Effects of DC bias on non-ohmic sample-electrode contact and grain boundary responses in giant-permittivity La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics

Abstract

The effects of DC bias on the giant dielectric properties and electrical responses of non-ohmic sample-electrode contact and grain boundaries of La_1.7Sr_0.3Ni_1−xMg_xO₄ (x = 0–0.5) ceramics were studied. La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics were prepared using a chemical combustion method with urea as a fuel. A pure phase and dense ceramic microstructure were achieved. Using impedance spectroscopy analysis under a DC bias, the giant dielectric properties of an un-doped La_1.7Sr_0.3NiO₄ ceramic were found to be due to a combination of the small polaronic hopping mechanism and non-ohmic sample-electrode contact effect. This was confirmed by a linear Mott–Schottky plot of 1/C² vs. DC bias voltage. Doping La_1.7Sr_0.3NiO₄ ceramics with Mg²⁺ ions caused an increase in the grain boundary resistance, leading to a decrease in the loss tangent and degradation of the electrode effect. The giant dielectric response in La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics (x = 0.3–0.5) was primarily attributed to the insulating grain boundary response (i.e., Maxwell–Wagner polarization) coupled with small polaronic hopping of charge carriers.

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1. Introduction

An Ln_2−xSr_xNiO₄ (Ln = La, Nd, and Sm) ceramic system is one of the most interesting giant dielectric materials investigated in recent years. This is because of its very high dielectric permittivity (ε′ ≈ 10⁵ to 10⁶).^1–14 For La_1.875Sr_0.125NiO₄ single crystal, high values of ε′ ≈ 10⁴ can be obtained even when the frequency is increased into the GHz range.² The origin of the giant dielectric response (GDR) in Ln_2−xSr_xNiO₄ ceramics has been intensively investigated.^1–5,15 It has been widely proposed that the GDR is attributable to the small polaronic hopping process in Ln_2−xSr_xNiO₄ ceramics.^1–4 Accordingly, the dielectric response has been directly linked to the concentration and size of small polarons and the hopping process is directly correlated to the charge ordering. Three mechanisms reflect the existence of the small polaronic hopping process: first, the ε′ value increases with increasing concentrations of small polarons.¹⁶ Second, the critical response frequency, at which a sudden drop in ε′ occurs, shifts to lower frequencies as the polaronic size is increased, since the bigger polaron will have a larger effective mass.^6,17,18 It was demonstrated that the polaronic size of Ln_2−xSr_xNiO₄ can be increased by decreasing Sr²⁺ concentration and by partially doping this ceramic material with Al³⁺ ions into Ni³⁺ sites.^6,18,19 Lastly, the long-range hopping of small polarons gives rise to electrical conductivity, leading to a large increase in the low-frequency tan δ value.¹¹

In addition to the intrinsic origin, it was suggested that the giant ε′ values of Ln_2−xSr_xNiO₄ ceramics were primarily associated with an extrinsic non-ohmic sample-electrode contact effect.¹⁵ Furthermore, the grain boundary (GB) (i.e., Maxwell–Wagner effect) response was also suggested to have an effect on the GDR in La_2−xSr_xNiO₄ (LSNO) thin films.⁵ The GDR in SiO₂/LSNO composite ceramics was described and attributed to a combination of small polaronic hopping and the GB response.¹¹ Although all of these explanations are reasonable, a significant controversy concerning the precise mechanism of GDR in Ln_2−xSr_xNiO₄ ceramic systems remains. Perhaps, none of these models can completely describe the GDR. Further studies are needed to clarify the relevant mechanisms and each of their contributions.

For Ln_2−xSr_xNiO₄ ceramics, the grain resistance (R_g ≈ 0.1 Ω) (or bulk resistance) and GB resistance (R_gb ≈ 17.5 Ω) at room temperature (RT) are very small.^1,7 R_gb is much smaller than for other giant dielectric materials (e.g., CCTO) by at least 3–4 orders of magnitude.^20,21 As a result, the grain and GB responses in Ln_2−xSr_xNiO₄ ceramics cannot be analyzed using impedance spectroscopy (IS), even if the measurements are performed at 10 K.¹⁵ According to an equivalent circuit consisting of three parallel RC elements connected in series (i.e., grain, GB, and electrode responses),²² it was theoretically demonstrated that when R_gb ≪ R_e (resistance of sample-electrode contact), the high ε′ plateau in a low-frequency range is dominated by the electrode effect at RT. When R_gb ≫ R_e and R_g, a high ε′ value in a low-frequency range is dominated by the GB response (high GB capacitance, C_gb).²³ In this case, the electrode effect is concealed by the GB effect. Furthermore, the electrode effect would not be dominant if the semiconducting surface becomes an insulating surface, i.e., the conductivity of the grains was greatly enhanced. R_gb of other giant dielectric materials (e.g., CaCu₃Ti₄O₁₂) can generally enhanced by doping with Mg²⁺.^24–27 Doping Mg²⁺ ions into LSNO may increase its R_gb. Thus, the electrical responses of the grain, GB, and electrode contact contributing to the GDR in an Ln_2−xSr_xNiO₄ ceramic system can be easily characterized. Dielectric measurements under a DC bias have given important clues to understand the GB and electrode responses.^22,28–30

In this work, Mg²⁺ doped-LSNO ceramics were prepared to demonstrate the dominant effects of the GB response and non-ohmic sample-electrode contact. The effects of DC bias on the GDR in Mg²⁺ doped-LSNO ceramics were investigated to clarify the underlying mechanism(s) of the GDR in LSNO ceramics. Details of each contribution to the GDRs in different temperature and frequency ranges are discussed.

2. Experimental details

A chemical combustion was used to synthesize nanosized La_1.7Sr_0.3Ni_1−xMg_xO₄ (x = 0, 0.3, 0.4 and 0.5) powders. The starting raw materials used as metal-ion sources were Ni(NO₃)₂·6H₂O (99.0%, Kanto Chemical), La(NO₃)₃·6H₂O (99.99%, Sigma-Aldrich), Sr(NO₃)₂ (99.0%, Sigma-Aldrich) and Mg(NO₃)₂·6H₂O (99.999%, Sigma-Aldrich). Urea (CH₄N₂O, 99.0%) was used as a fuel. For La_1.7Sr_0.3Ni_1−xMg_xO₄ with x = 0, first, 3.6806 g of La(NO₃)₃·6H₂O, 0.3147 g of Sr(NO₃)₂ and 1.4540 g of Ni(NO₃)₂·6H₂O were dissolved in 80 mL of aqueous solution of citric acid (2.5 wt%) at RT with constant stirring using a magnetic bar on a hotplate. For La_1.7Sr_0.3Ni_1−xMg_xO₄ with x = 0.3, 0.4 and 0.5, 1.0178 g of Ni(NO₃)₂·6H₂O and 0.3846 g of Mg(NO₃)₂·6H₂O, 0.8724 g of Ni(NO₃)₂·6H₂O and 0.5128 g of Mg(NO₃)₂·6H₂O, and 0.7270 g of Ni(NO₃)₂·6H₂O and 0.6410 g of Mg(NO₃)₂·6H₂O were used, respectively. Second, 0.7 g of CH₄N₂O was mixed into the metal ion solution with constant stirring at 200 °C for 2 h. When a transparent viscous gel was observed, then the viscous gel was dried in a furnace at 300 °C for 30 min using heating rate 10 °C min⁻¹. On heating, a fast and strong combustion was observed when the temperature increased to ≈200–210 °C. To obtain a single phase of La_1.7Sr_0.3Ni_1−xMg_xO₄ powders, the dried porous precursors were ground and calcined in a furnace in air at 1000 °C for 6 h using heating rate 5 °C min⁻¹. The resulting nanosized powders were pressed by uniaxial compression at ≈200 MPa into a pellet shape of 9.5 mm in diameter and ∼1–2 mm in thickness. Finally, these pellets were sintered in air at 1375 °C for 6 h with a heating rate 5 °C min⁻¹ followed by natural furnace cooling to RT. The atmospheric pressure was ≈758 mmHg.

The particle size and shape of nanosized-La_1.7Sr_0.3Ni_1−xMg_xO₄ powders were determined using transmission electron microscopy (TEM; FEI Tecnai G²). Structure and phase composition of the sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics were characterized using an X-ray diffraction (XRD) technique (PANalytical, EMPYREAN). Rietveld quantitative phase analysis was carried out using the X'Pert High Score Plus v3.0e software package by PANalytical. Polished-surface morphologies of the sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics were characterized using scanning electron microscopy (SEM) (LEO 1450VP, UK). The chemical states of Ni were analyzed using X-ray photoelectron spectroscopy (XPS), PHI5000 VersaProbe II, ULVAC-PHI, Japan at the SUT-NANOTEC-SLRI Joint Research Facility, Synchrotron Light Research Institute (SLRI), Thailand. All binding energies of the samples were calibrated with the C1s peak at 284.8 eV. The XPS spectra were fitted with PHI MultiPak XPS software using a combination of Gaussian–Lorentzian lines.

Prior to dielectric and electrical measurements, Au electrodes were sputtered onto each polished-face at a current of 25 mA for 8 min using a Polaron SC500 sputter coating unit. The dielectric properties were measured using a KEYSIGHT E4990A impedance analyzer over the frequency range of 100 Hz to 1 MHz under different DC bias voltages. An oscillation voltage of 500 mV was used.

3. Results and discussion

The XRD patterns of the sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ (M-LSNO) ceramics, where x = 0, 0.3, 0.4 and 0.5, are shown in Fig. 1a, confirming the formation of an LSNO phase (JCPDS 32-1241) with a tetragonal structure. The identified crystal structure and the detected XRD patterns were similar to those reported in previous studies.^{6,7,9,11–14,31} No impurity phase diffraction peak was observed. Rietveld refinement profile fits were performed, as illustrated in Fig. 1b. Accordingly, lattice parameters of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0, 0.3, 0.4 and 0.5 were obtained to be a = 3.8306 and c = 12.7115 Å, a = 3.8371 and c = 12.7234 Å, a = 3.8463 and c = 12.7429 Å and a = 3.8653 and c = 12.8225 Å, respectively. These values are comparable to JCPDS 32-1241 for a = 3.817 and c = 12.766 Å and literature values [a = 3.8167 and c = 12.7410 Å].^{9,10,15,18,19} The effect of Mg²⁺ dopant on the crystal structure of LSNO ceramics is demonstrated in Fig. 1c. Both of a and c values of the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics increases with increasing Mg²⁺ dopant (x). The increased lattice parameters were primarily attributed to the larger ionic radius of the Mg²⁺ dopant (r₄ = 0.57 Å) compared to that of the host Ni²⁺ ion (r₄ = 0.55 Å). The crystal structure of La_1.7Sr_0.3Ni_1−xMg_xO₄ is illustrated in Fig. 1d.

Fig. 1 (a) XRD patterns of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with (1) x = 0, (2) x = 0.3, (3) x = 0.4, and (4) x = 0.5. (b) Profile fits for the Rietveld refinement of the undoped La_1.7Sr_0.3NiO₄ ceramic. (c) Lattice parameters (a and c) of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0–0.5. (d) The schematic of La_1.7Sr_0.3NiO₄ crystal structure.

Nanosized-La_1.7Sr_0.3Ni_1−xMg_xO₄ powders (x = 0 and 0.4) with grain sizes of about 200–400 nm are shown in Fig. 2a and b. The polished-surfaces of the sintered ceramics using these powders are shown in Fig. 2c–f. The grain size of the sintered LSNO ceramics was slightly enlarged by doping with Mg²⁺ ions with x = 0–0.4. However, the grain size of the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramic with x = 0.5 was significantly reduced. A large number of pores were observed in the microstructure of undoped-LSNO ceramics, while the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0.3–0.5 had a dense microstructure with no pores. The relative densities of the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0, 0.3, 0.4 and 0.5 were calculated using the Archimedes method and found to be ≈73, ≈87, ≈86, and ≈90%, respectively. It is likely that doping with Mg²⁺ ions caused an increase in densification of LSNO ceramics.

Fig. 2 (a and b) TEM images of La_1.7Sr_0.3Ni_1−xMg_xO₄ powders with x = 0 and 0.4. (c–f) SEM images of polished-surfaces of sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0, 0.3, 0.4 and 0.5, respectively.

The giant dielectric properties in the frequency range of 10² to 10⁶ Hz for the sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics were studied at RT, as shown in Fig. 3. All of the ceramics exhibited giant ε′ values of about 10⁵ to 10⁶ in a low-frequency range. At 10² Hz, the ε′ values of the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0–0.4 were nearly identical [Fig. 3a]. The ε′ value at 1 kHz increased from ≈4.3 × 10⁵ to ≈5.1 × 10⁵ as x increased from 0–0.5. The difference in the frequency dependence of ε′ and tan δ for the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with different x values was observed. In the frequency range of 10² to 10⁵ Hz, ε′ of the La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramic with x = 0 was independent of frequency. ε′ began to decrease to a lower value when the frequency was increased to 10⁶ Hz. A step-like decrease in ε′ (or a critical response frequency) of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics shifted to lower frequencies as x increased. This result is similar to that observed in Al-doped LSNO (ref. 10) and Al-doped Sm_1.5Sr_0.5NiO₄ (ref. 32) ceramics. As shown in Fig. 3b, tan δ of the undoped-LSNO ceramic (x = 0) increased sharply, by about two orders of magnitude, as the frequency was decreased from 10⁴ to 10² Hz. This behavior is generally considered the effect of DC conduction in the bulk ceramics and/or the effect of non-ohmic sample-electrode contact.^33–35 It was also found that, for the ceramics with x = 0–0.4, tan δ increased sharply with increasing frequency in a high frequency range, corresponding to a rapid decrease in ε′. For the ceramic with x = 0.5, the critical response frequency was the lowest and a corresponding tan δ-peak appeared. This behavior indicated that a dielectric relaxation mechanism exists in the bulk ceramic under an applied AC electric field. According to the small polaronic model,^11,19,32 the decrease in a critical response frequency of the M-LSNO ceramic with x = 0.5 can be ascribed to the effect of polaronic size, which may be increased by doping with a high concentration of Mg²⁺ ions. Alternatively, it is possible but unlikely that this dielectric relaxation behavior can be described based on the electrode effect or that the electrode effect may be quite small in M-LSNO ceramics with high concentrations of Mg²⁺ ions.

Fig. 3 Frequency dependence of (a) ε′ and (b) tan δ at RT for La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics.

To clarify the effect of Mg²⁺ doping ions on the small polaronic hopping behavior in LSNO ceramics, all the sintered ceramics were characterized by XPS. Fig. 4 shows the XPS spectra of Ni 3p regions of the sintered La_1.7Sr_0.3Ni_1−xMg_xO₄ (M-LSNO) ceramics with x = 0, 0.3, 0.4 and 0.5. The Ni 3p peaks of all sintered ceramics can be deconvoluted into three main peaks. The peaks at ≈67.2–67.5 eV are assigned to Ni²⁺,³⁶ while the peaks at ≈68.7–69.0 eV are attributed to Ni³⁺. The peaks at ≈73.0–73.3 eV are assigned to a satellite peak associated with Ni²⁺. This observation is consistent with that reported in literature.³⁷ The result confirms the coexistence of Ni²⁺ and Ni³⁺ in the samples. The presence of Ni³⁺ indicated that the conduction was attributable to charge hopping between Ni³⁺ ↔ Ni²⁺. As shown in Fig. 4, the ratios of Ni³⁺/Ni²⁺ in the undoped-LSNO ceramic and M-LSNO ceramics with x = 0.3, 0.4 and 0.5 changed slightly. This means that Mg²⁺ ions preferentially substituted into Ni²⁺ sites. It is reasonable to suggest that the small polaronic concentration the M-LSNO ceramics should not significantly change. This result is consistent with the observed GDR in M-LSNO ceramics, in which the ε′ value in a low frequency range was not decreased by Mg²⁺ doping. Changes in the critical response frequency were likely due to an increase in polaronic sizes, just as was proposed in Al-doped LSNO ceramics.⁶

Fig. 4 XPS spectra of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0, 0.3, 0.4 and 0.5.

The small polaronic hopping mechanism or the electrode effect is now the most likely origin of the GDR in LSNO ceramics.^10,15,32 Electrical conduction inside the grains is therefore considered the primary factor. In the M-LSNO ceramics, however, the GB response may be another important factor. This is because the large decrease in tan δ may have been caused by the dominant effect of the GB response. Impedance spectroscopy is a powerful tool for separating the electrical responses of grains, GB and the electrode effect.^22,28,29 It was used to determine the total resistance, which can be estimated from a large semicircular arc. Total resistance increases with increasing Mg²⁺ dopant concentration [Fig. 5]. A Z* plot of the M-LSNO ceramic with x = 0 (undoped-LSNO) cannot be seen in Fig. 5 and inset (a). This was due to its very low total resistance compared to that of the other ceramics [inset (b)]. Furthermore, a nonzero intercept on the Z′ axis was observed, indicating that there exists some component of the ceramic with relatively low conductivity, which may be the grains. Usually, R_g values at RT of LSNO ceramics are about 0.1–2.5 Ω cm.³² This is quite consistent with the value obtained from the observed nonzero intercept, which corresponds to R_g. The total resistance is usually governed by R_gb or R_gb + R_e. Generally, the grain (bulk), GB, and electrode responses can each be described by a parallel R–C element, whereas the macroscopic dielectric response is usually represented by a series connection of three R–C elements.³⁸ To clarify, impedance data were fitted to a single R–C parallel circuit for a Z* plot,

where R and C are the resistance and capacitance of each element, and ω is the angular frequency of an applied electric field. As shown in the inset (b) of Fig. 5, two overlapping arcs in Z* plot of the undoped-LSNO ceramic are observed and fitted by eqn (1). The observed small and large arcs in the relatively high and low-frequency ranges can be ascribed to be the electrical responses of the GBs (R_gbC_gb) and non-ohmic sample-electrode contact (R_eC_e), respectively.²⁹

Fig. 5 Impedance complex plane (Z*) plot at RT for La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0–0.5. Inset (a) shows an expanded view of the high-frequency data close to the origin. Inset (b) shows an expanded view of the inset (a), revealing the electrical responses of grain, GB, and sample-electrode contact.

It is notable that the capacitance of the non-ohmic sample-electrode contact (C_e = 1/2πf_maxR_e) was ≈4.8 × 10⁻⁸ F, which was lower than that of the apparent capacitance of the sample (≈1.2 × 10⁻⁷ F at 1 kHz). This indicates that there is another source of polarization contributing to the overall GDR in the undoped-LSNO ceramic. Interfacial polarization at the GBs can be ruled out because R_gb (≈5.34 Ω cm) was just slightly larger than R_g (≈2.65 Ω cm). Thus, the polaronic hopping process is the most probable factor contributing to the overall GDR in the undoped-LSNO ceramic coupled with the electrode effect, but its intensity was too great. In inset (a) of Fig. 5, a relatively small semicircular arc was observed in the Z* plot of the M-LSNO ceramic with x = 0.5 that could be ascribed to the grain response with R_g ≈ 1120 Ω cm (at RT). This value is comparable to R_g ≈ 1100 Ω (at 300 K) for Sm_1.5Sr_0.5Ni_0.5Al_0.5O₄ ceramic³² and R_g ≈ 2663 Ω (at 300 K) for La_1.75Sr_0.25Ni_0.7Al_0.3O₄ ceramic.⁶ According to the Z* plot of the M-LSNO ceramic with x = 0.5, the large semicircular arc can be ascribed to the R_gbC_gb response, since the R_eC_e response was less dominant due to large increases in R_g and R_gb.^22,23 Thus, it is reasonable that R_g and R_gb of the M-LSNO ceramics increased with increasing Mg²⁺ dopant concentration, as shown in Fig. 6.

Fig. 6 R_g and R_gb values of La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with different doping concentrations.

The R_g values of the M-LSNO ceramics with x = 0.3, 0.4 and 0.5 were, respectively, enhanced by factors of ≈2, ≈21 and ≈422 compared to that of the undoped-LSNO ceramic. As represented in Fig. 4, giving a real overall composition of La_1.7Sr_0.3(Ni²⁺, Ni³⁺)_1−xMg_xO₄, the amount of both Ni²⁺ and Ni³⁺ ions decreased with increasing Mg²⁺ dopant concentration because of a slight change in the ratios of Ni³⁺/Ni²⁺ for all ceramics. The conductivity of M-LSNO ceramics, which was primarily caused by charge hopping between Ni³⁺ ↔ Ni²⁺ ions, was decreased due to reduction in concentration of charge carriers. It is notable that the total amount of Ni²⁺ and Ni³⁺ ions and the amount of Mg²⁺ dopant ions are the same in value for the M-LSNO ceramic with x = 0.5. Therefore, the long range motion of hopping charges inside the grains was also strongly inhibited by Mg²⁺ ions.

It was also observed that the R_gb value of the M-LSNO ceramic with x = 0.5 was much larger than that of the ceramics with x = 0.3 and 0.4. The GB response in M-LSNO ceramics was dominant and the total resistance is therefore governed by R_gb. Substitution of Mg²⁺ into LSNO ceramics can cause a great increase in R_gb. Usually, both of the intrinsic and geometric factors have an influence on the electrical properties of the GBs. As clearly shown in the SEM images, the grain size of the M-LSNO ceramic with x = 0.5 was significantly reduced. This is the primary cause of the remarkable increase in R_gb due to the increase in insulating GB layers. Accordingly, the significant decrease in tan δ in a low-frequency range for M-LSNO ceramics was clearly due to the large increase in R_gb.

Generally, investigation of the electrical and dielectric properties under different DC bias voltages can be done to analyze the electrical responses of GB and electrode effects.^28,29 As shown in Fig. 7a, the observed semicircular arc of the undoped-LSNO ceramic decreased with increasing DC bias. As previously discussed, such a semicircular arc may have been due to the R_eC_e response. This was confirmed using a Mott–Schottky plot of 1/C² vs. DC bias voltage, as shown in the inset of Fig. 8a. It showed a linear response, i.e., variation in the capacitance value with DC bias obeys the Mott–Schottky law for the formation Schottky barrier between metal electrodes and a semiconducting surface.²⁹

Fig. 7 Impedance complex plane (Z*) plot at RT under different DC bias voltages for La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0 (a), x = 0.3 (b), x = 0.4 (c), and x = 0.5 (d), insets of (a–c) show an expanded view of the high-frequency data close to the origin.

Fig. 8 Frequency dependence of ε′ and tan δ at RT under different DC bias voltages for La_1.7Sr_0.3Ni_1−xMg_xO₄ ceramics with x = 0 (a and b) and x = 0.5 (c and d); insets (a) and (c) demonstrate their 1/C² vs. V plots, revealing the possible formation of a Schottky–Mott barrier height due to the electrode effect.

In Fig. 7b and c, the semicircular arc of the M-LSNO ceramics with x = 0.3 and 0.4 decreased with increasing DC bias voltage, while the nonzero intercept did not change as shown in the insets. The R_gb values of the M-LSNO ceramics with x = 0.3 and 0.4 were enhanced by factors of ≈930 and ≈1200, respectively, compared that of the undoped-LSNO ceramic. These R_gb values were much larger than that of R_e of the undoped-LSNO ceramic. When R_gb ≫ R_e, the electrode effect was dominant in these samples.²² In Fig. 7d and its inset, the R_gb of the M-LSNO ceramic with x = 0.5 was greatly reduced from 36 kΩ cm to 222 Ω cm by increasing the DC bias from 0 to 13 V, while R_g decreased slightly from 1120 to 1009 Ω cm. The reduction in R_g may have been caused by injected electrons, which were trapped by oxygen vacancies or other defects.³⁹ A Mott–Schottky plot of 1/C² (extracted from the large arc in the Z* plots) vs. DC bias voltage showed a nonlinear response (inset of Fig. 8c). Therefore, the electrode effect can be excluded as the origin of this electrical response. The GB capacitance of the M-LSNO ceramic with x = 0.5 was extracted from Z* plots (C_gb = 1/2πf_maxR_gb) and found to be ≈7.5 × 10⁻⁸ F. This was lower than that of the apparent capacitance value of the sample (≈1.2 × 10⁻⁷ F at 1 kHz). In contrast to the undoped-LSNO ceramic, further contribution from the electrode effect can be ignored because R_gb ≫ R_e. The polaronic hopping process is also hypothesized as another important factor contributing to the GDR in the M-LSNO ceramic with x = 0.5 as well as in the x = 0.3 and 0.4 samples.

As illustrated in Fig. 8a and b, the ε′ value over the measured frequency range of the undoped-LSNO ceramic decreased as the DC bias was increased from 0–1.5 V, while tan δ increased. These results were due to the decrease in Schottky barrier height at the sample-electrode contact as a result of the effect of DC bias. When the DC bias was increased to 2 V, an overload limited measurement occurred. The overload DC bias was at 15 V. This occurred in the M-LSNO ceramic with x = 0.5, but only in the frequency range below 10⁴ Hz. However, the mechanisms in these two cases were totally different. The mechanisms in the former and later ceramics were correlated with the electrical responses at the sample-electrode contact and GBs, respectively.

4. Conclusions

The origins of the giant dielectric responses in LSNO ceramics were demonstrated via DC bias measurements. For the undoped-LSNO ceramic, the giant ε′ and R_e values decreased with increasing DC bias over the measured frequency range, while tan δ linearly increased. Furthermore, the decreased C values with increasing DC bias voltage were found to follow the Mott–Schottky law, confirming the dominant electrode effect. By comparing the apparent C value of the sintered ceramic with C_e value extracted from IS analysis, the giant ε′ response in the undoped-LSNO ceramic can be attributed to the electrode effect and the small polaronic hopping mechanism. For M-LSNO ceramics, changes in ε′, R_gb and tan δ were similar to those observed in an undoped-LSNO ceramic. However, a linear Mott–Schottky plot of 1/C² vs. DC bias voltage was not obtained, indicating that the electrode effect was not dominant in the M-LSNO ceramics due to a large increase in R_gb. The origins of the giant ε′ behavior in M-LSNO ceramics can be well described based on the Maxwell–Wagner polarization at insulating GBs and the small polaronic hopping mechanism.

Acknowledgements

This work was financially supported by the Thailand Research Fund (TRF) and Khon Kaen University, Thailand [Grant No. RSA5880012]. The authors would like to thank the SUT-NANOTEC-SLRI (BL5.1) Joint Research Facility for use of their XPS facility. K. Meeporn would like to thank the Thailand Research Fund through the Royal Golden Jubilee PhD Program (Grant No. PHD/0191/2556) for his PhD scholarship.

References

1. X. Q. Liu, S. Y. Wu, X. M. Chen and H. Y. Zhu, J. Appl. Phys., 2008, 104, 054114.
2. S. Krohns, P. Lunkenheimer, C. Kant, A. V. Pronin, H. B. Brom, A. A. Nugroho, M. Diantoro and A. Loidl, Appl. Phys. Lett., 2009, 94, 122903.
3. X. Q. Liu, Y. J. Wu and X. M. Chen, Solid State Commun., 2010, 150, 1794–1797.
4. B. W. Jia, W. Z. Yang, X. Q. Liu and X. M. Chen, J. Appl. Phys., 2012, 112, 024104.
5. A. Podpirka and S. Ramanathan, J. Appl. Phys., 2011, 109, 014106.
6. X. Q. Liu, S. Y. Wu and X. M. Chen, J. Alloys Compd., 2010, 507, 230–235.
7. X. Q. Liu, Y. J. Wu, X. M. Chen and H. Y. Zhu, J. Appl. Phys., 2009, 105, 054104.
8. P. Thongbai, T. Yamwong and S. Maensiri, Mater. Lett., 2012, 82, 244–247.
9. K. Meeporn, T. Yamwong and P. Thongbai, Jpn. J. Appl. Phys., 2014, 53, 06JF01.
10. A. Chouket, O. Bidault, V. Optasanu, A. Cheikhrouhou, W. Cheikhrouhou-Koubaa and M. Khitouni, RSC Adv., 2016, 6, 24543–24548.
11. X. Q. Liu, G. Liu, P. P. Ma, G. J. Li, J. W. Wu and X. M. Chen, J. Electroceram., 2016 DOI:10.1007/s10832-016-0041-2.
12. T. I. Chupakhina, N. I. Kadyrova, N. V. Melnikova, O. I. Gyrdasova, E. A. Yakovleva and Y. G. Zainulin, Mater. Res. Bull., 2016, 77, 190–198.
13. A. Chouket, W. Cheikhrouhou-Koubaa, A. Cheikhrouhou, V. Optasanu, O. Bidault and M. Khitouni, J. Alloys Compd., 2016, 662, 467–474.
14. A. Chouket, V. Optasanu, O. Bidault, A. Cheikhrouhou, W. Cheikhrouhou-Koubaa and M. Khitouni, J. Alloys Compd., 2016, 688, 163–172.
15. M. Li and D. C. Sinclair, J. Appl. Phys., 2012, 111, 054106.
16. E. Winkler, F. Rivadulla, J. S. Zhou and J. B. Goodenough, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 094418.
17. G. Liu, X. Q. Liu and X. M. Chen, Appl. Phys. A: Mater. Sci. Process., 2014, 116, 1421–1427.
18. G. Liu, T. T. Chen, J. Wang, X. Q. Liu and X. M. Chen, J. Alloys Compd., 2013, 579, 502–506.
19. J. Wang, G. Liu, B. W. Jia, X. Q. Liu and X. M. Chen, Ceram. Int., 2014, 40, 5583–5590.
20. X. Huang, H. Zhang, J. Li and Y. Lai, J. Mater. Sci.: Mater. Electron., 2016, 1–7.
21. S. Wu, P. Liu, Y. Lai, W. Guan, Z. Huang, J. Han, Y. Xiang, W. Yi and Y. Zeng, J. Mater. Sci.: Mater. Electron., 2016, 1–6.
22. M. Li, D. C. Sinclair and A. R. West, J. Appl. Phys., 2011, 109, 084106.
23. M. Li, Z. Shen, M. Nygren, A. Feteira, D. C. Sinclair and A. R. West, J. Appl. Phys., 2009, 106, 104106.
24. L. Sun, R. Zhang, Z. Wang, E. Cao, Y. Zhang and L. Ju, J. Alloys Compd., 2016, 663, 345–350.
25. A. Nautiyal, C. Autret, C. Honstettre, S. De Almeida-Didry, M. El Amrani, S. Roger, B. Negulescu and A. Ruyter, J. Eur. Ceram. Soc., 2016, 36, 1391–1398.
26. J. Boonlakhorn and P. Thongbai, Jpn. J. Appl. Phys., 2015, 54, 06FJ06.
27. J. Boonlakhorn, P. Kidkhunthod and P. Thongbai, J. Eur. Ceram. Soc., 2015, 35, 3521–3528.
28. T. Adams, D. Sinclair and A. West, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 094124.
29. M. Li, A. Feteira and D. C. Sinclair, J. Appl. Phys., 2009, 105, 114109.
30. P. Thongbai, T. Yamwong and S. Maensiri, Appl. Phys. Lett., 2009, 94, 152905.
31. C. L. Song, Y. J. Wu, X. Q. Liu and X. M. Chen, J. Alloys Compd., 2010, 490, 605–608.
32. X. Q. Liu, B. W. Jia, W. Z. Yang, J. P. Cheng and X. M. Chen, J. Phys. D: Appl. Phys., 2010, 43, 495402.
33. K. Meeporn, T. Yamwong, S. Pinitsoontorn, V. Amornkitbamrung and P. Thongbai, Ceram. Int., 2014, 40, 15897–15906.
34. J. Boonlakhorn and P. Thongbai, J. Electron. Mater., 2015, 44, 3687–3695.
35. B. Wen Jia, X. Qiang Liu and X. Ming Chen, J. Appl. Phys., 2011, 110, 064110.
36. A. N. Mansour, Surf. Sci. Spectra, 1994, 3, 231–238.
37. A. N. Mansour, Surf. Sci. Spectra, 1994, 3, 279–286.
38. R. Schmidt, M. C. Stennett, N. C. Hyatt, J. Pokorny, J. Prado-Gonjal, M. Li and D. C. Sinclair, J. Eur. Ceram. Soc., 2012, 32, 3313–3323.
39. Y. Song, X. Wang, Y. Sui, Z. Liu, Y. Zhang, H. Zhan, B. Song, Z. Liu, Z. Lv, L. Tao and J. Tang, Sci. Rep., 2016, 6, 21478.

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