequently, the low-frequency dielectric loss is significantly reduced, with the x = 0.10 composition sintered at 1450 °C exhibiting a minimal loss tangent. Complex impedance analysis reveals the introduction of a new interfacial polarization associated with the ZrTiO₄/INTO phase boundaries. XPS analysis confirms that Zr doping suppresses oxygen vacancy concentration without altering the Ti³⁺/Ti⁴⁺ ratio crucial for electron-pinned defect dipoles. The optimized composition (x = 0.10) also shows improved nonlinear coefficient (α = 2.8) and breakdown field (E_b = 530 V/cm), alongside stable low loss (tanδ < 0.05) over a broad temperature range at 1 kHz. This study presents a viable defect-engineering strategy utilizing Zr⁴⁺ doping to achieve low-loss colossal permittivity in (In,Nb) codoped TiO₂-based ceramics for practical applications.

1. Introduction

Colossal permittivity (CP) materials are crucial for advancing next-generation microelectronics, including miniaturized capacitors, high-voltage filters, and energy-storage devices, due to their exceptional ability to store large amounts of electric charge in compact volumes. Among various CP candidates, (In,Nb) codoped TiO₂ (INTO) ceramics have attracted considerable attention for their remarkably high permittivity (ε′, > 10⁴), relatively low dielectric loss (tan δ, < 0.05 at 1 kHz), and good temperature stability. − However, a persistent challenge hindering their practical application is the typically high low-frequency dielectric loss, which is primarily governed by leakage currents across grain boundaries. Therefore, developing effective strategies to suppress this loss is imperative for realizing the full potential of INTO-based dielectrics in high-performance applications.

The origin of CP in INTO ceramics is widely understood to stem from the synergy of two mechanisms. At the atomic scale, the codoping of In³⁺ and Nb⁵⁺ into the TiO₂ lattice induces the formation of complex defect clusters, such as [In³⁺-V _O -Ti³⁺] and [Nb⁵⁺-Ti³⁺] associated with oxygen vacancies and Ti³⁺ ions. These defect clusters act as highly polarizable dipoles that can effectively localize free electrons, preventing long-range charge transport. Under an external electric field, the bound electrons within these defect dipoles can undergo short-range hopping, generating a large local polarization that contributes to the overall high dielectric permittivity. ,− Concurrently, an extrinsic internal barrier layer capacitor (IBLC) effect arises from the electrically heterogeneous microstructure, where semiconducting grains are separated by more insulating grain boundaries. ,− The resistance of these grain boundaries (R_gb) is a critical parameter that directly controls the low-frequency dielectric loss. Consequently, effective loss reduction strategies must focus on optimizing both grain and grain boundary properties. Grain refinement increases the density of grain boundary barriers, impeding long-range charge migration. − More directly, enhancing the intrinsic resistivity of the grain boundaries themselves is a powerful approach to suppress leakage currents and minimize energy dissipation. ,,−

Existing strategies to enhance grain boundary resistance in dielectric ceramics primarily encompass optimizing sintering parameters, introducing secondary insulating phases, and employing chemical doping to modify grain boundary compositions. Among these approaches, chemical doping has demonstrated significant efficacy in regulating grain boundary properties owing to its capacity to tailor defect structures and phase formations. − Specifically, Zr⁴⁺ doping demonstrates efficacy in modifying grain boundary characteristics across diverse titanate-based ceramics, leveraging its inherent chemical stability and tendency to form insulating titanium compounds. − With an ionic radius (0.80 Å) larger than that of Ti⁴⁺ (0.68 Å) and an equivalent high valence state, Zr⁴⁺ substitutes for Ti⁴⁺ sites to refine grain size while concurrently promoting the precipitation of secondary insulating phases such as ZrTiO₄. −

In this work, we systematically investigate the effects of Zr⁴⁺ doping on the microstructure, defect chemistry, and dielectric properties of (In_0.5N_b0.5)_0.05Ti_0.95O₂ ceramics. A series of (In_0.5N_b0.5)_0.05Ti_0.95‑xZr _x O₂ (0 ≤ x ≤ 0.20) compositions were synthesized via solid-state reaction. We demonstrate that Zr⁴⁺ doping effectively mitigates the low-frequency dielectric loss through a synergistic mechanism involving substantial grain refinement, the formation of insulating ZrTiO₄ phase at grain boundaries for x ≥ 0.10, and the suppression of oxygen vacancy concentration. These modifications collectively lead to a dramatic increase in grain boundary resistance and a significant reduction in dielectric loss, while maintaining CP characteristics. The optimized composition exhibits excellent temperature stability, presenting a viable defect-engineering strategy for developing low-loss CP materials for capacitive applications.

2. Experimental Details

The (In_0.5N_b0.5)_0.05Ti_0.95‑xZr _x O₂ (denoted as Zr-INTO, with x = 0.05, 0.10, 0.15, and 0.20, corresponding to Zr05-INTO, Zr10-INTO, Zr15-INTO, and Zr20-INTO, respectively) ceramics were synthesized via a conventional solid-state reaction route. High-purity commercial powders of In₂O₃, Nb₂O₅, TiO₂, and ZrO₂ (99.99%, Aladdin Biochemical Technology Co., Ltd.) were used as starting materials. Stoichiometric amounts of the raw powders were mixed and ball-milled in deionized water for 12 h at 120 rpm. The resultant slurry was dried and subsequently calcined at 1050 °C for 5 h in air. The calcined powder was subjected to a second ball-milling step for 12 h, followed by drying to obtain the final Zr-doped INTO powder. The powder was uniaxially pressed under 180 MPa into green pellets with dimensions of 12 mm in diameter and approximately 1 mm in thickness. The pellets were sintered in air at temperatures ranging from 1350 to 1500 °C for 2 h, with controlled heating and cooling rates of 10 °C/min and 20 °C/min, respectively. For comparison, undoped (In_0.5N_b0.5)_0.05Ti_0.95O₂ (denoted as INTO) ceramics were prepared following identical procedures.

The bulk densities of the sintered ceramics were measured by the Archimedes method using deionized water as the immersion medium. Prior to microstructural observation, the ceramic surfaces were polished and then thermally etched in air at 1150 °C for 30 min. The microstructures of the powder precursors (after calcination and ball milling) and the sintered ceramics were examined using a JEOL JSM-7900F thermal field-emission scanning electron microscope (SEM). The crystal structures and phase compositions were analyzed by X-ray diffraction (XRD) using a Beijing Purkinje XD-2 diffractometer with Cu Kα radiation. The chemical states of elements were investigated by X-ray photoelectron spectroscopy (XPS) on a Thermo Fisher Scientific ESCALAB 250 XI spectrometer equipped with a monochromatic Al Kα X-ray source. The XPS spectra were fitted using a combination of Gaussian–Lorentzian line shapes after Shirley background subtraction with the XPSPEAK software. For electrical measurements, silver electrodes were coated on both surfaces of the polished ceramics and fired at 650 °C for 30 min. The dielectric spectra and complex impedance were measured using an Agilent E4980A LCR meter under an applied voltage of 0.5 V, over a frequency range of 20 Hz to 2 MHz and a temperature range from room temperature to 250 °C. The current density-electric field (J-E) characteristics were evaluated using a Keithley 2410 source measurement unit. The nonlinear coefficient (α) was calculated from the formula α = log­(J₁/J₂)/log­(E₁/E₂), where E₁ and E₂ are the electric fields corresponding to current densities of J₁ = 0.1 mA/cm² and J₂ = 1 mA/cm², respectively. The breakdown field strength (E_b) was defined as the macroscopic average electric field at which the current density reached 1 mA/cm².

3. Results and Discussion

Figure compares the room-temperature dielectric spectra of Zr10-INTO and INTO ceramics sintered from 1350 to 1500 °C. As shown in Figure (a1), the Zr10-INTO ceramics exhibit ε′ consistently above 10³, with the low-frequency ε′ increasing progressively with sintering temperature, reaching approximately 3 × 10⁴ at 1500 °C. However, this value is significantly lower than that of the INTO ceramic sintered at the same temperatures, as shown in Figure (b1). The dielectric loss spectra reveal distinct relaxation behaviors. For Zr10-INTO (Figure (a2)), two clear dielectric relaxations are observed, with one peak located in the 100 Hz-10 kHz range and the other above 1 MHz. The magnitude of the low-frequency tanδ shows a nonmonotonic dependence on sintering temperature, reaching a minimum for the sample sintered at 1450 °C. In contrast, the INTO ceramics (Figure (b2)) also exhibit two relaxations, one below 1 kHz and the other above 1 MHz, but with consistently high low-frequency loss (>0.1) across all temperatures, which increases with sintering temperature. A key observation is that Zr doping modifies the relaxation behavior. The low-frequency relaxation observed in INTO ceramics (below 1 kHz) is attributed to the electrode effect arising from a non-Ohmic contact between the sample and the electrodes. , In Zr10-INTO ceramics, the corresponding electrode relaxation shifts to frequencies below the measured range (<20 Hz), rendering it invisible. Concurrently, Zr doping introduces a new, distinct relaxation peak in the 100 Hz-10 kHz range for Zr10-INTO, which is not observed in INTO. These changes suggest that Zr⁴⁺ substitution alters the underlying defect structures and polarization mechanisms governing the low-frequency response.

1.

Sintering temperature-dependent dielectric spectra of (a) Zr10-INTO and (b) INTO ceramics sintered at 1350–1500 °C. (a1, b1) real permittivity (ε′) and (a2, b2) loss tangent (tanδ), respectively.

Figure presents the room-temperature dielectric spectra of all Zr-INTO ceramics sintered at 1450 °C. All compositions exhibit giant ε′, although the low-frequency ε′ decreases progressively with increasing Zr content x, from >10⁴ at x = 0.05 to ∼10³ at x = 0.20. For Zr05-INTO, a distinct low-frequency relaxation (analogous to that in the INTO ceramics) is evident in the tanδ spectrum. As the doping content increases to x ≥ 0.10, this relaxation shifts to frequencies below the measured range, becoming no longer discernible within the measured frequency range. Concurrently, a new relaxation peak emerges in the 100 Hz-10 kHz range for x ≥ 0.10. The low-frequency tanδ exhibits a nonmonotonic dependence on the Zr content, initially decreasing to a minimum for the x = 0.10 composition and then increasing for x = 0.15 and 0.20.

2.

Zr content-dependent dielectric spectra of all Zr-INTO ceramics sintered at 1450 °C. (a) ε′ and (b) tanδ, respectively.

The phase composition and structural evolution of the Zr-INTO and INTO ceramics sintered at 1450 °C were investigated by XRD. Figure provides the XRD patterns. For INTO and Zr05-INTO, all diffraction peaks correspond to the tetragonal rutile TiO₂ phase (space group P4₂/mnm), indicating phase purity. For the Zr-INTO with higher Zr content (x ≥ 0.10), additional peaks belonging to the orthorhombic ZrTiO₄ phase emerge, with intensity increasing with the Zr content. Rietveld refinement was performed to determine the lattice parameters. Figure describes the Rietveld refinement profiles, and the refined parameters are summarized in Table . As Zr content increases from 0 to 0.15, both a and c parameters expand continuously, confirming the substitution of smaller Ti⁴⁺ (0.68 Å) by larger Zr⁴⁺ (0.80 Å) in the rutile lattice. At x = 0.20, a slight lattice contraction occurs, attributed to the pronounced precipitation of ZrTiO₄ phase which consumes Zr and Ti from the solid solution, likely introducing lattice strain. Quantitative phase analysis reveals ZrTiO₄ mass fractions of ∼ 6.2, 16.2, and 26.0 wt % for x = 0.10, 0.15, and 0.20, respectively. Based on this, the solid solubility limit of Zr in the (In_0.5Nb_0.5)_0.05Ti_0.95O₂ matrix under these conditions is estimated to be ∼ 7–8 mol %. In analogous codoped TiO₂ ceramics, secondary phases that form upon exceeding the dopant solubility limit have been consistently demonstrated to be predominantly located at grain boundaries. ,, Therefore, the ZrTiO₄ phase in the Zr-INTO ceramics is also inferred to primarily resides at the grain boundaries.

3.

XRD patterns of the Zr-INTO and INTO ceramics sintered at 1450 °C.

4.

Rietveld refinement of XRD data for the Zr-INTO and INTO ceramics sintered at 1450 °C.

1. Refined Lattice Parameters of the Zr-INTO and INTO Ceramics Sintered at 1450 °C.

	Sample
Lattice parameter (Å)	x = 0.05	x = 0.10	x = 0.15	x = 0.20	x = 0
a = b	4.603	4.603	4.611	4.601	4.598
c	2.974	2.977	2.986	2.982	2.966

Figure gives the SEM image of the calcined and ball-milled powder for the representative Zr15-INTO, consisting of well-dispersed submicron particles (0.2–1 μm). Figure reveals SEM images of thermally etched surfaces for all Zr-INTO and INTO ceramics sintered at 1450 °C, with corresponding grain size distribution histograms as insets. The microstructure is significantly influenced by Zr content. The INTO ceramic exhibits relatively uniform, oversized grains with an average size of ∼56.1 μm. In contrast, all Zr-INTO ceramics show broader grain size distributions and progressive grain refinement. The average grain size decreases to ∼9.7, 7.1, 3.5, and 2.5 μm for x = 0.05, 0.10, 0.15, and 0.20, respectively, indicating effective inhibition of grain growth by Zr doping. For the ceramics with x = 0.15 and 0.20, granular or rod-like features with lengths ranging from several hundred nanometers to 2 μm are observed between the grains. To identify the composition of these features, EDS point analysis was performed on the x = 0.15 ceramic. As shown in Figure , these features contain a high Zr content. Combined with the XRD results, these features are identified as the ZrTiO₄ phase. The grain refinement induced by Zr doping in the Zr-INTO ceramics originates from two synergistic mechanisms: at lower Zr concentrations, the solute drag effect due to lattice strain from Zr⁴⁺ substitution impedes grain boundary migration; for x ≥ 0.10, the Zener pinning effect by insulating ZrTiO₄ particles precipitated at grain boundaries further suppresses grain coarsening. Furthermore, porosity is observed to increase with higher Zr doping levels. As summarized in Table , while the theoretical density (calculated from refined lattice parameters, neglecting secondary phases) increases with x, the measured bulk density shows a decreasing trend, consistent with the increased porosity observed via SEM. This increase in porosity is caused by the suppression of grain growth through Zr doping, which leads to the formation of numerous pores between grains.

5.

SEM image of the Zr10-INTO powder after calcination and ball milling.

6.

SEM image of thermal etching the Zr-INTO and INTO ceramics sintered at 1450 °C. (a) Zr05-INTO, (b) Zr10-INTO, (c) Zr15-INTO, (d) Zr20-INTO, and (e) INTO, respectively. The inset shows the grain size distribution.

7.

EDS point of the Zr15-INTO ceramic sintered at 1450 °C.

2. Densities of the Zr-INTO and INTO Ceramics Sintered at 1450 °C.

Sample	Density (g/cm3)	Theoretical density (g/cm3)	Relative theoretical density (%)
x = 0.05	4.231	4.472	94.6
x = 0.10	4.220	4.582	92.1
x = 0.15	4.167	4.666	89.3
x = 0.20	4.089	4.805	85.1
x = 0	4.170	4.380	95.2

The electrical heterogeneity of codoped TiO₂ ceramics is typically modeled using an equivalent circuit comprising series-connected RC units, representing contributions from grains, grain boundaries, and other interfaces. , To comprehensively understand the impact of Zr doping, complex impedance spectra for all Zr-INTO and INTO ceramics sintered at 1450 °C were analyzed, as displayed in Figure . Equivalent circuit models were tailored based on the discernible semicircular arcs within the measured frequency range. For INTO and Zr05-INTO, only one dominant arc is observed, which is modeled by a single parallel R_gbC_gb element in series with a grain resistance R _g, the latter indicated by the nonzero intercept on the Z′ axis in the high-frequency region (inset, Figure a). In contrast, the Zr-INTO ceramics with higher Zr content (x ≥ 0.10) exhibit two clear arcs. The low-frequency arc corresponds to the grain boundary response, while a new intermediate-frequency arc emerges. This new arc is associated with the distinct dielectric relaxation peak below 10 kHz observed in the loss spectra, necessitating an additional parallel R _x C _x element in the equivalent circuit (inset, Figure b). The high-frequency response of the grains (R_gb) is again indicated by the nonzero intercept on the Z′ axis. The fitted resistance parameters for all ceramics are summarized in Table . Zr doping markedly alters the electrical landscape. R _g increases monotonically with Zr content, from 43.29 Ω·cm (INTO) to 450.8 Ω·cm (Zr20-INTO). More dramatically, R_gb first surges to a maximum of 10.50 × 10⁶ Ω·cm for Zr10-INTO, which is nearly an order of magnitude higher than that of the undoped ceramic, and then decrease to 2.74 × 10⁶ Ω·cm for Zr20-INTO. The newly introduced resistance R _x also increases significantly with Zr content, reaching 45.92 × 10⁵ Ω·cm for Zr20-INTO. To further deconvolute the electrical contributions and investigate their thermal activation behaviors, temperature-dependent impedance spectroscopy was performed on Zr10-INTO ceramic, as presented in Figure . Notably, the arc corresponding to the R _x C _x element became indistinguishable at temperatures above 60 °C. The fitted R _g, R _x , and R_gb values (Table ) all decrease with increasing temperature, confirming their thermally activated conduction nature. The activation energies (E _a) for these processes, extracted from Arrhenius plots of conductivity, are approximately 0.021, 0.139, and 0.59 eV for R _g, R _x , and R_gb, respectively. The very low E _a for R _g (∼0.02 eV) is characteristic of electron hopping between Ti³⁺ and Ti⁴⁺ within the semiconducting grains. The intermediate E _a for R _x suggests a polarization process related to the ZrTiO₄/Zr-INTO phase boundaries, possibly involving trapped charge carriers at these interfaces. The highest E _a for R_gb is consistent with conduction across grain boundary barriers, often associated with oxygen vacancy migration or emission/capture at deep trap states. These distinct activation energies provide strong, property-based evidence for the separation of electrical components. They confirm that the high-frequency relaxation (>1 MHz) is attributed to interfacial polarization at the grain/grain-boundary interfaces, while the new intermediate-frequency peak (<10 kHz) is associated with polarization at the ZrTiO₄/INTO phase boundaries.

8.

Complex impedance spectra and equivalent circuit of the Zr-INTO and INTO ceramics sintered at 1450 °C.

3. Fitted Resistance Parameters of the Zr-INTO and INTO Ceramics Sintered at 1450 °C.

	Sample
	x = 0.00	x = 0.05	x = 0.10	x = 0.15	x = 0.20
R g /Ω·cm	43.29	48.53	71.5	262.6	450.8
R x /105 Ω·cm			6.86	17.45	45.92
R gb /106 Ω·cm	1.38	3.94	10.50	7.46	2.74

9.

(a, b) Temperature-dependent complex impedance spectra and (c) Arrhenius plot of resistivity for the Zr10-INTO ceramic sintered at 1450 °C.

4. Temperature-Dependent Fitted Resistance Parameters of the Zr10-INTO Ceramics Sintered at 1450 °C.

	Temperature/°C
	25	60	100
R g /Ω·cm	71.5	59.4	50.7
R x /105 Ω·cm	6.86	3.93
R gb /106 Ω·cm	10.50	0.97	0.11

To elucidate the origin of the colossal permittivity, XPS was employed to investigate the chemical states. Figure depicts the results for the Zr10-INTO and INTO ceramics sintered at 1450 °C. For Zr10-INTO, the Zr 3d spectrum exhibits characteristic doublet peaks at binding energies of 181.8 eV (3d_5/2) and 184.2 eV (3d_3/2), confirming the exclusive presence of Zr⁴⁺. Parallel analyses confirmed that In and Nb maintain +3 and +5 oxidation states (not described in figures), respectively, in both compositions. Detailed deconvolution of the Ti 2p spectrum reveals the coexistence of Ti⁴⁺ and Ti³⁺ states. Quantitative analysis shows the Ti³⁺ concentration is ∼5.7% of the total titanium content in the Zr10-INTO ceramic, a value that exhibits negligible variation from the 5.5% Ti³⁺ concentration observed in the undoped counterpart. This remarkable consistency suggests that Zr incorporation does not significantly alter the distribution of titanium valence states in INTO ceramics. Analysis of the O 1s spectrum provides crucial insight into the oxygen defect chemistry. Spectral fitting reveals a substantial reduction in oxygen vacancy concentration from 25.1% in the undoped ceramic to 20.9% in the Zr10-INTO ceramic, demonstrating that Zr incorporation significantly suppresses oxygen vacancies, likely due to lattice expansion raising their formation energy.

10.

XPS spectra of the (a) Zr10-INTO and (b) INTO ceramics sintered at 1450 °C.

The integration of impedance and XPS results clarifies the mechanisms behind the dielectric evolution. The increase in R _g with Zr content is attributed to the dilution of the Ti³⁺/Ti⁴⁺ conductive network as Zr⁴⁺ occupies Ti sites, reducing carrier concentration and mobility. The initial surge in R_gb is ascribed to the synergistic effect of increased grain boundary density from grain refinement and, more importantly, the blocking effect of precipitated insulating ZrTiO₄ phases at the boundaries. While the decrease in R_gb for x ≥ 0.15 correlates with the increased porosity observed via SEM, which may disrupt the continuity of the insulating boundary network. The preserved Ti³⁺ concentration maintains the source of localized dipole polarizability essential for intrinsic high permittivity. However, the overall decrease in permittivity with increasing Zr content stems from the attenuated contributions of both primary polarization mechanisms. For the EPDD mechanism, the reduced spatial density of Ti³⁺ sites and the lower oxygen vacancy concentration diminish the effective dipole density. For the IBLC effect, the precipitation of the insulating ZrTiO₄ secondary phase replaces part of the semiconducting Zr-INTO matrix, reducing the effective area for interfacial polarization at the primary Zr-INTO/grain boundary interfaces. Although the ZrTiO₄/Zr-INTO interface introduces a new dielectric relaxation, its contribution to the total static permittivity is less significant compared to the attenuation of the dominant IBLC effect. Concurrently, increased porosity between grains further reduces the overall permittivity. The reduction in low-frequency loss is explained by the shift of the electrode/sample interface relaxation to lower frequencies, caused by the drastically increased bulk resistivity (particularly R_gb), which limits charge carrier flux to the interface and prolongs the relaxation time (τ, where f _max ∝ 1/τ). The nonmonotonic behavior of the low-frequency loss at high Zr contents (x ≥ 0.15) correlates directly with the nonmonotonic trend of R_gb.

The nonlinear J-E characteristics of all Zr-INTO and INTO ceramics sintered at 1450 °C are presented in Figure . All ceramics exhibit distinct non-Ohmic behavior, characteristic of an IBLC structure. Both α and E_b are summarized in Table . These parameters exhibit a nonmonotonic dependence on Zr content, with their optimal values achieved at x = 0.10 (α = 2.8, E_b = 530 V/cm). This enhancement is directly correlated with the microstructural and electrical evolution. For Zr10-INTO, grain refinement increases the volumetric grain boundary area. These boundaries, along with the precipitated ZrTiO₄ phases, act as additional barriers that prolong the breakdown path, elevating E_b. Simultaneously, the peak R_gb effectively suppresses leakage currents and strengthens the Schottky-type barriers, leading to a higher α. The degradation of α and E_b at x ≥ 0.15 coincides with the reduction in R_gb and pronounced increase in porosity. Excessive porosity disrupts the continuity of grain boundary networks, creating localized current pathways and electric field concentrations that prematurely trigger breakdown, while the decline in R_gb weakens the barrier effect.

11.

Nonlinear J-E characteristics of the Zr-INTO and INTO ceramics sintered at 1450 °C.

5. Nonlinear Coefficient (α) and Breakdown Electric Field (E_b) of the Zr-INTO and INTO Ceramics Sintered at 1450 °C.

Sample	α	Eb (V/cm)
x = 0.05	2.1	270
x = 0.10	2.2	300
x = 0.15	2.8	530
x = 0.20	2.5	370
x = 0	2.5	350

To comprehensively assess the dielectric performance of the Zr10-INTO ceramic sintered at 1450 °C, its temperature-dependent behavior was evaluated. Figure describes the temperature-dependent dielectric spectra for this composition. At room temperature, two distinct dielectric relaxations are observed. As the temperature increases, a third relaxation emerges below 1 kHz. All three relaxation peaks shift systematically toward higher frequencies with increasing temperature, confirming the thermally activated nature of the underlying charge transport processes. Figure details the thermal evolution of ε′ and tanδ at selected frequencies. A significant increase in ε′ is observed with rising temperature. This enhancement is attributed to increased charge carrier mobility and intensified contributions from interfacial polarization, particularly associated with the low-frequency relaxation visible in Figure . As the measurement frequency increases, the characteristic temperatures corresponding to these relaxations shift to higher values, providing further evidence of their thermally activated character. Notably, the tanδ exhibits excellent stability within specific temperature windows at lower frequencies. At 100 Hz, tan δ remains below 0.05 from below room temperature up to 115 °C. At 1 kHz, tan δ is maintained below 0.05 across a wide temperature range from 40 to 155 °C. These results demonstrate the effectiveness of Zr doping in preserving low dielectric loss under elevated temperature conditions, a crucial property for practical capacitor applications where operational heating is inevitable.

12.

Temperature-dependent dielectric spectra of the Zr10-INTO ceramic sintered at 1450 °C. (a) ε′ and (b) tanδ, respectively.

13.

Thermal evolution of (a) ε′ and (b) tanδ at selected frequencies for the Zr10-INTO ceramic sintered at 1450 °C.

4. Conclusion

In this work, we demonstrate that Zr⁴⁺ doping in (In_0.5Nb_0.5)_0.05Ti_0.95O₂ ceramics achieves a synergistic combination of grain refinement and the formation of an insulating ZrTiO₄ secondary phase at grain boundaries, which dramatically enhances the grain boundary resistance. The optimized composition, x = 0.10 sintered at 1450 °C, exhibits a relative low low-frequency dielectric loss (tanδ < 0.05 at 1 kHz) while maintaining a colossal permittivity (ε′ > 10⁴). This well performance is attributed to the optimal balance among grain size, secondary phase content, and microstructural densification, which collectively maximize R_gb to 10.50 × 10⁶ Ω·cm. Furthermore, XPS analysis confirms that Zr doping suppresses oxygen vacancy concentration without compromising the Ti³⁺/Ti⁴⁺ ratio essential for electron-pinned defect dipoles. This work provides a viable defect-engineering strategy for achieving low-loss colossal permittivity in (In,Nb) codoped TiO₂-based ceramics, highlighting the critical role of grain boundary engineering in optimizing the performance of giant dielectric materials for practical capacitive applications.

Data will be made available on request.

Panpan Xu: Methodology, Investigation, Formal analysis, Validation, Visualization, Data Curation, Writing - Original Draft. Xiaole Qiu: Formal Analysis, Funding Acquisition, Methodology, Supervision. Bing Sun: Formal Analysis, Funding Acquisition, Methodology, Supervision. Li Sun: Formal Analysis, Methodology, Supervision. Ensi Cao: Formal Analysis, Funding Acquisition, Methodology, Supervision. Wentao Hao: Conceptualization, Resources, Funding Acquisition, Writing - Review and Editing.

The authors declare no competing financial interest.