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AC conductivity and frequency dependence of the dielectric properties for copper doped magnetite
ARTICLE IN PRESS
Physica B 363 (2005) 232–244 www.elsevier.com/locate/physb
AC conductivity and frequency dependence of the dielectric properties for copper doped magnetite H.M. Zaki Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Received 22 December 2004; received in revised form 19 March 2005; accepted 20 March 2005
Abstract A series of polycrystalline spinel ferrites with composition CuxFe3xO4+d (x ¼ 0:2, 0.4, 0.6, 0.8 and 1) were prepared by the standard ceramic method. The effect of Cu-ion substitution on the AC electrical conductivity and dielectric properties at different frequencies from 50 Hz up to 5 MHz was studied. The AC conductivity results were discussed in terms of the electron hopping model. The dispersion of the dielectric constant was discussed in the light of Koops’ phenomenological theory and the Rezlescu model. The dielectric loss tangent tan d curves exhibit dielectric relaxation peaks which are attributed to the coincidence of the hopping frequency of the charge carriers with that of the external fields. The frequency exponent factor (S) was estimated and it was found to vary between 0.4 for x ¼ 1 (CuFe2O4) and 0.83 for x ¼ 0:2. r 2005 Elsevier B.V. All rights reserved. PACS: 75.50.Gg; 77.22.Ch; 77.84.Bw Keywords: Ferrites; AC conductivity; Abnormal behavior; Exponential factor
1. Introduction Low cost, easy manufacturing, and interesting electrical and magnetic properties make polycrystalline ferrite one of the most important materials today. Ferrite as a semiconductor has attracted considerable attention in the field of technological application in a wide range of frequencies extendTel.: +20 103566955; fax: +20 55323252.
E-mail address: [email protected].
ing from microwave to radio frequency. Polycrystalline ferrites have very good dielectric properties that depend on several factors such as processing conditions, sintering temperature and time, chemical composition and substitution of different ions [1–4]. It was proposed that the air-sintered ferrites are characterized by relatively high conductive grains separated by high resistive thin layers (grain boundaries) [5,6]. Most of the external applied electric field to the specimen is concerned within the grain boundary regions.
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.03.026
ARTICLE IN PRESS H.M. Zaki / Physica B 363 (2005) 232–244
Therefore the electrical properties of the grain boundary phase control the electric and dielectric properties of these materials. Magnetite, Fe3O4, is the key system for all spinel ferrites, Fe3xMxO4, M representing a metallic constituent such as Cu, Mn, Zn, Ga, etc. There exists a vital interest in a more detailed knowledge of all material parameters of both the as-perfect basic material and its derivatives [7–9]. Abnormal thermal, magnetic and dielectric properties of Cu-containing ferrite have been reported [10,11]. In copper ferrite with a stoichiometric excess of oxygen, Cu1xFe2xO4+d cation vacancies are generated in tetrahedral and/or octahedral sites, which may influence the magnetic properties [12,13]. As witnessed by the large number of publications and the continued interest in the field, AC conduction in disordered solids is a subject of interest on its own. The present study is mainly concerned with experimental results of the dielectric properties of CuxFe3xO4+d . The aim of this work is to study the effect of Cu ions on the behavior of AC conductivity and dielectric properties at different frequencies.
2. Experimental technique Polycrystalline samples of CuxFe3xO4+d mixed ferrites (where x ¼ 0:2, 0.4, 0.6, 0.8 and 1 and 0pdX0:4, d ¼ 0:520:5x) were prepared by using the standard ceramic technique. High-purity oxide materials were used for the preparation. The mixed oxides were pre-sintered at 750 1C for 5 h soaking time and cooled slowly at a rate of 2 1C/min to room temperature. The pre-sintered mixture was ground and pressed at 3 tons pressure into a disk shape of 13 mm diameter. A small quantity of butyl alcohol as binding material was added to the powder. The samples were sintered as follows: 1000 1C for 5 h and slowly cooled at 2 1C/min and 1050 1C for 5 h and slowly cooled at 2 1C/min and 1100 1C for 5 h and slowly cooled at 2 1C/min. X-ray diffraction studies of the samples using a CuKa radiation source confirmed the spinel formation. The pellets were polished to obtain
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the form of circular discs with two parallel surfaces. Silver was pasted on both sides to ensure good electrical contacts. Both AC conductivity and dielectric loss tangent (tan d) were measured over a wide frequency range from 50 Hz up to 5 MHz at different temperatures, using a twoprobe method. The dielectric constant ð0 Þ and the dielectric loss ð00 Þ were calculated from AC conductivity ðsÞ and the dielectric loss tangent (tan d) data. A Hioki 3532 LCR Hitester bridge with PC was employed in measuring the AC conductivity and the dielectric measurements in the frequency range from 50 Hz up to 5 MHz. The drive voltage of the LCR meter used in the present work is 1 V.
3. Results and discussion 3.1. AC conductivity The AC conductivity ðsÞ, dielectric constant ð0 Þ and dielectric loss ð00 Þ were studied over a wide range of frequencies (50 Hz–5 MHz) for CuxFe3xO4+d at room temperature. The variations of s, 0 and 00 are shown in Fig. 1(a–e). It can be seen from these figures that the conductivity ðsÞ is nearly frequency independent at low frequency for low concentrations of copper. As Cu content increases ðx40:4Þ the conductivity becomes frequency dependent at low frequency. However, as the frequency increases the conductivity becomes more and more frequency dependent. The very basic fact about AC conductivity in disordered solids is that s is an increasing function of frequency (any hopping model has this feature). In a hopping model it is possible to distinguish different characteristic regions of frequency [14]. At low frequencies where the conductivity is constant, the transport takes place on infinite paths. For a region of frequencies where the conductivity increases strongly with frequency, the transport is dominated by contributions from hopping infinite clusters. Finally, the region where the high frequency cutoff starts to play a role (here saturation will be reached) is encountered. The electrical conduction mechanism can be explained in terms of the electron hopping model
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234
-1.5
106
-2.0
ε'
103
-3.0
ε' & ε''
σ
-2.5
102 103
104
105
106
ε''
105
-1.5
ε'
104
-2.5
102 101
107
-3.0 102
Frequency (Hz)
105
106
107
σ
103
105
106
-2.0
-2.5
107
-3.0 102
107
ε' & ε''
103
105
106
107
-0.50 ε''
x=1
-0.75
σ
ε'
105
-1.00
104
-1.25
103
-1.50
102
-1.75
101 101
104
Frequency (Hz)
Frequency (Hz)
106
-1.5
104
102 101
-2.5 104
σ
103
-2.0
103
-1.0
ε' ε' & ε''
-1.5
Log(σ σ Ω-1m-1)
104
102
ε''
105
Log(σ σ Ω-1m-1)
ε'
x=0.8
-0.5
Log(σ σ Ω-1m-1)
x=0.6
-1.0 ε' & ε''
104
106 ε''
102 101
103
Frequency (Hz)
106
105
-1.0
σ
103
-4.0 102
-0.5
-2.0
-3.5
101
0.0 x=0.4
Log(σ σ Ω-1m-1)
ε' & ε''
107
x=0.2 ε''
104
-1.0
σ Ω-1m-1) Log(σ
105
-2.00 102
103
104
105
106
107
Frequency (Hz) 0
00
Fig. 1. Plots of ; , s versus frequency at room temperature for x ¼ 0:2, 0.4, 0.6, 0.8 and 1.
by Heikes and Johnson [15]. In other words, the conduction mechanism could be due to the electron hopping between two adjacent octahedral
sites (B-sites) in the spinel lattice and a transition between Fe2+3Fe3+ ions or Cu2+3Cu+ might take place [16].
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For samples with a low concentration of x up to 0.4, in the range of frequency up to 103 Hz the frequency does not affect the exchange mechanism. But above this frequency electron exchange process effectivity appears. No saturation was observed for all samples, except for the sample with x ¼ 1 (CuFe2O4) which showed abnormal behavior. Accordingly, a maximum value of s was reached at F ¼ 5 105 Hz followed by a decrease in s with any further increase in frequency up to 5 MHz. The acceptable explanation for such decrease is that the applied field obstructs the hopping mechanism and consequently the conductivity decreases with increasing frequency. The behaviors of both 0 and 00 against frequency at room temperature are shown in Fig. 1. The general trend for all compositions is that 0 and 00 decrease with increasing frequency. For example, the dielectric constant for Cu ferrite ðx ¼ 1Þ has been reduced from 3 106 at 50 Hz to 103 at 5 MHz. The high values of dielectric constant can be attributed to the inhomogeneous structure of these ferrites. The same trend is also observed for CuxFe3xO4+d with a lower percentage. The complex dielectric constant is represented by ¼ 0 j00 ,
(1)
where 0 describes the stored energy while 00 describes the dissipated energy. It is clear that, according to Fig. 1, both 0 and 00 of the studied system show a decrease with increasing frequency. However, 00 decreases faster than 0 over the same range of frequency. In the high-frequency range the values of 0 become closer to the value of 00 . All samples exhibit dispersion due to Maxwell interfacial polarization [17], in agreement with phenomenological theory [5]. This behavior of dielectric may be explained qualitatively by supposing that the mechanism of the polarization process in ferrite is similar to that of the conduction process. Iwauchi [18] has pointed out that there is a strong correlation between the conduction mechanism and the dielectric behavior of ferrites. According to Heikes and Johnson [15] the electronic exchange in this ferrite may be
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considered as Fe2þ þ Cu2þ 3Fe3þ þ Cuþ .
(2)
One obtains local displacements of electron in the direction of the applied field. These displacements determine the polarization of the ferrite. It is known that the effect of polarization is to reduce the field inside the medium. Therefore, the dielectric constant of a substance may decrease substantially as the frequency is increased. Also, such a decrease can be attributed to the fact that the electric exchange between Fe2+ and Fe3+ ions cannot follow the external applied field beyond a certain frequency. Fig. 2(a–e) depicts the frequency dependence of the AC conductivity ðsÞ for all samples at different temperatures. It is clear that the dispersion of sðoÞ occurs at lower frequencies in the low-temperature range and vice versa. With the replacement of Cu2+ ions by Fe3+ ions, the dispersion tends to shift towards relatively lower frequencies. The dispersion in the AC electrical conductivity of polycrystalline ferrites was explained on the basis of interfacial polarization that formed due to the inhomogeneous structure of ferrite material. Generally, for all samples, dispersion of the AC conductivity decreases with increasing the temperature. At relatively high temperatures, the AC conductivity seems to be frequency independent until a certain frequency at which the conductivity begins to decrease. As mentioned before, at this frequency the applied field obstructs hopping conduction. 3.2. Frequency dependence of the dielectric constant (e0 ) and dielectric loss (e00 ) Figs. 3(a–e) and 4(a–e) illustrate the variation of the dielectric constant ð0 Þ and dielectric loss ð00 Þ with the frequency at different temperature for the studied compositions. Generally, the values of 0 for CuxFe3xO4+d are relatively high and 0 exhibits inversely peaking behavior with frequency. The observed minimum value depends on both temperature and composition. With increasing temperature the frequency at which the minimum occurs shifts to lower frequencies. On the other hand, with increasing Cu2+ content the minimum appears at relatively lower
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1.0 0.0
400
-0.5
300
x=0.2
-1.5 200
-2.5 -3.0 -3.5
-0.5 -1.0
300
200
-1.5 -2.0 -2.5
100
x=0.4
400
0.0
-1.0 -2.0
500
0.5
σ Ω−1m-1) Log (σ
0.5
Log (σ σ Ω−1m-1)
1.0
500
100
-3.0 R.T.
-4.0 101
102
103
104
105
106
R.T. -3.5 101 102
107
103
Frequency (Hz) 1.0
105
106
107
Frequency (Hz) 1.5
450
x=0.6
x=0.8
500
1.0
400
0.5
104
σ Ω−1m-1) Log (σ
σ Ω−1m-1) Log (σ
0.5 0.0
300
-0.5 -1.0 200 -1.5 100
-2.0 -2.5
10
-0.5
400 300
-1.0 -1.5
200
-2.0 -2.5
R.T. 1
0.0
102
103
104
105
106
107
100 R.T.
101
102
Frequency (Hz)
103
104
105
106
107
Frequency (Hz)
2.0
Log (σ σ Ω−1m-1)
1.5
500°C
x=1
1.0 400°C 0.5 0.0
300°C
-0.5 200°C -1.0 -1.5
100°C
R.T. -2.0 102 101
103
104
105
106
107
Frequency (Hz) Fig. 2. Variation of AC conductivity ðsÞ with frequency at fixed points of temperature for different Cu concentrations (x) for CuxFe3xO4+d.
ARTICLE IN PRESS H.M. Zaki / Physica B 363 (2005) 232–244
107 106
500
107
x=0.2
400
500 105
200 100
104
R.T.
400
ε'
ε'
200
104
300
100 103
103
R.T. 102
102 102
107
103 104 105 Frequency (Hz)
106
107
101
102
103 104 105 Frequency (Hz)
107
x=0.6
400 300
104
105 400 104 300
200 103
101
R.T. 102
103 104 105 Frequency (Hz)
106
107
500
450
105
106
x=0.8
106
106
ε'
101
ε'
x=0.4
106
300 105
237
103
200
100 101
107
102
103 104 105 Frequency (Hz)
R.T.
100
106
107
109 108
x=1
107
500°C
ε'
106
400°C 300°C 200°C
105
100°C
104 103
R.T.
102 101 101
102
103 104 105 Frequency (Hz)
106
107
Fig. 3. Relation between the dielectric constant ð0 Þ and frequency at fixed points of temperature for different concentrations (x) for CuxFe3xO4+d.
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238
1010
109
500
108 107 106 105
500
x=0.4
109
400
400
108
300
300 200
107
200
100
106
100
105
R.T.
104
x=0.2
ε''
ε''
1010
R.T.
103
104
102
103
101 10
1
102
103
104
105
106
102 101
107
102
Frequency (Hz)
109 108 ε''
107 106
106
107
106
107
1011
450 400 300
1010 500
x=0.6
x=0.8
109 400 108 300 107 200
200 100
ε''
1010
103 104 105 Frequency (Hz)
R.T. 105
106 100 105 R.T. 104
104
103
103 101
102
103
104
105
106
107
102 101
102
Frequency (Hz)
103 104 105 Frequency (Hz)
1011 1010 109 108 ε''
107 106
500 400 300 200 100 R.T.
x=1
105 104 103 102 101 101
102
103 104 105 Frequency (Hz)
106
107
Fig. 4. Relation between the dielectric loss ð00 Þ and frequency at fixed points of temperature for different concentrations (x) for CuxFe3xO4+d .
temperatures. The behavior of 0 for the compositions under investigation can be explained on the basis of Koops’ phenomenological theory [5] and
the Rezlescu model [10]. According to the Koops model, ferrite samples with homogeneous structure can be imagined as a system consisting
ARTICLE IN PRESS H.M. Zaki / Physica B 363 (2005) 232–244
of high conductive grains with 1 , s1 and thickness d1 separated by highly resistive thin grain boundaries with 2 , s2 and thickness d2. Koops assumed that y ¼ d 2 =d 1 51, s2 5s1 , 1 2 and the dielectric constant of the sample, 0 , is given by 0 ¼ 1 =y 2 =y.
(3)
Thus the grain boundary phase controls the behavior of 0 at lower frequencies. The thinner the grain boundary layers, the higher the value of 0 . The peaking behavior of 0 with frequency can be explained using the Rezlescu model. According to this model, the peaks of 0 ðF Þ curves can be ascribed to the presence of collective contribution to the polarization from two different types of charge carriers [10]. For the samples under investigation, the conduction process can be attributed to the presence of two types of charge carriers, n-type as electron transfer between Fe2+ and Fe3+, and p-type as hole exchange between Cu+ and Cu2+ at the octahedral sites [19,20]. These two coupling mechanisms can be represented by the following relations: Fe2þ 3Fe3þ þ e ,
Since the direction of displacement of electrons is opposite to that of holes under the application of external field, the mobility of holes is relatively very small with respect to that of electrons. The resultant polarization of both types of charge carriers will give peaking behavior as shown in Fig. 3. The shift of the peak to higher frequency with increasing temperature may be attributed to the corresponding increase of the mobility of the charge carriers with temperature. The peaking behavior was also observed for Cu–Ni, Cu–Mn and Cu–Zn ferrite [10], Cu–Cr ferrite [21] and Ni–Zn ferrite [22]. It can be seen from Fig. 4 that 00 decreases with increasing frequency. According to Smith and Wijn [23] for the same temperature, the ratio between the dielectric loss to the AC conductivity is inversely proportional to the applied frequency where 00 ¼ 1:8 1010
s . F
3.3. Dielectric loss tangent behavior Fig. 5(a–e) displays the variation of dielectric loss tangent, tan d, with frequency at different temperatures for all samples. It is shown that tan dðF Þ curves exhibit a peaking behavior for all compositions. The observed peaks are a function of both temperature and composition. As the temperature increases, the peak shifts towards lower frequencies. As Cu2+ ion content increases, new peaks at lower temperatures were observed and the peaks were shifted towards lower frequencies. It can also be noted that the height of the peak increases as the temperature increases. The observed peaks of tan d against frequency curves can be explained according to the fact that a strong correlation between the conduction mechanism and the dielectric behavior exists in ferrite [10,18]. Accordingly, a peak is expected when the hopping frequency of the electrons hopping between Fe2+ and Fe3+ ions is approximately equal to that of the external applied field, and in this case ot ¼ 1,
Cu2þ 3Cuþ þ eþ ðholeÞ.
(4)
239
(5)
where t is the relaxation time of the hopping process and o is the angular frequency of the external applied field ðo ¼ 2pF max Þ [13]. It is also known that the relaxation time t is inversely proportional to the jumping probability per unit time, p, according to the relation [24] t¼
1 . 2P
(6)
Therefore, from Eqs. (5) and (6), it is expected that Fmax is proportional to p. The shift of the peak of tan d towards low frequency with increasing temperature indicates that the jumping probability per unit time, p, decreases with increasing temperature. Also, the shift of the peak of tan d towards lower frequencies with increasing Cu2+ ion substitution indicates that the jumping probability decrease as Cu2+ ion content increases. This reduction of jumping probability may be ascribed to the decrease of iron ion in the B-site, which is responsible for the polarization
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240
104
103 500
x=0.2
400
400°c
500°c
x=0.4
103
102
101
300
Tan δ
Tan δ
102 300°c 101
200
100
100 R.T. 102
200°c
R.T.
100
10-1 101
100°c
103 104 105 Frequency (Hz)
10-1
106
107
101
102
103 104 105 Frequency (Hz)
106
107
104 400
450
400
100
Tan δ
102 200
101
101
300 200
100
100
100
x=0.8
103
300
102 Tan δ
500
x=0.6
103
R.T.
R.T. 10-1
10-1 101
102
103 104 105 Frequency (Hz)
106
10-2 101
107
102
103
104
105
106
107
Frequency (Hz)
104 400
500
300
103
Tan δ
102 101 100
x=1
200 100 R.T.
10-1 10-2 10-3 101
102
103
104
105
106
107
Frequency (Hz) Fig. 5. Variation of the dielectric loss tangent (tan d) with frequency at different selected temperatures for all samples.
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in this ferrite. A similar behavior was observed in zinc-substituted magnesium-rich manganese ferrite [25], Nd–Cu ferrite [26], Gd–Cu ferrite [27], Ni–Zn ferrite [22] and also in Cu–Zn ferrite [28].
241
3.4. Composition dependence of s, e0 and e00 Dependence of s, 0 and 00 on Cu ion content is shown in Fig. 6 at room temperature for 102 Hz. It can be seen that s, 0 and 00 increase as Cu2+ ion
108
1.0 0.5
F=102Hz 107
0.0
10 ε'& ε''
-1.0 -1.5
5
10
-2.0
Log(σ σ Ω− 1m-1)
-0.5 6
-2.5 104
-3.0 -3.5
103
-4.0 0.2
0.4
0.6 Composition (x)
0.8
1.0
Fig. 6. Composition dependence of AC conductivity ðsÞ, dielectric constant ð0 Þ and dielectric loss ð00 Þ at room temperature at fixed frequency 102 Hz.
Table 1 Frequency and composition dependence of s, e0 , e00 and tan d for CuxFe3xO4+d Frequency (Hz)
Dielectric symbol
x ¼ 0:2
0.4
0.6
0.8
1.0
102
log s (O1 m1) 0 00 tan d
3.66 6.19e3 3.97e4 6.41
2.82 3.57e4 2.76e5 7.72
2.15 3.12e5 1.27e6 4.07
2.57 1.33e5 4.87e5 3.68
1.76 1.5e6 3.16e6 2.04
103
log s (O1 m1) 0 00 tan d
3.57 1.24e3 4.86e3 3.93
2.72 8.61e3 3.4e4 3.96
2.042 3.3e4 1.63e5 4.96
2.4 2.65e4 7.19e4 2.72
1.52 2.22e5 5.4e5 2.44
104
log s (O1 m1) 0 00 tan d
3.3 5.82e2 9.03e2 1.55
2.49 3.3e3 5.9e3 1.76
1.88 1.13e4 2.4e4 2.13
2.12 7.7e3 1.37e4 1.78
1.22 6.41e4 1.08e5 1.68
105
log s (O1 m1) 0 00 tan d
2.57 5.29e2 2.42e2 0.46
1.46 6.24e2 8.81e2 0.71
0.85 2.57e3 2.61e3 0.99
1.32 7.07e2 8.58e2 1.22
0.84 2.38e3 2.6e3 1.09
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substitution increases. The number of vacancies may be established at the iron site as Cu content increases. Such vacancies initiate the thermal dissociation of oxygen, which in turn increases the number of electrons [29]. Also, a number of Fe2+ ions may be formed during the sample preparation. Such mechanisms will increase the
hopping process and may account for the increase in s, 0 and 00 as Cu content increases. Similar behavior has also been observed at higher frequencies (103–105 Hz) for all compositions at room temperature. Also according to Tawfik et al. [30], the substitution of Cu ions might cause the formation
-1 x=0.2(R.T.) S=0.83
-2 -3 -4 -1
x=0.4(R.T.) S=0.68
-2
Log (σ σ Ω− 1m-1)
-3
x=0.6(R.T.) (S)=0.64
-0.8 -1.6 -2.4
x=0.8(R.T.) (S)=0.46
-1.2 -1.8 -2.4
-0.6 x=1(R.T.) (S)=0.4 -1.2
-1.8 2
3
4
5 Log (ω)
6
7
8
Fig. 7. Variation of the exponential factor (S) with angular frequency ðoÞ at room temperature for all samples.
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of vacancies. If these are anion vacancies, they will retard the jump frequency away from the frequency of the applied field and hence a decrease in 0 occurs. But in case of the investigated system, the increase in 0 suggests that the formed vacancies are cations. The obtained results at different frequencies are tabulated in Table 1. 3.5. Determination of the frequency exponential factor (S) According to Jonscher [31] the real part of AC conductivity can be written as s ¼ sDC þ sAC ,
(7)
where sDC is the DC conductivity and sAC is the pure AC conductivity which can be represented as a power low of frequency as sAC ¼ AoS ,
(8)
where A is a parameter which has the conductivity unit, S is a dimensionless parameter and o is the angular frequency at which the conductivity s was measured. The value of S is usually, for physical convenience, between 0.4 and 0.8 [32]. The parameter S was calculated for all the compositions at room temperature over the studied range of frequencies. The results may be explained according to the hopping model proposed by Pike [33]. In the present work the values of S were calculated from the relation log s versus log o shown in Fig. 7. The obtained results agree well with the results of other workers [34–36].
4. Conclusions (1) The dispersion of AC electrical conductivity was observed at low temperatures and low frequencies. The replacement of Cu2+ ions by Fe3+ ions shifts the dispersion towards lower frequency. Abnormal behavior was observed for the sample with x ¼ 1 (Cu-ferrite). (2) The dielectric behavior can be explained in terms of the electron exchange between Fe2+ and Fe3+, and the hopping of a hole between Cu2+ and Cu+ ions at B-sites, suggesting that
243
the polarization in these compositions is similar to that of the conduction process in ferrites. (3) Abnormal behavior (peaks) was observed in tan d curves at relatively high temperatures. Such relaxation peaks take place when the jumping frequency of localized electrons between Fe2+ and Fe3+ ion equals that of the applied AC electric field. The broad maxima peaks tend to shift towards lower frequency as the temperatures increases. (4) The exponent factor (S) was calculated and found to be acceptable in the range of the reported values.
References [1] E.J.W. Verwey, P.W. Haaijmaan, F.C. Romeyn, G.M. Van Oosterhout, Philips. Res. Rep. 5 (1950) 173. [2] A. Vasiliu, F. Cuciureanu, N. Rezlescu, E. Luco, Phys. Status Solidi (a) 14 K (1972) 105. [3] M. Guyot, J. Magn. Magn. Mater. 18 (1980) 925. [4] K.K. Patankar, V.L. Mathe, R.P. Mahajan, S.A. Patil, R.M. Reddy, K.V. Sivakumar, Mater. Chem. Phys. 72 (2001) 23. [5] C. Koops, Phys. Rev. 83 (1951) 121. [6] A. Dias, R. Luiz Moreive, J. Mater. Res. 12 (1998) 2190. [7] S. Chikazumi, Physics of Magnetism, Krieger, Huntigton, New York, 1978. [8] A. Broesevan Groenou, P.F. Bongers, A.L. Stuyts, Mater. Sci. Eng. 3 (1969) 317. [9] V.A.M. Brabers, in: K.J. Buschow, (Ed.), Handbook of Magnetic Materials, vol. 8, North-Holland, Amsterdam, 1995 (Chapter 3). [10] N. Rezlescu, E. Rezlescu, Solid State Commun. 14 (1974) 69. [11] K.P. Belov, L.G. Antoshina, A.S. Markosyan, Sov. Phys. Solid State 25 (1983) 1609. [12] N. Nanba, J. Appl. Phys. 49 (1978) 2950. [13] N. Nanba, J. Appl. Phys. 53 (1982) 695. [14] H. Bottger, V.V. Bryksin, Hopping Conduction in Solids, Berlin, 1985. [15] R.R. Heikes, W.D. Johnson, J. Chem. Phys. 26 (1957) 582. [16] J.H. Jonker, J. Phys. Chem. Solids 9 (1959) 165. [17] J.C. Maxwell, Electricity and Magnetism, vol. 1, Oxford Press, London, 1973, p. 828. [18] K. Iwauchi, J. Appl. Phys. 10 (1971) 520. [19] X.-X Tang, A. Manthiram, J.B. Goodenough, J. Solid State Chem. 79 (1989) 250. [20] B.L. Patil, S.R. Sawant, S.A. Patil, Phys. Status Solidi (a) 133 (1992) 147. [21] M.A. El Hiti, M.A. Ahmed, M.M. Mossad, S.M. Ahia, J. Magn. Magn. Mater. 150 (1995) 399.
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H.M. Zaki / Physica B 363 (2005) 232–244
[22] R.V. Mangalaraja, S. Ananthakumar, P. Manohar, F.D. Gnanam, J. Magn. Magn. Mater. 253 (2002) 56. [23] J. Smith, H.P. Wijn, Ferrites, Wiley, New York, 1959. [24] M.B. Reddy, P.V. Reddy, Physica D 24 (1991) 975. [25] K.P. Thummer, H.H. Joshi, R.G. Kulkarni, J. Mater. Sci. Lett. 18 (1999) 1529. [26] J.W. Chen, J.C. Wang, Y.F. Chen, Physica C 289 (1997) 131. [27] J.B. Shi, Y. Hsu, C.L. Lin, Physica C 299 (1998) 272. [28] A.A. SaHar, S.A. Rahman, Phys. Status Solidi (a) 200 (2003) 415. [29] Y. Yamamoto, A. Makino, T. Nikaidou, J. Phys. IV, Collog (France) 7 c1-121 (1997).
[30] A. Tawfik, O.M. Hemeda, Mater. Lett. 56 (2002) 665. [31] A. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983. [32] N.F. Mott, E.A. Davis, Electronic Processes in NonCrystalline Materials, second ed., Clarendon Press, Oxford, 1979. [33] G.E. Pike, Phys. Rev. B 6 (1972) 1572. [34] S.A. Mazen, Mater. Chem. Phys. 62 (2000) 139. [35] S.A. Mazen, H.M. Zaki, J. Phys. D 28 (1995) 609. [36] S.A. Mazen, H.A. Dawoud, Mater. Chem. Phys. 82 (2003) 557.
Physica B 363 (2005) 232–244 www.elsevier.com/locate/physb
AC conductivity and frequency dependence of the dielectric properties for copper doped magnetite H.M. Zaki Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Received 22 December 2004; received in revised form 19 March 2005; accepted 20 March 2005
Abstract A series of polycrystalline spinel ferrites with composition CuxFe3xO4+d (x ¼ 0:2, 0.4, 0.6, 0.8 and 1) were prepared by the standard ceramic method. The effect of Cu-ion substitution on the AC electrical conductivity and dielectric properties at different frequencies from 50 Hz up to 5 MHz was studied. The AC conductivity results were discussed in terms of the electron hopping model. The dispersion of the dielectric constant was discussed in the light of Koops’ phenomenological theory and the Rezlescu model. The dielectric loss tangent tan d curves exhibit dielectric relaxation peaks which are attributed to the coincidence of the hopping frequency of the charge carriers with that of the external fields. The frequency exponent factor (S) was estimated and it was found to vary between 0.4 for x ¼ 1 (CuFe2O4) and 0.83 for x ¼ 0:2. r 2005 Elsevier B.V. All rights reserved. PACS: 75.50.Gg; 77.22.Ch; 77.84.Bw Keywords: Ferrites; AC conductivity; Abnormal behavior; Exponential factor
1. Introduction Low cost, easy manufacturing, and interesting electrical and magnetic properties make polycrystalline ferrite one of the most important materials today. Ferrite as a semiconductor has attracted considerable attention in the field of technological application in a wide range of frequencies extendTel.: +20 103566955; fax: +20 55323252.
E-mail address: [email protected].
ing from microwave to radio frequency. Polycrystalline ferrites have very good dielectric properties that depend on several factors such as processing conditions, sintering temperature and time, chemical composition and substitution of different ions [1–4]. It was proposed that the air-sintered ferrites are characterized by relatively high conductive grains separated by high resistive thin layers (grain boundaries) [5,6]. Most of the external applied electric field to the specimen is concerned within the grain boundary regions.
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.03.026
ARTICLE IN PRESS H.M. Zaki / Physica B 363 (2005) 232–244
Therefore the electrical properties of the grain boundary phase control the electric and dielectric properties of these materials. Magnetite, Fe3O4, is the key system for all spinel ferrites, Fe3xMxO4, M representing a metallic constituent such as Cu, Mn, Zn, Ga, etc. There exists a vital interest in a more detailed knowledge of all material parameters of both the as-perfect basic material and its derivatives [7–9]. Abnormal thermal, magnetic and dielectric properties of Cu-containing ferrite have been reported [10,11]. In copper ferrite with a stoichiometric excess of oxygen, Cu1xFe2xO4+d cation vacancies are generated in tetrahedral and/or octahedral sites, which may influence the magnetic properties [12,13]. As witnessed by the large number of publications and the continued interest in the field, AC conduction in disordered solids is a subject of interest on its own. The present study is mainly concerned with experimental results of the dielectric properties of CuxFe3xO4+d . The aim of this work is to study the effect of Cu ions on the behavior of AC conductivity and dielectric properties at different frequencies.
2. Experimental technique Polycrystalline samples of CuxFe3xO4+d mixed ferrites (where x ¼ 0:2, 0.4, 0.6, 0.8 and 1 and 0pdX0:4, d ¼ 0:520:5x) were prepared by using the standard ceramic technique. High-purity oxide materials were used for the preparation. The mixed oxides were pre-sintered at 750 1C for 5 h soaking time and cooled slowly at a rate of 2 1C/min to room temperature. The pre-sintered mixture was ground and pressed at 3 tons pressure into a disk shape of 13 mm diameter. A small quantity of butyl alcohol as binding material was added to the powder. The samples were sintered as follows: 1000 1C for 5 h and slowly cooled at 2 1C/min and 1050 1C for 5 h and slowly cooled at 2 1C/min and 1100 1C for 5 h and slowly cooled at 2 1C/min. X-ray diffraction studies of the samples using a CuKa radiation source confirmed the spinel formation. The pellets were polished to obtain
233
the form of circular discs with two parallel surfaces. Silver was pasted on both sides to ensure good electrical contacts. Both AC conductivity and dielectric loss tangent (tan d) were measured over a wide frequency range from 50 Hz up to 5 MHz at different temperatures, using a twoprobe method. The dielectric constant ð0 Þ and the dielectric loss ð00 Þ were calculated from AC conductivity ðsÞ and the dielectric loss tangent (tan d) data. A Hioki 3532 LCR Hitester bridge with PC was employed in measuring the AC conductivity and the dielectric measurements in the frequency range from 50 Hz up to 5 MHz. The drive voltage of the LCR meter used in the present work is 1 V.
3. Results and discussion 3.1. AC conductivity The AC conductivity ðsÞ, dielectric constant ð0 Þ and dielectric loss ð00 Þ were studied over a wide range of frequencies (50 Hz–5 MHz) for CuxFe3xO4+d at room temperature. The variations of s, 0 and 00 are shown in Fig. 1(a–e). It can be seen from these figures that the conductivity ðsÞ is nearly frequency independent at low frequency for low concentrations of copper. As Cu content increases ðx40:4Þ the conductivity becomes frequency dependent at low frequency. However, as the frequency increases the conductivity becomes more and more frequency dependent. The very basic fact about AC conductivity in disordered solids is that s is an increasing function of frequency (any hopping model has this feature). In a hopping model it is possible to distinguish different characteristic regions of frequency [14]. At low frequencies where the conductivity is constant, the transport takes place on infinite paths. For a region of frequencies where the conductivity increases strongly with frequency, the transport is dominated by contributions from hopping infinite clusters. Finally, the region where the high frequency cutoff starts to play a role (here saturation will be reached) is encountered. The electrical conduction mechanism can be explained in terms of the electron hopping model
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234
-1.5
106
-2.0
ε'
103
-3.0
ε' & ε''
σ
-2.5
102 103
104
105
106
ε''
105
-1.5
ε'
104
-2.5
102 101
107
-3.0 102
Frequency (Hz)
105
106
107
σ
103
105
106
-2.0
-2.5
107
-3.0 102
107
ε' & ε''
103
105
106
107
-0.50 ε''
x=1
-0.75
σ
ε'
105
-1.00
104
-1.25
103
-1.50
102
-1.75
101 101
104
Frequency (Hz)
Frequency (Hz)
106
-1.5
104
102 101
-2.5 104
σ
103
-2.0
103
-1.0
ε' ε' & ε''
-1.5
Log(σ σ Ω-1m-1)
104
102
ε''
105
Log(σ σ Ω-1m-1)
ε'
x=0.8
-0.5
Log(σ σ Ω-1m-1)
x=0.6
-1.0 ε' & ε''
104
106 ε''
102 101
103
Frequency (Hz)
106
105
-1.0
σ
103
-4.0 102
-0.5
-2.0
-3.5
101
0.0 x=0.4
Log(σ σ Ω-1m-1)
ε' & ε''
107
x=0.2 ε''
104
-1.0
σ Ω-1m-1) Log(σ
105
-2.00 102
103
104
105
106
107
Frequency (Hz) 0
00
Fig. 1. Plots of ; , s versus frequency at room temperature for x ¼ 0:2, 0.4, 0.6, 0.8 and 1.
by Heikes and Johnson [15]. In other words, the conduction mechanism could be due to the electron hopping between two adjacent octahedral
sites (B-sites) in the spinel lattice and a transition between Fe2+3Fe3+ ions or Cu2+3Cu+ might take place [16].
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For samples with a low concentration of x up to 0.4, in the range of frequency up to 103 Hz the frequency does not affect the exchange mechanism. But above this frequency electron exchange process effectivity appears. No saturation was observed for all samples, except for the sample with x ¼ 1 (CuFe2O4) which showed abnormal behavior. Accordingly, a maximum value of s was reached at F ¼ 5 105 Hz followed by a decrease in s with any further increase in frequency up to 5 MHz. The acceptable explanation for such decrease is that the applied field obstructs the hopping mechanism and consequently the conductivity decreases with increasing frequency. The behaviors of both 0 and 00 against frequency at room temperature are shown in Fig. 1. The general trend for all compositions is that 0 and 00 decrease with increasing frequency. For example, the dielectric constant for Cu ferrite ðx ¼ 1Þ has been reduced from 3 106 at 50 Hz to 103 at 5 MHz. The high values of dielectric constant can be attributed to the inhomogeneous structure of these ferrites. The same trend is also observed for CuxFe3xO4+d with a lower percentage. The complex dielectric constant is represented by ¼ 0 j00 ,
(1)
where 0 describes the stored energy while 00 describes the dissipated energy. It is clear that, according to Fig. 1, both 0 and 00 of the studied system show a decrease with increasing frequency. However, 00 decreases faster than 0 over the same range of frequency. In the high-frequency range the values of 0 become closer to the value of 00 . All samples exhibit dispersion due to Maxwell interfacial polarization [17], in agreement with phenomenological theory [5]. This behavior of dielectric may be explained qualitatively by supposing that the mechanism of the polarization process in ferrite is similar to that of the conduction process. Iwauchi [18] has pointed out that there is a strong correlation between the conduction mechanism and the dielectric behavior of ferrites. According to Heikes and Johnson [15] the electronic exchange in this ferrite may be
235
considered as Fe2þ þ Cu2þ 3Fe3þ þ Cuþ .
(2)
One obtains local displacements of electron in the direction of the applied field. These displacements determine the polarization of the ferrite. It is known that the effect of polarization is to reduce the field inside the medium. Therefore, the dielectric constant of a substance may decrease substantially as the frequency is increased. Also, such a decrease can be attributed to the fact that the electric exchange between Fe2+ and Fe3+ ions cannot follow the external applied field beyond a certain frequency. Fig. 2(a–e) depicts the frequency dependence of the AC conductivity ðsÞ for all samples at different temperatures. It is clear that the dispersion of sðoÞ occurs at lower frequencies in the low-temperature range and vice versa. With the replacement of Cu2+ ions by Fe3+ ions, the dispersion tends to shift towards relatively lower frequencies. The dispersion in the AC electrical conductivity of polycrystalline ferrites was explained on the basis of interfacial polarization that formed due to the inhomogeneous structure of ferrite material. Generally, for all samples, dispersion of the AC conductivity decreases with increasing the temperature. At relatively high temperatures, the AC conductivity seems to be frequency independent until a certain frequency at which the conductivity begins to decrease. As mentioned before, at this frequency the applied field obstructs hopping conduction. 3.2. Frequency dependence of the dielectric constant (e0 ) and dielectric loss (e00 ) Figs. 3(a–e) and 4(a–e) illustrate the variation of the dielectric constant ð0 Þ and dielectric loss ð00 Þ with the frequency at different temperature for the studied compositions. Generally, the values of 0 for CuxFe3xO4+d are relatively high and 0 exhibits inversely peaking behavior with frequency. The observed minimum value depends on both temperature and composition. With increasing temperature the frequency at which the minimum occurs shifts to lower frequencies. On the other hand, with increasing Cu2+ content the minimum appears at relatively lower
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236
1.0 0.0
400
-0.5
300
x=0.2
-1.5 200
-2.5 -3.0 -3.5
-0.5 -1.0
300
200
-1.5 -2.0 -2.5
100
x=0.4
400
0.0
-1.0 -2.0
500
0.5
σ Ω−1m-1) Log (σ
0.5
Log (σ σ Ω−1m-1)
1.0
500
100
-3.0 R.T.
-4.0 101
102
103
104
105
106
R.T. -3.5 101 102
107
103
Frequency (Hz) 1.0
105
106
107
Frequency (Hz) 1.5
450
x=0.6
x=0.8
500
1.0
400
0.5
104
σ Ω−1m-1) Log (σ
σ Ω−1m-1) Log (σ
0.5 0.0
300
-0.5 -1.0 200 -1.5 100
-2.0 -2.5
10
-0.5
400 300
-1.0 -1.5
200
-2.0 -2.5
R.T. 1
0.0
102
103
104
105
106
107
100 R.T.
101
102
Frequency (Hz)
103
104
105
106
107
Frequency (Hz)
2.0
Log (σ σ Ω−1m-1)
1.5
500°C
x=1
1.0 400°C 0.5 0.0
300°C
-0.5 200°C -1.0 -1.5
100°C
R.T. -2.0 102 101
103
104
105
106
107
Frequency (Hz) Fig. 2. Variation of AC conductivity ðsÞ with frequency at fixed points of temperature for different Cu concentrations (x) for CuxFe3xO4+d.
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107 106
500
107
x=0.2
400
500 105
200 100
104
R.T.
400
ε'
ε'
200
104
300
100 103
103
R.T. 102
102 102
107
103 104 105 Frequency (Hz)
106
107
101
102
103 104 105 Frequency (Hz)
107
x=0.6
400 300
104
105 400 104 300
200 103
101
R.T. 102
103 104 105 Frequency (Hz)
106
107
500
450
105
106
x=0.8
106
106
ε'
101
ε'
x=0.4
106
300 105
237
103
200
100 101
107
102
103 104 105 Frequency (Hz)
R.T.
100
106
107
109 108
x=1
107
500°C
ε'
106
400°C 300°C 200°C
105
100°C
104 103
R.T.
102 101 101
102
103 104 105 Frequency (Hz)
106
107
Fig. 3. Relation between the dielectric constant ð0 Þ and frequency at fixed points of temperature for different concentrations (x) for CuxFe3xO4+d.
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238
1010
109
500
108 107 106 105
500
x=0.4
109
400
400
108
300
300 200
107
200
100
106
100
105
R.T.
104
x=0.2
ε''
ε''
1010
R.T.
103
104
102
103
101 10
1
102
103
104
105
106
102 101
107
102
Frequency (Hz)
109 108 ε''
107 106
106
107
106
107
1011
450 400 300
1010 500
x=0.6
x=0.8
109 400 108 300 107 200
200 100
ε''
1010
103 104 105 Frequency (Hz)
R.T. 105
106 100 105 R.T. 104
104
103
103 101
102
103
104
105
106
107
102 101
102
Frequency (Hz)
103 104 105 Frequency (Hz)
1011 1010 109 108 ε''
107 106
500 400 300 200 100 R.T.
x=1
105 104 103 102 101 101
102
103 104 105 Frequency (Hz)
106
107
Fig. 4. Relation between the dielectric loss ð00 Þ and frequency at fixed points of temperature for different concentrations (x) for CuxFe3xO4+d .
temperatures. The behavior of 0 for the compositions under investigation can be explained on the basis of Koops’ phenomenological theory [5] and
the Rezlescu model [10]. According to the Koops model, ferrite samples with homogeneous structure can be imagined as a system consisting
ARTICLE IN PRESS H.M. Zaki / Physica B 363 (2005) 232–244
of high conductive grains with 1 , s1 and thickness d1 separated by highly resistive thin grain boundaries with 2 , s2 and thickness d2. Koops assumed that y ¼ d 2 =d 1 51, s2 5s1 , 1 2 and the dielectric constant of the sample, 0 , is given by 0 ¼ 1 =y 2 =y.
(3)
Thus the grain boundary phase controls the behavior of 0 at lower frequencies. The thinner the grain boundary layers, the higher the value of 0 . The peaking behavior of 0 with frequency can be explained using the Rezlescu model. According to this model, the peaks of 0 ðF Þ curves can be ascribed to the presence of collective contribution to the polarization from two different types of charge carriers [10]. For the samples under investigation, the conduction process can be attributed to the presence of two types of charge carriers, n-type as electron transfer between Fe2+ and Fe3+, and p-type as hole exchange between Cu+ and Cu2+ at the octahedral sites [19,20]. These two coupling mechanisms can be represented by the following relations: Fe2þ 3Fe3þ þ e ,
Since the direction of displacement of electrons is opposite to that of holes under the application of external field, the mobility of holes is relatively very small with respect to that of electrons. The resultant polarization of both types of charge carriers will give peaking behavior as shown in Fig. 3. The shift of the peak to higher frequency with increasing temperature may be attributed to the corresponding increase of the mobility of the charge carriers with temperature. The peaking behavior was also observed for Cu–Ni, Cu–Mn and Cu–Zn ferrite [10], Cu–Cr ferrite [21] and Ni–Zn ferrite [22]. It can be seen from Fig. 4 that 00 decreases with increasing frequency. According to Smith and Wijn [23] for the same temperature, the ratio between the dielectric loss to the AC conductivity is inversely proportional to the applied frequency where 00 ¼ 1:8 1010
s . F
3.3. Dielectric loss tangent behavior Fig. 5(a–e) displays the variation of dielectric loss tangent, tan d, with frequency at different temperatures for all samples. It is shown that tan dðF Þ curves exhibit a peaking behavior for all compositions. The observed peaks are a function of both temperature and composition. As the temperature increases, the peak shifts towards lower frequencies. As Cu2+ ion content increases, new peaks at lower temperatures were observed and the peaks were shifted towards lower frequencies. It can also be noted that the height of the peak increases as the temperature increases. The observed peaks of tan d against frequency curves can be explained according to the fact that a strong correlation between the conduction mechanism and the dielectric behavior exists in ferrite [10,18]. Accordingly, a peak is expected when the hopping frequency of the electrons hopping between Fe2+ and Fe3+ ions is approximately equal to that of the external applied field, and in this case ot ¼ 1,
Cu2þ 3Cuþ þ eþ ðholeÞ.
(4)
239
(5)
where t is the relaxation time of the hopping process and o is the angular frequency of the external applied field ðo ¼ 2pF max Þ [13]. It is also known that the relaxation time t is inversely proportional to the jumping probability per unit time, p, according to the relation [24] t¼
1 . 2P
(6)
Therefore, from Eqs. (5) and (6), it is expected that Fmax is proportional to p. The shift of the peak of tan d towards low frequency with increasing temperature indicates that the jumping probability per unit time, p, decreases with increasing temperature. Also, the shift of the peak of tan d towards lower frequencies with increasing Cu2+ ion substitution indicates that the jumping probability decrease as Cu2+ ion content increases. This reduction of jumping probability may be ascribed to the decrease of iron ion in the B-site, which is responsible for the polarization
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240
104
103 500
x=0.2
400
400°c
500°c
x=0.4
103
102
101
300
Tan δ
Tan δ
102 300°c 101
200
100
100 R.T. 102
200°c
R.T.
100
10-1 101
100°c
103 104 105 Frequency (Hz)
10-1
106
107
101
102
103 104 105 Frequency (Hz)
106
107
104 400
450
400
100
Tan δ
102 200
101
101
300 200
100
100
100
x=0.8
103
300
102 Tan δ
500
x=0.6
103
R.T.
R.T. 10-1
10-1 101
102
103 104 105 Frequency (Hz)
106
10-2 101
107
102
103
104
105
106
107
Frequency (Hz)
104 400
500
300
103
Tan δ
102 101 100
x=1
200 100 R.T.
10-1 10-2 10-3 101
102
103
104
105
106
107
Frequency (Hz) Fig. 5. Variation of the dielectric loss tangent (tan d) with frequency at different selected temperatures for all samples.
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in this ferrite. A similar behavior was observed in zinc-substituted magnesium-rich manganese ferrite [25], Nd–Cu ferrite [26], Gd–Cu ferrite [27], Ni–Zn ferrite [22] and also in Cu–Zn ferrite [28].
241
3.4. Composition dependence of s, e0 and e00 Dependence of s, 0 and 00 on Cu ion content is shown in Fig. 6 at room temperature for 102 Hz. It can be seen that s, 0 and 00 increase as Cu2+ ion
108
1.0 0.5
F=102Hz 107
0.0
10 ε'& ε''
-1.0 -1.5
5
10
-2.0
Log(σ σ Ω− 1m-1)
-0.5 6
-2.5 104
-3.0 -3.5
103
-4.0 0.2
0.4
0.6 Composition (x)
0.8
1.0
Fig. 6. Composition dependence of AC conductivity ðsÞ, dielectric constant ð0 Þ and dielectric loss ð00 Þ at room temperature at fixed frequency 102 Hz.
Table 1 Frequency and composition dependence of s, e0 , e00 and tan d for CuxFe3xO4+d Frequency (Hz)
Dielectric symbol
x ¼ 0:2
0.4
0.6
0.8
1.0
102
log s (O1 m1) 0 00 tan d
3.66 6.19e3 3.97e4 6.41
2.82 3.57e4 2.76e5 7.72
2.15 3.12e5 1.27e6 4.07
2.57 1.33e5 4.87e5 3.68
1.76 1.5e6 3.16e6 2.04
103
log s (O1 m1) 0 00 tan d
3.57 1.24e3 4.86e3 3.93
2.72 8.61e3 3.4e4 3.96
2.042 3.3e4 1.63e5 4.96
2.4 2.65e4 7.19e4 2.72
1.52 2.22e5 5.4e5 2.44
104
log s (O1 m1) 0 00 tan d
3.3 5.82e2 9.03e2 1.55
2.49 3.3e3 5.9e3 1.76
1.88 1.13e4 2.4e4 2.13
2.12 7.7e3 1.37e4 1.78
1.22 6.41e4 1.08e5 1.68
105
log s (O1 m1) 0 00 tan d
2.57 5.29e2 2.42e2 0.46
1.46 6.24e2 8.81e2 0.71
0.85 2.57e3 2.61e3 0.99
1.32 7.07e2 8.58e2 1.22
0.84 2.38e3 2.6e3 1.09
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242
substitution increases. The number of vacancies may be established at the iron site as Cu content increases. Such vacancies initiate the thermal dissociation of oxygen, which in turn increases the number of electrons [29]. Also, a number of Fe2+ ions may be formed during the sample preparation. Such mechanisms will increase the
hopping process and may account for the increase in s, 0 and 00 as Cu content increases. Similar behavior has also been observed at higher frequencies (103–105 Hz) for all compositions at room temperature. Also according to Tawfik et al. [30], the substitution of Cu ions might cause the formation
-1 x=0.2(R.T.) S=0.83
-2 -3 -4 -1
x=0.4(R.T.) S=0.68
-2
Log (σ σ Ω− 1m-1)
-3
x=0.6(R.T.) (S)=0.64
-0.8 -1.6 -2.4
x=0.8(R.T.) (S)=0.46
-1.2 -1.8 -2.4
-0.6 x=1(R.T.) (S)=0.4 -1.2
-1.8 2
3
4
5 Log (ω)
6
7
8
Fig. 7. Variation of the exponential factor (S) with angular frequency ðoÞ at room temperature for all samples.
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of vacancies. If these are anion vacancies, they will retard the jump frequency away from the frequency of the applied field and hence a decrease in 0 occurs. But in case of the investigated system, the increase in 0 suggests that the formed vacancies are cations. The obtained results at different frequencies are tabulated in Table 1. 3.5. Determination of the frequency exponential factor (S) According to Jonscher [31] the real part of AC conductivity can be written as s ¼ sDC þ sAC ,
(7)
where sDC is the DC conductivity and sAC is the pure AC conductivity which can be represented as a power low of frequency as sAC ¼ AoS ,
(8)
where A is a parameter which has the conductivity unit, S is a dimensionless parameter and o is the angular frequency at which the conductivity s was measured. The value of S is usually, for physical convenience, between 0.4 and 0.8 [32]. The parameter S was calculated for all the compositions at room temperature over the studied range of frequencies. The results may be explained according to the hopping model proposed by Pike [33]. In the present work the values of S were calculated from the relation log s versus log o shown in Fig. 7. The obtained results agree well with the results of other workers [34–36].
4. Conclusions (1) The dispersion of AC electrical conductivity was observed at low temperatures and low frequencies. The replacement of Cu2+ ions by Fe3+ ions shifts the dispersion towards lower frequency. Abnormal behavior was observed for the sample with x ¼ 1 (Cu-ferrite). (2) The dielectric behavior can be explained in terms of the electron exchange between Fe2+ and Fe3+, and the hopping of a hole between Cu2+ and Cu+ ions at B-sites, suggesting that
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the polarization in these compositions is similar to that of the conduction process in ferrites. (3) Abnormal behavior (peaks) was observed in tan d curves at relatively high temperatures. Such relaxation peaks take place when the jumping frequency of localized electrons between Fe2+ and Fe3+ ion equals that of the applied AC electric field. The broad maxima peaks tend to shift towards lower frequency as the temperatures increases. (4) The exponent factor (S) was calculated and found to be acceptable in the range of the reported values.
References [1] E.J.W. Verwey, P.W. Haaijmaan, F.C. Romeyn, G.M. Van Oosterhout, Philips. Res. Rep. 5 (1950) 173. [2] A. Vasiliu, F. Cuciureanu, N. Rezlescu, E. Luco, Phys. Status Solidi (a) 14 K (1972) 105. [3] M. Guyot, J. Magn. Magn. Mater. 18 (1980) 925. [4] K.K. Patankar, V.L. Mathe, R.P. Mahajan, S.A. Patil, R.M. Reddy, K.V. Sivakumar, Mater. Chem. Phys. 72 (2001) 23. [5] C. Koops, Phys. Rev. 83 (1951) 121. [6] A. Dias, R. Luiz Moreive, J. Mater. Res. 12 (1998) 2190. [7] S. Chikazumi, Physics of Magnetism, Krieger, Huntigton, New York, 1978. [8] A. Broesevan Groenou, P.F. Bongers, A.L. Stuyts, Mater. Sci. Eng. 3 (1969) 317. [9] V.A.M. Brabers, in: K.J. Buschow, (Ed.), Handbook of Magnetic Materials, vol. 8, North-Holland, Amsterdam, 1995 (Chapter 3). [10] N. Rezlescu, E. Rezlescu, Solid State Commun. 14 (1974) 69. [11] K.P. Belov, L.G. Antoshina, A.S. Markosyan, Sov. Phys. Solid State 25 (1983) 1609. [12] N. Nanba, J. Appl. Phys. 49 (1978) 2950. [13] N. Nanba, J. Appl. Phys. 53 (1982) 695. [14] H. Bottger, V.V. Bryksin, Hopping Conduction in Solids, Berlin, 1985. [15] R.R. Heikes, W.D. Johnson, J. Chem. Phys. 26 (1957) 582. [16] J.H. Jonker, J. Phys. Chem. Solids 9 (1959) 165. [17] J.C. Maxwell, Electricity and Magnetism, vol. 1, Oxford Press, London, 1973, p. 828. [18] K. Iwauchi, J. Appl. Phys. 10 (1971) 520. [19] X.-X Tang, A. Manthiram, J.B. Goodenough, J. Solid State Chem. 79 (1989) 250. [20] B.L. Patil, S.R. Sawant, S.A. Patil, Phys. Status Solidi (a) 133 (1992) 147. [21] M.A. El Hiti, M.A. Ahmed, M.M. Mossad, S.M. Ahia, J. Magn. Magn. Mater. 150 (1995) 399.
ARTICLE IN PRESS 244
H.M. Zaki / Physica B 363 (2005) 232–244
[22] R.V. Mangalaraja, S. Ananthakumar, P. Manohar, F.D. Gnanam, J. Magn. Magn. Mater. 253 (2002) 56. [23] J. Smith, H.P. Wijn, Ferrites, Wiley, New York, 1959. [24] M.B. Reddy, P.V. Reddy, Physica D 24 (1991) 975. [25] K.P. Thummer, H.H. Joshi, R.G. Kulkarni, J. Mater. Sci. Lett. 18 (1999) 1529. [26] J.W. Chen, J.C. Wang, Y.F. Chen, Physica C 289 (1997) 131. [27] J.B. Shi, Y. Hsu, C.L. Lin, Physica C 299 (1998) 272. [28] A.A. SaHar, S.A. Rahman, Phys. Status Solidi (a) 200 (2003) 415. [29] Y. Yamamoto, A. Makino, T. Nikaidou, J. Phys. IV, Collog (France) 7 c1-121 (1997).
[30] A. Tawfik, O.M. Hemeda, Mater. Lett. 56 (2002) 665. [31] A. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983. [32] N.F. Mott, E.A. Davis, Electronic Processes in NonCrystalline Materials, second ed., Clarendon Press, Oxford, 1979. [33] G.E. Pike, Phys. Rev. B 6 (1972) 1572. [34] S.A. Mazen, Mater. Chem. Phys. 62 (2000) 139. [35] S.A. Mazen, H.M. Zaki, J. Phys. D 28 (1995) 609. [36] S.A. Mazen, H.A. Dawoud, Mater. Chem. Phys. 82 (2003) 557.