Results and Discussion of Co1..CdFe204 Ferrites
4.3 Electrical Transport Property
4.3.1 Compositional Dependence of DC Electrical Resistivity
DC resistivity is an important electrical property of ferrites in high frequency application.
Fig. 4.16 gives the room temperature values of resistivity (Pdc) versus Cd content of the samples of series CoCdFe204 ferrites by using a Keithley Electrometer. For measurements, the pellet shaped samples were coated with silver paint on the both surfaces of each sample to obtain good ohmic contact. Table 4.1 gives the DC resistivity values for all the samples under study. The DC resistivity is found to increase with Cd content up to x = 0.4. Resistivity is found to decrease with further addition of Cd content.This decrease of resistivity may be attributed to the entrapped intragranular porosity, Sankpal
et.al.
and Shaikhet.al.
measured resistivity as a function of composition in their work on Ni-Cu and Li-Cd ferrites [4.38, 4.39].They obtained the similar trend of decreasing resistivity with the increase of Cu content. This trend could be attributed to the high activation energy, which is associated with high resistivity at room temperature. The decrease of resistivity has been related to the decrease of porosity since pores are non-conductive, which increase the resistivity of the materials [3.40].
800(
700(
600(
500(
I
400CE 300C 200C boG 0
0.0 0.0
Cd content (x)
Fig. 4.16 Room temperature DC resistivity as a function of Cd content of Co 1CdFe2O4 ferrites.
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4.3.2 Frequency Dependence of AC Resistivity
The electrical properties of ferrite materials depend upon the method of preparation, chemical composition, grain size and sintering temperature. The frequency dependence of AC electrical resistivity of ferrites is crucial because of its huge applications with frequency characteristics. The AC resistivity decreases as the frequency increases from I kHz to 13 MHz and is shown in Fig 4.17 at room temperature. All the samples show the significant dispersion with frequency which is the normal ferrimagnetic behavior. The resistivity of the ferrites is expected to decrease with an increase in the frequency; this may be due to the low dielectric constant and also depends on the porosity and composition [4.41]. Ferrite structurally forms cubic closed packed oxygen lattices with the cations at the octahedral (B) and the tetrahedral (A) sites. The distance between two metal ions at B site is smaller than the distance between a metal ion at B site and another metal ion at A-site. The electron hopping between A and B sites under normal conditions therefore has a very small probability compared with that for B- B hopping. Hopping between A and A sites does not exist for the reason that there are only Fe3 ions at the A site and Fe2F ions formed during processing preferentially occupy B sites only.
4.0 3.5 3.0
. 2.5 0
0.
0
ao 1.5 1P,2P4 -1-x=0.0 r=1(O°G2-ws -4-x=0.1
L. -A-- x = 0.2
-A- x = 0.3
- 4.4 444 -0- x 0.4
-I-x=0.5
-.-.-. ..-.-.
c01.XcdXFe2o4 -.- x = 0.6 ' N = 1050°Cl2frs-A-- x = 0.7
-A- x= 0.8 -O-x0.9 --x1.0
IIII._
. p.
4.0
ae
a6
3.4
a2
ao
28 26
3 4 5 6 7 8 3 4 5 6 7 8
log f(F) log f(}lz)
Fig. 4.17 Frequency dependence of AC resistivity ofCo1 CdFe2O4 ferrites sintered at 1050°C/2hrs.
The conduction mechanism in ferrites is explained on the basis of hopping of charge carriers between the Fe2 and Fe3 ions on octahedral site. The increase in frequency enhances the hopping frequency of charge carriers resulting in an increase in the conduction process
107
thereby decreasing the resistivity. Fen-ites are low mobility materials and the increase in conductivity does not mean that the number of charge carriers increases, but only the mobility of charge carriers increases. The minimum resistivity occurred when the frequency of the hopping charge carriers is equal to the applied field frequency termed as resonance frequency i.e. the jumping frequency of hopping charge carriers are almost equal to that of the applied AC electric field.
4.3.3 Frequency Dependence of Dielectric Constant
Fig. 4.17 shows the variation of dielectric constant, ' with frequency for different composition of Co1 .CdFe204 ferrites sintered at 1050°C/2hrs from 100 Hz to 13 MHz at room temperature. It can be seen from the figure that the dielectric constant is found to decrease continuously with increasing frequency for all the specimens exhibiting a normal dielectric behavior of ferrites. The dielectric dispersion is rapid at lower frequency region and it remains almost independent at high frequency side. The incorporation of Cd into Co-Cd ferrites has no pronounced effect on the dielectric constant in high frequency, but significantly decreases the dielectric constant in the low frequency range.
—u— x=O.O CO1 Cd Fe2O4
= 0.1 I = 1050°C/2hrs —y—x=O.2
*x=03
—y—x=O.4
——x=0.5
—1—x=0.6
—v—x0.7
= 0.9
\\ 1.0
\\\
3 4 5 6 7
Iogf(Hz)
Fig. 4.18 Dielectric constant as a function of frequency of the ferrite system Co1 CdFe204 ferrite sintered at 1050°C/2hrs.
2.5x1O
2.0x106
l.5x10e
A.
- 1.0x108
5.Oxl
0.0
This type of behavior was observed in a number of ferrites such as Li—Co ferrites [4.42], Cu—Cd ferrites [4.43] Ni—Cu—Zn ferrites [4.44], Li—Mg—Ti ferrites [4.45], Mg—Cu—Zn ferrites [4.46, 4.47]. The dielectric behavior of ferrites may be explained on the basis of the mechanism of the dielectric polarization process and is similar to that of the conduction process. The electronic exchange Fe2 Fe3 gives the local displacement of electrons in the direction of applied electric field, which induces the polarization in ferrites [4.43, 4.48].
The magnitude of exchange depends on the concentration of Fe 2
'
/Fe 31 ion pairs present on B site for the present ferrite. The sample x = 0.0 and 0.3 showed the maximum dispersion while that with x = 1.0 showed a least frequency dependence. The presence of Fe2 ions in excess amount favors the polarization effects. Thus, the more dispersion observed in the sample with x = 0.0 and 0.3 can be attributed to the presence of Fe2 ions in excess amount which could be formed at elevated sintering temperature. Similarly the weak dependence of dielectric constant on frequency can be due to lack of Fe 2'/Fe 31 ions concentration. All samples have high values of €' in the order of 105_108 at low frequencies. This could be explained using Koop's phenomenological theory [4.49] which was based on the Maxwell- Wagner model [4.50, 4.51] for the inhornogeneous double layer dielectric structure. The dielectric structure was supposed to be composed of the fairly well conducting ferrite grains.These are separated by the second thin layer of grain boundaries which are poorly conducting substances. These grain boundaries could be formed during the sintering process due to the superficial reduction or oxidation of crystallites in the porous materials as a result of their direct contact with the firing atmosphere [4.52]. The grain boundaries of lower conductivity were found to be effective at lower frequencies while ferrite grains of high conductivity are effective at high frequencies [4.49, 4.53].