Effect of sintering conditions on colossal dielectric properties of (Tb1/2Nb1/2)0.01Ti0.99O2 ceramics

In this study, we investigated various sintering temperatures (1200 °C−1450 °C) and durations (2–6 h) conditions for preparing (Tb1/2Nb1/2)0.01Ti0.99O2 (TNTO) ceramics. By employing high sintering temperatures (≥1350 °C) and extended sintering durations (≥4 h), we successfully achieved ultra–high dielectric permittivity values (ε′ ∼ 2.2 − 4.1 × 104) and remarkably low loss tangent values (∼0.025−0.079). Remarkably, the temperature coefficient of the TNTO ceramic, sintered at 1350 °C, exhibited exceptional stability, maintaining a value of approximately 15% even at 200 °C. Additionally, we examined the phase structure and microstructure of the TNTO ceramics to gain insights into their colossal permittivity (CP) behavior. The analysis revealed the presence of rutile TiO2 and TbNbTiO6 phases, and the ceramics exhibited a high–density microstructure under high–temperature sintering conditions. The impedance spectroscopy analysis revealed that the primary contributor to the observed CP behavior was the interfacial polarization mechanism. The observed increase in the ε′ value, correlated with the enlargement of the average grain size, can be attributed to the effect of the internal barrier layer capacitor. However, when the sintering time ≥4 h, the grain size did not significantly affect the ε′ value, possibly due to reaching the maximum capacity of electron production for the interfacial polarization process (i.e., the maximum intensity of polarizability). This study provides valuable insights into optimizing the sintering conditions for TNTO ceramics and related compounds, laying the groundwork for the development of a new CP oxide suitable for practical applications.

A newly proposed CP oxide, INTO ceramic, was achieved through the co-doping of TiO 2 with In +3 and Nb +5 ions.This material exhibits an extraordinary frequency and temperature-independent colossal ε′ exceeding 10 4 , coupled with an exceptionally low tanδ of less than 0.05, across a broad temperature spectrum ranging from 80 to 450 K [11].The defect complex clusters, characterized by a triangular configuration denoted as ' + + In V Ti ( ) ', serve distinct roles in the electron dynamics.The electrons induced from the diamond-shaped defects are highly localized by the triangular-shaped defect, resulting in CP performance.This process is recognized as the electron-pinned defect-dipoles (EPDD) mechanism.
Consequently, co-doped TiO 2 systems with various co-dopant elements such as Al +3 +Nb +5 [12], Bi +3 +Nb +5 [13], Ga +3 +Nb +5 [14], Al +3 +Ta +5 [15], Ga +3 +Ta +5 [16], and In +3 +Ta +5 [17] among others, have been further investigated.In addition to the EPDD effect, the CP behavior in these co-doped TiO 2 ceramics is attributed to various effects, including the internal barrier layer capacitor (IBLC) [18,19], surface barrier layer capacitor (SBLC) [14], and electron hopping mechanism [20].Research on TiO 2 ceramics co-doped with Al +3 +Nb +5 and Ga +3 +Nb +5 [12,14] indicated that the presence of Al +3 ions in the interstitial sites of the rutile structure, along with the slight distortion of the defect structure caused by Ga +3 dopants, contributes to the development of unstable electron localization within the EPDD structure.This phenomenon is attributed to the significantly smaller ionic radius of Al +3 and the slightly larger ionic radius of Ga +3 , compared to the ionic radius of Ti +4 .The respective ionic radii (r 6 ) are 53.5 pm for Al +3 , 60.5 pm for Ti +4 , and 62.0 pm for Ga +3 .Therefore, when substituting at the host Ti site, accounting for the ionic radius of trivalent dopants is of paramount importance.Large ionic radius dopants like lanthanide (Ln) group elements, as previously reported in Dy +3 +Nb +5 [21], Er +3 +Nb +5 [22], La +3 +Nb +5 [20], La +3 +Ta +5 [23], Sm +3 +Ta +5 [24], and Nd +3 +Ta +5 [25] co-doped TiO 2 ceramics, are good candidates to ensure tight substitution of the Ti site by trivalent dopants.These co-doped TiO 2 systems exhibited outstanding dielectric performance, highlighting the need for further investigation of a new system related to Ln dopants.This will facilitate a deeper understanding of the origins of their dielectric behavior and aid in optimizing the sintering conditions for practical applications.
In this study, we selected Tb and Nb elements as dopants to replace positions at the Ti site within the rutile TiO 2 structure.Notably, the Tb element exhibits two oxidation states, Tb +3 and Tb +4 , with one functioning as an acceptor ion and the other as an isovalent dopant within the TiO 2 structure.According to the IBLC model, the mean grain size has a significant influence on the ε′ value [2], a factor that can be fine-tuned through modifications in the preparation methodology, including adjusting the particle size of the initial materials and enhancing the sintering process.Consequently, our research focuses on examining the influences of sintering temperature and duration on the dielectric properties, designating a temperature range of 1200 °C-1450 °C as the sintering conditions for this investigation.Furthermore, to investigate the influence of sintering time on the properties of TNTO ceramics, we conducted experiments with sintering durations of 2, 4, and 6 h at a constant temperature of 1450 °C.Furthermore, we have analyzed the phase structure and microstructure of all sintered ceramics.Subsequently, we have investigated their dielectric properties and impedance spectra (IS).Notably, we have achieved high ε′ (>10 4 ) and low tanδ (<0.1) in this co-doped system sintered at high temperatures (1350 °C) and for a long duration (4 h).A detailed discussion on the origin of the dielectric behavior is provided.

Experimental details
(Tb 1/2 Nb 1/2 ) 0.01 Ti 0.99 O 2 (TNTO) ceramics were synthesized using the solid-state reaction (SSR) method, with TiO 2 (99.9% purity, St Louis, MO, USA), Tb 4 O 7 (99.95%purity, NanoAmor, Texus, USA), and Nb 2 O 5 (99.99% purity, St Louis, MO, USA) as starting materials.The starting materials were mixed through a wet ball-milling process, employing ethanol as the mixing medium.The resulting mixture was dried at 80 °C to remove ethanol and obtain dried TNTO powder.The powder was then uniaxially pressed into pellets with a diameter of 9.5 mm and a thickness of approximately 1.3 mm at a pressure of 180 MPa.Subsequently, the TNTO pellets were subjected to different sintering temperatures (1200-1450 °C) for 4 h, and 1450 °C with varying sintering times (2-6 h).The densities of all the sintered ceramics were measured using the Archimedes method.
X-ray diffractometry (XRD, PANalytical, EMPYREAN) and scanning electron microscopy (SEM, SEC, SNE-4500 M) were used to investigate the phase structure and surface morphologies of the TNTO ceramics.Before measuring the dielectric properties, the TNTO ceramics were coated with Ag paint and then evaluated at room temperature (RT) across the frequency range of 40 to 10 6 Hz using an impedance analyzer (KEYSIGHT E4990A).The dielectric properties as a function of temperature were measured in the range of −20 to 150 °C using an environmental chamber (ESPEC, SH-222 model).

Results and discussion
Figure 1 illustrates the XRD results of TNTO ceramics sintered under various temperature/time conditions.The analysis confirmed the presence of a tetragonal structure, corresponding to the rutile TiO 2 phase with P4 2 /mnm space group (JCPDS 21-1276) in all sintering conditions.The lattice constants (a and c) for this tetragonal structure were calculated and listed in table 1.With the exception of the 1200 °C condition, the a and c values for all sintering ceramics were larger than the reference lattice constants of TiO 2 .It was observed that as the sintering temperature increased, the a and c values tended to slightly increase as well, suggesting the potential substitution of the Ti site by the co-dopants (Tb and Nb), as anticipated.The higher sintering temperature likely Table 1.Lattice constant, mean grain size, relative density, e¢ value, and tanδ value at 1 kHz and RT for TNTO ceramics sintered at various conditions.
Figure 2 illustrates the surface morphologies of the TNTO ceramics sintered at various temperatures.The TNTO ceramics sintered at 1200 °C-1300 °C exhibited a porous ceramic structure, corresponding to their relative densities that lower than 90%, as summarized in table 1.As the sintering temperature increased, the pore content decreased.Notably, at higher sintering temperatures (1350 °C-1450 °C), the TNTO ceramic's microstructure showed no pores with relative densities higher than 98%, as observed in figures 2(d)−(g), indicating a highly compacted microstructure.The overall results showed that the relative density increased with increasing the sintering temperature.The mean grain size of the TNTO ceramics sintered at different temperatures was evaluated and listed in table 1. Increasing the sintering temperature resulted in an enlargement of the mean grain size in the TNTO ceramic [27].
Figure 3 shows the surface morphologies of the TNTO ceramics sintered at 1450 °C over varying sintering durations.A highly dense microstructure was consistently observed, with a relative density exceeding 95% under all sintering time conditions.As summarized in table 1, the mean grain size exhibited a trend of increase with extended sintering durations [28].This extended period of sintering allows for more significant grain growth, consequently enhancing the grain size.
According to the IBLC model, the grain size of a ceramic typically influences its dielectric properties, as observed in previous studies on CCTO ceramics [29] and some co-doped TiO 2 systems [27,30].Therefore, it is important to study the correlation between the grain size and dielectric properties to describe the origin of the CP of the TNTO ceramics.To explore the impact of the microstructure-closely tied to varying sintering conditions-on the dielectric properties of TNTO ceramics, we conducted dielectric property analyses at R), within the frequency range of 40 to 10 6 Hz.
When considering the dielectric properties and sintering temperature conditions, as depicted in figure 4(a), two distinct dielectric property groups can be clearly distinguished.Firstly, the non-colossal dielectric properties (non-CDP properties) exhibit low ε′ (<10 4 ) and high tanδ (>0.1) for the 1200 °C-1300 °C condition.Secondly, the colossal dielectric properties (CDP properties) display high ε′ (>10 4 ) and low tanδ (<0.1) for the 1350 °C-1450 °C condition.Taking into account the mean grain size data in table 1, it appears that both ε′ and the mean grain size increased with an increase in sintering temperature.However, this correlation does not manifest as a linear relationship.This suggests that in addition to the IBLC effect, other factors such as SBLC or non-Ohmic sample-electrode interactions might be influencing the dielectric response at RT.
Figure 5 illustrates the frequency dependence of the dielectric properties for the TNTO ceramics under different sintering temperatures.The non-CDP materials (sintered at 1200 °C-1300 °C) demonstrates a significant frequency-dependent ε′ value.In contrast, the CDP materials (sintered at 1350 °C-1450 °C) exhibits a highly frequency-stable ε′ value.Below a frequency of approximately 10 5 Hz.The tanδ values of the non-CDP materials are higher compared to those of the CDP materials.These findings suggest that the TNTO ceramics sintered at temperatures 1350 °C delivers satisfactory dielectric performance, whereas sintering at lower temperatures ( 1300 °C) leads to unsatisfactory dielectric performance probably due to the presence of pores in the TNTO ceramic's microstructure.
To further investigate the electrical response inside the TNTO ceramics sintered at different temperatures, impedance spectroscopy (IS) was employed, as shown in figure 6.For the non-CDP materials, semicircular arc sections (at 40-10 6 Hz) and zero-intercept plots at high frequencies (>10 6 Hz) were presented via arc lines, as seen in the IS plot in figure 6(a) and its inset.These semi-circular arcs signify an exceptionally high resistivity (ρ >10 6 Ω•cm), attributable to the insulating grain boundaries (GB) and/or an insulating surface layer.Moreover, the observation of the zero-intercept at high frequencies, as shown in the inset in figure 6(a), indicates the absence of an electrical response from semiconducting grains (G) with low ρ.In other words, this may suggest that a high ρ value is detected in the G region, which contains fewer semiconducting grains.This might be due to the presence of either no or a very low concentration of induced electrons caused by the Nb dopant, resulting in the absence of a non-zero intercept, which would typically signify a response from insulating Gs.Consequently, low ε′ values are observed due to weakened interfacial polarization at the GBs, which results from a small amount of free electrons in the insulating Gs.However, the observed increase in ε′ with increasing sintering temperature in the non-CDP materials could be attributed to the extrinsic (IBLC and/or SBLC) and intrinsic mechanism, resulting from the defect clusters induced by nominal dopant substitutions, such as • and ¢ Ti Ti are generated when TiO 2 is substituted by Nb in defect reactions (1) and (2) [11,31], and by Tb in defect reaction (3) [11,32] .
Tb element can exhibit two oxidation states: Tb +3 and Tb +4 .In the case of Tb +3 ions, an oxygen vacancy (V O •• ) is generated, as described in question (3).In the CDP materials, very large semicircular arcs (at 40−10 6 Hz) and small deviated semicircular arcs at high frequencies (∼10 6 Hz) were observed, as seen in figure 6(b) and its inset, respectively.This indicates that very high and low ρ parts contribute to their electrical responses at RT. Based on the microstructure observed in the SEM images in figures 2(d)-(f), it can be inferred that the markedly low ρ value, which corresponds to the semiconducting part, can be attributed to the G response, while the extremely high ρ value originates from the electrical response of the insulating GB and/or surface layer.These very high ρ values at near RT are similar to reports on Dy +3 +Nb +5 [21], Gd +3 +Nb +5 [33], and V +3 +Ta +5 [27] co-doped TiO 2 .Furthermore, for the G responses, as shown in the inset in figure 6(b), it is difficult to estimate their exact grain resistivity (ρ G ) value, but their ρ G values can be estimated to be approximately in the order of 10 2 Ω•cm.The presence of regions with low resistivity (indicative of semiconducting G response) and areas with high resistivity (denoting insulating components) in the TNTO ceramics hints at a prevalent interfacial polarization mechanism in ceramics sintered at temperatures ranging from 1350 to 1450 °C, leading to the emergence of colossal ε′ values.Regarding the phenomenon of the existence of low ρ G with enhanced sintering temperature compared to the non-CDP materials, it can be explained by the increased induced free electrons due to Ti +4 substitution by the pentavalent Nb +5 ion, as expressed in the defect reactions (1) and (2).As the sintering temperature increased, there was a higher availability of energy to facilitate better substitution.Consequently, a higher content of Nb dopant was likely to replace the Ti site, resulting in an increased production of electrons and lower ρ G values.This outcome can enhance the interfacial polarization process and promote an increase in the ε′ value.On the other hand, the enhanced ε′ value can be attributed to the evolution of the microstructure.By considering the evaluated mean grain size in table 1 and the SEM image in figure 2, it can be noted that a rise in the ε′ value is associated with an increase in the mean grain size of the TNTO ceramic, a consequence of elevated sintering temperatures.This finding can also be explained by the IBLC model, as expressed in equation (4) [2]: where e ¢ , gb d , g and d gb are the dielectric constant of the GB, the mean grain size, and the thickness of the GB, respectively, when d g ?d .
gb It can be observed that the microstructural changes in TNTO ceramics, such as the enhancement of the mean grain size and the presence of highly dense grains without pores, contribute to the increase in the ε′ value with the positive adjustment of the sintering temperature.
In the IS study, for the resistivity values of insulating parts (ρ insulating ), it is difficult to estimate due to the incomplete semicircular arc.However, in figure 6(c), the ρ insulating of the CDP materials seems to be larger than that of the non-CDP materials.This finding could elucidate why the tanδ values of the CDP materials are lower compared to those of the non-CDP materials.Electron motion between the adjacent grains can be impeded by a high insulating barrier.The greater the ρ insulating of the insulating part, the more restricted the free electron movement becomes, leading to lower tanδ values [21,27].
The study of the sintering duration effect involved a comparative analysis of the dielectric properties of TNTO ceramics sintered at 1450 °C under different sintering durations, as presented in figure 4(b).Figure 7 presents the ε′ and tanδ values at RT for the TNTO ceramics sintered for different durations over the frequency range from 40 to 10 6 Hz.Noticeably, a slightly varied colossal ε′ value with frequencies was observed in all ceramics.Meanwhile, in figure 7(b), tanδ peaks were also observed in all ceramics, indicating the appearance of dielectric relaxation.It was observed that the ε′ value tended to increase as the sintering time extended from 2 to 4 h.For sintering times 4 h, there were no significant variations in their ε′ values.Based on the SEM images depicted in figures 3(a)-(c) and the calculated mean grain size listed in table 1, it was noted that the mean grain size increased with the extended sintering time.Particularly, the mean grain size of the ceramic sintered for 6 h displayed a significant increase.However, the ε′ values of the ceramics sintered at 4 and 6 h conditions were close together.Therefore, it can be inferred that the effect of grain size might not be the only contributing factor for the ceramic sintered for 4 h.This issue will be discussed in a later section.
To analyze the electrical responses in the TNTO ceramics sintered over various durations, it is essential to examine the IS plot, as illustrated in figure 8.The high ρ (insulating part) of large semicircular arcs (ρ insulating ) in figure 8(a), and the low ρ (semiconducting part) of nominal distorted arcs (ρ G ) at high frequencies (∼10 6 Hz) in figures 8(b)-(c), were observed in all ceramics.Thus, the interfacial polarization can be induced alongside the insulating part under an applied electric field [21,27,33].Although the ρ G value is difficult to evaluate due to the overlapping semicircular arcs, they can be primarily approximated to be in the order of 10 3 Ω•cm and 10 2 Ω•cm for the ceramics sintered for 2 h and 4-6 h conditions, respectively.It is evident that higher ε′ values can be achieved in the ceramics sintered for 4 and 6 h compared to the ceramic sintered for 2 h.This can be attributed to the lower ρ G values of the TNTO ceramics sintered for 4 and 6 h, compared to the TNTO ceramic sintered for 2 h.This may be a consequence of the extended duration allowing for more substantial substitution of Nb +5 ions into the Ti +4 sites, which facilitates the generation of free electrons, as demonstrated by defect reactions (1) and (2).Furthermore, the extended duration of the sintering process could potentially create more oxygen vacancies, thereby producing a higher number of electrons.As the sintering duration increased from 2 to 4 h, the ε′ value increased.However, beyond the sintering time of 4 h (from 4 to 6 h), the ε′ values of the ceramic sintered for 4 and 6 h are nearly the same in value even though the mean grain size significantly increased.This suggests that the grain size effect alone cannot comprehensively explain the dielectric properties of the TNTO ceramics sintered at 1450 °C for durations of 4 h.At this point, the intensity of the total interfacial polarizations had reached its saturation point (i.e., there was no longer an increase in induced electrons to create the interfacial polarization process), resulting in similar ε′ values in both the ceramics sintered for 4 and 6 h.Therefore, although extending the sintering time can affect grain growth, the resultant grain size effect cannot fully account for the ε′ value for the ceramics sintered for 4 h.However, the effect of grain size remained applicable for sintering times 4 h.Now it is evident that the interfacial polarization mechanism is the primary contributor to inducing CP properties at RT in the TNTO ceramics.Based on the investigations of the effect of sintering temperature and time on the dielectric properties of TNTO ceramics, to achieve the CDP ceramic, the INTO ceramic should be sintered at high temperatures (1350 °C) with an extended duration (4 h) to promote the formation of semiconducting G, thereby facilitating a sufficient interfacial polarization process.Conversely, at lower sintering temperatures where the interfacial polarization process cannot occur in the TNTO ceramics, other factors may influence the dielectric properties of TNTO ceramics, including the effects of surface layer and/or defect structures.However, these effects are not the primary contributors.Nevertheless, this aspect should be further investigated in future studies.
Although optimal CP properties can be achieved by modifying the sintering temperatures, in addition to the CP properties and low tanδ, the temperature dependence of the εε′-particularly at high temperatures-is another vital factor in selecting dielectric materials for capacitor applications.Consequently, the temperature dependence of the ε′ and tanδ at 1 kHz for the TNTO ceramics, which can exhibit CP behavior, are illustrated in figure 9 and its respective insets.As depicted in figure 9(a), the ε′ increased as the sintering temperature rose from 1350 to 1450 °C over the measured temperature range.A similar trend is noted with extended sintering time, as illustrated in figure 9(b).Despite these variations, all the ceramics demonstrated CP properties within the evaluated temperatures.However, as indicated in the insets of figures 9(a) and (b), not all the ceramics examined managed to achieve a low tanδ.The tanδ of some ceramics increased significantly with a rise in temperature, rendering them unsuitable for capacitor applications.
Unfortunately, high-performance CP properties cannot be attained in ceramics sintered at 1400 and 1450 °C for 4 ho.Moreover, the ε′ of these ceramics exhibited a significant dependency on temperature.The fluctuation percentages in the ε′ values at high temperatures, relative to RT, were calculated.At 1 kHz and 200 °C (the maximum temperature consideration for X9R capacitor), the dielectric constant altered by 15%, 52%, and 28% for the ceramics sintered at 1350, 1400, and 1450 °C for 4 h, respectively.Fluctuations of 27% and 22% were recorded for the ceramic sintered at 1450 °C for durations of 2 and 6 h, respectively.Considering at 150 °C (the maximum temperature stipulated for X8R capacitors), the observed variations were 4%, 38%, 14%, 13%, and 9% for these ceramics, respectively.Note that both X9R and X8R capacitors maintain a fluctuation percentage within a window of ±15%.Sintering at incrementally higher temperatures led to deteriorating CP properties at high temperatures, attributed to a substantial increase in the tanδ and notable variations in the ε′ with temperature.This study offers crucial guidance for optimizing high-performance CP properties.

Conclusions
All TNTO ceramics, regardless of the different sintering conditions used, encompassed both the rutile phase and a secondary phase of TbNbTiO 6 .Both the mean grain size and the ε′ value of TNTO ceramics increased with a rise in the sintering temperature.The heightened ε′ value, which is correlated with a larger mean grain size, can be precisely delineated by the IBLC model, except in the ceramics sintered at 1200 °C-1300 °C, where the interfacial polarization process was either diminished or absent.Notably, CP properties become evident at sintering temperatures of 1350 °C.In relation to the study on the impact of sintering time, there was a noticeable increase in the mean grain size with extended sintering durations, and a concurrent tendency for the ε′ value to increase as well.However, when the sintering time was 4 h, the ε′ value stabilized, likely as a result of the saturation of the interfacial polarization process.It was advised to sinter the TNTO ceramics at temperatures of 1350 °C and for a duration of 4 h to achieve CP properties.Nevertheless, when taking into account the three critical factors for selecting the primary CP material utilized in capacitors, the optimized condition was identified as 1350 °C for a duration of 4 h.Additionally, other aspects like surface layer effects and/or defect structures within TNTO ceramics could potentially influence its properties.Further research is warranted to delve deeper into understanding the sources of the dielectric properties of TNTO ceramics.

3 '
and a diamond-shaped configuration represented as '

Figure 1 .
Figure 1.XRD patterns of TNTO ceramics are presented for two different conditions: (a) sintered for 4 h at various sintering temperatures, and (b) sintered at 1450 °C for different sintering times.
facilitated the replacement of dopant ions within the rutile structure, leading to an enlargement of the lattice constant values.Meanwhile, even at varied sintering times, the a and c values remained larger than those of the reference values for TiO 2 .

Figure 2 .
Figure 2. SEM images of TNTO ceramics sintered at different temperature conditions from 1200 to 1450 °C.

Figure 3 .
Figure 3. SEM images of TNTO ceramics sintered at 1450 °C under different durations.

Figure 4 .
Figure 4. Comparative plot of ε′ and tanδ value for TNTO ceramics sintered under various (a) temperature conditions, and (b) time conditions.

Figure 5 .
Figure 5. Frequency dependence of (a) ε′ and (b) tanδ value at RT for TNTO ceramics sintered at different temperature conditions.

Figure 6 .
Figure 6.Impedance spectroscopy plot at RT for TNTO ceramics: (a) sintered at 1200-1300 °C conditions, (b) sintered at 1350-1450 °C conditions, and (c) comparison of insulating responses between CDP and non-CDP ceramic groups.The inset in (a) and (b) shows their grain responses at high frequencies.

Figure 7 .
Figure 7. Frequency dependence of (a) ε′ and (b) tanδ value at RT for TNTO ceramics sintered at different duration conditions.

Figure 8 .
Figure 8. Impedance spectroscopy plot at RT for (a) TNTO ceramics sintered at 1450 °C with different duration conditions and their grain response at high-frequency range for (b) 2 h, (c) 4 h, and (d) 6 h condition.