Appl. Phys. A (2015) 118:907–912 DOI 10.1007/s00339-014-8810-8
Frequency-dependent dielectric permittivity and electric modulus studies and an empirical scaling in (1002x)BaTiO3/ (x)La0.7Ca0.3MnO3 composites Momin Hossain Khan • Sudipta Pal Esa Bose
•
Received: 5 June 2014 / Accepted: 30 September 2014 / Published online: 9 October 2014 Ó Springer-Verlag Berlin Heidelberg 2014
Abstract We have studied the dielectric permittivity and electrical modulus behavior in (100-x)BaTiO3/(x)La0.7Ca0.3MnO3 (x = 20, 30, 40, 50, 60 %) composites over a frequency range from 42 Hz to 5 MHz at room temperature. The dielectric permittivity data have been well interpreted using the Curie–Von Schweidler function adding the conduction contribution. The electric modulus data have been analyzed by invoking the decay relaxation function. Both formalisms describing a non-Debye type relaxation have been obtained in the composites. The electric modulus formalism indicates the Maxwell–Wagner–Sillars relaxation involved in the composite. In the scaled coordinate, the dielectric permittivity and electrical modulus for different x fall on a single master curve, indicating the existence of a general scaling formalism. The empirical scaling also signifies that the relaxation mechanism is independent of composition. In addition, we have proposed an Arrheniuslike equation for x-dependent dc conductivity and characteristic peak frequency in this composite system.
1 Introduction The composites of ferroelectric and ferromagnetic oxides which offer a pathway to the discovery of a number of new multiferroic materials have attracted renewed interest in recent years [1–3]. Based on the applications, there are M. H. Khan S. Pal (&) Department of Physics, University of Kalyani, Kalyani 741235, W.B., India e-mail:
[email protected] E. Bose Department of Engineering Physics, B. P. P. I. M. T., Kolkata 700052, W.B., India
different needs for dielectric materials [4, 5]. For some applications, such as IC insulation materials, dielectrics with a low dielectric constant (i.e., low-k materials) are highly desirable, while for some other applications, such as gate dielectrics in field-effect transistors, dielectrics with a high dielectric constant are preferred [6]. At present, there is considerable interest in ferroelectric perovskite BaTiO3 (BTO) because of their excellent ferroelectric responses and dielectric behavior at room temperature. Hence, it is widely utilized to manufacture electronic components such as multilayer capacitors (MLCs), PTC thermistors, piezoelectric transducers and variety of electro-optic devices [7]. On the other hand, La0.7Ca0.3MnO3 (LCMO) ceramic is a typical ferromagnetic perovskite with phase transition from ferromagnetic metal to paramagnetic semiconductor around 250 K. The functional properties of LCMO, such as good ferromagnetic metallic phase with colossal magnetoresistance and low resistivity, have made them interesting candidates for data storage devices, video tape recorders and spintronic devices [8]. In this regard, the integrated BTO/LCMO offers a great potential for new multifunctional device applications, such as multistate memories and dual read–write devices. Beyond these applications, the coupling between ferroelectric BTO and ferromagnetic LCMO phase allowing additional degrees of freedom can produce a number of interesting phenomenas [9, 10]. The frequency dependence of dielectric properties in this composite largely depends on the grains, grain boundaries, interfaces, etc. [11]. The relaxation behavior also highly depends on the lattice properties, frequency and temperature [12–14]. For these reasons, detail study on dielectric relaxation and electric modulus behavior in this composite is much important to estimate the morphology and to extract the structure, property, etc. [15]. The use of the electric modulus formalism enables one to investigate the
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Maxwell–Wagner–Sillars (MWS) polarization which is masked by a strong conductivity effect, when the conventional complex permittivity formalism is adopted. In general, the relaxation mechanism varies rapidly with the change of the ratio of different phases in the composite materials. To get significant information about the dispersion effects and to enhance the dielectric constant of BTO incorporating the LCMO phase, we have investigated the frequency dependence of dielectric permittivity and the electric modulus behavior in the BTO/LCMO composites at room temperature.
2 Experimental procedure The composite ceramic samples of ferroelectric BaTiO3 (BTO) and ferromagnetic La0.7Ca0.3MnO3 (LCMO) were prepared by high-temperature solid-state reaction method in two steps. At first, the LCMO powder was prepared using required stoichiometric amounts of basic oxides La2O3, CaO, MnO2 (from Aldritch each of purity 99.99 %), as starting materials. The detail is given elsewhere [16]. (100-x)BTO/(x)LCMO was prepared next by mixed calculated amount of commercially available BaTiO3 (from Aldritch with 99.99 % purity) and LCMO. The powders were mixed thoroughly and calcined in air at 1,100 °C for 12 h. In Fig. 1, the XRD pattern is shown for the sample corresponding to x = 60 %. Two distinct phases of BTO and LCMO are clearly observed without any intermediate phase. In the XRD pattern for other samples (not shown here), the relative intensities between two phases systematically change with x. In order to measure the electrical properties of the samples, silver paint was applied on both the flat faces of the samples to serve as electrodes. Capacitance (C) and conductance (G) were
Intensity (a.u)
BTO LCMO
20
30
40 50 2θ (degree)
60
Fig. 1 XRD pattern of the 40 % BTO/60 % LCMO composite
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measured as a function of frequency in the range of 42 Hz– 5 MHz at room temperature using an impedance analyzer (Hioki Model 3532-50).
3 Results and discussion 3.1 Dielectric studies Figure 2a, b shows frequency-dependent real (e0 ) and imaginary parts (e00 ) of the dielectric permittivity of BTO/ LCMO composite at room temperature. It has been observed that e0 and e00 both decrease very fast with the increase of frequency up to 10 kHz. It is also clear that the real part of the dielectric permittivity decreases slowly in the intermediate frequency region 10–200 kHz. But, it is independent on frequency in higher region, above 200 kHz. At low frequency, the interfacial polarizations are effective to the dielectric constant. In the high-frequency region the contribution of dielectric constant mainly arises from ionic and electronic polarizations that are frequency independent [17, 18]. In other words, the decrease in e0 and e00 with increasing frequency can be explained by the fact that as the frequency is raised, the interfacial dipoles have less time to orient themselves in the direction of the signal [19]. It is clear that at high frequencies, e0 values for different x approach each other. Similar observation has been found for the imaginary part e00 . Moreover, it is important to mention here that in case of composite compounds, there are two kinds of conduction channels connected parallel to each other. One is through direct contact between BTO grains (intrinsic effect), whereas the other is through embedded LCMO grains (extrinsic effect). As the interfacial area is quite enhanced, due to the presence of LCMO phase, the extrinsic effect is more dominating. Across these different grains, the charge carriers meet different resistances due to insulating BTO and conducting LCMO grains. On application of an electric field, interfacial polarization mechanisms take place because of the accumulation of electric charges at the interfaces of this composite. This effect is known as MWS relaxation. The dielectric constant value is highly raised to the presence of LCMO phase due to this accumulation of charge. The dielectric loss for the samples also followed similar trend like dielectric constant in the frequency range of 42– 10 kHz as shown in Fig. 2b. It has been observed that in our composite system, the dielectric loss consists of two factors as (a) conduction and (b) relaxation components. The higher values of e00 at relatively low frequency may be attributed to the contribution arising from both the conduction and relaxation losses. At higher frequencies, the relaxation losses are the only sources of dielectric loss. It is also noticed that e00 increases with increasing conducting
Frequency-dependent dielectric permittivity
(a)
3.5
909 Table 1 Values of e0 , n, rdc and b obtained from best fitting of Eqs. (1a), (1b) and (4)
2100
1 kHz
1800
3.0
x (wt%)
'
1500
2.5
' (103)
2.0
0.59
0.152
0.42
600
30
467
0.57
0.469
0.40
300
40
775
0.56
4.48
50
1,479
0.55
60
1,928
0.54
30
40
x
50
60
x = 60 x = 50 x = 40 x = 30 x = 20 fit
0.5
4
5
10 10 frequency (Hz)
10
6
10
7
(b) 50
x =60 x =50
40
x =40
'' (104)
x =30
30
x =20 fit
20
10
0 10
2
10
3
10
4
5
10 frequency (Hz)
10
6
10
7
Fig. 2 a Frequency dependence of real part e0 and b imaginary part e00 of dielectric constant of (100-x)BTO/(x)LCMO composites with x = 20, 30, 40, 50 and 60 wt%. The solid lines are the best fit of Eqs. (1a) and (1b) (inset). Inset of 1 (a) shows the variation of e0 with x
LCMO phase. As the concentration of LCMO phase increases, the conduction loss component increases more rapidly and the relaxation loss component reduces. Introducing the conduction contribution (rdc/xe0) into the imaginary part of dielectric constant and separating the real and imaginary parts of the Curie–Von Schweidler (CS) function give the relation of e0 and e00 with frequency [20], viz. e0 ðxÞ ¼ e1 þ Bxn1 00
e ðx Þ ¼
e00ac
e00ac
þ rdc =xe0 n1
b
314
1.0
3
rdc 9 10-8 (X cm)-1
20
1.5
10
n
900
20
0.0 2 10
e0 (at 1 kHz)
1200
ð1aÞ ð1bÞ
where ¼ Cx is the dielectric loss due to only relaxation process, B and C are constants, e0 is the vacuum dielectric constant, rdc is the frequency-independent conductivity, and x is the frequency. The exponent n (0 B n B 1; n = 1 for perfectly Debye relaxation) indicates the degree of dielectric relaxation [21]. The values of
61.7 108
0.37 0.36 0.35
rdc and n have been found from the best fit with the Eqs. (1a) and (1b) shown in Table 1. The observed value of n (\1) clearly indicates non-Debye type relaxation involved in our composite. From Table 1, comparing n values to e0 values, it seems that the larger e0 value suffers from more severe dielectric relaxation (i.e., smaller n value). This could be related to the size of conducting grains formed depending on LCMO phase [22]. In order to study the composition dependence of the dielectric constant for this composite, the dielectric constant at 1 kHz is plotted against the content of LCMO phase as shown in the inset of Fig. 2a. It appears that the dielectric constant of the composites increases very fast on the content of LCMO phase. The permittivity of BTO/LCMO composites increases from 314 to 1,928 as the content of LCMO phase increases from 20 to 60 %, whereas Zhang et al. [23] reported that the dielectric constant is linearly dependent on the content of CaCu3Ti4O12 ceramic in the ceramic– polymer composite. Hence, the ceramic–manganite composites are more effective to enhance the dielectric constant than the ceramic–polymer composites. Similar composition dependence of the dielectric constant was also reported in other ceramic composite systems [24, 25]. However, as loss spectra do not show evidence of relaxation phenomena due to the absence of the loss peak and exhibit a dc conduction phenomenon, the analysis of the dielectric spectra can be done using the complex electric modulus for the demonstration of the relaxation properties. 3.2 Electric modulus studies The complex electric modulus formalism M is often used to analyze the space charge relaxation phenomena, which is not clearly detected, when the complex permittivity formalism is used. This approach also highlights the space charge phenomena with smallest capacitance, and it can suppress the contribution of electrode polarization effects [26]. The complex electric modulus M is defined as the inverse of the complex relative permittivity e ði:e: M ¼ 1=e Þ. The real part and the imaginary part of the complex modulus have been obtained from the frequency-dependent permittivity data as [27]
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2
(a)
M ¼ M 0 þ iM 00 ¼ M1 41
5
-3
M' (10 )
ð3Þ
3 2
x = 60 x = 50 x = 40 x = 30 x = 20
1 0 10
2
10
3
4
5
10 10 frequency (Hz)
10
(b) 1.4
6
10
x = 60
1.0 -3
M" (10 )
7
0.8
M 00 ¼
0.6 0.4 0.2 0.0 2
10
3
10
4
5
10 10 frequency (Hz)
6
10
7
10
8
Fig. 3 Frequency dependence of a real part (M0 ) and b imaginary part (M00 ) of electric modulus of BTO/LCMO composite. The solid lines are the best fit of Eq. (4)
M 00 ¼
where M1 ¼ 1=e1 the reciprocal of high-frequency dielectric constant, and /(t) is the decay function describing the decay of electric field within the ionic conductor in the time domain. In the ideal Debye case, /(t) is simple exponential. However, in the case of non-Debye behavior, as in the present case, /(t) can be well approximated by a stretched exponential decay function given by the Kohlrausch–Williams–Watts (KWW) function [29] as n o /ðtÞ ¼ exp ðt=sm Þb , where sm is the characteristic relaxation time, and b is the stretched exponent (0 \ b \ 1) which indicates the deviation from ideal Debye type relaxation for which its value is unity. However, the imaginary part M00 from Eq. (3) above can be written as [30]
x = 50 x = 40 x = 30 x = 20 fit
1.2
M0 ¼
3 d/ðtÞ expðixtÞ dt5 dt
0
4
10
Z1
e0 e02 þ e002
ð2aÞ
e00 þ e002
ð2bÞ
e02
where M0 and M00 are the real and imaginary parts of the electric modulus, respectively, while e0 and e00 are those of the dielectric constant. Figure 3a, b displays the variation of the real part, M0 , and the imaginary part, M00 , of the complex electric modulus as a function of frequency. It can be clearly seen that the values of M0 increased with the frequency and present a constant value at both high and low frequencies. Between these plateaus, the polarization effect is evidenced, whereas M00 increases with the increase of frequency and shows a peak, thereafter it decreases. Similar nature has also been noticed in other system for instance carbon–polymer composite [28]. However, the complex modulus M can be expressed in terms of Fourier transform of a decay function u(t) [28] as
123
h
00 Mmax
b ð1 bÞ þ 1þb bðxmax =xÞ þ ðx=xmax Þb
i
ð4Þ
where Mmax00 is the peak value of M00 , and xmax = 2pfm is the corresponding frequency. In case of the heterogeneous materials containing components with different conductivities and permittivities, the charges accumulate to the interfaces, when an electric field is applied (MWS relaxation) as mentioned earlier. The experimental data have been fitted using Eq. (4) to get the values of b. From the value of b \ 1 (see Table 1), it is confirmed that the relaxation behavior is non-Debye type. Similar behaviors have been observed in other materials such as polymers or oxides [31]. In Fig. 3b, we have also observed that the peak is blue-shifted upon increasing the LCMO phase in the composite. As the concentration (x) of LCMO is raised, neighboring LCMO grains connect each other and form large conducting grains. So, the ions can move long distance through successful hopping; hence, the relaxation peak shifts to a higher frequency. The low-frequency side of the peak represents the range of frequencies in which the ions are capable of moving long distances, i.e., performing successful hopping from one site to the neighboring sites, whereas for the high-frequency side, the ions are spatially confined to their potential wells and can execute only localized motion [32, 33]. 3.3 Dielectric and Electric moduli scaling studies To gain better understanding of the relaxation mechanism, we have tried to investigate the scaling behavior of the real
Frequency-dependent dielectric permittivity
6.0
10
f m (Hz)
( '- )/
10
3
10
2
10
-6
10
-7
10
-8
10
-9
10
10
1.5
10 10
0.0
10
(b)
x = 60 x = 50 x = 40 x = 30
1.0
0.8
M"/M"max
4
10
10
0.6
0.4
0.2
0.0 10
-3
10
-2
10
-1
10
0
10
f / fm
1
10
2
10
3
10
4
Fig. 4 a Scaled spectra of real part of dielectric constant (e0 ) according to Eq. (5a). b Scaled spectra of the imaginary part of electric modulus (M00 ) according to Eq. (5b) of (100-x)BTO/ (x)LCMO composite
part of the dielectric permittivity and imaginary part of the electric modulus by using the relations [34]: e0 e1 f ¼ F1 ð5aÞ fm De M 00 f ¼ F2 ð5bÞ 00 fm Mmax In the above equations, e? is dielectric permittivity at high frequency, and F1 and F2 are temperature-independent functions. De is dielectric loss strength, defined as es–e? (e? and es are, respectively, the relative permittivity values at infinite and near-zero frequencies, and the values have been calculated from the dielectric data). The scaled permittivity spectrum is shown in Fig. 4a for different LCMO concentrations, where the ac permittivity is subtracted by e?, then scaled by De, and the frequency axis scaled by peak frequency fm. Interestingly, Fig. 4a clearly reveals the perfect overlap of all the curves corresponding to the LCMO compositions (x) to a single master curve. This
10
10 10
10
3.0
6
5
10
4.5
10
7
6
5
4
3
2
-1
x = 60 x = 50 x = 40 x = 30 x = 20
7
-10
20
30
40 x (wt%)
50
60
10
-6
(S-cm)
10
7.5
dc
(a)
911
-7
-8
-9
-10
Fig. 5 Variation of rdc versus x (right panel) and fm versus x (left panel). The solid line is the best fit according to the Arrhenius-like law [Eqs. (6) and (7), respectively]
study suggests that the permittivity relaxation mechanism is independent of the compositional variation in the composite. In the electric modulus spectrum, we have scaled each 00 M00 by Mmax for different compositions shown in Fig. 4b. It was shown that the hopping mechanism comes into play the roles in case of temperature-dependent study, and the dynamical process is independent of temperature. However, in Fig. 4b, we have observed a similar effect with composition-dependent study. The superposition of the curves for all the compositions similar to the dielectric permittivity confirmed that the nature and the shape of the electric modulus of the composites BTO/LCMO are composition independent. Interestingly, an Arrhenius-like equation has been proposed in our composite systems to describe both the dc conductivity and the characteristic peak frequency as [35]: rdc ðxÞ ¼ A expðpxÞ
ð6Þ
fm ðxÞ ¼ f0 expðkxÞ
ð7Þ
where A and f0 are the pre-exponential factors, and the exponents p and k are constants. The values of p and k highly depend on the conductance and capacitance of the grains [35]. The composition-dependent dc conductivity (rdc) and peak frequency (fm) obtained from Eqs. (1b) and (4), respectively, have been plotted in Fig. 5. It is clear that the obtained data fall on straight lines and have been fitted according to Eqs. (6) and (7), respectively. The exponents p and k have been determined from the best fit to be 0.21 and 0.15. Most interestingly, these values obtained from the dielectric and electric moduli are almost equal to the expected values (0.25 and 0.15, respectively) obtained
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from frequency-dependent conductivity reported in our previous paper [35]. Thus, frequency-dependent dielectric and scaling formalism of the electric modulus approach correlating to the frequency-dependent conductivity study.
4 Conclusion To summarize, the dielectric spectra of BaTiO3/La0.7Ca0.3MnO3 composites at room temperature have been modeled to the CS law introducing the conduction contribution due to conducting LCMO phase. The electric modulus spectra have been analyzed by invoking KWW function. The imaginary modulus shows a peak of relaxation related to the MWS relaxation. We have also observed that the peak is blue-shifted upon increasing the LCMO phase in the composites. The values of the exponent b decrease with conductivity of the sample. The values of b and shape of the curves confirmed the presence of nonDebye type relaxation. The scaling formalism of the dielectric permittivity and electric modulus spectra as a function of frequency results in a single master curve. This formalism signifies that the relaxation mechanism involved in the composite is independent of composition. Finally, composition dependence of rdc(x) and fm(x) has been found Arrhenius-like in our composite systems. Acknowledgments This work was supported by DST-FAST TRACK Project No-SR/FTP/PS-101/2010 Government of India. Author M. H. Khan would like to acknowledge the University for providing financial support. It is pleasure to acknowledge Dr. S. Bhattacharya, University of Kalyani, for helpful discussions and help in performing the measurements.
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