Bull. Mater. Sci., Vol. 4, Number 1, March 1982, pp. 11-15. O Printed in India.
Dispersion of dielectric constant and resistivity of Cu~ Znl.xFe20t samples
S R S A W A N T and R N P A T I L
Department of Physics, Shivaji University, Kolhapur 416 004, India MS received 24 April 1981; revised 1 September 1981
Abstract. Cox Znl- x Fe204 samples exhibit dispersion of dielectric constant, tan8 and resistivity in the frequency range of 1 kHz to 50 MHz. The dispersion exhibited is in general accord with Koops' model. However, the details of the conducting and non-conducting regions must be taken into account when composition tends to change interrelationship between the elementary capacitor resistor circuits.
On quenching these samples from 800°C the dielectric constant ~I showed an increase for CuFe204 and Cuo.8Zn0.2Fe204 samples. The dielectric constant of the remaining samples showed no influence on quenching. The compositional variation showed that the dielectric constant has higher value for the ferrite Cu0.4Zn0.6Fe204
The results are explained on the basis of cation transfer.
Keywords. Dispersion; quenching; interfacial polarisation ; dielectric constant.
1. Introduction
Ferrites show abnormally high dielectric c o n s t a n t and dispersion o f dielectric constant and resistivity (Kamiyoshi 1951). The dispersion is explained by K o o p s (1951) and Moltgen (1952} to be due to inhomogeneous dielectric structure suggested by Maxwell (1873) and Wagner (1915).
The K o o p s model does n o t give details o f the c o n d u c t i n g and n o n - c o n d u c t i n g regions. These studies are therefore essential.
In the present paper we r e p o r t o u r studies on dielectric constant, resistivity and tan$ for Cux Zns-x Fe204 samples in the frequency range o f 1 k H z to 50 MHz. T h e dielectric constants o f the samples o f C u x Z n l - x F e 2 0 4 quenched f r o m 800°C are also presented.
2. Experimental
Samples o f C u x Z n l - x F e 2 0 4 ( x = 0 , 0. 2, 0.4,0. 6, 0. 8 and 1) were prepared by standard ceramic method. Weighed quantities o f A R grade oxides o f CuO, Z n O a n d 11
12 S R Sawant and R N Patil
Fe203 were calcinated at 700°C for 24 hr. Powders of these oxides were fired to 950°C for 24 hr and furnace cooled at the rate of 80°C/hr. Pellets of 1 cm diameter and 2 mm thickness were prepared and sintered at a temperature 950°C for 8 hr and furnace cooled at the rate o f 80°C/hr. Retaining a series of Cu~ Zni-x Fe204 as slow cooled, quenching in air of the samples from 800°C was carried out. The LCR bridge T F 1245 (series)--circuit magnification meter-- Marconi Instruments were used for measurements of resistivity and dielectric constant in the range 40'kHz up to 50 MHz. For low frequency measurements Marconi--TF 2700 LCR bridge was used.
3. R e s u l t a n d d i s c u s s i o n
Figure 1 shows variation of dielectric constant E" as a function of frequency for the samples of CuxZn~-xFe204. It is observed that as the frequency increases the dielectric constant decreases. The dispersion of dielectric constant is similar for all the samples.
Figure 2 shows variation of tan ~ against the frequency for these samples.
Though'the atnure o f the variation for all the samples is similar, the peaks observed change differently lying between 105 Hz to 106 Hz. The nature of the graph is as expected and agrees well with that reported for other ferrites (Iwauehi 1971; Murthy and Sobhanandri 1975).
Figure 3 shows variation of resistivity as a function of frequency. The resistivity also shows dispersion. Table 1 gives values of ~' for Cux Znl-x Fe2Oa slow cooled and quenched samples obtained from the experiment.
~0
30
. ~ l 20
10
@ I
' \ " " 'i'
• +
+°
4 \. % ',.
• \ , t
L
• Cu.8Zn.2 F..e 20/, Q Cu.6Zn/, Fe204
- Z6 Fe2.04 Cu./Zn 6Fe204
• 'it . . •
. "<,.-
- _-:.=..-- - ,~ _
10 3 10 "~ 105 106 10 7
Hz
Figure 1. Dielectric constant variation with log F.
Dielectric constants etc, o f Cux Znl-x Fez04 samples 13
'.-o
i,,-
0.4
0.2
0'1
0 10 4
C u6 Z n.z ' Fe20~ ~k k
10 5 10 6. 10 7
Hz ---,,-
Figure 2. Loss angle, tan~ as a function o f log (frequency.)
L Cu.& Zn.6Fe
20/.I
~o5I'
_qv i0 L,
10 3
Cu-8 Zn 2 Fe204
Cu 6Z~4. Fe 2 0 z . - - q k " " ~ ~ . .
b ,i i ! |
;0 4 ~0 s 10 6 10 ~
HZ
Figure 3. Resistivity change with log F.
Our value of ~ ' = 7 for CuFe204 agrees well with its previously reported value (Okamura et al 1952).
From table 1, it is seen that on quenching the samples from 800°C the dielectric constants of CuFe204 and C uo.sZn0.2FezO4 samples increase. The dielectric constants are almost unaffected on quenching the remaining samples.
The compositional variation of the dielectric constant at 20 kHz indicates that for the slow cooled ferrite Cu0o4Zn0.6Fe204 the dielectric constant is large.
14 S R Sawant and R N Patil
tO 8
2
Cole -Cole plot for Cu.6Zn.¢ Fe2Ol.
1 kHz
10 20 30 /.0 50 60
E.. E'--- ~°
Figure 4. Arc plot o f ~' vs ~'" in complex plane.
The cation transfer from B-site to A-site may be responsible for the changes in dielectric constant on quenching the samples and on addition o f Zn in Cux Znl-x Fe204 system.
Dielectric constants o f Cux Z n l - x FezO4 slow cooled a n d quenched samples at v a r i o u j Yable 1.
frequencies.
Samples
21 k H z 250 k H z 500 k H z 1 M H z 10 M H z
i i , |
C u F e 2 0 4 7 - - - - - - 2.0
C u F e 2 0 4 quenched from 800°C . . . . 3.0
Cu0.aZn0.2Fe204 9 1.9 1.8 1.8 1.7
Cuo.sZno.2Fe204 quenched from 800°C - - 3.5 3.4 2.8 2.7
Cuo.oZno.4Fe204 12 3.3 2.9 2.8 2.8
Cuo.oZno.4Fe204 quenched from 800°C m 2.8 2.7 2.6 1.9
Cuo.4Zno.6Fe204 16 2.6 2.5 2.3 2.3
Cuo4Zno.6Fe~O4 quenched f r o m 800°C w 2.4 2.4 2.3 2.1
Cuo.2Zno.8Fe204 14 2.6 2.6 2.4 2.4
Cuo.2Zn0.BFe20~ q u e n c h e d f r o m 800°C ~ 2.5 2.5 2.4 2.1
Z n F e 2 0 4 13 2.6 2.4 2.4 1.98
Z n F e 2 0 4 quenched f r o m 800°C m 2.1 1.9 1.9 1.60
Dielectric c o n s t a n t E"
Figure 4 is a graph of ~' vs ~" in complex plane for the sample C u 0 . 6 Z n 0 . 4 F e 2 0 4 .
Other samples behave in a similar fashion hence their plots are not reported.
From this plot it is clear that there is distribution of relaxation time suggesting a distribution of critical resistivity as well. Other ferrites are also reported to have shown similar behaviour (Iwauchi 1971). The nature of the plot suggests that heterogeneities producing interfacial polarisation exist in the sample.
Koops (1951) has explained the dispersion phenomenologically by considering the conducting regions and insulating layers as made up of parallel capacitors and resistor circuits giving rise to an equivalent parallel resistor capacitor
Dielectric canstants etc, o f Cux Znl-x Fe,.04 samples 15
circuit i . e . the interrelt~ionship between the dielectric and the conducting properties of the regions change with frequency and thus effectively constitute polarisation.
Figures 1, 2 and 3 exhibit dispersion characteristics o f e', p and tan 3 respectively which are in general agreement with K o o p s model showing relaxation due to interracial polarisation. However, the change in the characteristics with composition indicates that this simplistic model will have to take into consideration the details o f ~he conducting and n o n - c o n d u c t i n g regions. There is a possibility that the regions themselves m a y be inhomogeneous within as multidomain grains or other d o m a i n geometries are possible. These considerations appear to be essential especially for the studies o f the present type when composition tends to change the interrelationship between the so-called elementary capacitor resistor circuits giving rise to the change in lhe trend in the relative properties o f the composition in the f r e q u e n c y regions separated by the relaxation frequency.
References
Iwauchi K 1971 Ypn. J. Appl. Phys. 10 1520
Kamiyoshi K 1951 Sci. Rep. Res. Inst. Tohoku Univ. A3 716 Koops C G 1951 Phys. Rev. 68 121
Maxwell J C 1873 Electricity and magnetism, (London; Oxford Univ, Press) Vol. I Moltgen G 1952 Z. Angew. Phys. 4 216
Murthy V R K and Sobhanandri J 1975 NP and SSP Symposium. 18C SSP Okamura T, Fujimura and Date M 1952 Phys. Rev. 185 1041
Wanger K W 1915 Ann. Phys. 40 817
