High-Performance Giant Dielectric Properties of Cr³⁺/Ta⁵⁺ Co-Doped TiO₂ Ceramics

Abstract

The effects of the sintering temperature on microstructures, electrical properties, and dielectric response of 1%Cr³⁺/Ta⁵⁺ co-doped TiO₂ (CrTTO) ceramics prepared using a solid-state reaction method were studied. The mean grain size increased with an increasing sintering temperature range of 1300–1500 °C. The dielectric permittivity of CrTTO ceramics sintered at 1300 °C was very low (ε′ ∼198). Interestingly, a low loss tangent (tanδ ∼0.03–0.06) and high ε′ (∼1.61–1.9 × 10⁴) with a temperature coefficient less than ≤ ±15% in a temperature range of −60 to 150 °C were obtained. The results demonstrated a higher performance property of the acceptor Cr³⁺/donor Ta⁵⁺ co-doped TiO₂ ceramics compared to the Ta⁵⁺-doped TiO₂ and Cr³⁺-doped TiO₂ ceramics. According to a first-principles study, high-performance giant dielectric properties (HPDPs) did not originate from electron-pinned defect dipoles. By impedance spectroscopy (IS), it was suggested that the giant dielectric response was induced by interfacial polarization at the internal interfaces rather than by the formation of complex defect dipoles. X-ray photoelectron spectroscopy (XPS) results confirmed the existence of Ti³⁺, resulting in the formation of semiconducting parts in the bulk ceramics. Low tanδ and excellent temperature stability were due to the high resistance of the insulating layers with a very high potential barrier of ∼2.0 eV.

Introduction

Since an ultrahigh dielectric permittivity was reported in a CaCu₃Ti₄O₁₂ (CCTO) ceramic,¹ high dielectric response in various ceramics of related materials has been studied extensively. Accordingly, CCTO can be called a pioneering giant dielectric material. The dielectric properties of CCTO have been extensively investigated because it exhibits a very high dielectric permittivity (ε′ ∼ 10³–10⁶).¹⁻⁵ In addition to CCTO ceramics, other ultrahigh permittivity materials have also been extensively investigated, including CuO,⁶Ln_2-xSr_xNiO₂ (Ln = Nd, La, and Sm),⁷ and NiO₂-based oxides.^8,9 Because these ceramics can be applied in electronic devices and highly energy-dense storage devices, their dielectric properties were studied to improve them. This is because the dielectric loss tangents (tanδ) of these ceramics were still higher than the standard values for applications.^1,4,6−8 Furthermore, the dielectric properties of these materials were largely dependent on temperature. These two serious factors are undesirable for use in electronic devices.

In addition to potential applications, the intrinsic origin of the unusual dielectric response of each kind of giant dielectric oxide has been studied from many points of view. As a result, many exciting models were proposed: the surface barrier layer capacitor (SBLC),^10,11 internal barrier layer capacitor (IBLC),^5,12,13 small polaron hopping models,^7,14 polaronic stacking fault defect model,¹⁵ and non-Ohmic sample-electrode contact model.^3,11

Most recently, one of the most interesting dielectric oxides was discovered, that is, acceptor/donor co-doped rutile–TiO₂ (A/D-TiO₂) ceramics. For example, In³⁺/Nb⁵⁺ co-doped TiO₂ ceramics (INTO) exhibited high dielectric permittivity (ε′ ∼ 10⁴) while retaining a very low loss tangent (tanδ ∼0.02).¹⁶⁻¹⁸ Although such high dielectric permittivity with a low loss tangent can also be accomplished in CCTO and related oxides, the temperature stability was very poor.² The temperature coefficient of the CCTO ceramics reached > > 15% when the temperature was increased higher than 100 °C.

Many kinds of A/D-TiO₂ ceramics exhibited excellent temperature stability although the temperature was increased to 150 °C or higher.^16,19,20 Accordingly, an efficient model was proposed to explain the observed high-performance giant dielectric properties (HPDPs) of INTO,¹⁶ that is, an electron-pinned defect-dipole (EPDD) model. Delocalized electrons originated as a result of doping with Nb⁵⁺ ions and localized in the defect clusters of .¹⁶ Moreover, several models were proposed to explain the HPDPs, including the IBLC model, SBLC model, and sample-electrode contact effect.^{12,17,21−23} Furthermore, it was reported that the HPDPs of any A/D-TiO₂ system were obtained by optimizing the sintering conditions.^20,24,25

To date, in addition to In³⁺/Nb⁵⁺ co-doped TiO₂, HPDPs were discovered in other A/D-TiO₂ systems such as Ga³/Nb⁵⁺,¹⁰ Al³/Ta⁵⁺,²⁶ Al³⁺/Nb⁵⁺,²⁵ Zn²⁺/Nb⁵⁺,^27,28 Pr³⁺/Nb⁵⁺,²⁹ Ag⁺/Nb⁵⁺,³⁰ Ag⁺/Ta⁵⁺,³¹ Sc³⁺/Nb⁵⁺,²⁴ Ga³/Ta⁵⁺,²⁰ Li⁺/Nb⁵⁺,³² Bi³⁺/Sb⁵⁺,³³ Dy³⁺/Nb⁵⁺,³⁴ Gd³⁺/Nb⁵⁺,³⁵ and Er³⁺/Nb⁵⁺ co-doped TiO₂ ceramics.³⁶ There are fewer reports on the A/Ta⁵⁺-doped TiO₂ compounds compared to A/Nb⁵⁺. All these A/D-TiO₂ ceramic systems exhibited a low loss tangent (tanδ <0.05) and high dielectric permittivity (ε′ >10⁴) with low temperature coefficients of dielectric permittivity (Δε′ ≤ ±15%). Because the A/D-TiO₂ ceramics have a high potential for use in electronic device technology, the development of new A/D-TiO₂ materials is an important research topic and should be actively studied for practical applications.

In the present study, a new 1%Cr³⁺/Ta⁵⁺ co-doped TiO₂ system has been investigated with regard to its sintering optimization, structural analysis, and dielectric properties. The Cr³⁺ ions of a transition metal are a new candidate for the acceptor +3 ions in the A/Ta⁵⁺-doped TiO₂ compounds. However, in previous reports, the boron-group metals were treated as acceptors. The grain size was continuously enlarged with increasing sintering temperature. As a result, the dielectric response also increased when the grain size increased. Notably, a high permittivity (ε′ ∼1.92 × 10⁴) and a low loss tangent (tanδ ∼0.031) at 1 kHz and room temperature (RT) were achieved. Interestingly, the temperature coefficient was found to be ≤ ±15% in a temperature range of −60–150 °C.

Results and Discussion

The X-ray diffraction (XRD) patterns of the CrTTO-1, CrTTO-2, and CrTTO-3 ceramics are shown in Figure 1. Only the main phase of rutile-TiO₂ (JCPDS 21–1276) was observed in the XRD patterns of all the CrTTO ceramics sintered at different temperatures with a tetragonal structure (the space group symmetry of P4₂/mnm). No impurity phase was detected. The overall XRD patterns of the CrTTO ceramics were similar to those of other A/D-TiO₂ compounds reported in the literature.^{11,13,23,37,38} The lattice parameters were calculated from the XRD patterns. The calculated a and c values are summarized in Table 1. The a and c values for all the CrTTO ceramics are close to the values obtained in the undoped rutile-TiO₂ ceramics because of a small amount of co-doping concentration and a slightly different ionic radii between the host (Ti⁴⁺) and the doping ions (Cr³⁺ and Ta⁵⁺). Nevertheless, we found that the lattice parameters of the CrTTO ceramics significantly enlarged when the co-doping concentration was increased to 10% with a = 4.598(2) and c = 2.966(1) Å (not shown). Thus, it is likely that the Ta⁵⁺ and Cr³⁺ doping ions can be substituted into the Ti site in the rutile structure because the ionic radius of the host and dopants are not significantly different, and no secondary phase was detected.

Figure 1.

XRD patterns of the CrTTO-1, CrTTO-2, and CrTTO-3 ceramics sintered at 1300, 1400, and 1500 °C for 5 h, respectively.

Table 1. Lattice Parameters of the TiO₂ and Cr³⁺/Ta⁵⁺ Co-Doped TiO₂ Ceramics Sintered under Various Conditions.

ceramic sample (sintering temperature/time)	lattice parameters (Å)
	a	c
TiO2	4.593	2.960
CrTTO-1 (1300 °C/5 h)	4.593 (4)	2.961 (0)
CrTTO-2 (1400 °C/5 h)	4.593 (3)	2.961 (5)
CrTTO-3 (1500 °C/5 h)	4.592 (6)	2.960 (8)

According to the XRD results, the lattice parameters of the CrTTO ceramics did not change with the sintering conditions. The effects of co-doping concentrations and sintering conditions on the dielectric properties were further investigated. By optimizing the sintering conditions, we found that HPDPs (i.e., low tanδ <0.05 and high ε′ > 10⁴ with excellent temperature stability) can be obtained in the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramics with x = 0.01 (x = 1%) only. However, when x = 0.025–0.1, HPDPs cannot be achieved even when varying the sintering conditions, as shown in Figure S1a–c (Supplementary Information). As demonstrated in Figure 2a, different aliovalent dopants (+3/+5) and single–/co-dopants have a significant influence on the dielectric response in the TiO₂-based ceramics. For the single-doped TiO₂ ceramics, the dielectric permittivities of the CrTO (ε′ ∼2.0 × 10²) and TaTO (ε′ ∼3.5 × 10⁵) ceramics are completely different. The extremely enhanced permittivity of the TaTO ceramic is similar to that observed in Nb⁵⁺-doped TiO₂ ceramics. This was attributed to the effect of polaron hopping between the Ti³⁺/Ti⁴⁺ ions.^16,18 The low permittivity of the CrTO ceramic is similar to those reported for In³⁺-doped TiO₂,¹⁶ Al³⁺-doped TiO₂,³⁷ and Ga³⁺-doped TiO₂¹⁰ ceramics. These results indicate that the substitution of Cr³⁺ and Ta⁵⁺ ions into the rutile-TiO₂ structure generated different types of defects, as shown in the following equations:

1

2

3

Figure 2.

Room-temperature dielectric properties in the frequency range of 40–10⁶ Hz; (a) dielectric permittivity (ε′) and (b) loss tangent (tanδ) for the CrTO, TaTO, CrTTO-1, CrTTO-2, and CrTTO-3 ceramics.

Generally, doping rutile-TiO₂ with +3 ions can produce an oxygen vacancy in the structure,^{19,20,26,39,40} while doping with +5 ions results in the creation of free electrons.^16,18 As depicted in Figure 2b, the loss tangent of the TaTO ceramic was very large compared to that of the other ceramics, and it increased as the frequency increased. This observation clearly indicates that the giant dielectric properties of the TaTO ceramic are associated with the high conductivity of the ceramic sample, which is due to the long-range motion of free electrons. On the other hand, the loss tangent of the CrTO ceramic was very low and continuously decreased as the frequency increased. This result is similar to that observed for In³⁺-doped TiO₂,¹⁶ Al³⁺-doped TiO₂,³⁷ and Ga³⁺-doped TiO₂,¹⁰ which are associated with the ionic polarization in the rutile structure.⁴¹ There is no significant difference in the dielectric performance with the acceptor +3 doping ions of the boron group substituted into the TiO₂ ceramics.

The dielectric permittivities of the single-doped CrTO and co-doped CrTTO-1 ceramics are nearly the same over a measured frequency range, as shown in Figure 2a. A low permittivity of the CrTTO-1 ceramic resulted from a low sintering temperature because the color of the sintered sample did not change and remained white. This result is similar to that of other A/D-TiO₂ systems.^25,42 Thus, giant dielectric permittivity cannot be obtained in the CrTTO ceramic sintered at ≤1300 °C for 5 h. Giant dielectric permittivity was obtained in the CrTTO-2 and CrTTO-3 ceramics, which were sintered at temperatures ≥1400 °C. Furthermore, the dielectric permittivity increased as the sintering temperature increased. Considering the loss tangent shown in Figure 2b, it was found that the loss tangent at RT for all the co-doped CrTTO ceramics was lower than that of the single-doped TaTO ceramics, indicating the critical role of Cr³⁺ doping ions in reducing the loss tangent in the TaTO ceramics.

As summarized in Table 2, high permittivity (ε′ > 10⁴) and a low loss tangent (tanδ < 0.1) can be obtained by optimizing the sintering conditions, which are similar to that obtained in the Sc³⁺/Nb⁵⁺ co-doped TiO₂ ceramics.²⁴Figure 3 displays dielectric permittivity at 10³ Hz in a temperature range of −60 to 210 °C. It is likely that the giant dielectric permittivity with good temperature stability was obtained in the CrTTO-2 and CrTTO-3 ceramics. The temperature coefficient of the dielectric permittivity (Δε′(T)/ε′_RT) is summarized in Table 2. The CrTTO-3 ceramic exhibits the best dielectric performance with a temperature coefficient of less than ±15% in the widest temperature range (−60 to 150 °C). As shown in the inset of Figure 3, the loss tangent of the CrTTO-3 ceramic was still lower than 0.1 over a wide temperature range of −60 to 100 °C. As with other A/D-TiO₂ systems,^{10,16,19,20,24} HPDPs were obtained in the Cr³⁺/Ta⁵⁺ co-doped TiO₂ ceramic system by optimizing the doping concentration coupled with a sintering condition. It is to be noted that the high permittivity was not obtained in the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramics with x > 0.01, while a high loss tangent was obtained. The color of the sintered sample for the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramics with x > 0.01 was still white, as reported in the literature.^25,42 The dielectric properties of the Cr³⁺/Ta⁵⁺ co-doped TiO₂ ceramic system can be compared to those reported in the literature, as summarized in Table 3. It is worth noting that the Cr³⁺/Ta⁵⁺ co-doped TiO₂ ceramic system is one of the most interesting giant dielectric oxides that can exhibit a low loss tangent and high dielectric permittivity that are nearly independent of temperature ranging from −60 to 150 °C.

Table 2. Dielectric Permittivity (ε′) and Loss Tangent (tanδ) at 10³ Hz, Temperature Coefficient (Δε′(T)/ε′_RT), and Conduction Activation Energy at the Insulating Parts of the CrTTO Ceramics.

ceramic sample (sintering temperature/time)	dielectric properties		Δε′(T)/ε′RT ≤ ±15%	Ea (eV)
	ε′ (30 °C)	tanδ (30 °C)
CrTTO-1 (1300 °C/5 h)	198	0.043	20–150	1.788
CrTTO-2 (1400 °C/5 h)	16,155	0.062	–20–130	2.055
CrTTO-3 (1500 °C/5 h)	19,170	0.031	–60–150	2.181
CrTO (1400 °C/5 h)	216	0.037	–60–140
TaTO (1400 °C/5 h)	351,992	0.104	–30–160

Figure 3.

Dielectric permittivity (ε′) as a function of temperature at 10³ Hz for all the co-doped CrTTO ceramics; inset shows the temperature dependence of the loss tangent (tanδ) at 10³ Hz.

Table 3. Dielectric Permittivity (ε′) and Low Tangent (tanδ) (at 1 kHz and ∼RT) for Various Co-Doped (A_1/2D_1/2)_xTi_1–xO₂ Ceramic Systems.

(A1/2D1/2)xTi1-xO2			ε′	tanδ	reference
A2+, 3+	D5+	x
Ga	Nb	0.1–10%	∼103–105	∼0.05–0.30	(10)
In	Nb	0.05–10%	∼2–6 × 104	< ∼0.02–0.05	(16)
V	Ta	1%	2.4–6.8 × 103	∼0.04–0.08	(19)
Sc	Nb	10%	∼0.48–1.25 × 104	∼0.05–0.10	(24)
Al	Ta	2–12.5%	0.04–2 × 104	< ∼0.03–0.10	(26)
Zn	Nb	1–10%	∼5–8 × 104	∼0.10–0.30	(27)
Dy	Nb	0.5–5%	∼5–6.5 × 104	< ∼0.08	(34)
Er	Nb	0.25–10%	∼2–9 × 104	∼0.02–0.08	(36)
Ga	Sb	2–6%	3.5–7.8 × 104	∼0.06–0.1	(48)
Cr	Ta	1%	19,170	0.031	In this work

For many giant dielectric materials such as CaCu₃Ti₄O_12,² Li⁺/Ti⁴⁺ co-doped NiO,⁹ and V³⁺/Ta⁵⁺ co-doped TiO₂ ceramics,¹⁹ it is usually observed that the dielectric response correlates to a micrograin structure. As shown in Figure 4, the grain size of the CrTTO ceramics increased with increasing sintering temperature. Many pores were observed in the microstructure of the CrTTO-1 ceramic, while a highly dense microstructure was observed in the microstructures of the CrTTO-2 and CrTTO-3 ceramics. The mean grain sizes of the CrTTO-1, CrTTO-2, and CrTTO-3 ceramics were 4.0 ± 1.2, 8.8 ± 2.6, and 19.9 ± 4.1 μm, respectively. The insets of Figure 4a–c show their statistical distributions of the grain sizes. The densities were found to be 4.018, 4.176, and 4.213 g/cm³, respectively, while the relative densities were 94.98, 98.72, and 99.59%. Evidently, the dielectric permittivity and the mean grain size of the CrTTO ceramics increased with increasing sintering temperature.

Figure 4.

SEM images of the (a) CrTTO-1, (b) CrTTO-2, and (c) CrTTO-3 ceramics sintered at 1300, 1400, and 1500 °C for 5 h, respectively.

The effects of single- and co-doping ions on the microstructure changes of the TiO₂ ceramics were also studied, as shown in Figure S2a–c (Supporting Information). It is clearly shown that the Ta⁵⁺ dopant significantly inhibited the grain growth of the TiO₂ ceramics, while the Cr³⁺ dopant has a slight effect on the microstructure of the TiO₂ ceramics. According to a microstructure analysis, it is likely that the HPDPs of the CrTTO ceramics are correlated with the interfacial polarization effect.² Accordingly, the giant dielectric response follows a simple series layer model, ε′ = ε_gbt_g/t_gb, where t_g and t_gb are the mean grain size and the thickness of the grain boundary, respectively. ε_gb is the dielectric permittivity of the grain boundary.^8,41 Thus, as summarized in Table 2, the dielectric permittivity of the CrTTO ceramics increased with the increase in the sintering temperature, corresponding to the increased mean grain size resulting from the increase in the sintering temperature. According to the IBLC model of Schottky barriers at the grain boundaries,⁴³ the grain boundary capacitance (C_gb) is determined by the area of the grain boundary, which is approximately equal to the grain size. Under an applied electric field, more charge carriers inside the semiconducting grains were accumulated at the insulating grain boundary with a large interfacial area, producing a high C_gb. This result is responsible for the observed increase in the dielectric permittivity of the CrTTO ceramics with large grain sizes.

According to the pioneering work on INTO ceramics,¹⁶ the HPDPs are described by an EPDD model in which the dielectric properties change with the creation of oxygen vacancies and free electrons. Raman spectroscopy is an effective technique that has been widely used to characterize oxygen vacancies in rutile-TiO₂.^25,44 According to eq 1, oxygen vacancies in the CrTTO ceramics was produced by the Cr³⁺ doping ions. Thus, the changes in the oxygen vacancy concentration in the CrTTO ceramics could be due to the variation in the sintering temperature only. As shown in Figure 5, the Raman peak of the E_g mode, which is correlated with the concentration of oxygen vacancies,^13,25,38 changed slightly compared to that of the pure rutile-TiO₂ ceramic. In addition, compared to the pure rutile-TiO₂ ceramic, the greatest difference in the peak positions of the E_g mode was found in the CrTTO-3 ceramic, which was sintered at the highest temperature. Furthermore, the A_1g mode, which is due to the O–Ti–O bonds, was also unchanged. Thus, the EPDDs may not be the primary origin of the HPDPs of the CrTTO ceramics.

Figure 5.

Raman spectra of pure TiO₂, CrTTO-1, CrTTO-2, and CrTTO-3 ceramics.

According to the EPDD model for the A/D-TiO₂ ceramics, the loss tangent was controlled by the A³⁺ or A²⁺ acceptor dopants.^16,45 On the other hand, the giant dielectric permittivity is dependent on the doping concentration of the D⁵⁺ doping ions.^16,46 This is because the number of free electrons that can be polarized in the defect clusters can be changed by varying the D⁵⁺ doping concentration. In this work, the doping concentrations of the A/D dopants in all the CrTTO ceramics are the same in value (1%Cr³/Ta⁵⁺). Thus, the difference in the dielectric permittivity or polarization of the sintered ceramics should be associated with other factors rather than the doping concentration of A/D.

The interfacial polarization at the internal interfaces of the CrTTO ceramics was likely the primary cause for the observed HPDPs. Accordingly, the insulating and semiconducting parts in the sintered ceramics must exist in the ceramics. Usually, the substitution of pentavalent ions (+5) into the rutile-TiO₂ structure can increase the conductivity of the TiO2 ceramics by the creation of free electrons, and hence, Ti4+ → Ti3+ follows eqs 2 and 3. In this work, the presence of Ti³⁺ was confirmed by X-ray photoelectron spectroscopy (XPS). As seen in Figure 6, two Ti species were observed in the XPS spectrum. The main species (red peak) at a binding energy of 495.4 eV corresponds to the Ti⁴⁺ bulk state, while the secondary species (blue peak) at a lower binding energy of 458.0 eV is due to the Ti³⁺ defect state. The calculated area ratio of Ti³⁺/Ti⁴⁺ is approximately 7.2 ± 2.7%. Considering the chemical formula of all the sintered CrTTO ceramics, a small amount of 0.5 at.% Ta was desired to substitute in the TiO₂ structure. Thus, according to eqs 2 and 3, only a small amount of Ti³⁺ in the CrTTO ceramics should be produced in this way. Experimentally, a large ratio of Ti³⁺/Ti⁴⁺ may be due to the existence of oxygen vacancies because of oxygen loss during sintering at high temperatures, which is expressed in the following equation:

4

where 2e′ can occupy the Ti 3d conduction band, producing Ti³⁺ in the formula (Cr_0.005Ta_0.005)Ti_0.005³⁺Ti_{0.995 – x}Ti_x³⁺O_2 – x/2. Ti_0.005 and Ti_x³⁺ were produced by 0.5 at.% Ta doping ions and oxygen vacancies, respectively. As shown in Figure 5, the Raman peak of the E_g mode of the CrTTO ceramic shifted slightly from 447.8 to 446.8 cm^–1. Furthermore, the existence of oxygen vacancies in the CrTTO ceramics can be confirmed using the XPS technique, as shown in Figure S3 (Supporting Information) for the O 1 s profile in the CrTTO–3 ceramic. Therefore, the semiconducting part can be formed in the CrTTO ceramics, owing to the existence of the Ti³⁺ ions.

Figure 6.

X-ray photoelectron spectrum of Ti 2p for the CrTTO-3 ceramic.

Usually, the semiconducting and insulating parts in polycrystalline ceramics are studied by impedance spectroscopy (IS). Therefore, the origin of the HPDPs of CrTTO ceramics was further investigated using the IS technique. As illustrated in Figure 7a,b, a semicircular arc can be observed in the CrTTO-2 and CrTTO-3 ceramics. A nonzero intercept on the Z′-axis was also observed in the Z* plots, as shown in the inset of Figure 7a,b. These results are similar to those observed in the literature for other A/D-TiO₂ ceramics.^{20,24,47−49} The observed large semicircular arc can be assigned to the electrical responses of the insulating parts (e.g., the grain boundary and insulative outer surface layer), while the nonzero intercept is attributed to the electrical response on the semiconducting grain.^20,42 Thus, the giant dielectric responses in the CrTTO-2 and CrTTO-3 samples should be due to the interfacial polarization effect.^4,13,23

Figure 7.

Impedance complex plane (Z*) plots at 160–180 °C for (a) CrTTO-2 and (b) CrTTO-3; insets show the expanded views of impedance data at high frequencies. (c) Z* plot at 0 °C for CrTTO-1. (d) Arrhenius plot of conduction in the insulating part.

According to IS for polycrystalline ceramics,^2,50 the grain resistance (R_g) and the total resistance of the insulative phases (R_total) can be calculated from the nonzero intercept on the Z′-axis and the diameters of the large semicircular arc(s), respectively. Thus, the low loss tangent of the CrTTO-2 and CrTTO-3 samples originated from a high total resistance of the insulating parts. The total resistance was higher than 10⁵ even at a high temperature of 150 °C, while the resistance of other giant dielectric oxides (e.g., CCTO, CuO, NiO-based, and Ln_2-xSr_xNiO₂ ceramics) was very low at such a high temperature.^5−7,9 Furthermore, the giant dielectric response in the CrTTO-2 and CrTTO-3 samples may be attributed to the interfacial polarization at the inner interfaces of the sintered samples because these samples consisted of semiconducting and insulating parts. As shown in Figure 7c, high-frequency data of the Z* plot for the CrTTO-1 sample tended to converge to the origin. There was no nonzero intercept on the Z′-axis for the CrTTO-1 sample, and hence, there was no semiconducting part in the CrTTO-1 sample. Interfacial polarization at the interface between the semiconducting and insulating parts could not be produced in the CrTTO-1 sample, and hence, it has a low dielectric permittivity. It is important to note that the dielectric permittivity of ∼198 was close to that of a pure TiO₂ polycrystalline ceramic. This result was primarily attributed to the ionic (atomic) polarization.

As shown in Figure 7d, the E_a values of the CrTTO-1, CrTTO-2, and CrTTO-3 samples were calculated from the Arrhenius law and found to be 1.788, 2.055, and 2.181 eV, respectively. The conduction activation energy (E_a) of the insulating part for all of the CrTTO ceramics was much higher than that of other giant dielectric oxides such as Ba(Fe_1/2Nb_1/2)O₃ (E_a ∼0.8–1.0 eV)^51,52 and CCTO (E_a ∼0.6–0.8 eV).^4,50 For CCTO and Ba(Fe_1/2Nb_1/2)O₃ ceramics, the large increase in the dielectric permittivity and the loss tangent at temperatures higher than 100 °C originated in the conduction of free charges. Thus, it is reasonable to conclude that the HPDPs of the CrTTO-2 and CrTTO-3 samples were due to interfacial polarization at the internal interfaces, in which the conduction of free change carriers was effectively inhibited by insulating layers (e.g., grain boundaries and/or insulative outer surfaces) with ultrahigh resistivity and large E_a.

Usually, the substitution of Ta⁵⁺ ions into the rutile-TiO₂ structure can cause the formation of a diamond-shaped (C = Ti³⁺ or Ti⁴⁺) defect complex,⁵³ as shown in Figure 8a. On the other hand, a triangular-shaped defect complex can be formed by doping with trivalent dopants (e.g., A = In³⁺ or Ga³⁺).^16,20 The HPDPs can be obtained in the A/D-TiO₂ ceramics when the triangular and diamond-shaped defect complexes are strongly correlated or overlapped.¹⁶ The formation of a triangular-shaped defect complex is dependent on the ionic size of the trivalent acceptor dopants compared to the host Ti⁴⁺ ion (0.605 Å).^10,25 For example, the triangular-shaped defect complexes cannot be formed when A = Al³⁺ because of a small ionic radius.²⁵ The ionic radius of Cr³⁺ (0.615 Å) was larger than that of Al³⁺ (0.535 Å) and smaller than that of Ga³⁺ (0.620 Å).⁵⁴ According to a first-principles study, two Cr atoms were substituted by two Ti atoms, and an oxygen vacancy (V_o) existed in this structure. To determine the most stable configuration of Cr and oxygen vacancy (V_o) in the TiO₂ host, various configurations of both Cr atoms and V_o in TiO₂ were generated. Our calculation results revealed that two Cr atoms and V_o are isolated, as shown in Figure 8a. A triangular defect is unstable in Cr-doped TiO_2. For the Ta₂Ti₄₆O₉₆ structure, we found that two Ta atoms prefer to form a diamond-shaped defect [Figure 8a], as observed in (In+Nb) co-doped TiO₂.¹⁶ Thus, the HP-GDPs in the CrTTO-2 and CrTTO-3 samples should be attributed to the IBLC and SBLC effects, as shown in Figure 8a,b. Interfacial polarization occurred at the grain boundaries and the interface between the insulating outer surface layer and the inner core of the semiconducting grains. The IBLC and SBLC effects can cause a great increase in the dielectric permittivity and a low loss tangent. As shown in Figure 2, the dielectric permittivity and the loss tangent of the single-doped CrTO ceramic that was sintered at 1400 °C were very low (∼216 and 0.037, respectively). After doping Ta⁵⁺ into the CrTO ceramic (CrTTO-2), the dielectric permittivity increased to ∼1.6 × 10,⁴ while the loss tangent was still low (∼0.062) compared to that of the single-doped TaTO ceramic. These results clearly indicated that the substitution of Ta⁵⁺ into the rutile-TiO₂ structure can cause a significant increase in the dielectric permittivity. According to eqs 2 and 3, free electrons in the TiO₂ structure can be induced by doping with Ta⁵⁺ ions. Thus, the enhanced dielectric permittivity in the single-doped TaTO and co-doped CrTTO-2 ceramics should be due to the electron hopping and interfacial polarization effects. According to the IBLC and SBLC models, the dc conductivity and loss tangent were controlled by the insulating parts in the polycrystalline ceramics. Thus, the important role of the Cr³⁺ doping ions is to enhance the insulating properties in the co-doped CrTTO ceramics by behaving as acceptor dopants.

Figure 8.

(a) Schematic structures of defects inside the grain and interfacial polarization at grain boundaries. (b) Schematic microstructure with the formation of interfacial polarizations at the grain boundaries and the interface between the insulating outer surface layer and semiconducting inner core (b).

It is worth noting that a high dielectric permittivity of (>10⁴) with low loss tangent (<0.1) was achieved only in the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramic with x = 1% (CrTTO-2 and CrTTO-3 samples). When x ≥ 2.5%, the loss tangent was significantly increased. Based on the IBLC and SBLC effects, the loss tangent in a low-frequency range is usually caused by the long-range motion of some free charge carriers (i.e., dc conduction) across the grain boundary with low resistivity. According to eqs 2 and 3, free charges in the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramics should increase with increasing x, giving rise to an increased dc conduction. Furthermore, according to the IBLC model of Schottky barriers at the grain boundaries,⁴⁶ the potential barrier height (Φ_b) at the grain boundary would be reduced by increasing the charge-carrier concentration in the grains (N_d). Thus, the resistance of an individual grain boundary layer in the (Cr_0.5Ta_0.5)_xTi_1-xO₂ ceramics decreased with increasing x, resulting in an increased dc conductivity.

Conclusions

The 1%Cr³⁺/Ta⁵⁺ co-doped TiO₂ ceramics were synthesized via a solid-state reaction (SSR) method and sintered at 1300–1500 °C for 5 h. A single-phase ceramic with a rutile structure was obtained without any significant change in the lattice parameters. As the sintering temperature increased, the mean grain size and dielectric permittivity significantly increased. Giant dielectric permittivity with excellent temperature stability was only obtained in the CrTTO ceramics sintered at 1400–1500 °C. Notably, a low loss tangent of ∼0.03–0.06 was obtained. The high dielectric permittivity of CrTTO ceramics is in contrast to that of the single-doped TiO₂ ceramics of CrTO with a very low dielectric permittivity of ∼200 and TaTO with a high loss tangent over 0.1. The CrTTO ceramics sintered at 1400–1500 °C were electrically heterogeneous and consisted of insulating and semiconducting parts. Thus, the giant dielectric response was described by the interfacial polarization at the internal interfaces. The low loss tangent and excellent temperature stability of the dielectric permittivity were attributed to the high resistance of the insulating layers with a very large conduction activation energy of ∼2.0 eV.

Experimental Section

Experimental Details

1%Cr³/Ta⁵⁺ co-doped TiO₂ ceramics with a nominal composition of the (Cr_0.5Ta_0.5)_0.01Ti_0.99O₂ (CrTTO) ceramics were prepared using an SSR method. Cr₂O₃ (Sigma-Aldrich, 98% purity), Ta₂O₅ (Sigma-Aldrich, 99.99% purity), and rutile-TiO₂ (Sigma-Aldrich, >99.9% purity) were used as the starting raw materials. Complete details of the preparation method are given elsewhere.⁴⁶ The mixture of the starting raw oxides without calcination was uniaxially pressed into a pellet shape of ∼1.2 in thickness and 0.95 mm in diameter. The pellets were sintered under different conditions. The ceramic samples sintered at 1300, 1400, and 1500 °C for 5 h were referred to as the CrTTO-1, CrTTO-2, and CrTTO-3 ceramics, respectively. It is to be noted that the Cr_xTi_1-xO₂ (CrTO) and Ta_xTi_1-xO₂ (TaTO) ceramics with x = 0.005 were also prepared using an SSR method and sintered at 1400 °C for 5 h to compare the dielectric properties of the co-doped ceramics.

The sintered ceramics were characterized by XRD and SEM. The details of characterization using XRD and SEM were given in the previous work.⁴⁶ The lattice parameters were calculated using the Cohen’s method of least squares. Raman spectra were collected on a UV–vis Raman system (Horiba Jobin-Yvon T64000) at an excitation wavelength of 532 nm. The oxidation states of Ti were characterized by XPS (PHI5000 VersaProbe II, ULVAC-PHI, Japan) at the SUT-NANOTEC-SLRI Joint Research Facility, Synchrotron Light Research Institute (SLRI), Thailand. The XPS spectrum of the Ti species was fitted with the PHI MultiPak XPS software using a combination of Gaussian–Lorentzian lines. The densities of all the ceramic samples were measured using the Archimedes method.

Au-sputtered electrodes were prepared. The dielectric properties were corrected using a KEYSIGHT E4990A Impedance Analyzer over the frequency and temperature ranges of 40–10⁶ Hz. The temperature dependence of the dielectric properties was measured in the temperature range of −60 to 210 °C. The heating stage of each measurement temperature used was 10 °C, and it was kept constant with a precision of ±0.1 °C.

Computational Details

The lowest energy configuration of both Cr- and Ta-doped rutile TiO₂ is determined by the Vienna Ab initio Simulation Package (VASP).⁵⁵ In the present calculations, the Perdew–Burke–Ernzerhof⁵⁶ exchange-correlation functional was chosen. With the projector augmented-wave (PAW) approach,⁵⁷ the valence states of both Ti and Cr are 3 s, 3p, 3d, and 4 s. In addition, the valence states are 5p, 5d, and 6 s for Ta and 2 s and 2p for O. The cutoff energy, which is 600 eV, was successfully tested for energy convergence. For Brillouin zone integration, the Monkhorst–Pack Scheme⁵⁸ was carried out. It was found that the 4×4×2 k-point mesh is an appropriate value. In the current study, we used the 2×2×6 supercells of the rutile TiO₂ consisting of 48 and 96 atoms of Ti and O, respectively.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c04666.

• Dielectric properties at the RT of (Cr_0.5Ta_0.5)_xTi_1-xO₂, where x = 0.025–0.10, sintered at 1300, 1400, and 1500 °C for 5 h. SEM images of Cr_0.005Ti_0.995O₂, (Cr_0.5Ta_0.5)_xTi_1-xO₂ with x = 0.01, and Ta_0.005Ti_0.995O₂ ceramics sintered at 1400 °C for 5 h. XPS spectra of O 1 s and the corresponding fitted results of (Cr_0.5Ta_0.5)_xTi_1-xO₂ with x = 0.01 sintered at 1500 °C for 5 h (CrTTO–3) (PDF)

The authors declare no competing financial interest.