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Dielectric relaxation of the Ca2MnO4−δ system
Journal of Alloys and Compounds 577S (2013) S483–S487
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Dielectric relaxation of the Ca2 MnO4−␦ system N. Chihaoui a , M. Bejar a,∗ , E. Dhahri a , M.A. Valente b , M.P.F. Grac¸a b , L.C. Costa b a b
Faculty of Sciences of Sfax, Route Soukra Km 3.5, Sfax 3018, Tunisia I3N – Aveiro, Physics Department, Aveiro University, Campus Universitário de Santiago, 3800-193 Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 23 January 2012 Received in revised form 5 March 2012 Accepted 7 March 2012 Available online 16 March 2012 Keywords: Ceramic Dielectric relaxation Cole–Cole model
a b s t r a c t Dielectric properties were measured in the frequency range from 40 Hz to 2 MHz and temperatures between 100 and 360 K using impedance spectroscopy technique. A single relaxation process was observed for ı = 0.00, but a second relaxation behavior can be identified for intermediate values of ı. For both processes the Cole–Cole relaxation model can be used to explain the results, corresponding to a distribution of relaxation times. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Ruddlesden–Popper manganites with general formula (R, A)n+1 Mnn O3n+1 (R = trivalent lanthanides, A = divalent alkalineearth ions) have become very exciting materials for researchers not only for their interesting physical properties but also for their inherent ability to accommodate a wide range of elemental compositions and to display a wealth of structure variants. The physical properties of interest among the Ruddlesden–Popper manganites include ferroelectricity [1], charge-ordering [2,3], superconductivity [4], colossal magnetoresistance [5–7], catalytic activity [8] and a multitude of dielectric properties, which are of great importance in microelectronics and telecommunication. In our group, and in the framework of dielectric properties of these manganese oxides, we have focused our work on Ca2 MnO4−␦ compounds. In our previous paper [9], the structural, magnetic, electrical and dielectric studies have revealed that these compounds exhibit a dc conductivity which decreases with the increase of the ı-value. Also, these studies have exposed that the activation energy is independent of ı with a non-Debye relaxation processes which is thermally activated. In this context, we have performed a detailed characterization of the dielectric properties of the Mn3+ /Mn4+ mixed valence of Ca2 MnO4−␦ compounds with ı = 0.00, 0.15, 0.20 and 0.30. In order to check the influence of the oxygen deficiency on their dielectric behavior in general purpose, and especially on the relaxation process, we have also studied the dielectric properties of the Ca2 MnO4
∗ Corresponding author. Tel.: +216 98 333 873; fax: +216 74 676 609. E-mail address: bejar [email protected] (M. Bejar). 0925-8388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2012.03.039
phase where the Mn cations have a formal oxidation state of +4. In the other hand, we will try to find a correlation between the dielectric properties highlighted and its magnetic properties mentioned in Ref. [10]. The most outstanding results of these studies are presented in this paper.
2. Experimental Sol–gel method was used to synthesize the Ca2 MnO4 parent compound. Vacancies in oxygen site were created by reacting the oxide in a quartz tube containing titanium in the appropriate stoichiometric proportion. This preparation was done in the LPA Laboratory at the University of Sfax. The detailed preparation procedure is discussed in our previous works [9,10]. The structure of samples was characterized by X-ray diffraction at room temper˚ Data were collected ature using a Siemens D5000 diffractometer (CuK␣ = 1.5406 A). over range of 10◦ ≤ 2 ≤ 90◦ with a step scanning of 0.02◦ and a counting time of 5 s per step. For the electrical measurements, the opposite sides of the samples were painted with silver conducting paste. During the electrical measurements, samples, with a thickness about 1 mm, were maintained in a helium atmosphere in order to improve the heat transfer and eliminate the moisture. The impedance spectroscopy measurements were performed in the frequency range of 40 Hz–2 MHz, as a function of the temperature (100–360 K), using an Agilent 4294A Precision Impedance Analyser, measuring in the Cp-Rp configuration. The X-ray diffraction and impedance spectroscopy measurements were performed in Physics Department – I3N, University of Aveiro (Portugal).
3. Results and discussion Fig. 1 shows the XRD patterns of the Ca2 MnO4−␦ compounds. These samples are found to crystallize in the tetragonal system with I41/acd space group for the ı = 0 and in the orthorhombic system with Bbcm space group for the other samples.
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N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
3
9
δ = 0.15
6 Z''(x 105)
Intensity (arb. Units)
δ = 0.30
2
δ = 0.15
40
60
2θ (°)
1
10
d 1 A ε0
(1) (2)
1 (jωCe ) ε∗
(3)
where Ce represents the capacitance of the empty space. Figs. 2–4 show the imaginary component of the impedance (Z”) as a function of frequency, for several temperatures of measurement, for ı = 0.0 (Fig. 2), ı = 0.15 (Fig. 3) and ı = 0.30 (Fig. 4). Sample with ı = 0.20 presents a similar behavior to the one observed for the ı = 0.15 sample. In all the samples, a Z” peak is observed for temperatures above 270 K, shifting to higher frequencies with the increase of the temperature. That is, the relaxation time of the dipoles decreases with temperature revealing higher mobility. The
1
10
2
10
3
10
4
10
δ = 0.30
330 K
320 K
0
360 K 1
10
2
350 K
1
360 K
6
10 K
10 K
Z''(x 106)
340 K
Z''(x 10 )
Z''(x 106)
7
Z''(x 10 )
2
6
3
20 2
10
ı = 0.15 (Fig. 3 – right-top corner) and ı = 0.20 samples present a second Z” peak, at lower frequencies. This second peak, only visible for the highest temperature measurements (T > 330 K), which is thermally activated, shifts to higher frequencies with increasing temperature. As can be seen, this second peak is not observed for the ı = 0.30 sample. Figs. 5 and 6 show the real (Z’) and imaginary (Z”) components of the impedance as a function of frequency, at the constant temperature of 360 K, for all the samples. It can be observed the presence of one relaxation mechanism in the sample with ı = 0.0 and two relaxation mechanisms in the samples with ı = 0.15 and ı = 0.20. Again, the second relaxation process cannot be observed for ı = 0.30 sample. The presence of two relaxation processes should be assigned to the presence of two different types of dipoles. As known, in this type of materials an extrinsic and an intrinsic response are expected. The extrinsic one is normally associated with the dipoles formed between interfaces, namely, between grains and between the surface and the electrode. This extrinsic response is responsible for relaxations at very low frequencies, typically below 100 Hz in this range of temperature. As this is not the case of our results, we suggest that the two observed relaxation phenomena are due to intrinsic characteristics. Fig. 7 illustrates the relaxation behavior, using the Nyquist plot, at constant temperature of T = 360 K. According to the composition of the ı = 0.0 sample, Mn4+ is the only manganese ion present. Then, the dielectric dipole formed
δ = 0.00
280 K
5
Fig. 3. Imaginary part (Z”) of the complex impedance for ı = 0.15 sample. Inset: Z” vs. frequency for some values of temperature (320–360 K).
4
3
6
10
Frequeny (Hz)
1 1 d 1 ω Rp A ε0
4
5
360 K
0
where A is the electrode area, d is the sample thickness, ε0 is the dielectric permittivity of free space (8.854 × 10−12 F/m) and ω is the angular frequency. ε’ and ε” are, respectively, the real and imaginary parts of complex permittivity ε* (ε* = ε’ + j ε”). Then, the real and imaginary parts of the complex impedance (Z* = Z’ − j Z”) were deduced using the relationship: Z∗ =
4
10 K
80
From the capacitance (Cp ) and resistance (Rp ) measured values, the real and imaginary parts of the impedance were obtained using the following equations [11–13]:
ε =
3
10 10 10 Frequeny (Hz)
290 K
Fig. 1. XRD patterns of the system Ca2 MnO4−␦ (ı = 0.00–0.30) samples.
ε = Cp
320 K
0 360 K 1 2 10 10
δ = 0.00
20
3
10 K
6
Z''(x 10 )
δ = 0.20
2
10
3
4
5
10 10 10 Frequeny (Hz)
6
10
0
280 K
1
10
10
1
2
10
3
10
4
10
5
10
6
10
Frequeny (Hz)
10 K
0
0
360 K
10
1
10
2
10
3
4
10
10
5
10
6
Frequeny (Hz) Fig. 2. Imaginary part (Z”) of the complex impedance for ı = 0.00 sample. Inset: Z” vs. frequency for some values of temperatures (320–360 K).
360 K 1
10
2
10
3
4
10 10 Frequeny (Hz)
5
10
6
10
Fig. 4. Imaginary part (Z”) of the complex impedance for ı = 0.30 sample. Inset: Z” vs. frequency for some values of temperature (330–360 K).
N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
8 δ = 0.15
9
4 Z''(x 105)
Z'(x 105)
δ = 0.30
12
T = 360 K
4
3 1
10
2
2
3
10
10
4
5
10
6
10
10
Frequency (Hz)
6
0
Z''(x 10 )
6
Z'(x 10 )
4
5
12 δ = 0.20
360 K
δ = 0.00
S485
δ = 0.20 δ = 0.15
6 3 0
2
δ = 0.20 δ = 0.15
0
3
6 Z'(x 105)
1
1
2
10
3
10
4
10
5
10
0
6
10
10
Frequency (Hz)
δ = 0.30
0
between Mn4+ and O2− ions can be considered as the responsible for the dielectric relaxation. In sample with ı = 0.15, the content of Mn4+ ion decreases and Mn3+ increases, as shown in Table 1. Therefore, we suggest that the relaxation mechanism, which is observed in the low frequency range for ı = 0.15 and ı = 0.20 samples, should be assigned to these new dipoles between Mn3+ and O2− ions. The increase of the content of Mn3+ ion, and consequently the decrease
360 K
1.5
δ = 0.00
Z''(x 10 )
6
δ = 0.30
0.0 10
2
10
3
10
4
10
5
6
10
Frequency (Hz) 360 K
2 5
Z''(x 10 )
2
6
3
4
5
Fig. 7. Nyquist plot of different samples at T = 360 K.
of the content of Mn4+ one, is accompanied by a shift to higher frequencies of the dielectric relaxation associated with these dipoles. In our previous work, the magnetic characteristics of these samples [10] have revealed a divergence between ZFC and FC curves for the samples with ı < 0.2, starting around 50 K, which is above the blocking temperature (TB ). This is typical of a spin glass behavior, present in compounds with a strong exchange interactions and/or short-ranged ordering occurring at higher temperatures, is in deep relation with the Mn3+ /Mn4+ ratio. According to the electrical neutrality, the increase of the oxygen deficiency content Mn4+ Mn3+ O2− compounds leads to the increase of (ı) in Ca2+ 2 1−2ı 2ı 4−ı
the Mn3+ ions number. Thus, as ı increases, there is augmentation of Mn3+ /Mn4+ ratio (Table 1) leading to an enhancement of the spin-glass component and the introduction of a robust frustration magnetic phenomenon. As a result, there is apparition of an unusual magnetic behavior, which is, generally, accompanied by the absence of any magnetic transition as observed for samples with ı > 0.2. A similar behavior is observed by dielectric spectroscopy. Therefore, the ı = 0.30 sample presents only one relaxation process, which should be assigned to Mn3+ –O2− dipoles. From Fig. 7 we can observe that the arcs are not centered in the horizontal axe, confirming that a single relaxation time described by the equation of Debye cannot be used to explain this dielectric relaxation. We have analyzed the data using the Cole–Cole function [14] given by ε∗ (ω) = ε∞ +
δ = 0.20
ε 1 + (jωcc )
(4)
1−˛
In this equation, which is an empirical modification of the Debye equation, ε∞ is the relaxed dielectric constant, ε the dielectric relaxation strength, cc the relaxation time and ˛ a parameter between 0 and 1 that reflects the dipole interaction. The relaxation frequency is as fr =
1
1
Z'(x 10 )
Fig. 5. Real part of the complex impedance determined at T = 360 K. Inset: Real part of the complex impedance vs. frequency for ı = 0.15 and 0.20 samples.
0.5
12
δ = 0.00
0
1.0
9
1 ωcc
(5)
δ = 0.15
Table 1 The molar ratio between Mn3+ and Mn4+ in all samples, the resistance R1 and R2 and the capacitance C1 and C2 of the equivalent circuit model, determined at 360 K.
0
2
10
3
10
10
4
5
10
10
6
Frequency (Hz) Fig. 6. Imaginary part (Z”) of the complex impedance determined at T = 360 K.
Sample
Mn3+ /Mn4+ (%)
R1 [M]
C1 [pF]
0.00 0.15 0.20 0.30
0/100 30/70 40/60 60/40
4.860 0.795 0.804
10.5 8.03 11.6
R2 [M]
C2 [nF]
0.175 0.401 3.92
4.31 89.1 4820
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N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
Table 2 Calculated relaxation parameters using the Cole–Cole model determined at T = 300 K, fr is relaxation frequency; ˛: is depression angle; Z is the strength in resistance. Sample
fr (Hz)
˛
Z (M)
0.00 0.15 0.15 0.20 0.20 0.30
346 243 1508 312 2297 776
0.32 0.30 0.37 0.32 0.37 0.32
4.9 0.8 0.2 0.8 0.4 3.8
Fig. 9. Equivalent circuit. R1,2 : Parallel resistance and CPE1,2 : constant phase element.
To determine the cc and ˛ parameters, we have calculated firstly the approximate values from the asymptotic part of the data, and then we have used them as starting values in a non-linear curve fitting algorithm [15]. Table 2 resume the calculated relaxation parameters. To analyze the relaxation characteristics, the impedance data were interpreted considering a distribution of relaxation times. Therefore, considering cc the relaxation time, we can write:
+∞ ∗
Z (ω) = Z∞ + (Z0 − Z∞ )
(1 + jωcc )
−1
G()d()
(6)
0
where • G() is the distribution function of time constants; • G() d() is the probability of finding a Debye element in the differential time element with:
+∞
G() d ln () = 1
(7)
0
For the Cole–Cole model, the derived distribution function is given by the following equation [16]: G() =
1 sin (˛ ) 2 cos h (1 − ˛) log (/cc ) − cos (˛ )
(8)
Fig. 8 illustrates the variation of the distribution function determined at T = 300 K. The differences between the samples are observed in the relaxation time, but not in the ˛ parameter. The non-Debye character of the relaxations processes is obvious. An equivalent circuit was used (Fig. 9) in order to adjust the dielectric data at various temperatures. Usually, an ideal relaxation
δ =0.15, HF
2
δ =0.30
δ =0.00 δ =0.20, LF
G (τ )
δ = 0.20, HF
δ =0.15, LF
1
0 -6 10
-5
10
-4
10
-3
10
-2
10
-1
10
t (s) Fig. 8. Distribution function of relaxation times at T = 300 K for low frequency (LF) and high frequency (HF).
process is modeled by an ideal RC element of parallel resistance and capacitance. These samples present non-Debey behavior, which manifests itself by slightly suppressed semi-circles (Fig. 7). This can be solved by replacing the capacitance with a constant phase element (CPE). The CPE capacitance values were corrected to conventional capacitance (CCPE ). The results are registered in Table 1. Resistor R1 and capacitance C1 are related with the high frequency relaxation mechanism, associated with the dipoles formed by the Mn4+ ions. In samples with ı = 0.15 and 0.20, a difference is observed between the values of the capacitances associated with the high frequency relaxation (C1) and the low frequency relaxation (C2), which can be related with the two different dipoles. Sample with ı = 0.30 presents a different result. From all these curves, it should be noted that there is a huge and remarkable change in Z values. They are about 5 and 4 M for ı = 0 and 0.3, respectively, and ranging between only 0.2 and 0.8 M for other ı values. To explain this difference, we must consider the Mn3+ /Mn4+ ratio and the kind of the relaxation process (LF or HF). Indeed, for the samples with ı = 0.0, 0.15 and 0.20, the calculated Z corresponds to the low frequency relaxation process. In fact, these values are close to the resistance R1 in the equivalent circuit. The increase of ı leads to an augmentation of the Mn3+ /Mn4+ ratio, with a consequent increase of the conductivity at low frequencies. This behavior is confirmed by the dc electrical measurement made in the same samples, and already published in Ref. [9]. On the other hand, the value of Z obtained for the ı = 0.30 sample, corresponds not only to the low frequency relaxation process but also to the high frequency relaxation one, that is close to R2. As a consequence, this cannot be compared with the previous conductivities, as we are in a different relaxation process. In fact, in this second relaxation process, the values of R2 increase with ı. In particular the high value for the sample ı = 0.30 is responsible for the lower relaxation frequency calculated for this sample (see Fig. 8 for the distribution of relaxation times, where ı = 0.30 has lower relaxation frequency and higher relaxation time when compared with the HF relaxations of the other samples). 4. Conclusions The Ca2 MnO4−␦ compounds were prepared using the Sol–gel method. The magnetic study has revealed that the oxygendeficiency induces very interesting magnetic properties namely the magnetic frustration and spin glass behaviors. These behaviors were found to affect very closely the dielectric properties. Indeed, to highlight these properties, broadband dielectric spectroscopy was used to study the relaxation processes in Ca2 MnO4−␦ system. For the samples with ı = 0.00 and 0.30, we have observed one relaxation process. Therefore, for ı = 0.15 and 0.20 samples, a second relaxation mechanism was observed in the low frequency range which should be assigned to the Mn3+ –O2− dipoles. The higher frequency process is due to Mn4+ –O2− dipoles and this is the only one present in the sample with ı = 0.30. Both processes are found to be non-Debye and are well fitted by the Cole–Cole model of dielectric relaxation. Distribution functions of relaxation times have confirmed this behavior.
N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
Acknowledgments The authors would like to acknowledge the financial support by FCT-Portugal and Tunisia for the scientific cooperation between Portugal and Tunisia (project reference Tunisia 124623103412840). References [1] P.W. Rehrig, S.E. Park, S. Trolier-McKinstry, G.L. Messing, B. Jones, T.R. Shrout, J. Appl. Phys. 86 (1999) 1657. [2] M.T. Tlili, N. Chihaoui, M. Bejar, E. Dhahri, M.A. Valente, E.K. Hlil, J. Alloys Compd. 509 (2011) 6447. [3] A. Castro-Couceiro, M. Sanchez-Andujar, B. Rivas-Murias, J. Mira, J. Rivas, M.A. Senaris-Rodriguez, Solid State Sciences 7 (2005) 905. [4] P.A. Salvador, K.B. Greenwod, J.R. Mawdsley, K.R. Poeppelmeier, T.O. Mason, Chem. Mater. 11 (1999) 1760.
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[5] R.N. Mahato, K. Sethupathi, V. Sankaranarayanan, R. Nirmala, J. Magn. Magn. Mater. 322 (2010) 2537. [6] L. Han, C. Chen, J. Mater. Sci. Technol. 26 (3) (2010) 234. [7] J. Androulakis, J. Giapintzakis, Physica B 405 (2010) 107. [8] Z. Liang, K. Tang, Q. Shao, G. Li, S. Zeng, H. Zheng, J. Solid State Chem. 181 (2008) 964. [9] N. Chihaoui, R. Dhahri, M. Bejar, E. Dhahri, L.C. Costa, M.P.F. Grac¸a, Solid State Commun. 151 (2011) 1331. [10] N. Chihaoui, M. Bejar, E. Dhahri, M.A. Valente, M.P.F. Grac¸a, J. Alloys Compd. 509 (2011) 8965. [11] M.P.F. Grac¸a, M.G.F. da Silva, M.A. Valente, Solid State Sci. 11 (2) (2009) 570. [12] K.L.N. Gai, R.W. Rendell, Handbook of Conducting Polymers, vol. II, Marcel Dekker, NY, 1986. [13] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (6) (1972) 171. [14] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1991) 341. [15] L.C. Costa, S. Mendiratta, J. Non-Cryst. Solids 1324 (1994) 172. [16] S.N. Al-Refaie, Appl. Phys. A 52 (1991) 234.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Dielectric relaxation of the Ca2 MnO4−␦ system N. Chihaoui a , M. Bejar a,∗ , E. Dhahri a , M.A. Valente b , M.P.F. Grac¸a b , L.C. Costa b a b
Faculty of Sciences of Sfax, Route Soukra Km 3.5, Sfax 3018, Tunisia I3N – Aveiro, Physics Department, Aveiro University, Campus Universitário de Santiago, 3800-193 Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 23 January 2012 Received in revised form 5 March 2012 Accepted 7 March 2012 Available online 16 March 2012 Keywords: Ceramic Dielectric relaxation Cole–Cole model
a b s t r a c t Dielectric properties were measured in the frequency range from 40 Hz to 2 MHz and temperatures between 100 and 360 K using impedance spectroscopy technique. A single relaxation process was observed for ı = 0.00, but a second relaxation behavior can be identified for intermediate values of ı. For both processes the Cole–Cole relaxation model can be used to explain the results, corresponding to a distribution of relaxation times. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Ruddlesden–Popper manganites with general formula (R, A)n+1 Mnn O3n+1 (R = trivalent lanthanides, A = divalent alkalineearth ions) have become very exciting materials for researchers not only for their interesting physical properties but also for their inherent ability to accommodate a wide range of elemental compositions and to display a wealth of structure variants. The physical properties of interest among the Ruddlesden–Popper manganites include ferroelectricity [1], charge-ordering [2,3], superconductivity [4], colossal magnetoresistance [5–7], catalytic activity [8] and a multitude of dielectric properties, which are of great importance in microelectronics and telecommunication. In our group, and in the framework of dielectric properties of these manganese oxides, we have focused our work on Ca2 MnO4−␦ compounds. In our previous paper [9], the structural, magnetic, electrical and dielectric studies have revealed that these compounds exhibit a dc conductivity which decreases with the increase of the ı-value. Also, these studies have exposed that the activation energy is independent of ı with a non-Debye relaxation processes which is thermally activated. In this context, we have performed a detailed characterization of the dielectric properties of the Mn3+ /Mn4+ mixed valence of Ca2 MnO4−␦ compounds with ı = 0.00, 0.15, 0.20 and 0.30. In order to check the influence of the oxygen deficiency on their dielectric behavior in general purpose, and especially on the relaxation process, we have also studied the dielectric properties of the Ca2 MnO4
∗ Corresponding author. Tel.: +216 98 333 873; fax: +216 74 676 609. E-mail address: bejar [email protected] (M. Bejar). 0925-8388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2012.03.039
phase where the Mn cations have a formal oxidation state of +4. In the other hand, we will try to find a correlation between the dielectric properties highlighted and its magnetic properties mentioned in Ref. [10]. The most outstanding results of these studies are presented in this paper.
2. Experimental Sol–gel method was used to synthesize the Ca2 MnO4 parent compound. Vacancies in oxygen site were created by reacting the oxide in a quartz tube containing titanium in the appropriate stoichiometric proportion. This preparation was done in the LPA Laboratory at the University of Sfax. The detailed preparation procedure is discussed in our previous works [9,10]. The structure of samples was characterized by X-ray diffraction at room temper˚ Data were collected ature using a Siemens D5000 diffractometer (CuK␣ = 1.5406 A). over range of 10◦ ≤ 2 ≤ 90◦ with a step scanning of 0.02◦ and a counting time of 5 s per step. For the electrical measurements, the opposite sides of the samples were painted with silver conducting paste. During the electrical measurements, samples, with a thickness about 1 mm, were maintained in a helium atmosphere in order to improve the heat transfer and eliminate the moisture. The impedance spectroscopy measurements were performed in the frequency range of 40 Hz–2 MHz, as a function of the temperature (100–360 K), using an Agilent 4294A Precision Impedance Analyser, measuring in the Cp-Rp configuration. The X-ray diffraction and impedance spectroscopy measurements were performed in Physics Department – I3N, University of Aveiro (Portugal).
3. Results and discussion Fig. 1 shows the XRD patterns of the Ca2 MnO4−␦ compounds. These samples are found to crystallize in the tetragonal system with I41/acd space group for the ı = 0 and in the orthorhombic system with Bbcm space group for the other samples.
S484
N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
3
9
δ = 0.15
6 Z''(x 105)
Intensity (arb. Units)
δ = 0.30
2
δ = 0.15
40
60
2θ (°)
1
10
d 1 A ε0
(1) (2)
1 (jωCe ) ε∗
(3)
where Ce represents the capacitance of the empty space. Figs. 2–4 show the imaginary component of the impedance (Z”) as a function of frequency, for several temperatures of measurement, for ı = 0.0 (Fig. 2), ı = 0.15 (Fig. 3) and ı = 0.30 (Fig. 4). Sample with ı = 0.20 presents a similar behavior to the one observed for the ı = 0.15 sample. In all the samples, a Z” peak is observed for temperatures above 270 K, shifting to higher frequencies with the increase of the temperature. That is, the relaxation time of the dipoles decreases with temperature revealing higher mobility. The
1
10
2
10
3
10
4
10
δ = 0.30
330 K
320 K
0
360 K 1
10
2
350 K
1
360 K
6
10 K
10 K
Z''(x 106)
340 K
Z''(x 10 )
Z''(x 106)
7
Z''(x 10 )
2
6
3
20 2
10
ı = 0.15 (Fig. 3 – right-top corner) and ı = 0.20 samples present a second Z” peak, at lower frequencies. This second peak, only visible for the highest temperature measurements (T > 330 K), which is thermally activated, shifts to higher frequencies with increasing temperature. As can be seen, this second peak is not observed for the ı = 0.30 sample. Figs. 5 and 6 show the real (Z’) and imaginary (Z”) components of the impedance as a function of frequency, at the constant temperature of 360 K, for all the samples. It can be observed the presence of one relaxation mechanism in the sample with ı = 0.0 and two relaxation mechanisms in the samples with ı = 0.15 and ı = 0.20. Again, the second relaxation process cannot be observed for ı = 0.30 sample. The presence of two relaxation processes should be assigned to the presence of two different types of dipoles. As known, in this type of materials an extrinsic and an intrinsic response are expected. The extrinsic one is normally associated with the dipoles formed between interfaces, namely, between grains and between the surface and the electrode. This extrinsic response is responsible for relaxations at very low frequencies, typically below 100 Hz in this range of temperature. As this is not the case of our results, we suggest that the two observed relaxation phenomena are due to intrinsic characteristics. Fig. 7 illustrates the relaxation behavior, using the Nyquist plot, at constant temperature of T = 360 K. According to the composition of the ı = 0.0 sample, Mn4+ is the only manganese ion present. Then, the dielectric dipole formed
δ = 0.00
280 K
5
Fig. 3. Imaginary part (Z”) of the complex impedance for ı = 0.15 sample. Inset: Z” vs. frequency for some values of temperature (320–360 K).
4
3
6
10
Frequeny (Hz)
1 1 d 1 ω Rp A ε0
4
5
360 K
0
where A is the electrode area, d is the sample thickness, ε0 is the dielectric permittivity of free space (8.854 × 10−12 F/m) and ω is the angular frequency. ε’ and ε” are, respectively, the real and imaginary parts of complex permittivity ε* (ε* = ε’ + j ε”). Then, the real and imaginary parts of the complex impedance (Z* = Z’ − j Z”) were deduced using the relationship: Z∗ =
4
10 K
80
From the capacitance (Cp ) and resistance (Rp ) measured values, the real and imaginary parts of the impedance were obtained using the following equations [11–13]:
ε =
3
10 10 10 Frequeny (Hz)
290 K
Fig. 1. XRD patterns of the system Ca2 MnO4−␦ (ı = 0.00–0.30) samples.
ε = Cp
320 K
0 360 K 1 2 10 10
δ = 0.00
20
3
10 K
6
Z''(x 10 )
δ = 0.20
2
10
3
4
5
10 10 10 Frequeny (Hz)
6
10
0
280 K
1
10
10
1
2
10
3
10
4
10
5
10
6
10
Frequeny (Hz)
10 K
0
0
360 K
10
1
10
2
10
3
4
10
10
5
10
6
Frequeny (Hz) Fig. 2. Imaginary part (Z”) of the complex impedance for ı = 0.00 sample. Inset: Z” vs. frequency for some values of temperatures (320–360 K).
360 K 1
10
2
10
3
4
10 10 Frequeny (Hz)
5
10
6
10
Fig. 4. Imaginary part (Z”) of the complex impedance for ı = 0.30 sample. Inset: Z” vs. frequency for some values of temperature (330–360 K).
N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
8 δ = 0.15
9
4 Z''(x 105)
Z'(x 105)
δ = 0.30
12
T = 360 K
4
3 1
10
2
2
3
10
10
4
5
10
6
10
10
Frequency (Hz)
6
0
Z''(x 10 )
6
Z'(x 10 )
4
5
12 δ = 0.20
360 K
δ = 0.00
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δ = 0.20 δ = 0.15
6 3 0
2
δ = 0.20 δ = 0.15
0
3
6 Z'(x 105)
1
1
2
10
3
10
4
10
5
10
0
6
10
10
Frequency (Hz)
δ = 0.30
0
between Mn4+ and O2− ions can be considered as the responsible for the dielectric relaxation. In sample with ı = 0.15, the content of Mn4+ ion decreases and Mn3+ increases, as shown in Table 1. Therefore, we suggest that the relaxation mechanism, which is observed in the low frequency range for ı = 0.15 and ı = 0.20 samples, should be assigned to these new dipoles between Mn3+ and O2− ions. The increase of the content of Mn3+ ion, and consequently the decrease
360 K
1.5
δ = 0.00
Z''(x 10 )
6
δ = 0.30
0.0 10
2
10
3
10
4
10
5
6
10
Frequency (Hz) 360 K
2 5
Z''(x 10 )
2
6
3
4
5
Fig. 7. Nyquist plot of different samples at T = 360 K.
of the content of Mn4+ one, is accompanied by a shift to higher frequencies of the dielectric relaxation associated with these dipoles. In our previous work, the magnetic characteristics of these samples [10] have revealed a divergence between ZFC and FC curves for the samples with ı < 0.2, starting around 50 K, which is above the blocking temperature (TB ). This is typical of a spin glass behavior, present in compounds with a strong exchange interactions and/or short-ranged ordering occurring at higher temperatures, is in deep relation with the Mn3+ /Mn4+ ratio. According to the electrical neutrality, the increase of the oxygen deficiency content Mn4+ Mn3+ O2− compounds leads to the increase of (ı) in Ca2+ 2 1−2ı 2ı 4−ı
the Mn3+ ions number. Thus, as ı increases, there is augmentation of Mn3+ /Mn4+ ratio (Table 1) leading to an enhancement of the spin-glass component and the introduction of a robust frustration magnetic phenomenon. As a result, there is apparition of an unusual magnetic behavior, which is, generally, accompanied by the absence of any magnetic transition as observed for samples with ı > 0.2. A similar behavior is observed by dielectric spectroscopy. Therefore, the ı = 0.30 sample presents only one relaxation process, which should be assigned to Mn3+ –O2− dipoles. From Fig. 7 we can observe that the arcs are not centered in the horizontal axe, confirming that a single relaxation time described by the equation of Debye cannot be used to explain this dielectric relaxation. We have analyzed the data using the Cole–Cole function [14] given by ε∗ (ω) = ε∞ +
δ = 0.20
ε 1 + (jωcc )
(4)
1−˛
In this equation, which is an empirical modification of the Debye equation, ε∞ is the relaxed dielectric constant, ε the dielectric relaxation strength, cc the relaxation time and ˛ a parameter between 0 and 1 that reflects the dipole interaction. The relaxation frequency is as fr =
1
1
Z'(x 10 )
Fig. 5. Real part of the complex impedance determined at T = 360 K. Inset: Real part of the complex impedance vs. frequency for ı = 0.15 and 0.20 samples.
0.5
12
δ = 0.00
0
1.0
9
1 ωcc
(5)
δ = 0.15
Table 1 The molar ratio between Mn3+ and Mn4+ in all samples, the resistance R1 and R2 and the capacitance C1 and C2 of the equivalent circuit model, determined at 360 K.
0
2
10
3
10
10
4
5
10
10
6
Frequency (Hz) Fig. 6. Imaginary part (Z”) of the complex impedance determined at T = 360 K.
Sample
Mn3+ /Mn4+ (%)
R1 [M]
C1 [pF]
0.00 0.15 0.20 0.30
0/100 30/70 40/60 60/40
4.860 0.795 0.804
10.5 8.03 11.6
R2 [M]
C2 [nF]
0.175 0.401 3.92
4.31 89.1 4820
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N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
Table 2 Calculated relaxation parameters using the Cole–Cole model determined at T = 300 K, fr is relaxation frequency; ˛: is depression angle; Z is the strength in resistance. Sample
fr (Hz)
˛
Z (M)
0.00 0.15 0.15 0.20 0.20 0.30
346 243 1508 312 2297 776
0.32 0.30 0.37 0.32 0.37 0.32
4.9 0.8 0.2 0.8 0.4 3.8
Fig. 9. Equivalent circuit. R1,2 : Parallel resistance and CPE1,2 : constant phase element.
To determine the cc and ˛ parameters, we have calculated firstly the approximate values from the asymptotic part of the data, and then we have used them as starting values in a non-linear curve fitting algorithm [15]. Table 2 resume the calculated relaxation parameters. To analyze the relaxation characteristics, the impedance data were interpreted considering a distribution of relaxation times. Therefore, considering cc the relaxation time, we can write:
+∞ ∗
Z (ω) = Z∞ + (Z0 − Z∞ )
(1 + jωcc )
−1
G()d()
(6)
0
where • G() is the distribution function of time constants; • G() d() is the probability of finding a Debye element in the differential time element with:
+∞
G() d ln () = 1
(7)
0
For the Cole–Cole model, the derived distribution function is given by the following equation [16]: G() =
1 sin (˛ ) 2 cos h (1 − ˛) log (/cc ) − cos (˛ )
(8)
Fig. 8 illustrates the variation of the distribution function determined at T = 300 K. The differences between the samples are observed in the relaxation time, but not in the ˛ parameter. The non-Debye character of the relaxations processes is obvious. An equivalent circuit was used (Fig. 9) in order to adjust the dielectric data at various temperatures. Usually, an ideal relaxation
δ =0.15, HF
2
δ =0.30
δ =0.00 δ =0.20, LF
G (τ )
δ = 0.20, HF
δ =0.15, LF
1
0 -6 10
-5
10
-4
10
-3
10
-2
10
-1
10
t (s) Fig. 8. Distribution function of relaxation times at T = 300 K for low frequency (LF) and high frequency (HF).
process is modeled by an ideal RC element of parallel resistance and capacitance. These samples present non-Debey behavior, which manifests itself by slightly suppressed semi-circles (Fig. 7). This can be solved by replacing the capacitance with a constant phase element (CPE). The CPE capacitance values were corrected to conventional capacitance (CCPE ). The results are registered in Table 1. Resistor R1 and capacitance C1 are related with the high frequency relaxation mechanism, associated with the dipoles formed by the Mn4+ ions. In samples with ı = 0.15 and 0.20, a difference is observed between the values of the capacitances associated with the high frequency relaxation (C1) and the low frequency relaxation (C2), which can be related with the two different dipoles. Sample with ı = 0.30 presents a different result. From all these curves, it should be noted that there is a huge and remarkable change in Z values. They are about 5 and 4 M for ı = 0 and 0.3, respectively, and ranging between only 0.2 and 0.8 M for other ı values. To explain this difference, we must consider the Mn3+ /Mn4+ ratio and the kind of the relaxation process (LF or HF). Indeed, for the samples with ı = 0.0, 0.15 and 0.20, the calculated Z corresponds to the low frequency relaxation process. In fact, these values are close to the resistance R1 in the equivalent circuit. The increase of ı leads to an augmentation of the Mn3+ /Mn4+ ratio, with a consequent increase of the conductivity at low frequencies. This behavior is confirmed by the dc electrical measurement made in the same samples, and already published in Ref. [9]. On the other hand, the value of Z obtained for the ı = 0.30 sample, corresponds not only to the low frequency relaxation process but also to the high frequency relaxation one, that is close to R2. As a consequence, this cannot be compared with the previous conductivities, as we are in a different relaxation process. In fact, in this second relaxation process, the values of R2 increase with ı. In particular the high value for the sample ı = 0.30 is responsible for the lower relaxation frequency calculated for this sample (see Fig. 8 for the distribution of relaxation times, where ı = 0.30 has lower relaxation frequency and higher relaxation time when compared with the HF relaxations of the other samples). 4. Conclusions The Ca2 MnO4−␦ compounds were prepared using the Sol–gel method. The magnetic study has revealed that the oxygendeficiency induces very interesting magnetic properties namely the magnetic frustration and spin glass behaviors. These behaviors were found to affect very closely the dielectric properties. Indeed, to highlight these properties, broadband dielectric spectroscopy was used to study the relaxation processes in Ca2 MnO4−␦ system. For the samples with ı = 0.00 and 0.30, we have observed one relaxation process. Therefore, for ı = 0.15 and 0.20 samples, a second relaxation mechanism was observed in the low frequency range which should be assigned to the Mn3+ –O2− dipoles. The higher frequency process is due to Mn4+ –O2− dipoles and this is the only one present in the sample with ı = 0.30. Both processes are found to be non-Debye and are well fitted by the Cole–Cole model of dielectric relaxation. Distribution functions of relaxation times have confirmed this behavior.
N. Chihaoui et al. / Journal of Alloys and Compounds 577S (2013) S483–S487
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