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Electrical and Dielectric Properties of NixMg1-xFe2O4
M.A. El Hiti
To cite this version:
M.A. El Hiti. Electrical and Dielectric Properties of NixMg1-xFe2O4. Journal de Physique III, EDP Sciences, 1996, 6 (10), pp.1307-1313. �10.1051/jp3:1996188�. �jpa-00249528�
Electrical and Dielectric Properties of Nixmgi-xFe~04
MA. El Hiti
Physics Department, Faculty of Science, Tanta University, Tanta, Egypt
(Received 21 December 1995, revised 9 April 1996, accepted 27 June 1996)
PACS.72. Electronic transport in condensed matter
PACS.51.20.+d Viscosity, diffusion and thermal conductivity
PACS.77. Dielectrics, piezoelectrics and ferroelectrics and their properties
Abstract. The electrical conductivity and dielectric behavior were studied at room tem-
perature for Ni~mgi-~Fe204 samples prepared by usual ceramic technique. The experimental results indicated that the real dielectric constant e' and loss factor tan 6 decrease while the AC electrical conductivity a2(w) increases as the frequency increases. The DC and AC electrical conductivity, e' and tan 6 decrease as Ni-ion substitution increases. The parameters n and B for the AC electrical conductivity a2(w) were found to be composition dependent, n and B de-
crease as Ni-ion substitution increases. Empirical formulae were suggested for the compositional
dependence of both n and B respectively.
1. Introduction
The magnetic semiconductor ferrites with high dielectric constant and low electrical resistivity
cover a wide field of technological applications. The study of the electrical and dielectric
properties of ferrites give good information about the localized electric charge carriers which leads to good understanding and explanation of electric conduction mechanism and dielectric
behavior in ferrites.
The DC [i] and AC [2] electrical conductivity and the dielectric behavior [3] studies were
performed above room temperature while X-ray and IR [4] studies were carried out at room
temperature for ferrite system Ni~mgi-~Fe204. The electrical and dielectric properties for the Ni-Mg ferrites were treated rarely in the literature. Therefore, the author aimed to study
the effect of frequency and composition on these properties at room temperature for Ni-Mg
ferrites.
2. Experimental
Ni~mgi-~Fe204 ferrite samples with X
= 0, 0.2, 0A, 0.6, 0.8 and i were prepared in the form of discs using the usual ceramic technique as mentioned earlier [4]. The analysis of X-ray
diffraction showed that the samples have single phase cubic spinet structure [4]. The samples
were polished carefully, rubbed by silver paste as contact material for electrical measurements.
The samples were placed between two electrodes inside an evacuated silica tube to avoid the moisture absorption on surfaces of the samples. The measuring complex impedance technique (Lock-in amplifier Stanford SR 510 type) was used to measure the frequency, voltage drop and
© Les #ditions de Physique 1996
1308 JOURNAL DE PHYSIQUE III N°10
105
l10~
10~
x.1
10~
10~
F0Izi
Fig. 1. Frequency dependence of e'.
phase angle simultaneously. From the variation of both the DC current and voltage for each sample, the DC electrical conductivity was determined. The experimental measurements were
carried out at room temperature at Physics Department, Faculty of Science, Tanta University, Tanta, Egypt.
3. Results and Discussion
3. I. FREQUENCY DEPENDENCE. The frequency dependence of the real dielectric constant
e', loss factor tan b and AC electrical conductivity a2(w) is shown in Figures 1, 2 and 3 re-
spectively at room temperature. e' (Fig. I) and tan b (Fig.2) decrease while a2(w) (Fig.3)
increases as frequency increases. e' has high values of the order of103 to 10~ which are in accordance with the early observed values of the order of10~ for Mn-Mg ferrites [5] and lo~
for each of Ni-Zn ferrites [5-7], Li-Ni ferrites [8] and Cu-Zn ferrites [9]. The dispersion or
decrease in e' and tan b is rapid at lower frequency and becomes slower at the higher frequency
values. This dispersion takes place when the electron exchange between the ferrous Fe~+ and ferric Fe3+ ions can not follow the alternation of applied AC electric field beyond a certain
critical frequency [10]. The effect of angular frequency on the real dielectric constant e' loss factor tan b and real AC electrical conductivity a[~ was studied theoretically [6,9,11,12]. A
good agreement was found between the experimental and theoretical results [9]. The simplest theoretical relation ill] predicted that e' and tan b are inversely proportional to the angular frequency w
= 2x f while a[~ is in direct proportion, it could be written as ill]:
~
(uJ tan b)
The real AC electrical conductivity a[~ consists of two parts [13], the temperature dependent
term ado or the DC electrical conductivity and the second term a2(w) which is temperature and frequency dependent. ado is due to the drift mobility of electric charge carriers and obeys
Arrhenius relation. a2(w) is attributed to the dielectric relaxation caused by localized electric
x.O.4
~cj
~~~
~~~
10~ 10~ 105
F(Hzi
Fig. 2. Frequency dependence of tan b.
b0 O
~
2.5 3 3.5 4 4.5 5 5.5 6
Log m
Fig. 3. Frequency dependence of a2(w).
charge carriers and follows the form [14]
a2(w)
= Bw" (2)
where n is a non-dimensional exponent. n and B (which has conductivity units fi~~ cm~~) are
composition and temperature dependent parameters. As shown in Figure 3, the logarithmic representation of equation (2) gives a straight line of a slope equal to the exponent n and intercept a part equal to log B on the vertical axis at logw = 0. The values of n and B could be determined from Figure 3 for each composition.
The high values of e' and tan b (Figs. I and 2) and lower values of a2(w) in Figure 3 at lower frequencies, the decrease in e' and tan b and increase in a2(w) as the frequency increases could be explained by the double layer dielectric structure [6] which was based on the Maxwell- Wagner model [15]. The inhomogeneous dielectric structure was supposed to be consisted by
1310 JOURNAL DE PHYSIQUE III N°10
a)
b)
~oI
0 0.2 0.4 0.6 0.8
x
Fig. 4. Compositional dependence at the selected frequencies of ii) 100 kHz, (2) 10 kHz, and (3)
1 kHz for: a) e' and b) tan 6.
two layers. The first one is the fairly well conducting ferrite grains which is separated by
the second layer or the poorly conducting grain boundaries. The grain boundaries of low
conductivity and high dielectric constants are more effective at lower frequencies while the ferrite grains of higher conductivity and lower dielectric constants are more effective at higher frequencies [6,9]. This explains the abnormal high values of e' and the decrease in both e' and tan b and the increase in a[~ as the frequency increases. Equation (2) also predicts that the
electrical conductivity a2(w) increases with increasing the frequency [14].
3.2. COMPOSITIONAL-DEPENDENCE. The compositional dependence of the real dielectric
constant and loss factor (e', tan b) is presented in Figure 4 (a and b) while the DC and AC
electrical conductivity (ado, a[~) is illustrated in Figure 5. a~, e' and tan b were drawn at selected frequencies of100, 10 and I kHz respectively. e' and tan (Fig. 4), ado and a2(w) (Fig. 5) decrease as the Ni-ion substitution increases. The electrical conductivity is equal to 1.02 x 10~, 1.43 x 10~ and 2.33 x 10~ fi~~ cm~l for Fe, Ni and Mg [16] respectively. The
replacement of less conductive Ni-ions to the more conductive Mg-ions leads to a marked decrease in the electrical conductivity as shown in Figure 5. This figure showed that the DC electrical conductivity ado is lower than AC conductivity a[~. This could be attributed to the fact that ado is a part of a[~ [13] where a[~
= ado + a2(w).
It was reported that Ni-ion has a strong preference to occupy the octahedral sites (B) [17-19]
while Mg-ion [20] and Fe-ion [17-20] occupy both A-sites (tetrahedral) and B-sites. Increasing
the Ni-ion substitution (which occupy B-sites), some Fe-ions will migrate from B-sites to A- sites [20]. This leads to a marked decrease in the number of Fe~+ and Fe3+ ions at B-sites
between which the electron exchange interaction takes place and is responsible for the electric
_~s
_°E 104 d
~ Dc
10~
10~
0 0.2 0.4 0.6 0.8
x
Fig. 5. Compositional dependence of a2(w) at the selected frequencies of 11) 100 kHz, (2) 10 kHz, (3) 1 kHz and (4) DC.
o 11.5
it.7 -o.5
~ -tt.9
~
" ©Q
-q
~
_~~
j
t2.3
t2.5
0 0.2 0.4 0.6 0.8 t
x
Fig. 6. Compositional dependence of n and B.
conduction in ferrites. The local displacement of charge carriers in direction of external electric field results in dielectric polarization. Therefore, the electrical conductivity (ado, a[~) and
dielectric polarization (e', tan b) decrease on increasing the Ni-ion substitution.
The effect of Ni-ion substitution on the parameters n and B for the electrical conductivity a2(w) is represented in Figure 6. Both n and B decrease as the Ni-ion substitution increases.
It was stated that n lies between 0 and [13]. The electric conduction is DC conduction or
frequency independent for n
= 0 and frequency dependent for n > 0. Since the values of n in this study are in the range of 0.15 to 0.45, the electric conduction is frequency dependent at
room temperature. Since the electrical conductivity a[~ and a2(w) decrease as Ni-ion substi- tution increases (Fig. 5), consequently n and B will decrease too according to equation (2).
B has the conductivity units therefore, it must follow the behavior of conductivity with the
1312 JOURNAL DE PHYSIQUE III N°10
composition, I.e. B decreases with increasing the Ni-ion substitution.
To get the real dependence of n and B on the composition, the relation between lnn and
lnB ~ersus the composition x was drawn as shown in Figure 6. The relation represents a
straight line with a slope equal to 1.073 for n and 0.54 for B, intercepted parts are present
on the vertical axis at x = o. Therefore, the compositional dependence of n and B could be
empirically suggested in the following form:
nix) = Ae~~ j3)
Bjx) =
A'e~'~ j4)
where A, a and a' are non-dimensional parameters. A' has conductivity units like B, the exponents a = 1.073 and a'
= 0.54. The expressions in equations (3) and (4) were suggested
earlier for NiZnmg ferrites [21] and BacoZn ferrites [22]. These empirical formulae have to be studied extensively for many ferrite systems before generalization.
4. Conclusion
The results of this work could be summarized as follows: the real dielectric constant e' and dielectric loss tan b decrease while the electrical conductivity a2(w) increases as the frequency of applied AC electric field increases. This was explained on the basis of the double-layer
dielectric structure. The real dielectric constant e', loss factor tan b, DC and AC electrical
conductivity (ado and a[~) decrease as the Ni-ion substitution increases. This was explained
on basis of electron hopping between Fe~+ and Fe3+ ions at B-sites. The parameters n and B for electrical conductivity a2(w) were found to be composition dependent. n and B decrease
as the Ni-ion substitution increases. Empirical formulae were suggested for the composition dependence of both n and B respectively.
References
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