High Dielectric Constant and Dielectric Relaxations in La_2/3Cu₃Ti₄O₁₂ Ceramics

Abstract

La_2/3Cu₃Ti₄O₁₂ ceramics were prepared by the same method of solid-state reaction as CaCu₃Ti₄O₁₂ ceramics. The structure and dielectric responses for La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics were systematically investigated by X-ray diffraction, scanning electron microscope, X-ray photoelectron spectroscopy, and impedance analyzer. Compared with CaCu₃Ti₄O₁₂ ceramics, La_2/3Cu₃Ti₄O₁₂ ceramics with higher density and refined grain exhibit a high dielectric constant (ε′ ~ 10⁴) and two dielectric relaxations in a wide temperature range. The dielectric relaxation below 200 K with an activation energy of 0.087 eV in La_2/3Cu₃Ti₄O₁₂ ceramics is due to the polyvalent state of Ti³⁺/Ti⁴⁺ and Cu⁺/Cu²⁺, while the dielectric relaxation above 450 K with higher activation energy (0.596 eV) is due to grain boundary effects. These thermal activated dielectric relaxations with lower activation energy in La_2/3Cu₃Ti₄O₁₂ ceramics both move to lower temperatures, which can be associated with the enhanced polyvalent structure in La_2/3Cu₃Ti₄O₁₂ ceramics. Such high dielectric constant ceramics are also expected to be applied in capacitors and memory devices.

1. Introduction

CaCu₃Ti₄O₁₂ ceramics have always been of interest in the field of high dielectric constant materials, not only for their high dielectric constant with better temperature and frequency stability but also for their unique dielectric relaxation [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. In the process of exploring the origin of giant dielectric properties and improving the performance of CaCu₃Ti₄O₁₂ ceramics, it is quite impressive that many perovskite-like ceramics ACu₃Ti₄O₁₂ (A = Cd, Y_2/3, Sm_2/3, La_2/3, Na_0.5Bi_0.5, etc.) [9,13,14,15,16,17,18,19,20,21] have been found to have the similar high dielectric constant as CaCu₃Ti₄O₁₂, which revises the report by Subramanian [2] and brings new questions about the physical origin of dielectric response in ACu₃Ti₄O₁₂ ceramics. Internal barrier layer capacitor (IBLC) effects related to defect structure in grain and grain boundaries have been widely adopted to explain the origin of high dielectric response in these ACu₃Ti₄O₁₂ ceramics [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].

La_2/3Cu₃Ti₄O₁₂, one of the typical members of the ACu₃Ti₄O₁₂ family, was reported for the first time with a low dielectric constant of 418 (measured at 100 kHz and 25 °C) [2]. However, Zhang [15] and Yang [19] et al. have shown extremely high dielectric constant (about 10⁴ below 100 kHz) in La_2/3Cu₃Ti₄O₁₂ ceramics, which has challenged the former results and immediately stimulated research enthusiasm. Some works [20,21,22,23,24,25,26,27,28] have focused on the effects of fabrication conditions and doping on the structure and properties of La_2/3Cu₃Ti₄O₁₂ ceramics. However, there are few comparative studies on the dielectric relaxation and relative mechanism of La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics with similar sintering parameters, and there are still some questions unsolved, such as, what are the changes in structure, dielectric relaxation caused by the complete substitution of hetero-valent ions on A site in ACu₃Ti₄O₁₂ ceramics. Therefore, it is worthy to comparatively investigate the similarity and difference in structure and dielectric properties in La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics.

In the present work, La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics were prepared by the same process. The structure and dielectric properties of La_2/3Cu₃Ti₄O₁₂ ceramics were systematically investigated and compared with CaCu₃Ti₄O₁₂ ceramics. The similarity and difference of dielectric properties and relative mechanism were discussed in detail.

2. Materials and Methods

La_2/3Cu₃Ti₄O₁₂ were prepared by the solid-state reaction process (as shown in Figure 1) from the high-purity powders of TiO₂ (99.99%, Aladdin Reagent Co., Ltd., Shanghai, China), CuO (99.9%, Aladdin Reagent Co., Ltd.), and La₂O₃ (99.99%, Aladdin Reagent Co., Ltd.). Raw materials were weighed and mixed in a planetary muller for 10 h, were heated twice at 950 °C for 4 h, and then pressed into disks (diameter: 12 mm). The disks were sintered from 1050 °C to 1125 °C in the air for 3 h to find their highest density. The ceramics sintered at 1075 °C with the highest theoretical density (98.6%) were analyzed in further investigations. CaCu₃Ti₄O₁₂ ceramics for comparison were prepared by the same experimental process.

The crystal structure of La_2/3Cu₃Ti₄O₁₂ ceramics was confirmed by X-ray diffraction (XRD, Bruker D8Advance, Billerica, MA, USA) with Rietveld analysis. The microstructure of samples (cleaned and broken in half) was observed by scanning electron microscopy (SEM, JSM-5610LV, JEOL, Tokyo, Japan) on their fractured surface. The valent state of different ions was analyzed by X-ray photoelectron spectroscopy (XPS, PHI-5000C ESCA, Perkin Elmer, Waltham, MA, USA) combining the XPSpeak4.1 fitting tool. Both sides of the samples were coated with silver paste. Turnkey Concept 50, the broadband dielectric spectrometer (Turnkey Concept 50, Novocontrol Technologies, Montabaur, Germany) was applied to measure the dielectric properties of samples in the frequency range of 1 Hz to 2 MHz from 123 to 600 K. The modified Debye equation is applied to analyze the frequency dependence of the dielectric constant. Arrhenius equations are used to analyze the temperature dependence of relaxation time and dc conductivity, respectively.

3. Results

The XRD data with the Rietveld refinement of La_2/3Cu₃Ti₄O₁₂ ceramics is shown in Figure 2. Almost all peaks are indexed, but one weak peak representing the secondary phase of TiO₂ (1.39 wt %) was found. As shown in

Table 1. Structure Parameters for La_2/3Cu₃Ti₄O₁₂ ceramics.

Atom	Wyckoff Prosition	x	y	z	Biso(Å2)	Occupies
La	2a	0.000	0.000	0.000	0.021(39)	0.028(0)
Cu	6b	0.000	0.500	0.500	0.373(29)	0.125(0)
Ti	8c	0.250	0.250	0.250	0.499(26)	0.167(0)
O	24g	0.30336	0.18024	0.000	0.030(0)	0.500(0)

Lattice parameters: a = 7.41773 Å, V = 408.144 ų, space group $\mathrm{Im}\overline{3}$ (204). Agreement indices: R_p = 2.68, R_wp = 3.48, χ² = 2.2.

, La³⁺ ions are partially located in the A site for charge balance, and the lattice parameter of La_2/3Cu₃Ti₄O₁₂ ceramics with cubic structure is 7.418 Å. The increased lattice constant compared with CaCu₃Ti₄O₁₂ ceramics (7.392 Å) may be due to the much larger La ions (r(La³⁺) = 1.061 Å > r(Ca²⁺) = 0.99 Å).

Figure 3 represents the SEM pictures of the cross-section for La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics. Both the samples prepared by the same process were chosen with their highest densification. The average grain size of La_2/3Cu₃Ti₄O₁₂ ceramics is about 2 μm, and the complete substitution of rare earth elements La on Ca site in CaCu₃Ti₄O₁₂ ceramics seems to improve the density of ceramics and refine the grain size to a certain extent.

The temperature dependence of dielectric properties for La_2/3Cu₃Ti₄O₁₂ ceramics is represented in Figure 4. Dielectric properties of La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics at room temperature and different frequencies are listed in

Table 2. Dielectric properties of La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics at 298 K and different frequencies.

Compound	1 kHz		100 kHz
	ε′	tanδ	ε′	tanδ
La2/3Cu3Ti4O12	27,753	0.63	9,396.5	0.31
CaCu3Ti4O12	13,761	0.90	6,904.2	0.14

. The total substitution of La³⁺ for Ca²⁺ ions in CaCu₃Ti₄O₁₂ ceramics has greatly increased the room temperature dielectric constant. Two dielectric relaxations are observed at two different temperature ranges (low-T: 123–200 K; high-T range 300–550 K), which is similar to those observed in CaCu₃Ti₄O₁₂ ceramics. The dielectric constant ε′ decreases suddenly when the samples are cooled to a critically low temperature and the dielectric constant plateaus reduce slightly with increasing the frequency, while the dielectric peaks (about 6 × 10⁴) at high temperatures significantly decrease with increasing frequency. The low-T and high-T dielectric relaxations both show obvious frequency dispersion. Two parts of dielectric loss peaks are observed at the corresponding critical temperatures. However, two dielectric relaxations in La_2/3Cu₃Ti₄O₁₂ ceramics both move to a lower temperature (as shown in Figure 5).

Figure 6 represents the low-T dielectric properties of La_2/3Cu₃Ti₄O₁₂ ceramics as a function of frequency compared with CaCu₃Ti₄O₁₂. The dielectric constant in CaCu₃Ti₄O₁₂ ceramics exhibits better frequency stability than that of La_2/3Cu₃Ti₄O₁₂ ceramics as frequency decreases below about 1 kHz. However, the dielectric constant of both samples decreases abruptly as increasing the frequency above 1 kHz. Meanwhile, dielectric loss peaks associated with the abrupt change of dielectric constant show frequency dispersion characteristics, which can be well expressed with the modified Debye Equation.

$$\epsilon ={\epsilon }^{\prime }-i{\epsilon }^{″}={\epsilon }_{\infty }+\left({\epsilon }_s-{\epsilon }_{\infty }\right)/[1+\left(i\omega \tau {)}^{1-\alpha }\right]$$

(1)

where ε_s and ε_∞ are static and the infinite frequency dielectric constant, ω represents the angular frequency, τ is the mean relaxation time, and α is the distribution of relaxation time. The temperature dependence of τ can be fitted with the Arrhenius equation

$$\tau ={\tau }_{0}exp(E_{\mathrm{relax}}/k_{B}T)$$

(2)

τ₀, E_relax and k_B represented the prefactor, activation energy, and the Boltzmann constant, respectively. The activation energy for low-T dielectric relaxation of La_2/3Cu₃Ti₄O₁₂ ceramics (E_a = 0.087 eV) is smaller than that of CaCu₃Ti₄O₁₂ ceramics (E_a = 0.125 eV), which result in a lower critical temperature and is easier for inducing dielectric response. Moreover, the decrease in activation energy for low-T dielectric relaxation may indicate the stronger grain effect related to increased dipoles from polyvalent Ti and Cu ions.

XPS was applied to further investigate the electronic configuration of La_2/3Cu₃Ti₄O₁₂. Figure 7 shows the XPS spectra of Ti and Cu ions in La_2/3Cu₃Ti₄O₁₂ ceramics compared with CaCu₃Ti₄O₁₂ ceramics. According to the NIST XPS database and Gaussian-Lorentzian fitting method, the 2p_3/2 peaks for Ti and Cu ions are split into two peaks, indicating the coexistence of variable ions with low states such as Ti³⁺ and Cu⁺. Both the area ratios related to the atomic ratio (Ti³⁺/Ti⁴⁺, Cu⁺/Cu²⁺) for La_2/3Cu₃Ti₄O₁₂ ceramics increase compared with that for CaCu₃Ti₄O₁₂ ceramics as shown in

Table 3. XPS parameters of CaCu₃Ti₄O₁₂ and La_2/3Cu₃Ti₄O₁₂ ceramics.

Compound	Bingding Energy (eV)				Area Ratio
	Cu+	Cu2+	Ti3+	Ti4+	Cu+/Cu2+	Ti3+/Ti4+
CaCu3Ti4O12	931.826	932.232	457.657	458.261	0.799	0.686
La2/3Cu3Ti4O12	931.864	932.108	457.691	458.233	0.822	1.007

. The increased concentration of Cu⁺ and Ti³⁺ ions in La_2/3Cu₃Ti₄O₁₂ ceramics may produce more dipoles, thus reducing the activation energy of low-temperature relaxation.

The frequency dependence of the high-T dielectric constant in La_2/3Cu₃Ti₄O₁₂ ceramics from 357 K to 505 K is shown in Figure 8, and the fitting result with Equations (1) and (2). The activation energy E_relax for high-T dielectric relaxation is 0.596 eV close to the those reported values in other ACu₃Ti₄O₁₂ (A = Ca, Dy_2/3 et al.) compounds, which can be related to the grain boundary barrier effect.

Figure 9 represents the frequency dependence of ac conductivity of La_2/3Cu₃Ti₄O₁₂ ceramics in a high-temperature range from 357 to 505 K. The extrapolated dc conductivity at a low frequency well obeys the Arrhenius relation [18] as a function of temperature (as shown in the inset of Figure 9). The calculated activation energy of conductivity (E_dc = 0.571 eV) is similar to the previously reported value for La_2/3Cu₃Ti₄O₁₂ ceramics [26,27,28], and is close to that of high-T dielectric relaxation (E_relax = 0.596 eV) and also implies the correlation between dielectric relaxation and conduction at high temperature.

According to IBLC electrical model, the imaginary part of impedance Z″ can be expressed as a function of frequency.

$$Z_{″}(\omega )=R_g\left[\frac{\omega R_g{C}_g}{1+{(\omega R_g{C}_g)}^2}\right]+R_{gb}\left[\frac{\omega R_{gb}{C}_{gb}}{1+{(\omega R_{gb}{C}_{gb})}^2}\right]$$

(3)

where R_g and R_gb are the resistance of grains and grain boundaries, C_g and C_gb are the capacitance of grains and grain boundaries, respectively. Z″ peaks in Figure 10 indicate a thermally activated electrical property of grain boundaries according to the equation R_gb ≈ 2Z″ max [14]. The shift of the Z″ peak towards higher frequencies with the increasing temperature well follows the Arrhenius law [18] with the conductive activation energy as 0.598 eV in La_2/3Cu₃Ti₄O₁₂ ceramics. The activation energy for conduction is close to that of the high-T dielectric relaxation, which may imply that conductivity and dielectric relaxation in La_2/3Cu₃Ti₄O₁₂ ceramics at high temperature have similar mechanisms due to the grain boundaries effects. Compared with CaCu₃Ti₄O₁₂ ceramics (E_gb = 0.639 eV), the reduction of high-T activation energies for both conductivity and dielectric relaxation in La_2/3Cu₃Ti₄O₁₂ ceramics can be associated with increased defects (such as oxygen vacancy, polyvalent ions) mainly due to the charge compensation effect from the complete substitution of La³⁺ ions on Ca site in CaCu₃Ti₄O₁₂ ceramics. The detailed mechanism still needs further investigation.

4. Conclusions

La_2/3Cu₃Ti₄O₁₂ and CaCu₃Ti₄O₁₂ ceramics were prepared by the same process of solid-state reaction. The similarity and difference in structure, dielectric properties, and relative mechanism in these ceramics were comparatively investigated. The similarities are that La_2/3Cu₃Ti₄O₁₂ ceramics exhibit a similar high dielectric constant (ε′~10⁴) and two distinct dielectric relaxations to CaCu₃Ti₄O₁₂ ceramics. The dielectric relaxation below 200 K with an activation energy of 0.087 eV in La_2/3Cu₃Ti₄O₁₂ ceramics is due to the polyvalent state of Ti³⁺/Ti⁴⁺ and Cu⁺/Cu²⁺, while the dielectric relaxation above 450 K with higher activation energy (0.596 eV) is due to grain boundary effects. The origin of the giant dielectric constant in La_2/3Cu₃Ti₄O₁₂ ceramics can be also explained by the IBLC mechanism. Meanwhile, the differences in structure are that the density has been increased and the grain size has been refined in La_2/3Cu₃Ti₄O₁₂ ceramics, which can be due to the introduction of La rare earth elements (proved by other groups [24]). Moreover, the two thermal activated dielectric relaxations with increased dielectric constant and decreased activation energy in La_2/3Cu₃Ti₄O₁₂ ceramics both move to lower temperatures, which can be related to the enhanced defect structure. The heterovalent ion substitution of La³⁺ on Ca²⁺ ions can induce more ions to get electrons for share conservation, which will increase the lower valence state of Ti³⁺ and Cu⁺ ions that could produce more dipoles and defects, and as the result decrease the activation energy of dielectric relaxation.