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RC circuit and conductivity properties of Mn0.6Co0.4Fe2O4 nanocomposite synthesized by hydrothermal method
Journal of Alloys and Compounds 578 (2013) 90–95
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
RC circuit and conductivity properties of Mn0.6Co0.4Fe2O4 nanocomposite synthesized by hydrothermal method E. Sß entürk a,⇑, Y. Köseog˘lu b, T. Sß asßmaz a, F. Alan b, M. Tan b a b
Sakarya University, Department of Physics, Esentepe Campus, Sakarya, Turkey Fatih University, Department of Physics, Buyukcekmece 34500, Istanbul, Turkey
a r t i c l e
i n f o
Article history: Received 16 July 2012 Received in revised form 15 February 2013 Accepted 30 April 2013 Available online 7 May 2013 Keywords: Nanoparticles Hydrothermal method Interfacial polarization
a b s t r a c t Mn containing cobalt ferrite (CoFe2O4) nanocomposites were synthesized by polyethylene glycol (PEG) assisted hydrothermal method. Dielectric studies were carried out as a function of frequency and temperature using broadband dielectric measurement system. Dielectric properties were explained in terms of interfacial polarization and equivalent resistance–capacitor (RC) circuit. Frequency dependent dielectric loss factor has found to have two different behaviors which are explained by conductivity. DC conductivity obeys the Arrhenius law and exhibits two different behaviors corresponding to low and high temperature regions. It has two activation energies as 0.33 eV for low temperature region and 0.55 eV for high temperature region. Frequency dependent AC conductivity was analyzed by Jonscher’s universal power law which is varying as ws and the temperature dependent power parameter supported with the Correlated Barrier Hopping (CBH) model. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Nanosized magnetic materials, actually spinel ferrites have attracted considerable interest, and efforts in the last few decades because of the large number of applications where they can be used: ferrofluids, magnetoptics, spintronics, microwave industries, disk recording, refrigeration systems, electrical devices, anodes for batteries, etc. [1–6]. The magnetic properties of spinel ferrites can be varied systematically by changing the identity of the divalent Me2+ cations (Me@Co, Mn, Ni, Zn, etc.) without changing the spinel crystal structure [7–10]. The magnetic properties of nanosized particles show large differences when compared to bulk materials and they are widely studied because of the demanding increase in miniaturization and data storage densities. When the particle size is reduced, the surface-to-volume ratio becomes larger and the magnetic characteristics are strongly affected due to the influence of thermal energy over the magnetic moment ordering, originating the superparamagnetic phenomenon [11–14]. Cobalt based spinel ferrites (CoFe2O4) are well known hard magnetic materials, which has been studied in detail because of their interesting physical properties such as high Curie temperature, large magnetic anisotropy, high coercivity (5400 Oe), moderate saturation magnetization (80 emu/g) at room temperature, excellent chemical stability and mechanical hardness. Cobalt ferrites play an important role in high frequency magnetic applica⇑ Corresponding author. Tel.: +90 264 295 60 78; fax: +90 264 295 59 50. E-mail address: [email protected] (E. S ß entürk). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.04.206
tions due to their high electrical resistivity and negligible eddy current losses. However, in the case of CoFe2O4 nanoparticles, different values of coercivity and saturation magnetization have been reported [7,15,16]. The reason is that the structural, magnetic and electrical properties of nano ferrites depend on the particle size, the preparation methods, sintering temperatures, chemical compositions, the kind of cation substitutions, etc. [4,6,17,18,3]. Besides, aging is one of the most important factors that affect the electrical properties of materials [19]. In literature, only the limited number of report is available for the synthesis and dielectric characterization of Mn doped cobalt ferrite nanoparticles (NPs) by various methods such as solid state reaction method [20,21], sol–gel combustion technique [22,23], glycol-thermal method [24–26], auto-combustion technique [27], and high-temperature thermal decomposition method [28]. Most of them are expensive and require more energy, time consumption and annealing. There are a few reports on dielectric behavior MnACo nanoparticles (NPs) prepared be different methods. The electrical properties of MnACo nanoparticle systems (prepared by autocombustion route) with different ratios has been revealed that the dielectric loss is much lower than our results [29]. On the other hand, there are some dielectric studies similar to these nanoparticles systems. The dielectric properties of NiACo ferrites prepared by chemical co-precipitation technique have been showed extraordinary temperature dependence with ferri-paramagnetic state [30]. The dielectric properties of NiAZn ferrites prepared by flash combustion technique have been showed that the increase in Zn
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substitution decreases the values of imaginary part of the dielectric constant and dielectric loss [31]. CoAZn nanoparticles systems prepared by mechanical alloying and sintering have been studied at high frequencies. The convenient dielectric properties of the NPs systems showed electromagnetic absorbance [32]. ZnAZr effect of on Co ferrite nanoparticles prepared by chemical co-precipitation technique showed that both the dielectric constant and loss factor diminish with increasing frequency for all Co ferrite nanoparticles’ compositions [33]. In the present study, we aim to prepare Mn0.6Co0.4Fe2O4 NPs with a low sintering temperature involving less energy and low cost metal nitrates as raw materials by using surfactant PEG assisted hydrothermal method and investigate the dielectric properties of the sample. 2. Experimental All the chemical reagents were purchased from MERC Company and were analytically pure (99%), and were used as received without further purification. Nanoparticles of Mn doped Cobalt ferrite (Mn0.6Co0.4Fe2O4) has been synthesized by using hydrothermal method which is similar to that of Ref. [20]. For the synthesis, stoichiometric molar amounts of hydrous manganese nitrate (Mn(NO3)24H2O), cobalt nitrate (Co(NO3)26H2O) and ferric nitrate (Fe(NO3)39H2O) were weighted properly and dissolved in ion-free distilled water. Then all of the solutions were each stirred with the aid of a magnetic stirrer, and after that, the solutions were mixed. During the last stirring, 10 mL of PEG-400 was poured into the obtained solution of composition to serve as surfactant that covers nanoparticles and prevents agglomeration. Then, the pH of the solution was adjusted to 11. The obtained solution was put into the autoclave and then the autoclave was left in an oven at 180 °C for 24 h and cooled down to room temperature naturally. The samples were taken out of the autoclave, washed and dried for characterization. Structural, morphological and magnetic characterizations of the obtained Mn0.6Co0.4Fe2O4 sample are explained elsewhere [34]. Dielectric property and conductivity (AC–DC) measurements of the sample were made by Novocontrol dielectric spectroscopy system in the range 20–120 °C with a step of 10 °C (frequency range 1 Hz to 3 MHz). The samples were used in the form of circular pellets of diameter 1.3 and 0.3 cm thickness. The pellets were sandwiched between gold electrodes. The temperature was controlled with a Novocontrol Cryosystem, which is applicable between 100 °C and 250 °C. The dielectric data were collected during heating as a function of frequency.
3. Results and discussion Variation of dielectric constant by temperature is given in Fig. 1. There is a diffuse phase transition (DFT) centered at 320 K and spanning around 100 K covering the lower temperature region unseen in the figure. The diffusion of the dielectric constant with temperature is connected with the oxygen vacancy properties in perovskite type ceramics [35] and a lot of system. Oxygen vacan-
Fig. 1. Temperature variation of dielectric constant at specific frequencies.
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cies make the system inhomogeneous, as a result of this, the dielectric properties reveal a diffused type dielectric anomaly. Decreasing peak intensities with increasing frequency indicate an increasing diffuseness parameter. Changes of dielectric constant with frequencies up to 1 kHz is generally explained by dipolar and (interfacial) surface polarization. However, as temperature rises, dipolar polarization loses its effect since surface polarization becomes more dominant [30]. Thus, sudden and fast decrease of dielectric constant with a small frequency increase (in the low frequency region) is attributed to a mechanism of surface polarization. Furthermore, so fast decrease in dielectric constant at low frequencies supports the presence of strongly effective surface polarization. Variation of the real part of dielectric constant with frequency at some selected temperatures is shown in Fig. 2. It is very clear that the dielectric constant tends to decrease with increasing frequency. This decrement can be investigated in terms of two regions. Dielectric constant initially falls rapidly up to 100 Hz. Decreasing in dielectric constant gets slower beyond 100 Hz. Rapid decrease is particularly dominant at lower temperatures. Moreover, a peak centered at 5 kHz with a very slight intensity is also seen. The peak is stretched to a very wide frequency range and transforms to a linear response especially at higher temperatures. This behavior is an obvious result of existence of weak dipoles that cannot align themselves by the effect of an applied field. This situation can be expressed by using static and dynamic dielectric constants (De = es e1). Thus, it is very low at lower temperatures including the room temperature and relatively higher (around 20–25) at higher temperatures. At the ultimate frequencies, dielectric constant takes the value of 15 for all temperatures and stays almost unchanged. This can be explained by the fact that dipoles cannot follow the applied electric field and thus looses the effect of rotation at high frequencies. However, relaxor type diffused dielectric anomaly does not obey classical Curie-Weiss (CW) law. It can be symbolized with modified CW law as 1/e0 1/e0m = (T/Tm)c/C [36]. In here, em and Tm maximum values for dielectric constant and temperature, respectively. c is diffuseness parameter and it takes the value of c = 1.9 for 1 Hz. According to basic modulus formalism of M ¼ M 0 þ i:M 00 ¼ 1=e , electrical modulus’ not going to zero especially at low frequencies confirms surface polarization in the sample [37]. Furthermore, converging of the curves at high frequencies is an indicator of disordered solid formation [38]. This outcome supports the DFT model
Fig. 2. Frequency dependent variation of dielectric constant at some selected temperatures.
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mentioned above. Also, high dielectric constant at low frequencies is explained by properties related to non-homogeneous ferroelectric and ferromagnetic phases [39,40]. These layers form the base of present dielectric structure of the sample [41]. These layers naturally have different conductivities [40]. Well-conducting regions are separated by grain boundaries that have high resistance. As a result, motion of charge carriers in between two regions is blocked by grain boundaries whose physical interpretation means a potential barrier. This causes the charges to be more localized and accumulated. Such an accumulation results in an interfacial polarization as mentioned previously [42]. Grain boundaries as the cause of interfacial polarization are effective particularly at low frequencies, while ferrite grains separated by these boundaries are more effective at high frequencies [43]. The decrease in dielectric constant with rising frequency is explained by charge carriers’ not catching up the speed of applied electric field [41]. Thus, a dielectric response which is highly frequency dependent at low frequencies and less frequency dependent (or even frequency independent) at high frequencies is revealed. As DC conductivity is more dominant than the real part of the dielectric constant at low frequencies for low temperatures, we can see dielectric anomaly for only high temperatures. This anomaly shifts to higher frequencies at high temperatures. This is clearly a thermally activated process that can be characterized with classical Arrhenius law in an exponential form [44]. The frequency dependent dielectric constant also shows a universal dielectric response (e0 = A(T)fs(T)1) behavior [45]. Here, A(T) is a prefactor and s(T) is power parameter which is connected with the AC conductivity. Loss factor, tan d represents the part of electromagnetic wave energy that is converted to heat energy at a given frequency and temperature. Frequency variation of the loss factor of the sample under investigation at some selected temperatures is shown in Fig. 3. As seen in Fig. 3, there is not any loss peak at any temperature. For all temperatures, it is seen that loss factor decreases with frequency. Slowly moving ions can be said to be dominant in this dielectric behavior. Loss factor is generally greater at low frequencies than at high frequencies, and this is attributed to conductivity losses [46]. As temperature increases, conductivity losses increase along with DC conductivity. Furthermore, behavior of loss factor that is rapidly decreasing at low frequencies and slowly decreasing with 1/w at high frequencies is attributed to ions’ movements [47]. These curves’ slopes increase as the temperature rises. This can be evaluated that ion losses increases with temperature. The conduc-
tivity loss corresponding to ion movements is also known as migration loss. Therefore, loss factor is expressed with an addition to its classical formula as follows,
tan d ¼
e00 r þ e00 eo e00 w
Here, eo is the dielectric constant of the vacuum, r is the conductivity and w is the angular frequency. Decrement in dielectric loss is fast up to 10 kHz while it is slower for higher frequencies. At ultimate frequencies, loss factor is almost constant and equals to 0.1 for all temperatures. This value is around 0.05 at room temperature. This small value of the sample’s room temperature loss factor which corresponds to absorption of applied electromagnetic wave energy at these frequencies makes the sample technologically important. Evaluation of the real and imaginary impedance curves is preferred in terms of equivalent circuit representation of the sample and evaluation of any relaxation mechanism if there exists. Variation of the imaginary part of impedance with its real part is given in Fig. 4. All curves represent the grain boundaries corresponding to low frequencies and the grains (bulk properties as well) corresponding to high frequencies. Interception of the low frequency region of curves with the real part axis of impedance gives the total impedance due to grains and grain boundaries at that examined temperature and it decreases with increasing temperature. As can be seen from the figure, the value of total impedance parameter equals to 2.1 107 ohm-m at 293 K and 2.5 105 ohm-m at 393 K. Thus one can conclude that this parameter decreases with increasing temperature. From the form of these curves, it is clear that their centers lie in the real impedance axis but at different locations and they can be regarded as overlapping of two semicircles corresponding to grain and grain boundary. Again from the shape of the curves, one can understand that the radius of the circle corresponding to low frequencies is greater than that of the circle corresponding to high frequencies. Therefore, it can be stated that contribution of the grain boundaries to resistance is more effective than that of grains for all temperatures. Here, what has been said for grain and grain boundaries can be applied to capacitances as well in RC circuit. In the light of these foresights, dielectric constant’s variation with frequency, or in other words equivalent circuit representation can be modeled in terms of resistors and capacitors connected both in parallel and series as follows [48,49].
e ðwÞ ¼ e00 ðwÞ ie00 ðwÞ ¼ e1 þ e00 ðwÞ ¼ e1 þ e00 ðwÞ ¼ e1 ¼
es ¼
Fig. 3. Frequency variation of tangent loss factor at some selected temperatures.
es e1 r i 1 þ iws w
es e1 1 þ w2 s2
wsðes e1 Þ r 1 þ w2 s2 w
C g C gb C o ðC g þ C gb Þ
R2g C g þ R2gb C gb C o ðRg þ Rgb Þ2
s¼
Rg Rgb ðC g þ C gb Þ ðRg þ Rgb Þ
r¼
1 C o ðRg þ Rgb Þ
Here, w is the angular frequency, Co is the capacitance of free electrode, Cg is the grain’s capacitance, Cgb is the grain boundary’s
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Fig. 4. Variation of the imaginary part of impedance with its real part at some selected temperatures and the equivalent circuit design representing grain and grain boundaries.
capacitance, Rg is the grain’s resistance and Rgb stands for the grain boundary’s resistance. For such a system, grain and grain boundary responses occur at frequency points of (2pRgCg)1 and (2pRgbCgb)1 [50]. These frequencies definitely change with temperature and the first one represents the high frequencies and the latter stands for the low frequencies. Frequency variation of the conductivity of the sample at some temperatures is shown in Fig. 5. From the figure, it can be seen that the conductivity has two types of behavior at two regions that is valid for all temperatures. The flat region with only electronic contribution at low frequencies represents the DC conductivity. Frequency independent conductivity can be attributed to the long range transport of charge carriers as a response to the applied external electric field. This is totally related to the insufficient magnitude of applied field at low frequencies to initiate hopping conductivity. Second region of conductivity which increases with frequency represents AC conductivity. As temperature rises, probability of electron hopping between Fe2+ and Fe3+ increases resulting in an advancement of conductivity [41]. Therefore, AC conductivity increases with temperature as seen from the figure. Characteristic transition frequency between these two sites is around 100 Hz at 293 K and reaches to 10 kHz at 393 K. As seen from the figure, this frequency parameter shifts to higher values as temperature rises up. This behavior is due to the increment in
Fig. 5. Frequency dependence of AC conductivity at some temperatures.
the temperature of the sample by heat and a higher energy need of the mechanism which causes AC conductivity corresponding to higher frequencies. In such a case, total conductivity is expressed as the sum of conductivities in these two sites. Therefore, the frequency dependent conductivity for the sample was analyzed using universal Jonscher’s power law [51]:
rðw; TÞ ¼ rDC ðTÞ þ AwsðTÞ where w = 2pf is angular frequency and A is a constant. s is a power parameter whose index is lower than or very close to one. This parameter is obtained from the slope of the log r log w curve. For the examined sample, this parameter varies with temperature as given in Fig. 6. Temperature variation of ‘‘s’’ parameter determines the conductivity mechanism of the sample [52]. The exponent s has values decreasing with increasing temperature. So we may say that our results for temperature dependence of s and its values ranging between 0.84 and 0.66 are consistent with the Correlated Barrier Hopping (CBH) model [53]. This mechanism for ferrites containing Fe+2 and Fe+3 ions is explained by hopping of electrons between the octahedral sites of the spinel lattice [54]. According to this model, temperature dependent s parameter is given with the following equation [55].
s¼1
6kB T Wm
Fig. 6. Temperature variation of power parameter, s.
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found to be 0.33 eV for the temperature range of 293–348 K and 0.55 eV for 348–393 K as calculated from the slope of the curve in ln rDC 1000/T graph. Two regions of graph that have different slopes require two different transport mechanisms for the DC conductivity. The first of these is hopping of charge carriers between the localized states at around Fermi level. This region corresponding to low temperatures stands for a short range transport mechanism. Activation energy in this region is lower. The second one is the charge transport mechanism which is carried out by charge carriers excited beyond a mobility edge into the extended states leading to an activated energy at high temperatures. This second region corresponding to high temperatures represents a long-range transport mechanism. Activation energy in this region is higher. 4. Conclusion
Fig. 7. Temperature dependence of DC conductivity.
In this equation, T is temperature, kB is Boltzman’s constant and Wm is the maximum barrier height that electrons can make hopping over. This model can be explained by considering thermally activated charge carriers and two localized sites of different heights separated by an energy barrier [56]. Fitting of the dots in Fig. 6 with power parameter (s) equation produces barrier height to be 0.31 eV. Based on this, mathematical interpretation of CBH model for the conductivity can be expressed as follows.
rðwÞ ¼
p2 N2 e 8e2 24 eW m
6
ws
m1s
where e is electron charge, e is the effective dielectric constant, N is the density of localized states and m is the characteristic phonon frequency which is in the order of an atomic vibrational frequency (1013 s). After fitting experimental results with this expression, it is determined that densities of localized states are in a range of (7.7–3.2) 1023 eV1 cm3 and decreases very slowly with temperature. This model has been based on electron transfer between two different sites separated by an energy barrier. Any of these sites has a peculiar Coulomb potential. Maximum barrier height Wm decreases at any point between these sites, and this barrier height can be named W. So according to this model, electrons in charged defect states gets transferred over the Coulombic potential barrier whose height W is as follows [57].
W ¼ Wm
e2
h
e2
pe0 e W m kB T lnðw1s0 Þ
i
By this expression, lower bound (cut-off) to the hopping distance has been calculated as Rmin = 1.98 109 m. DC conductivity can also be obtained from extrapolation of the frequency independent linear part of the conductivity curve with the horizontal axis in Fig. 4. Hence, graph of DC conductivity with 1000/T is exhibited in Fig. 7. As seen from the figure, DC conductivity is composed of two regions with lines of different slopes. Therefore, DC conductivity is expressed as the sum of these two regions as follows, E1
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pe0 eR
where R is the hopping distance between two sites and given by,
R¼
As a result of experiments done, valuable scientific and technological information about the examined sample has been obtained. The sample has been identified to have DFT centered around 320 K. Frequency dependent dielectric constant and loss factor have been found to have two regions, and dielectric constant has been explained by surface polarization resulting from grain and grain boundaries. Dielectric constant has been modeled in terms of an equivalent RC circuit. Likewise, dielectric loss has been determined to possess two regions just like in the case of dielectric constant. Loss factor has been explained by considering an additional conductivity term to its classical form in literature. From analysis of DC conductivity data, again two different regions and corresponding two different types of DC conductivity have been revealed along with their activation energies found as 0.33 eV and 0.55 eV. From analysis of AC conductivity, the maximum barrier height for hopping electrons is found to be 0.31 eV, the density of states is calculated to be in the scale of 1023 eV1 cm3 and the minimum hopping distance is determined to be 1.98 nm. The sample can be evaluated further for its equivalent RC circuit design as well as its extraordinary loss factor behavior in terms of technological applications.
E2
rDC ðTÞ ¼ r01 ekB T þ r02 ekB T Here, E1 and E2 are the activation energies of charge carriers corresponding to two regions of the curve which is separated by a break. r01 and r02 are pre-exponential factors. Activation energies are
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
RC circuit and conductivity properties of Mn0.6Co0.4Fe2O4 nanocomposite synthesized by hydrothermal method E. Sß entürk a,⇑, Y. Köseog˘lu b, T. Sß asßmaz a, F. Alan b, M. Tan b a b
Sakarya University, Department of Physics, Esentepe Campus, Sakarya, Turkey Fatih University, Department of Physics, Buyukcekmece 34500, Istanbul, Turkey
a r t i c l e
i n f o
Article history: Received 16 July 2012 Received in revised form 15 February 2013 Accepted 30 April 2013 Available online 7 May 2013 Keywords: Nanoparticles Hydrothermal method Interfacial polarization
a b s t r a c t Mn containing cobalt ferrite (CoFe2O4) nanocomposites were synthesized by polyethylene glycol (PEG) assisted hydrothermal method. Dielectric studies were carried out as a function of frequency and temperature using broadband dielectric measurement system. Dielectric properties were explained in terms of interfacial polarization and equivalent resistance–capacitor (RC) circuit. Frequency dependent dielectric loss factor has found to have two different behaviors which are explained by conductivity. DC conductivity obeys the Arrhenius law and exhibits two different behaviors corresponding to low and high temperature regions. It has two activation energies as 0.33 eV for low temperature region and 0.55 eV for high temperature region. Frequency dependent AC conductivity was analyzed by Jonscher’s universal power law which is varying as ws and the temperature dependent power parameter supported with the Correlated Barrier Hopping (CBH) model. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Nanosized magnetic materials, actually spinel ferrites have attracted considerable interest, and efforts in the last few decades because of the large number of applications where they can be used: ferrofluids, magnetoptics, spintronics, microwave industries, disk recording, refrigeration systems, electrical devices, anodes for batteries, etc. [1–6]. The magnetic properties of spinel ferrites can be varied systematically by changing the identity of the divalent Me2+ cations (Me@Co, Mn, Ni, Zn, etc.) without changing the spinel crystal structure [7–10]. The magnetic properties of nanosized particles show large differences when compared to bulk materials and they are widely studied because of the demanding increase in miniaturization and data storage densities. When the particle size is reduced, the surface-to-volume ratio becomes larger and the magnetic characteristics are strongly affected due to the influence of thermal energy over the magnetic moment ordering, originating the superparamagnetic phenomenon [11–14]. Cobalt based spinel ferrites (CoFe2O4) are well known hard magnetic materials, which has been studied in detail because of their interesting physical properties such as high Curie temperature, large magnetic anisotropy, high coercivity (5400 Oe), moderate saturation magnetization (80 emu/g) at room temperature, excellent chemical stability and mechanical hardness. Cobalt ferrites play an important role in high frequency magnetic applica⇑ Corresponding author. Tel.: +90 264 295 60 78; fax: +90 264 295 59 50. E-mail address: [email protected] (E. S ß entürk). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.04.206
tions due to their high electrical resistivity and negligible eddy current losses. However, in the case of CoFe2O4 nanoparticles, different values of coercivity and saturation magnetization have been reported [7,15,16]. The reason is that the structural, magnetic and electrical properties of nano ferrites depend on the particle size, the preparation methods, sintering temperatures, chemical compositions, the kind of cation substitutions, etc. [4,6,17,18,3]. Besides, aging is one of the most important factors that affect the electrical properties of materials [19]. In literature, only the limited number of report is available for the synthesis and dielectric characterization of Mn doped cobalt ferrite nanoparticles (NPs) by various methods such as solid state reaction method [20,21], sol–gel combustion technique [22,23], glycol-thermal method [24–26], auto-combustion technique [27], and high-temperature thermal decomposition method [28]. Most of them are expensive and require more energy, time consumption and annealing. There are a few reports on dielectric behavior MnACo nanoparticles (NPs) prepared be different methods. The electrical properties of MnACo nanoparticle systems (prepared by autocombustion route) with different ratios has been revealed that the dielectric loss is much lower than our results [29]. On the other hand, there are some dielectric studies similar to these nanoparticles systems. The dielectric properties of NiACo ferrites prepared by chemical co-precipitation technique have been showed extraordinary temperature dependence with ferri-paramagnetic state [30]. The dielectric properties of NiAZn ferrites prepared by flash combustion technique have been showed that the increase in Zn
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substitution decreases the values of imaginary part of the dielectric constant and dielectric loss [31]. CoAZn nanoparticles systems prepared by mechanical alloying and sintering have been studied at high frequencies. The convenient dielectric properties of the NPs systems showed electromagnetic absorbance [32]. ZnAZr effect of on Co ferrite nanoparticles prepared by chemical co-precipitation technique showed that both the dielectric constant and loss factor diminish with increasing frequency for all Co ferrite nanoparticles’ compositions [33]. In the present study, we aim to prepare Mn0.6Co0.4Fe2O4 NPs with a low sintering temperature involving less energy and low cost metal nitrates as raw materials by using surfactant PEG assisted hydrothermal method and investigate the dielectric properties of the sample. 2. Experimental All the chemical reagents were purchased from MERC Company and were analytically pure (99%), and were used as received without further purification. Nanoparticles of Mn doped Cobalt ferrite (Mn0.6Co0.4Fe2O4) has been synthesized by using hydrothermal method which is similar to that of Ref. [20]. For the synthesis, stoichiometric molar amounts of hydrous manganese nitrate (Mn(NO3)24H2O), cobalt nitrate (Co(NO3)26H2O) and ferric nitrate (Fe(NO3)39H2O) were weighted properly and dissolved in ion-free distilled water. Then all of the solutions were each stirred with the aid of a magnetic stirrer, and after that, the solutions were mixed. During the last stirring, 10 mL of PEG-400 was poured into the obtained solution of composition to serve as surfactant that covers nanoparticles and prevents agglomeration. Then, the pH of the solution was adjusted to 11. The obtained solution was put into the autoclave and then the autoclave was left in an oven at 180 °C for 24 h and cooled down to room temperature naturally. The samples were taken out of the autoclave, washed and dried for characterization. Structural, morphological and magnetic characterizations of the obtained Mn0.6Co0.4Fe2O4 sample are explained elsewhere [34]. Dielectric property and conductivity (AC–DC) measurements of the sample were made by Novocontrol dielectric spectroscopy system in the range 20–120 °C with a step of 10 °C (frequency range 1 Hz to 3 MHz). The samples were used in the form of circular pellets of diameter 1.3 and 0.3 cm thickness. The pellets were sandwiched between gold electrodes. The temperature was controlled with a Novocontrol Cryosystem, which is applicable between 100 °C and 250 °C. The dielectric data were collected during heating as a function of frequency.
3. Results and discussion Variation of dielectric constant by temperature is given in Fig. 1. There is a diffuse phase transition (DFT) centered at 320 K and spanning around 100 K covering the lower temperature region unseen in the figure. The diffusion of the dielectric constant with temperature is connected with the oxygen vacancy properties in perovskite type ceramics [35] and a lot of system. Oxygen vacan-
Fig. 1. Temperature variation of dielectric constant at specific frequencies.
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cies make the system inhomogeneous, as a result of this, the dielectric properties reveal a diffused type dielectric anomaly. Decreasing peak intensities with increasing frequency indicate an increasing diffuseness parameter. Changes of dielectric constant with frequencies up to 1 kHz is generally explained by dipolar and (interfacial) surface polarization. However, as temperature rises, dipolar polarization loses its effect since surface polarization becomes more dominant [30]. Thus, sudden and fast decrease of dielectric constant with a small frequency increase (in the low frequency region) is attributed to a mechanism of surface polarization. Furthermore, so fast decrease in dielectric constant at low frequencies supports the presence of strongly effective surface polarization. Variation of the real part of dielectric constant with frequency at some selected temperatures is shown in Fig. 2. It is very clear that the dielectric constant tends to decrease with increasing frequency. This decrement can be investigated in terms of two regions. Dielectric constant initially falls rapidly up to 100 Hz. Decreasing in dielectric constant gets slower beyond 100 Hz. Rapid decrease is particularly dominant at lower temperatures. Moreover, a peak centered at 5 kHz with a very slight intensity is also seen. The peak is stretched to a very wide frequency range and transforms to a linear response especially at higher temperatures. This behavior is an obvious result of existence of weak dipoles that cannot align themselves by the effect of an applied field. This situation can be expressed by using static and dynamic dielectric constants (De = es e1). Thus, it is very low at lower temperatures including the room temperature and relatively higher (around 20–25) at higher temperatures. At the ultimate frequencies, dielectric constant takes the value of 15 for all temperatures and stays almost unchanged. This can be explained by the fact that dipoles cannot follow the applied electric field and thus looses the effect of rotation at high frequencies. However, relaxor type diffused dielectric anomaly does not obey classical Curie-Weiss (CW) law. It can be symbolized with modified CW law as 1/e0 1/e0m = (T/Tm)c/C [36]. In here, em and Tm maximum values for dielectric constant and temperature, respectively. c is diffuseness parameter and it takes the value of c = 1.9 for 1 Hz. According to basic modulus formalism of M ¼ M 0 þ i:M 00 ¼ 1=e , electrical modulus’ not going to zero especially at low frequencies confirms surface polarization in the sample [37]. Furthermore, converging of the curves at high frequencies is an indicator of disordered solid formation [38]. This outcome supports the DFT model
Fig. 2. Frequency dependent variation of dielectric constant at some selected temperatures.
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mentioned above. Also, high dielectric constant at low frequencies is explained by properties related to non-homogeneous ferroelectric and ferromagnetic phases [39,40]. These layers form the base of present dielectric structure of the sample [41]. These layers naturally have different conductivities [40]. Well-conducting regions are separated by grain boundaries that have high resistance. As a result, motion of charge carriers in between two regions is blocked by grain boundaries whose physical interpretation means a potential barrier. This causes the charges to be more localized and accumulated. Such an accumulation results in an interfacial polarization as mentioned previously [42]. Grain boundaries as the cause of interfacial polarization are effective particularly at low frequencies, while ferrite grains separated by these boundaries are more effective at high frequencies [43]. The decrease in dielectric constant with rising frequency is explained by charge carriers’ not catching up the speed of applied electric field [41]. Thus, a dielectric response which is highly frequency dependent at low frequencies and less frequency dependent (or even frequency independent) at high frequencies is revealed. As DC conductivity is more dominant than the real part of the dielectric constant at low frequencies for low temperatures, we can see dielectric anomaly for only high temperatures. This anomaly shifts to higher frequencies at high temperatures. This is clearly a thermally activated process that can be characterized with classical Arrhenius law in an exponential form [44]. The frequency dependent dielectric constant also shows a universal dielectric response (e0 = A(T)fs(T)1) behavior [45]. Here, A(T) is a prefactor and s(T) is power parameter which is connected with the AC conductivity. Loss factor, tan d represents the part of electromagnetic wave energy that is converted to heat energy at a given frequency and temperature. Frequency variation of the loss factor of the sample under investigation at some selected temperatures is shown in Fig. 3. As seen in Fig. 3, there is not any loss peak at any temperature. For all temperatures, it is seen that loss factor decreases with frequency. Slowly moving ions can be said to be dominant in this dielectric behavior. Loss factor is generally greater at low frequencies than at high frequencies, and this is attributed to conductivity losses [46]. As temperature increases, conductivity losses increase along with DC conductivity. Furthermore, behavior of loss factor that is rapidly decreasing at low frequencies and slowly decreasing with 1/w at high frequencies is attributed to ions’ movements [47]. These curves’ slopes increase as the temperature rises. This can be evaluated that ion losses increases with temperature. The conduc-
tivity loss corresponding to ion movements is also known as migration loss. Therefore, loss factor is expressed with an addition to its classical formula as follows,
tan d ¼
e00 r þ e00 eo e00 w
Here, eo is the dielectric constant of the vacuum, r is the conductivity and w is the angular frequency. Decrement in dielectric loss is fast up to 10 kHz while it is slower for higher frequencies. At ultimate frequencies, loss factor is almost constant and equals to 0.1 for all temperatures. This value is around 0.05 at room temperature. This small value of the sample’s room temperature loss factor which corresponds to absorption of applied electromagnetic wave energy at these frequencies makes the sample technologically important. Evaluation of the real and imaginary impedance curves is preferred in terms of equivalent circuit representation of the sample and evaluation of any relaxation mechanism if there exists. Variation of the imaginary part of impedance with its real part is given in Fig. 4. All curves represent the grain boundaries corresponding to low frequencies and the grains (bulk properties as well) corresponding to high frequencies. Interception of the low frequency region of curves with the real part axis of impedance gives the total impedance due to grains and grain boundaries at that examined temperature and it decreases with increasing temperature. As can be seen from the figure, the value of total impedance parameter equals to 2.1 107 ohm-m at 293 K and 2.5 105 ohm-m at 393 K. Thus one can conclude that this parameter decreases with increasing temperature. From the form of these curves, it is clear that their centers lie in the real impedance axis but at different locations and they can be regarded as overlapping of two semicircles corresponding to grain and grain boundary. Again from the shape of the curves, one can understand that the radius of the circle corresponding to low frequencies is greater than that of the circle corresponding to high frequencies. Therefore, it can be stated that contribution of the grain boundaries to resistance is more effective than that of grains for all temperatures. Here, what has been said for grain and grain boundaries can be applied to capacitances as well in RC circuit. In the light of these foresights, dielectric constant’s variation with frequency, or in other words equivalent circuit representation can be modeled in terms of resistors and capacitors connected both in parallel and series as follows [48,49].
e ðwÞ ¼ e00 ðwÞ ie00 ðwÞ ¼ e1 þ e00 ðwÞ ¼ e1 þ e00 ðwÞ ¼ e1 ¼
es ¼
Fig. 3. Frequency variation of tangent loss factor at some selected temperatures.
es e1 r i 1 þ iws w
es e1 1 þ w2 s2
wsðes e1 Þ r 1 þ w2 s2 w
C g C gb C o ðC g þ C gb Þ
R2g C g þ R2gb C gb C o ðRg þ Rgb Þ2
s¼
Rg Rgb ðC g þ C gb Þ ðRg þ Rgb Þ
r¼
1 C o ðRg þ Rgb Þ
Here, w is the angular frequency, Co is the capacitance of free electrode, Cg is the grain’s capacitance, Cgb is the grain boundary’s
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Fig. 4. Variation of the imaginary part of impedance with its real part at some selected temperatures and the equivalent circuit design representing grain and grain boundaries.
capacitance, Rg is the grain’s resistance and Rgb stands for the grain boundary’s resistance. For such a system, grain and grain boundary responses occur at frequency points of (2pRgCg)1 and (2pRgbCgb)1 [50]. These frequencies definitely change with temperature and the first one represents the high frequencies and the latter stands for the low frequencies. Frequency variation of the conductivity of the sample at some temperatures is shown in Fig. 5. From the figure, it can be seen that the conductivity has two types of behavior at two regions that is valid for all temperatures. The flat region with only electronic contribution at low frequencies represents the DC conductivity. Frequency independent conductivity can be attributed to the long range transport of charge carriers as a response to the applied external electric field. This is totally related to the insufficient magnitude of applied field at low frequencies to initiate hopping conductivity. Second region of conductivity which increases with frequency represents AC conductivity. As temperature rises, probability of electron hopping between Fe2+ and Fe3+ increases resulting in an advancement of conductivity [41]. Therefore, AC conductivity increases with temperature as seen from the figure. Characteristic transition frequency between these two sites is around 100 Hz at 293 K and reaches to 10 kHz at 393 K. As seen from the figure, this frequency parameter shifts to higher values as temperature rises up. This behavior is due to the increment in
Fig. 5. Frequency dependence of AC conductivity at some temperatures.
the temperature of the sample by heat and a higher energy need of the mechanism which causes AC conductivity corresponding to higher frequencies. In such a case, total conductivity is expressed as the sum of conductivities in these two sites. Therefore, the frequency dependent conductivity for the sample was analyzed using universal Jonscher’s power law [51]:
rðw; TÞ ¼ rDC ðTÞ þ AwsðTÞ where w = 2pf is angular frequency and A is a constant. s is a power parameter whose index is lower than or very close to one. This parameter is obtained from the slope of the log r log w curve. For the examined sample, this parameter varies with temperature as given in Fig. 6. Temperature variation of ‘‘s’’ parameter determines the conductivity mechanism of the sample [52]. The exponent s has values decreasing with increasing temperature. So we may say that our results for temperature dependence of s and its values ranging between 0.84 and 0.66 are consistent with the Correlated Barrier Hopping (CBH) model [53]. This mechanism for ferrites containing Fe+2 and Fe+3 ions is explained by hopping of electrons between the octahedral sites of the spinel lattice [54]. According to this model, temperature dependent s parameter is given with the following equation [55].
s¼1
6kB T Wm
Fig. 6. Temperature variation of power parameter, s.
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found to be 0.33 eV for the temperature range of 293–348 K and 0.55 eV for 348–393 K as calculated from the slope of the curve in ln rDC 1000/T graph. Two regions of graph that have different slopes require two different transport mechanisms for the DC conductivity. The first of these is hopping of charge carriers between the localized states at around Fermi level. This region corresponding to low temperatures stands for a short range transport mechanism. Activation energy in this region is lower. The second one is the charge transport mechanism which is carried out by charge carriers excited beyond a mobility edge into the extended states leading to an activated energy at high temperatures. This second region corresponding to high temperatures represents a long-range transport mechanism. Activation energy in this region is higher. 4. Conclusion
Fig. 7. Temperature dependence of DC conductivity.
In this equation, T is temperature, kB is Boltzman’s constant and Wm is the maximum barrier height that electrons can make hopping over. This model can be explained by considering thermally activated charge carriers and two localized sites of different heights separated by an energy barrier [56]. Fitting of the dots in Fig. 6 with power parameter (s) equation produces barrier height to be 0.31 eV. Based on this, mathematical interpretation of CBH model for the conductivity can be expressed as follows.
rðwÞ ¼
p2 N2 e 8e2 24 eW m
6
ws
m1s
where e is electron charge, e is the effective dielectric constant, N is the density of localized states and m is the characteristic phonon frequency which is in the order of an atomic vibrational frequency (1013 s). After fitting experimental results with this expression, it is determined that densities of localized states are in a range of (7.7–3.2) 1023 eV1 cm3 and decreases very slowly with temperature. This model has been based on electron transfer between two different sites separated by an energy barrier. Any of these sites has a peculiar Coulomb potential. Maximum barrier height Wm decreases at any point between these sites, and this barrier height can be named W. So according to this model, electrons in charged defect states gets transferred over the Coulombic potential barrier whose height W is as follows [57].
W ¼ Wm
e2
h
e2
pe0 e W m kB T lnðw1s0 Þ
i
By this expression, lower bound (cut-off) to the hopping distance has been calculated as Rmin = 1.98 109 m. DC conductivity can also be obtained from extrapolation of the frequency independent linear part of the conductivity curve with the horizontal axis in Fig. 4. Hence, graph of DC conductivity with 1000/T is exhibited in Fig. 7. As seen from the figure, DC conductivity is composed of two regions with lines of different slopes. Therefore, DC conductivity is expressed as the sum of these two regions as follows, E1
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pe0 eR
where R is the hopping distance between two sites and given by,
R¼
As a result of experiments done, valuable scientific and technological information about the examined sample has been obtained. The sample has been identified to have DFT centered around 320 K. Frequency dependent dielectric constant and loss factor have been found to have two regions, and dielectric constant has been explained by surface polarization resulting from grain and grain boundaries. Dielectric constant has been modeled in terms of an equivalent RC circuit. Likewise, dielectric loss has been determined to possess two regions just like in the case of dielectric constant. Loss factor has been explained by considering an additional conductivity term to its classical form in literature. From analysis of DC conductivity data, again two different regions and corresponding two different types of DC conductivity have been revealed along with their activation energies found as 0.33 eV and 0.55 eV. From analysis of AC conductivity, the maximum barrier height for hopping electrons is found to be 0.31 eV, the density of states is calculated to be in the scale of 1023 eV1 cm3 and the minimum hopping distance is determined to be 1.98 nm. The sample can be evaluated further for its equivalent RC circuit design as well as its extraordinary loss factor behavior in terms of technological applications.
E2
rDC ðTÞ ¼ r01 ekB T þ r02 ekB T Here, E1 and E2 are the activation energies of charge carriers corresponding to two regions of the curve which is separated by a break. r01 and r02 are pre-exponential factors. Activation energies are
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