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Impedance Spectroscopy of (Pb0.5Na0.5) (Mn0.5Nb0.5)O3 Ceramics a
b
J. Macutkevic , A. Molak & J. Banys
a
a
Faculty of Physics, Vilnius University, Sauletekio al. 9, LT-10222 Vilnius, Lithuania, b
Institute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, Poland Published online: 02 May 2014.
To cite this article: J. Macutkevic, A. Molak & J. Banys (2014) Impedance Spectroscopy of (Pb0.5Na0.5) (Mn0.5Nb0.5)O3 Ceramics, Ferroelectrics, 463:1, 40-47, DOI: 10.1080/00150193.2014.891917 To link to this article: http://dx.doi.org/10.1080/00150193.2014.891917
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Ferroelectrics, 463:40–47, 2014 Copyright © Taylor & Francis Group, LLC ISSN: 0015-0193 print / 1563-5112 online DOI: 10.1080/00150193.2014.891917
Impedance Spectroscopy of (Pb0.5 Na0.5 )(Mn0.5 Nb0.5 )O3 Ceramics J. MACUTKEVIC,1,∗ A. MOLAK,2 AND J. BANYS1 1
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Faculty of Physics, Vilnius University, Sauletekio al. 9, LT-10222 Vilnius, Lithuania 2 Institute of Physics, University of Silesia, Uniwersytecka 4, PL-40-007 Katowice, Poland Results of broadband dielectric/electric investigations of (Na0.5 Pb0.5 )(Mn0.5 Nb0.5 )O3 ceramics are presented in wide frequency range 20 Hz–3 GHz. The electric properties of (Na0.5 Pb0.5 )(Mn0.5 Nb0.5 )O3 ceramics are mainly governed by high ionic conductivity. One ionic and three polaronic contributions to electrical conductivity were successfully separated by employing impedance formalism. Keywords impedance spectroscopy; polaronic conductivity; distribution of relaxation times; perovskite
Introduction
Perovskite solid solutions, (A 1−x A x )(B 1−y B y )O3 showing a combination of electrical, mechanical or magnetic properties attracts attention due to potential use in the electronic industry [1]. Particularly, the niobate-based materials exhibit high-value dielectric permittivity in a wide temperature range combined with a marked dispersion but due to different mechanisms [2, 3]. The (Na0.5 Pb0.5 )(Mn0.5 Nb0.5 )O3 (NPMNO) ceramics show semiconductor properties and mixed ionic-electronic conductivity that attracts attention due to possible applications. Basic structural and dielectric of NPMNO has been reported, e.g. two relaxation processes have been distinguished and mixed polaronic and ionic conductivity was postulated in these ceramics [4, 5]. However, electrical features were not analyzed in details therein. The AC response of ionic conductors is usually described by the use of the empirical frequency domain functions associated with certain properties of unknown time domain function (for example, see [6]). This response is also usually associated with an equivalent electric circuit, however a drawback of such approach is the inherent difficulty of separating processes with comparable relaxation times. In this paper the impedance spectra were analyzed without any predefined assumption about corresponding time domain function. The aim of this paper to investigate different relaxation processes in NPMNO via broadband dielectric/electrical spectroscopy study.
Received September 2, 2013; in final form September 26, 2013. ∗ Corresponding author. E-mail:
[email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gfer.
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Figure 1. Frequency dependence of electrical conductivity measured at different temperatures.
Experimental The sintering of NPMNO ceramics, using a two-stage synthesis process in air, and the sample preparation was described previously [4]. The complex dielectric permittivity ε∗ = ε - iε was measured by a LCR meter HP4284A in the frequency range 20 Hz – 1 MHz and by a vector network analyzer Agilent 8714ET in the frequency range 1 MHz – 3 GHz. The temperature was changed within the range 150–700 K (for the frequencies 20 Hz – 1 MHz) and 300–500 K (for the frequencies 1 MHz – 3 GHz) at a constant rate 1 K min−1. The silver paint was used for contacts.
Results and Discussion The real part of electrical conductivity σ has been calculated according to the formula: σ = ωε0 ε . The obtained results are presented in Fig. 1. The frequency behavior of σ has been fitted according to the Almond-West equation: σ = σDC + Aωs = σDC 1 + (ω/ωh )s ,
(1)
where σ DC is the dc conductivity, Aωs is ac conductivity, ωh is hopping frequency. The Almond-West fit describes dynamic properties of conductivity satisfactorily; however discrepancies appear at higher frequencies and lower temperatures (T < 550 K) due to an additional contribution to the semiconductor type electrical conductivity. The different conductivity processes can not be separated by modified Almond-West fit: σ = σDC1 1 + (ω/ωh1 )s1 + σDC2 1 + (ω/ωh2 )s2 ,
(2)
due the fact that values of ωh1 and ωh2 can be very close each to other. Therefore, we will discuss the electrical conductivity in other terms. Below room temperature no DC conductivity can be estimated in our frequency range.
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Figure 2. Temperature dependence of DC conductivity. The inset shows DC conductivity derivative. Note, that fit lines are shifted by –1 in the temperature range 425–625 K, and by 0.5 in other temperature ranges.
The DC conductivity decreases on cooling (see Fig. 2) and exhibits change in the slope. The derivative ∂σ /∂(T −1) was calculated to determine the temperature ranges where conductivity can be fitted with the Arrhenius law (see inset in Fig. 2). A sharp change occurs at 625 K. Deviation from linearity is seen below ∼425 K and also in vicinity of 330 K. Therefore the temperature dependence of DC conductivity was fitted with the Arrhenius law σ = (σ0 /T ) exp(EDC /kT ) separately in 690–630 K, 620–440 K, 420–370 K, and also in 327–315 K range. Obtained parameters are EDC = 0.60 eV and σ 0 = 2330 S/cm, EDC = 0.53 eV and σ 0 = 592 S/cm, EDC = 0.45 eV and σ 0 = 82.6 S/cm, EDC = 0.26 eV and σ 0 = 5.8 S/m, respectively, in good agreement with previously published results [1, 4, 5]. The estimated from numerical fitting value of s ≈ 0.5 (in 450–700 K range) is typical for ionic conductors containing moderate to high concentration of mobile ions [7]. The parameter s shows abrupt increase below T = 450 K (Fig. 3(b)). Despite of inaccuracy in Almond – West fit at low temperatures (T < 550 K), the increase in s value is reliable due the fact that the curvature of σ (ω) also increases below T = 450 K (Fig. 1). The temperature dependence of hopping frequency ωh is quite similar to temperature dependence of DC conductivity (Fig. 3(a)). This dependence was fitted with the Arrhenius law ωh = ωh0 exp(Eh /kT) separately below and above T = 425 K. Obtained parameters are Eh = 0.56 eV, ωh0 = 0.27 THz for T > 425 K and Eh = 0.26 eV, ωh0 = 109 GHz for T < 425 K in satisfactorily good agreement with the activation energies obtained from DC conductivity. Such values of hopping frequencies indicate the polaronic mechanism of electric conductivity. The increase in s and decrease in hopping frequency ωh values at low temperatures (T < 425 K) is related to the fact that conductivity relaxation occurs mainly at radio frequencies, what will be clearly demonstrated below. The complex impedance Z ∗ is related to the complex electrical conductivity σ ∗ and the complex dielectric permittivity ε∗ via the relation: Z∗ =
1 = 1/ iε∗ ε0 ω . σ∗
(3)
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Figure 3. Temperature dependence of Almond-West fit parameter hopping frequency ωh (a) and s (b).
The obtained frequency dependence of complex impedance Z ∗ is presented in Fig. 4. The impedance spectra demonstrate at least two overlapped contributions. The both contributions are broad enough and cannot be adequately described by single RC circuit. These spectra of ceramics were modeled as infinite chain of RC circuits connected in serial and corresponding distribution of relaxation times was calculated by solving integral equation: ∞
Z ∗ (ν) = Z∞ + Z ∫
−∞
f (τ ) dlgτ . 1 + iωτ
(4)
The method has been described elsewhere [8]. The calculated distributions in the relaxation times f (τ ) are presented in Fig. 5. Four contributions to complex electrical impedance were distinguished. Because of the contributions overlap, the distribution function is shown also separately for temperatures T > 425 K and T < 425 K. The main peaks in the f (τ ) dependence corresponds to the contribution B and C. The contribution A manifests the long relaxation times at high temperatures. The contribution D emerges at low temperatures for short relaxation times (see Fig. 5(a), 5(b) and 5(c), respectively). Hopping frequency ωh at higher temperatures (T > 425 K) corresponds mainly to fast conductivity process, while at lower temperatures it is strongly affected also by slow conductivity process. This can explain the change in slope in temperature dependence of hopping frequency ωh close to 425 K. We would like to note that the studied compound exhibits the same symmetry from 15 K up to 883 K as has been shown by former XRD test [9]. Therefore, a crossover which occurs in the f (τ ) plots does not originate from a structural phase transition.
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Figure 4. Frequency dependence of complex impedance Z ∗ .
We relate the A contribution, which occurs at low frequencies and high temperatures, to blocking contacts effect. The other contributions (B, C, and D), which dominate at intermediate and high frequencies, are assigned to bulk conductivity i.e. polaronic mechanism of electric conductivity. The most probable relaxation times τ were obtained for the B and C processes from position of the peaks in the f (τ ) dependence. These two dependences, τ vs. T−1, are thermally activated (Fig. 6). The relaxation times plot is fitted with Arrhenius law τ = τ 0 exp (Eτ /kT). Obtained parameters are Eτ = 0.48 eV, τ 0 = 22.4 ps for the maximum related to process C and Eτ = 0.47 eV, τ 0 = 327 ps for the longer relaxation times (process B). The process D occurred in narrow temperature range, T < 425 K, and it was not possible to determine its relaxation times temperature dependence. The analysis and interpretation of complex impedance spectra by solving integral Eq. (1) has been already performed in former works [10, 11]. Two maxima in distribution of relaxation times were explained by conductivity in bulk and grain boundary in Cu6 PS5 Br [11] or by two stage Grotthus transport proton mechanism in Rb3 H(SeO4 )2 [10]. In presented materials the situation is different because two different conductivity processes are very close to each to other (Figs. 1 and 4) and cannot be separated without solving integral Eq. 1. Oxygen vacancies VO may be thermally ionized according to equation: VO ↔ V∗O + e ↔ V∗∗ O + 2e .
(5)
The activation energies for singly and doubly ionized oxygen vacancies VO ∗ and VO relates to shallow and deep energy level. In perovskite structures, they are usually equal about 0.1–0.3 eV and 0.6–0.8 eV [13]. Hence, the process D, related to EDC = ∗∗
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Figure 5. Distribution of relaxation times obtained from complex impedance spectra. Isotherms shown in semi-log plot (a), isotherms at T > 425 K plotted in log-log scale (b), isotherms at T < 425 K plotted in log-log scale (c).
0.26 eV and Eh = 0.26 eV, can be assigned to the shallow level of singly ionized VO ∗ vacancy. Let us consider now the two relaxation processes observed in dielectric properties of NPMNO ceramics which show values of activation energies close to each other. The values EDC = 0.53 eV, Eh = 0.56 eV, and Eτ = 0.47 eV were estimated for the process B, while the values EDC = 0.45 eV and Eτ = 0.48 eV were estimated for the process C. Two processes related to oxygen vacancies and similar set of activation energy values were reported for the NPMNO ceramics in the former works carried out by Molak et al. [4, 5, 9]. It has been shown also, by the XPS test analysis, that valence band of NPMNO ceramics consists of O 2p states which hybridize with Nb 4d, Mn 3d, and Pb 6p states [4]. Since the complex dielectric permittivity ε∗ is related with complex impedance Z ∗ via: ε∗ = 1/ Z ∗ iε0 ω ,
(6)
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Figure 6. Temperature dependence of characteristic relaxation times.
so if Z is not equal to zero, i.e. if a frequency Fig. 7 dependence of Z ∗ is observed, the complex dielectric permittivity ε∗ should also exhibit a dispersion. Moreover, if we assume that Z ∗ (ω) is a sum of two different RC circuits impedances the dielectric dispersion will be simple Debye-like according to [12]: ε∗ = ε∞ +
εs − ε∞ σ∗ −i , 1 + iωτ ω
(7)
where εs , ε∞ , τ , are parameters of Debye dielectric dispersion. However, if we assume more complicated form of Z ∗ (ω), as for example can be seen in Fig. 4, the dielectric dispersion
Figure 7. Real and imaginary parts of complex dielectric permittivity ε∗ = ε -i ε vs. T at 1 MHz.
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becomes also more complicated. Thus, the two maxima in distribution of relaxation times (Fig. 5) correspond to two different dielectric dispersions (Fig. 7). We deduce that the both processes, B and C, originate from polaronic mechanism of electric conductivity, and the slight differences in EDC values can be ascribed to different environments of the oxygen vacancies. Hence, one type of oxygen vacancy would be placed in the Nb O sublattice and the other in the Mn O sublattice.
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Conclusions The dielectric properties of NPMNO ceramics are mainly governed by high electrical conductivity. One ionic and three polaronic contributions were separated from complex impedance spectra by calculating distribution of relaxation times. They are originated from hopping of carriers between oxygen vacancies placed in different crystallographic surroundings, in Nb O and Mn O sublattice. The conductivity part related with longer relaxation times is observed in temperature range 550–300 K, while conductivity associated with shorter relaxation times does not vanish down to the lowest temperatures.
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