Structural characterization
XRD patterns of the sintered Ni0.7-xZnxCu0.3Fe2O4 ferrites are shown in Figure 1. The most intense peaks in all specimens, indexed as (220), (311), (222), (400), (422), (333), and (440), are found to match well with single-phase cubic spinel (JCPS card number 08-0234). No additional phase corresponding to any structure in starting and doped samples was detected.
<p>Figure 1</p>XRD pattern of powdered Ni0.7-xCu0.3ZnxFe2O4 (0.0 ≤ x ≤ 0.2, x = 0.05) ferrite nanoparticles
XRD pattern of powdered Ni0.7-xCu0.3ZnxFe2O4 (0.0 ≤ x ≤ 0.2, x = 0.05) ferrite nanoparticles.
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The lattice parameter of the samples was determined using this relation 14:
a
exp
=
d
h
k
l
h
2
+
k
2
+
l
2
.
The average crystallite size was determined from the diffraction peak broadening with the use of the Scherrer's equation 15:
t
=
0
.
98
λ
β
cos
θ
.
Here, λ is the wavelength of the CuKα radiation (λ = 1.54060), and β is the full width at half maximum in radians.
The lattice parameters and crystallite sizes of the sintered ferrite specimens, evaluated by XRD analysis, are shown in Table 1 along with other structural parameters. It is seen that the grown ferrite samples show a narrow size distribution ranging from 28 to 32 nm. Also, the lattice constant is found to increase from 8.361 to 8.368 Å with increasing Zn content. The lattice parameter values are in expected range with the lattice parameters of spinel cubic ferrites 1617. The behavior can be attributed to the mismatching of ionic radii, where the ionic radius of Zn2+ ion (0.84 Å) is larger than that of Ni3+ ion (0.74 Å).
<p>Table 1</p>Grain size, lattice parameters, and ionic radii data of Ni0.7-xCu0.3ZnxFe2O4 ferrite nanoparticles
Zn content
Grain size
Lattice constant
Ionic radii
(x)
D (nm)
aexp (Å)
ath (Å)
rA (Å)
rB (Å)
0.00
28.2
8.361
8.359
0.680
0.755
0.05
28.6
8.363
8.362
0.682
0.755
0.10
29.8
8.365
8.363
0.683
0.755
0.15
30.5
8.367
8.365
0.685
0.755
0.20
31.3
8.368
8.366
0.688
0.755
The theoretical lattice parameter (ath) can then be calculated using this equation 14:
a
th
=
8
3
3
r
A
+
r
B
+
3
r
B
+
r
o
,
where ro is the radius of the oxygen ion (0.138 nm), and rA and rB are the ionic radii of tetrahedral (A) and octahedral (B) sites, respectively. The values of rA and rB will depend critically on the cation distribution of the given system. To calculate for rA and rB, the following cation distribution is proposed:
Zn
x
2
+
,
Fe
1
-
δ
3
+
Ni
0
.
7
-
x
2
+
,
Fe
1
+
δ
3
+
,
Fe
δ
2
+
O
4
-
.
This cation distribution is based on the following:
1. NiFe2O4 and CuFe2O4 1819 are both inverse spinel in structure in which half of the ferric ions preferentially occupy the tetrahedral (A sites) and the other half occupy the octahedral sites (B sites).
2. On the other hand, Zn ions prefer to occupy the tetrahedral sites 20.
3. During the sintering process, oxygen loss occurs, leading a part of Fe3+ ions to transform to Fe2+ for charge compensation 14.
The data in Table 1 reveals that the values of the theoretical lattice parameter (ath), calculated assuming the suggested cation distribution formula, agree well with those experimentally obtained (aexp).
The mean radius of the ions at the tetrahedral site rtetr and the octahedral site roct has been calculated according to these equations 21:
r
tetra
=
a
3
μ
-
0
.
25
-
R
o
and
r
oct
=
a
5
8
-
μ
-
R
o
,
where Ro is the radius of the oxygen ion (Ro = 1.26 Å), and μ is the oxygen parameter. Here, we have taken the value μ = 0.375 by assuming that the spinel structure is not deformed by Zn2+ doping 2223.
The variation of X-ray density Dhkl (theoretical), apparent density (experimental) Dx, and porosity P as a function of Zn2+ ion concentration (x) is reported in Table 2. The X-ray density of the prepared samples was calculated using this formula 24:
<p>Table 2</p>X-ray density, apparent density, porosity, and FT-IR spectral data of Ni0.7-xCu0.3ZnxFe2O4 ferrite nanoparticles
Zn content
X-ray density
Apparent density
Porosity
Vibrational modes
(x)
Dhkl (nm)
Dx (g cm-3)
P (%)
v1(cm-1)
v2(cm-1)
0.00
5.5030
5.2095
5.33
611
421
0.05
5.4969
5.2199
5.35
613
421
0.10
5.4780
5.1810
5.42
613
422
0.15
5.4730
5.1695
5.54
615
421
0.20
5.4653
5.1486
5.79
617
421
D
h
k
l
=
Z
M
N
a
3
,
where Z is the number of molecules per unit cell (Z = 8), M is the molecular weight, a is the lattice parameter, and N is the Avogadro's number. The theoretical density of the samples was calculated using this formula 24:
D
x
=
m
V
r
2
h
,
where m, V, r, and h are the mass, volume, radius, and thickness of the samples, respectively. The porosity of the samples was calculated using this formula:
P
= 1
-
D
x
D
h
k
l
×
100
.
The apparent density of the specimens is about 94% to 95% of the corresponding X-ray densities. The data in Table 2 show that both densities decrease with increasing Zn content, i.e., the apparent density nearly reflects the same general behavior with the X-ray density.
The increase of porosity and decrease of shrinkage with increasing Zn2+ ion content are related to the rapid densification of ferrite samples and also to the difference in specific gravity of the ferrite components since NiO (6.72 g cm-3) is heavier than ZnO (5.6 g cm-3) 25. Also, it is known that the porosity of ceramic samples is a result that came from two sources: the intragranular porosity [Pintra] and intergranular porosity [Pinter] 26. Thus, the total porosity P (in percent) could be written as the sum of the two types:
P
%
=
P
intra
+
P
inter
.
Furthermore, it is reported that Pinter depends on the grain size 27. By the study of XRD and transmission electron microscopy [TEM] data of the samples, it is found that as the Zn concentration increases from x = 0.0 up to x = 0.2, there is no major change in the grain size. Therefore, as Zn2+ ion content increases, Pinter remains almost constant. Thus, according to Equation 10, the increase of the total porosity P (in percent) is mainly due to the increase of Pintra with Zn2+ doping 2829.
The FETEM and FESEM micrographs of the synthesized nanoparticles along with the selected area electron diffraction [SAED] pattern for pure and doped Ni-Cu-Zn ferrite nanoparticles are shown in Figures 2a, b, c, 3a, b, and 4a, b, c. The micrographs show largely agglomerated nanoparticles of the sample powder. An overview of the TEM image of nanoparticles shows that the particles have a size distribution of 28 to 32 (± 1) nm. The average size of the agglomerates is found to be 30 nm. Such aggregate formation and broader size distribution are characteristic of mechanically activated nanosized particles. The agglomeration of particles is also because they experience a permanent magnetic moment proportional to their volume 30. Very few large particles having a size at approximately 40 nm have also been observed. It is clear from Table 1 that the particle size obtained from FETEM measurements corroborates well with the crystallite size obtained from XRD analysis. The shape of majority of the particles appears to be non-spherical. In the SAED image of synthesized nanoparticles, distinct rings that confirm good crystallinity are clearly visible. The observed crystallographic d values of 2.52 Å correspond to the lattice space of (311) plane of the Ni-Cu-Zn ferrite system. The observed crystallographic d values agree well with those obtained from XRD analysis. The results of the XRD and TEM study divulge that all the samples are well crystalline-nanosized spinel ferrites. The average particle diameter was found to be 29 nm which agrees well with that estimated from XRD data.
<p>Figure 2</p>TEM micrographs of (a) 0.0, (b) 0.5, and (c) 0.1 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles
TEM micrographs of (a) 0.0, (b) 0.5, and (c) 0.1 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles.
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<p>Figure 3</p>SAED patterns of (a) 0.0 and (b) 0.5 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles
SAED patterns of (a) 0.0 and (b) 0.5 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles.
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<p>Figure 4</p>SEM micrographs of (a) 0.0, (b) 0.5, and (c) 0.1 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles
SEM micrographs of (a) 0.0, (b) 0.5, and (c) 0.1 compositions of Ni0.7-xZnxCu0.3Fe2O4 ferrite nanoparticles.
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Electrical measurements
Dielectric measurements
The dielectric constant [ε'] of the samples was calculated using this formula:
ε
′
=
C
p
t
ε
0
A
,
where ε0 = 8.854 × 10-12 F/m, known as permittivity of free space, and t is the thickness of the pellet. A is the area of cross section of the pellet, and Cp is the capacitance of the pellet. The complex dielectric constant was calculated from this relation:
ε
"
=
ε
′
tan
δ
.
The frequency dependence of the dielectric constant for all the samples was studied at room temperature. Figures 6 and 7 depict the variation of real and complex parts of the dielectric constant with frequency. It is clear that all the studied samples exhibit dielectric dispersion where the values of both real (ε') and imaginary (ε″) parts of the dielectric constant decrease with increasing frequency of the field. The data reveal that none of the samples exhibit any anomalous behavior or peaking behavior. The observed dielectric behavior can be explained in the light of space charge polarization and hopping model 313233.
<p>Figure 6</p>The real part variation of the dielectric constant (ε') with frequency at room temperature
The real part variation of the dielectric constant (ε') with frequency at room temperature.
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<p>Figure 7</p>The imaginary part variation of the dielectric constant (ε″) with frequency at room temperature
The imaginary part variation of the dielectric constant (ε″) with frequency at room temperature.
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The presence of Fe3+ and Fe2+ ions render ferrite materials to be dipolar. Polarization is also affected by factors such as structural homogeneity, stoichiometry, density, grain size, and porosity of the ferrites. The rotational displacement of dipoles results in orientational polarization. In ferrites, rotation of Fe2+ to Fe3+ and vice versa can be visualized as the exchange of electrons between two ions so that the dipoles align themselves with respect to the applied field. The polarization at lower frequencies may result from electron hopping between Fe3+ ⇔Fe2+ ions in the ferrite lattice. The polarization decreases with increasing frequency and reaches a constant value due to the fact that beyond a certain frequency of external field, the electron exchange Fe3+ ⇔ Fe2+ cannot follow the changes in the applied field. Also, the presence of Ni3+/Ni2+ ions, which give rise to p-type carriers, contributes to the net polarization though it is small. The net polarization increases initially and then decreases with increasing frequency 34.
Dielectric loss
Figure 8 shows the variation of dielectric loss tangent (tanδ) with frequency (42 Hz to 5 MHz) at room temperature. The dielectric loss decreases with the increasing frequency which is a normal behavior of any ferrite material. The dielectric loss decreases rapidly in the low-frequency region, while the rate of decrease is slow in the high-frequency region, and it shows an almost frequency independent behavior in the high-frequency region. The low loss values at higher frequencies show the potential applications of these materials in high-frequency microwave devices. The behavior can be explained on the basis that in the low-frequency region, which corresponds to a high resistivity (due to the grain boundary), more energy is required for electron exchange between Fe2+ and Fe3+ ions; as a result, the loss is high. In the high-frequency region, which corresponds to a low resistivity (due to the grains), small energy is required for electron transfer between the two Fe ions at the octahedral site. Moreover, the dielectric loss factor also depends on a number of factors, such as stoichiometry, Fe2+ content, and structural homogeneity, which in turn depend upon the composition and sintering temperature of the samples 3536.
<p>Figure 8</p>The loss tangent (tanδ) variation with frequency at room temperature
The loss tangent (tanδ) variation with frequency at room temperature.
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ac Conductivity
The ac part of the electrical conductivity was calculated from this relation:
σ
ac
=
ε
′
ε
0
ω
tan
δ
,
where ω is the angular frequency. Figure 9 shows the variation of ac conductivity with frequency (42 Hz to 5 MHz) at room temperature. The ac conductivity increases with increasing frequency above 200 KHz. Before that, it shows an almost frequency-independent behavior. The electrical conductivity in ferrites is mainly due to the hopping of electrons between ions of the same element present in more than one valence state and distributed randomly over crystallographic equivalent lattice sites. Ferrites have a cubic close-packed oxygen lattice with the cations at the octahedral (B) and tetrahedral (A) sites. The distance between two metal ions on the B sites is smaller (0.292 nm) than the distance between two metals ions on the A sites (0.357 nm). Therefore, the hopping between A⇔B sites has a very small probability compared with that at the B⇔B sites. The hopping between A⇔A sites does not exist due to the fact that there are only Fe3+ ions at the A sites, and any Fe2+ ions formed during the sintering process preferentially occupy the B sites only 37. The charges migrate under the influence of the applied field, contributing to the electrical response of the system.
<p>Figure 9</p>The σac variation with frequency at room temperature
The σac variation with frequency at room temperature.
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The conductivity is an increasing function of frequency in the case of conduction by hopping and a decreasing function of frequency in the case of band conduction 38. The conductivity of a semiconductor material σ can be expressed as:
σ
=
σ
dc
+
σ
ac
.
The first term (σdc) is the direct current [dc] conductivity, which is due to band conduction, and it is frequency independent. The second term (σac) is the pure ac conductivity, which is due to the hopping processes at the octahedral site. The ac conductivity follows the empirical formula of the frequency dependence given by the ac power law 39:
σ
(
ω
)
=
B
ω
n
,
where B and n are constants which depend both on temperature and composition; n is dimensionless, whereas B has units of electrical conductivity.
In the present study, the conduction mechanism is due to electron hopping between Fe2+⇔Fe3+ ions and hole hopping between Ni2+⇔Ni3+ at two adjacent B sites. The charge exchange frequency increases with increasing frequency of the applied field, but the charge exchange mechanism does not follow the frequency of applied field beyond a certain frequency limit because at high frequencies, the resistivity remains invariant with the frequency, and as a result, the hopping frequency no longer follows the changes of external field beyond a certain frequency limit and thus lags behind 36.
Figure 10 shows the variation of ln σ versus ln ω in the frequency range of 42 Hz to 5 MHz at room temperature, with the inset showing the variation of exponent n with composition. The exponent n was calculated as a function of composition by plotting ln σ versus ln ω according to Equation 15, which represents straight lines with the slope equal to the exponent n and the intercept equal to ln B on the vertical axis at ln ω = 0. It is well known that n takes values between 0 and 1. When n = 0, the electrical conduction is frequency independent or becomes the dc conduction, but when n > 0, the conduction is frequency dependent or becomes the ac conduction 40. In the present study, the value of n varies between 0.073 and 0.086, which suggests that the conduction phenomenon in the studied samples is ac conduction and is due to the hopping of charges.
<p>Figure 10</p>The variation of lnσ versus lnω with inset showing variation of exponent n with composition
The variation of lnσ versus lnω with inset showing variation of exponent n with composition.
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Composition dependence of dielectric properties
Figure 11 shows the variation of ε', ε″, tanδ, and σac with composition at selected frequencies. All the investigated electrical parameters show their maximum value for Ni0.6Cu0.3Fe2Zn0.1O4 composition. The composition-dependent behavior of the investigated samples can be explained on the basis that Ni as well as Cu ferrites are inverse spinel in structure, and the degree of inversion depends upon the heat treatment 4142.
<p>Figure 11</p>The variation of ε', ε″, tanδ, and σac with Zn composition at room temperature
The variation of ε', ε″, tanδ, and σac with Zn composition at room temperature.
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In the investigated samples, the presence of Ni3+/Ni2+ ions leads to the formation of the p-type charge carriers, and their local displacement in the direction of applied field also contributes to net polarization, in addition to the n-type charge carriers. However, the contribution of the p-type carriers is small as compared with the electron exchange between Fe3+⇔Fe2+ and is directed opposite to the flow of the n-type carriers 43. It is believed that the hopping of electrons between Fe2+⇔Fe3+ (n-type semiconductor) and the hopping of holes between Ni3+⇔Ni2+ (p-type semiconductor) are responsible for the conduction process and dielectric polarization of the studied samples 4445. The maximum values of ε', ε″, tanδ, and σac for x = 0.1 can be explained on the basis that Zn2+ ions doped in the Ni-Cu ferrite occupy the A sites, where the Fe3+ ions present are forced to migrate from the A sites to the B sites. The increase in number of Fe3+ ions at the B sites increases the rate of hopping which in turn increases the conductivity values for the composition x = 0.1, whereas the decrease in conductivity beyond x = 0.1 may be explained on the basis that further doping of Zn2+ ions beyond x = 0.1 replace the Fe3+ ions at the B sites which depletes the number of Fe ions available for the conduction phenomena, hence, the decrease in probability of following the exchange process:
N
i
2
+
+
F
e
3
+
↔
N
i
3
+
+
F
e
2
+
Since dielectric polarization in ferrites is similar to electrical conduction, it is therefore expected that the behavior of ε', ε″, and tanδ is similar to that of σac for x = 0.1.
Impedance spectroscopy
It is well known that impedance spectroscopy is an important method to study the electrical properties of ferrites since impedance of the grains can be separated from the other impedance sources, such as impedance of electrodes and grain boundaries. One of the important factors, which influence the impedance properties of ferrites, is the nano- or microstructural effect. The complex impedance measurement gives us information about the resistive (real part) and reactive (imaginary part) components in the material. The complex impedance plot known as the Cole-Cole plot can give three semicircles, depending upon the electrical properties of the material. Since the ionic polarization in ferrites is not present, as a result, we have only two semicircles because of the space charge and orientation polarization in the ferrite materials. The first semicircle at low frequency represents the resistance of grain boundary. The second one obtained for high-frequency domain corresponds to the resistance of grain or bulk properties 4647.
Figure 12 shows the complex impedance plot for the different compositions of Ni-Cu-Zn ferrite nanoparticles taken at room temperature in the frequency range of 42 Hz to 5 MHz. The grain boundary (Rgb), the grain resistance (Rg), and the capacitance of grain and grain boundary (Cgb and Cg) were calculated at room temperature by analyzing the data using the nonlinear least square fitting routine and are presented in Table 3. The resistances were calculated from the circular arc intercepts on the Z'-axis, while the capacitance values were derived from the height of the circular arcs 484950. The plot obtained shows only one semicircular arc corresponding to the conduction due to the grain boundary volume in the low-frequency region, which suggests that conduction mechanism takes place predominantly through the grain boundary volume. Furthermore, the contribution from the grain was not well resolved in the samples. The higher value of the grain boundary can be due to the decrease in Fe3+ number, increase in surface-to-volume ratio, porosity, and disordered atomic arrangement near the grain boundary.
<p>Figure 12</p>The Cole-Cole plot of Ni0.7-xCu0.3ZnxFe2O4 ferrite nanoparticles at room temperature
The Cole-Cole plot of Ni0.7-xCu0.3ZnxFe2O4 ferrite nanoparticles at room temperature.
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