Solid State Communications 150 (2010) 1794–1797
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Giant dielectric response and polaronic hopping in charge-ordered Nd1.75 Sr0.25 NiO4 ceramics X.Q. Liu ∗ , Y.J. Wu, X.M. Chen Laboratory of Dielectric Materials, Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
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Article history: Received 12 June 2010 Received in revised form 4 July 2010 Accepted 7 July 2010 by P. Sheng Available online 14 July 2010 Keywords: C. Crystal structure and symmetry D. Dielectric response D. Electronic transport
abstract The structure and dielectric properties of charge-ordered Nd1.75 Sr0.25 NiO4 ceramics are presented. The giant dielectric constant about 30 000 is observed in the present ceramics even the frequency is up to 5 MHz. There are three dielectric relaxations at the curve of temperature dependence of dielectric constant in the considered temperature range. Based on the comparison of activation energies of dielectric relaxation and electrical conductivity, the giant dielectric response should be attributed to the bulk factor, that is, thermally activated small polaronic hopping in the present ceramics, while the dielectric relaxation around room temperature should cause from the effect of grain boundaries. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Materials with giant dielectric constant have been of interest since the discovery of CaCu3 Ti4 O12 (CCTO) for their potential application in the microelectronics [1–15]. The common feature of these materials is a giant dielectric constant (ε 0 > 104 ) over a wide range of temperature, and a sharp decrease of permittivity with increasing frequency or decreasing temperature to a critical point. Among these materials, the nickelates with a K2 NiF4 structure are highlighted for their giant dielectric response at high frequencies. The giant dielectric response can be observed even up to gigahertz at room temperature [13,15], and this feature maybe allow a potential application of these materials at high frequencies. In our previous work, the giant dielectric responses up to high frequency were observed in the Ln1.5 Sr0.5 NiO4 (Ln = La, Nd, Sm) ceramics [8,9]. The dielectric constant increases with increasing strontium content or decreasing ionic radius of rare earth, while the dielectric losses are nearly unaffected. The best dielectric properties are obtained in Sm1.5 Sr0.5 NiO4 ceramics, that is, the dielectric constant is about 100 000 at high frequency even up to 5 MHz, and the dielectric loss is only about 0.1. The valuable characteristic of this ceramics is that this giant dielectric constant is stable over a wide temperature and frequency range. We have well proved the giant dielectric response in these ceramics originates from the thermally activated hopping of small polarons, and the significant decrease of
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dielectric constant under a critical temperature is readily explained by the segregation of these polarons, which results from the formation of stripe charge ordering at temperatures below the charge order–disorder transition. As shown in the work of Winkler et al. [16], the polaron size, i.e., the number of Ni sites over which the hole is delocalized, increases with decreasing the content of strontium ion. If the dielectric response is attributed to the polaronic hopping process as assumed by our previous work, it will degenerate with decreasing content of strontium ion due to the decreased polaronic concentration, and the activation frequency should decrease as the result of the increasing polaronic size. So, one can confirm the correlation between the dielectric response and polaronic hopping process from the low strontium content samples, such as, x = 0.25. As shown in the previous work [17], dielectric constant of Sm1.75 Sr0.25 NiO4 ceramics is indeed lower than that of Sm1.5 Sr0.5 NiO4 ceramics, while the difference of the activation frequencies for giant dielectric response is not obvious. Unfortunately, the existence of the impurity phase in the Sm1.75 Sr0.25 NiO4 ceramics prevents one to examine the relationship between the dielectric response and polaronic concentration and/or size. So, in the present work, the single Nd1.75 Sr0.25 NiO4 phase is prepared and the correlation between these two factors is confirmed. 2. Experimental conditions Nd1.75 Sr0.25 NiO4 powders were prepared by a solid-state reaction with using Nd2 O3 (99.9%), NiO (99%) and SrCO3 (99.9%) as starting materials. The weighted raw materials were mixed by ball milling with ZrO2 media in ethanol for 24 h, and then the dried
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Fig. 1. X-ray diffraction patterns of Nd1.75 Sr0.25 NiO4 ceramics at room temperature. The inset is the micrograph of the as-sintered surface for the present ceramics.
mixtures were calcined at 1200 °C for 3 h to yield desired materials. The calcined products were reground with 8 vol% of polyvinyl alcohol (PVA) binder before being pressed uniaxially into pellets. The pellets were sintered at 1425 °C in air for 3 h to obtain the desired and dense Nd1.75 Sr0.25 NiO4 ceramics (relative density was larger than 99% of the theoretical density). The crystalline phases of sintered samples after crushing and grinding were identified by powder X-ray diffraction (XRD) using Cu Kα radiation (Rigaku D/max 2550 PC, Rigaku Co., Tokyo, Japan). The microstructures were observed from as-sintered surfaces of these ceramics with a field emission scanning electron microscopy (S-4800, Hitachi Co., Tokyo, Japan). The dielectric characteristics and ac conductivities of these ceramics were evaluated with a broadband dielectric spectrometer (Turnkey Concept 50, Novocontrol Technologies GmbH & Co. KG, Hundsangen, Germany) in a broad range of temperature (123–573 K) and frequency (1 Hz–10 MHz) with a heating rate of 2 K/min, and the silver paste was adopted as electrodes. 3. Results and discussion Fig. 1 shows the XRD pattern of Nd1.75 Sr0.25 NiO4 ceramics. A single tetragonal phase with the space group of I4/mmm is obtained, and it can be well indexed by the Nd1.6 Sr0.4 NiO4 (PDF# 80-2324) as the model. The cell parameters are refined as following: a = 3.80245(17) Å, and c = 12.423(7) Å, respectively. The inset of Fig. 1 shows the micrograph of the as-sintered surface of Nd1.75 Sr0.25 NiO4 ceramics. From this figure, the dense ceramics with an average grain size of about 5 µm is observed. Fig. 2 shows the temperature dependence of dielectric properties of Nd1.75 Sr0.25 NiO4 ceramics. Dielectric constant of the present ceramics is about 30 000, and it is lower than that of Nd1.5 Sr0.5 NiO4 ceramics [8]. This result is consistent with the previous statement, that is, the dielectric response decreases with decreasing strontium content for the Nd2−x Srx NiO4 ceramics. Around the temperature of 150 K, dielectric constant increases sharply with increasing temperature to a critical point, and then a giant dielectric constant step is established. While the dielectric loss decreases with increasing temperature at the same range, and a corresponding peak should appear at the curve if the temperature is low enough. The critical temperature increases with increasing testing frequency, and this is a typical dielectric relaxation. The stripe charge-ordering temperature of the present ceramics is around 150 K [18], which is consistent with the temperature of dielectric relaxation. This may provide a clue to the correction between the dielectric relaxation and charge ordering, and it is the common feature of dielectric response in charge-ordered nickelates [8–10,17]. Around the room temperature, another dielectric relaxation is observed at low
Fig. 2. Temperature dependence of (a) dielectric constant and (b) dielectric loss of Nd1.75 Sr0.25 NiO4 ceramics at various frequencies.
frequencies, and it disappears at high frequency. This indicates that this relaxation should be related to the extrinsic factor, such as, grain boundary. At high temperature, the dielectric constant increases sharply with increasing temperature, and this should be attributed to the increasing electrical conductivity [8,9]. To deeply insight the low temperature dielectric relaxation, the frequency dependence of dielectric constant is plotted at various temperatures as shown in Fig. 3(a). Dielectric constant decrease with increasing frequency, and two steps are observed at the curves. This behavior is also found in the Nd1.5 Sr0.5 NiO4 ceramics [8]. The first drop occurred around 1–100 kHz, which is lower than that of Nd1.5 Sr0.5 NiO4 ceramics. This drop should be related to the secondary dielectric relaxation around room temperature, and the dropping frequency increases with increasing temperature. Then the polydispersion Debye equation [19]
ε ∗ = ε 0 − iε 00 = ε∞ + (ε0 − ε∞ )/ 1 + (i$ τ )1−α ,
(1)
is used to fit the ε ∼ f curves (solid lines in Fig. 3(a)), where ε0 is the static dielectric constant, ε∞ is the dielectric constant at very high frequencies, ω is the angular frequency, τ is the mean relaxation time and α represents the degree of the distribution of relaxation time τ . By fitting these curves, the relaxation times at different temperatures are obtained and plot as the function of the reciprocal temperature. The variation of relaxation times with temperature follows the Arrhenius law, 0
τ = τ0 exp(Ea /kB T ),
(2)
where τ0 is the relaxation time at very high temperatures, Ea is the activation energy, and kB is the Boltzmann constant (Fig. 3(b)). The fitting parameters are obtained as Ea = 95 ± 4 meV and τ0 = 2.30 × 10−8 s. The corresponding frequency, f0 , of the relaxation time at high temperature, τ0 , is about 6.9 MHz, and this means that the dielectric relaxation is limited in the low frequency, which is consistent with the previous statement. The secondary drop is observed over 5 MHz, and this is the common feature of the nickelates with the K2 NiF4 structure [8–10,17].
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Fig. 3. (a) Frequency dependence of the dielectric constant of Nd1.75 Sr0.25 NiO4 ceramics at various temperatures. The closed square is the data for sample with the electrode of sputtered gold at 135 K. (b) Temperature dependence of relaxation time for Nd1.75 Sr0.25 NiO4 ceramics. Symbols are the experimental data and solid lines are fits.
To find out the origin of dielectric relaxation in the present ceramics, the effect of the electrode should be discussed first [20,21]. As shown in the previous work [12,15], the dielectric data for the nickelates with electrodes of sputtered gold and silver paint are the same only at low temperature and/or high frequency. The close square in Fig. 3(a) shows the dielectric constant of the sample with the sputtered gold electrode, and the same result is found in the present ceramics. So other factors should be responsible to the giant dielectric response, although the interface effect of electrode is indeed existed in the present ceramics. As shown in previous work, the dielectric relaxation is closed related to the electrical conduction in nickelates, and the impedance spectra are good tools to separate the contribution from bulk and grain boundary. For a typical electroceramics, the equivalent circuit consisting of two parallel RC elements connected in series with one RC element, Rgb Cgb , representing the grain boundary regions and the other one, Rb Cb , representing the bulks, is usually used to fit the experiment data [22]. The frequency dependences of imaginary impedance at various temperatures are shown as dots in Fig. 4(a). Then, the abovementioned equivalent circuit is used to fit these experimental data, and the results are shown as the solid lines in Fig. 4(a). The electrical resistivities of bulk and grain boundary for the present ceramics are extracted from the fitting, and results are shown in Fig. 4(b). The electrical conduction of the present ceramics should be the adiabatic polaronic hopping [8–10,17], and the model leads to the conductivity in the form of
σ = σ0 T −1 exp(−EA /kB T ),
(3)
where σ0 is a constant related to the polaron concentration and diffusion, and EA is the polaronic hopping energy. So the adiabatic polaronic hopping model is used to fit the obtained electrical resisitivities of bulk and grain boundary in the present ceramics, respectively. The electrical resisitivies obey the adiabatic polaronic
Fig. 4. (a) Frequency dependence of imagery impedances of Nd1.75 Sr0.25 NiO4 ceramics at various temperatures. (b) Temperature dependence of resistivities obtained from the equivalent circuit fitting for Nd1.75 Sr0.25 NiO4 ceramics. Symbols are the experimental data and solid lines are fits.
hopping model in the considered temperature range. The activation energies of electrical conduction of bulk and grain boundary are 114 ± 2 meV and 100 ± 3 meV, respectively. Noted that the activation energy of secondary, i.e. low frequency dielectric relaxation around room temperature, is similar to that of grain boundary; one can conclude that the dielectric relaxation around room temperature should be attributed to the effect of grain boundary in the present ceramcis. While the high frequency dielectric relaxation at low temperature may be attributed to the bulk effect, i.e. the adiabatic polaronic hopping process, which is closely related to the charge ordering in the present ceramics [8–10]. 4. Conclusion Dense Nd1.75 Sr0.25 NiO4 ceramics with single K2 NiF4 phase has been prepared by the solid-state sintering process. Giant dielectric constant about 30 000 is observed, which is smaller than that of Nd1.5 Sr0.5 NiO4 ceramics, and this is attributed to the low polaron concentration in the present ceramics. Three dielectric relaxations are observed in the consideration temperature range. The dielectric relaxation around room temperature is originated from the grain boundary effect, while the low temperature relaxation should be attributed to the adiabatic polaronic hopping process which is close related to charge ordering in the present ceramics. At high temperature, dielectric constant increases sharply with increasing temperature, which should be attributed to the high electrical conductivity. From this work, the correlation between dielectric response and polaronic hopping process is confirmed. Acknowledgement This work was supported by National Science Foundation of China under grant nos 50702049 and 50832005.
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