Significantly Improved Colossal Dielectric Properties and Maxwell—Wagner Relaxation of TiO2—Rich Na1/2Y1/2Cu3Ti4+xO12 Ceramics

In this work, the colossal dielectric properties and Maxwell—Wagner relaxation of TiO2–rich Na1/2Y1/2Cu3Ti4+xO12 (x = 0–0.2) ceramics prepared by a solid-state reaction method are investigated. A single phase of Na1/2Y1/2Cu3Ti4O12 is achieved without the detection of any impurity phase. The highly dense microstructure is obtained, and the mean grain size is significantly reduced by a factor of 10 by increasing Ti molar ratio, resulting in an increased grain boundary density and hence grain boundary resistance (Rgb). The colossal permittivities of ε′ ~ 0.7–1.4 × 104 with slightly dependent on frequency in the frequency range of 102–106 Hz are obtained in the TiO2–rich Na1/2Y1/2Cu3Ti4+xO12 ceramics, while the dielectric loss tangent is reduced to tanδ ~ 0.016–0.020 at 1 kHz due to the increased Rgb. The semiconducting grain resistance (Rg) of the Na1/2Y1/2Cu3Ti4+xO12 ceramics increases with increasing x, corresponding to the decrease in Cu+/Cu2+ ratio. The nonlinear electrical properties of the TiO2–rich Na1/2Y1/2Cu3Ti4+xO12 ceramics can also be improved. The colossal dielectric and nonlinear electrical properties of the TiO2–rich Na1/2Y1/2Cu3Ti4+xO12 ceramics are explained by the Maxwell–Wagner relaxation model based on the formation of the Schottky barrier at the grain boundary.


Introduction
Improvement of electronic device efficiency through the development of materials with enhanced electrical properties is significant. Colossal dielectric oxides (CDOs) with very high dielectric constant (ε ) are widely used to manufacture critical components in electronic devices, especially for multilayer ceramic capacitors (MLCCs) [1][2][3]. The ε of a CDO influences the geometry and performance of the MLCCs. The size of an MLCC can be miniaturized by using the insulating oxide between the metallic electrodes with a dielectric oxide with a higher ε value than the conventional oxide. Many CDOs have intensively been investigated, especially for CaCu 3 Ti 4 O 12 (CCTO) and related compounds, expecting to replace traditional CDOs such as BaTiO 3 -based ceramics.
For the nonlinear electrical and dielectric measurements, the surfaces of samples were polished. Next, the parallel and smooth surfaces were coated with silver paints and fired in the air at 600 • C for 30 min. The impedance and dielectric parameters of all sintered ceramics were measured with an impedance analyzer (KEYSIGHT E4990A, Santa Rosa, CA, USA). The dielectric properties were measured in the temperature range of −160 to 210 • C and the frequency range from 10 2 -10 7 Hz. The nonlinear relationship between current density (J) and electrical field strength (E) was analyzed by using a high-voltage measurement unit (Keithley 247 model, Cleveland, OH, USA).

Results and Discussion
The XRD patterns of the sintered NYCTO + xTiO 2 (x = 0, 0.1 and 0.2) ceramics are illustrated in Figure 1a, showing the single phase of NYCTO in all ceramics with a perovskite-structure (JCPDS 75-2188). The crystal structure of NYCTO is demonstrated in Figure 1b. The XRD peak corresponding to TiO 2 phase cannot be detected in the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics, which may be due to a small amount of an excess TiO 2 molar ratio that was lower than the resolution limit of the XRD technique. Accordingly, the lattice parameters (a) can be calculated and found to be 7.383, 7.383 and 7.384 Å for the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics, respectively. The a values are comparable to those reported in the literature [27][28][29][30]. The excess TiO 2 composition in NYCTO ceramics does not affect the lattice parameter. This result indicates that the TiO 2 -rich phase is segregated from the primary phase of NYCTO, which may exist as the TiO 2 -rich boundary. The XRD result shows that the NYCTO + xTiO 2 has successfully been fabricated using the SSR method.
Even though the excessive TiO 2 phase was not detected in the XRD patterns for all ceramics, the variation in compositions of the CuO and/or TiO 2 ratios in an ACu 3 Ti 4 O 12 compound usually affects the dielectric and electrical properties [6,10,24,45,[47][48][49]. Thus, we first investigated the dielectric properties of the NYCTO + xTiO 2 ceramics at around room temperature (30 • C). The relationship between the ε and frequency of the NYCTO + xTiO 2 ceramics is shown in Figure 2a. The ε value of the NYCTO ceramic is huge (2.07 × 10 4 at 10 3 Hz) with a quite low tanδ~0.115, which is similar to that reported in the previous works [27,28,30]. However, the ε of the NYCTO ceramic is largely dependent on the frequency in a low-frequency range, which is usually owing to the dominant effect of non-Ohmic sample-electrode interface [8,15,44,50]. At 10 6 Hz, the ε begins to decline due to the primary dielectric relaxation mechanism [12,19]. Interestingly, the ε values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are more stable with frequency than that of the NYCTO ceramic. The TiO 2 -rich phase can improve the frequency dependence of the ε of the NYCTO + xTiO 2 ceramics. The ε values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics at 30 • C and 10 3 Hz are 1.39 × 10 4 and 7.15 × 10 3 , respectively. Even though the dielectric response in the NYCTO + 0.1TiO 2 ceramic was decreased due to the excessive TiO 2 , its ε value was still larger than 10 4 over the measured frequency range. The decrease in the ε value of the NYCTO + xTiO 2 ceramics is similar to that observed in the CaCu 3 Ti 4+x O 12 [6]. Even though the excessive TiO2 phase was not detected in the XRD patterns for all ceramics, the variation in compositions of the CuO and/or TiO2 ratios in an ACu3Ti4O12 compound usually affects the dielectric and electrical properties [6,10,24,45,[47][48][49]. Thus, we first investigated the dielectric properties of the NYCTO + xTiO2 ceramics at around room temperature (30 °C). The relationship between the ε′ and frequency of the NYCTO + xTiO2 ceramics is shown in Figure 2a. The ε′ value of the NYCTO ceramic is huge (2.07  10 4 at 10 3 Hz) with a quite low tanδ  0.115, which is similar to that reported in the previous works [27,28,30]. However, the ε′ of the NYCTO ceramic is largely dependent on the frequency in a low-frequency range, which is usually owing to the dominant effect of non-Ohmic sample-electrode interface [8,15,44,50]. At 10 6 Hz, the ε′ begins to decline due to the primary dielectric relaxation mechanism [12,19]. Interestingly, the ε′ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics are more stable with frequency than that of the NYCTO ceramic. The TiO2-rich phase can improve the frequency dependence of the ε′ of the NYCTO + xTiO2 ceramics. The ε′ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics at 30 °C and 10 3 Hz are 1.39 × 10 4 and 7.15 × 10 3 , respectively. Even though the dielectric response in the NYCTO + 0.1TiO2 ceramic was decreased due to the excessive TiO2, its ε′ value was still larger than 10 4 over the measured frequency range. The decrease in the ε′ value of the NYCTO + xTiO2 ceramics is similar to that observed in the CaCu3Ti4+xO12 [6].  Figure 2b illustrates the tanδ at 30 • C for the NYCTO + xTiO 2 ceramics over the frequency range of 10 2 -10 6 Hz. In the frequency range of 10 2 -10 5 Hz, the tanδ values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are much lower than the NYCTO ceramic. Furthermore, in this frequency range, the tanδ values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are lower than 0.1. The rapid increase in tanδ of all the ceramics is attributed to the primary dielectric relaxation, i.e., Maxwell-Wagner polarization relaxation [12,19]. The tanδ values of the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics 10 3 Hz are 0.115, 0.020 and 0.016, respectively. Notably, the tanδ value of the NYCTO ceramics can be significantly reduced by increasing the excessive TiO 2 molar ratio. This result indicates the influential role of TiO 2 -rich on the significantly improved dielectric properties of the NYCTO ceramics.  Figure 2b illustrates the tanδ at 30 °C for the NYCTO + xTiO2 ceramics over the frequency range of 10 2 -10 6 Hz. In the frequency range of 10 2 -10 5 Hz, the tanδ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics are much lower than the NYCTO ceramic. Furthermore, in this frequency range, the tanδ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics are lower than 0.1. The rapid increase in tanδ of all the ceramics is attributed to the primary dielectric relaxation, i.e., Maxwell-Wagner polarization relaxation [12,19]. The tanδ values of the NYCTO, NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics 10 3 Hz are 0.115, 0.020 and 0.016, respectively. Notably, the tanδ value of the NYCTO ceramics can be significantly reduced by increasing the excessive TiO2 molar ratio. This result indicates the influential role of TiO2-rich on the significantly improved dielectric properties of the NYCTO ceramics.
The temperature dependence of the dielectric properties of the NYCTO + xTiO2 ceramics is illustrated in Figure 3a,b. In the temperature range from −125 to 110 °C, the ε′ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics are more stable with temperature than that of the NYCTO ceramic. At the temperature below −120 °C, the ε′ rapidly decreased, corresponding to the rapid increase in tanδ. This is the Maxwell-Wagner polarization relaxation in the NYCTO + xTiO2 ceramics. Considering in the high-temperature The temperature dependence of the dielectric properties of the NYCTO + xTiO 2 ceramics is illustrated in Figure 3a,b. In the temperature range from −125 to 110 • C, the ε values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are more stable with temperature than that of the NYCTO ceramic. At the temperature below −120 • C, the ε rapidly decreased, corresponding to the rapid increase in tanδ. This is the Maxwell-Wagner polarization relaxation in the NYCTO + xTiO 2 ceramics. Considering in the high-temperature range, the ε and tanδ significantly increase, which is associated with the DC conduction of free charge carriers associated with oxygen vacancies [11,33,51,52]. range, the ε′ and tanδ significantly increase, which is associated with the DC conduction of free charge carriers associated with oxygen vacancies [11,33,51,52]. It is widely accepted that the colossal dielectric properties of the ACu3Ti4O12 oxide groups is the result from the electrical heterogeneous in the microstructure [5,11,15,30,33,48]. The electrically heterogeneous microstructure can be confirmed using impedance spectroscopy [5,53]. Furthermore, the heterogeneous electrical microstructure can also be used to explain the nonlinear electrical properties of the ACu3Ti4O12 ceramics [21,23,24]. Generally, the semicircular arc due to the electrical response of the semiconducting grains of the ACu3Ti4O12 compounds can be observed in the impedance complex plane (Z*) plots at low temperatures [5,54]. Thus, to confirm the formation of semiconducting grains, Z* plots of all the NYCTO + xTiO2 ceramics are demonstrated at −100 °C, as shown in Figure 3c. The semicircular arcs of all the ceramics can be observed, while  It is widely accepted that the colossal dielectric properties of the ACu 3 Ti 4 O 12 oxide groups is the result from the electrical heterogeneous in the microstructure [5,11,15,30,33,48]. The electrically heterogeneous microstructure can be confirmed using impedance spectroscopy [5,53]. Furthermore, the heterogeneous electrical microstructure can also be used to explain the nonlinear electrical properties of the ACu 3 Ti 4 O 12 ceramics [21,23,24]. Generally, the semicircular arc due to the electrical response of the semiconducting grains of the ACu 3 Ti 4 O 12 compounds can be observed in the impedance complex plane (Z*) plots at low temperatures [5,54]. Thus, to confirm the formation of semiconducting grains, Z* plots of all the NYCTO + xTiO 2 ceramics are demonstrated at −100 • C, as shown in Figure 3c. The semicircular arcs of all the ceramics can be observed, while only parts of relatively large semicircular arcs can be observed. These two parts can be assigned as the electrical responses of the semiconducting grain and insulating GB, respectively [5,54]. The grain resistance (R g ), which can be calculated from the diameter of the semicircular arc of the NYCTO + xTiO 2 ceramics, was increased by increasing the TiO 2 molar ratio. In general, we expect that the TiO 2 -rich should not affect the electrical properties of the semiconducting grains but should only affect the insulating boundaries due to the segregation of the TiO 2 -rich phase. In this current study, the excessive TiO 2 molar ratio can affect the electrical properties inside the semiconducting grains, which will be discussed in the last section. Nevertheless, according to the impedance spectroscopy, the variation in the colossal dielectric properties and dielectric behavior of the NYCTO + xTiO 2 ceramics should be described in all aspects based on the IBLC model. Figure 4a displays the Z* plots of all the ceramics at 30 • C. Only parts of the relatively large arcs can be observed with a nonzero intercept (inset of Figure 4a), which is similar to that reported in the previous works [5,6,12,19,21,44,54]. The R g value at 30 • C, which can be calculated from the nonzero intercept, increases with increasing the excessive TiO 2 molar ratio. Even though an entire arc cannot be observed, the R gb values of all the NYCTO + xTiO 2 ceramics can be estimated. As shown in Figure 4b, the tanδ of the NYCTO + xTiO 2 ceramics is inversely proportional to the R gb value. According to the IBLC structure [20,44], the low-frequency tanδ value is correlated to the total resistance, which is governed by the R gb value. The low-frequency tanδ can be reduced by increasing R gb . Thus, the correlation of the tanδ and R gb values follows the IBLC model. only parts of relatively large semicircular arcs can be observed. These two parts can be assigned as the electrical responses of the semiconducting grain and insulating GB, respectively [5,54]. The grain resistance (Rg), which can be calculated from the diameter of the semicircular arc of the NYCTO + xTiO2 ceramics, was increased by increasing the TiO2 molar ratio. In general, we expect that the TiO2-rich should not affect the electrical properties of the semiconducting grains but should only affect the insulating boundaries due to the segregation of the TiO2-rich phase. In this current study, the excessive TiO2 molar ratio can affect the electrical properties inside the semiconducting grains, which will be discussed in the last section. Nevertheless, according to the impedance spectroscopy, the variation in the colossal dielectric properties and dielectric behavior of the NYCTO + xTiO2 ceramics should be described in all aspects based on the IBLC model. Figure 4a displays the Z* plots of all the ceramics at 30 °C. Only parts of the relatively large arcs can be observed with a nonzero intercept (inset of Figure 4a), which is similar to that reported in the previous works [5,6,12,19,21,44,54]. The Rg value at 30 °C, which can be calculated from the nonzero intercept, increases with increasing the excessive TiO2 molar ratio. Even though an entire arc cannot be observed, the Rgb values of all the NYCTO + xTiO2 ceramics can be estimated. As shown in Figure 4b, the tanδ of the NYCTO + xTiO2 ceramics is inversely proportional to the Rgb value. According to the IBLC structure [20,44], the low-frequency tanδ value is correlated to the total resistance, which is governed by the Rgb value. The low-frequency tanδ can be reduced by increasing Rgb. Thus, the correlation of the tanδ and Rgb values follows the IBLC model. In addition to the variation in tanδ, the IBLC model should be used to reasonably describe the overall dielectric properties of the NYCTO + xTiO 2 ceramics. Therefore, the microstructure of the sintered ceramics was studied. Figure 5 shows the SEM images of the polished surface of the NYCTO + xTiO 2 ceramics and their grain size distributions. All the ceramics reveal the grain and GB structure with a highly dense microstructure. The mean grain size of the NYCTO + xTiO 2 ceramics was extremely reduced by increasing x from 0 to 0.2. This result is similar to that reported in the previous reports for TiO 2 -rich CCTO ceramics [6]. The mean grain sizes of the NYCTO + xTiO 2 ceramics with x = 0, 0.1 and 0.2 are 32.80 ± 20.44, 4.05 ± 2.08 and 3.18 ± 1.35 µm, respectively. The excessive TiO 2 could intercept the grain growth rate of the NYCTO ceramics due to the pinning effect of excessive TiO 2 -rich phase particles during the sintering process [55]. We also found that the segregation of the Cu-rich phase is slightly observed along the grain boundaries, as remarked in the square area of Figure 5b.  In addition to the variation in tanδ, the IBLC model should be used to reasonably describe the overall dielectric properties of the NYCTO + xTiO2 ceramics. Therefore, the microstructure of the sintered ceramics was studied. Figure 5 shows the SEM images of the polished surface of the NYCTO + xTiO2 ceramics and their grain size distributions. All the ceramics reveal the grain and GB structure with a highly dense microstructure. The mean grain size of the NYCTO + xTiO2 ceramics was extremely reduced by increasing x from 0 to 0.2. This result is similar to that reported in the previous reports for TiO2-rich CCTO ceramics [6]. The mean grain sizes of the NYCTO + xTiO2 ceramics with x = 0, 0.1 and 0.2 are 32.80 ± 20.44, 4.05 ± 2.08 and 3.18 ± 1.35 μm, respectively. The excessive TiO2 could intercept the grain growth rate of the NYCTO ceramics due to the pinning effect of excessive TiO2-rich phase particles during the sintering process [55]. We also found that the segregation of the Cu-rich phase is slightly observed along the grain boundaries, as remarked in the square area of Figure 5b.
where G is the mean grain size, tgb is the thickness of the GB and ε′gb is the dielectric constant of the GBs. Furthermore, it is also suggested that, but does not clearly prove, the decrease in the ε′ might be due to the increase in tgb due to the TiO2-rich phase. The EDS and EDS-SEM mapping techniques were used to further characterize the microstructure and elemental distribution. As revealed in Figure 6a and its inset, all elements comprising the NYCTO + 0.1TiO2 ceramic are observed in the EDS spectra, confirming the existence of Na, Y, Cu, Ti and O elements. As demonstrated in Figure 6b-g, the Na, Y, Cu and O elements disperse well throughout the microstructure. It is observed that the relatively higher brightness of Ti mapping element along the GBs compared to that of the grains can be observed, confirming the segregation of TiO2-rich boundary. Thus, this is one of the The observed decrease in ε (Figure 2a) value of the NYCTO + xTiO 2 ceramics should be caused by the decrease in the mean grain size, following a simple series layer model of the IBLC structure [20,44,56], where G is the mean grain size, t gb is the thickness of the GB and ε gb is the dielectric constant of the GBs. Furthermore, it is also suggested that, but does not clearly prove, the decrease in the ε might be due to the increase in t gb due to the TiO 2 -rich phase. The EDS and EDS-SEM mapping techniques were used to further characterize the microstructure and elemental distribution. As revealed in Figure 6a and its inset, all elements comprising the NYCTO + 0.1TiO 2 ceramic are observed in the EDS spectra, confirming the existence of Na, Y, Cu, Ti and O elements. As demonstrated in Figure 6b-g, the Na, Y, Cu and O elements disperse well throughout the microstructure. It is observed that the relatively higher brightness of Ti mapping element along the GBs compared to that of the grains can be observed, confirming the segregation of TiO 2 -rich boundary. Thus, this is one of the most important factors contributing to the decrease in the ε values of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics. According to the microstructure analyses, the density of the insulating GB layers in the NYCTO + xTiO 2 ceramics was significantly increased by increasing TiO 2 -rich phase owing to the decreased mean grain size [9,20]. Obviously, The significantly increased R gb (Figure 4) is also attributed to the enhancement of insulating GB density. Furthermore, the increased R gb is also due to the increase in t gb . The XEX spectra detected at the grain and GB areas are shown in Figure 7. It was found that the percentage ratios of Ti(wt%)/Cu(wt%) at the grain and GB were found to be 0.808 and 0.834, respectively.
Molecules 2021, 26, x FOR PEER REVIEW 9 of 18 most important factors contributing to the decrease in the ε′ values of the NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics. According to the microstructure analyses, the density of the insulating GB layers in the NYCTO + xTiO2 ceramics was significantly increased by increasing TiO2-rich phase owing to the decreased mean grain size [9,20]. Obviously, The significantly increased Rgb (Figure 4) is also attributed to the enhancement of insulating GB density. Furthermore, the increased Rgb is also due to the increase in tgb. The XEX spectra detected at the grain and GB areas are shown in Figure 7. It was found that the percentage ratios of Ti(wt%)/Cu(wt%) at the grain and GB were found to be 0.808 and 0.834, respectively.  According to our previous work [28,29], it was found that the NYCTO ceramics exhibited the nonlinear J-E characteristics with nonlinear coefficients (α) of 5.7-6.6. Furthermore, it was reported that the nonlinear properties of CCTO ceramics could be enhanced by increasing the excessive TiO2 molar ratio [6,7]. The α value of the CaCu3Ti4+xO12+2x ceramic with x = 0.15 was increased to 7.9. As illustrated in Figure 8, all the NYCTO + xTiO2 ceramics exhibit the J-E characteristics. The α and electric breakdown (Eb) of the NYCTO, NYCTO + 0.1TiO2 and NYCTO + 0.2TiO2 ceramics are 4.96 and 724.50 V/cm, 4.71 and 910.59 V/cm, and 13.36 and 7948.04 V/cm, respectively. The Eb increased significantly with increasing TiO2-rich phase, similar to that observed in the CaCu3Ti4+xO12+2x ceramics [6]. Nevertheless, the enhanced α value of 13.36 is larger than that of the CaCu3Ti4+xO12+2x ceramics. The segregation of TiO2-rich boundary and the increased GB density are the key factors, giving rise to the significantly improved nonlinear J-E properties. The α value is often related to Eb value [4]. According to our previous work [28,29], it was found that the NYCTO ceramics exhibited the nonlinear J-E characteristics with nonlinear coefficients (α) of 5.7-6.6. Furthermore, it was reported that the nonlinear properties of CCTO ceramics could be enhanced by increasing the excessive TiO 2 molar ratio [6,7]. The α value of the CaCu 3 Ti 4+x O 12+2x ceramic with x = 0.15 was increased to 7.9. As illustrated in Figure 8, all the NYCTO + xTiO 2 ceramics exhibit the J-E characteristics. The α and electric breakdown (E b ) of the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are 4.96 and 724.50 V/cm, 4.71 and 910.59 V/cm, and 13.36 and 7948.04 V/cm, respectively. The E b increased significantly with increasing TiO 2 -rich phase, similar to that observed in the CaCu 3 Ti 4+x O 12+2x ceramics [6]. Nevertheless, the enhanced α value of 13.36 is larger than that of the CaCu 3 Ti 4+x O 12+2x ceramics. The segregation of TiO 2 -rich boundary and the increased GB density are the key factors, giving rise to the significantly improved nonlinear J-E properties. The α value is often related to E b value [4]. The nonlinear electrical behavior of ACu3Ti4O12 oxides is widely believed to be originated by the formation of the Schottky barrier at the GBs [4,5,7,18]. The increased Eb value is associated with the increase in Rgb due to the significantly increased GB density and GB thickness, which are classified as the geometric factors of the GBs [9]. Furthermore, the intrinsic factor of the GBs, i.e., the Schottky barrier height (Φb), can usually have a remarkable effect on the Rgb and Eb values [4,5,7,9]. The Φb is closely related to the conduction activation energy at the GBs (Egb) [7,13,14]. To calculate the Egb value, Rgb values at different temperatures were calculated. Figure 9a and its inset show Z* plots and nonzero intercept of the NYCTO ceramic at various temperatures. The Rg and Rgb values can be obtained and found to decrease with increasing temperature. Thus, Egb can be calculated by using the Arrhenius law [5,9]: where R0, kB and T are the per-exponential constant term, Boltzmann constant and absolute temperature, respectively. Figure 9b depicts the relationship between Rgb and 1000/T of the NYCTO + xTiO2 ceramics. The Egb values can be calculated from the slopes of the Rgb and 1000/T plots, which are linearly fitted by using the Arrhenius law. The Egb values of the NYCTO + xTiO2 ceramics are 0.547, 0.583 and 0.714 eV, respectively. Therefore, Φb of the NYCTO + xTiO2 ceramics can be increased by increasing the TiO2-rich phase. The improved nonlinear J-E properties and electrical properties of the GBs are also caused by the enhanced Φb, just as observed in the TiO2-rich CCTO ceramics [7]. The increased Φb values of the NYCTO + xTiO2 ceramics are likely attributed to the suppressed oxygen vacancies and/or oxygen enrichment at the GBs due to the segregation of TiO2-rich boundary [7,18]. The nonlinear electrical behavior of ACu 3 Ti 4 O 12 oxides is widely believed to be originated by the formation of the Schottky barrier at the GBs [4,5,7,18]. The increased E b value is associated with the increase in R gb due to the significantly increased GB density and GB thickness, which are classified as the geometric factors of the GBs [9]. Furthermore, the intrinsic factor of the GBs, i.e., the Schottky barrier height (Φ b ), can usually have a remarkable effect on the R gb and E b values [4,5,7,9]. The Φ b is closely related to the conduction activation energy at the GBs (E gb ) [7,13,14]. To calculate the E gb value, R gb values at different temperatures were calculated. Figure 9a and its inset show Z* plots and nonzero intercept of the NYCTO ceramic at various temperatures. The R g and R gb values can be obtained and found to decrease with increasing temperature. Thus, E gb can be calculated by using the Arrhenius law [5,9]: where R 0 , k B and T are the per-exponential constant term, Boltzmann constant and absolute temperature, respectively. Figure 9b depicts the relationship between R gb and 1000/T of the NYCTO + xTiO 2 ceramics. The E gb values can be calculated from the slopes of the R gb and 1000/T plots, which are linearly fitted by using the Arrhenius law. The E gb values of the NYCTO + xTiO 2 ceramics are 0.547, 0.583 and 0.714 eV, respectively. Therefore, Φ b of the NYCTO + xTiO 2 ceramics can be increased by increasing the TiO 2 -rich phase. The improved nonlinear J-E properties and electrical properties of the GBs are also caused by the enhanced Φ b , just as observed in the TiO 2 -rich CCTO ceramics [7]. The increased Φ b values of the NYCTO + xTiO 2 ceramics are likely attributed to the suppressed oxygen vacancies and/or oxygen enrichment at the GBs due to the segregation of TiO 2 -rich boundary [7,18]. In addition to the electrical properties of the GBs, the electrical properties of the semiconducting grains must also be characterized. The conduction activation energy of the grains (Eg) can be calculated from the temperature dependence of Rg. The Rg values at a low-temperature range can be easily calculated using the admittance spectroscopy (Y*) [28,29,57], as the following equation: * = where τgb = RgbCgb, τg = RgCg and τ = RgCgb and Cg and Cgb are the grain and GB capacitance values, respectively. According to the impedance spectroscopy, it was found that Rgb >> Rg and Cgb >> Cg. From Equation (3), Rg can be obtained from the relation = 1/2 ′′ , where ′′ is the maximum value at ′′ peak. As shown in Figure 10a-c, ′′ appears in the temperature range from −60 to 0 °C. Consequently, Eg can be calculated by using the Arrhenius law, In addition to the electrical properties of the GBs, the electrical properties of the semiconducting grains must also be characterized. The conduction activation energy of the grains (E g ) can be calculated from the temperature dependence of R g . The R g values at a low-temperature range can be easily calculated using the admittance spectroscopy (Y*) [28,29,57], as the following equation: where τ gb = R gb C gb , τ g = R g C g and τ = R g C gb and C g and C gb are the grain and GB capacitance values, respectively. According to the impedance spectroscopy, it was found that R gb >> R g and C gb >> C g . From Equation (3), R g can be obtained from the relation R g = 1/2Y max , where Y max is the maximum value at Y peak. As shown in Figure 10a-c, Y max appears in the temperature range from −60 to 0 • C. Consequently, E g can be calculated by using the Arrhenius law, σ g = σ 0 exp −E g /k b T , where σ g is the grain conductivity (σ g ∝1/R g ), and σ 0 is a per-exponential constant term. The E g can be calculated by the linear fitting data, as demonstrated in the insets of Figure 10a-c. The E g values are 0.112, 0.118 and 0.126 eV for the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics, respectively. The E g slightly increased with increasing the excessive TiO 2 , corresponding to the increase in R g (Figure 3c). The difference between E g and E gb clearly indicates the formation of IBLC microstructure, consisting of the semiconducting grains and insulating GBs. The XPS technique was further used to characterize the electrical properties of the grains. Figure 11a-c displays the XPS spectra of the Cu 2p 3/2 for the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics, respectively. According to the fitted curves, the XPS peak of the Cu 2p 3/2 can be divided into two peaks at relatively low and high binding energies, corresponding to the Cu + and Cu 2+ , respectively. Note that only Ti 4+ can be detected in the XPS spectra, as shown in Figure 11d-f. Thus, the conduction in the semiconducting grains of all the ceramics is attributed to the electron hopping between Cu + ↔ Cu 2+ . The Cu + /Cu 2+ ratios of the NYCTO, NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics are 0.069 ± 0.027, 0.053 ± 0.021 and 0.049 ± 0.020, respectively. The Cu + /Cu 2+ ratios decreased with increasing TiO 2 -rich phase. Generally, CCTO and related ACu 3 Ti 4 O 12 ceramics lose small amount of oxygen during sintering, giving rise to oxygen vacancies and associated free electrons [5,9]. Accordingly, a small amount of Cu + and/or Ti 4+ can be detected. For the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics, the diffusion of oxygen vacancies during the sintering process may be inhibited by the segregation of TiO 2 -rich phase along the GBs. Thus, the oxygen loss and related oxygen vacancies in the TiO 2 -rich NYCTO ceramics were reduced, leading to the decrease in Cu + ions. The increased R g (Figure 3c) can be proved to be caused by the decreased Cu + /Cu 2+ ratios. In addition to the grain size effect, the observed decrease in the ε of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics can be described based on the IBLC microstructure. Under al applied electric field, charge carriers inside the semiconducting grains are moved to trap at the insulating GB due to a high potential barrier height, inducing the interfacial polarization and hence high ε value. The intensity of the interfacial polarization of the NYCTO + 0.1TiO 2 and NYCTO + 0.2TiO 2 ceramics should be lower than that of the NYCTO ceramic because of a lower concentration of free carriers inside the grains, which is considered by a larger R g value.

Conclusions
In conclusion, we have successfully synthesized the TiO2-rich NYCTO ceramics prepared using the SSR method. The effects of Ti-excess on the microstructure, colossal dielectric properties and nonlinear J-E characteristics were studied. Only the main phase of the NYCTO structure was detected in the XRD patterns, which might be due to the presence of an amorphous phase of TiO2 along the GBs. Significantly reduced grain with  Figure 11. (a-c) XPS spectra of Cu 2p3/2 for all sintered NYCTO + xTiO 2 ceramics. (d-f) XPS spectra of Ti 2p for all sintered NYCTO + xTiO 2 ceramics.

Conclusions
In conclusion, we have successfully synthesized the TiO 2 -rich NYCTO ceramics prepared using the SSR method. The effects of Ti-excess on the microstructure, colossal dielectric properties and nonlinear J-E characteristics were studied. Only the main phase of the NYCTO structure was detected in the XRD patterns, which might be due to the presence of an amorphous phase of TiO 2 along the GBs. Significantly reduced grain with highly dense microstructure was observed in the TiO 2 -rich NYCTO ceramics, which was due to the pinning effect of the TiO 2 -rich phase particles. The reduced grain sizes, which can cause an increase in the GB density, resulted in the significant enhancement of R gb , and hence reduced tanδ. The colossal ε values of~0.7-1.4 × 10 4 was achieved in the TiO 2 -rich NYCTO ceramics. The TiO 2 -rich NYCTO ceramics also showed the enhanced nonlinear J-E properties due to the improved GB properties. The R g value was also increased owing to the decreased Cu + /Cu 2+ ratio, confirming by the XPS result. The overall colossal dielectric permittivity and nonlinear electrical properties were well described using the Maxwell-Wagner polarization relaxation model based on the formation of the Schottky barrier at the grain boundary.