J Supercond Nov Magn DOI 10.1007/s10948-015-3208-1
ORIGINAL PAPER
Effect of Zn Substitution on Structural, Magnetic, and Electric Properties of Ni1−x Znx Fe1.78Al0.2Gd0.02O4 Nanoparticles Mohamed Bakr Mohamed1,2 · Adel Maher Wahba3 · Zein K. Heiba2,4
Received: 30 July 2015 / Accepted: 27 August 2015 © Springer Science+Business Media New York 2015
Abstract Nanostructured Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 (x = 0.0, 0.1, 0.3, and 0.5) ferrites have been prepared by citrate precursor method. The samples were characterized by several techniques including X-ray diffraction, FTIR spectroscopy, and magnetic and DC and AC electrical measurements. Rietveld analysis revealed crystallite size ranging from 5.8 to 6.7 nm for all samples with an increase in the lattice parameter upon increasing Zn content. With Zn substitution, the saturation magnetization MS first increases for x = 0.1 then decreases for x ≥ 0.2 indicating variation of cation occupancies upon Zn doping. That behavior of magnetization obeys the Yafet–Kittel (Y–K) model, and canting angles θY−K were obtained for all samples. For the formed spinel structure, zinc substitution was found to induce a significant change in the cation distribution being proposed on the basis of the magnetization data and the lattice parameter obtained from the Rietveld analysis, and then confirmed by using theoretically calculated lattice parameter. DC electrical resistivity increases with the Zn
Mohamed Bakr Mohamed
[email protected] 1
Physics Department, Taibah University, Medina, Kingdom of Saudi Arabia
2
Faculty of Science, Physics Department, Ain Shams University, Cairo, Egypt
3
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt
4
Faculty of Science, Physics Department, Taif University, Al-Haweiah, Taif, Kingdom of Saudi Arabia
content, and for whole samples, it increases with temperature then decreases, exhibiting two different behaviors. Variation of activation energy of electrical conduction was deduced from DC measurements. The effect of Zn content on dielectric properties was fully characterized from the AC measurements. Keywords Nanostructures · Structure · Magnetic · Electric
1 Introduction Nickel–zinc ferrites are soft ferrite materials with high magnetic permeability, high electric resistivity, and low losses, and they are really useful in many applications such as ferrofluids, high-frequency devices, and radar-absorbing coatings [1, 2]. Various methods such as co-precipitation [3], reverse micelle [4], citrate precursor [5], and hydrothermal [6] were used to prepare nickel–zinc ferrite nanoparticles. The citrate precursor method for preparing nano ferrites has advantages including good stoichiometric control and narrow size distribution with lower-temperature and less-time processing. For the nanoscale spinel ferrites, magnetic properties show clear deviations when compared to their bulk counterparts. Bulk zinc ferrite, for example, is a normal spinel and nonmagnetic in the micron regime. However, nano zinc ferrites exhibit a degree of inversion and a net magnetization at room temperature. Although zinc cations are expected to occupy only tetrahedral (A) sites in spinel ferrites, nanoscale ferrites containing zinc are reported to have some of zinc cations present in octahedral (B) sites [7]. In the present work Zn-, Al-, and Gd-doped nickel–zinc ferrite powders were prepared by citrate method. The impact
J Supercond Nov Magn
of the Zn content on the structural, magnetic, and electric properties is thoroughly investigated.
2 Experimental Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 (x = 0.0, 0.1, 0.3, and 0.5) samples were synthesized using stoichiometric amounts of iron, nickel, zinc, aluminum, gadolinium nitrates, and citric acid while using deionized water as a solvent. The solution was heated under stirring to evaporate the solvent water. The gel was dried at 180 ◦ C for 1 h, heated at 400 ◦ C for an hour, and then cooled to room temperature. This powder was pressed under a pressure of 285 MPa into pellets of 1 cm diameter and around 2.5 mm thickness. Pellets were sintered at 400 ◦ C with a heating rate of 5 ◦ C/min for 1 h and then furnace-cooled to room temperature. Pellets’ surface were polished and coated with silver paste to provide the parallel-plate capacitor geometry with the ferrite acting as the dielectric medium.
(440)
(511)
(422)
(400)
(222)
(111)
(220)
(311)
(a)
x = 0.5 x = 0.3 x = 0.1
The X-ray powder diffraction patterns of the samples were collected on a Philips diffractometer (X’pert MPD) with a goniometer using Cu-Kα radiation. The diffracted intensities were collected in step-scan mode (step size 2θ = 0.02◦ ; counting time 2 s) in the angular range 10◦ to 80◦ . The crystal structure and microstructure were refined applying Rietveld profile method [8], using MAUD program [9]. The process of successive profile refinements modulates the different structural and microstructural parameters of the simulated pattern to fit the experimental diffraction pattern. No absorption correction was considered and the scattering background was refined with a 5th-order polynomial. Infrared (IR) spectroscopy (Bruker Tensor 27 FTIR Spectrometer) was used in the range of 200–1000 cm−1 . Dielectric properties were measured as a function of frequency at different temperatures using an impedance analyzer in the frequency range from 50 to 100 kHz. The value of the dielectric constant (ε) was calculated by using the following relation ε´ = Cd/ε0 A, where ε0 is the permittivity of the free space, d is the thickness of the pellets, A is the cross-sectional area of the pellets, and C is the recorded capacitance of the pellets. The complex dielectric constant ε of the samples is calculated using the relation ε = ε´ tan δ, where tan δ is the dielectric loss tangent which is proportional to the “loss” of energy into the sample and therefore denoted as dielectric loss. The AC conductivity of the sample is obtained using the relation; σac = ε´ ε0 ω tan δ, where ω is the angular frequency. The DC electrical resistivity of the samples was measured using the two-probe method in the temperature range 313–423 K.
x = 0.0
8.39 Ni1-xZnxFe1.78Al0.2Gd0.02O4
8.38
(b) a (A)
8.37 8.36 8.35 8.34 8.33 0.0
Fig. 1 a X-ray powder diffraction for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 (0 ≤ x ≤ 0.5) and b Rietveld refinement profile for Ni0.7 Zn0.3 Fe1.78 Al0.2 Gd0.02 O4 sample performed using MAUD program
0.1
0.2
0.3
0.4
0.5
x Fig. 2 Variation of lattice parameter (a) with Zn content (x) for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 system
J Supercond Nov Magn Table 1 Lattice parameter (a), crystallite size (D), oxygen positional parameter (u), and absorption band (ν1 and ν2 ) obtained from IR and magnetic properties for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 Composition x
a (A)
D (nm)
u
ν1 (cm−1 )
ν2 (cm−1 )
Ms (emu/g)
nobs B (μB )
nB(Neel) (μB )
0.0 0.1 0.3 0.5
8.33168 8.34817 8.36230 8.38156
5.8 6.1 6.7 6.4
0.374836 0.374629 0.371966 0.367225
405 404 418 400
588 589 587 571
20.17 36.75 31.05 25.50
0.857 1.557 1.308 1.068
2.391 3.040 2.808 2.703
3 Results and Discussion 3.1 X-ray Diffraction Analysis Figure 1a shows the X-ray diffraction patterns for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 (x = 0.0, 0.1, 0.3, and 0.5) system. The phase identification indicated that all patterns show single phase with cubic spinel structure of space group Fd-3m. Figure 1b illustrates the profile fitting resulting from the Rietveld analysis. Along the refinement procedure, the cation occupancies suggested from the analysis of magnetic measurements (next section) were used as fixed starting values. In a subsequent final refinement cycle, the cation occupancies were set free to be refined and the resulting values were almost the same without any significant changes, confirming the validity of the cation distribution proposed. The variation of the lattice parameter (a) with the Zn2+ substitution for various compositions is shown in Fig. 2, which illustrates the gradual increase of a for the Zn2+ substituted NiFe1.78 Al0.2 Gd0.02 O4 composition. This could be attributed to the substitution of the smaller Ni cations ˚ with the larger Zn ones (0.82 A) ˚ [10]; larger Zn2+ (0.78 A) 2+ replaces Ni ions therefore causing the lattice to slightly expand in agreement with Vegard’s law. Table 1 depicts crystallite size (D) obtained from Rietveld microstructural analysis. Clearly noted is that increasing the Zn content hardly changes the crystallite size and its mean value is around 6 nm for all samples.
The interatomic distance between the cations on the tetragonal (A) and octahedral (B) sites can be calculated using the following relations [11, 12]: √ 3 a MA − MA = 4 √ 11 MA − MB = a 8 √ 2 MB − MB = a 4 √ 1 M A − OA = a 3 δ + 8 √ M B − OB = a 3
δ 1 − + 3δ 2 16 2
1/2
where MA and MB are the cations at the center of the tetrahedral (A) and octahedral [B] sites, respectively, while OA and OB are the center of an oxygen anion defined in the same manner. The parameter δ reflects the deviation from the oxygen parameter (u) and is estimated δ|u − uideal | [12]. From Table 2, one can note that the tetrahedral bond length (MA − O) decreases while the octahedral bond length (MB − O) increases as the amount of Zn2+
Table 2 Refined values of bond lengths obtained from Rietveld refinements of Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 Composition x
MA − O (A)
MB − O (A)
MA − MA (A)
MA − MB (A)
MB − MB (A)
0.0 0.1 0.3 0.5
1.8014 1.8020 1.7665 1.7017
2.0842 2.0901 2.1162 2.1625
3.6077 3.6148 3.6209 3.6293
3.4541 3.4609 3.4668 3.4748
2.9456 2.9515 2.9565 2.9633
J Supercond Nov Magn x=0.5
Ni1-xZnxFe1.78Al0.2Gd0.02O4
80 x=0.3
Transmission (%)
x=0.1
60
x=0.0
40
20
0 1000
900
800
700
600
500
400
300
-1
Wave number (cm ) Fig. 3 FTIR spectra of Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrite samples
the applied magnetic fields extending up to 20 kOe. Values of the saturation magnetization MS for the samples were deduced from the extrapolation of the M vs. 1/H curves to 1/H → 0 [13]. Saturation magnetization is supposed to increase with Zn substitution due to its strong preference to occupy the tetrahedral site and, thus, reduce the amount of both magnetic Fe3+ and Ni2+ cations in the A site with a subsequent increase of the superexchange interaction. This does occur in our system for just the sample with x = 0.1. For the other samples with x = 0.3 and 0.5, MS decreased. Since the crystallite size did not change significantly with Zn substitution, the behavior of MS could be only explained according to the composition and the cation distribution. The suggested cation distribution (Table 3) is based on the magnetization data and those of the lattice parameter obtained from the Rietveld analysis [8, 9]. The observed magnetic moment (nobs B ) is calculated as [14] nobs B =
3.2 FTIR Spectroscopy FTIR of Znx Ni1−x Al0.20 Gd0.02 Fe1.78 O4 samples were recorded at room temperature and are shown in Fig. 3. All the samples show two main absorption bands, ν1 in the range 587–590 cm−1 and ν2 in the range 404–410 cm−1 , which further confirms the formation of the spinel ferrite structure. Well known is that the stretching of tetrahedral metal–oxygen bonding is the source of ν1 peaks and that the vibrations of oxygen ion in the direction perpendicular to the axis joining the octahedral ion and oxygen is the source of ν2 peaks. The behavior of ν1 and ν2 with Zn2+ substitution does not show a monotonic behavior. This reveals the fact that Zn2+ substitution really induces a significant change in the cation distribution and the degree of occupancy of either Al3+ , Fe3+ , and/or Ni2+ in the sublattice sites as will be explained later when considering the cation distribution in the next section. 3.3 Magnetic Properties Magnetic characterization of the Znx Ni1−x Al0.20 Gd0.02 Fe1.78 O4 samples was deduced by tracing room-temperature magnetic hysteresis curves, shown in Fig. 4, which illustrate the variation of the magnetization as a function of
where MW is the molecular weight. Values of nobs B are to be compared with the theoretical ones nB = MB − MA , obtained from the proposed cation distribution, where MA and MB are the A- and B-site sublattice magnetic moments, respectively. The used magnetic moments for each element in terms of the Bohr magneton μB are 5, 4, 2, 1, and 0 for Fe3+ , Fe2+ , Ni2+ , Ni3+ , and others, respectively. The magnetic moments for rare-earth ions originate generally from the localized 4f electrons, and they are characterized by lower ordering temperatures, i.e., less than 40 K [15]. So, in the present work where the magnetic properties are measured at room temperature, Gd3+ ions will be treated as diamagnetic ions [15]. Comparison between the variation of
30 20 Magnetization (emu/g)
increases. The variation of metal–metal bond lengths (MA − MA , MB − MB , and MA − MB ) with Zn2+ content is depicted also in Table 2. It is evident that all metal–metal bond lengths increase with Zn+ content. This is assigned to the substitution process and cation redistribution.
MW × MS 5585
10 0 -10 x=0.0 x=0.1 x=0.3 x=0.5
-20 -30 -5
-4
-3
-2
-1
0
1
2
3
4
5
H (kOe) Fig. 4 Room-temperature M–H loops for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrite samples
J Supercond Nov Magn Table 3 Cation distribution of Ni1−x Znx Al0.2 Gd0.02 Fe1.78 O4 (0.00 ≤ x ≤ 0.5) samples x
Cation distribution Ni2+ O2− Ni3+ Gd3+ Al3+ Fe2+ Fe3+ 0.772 0.039 0.02 0.152 0.084 0.933 3.978 2+ 3+ 3+ 2+ 2+ 3+ 3+ 3+ 2+ Ni Al Fe Ni Ni Gd Al Fe Fe3+ O2− Zn2+ Zn 0.090 0.102 0.089 0.719 0.010 0.767 0.031 0.02 0.111 0.031 1.030 4.000 Zn2+ Ni2+ Al3+ Fe3+ Zn2+ Ni2+ Ni3+ Gd3+ Al3+ Fe2+ Fe3+ O2− 0.203 0.048 0.027 0.722 0.097 0.630 0.022 0.02 0.173 0.058 1.000 3.982 2+ 3+ 3+ 2+ 3+ 3+ 2+ 3+ 2− Zn2+ Zn2+ 0.255 Ni0.037 Al0.010 Fe0.698 0.245 Ni0.463 Gd0.02 Al0.190 Fe0.069 Fe1.013 O3.966
0.0 0.1 0.3 0.5
3+ 3+ Ni2+ 0.189 Al0.048 Fe0.763
nNeel
1.6 1.4
2.8 1.2 2.6 1.0
(a) 0.1
0.2
0.3
0.4
0.5
Magnetic moment, obs (μB)
Magnetic moment, Neel (μB)
nBobs
3.0
0.0
0.8
1.00
Fe (B)
0.06 3+
0.95
0.04
3+
3+
Al (A) 3+ Fe (B) 2+ Fe (B)
0.02
(b) 0.1
0.2
0.3
0.4
2+
0.08
Al (A) & (Fe )(B)
Zinc content (x)
0.0
MA (emu/g)
θY−K (◦ )
rA ˚ (A)
rB ˚ (A)
6.584
4.193
39.90
0.497
0.661
6.839
3.799
38.43
0.508
0.660
6.514
3.706
39.65
0.518
0.660
6.267
3.564
42.33
0.523
0.664
2+ content is illustrated both nB (Table 1) and nobs B with Zn in Fig. 5a; they both show a quite similar trend. The small observed values of nobs B compared to those of nB is attributed to the surface effects of the remarkably small crystallite sizes of the present samples. A Yafet– Kittel magnetic ordering [16] of the local moments may be proposed to explain the small values of nobs B . The saturation magnetization in the Yafet–Kittle model is given by MS = MB cosθY−K − MA , where θY−K is the Yafet–Kittel canting angle, which is estimated for our samples and listed in Table 3. Surface effects could highly explain the observed
2.4
MB (emu/g)
0.5
Zinc content (x) Fig. 5 a, b The variation of observed and theoretical magnetization moment, the estimated Fe3+ , Fe2+ content in the B site and Al3+ in the A site with Zn amount for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrite samples
small MS values for the present system compared to other works [17], with the crystallite sizes achieved in our work being the smallest. Furthermore, the small crystallite size of our samples revealed itself in the extremely small values of remanent field reflecting the superparamagnetic behavior of all the samples. The suggested cation distribution could explain the increase of MS for the sample with x = 0.1. With Zn substituting Ni2+ , the degree of occupancy of Al+3 , Ni2+ , and Fe3+ in the B sites changes and also does the amount of Fe2+ , which is formed during the autocombustion process [18] by either reduction of Fe3+ or loss of Zn2+ cations [19]. Electron neutrality requires that the presence of Fe2+ would, to some degree, be associated with the formation of Ni3+ with low-spin magnetic moment of 1 μB . According to the proposed cation distribution, the variation of Ms with x are quite similar to that of the amount of Fe3+ and Al3+ in B and A sites, respectively, and quite opposite to those of Fe2+ in the B site (see Fig. 5b). Furthermore, and according to the proposed cation distribution, the zinc occupancy in the tetrahedral site decreases with increasing x, which explains more the reduction of MS with increasing Zn content above x = 0.1. That unusual B-site occupation of Zn2+ has been previously recorded for nanoscale zinc-enriched ferrite nanoparticles [20, 21]. Confirmation of the suggested cation distribution is more achieved by applying a theoretical estimation of the lattice parameter for each composition and comparing it with that obtained by Rietveld analysis. For each sample, the average ionic radii per molecule of the tetrahedral and octahedral sites, rA and rB , were calculated based on the suggested cation distribution of Table 3, using the formulae [22]: rA =
i
αi ri ,
rB =
1
αi ri 2 i
where αi is the concentration of the element i of ionic radius ri on the respective side. The ionic radii for Zn2+ (0.60 and ˚ Ni2+ (0.55 and 0.69 A), ˚ Fe3+ (0.49 and 0.645 A), ˚ 0.74 A), 3+ ˚ are taken with reference to and Al (0.39 and 0.535 A) both sites [23], with the first value corresponding to that of ˚ was assumed to occupy only the the A site. Fe2+ (0.78 A) B site. Values of estimated rA and rB are listed in Table 3.
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Theoretical values of lattice parameters are then calculated from the relation [21]: √ 8 ath = √ (rA + RO ) + 3 (rB + RO ) 3 3 ˚ For all where RO is the ionic radius of oxygen (1.38 A). samples, the values of ath exactly match those obtained from Rietveld analysis (see Table 1). Worthy to be noticed in Table 3 is that rB hardly changes with Zn content, while the change of rA with x is analogous to that of the lattice parameter. This sublattice expansion and the subsequent weakening of the superexchange interactions could further explain the reduction of MS for x > 0.1. 3.4 DC Resistivity
ρ (ohm.m)
Nano ferrite materials are generally characterized by very high DC electrical resistivity as compared to bulk ferrites, which is one of the potential considerations for microwave and absorbing material applications. The variation of the DC electrical resistivity for Znx Ni1−x Al0.20 Gd0.02 Fe1.78 O4
1.5x10
9
1.0x10
9
5.0x10
8
(a)
ρ = ρ0 e E/kB T where ρ0 depends on the nature of the material, T is the absolute temperature, kB is the Boltzmann constant, and E is the activation energy [28]. The values of activation energy have been obtained from the slope of ln ρ vs.1000/T graph for the ferromagnetic region (I, Eferri ) and the paramagnetic region (II, Epara ). It is observed that the energy of activation for electrical conduction in the low-temperature region (I) lies within the range 0.490–0.544 eV and in the hightemperature region (II) lies between 0.748 and 0.958 eV which were calculated from the slopes of lines on both sides of Tc . So the activation energy in the paramagnetic region is greater than that in the ferrimagnetic region and is in agreement with the theory of Irkhin and Turov [29].
0.0 300
350
400
450
500
Temperature (K)
21
(b) II
lnρ (ohm.m)
(x = 0.0, 0.3, and 0.5) temperature is shown in Fig. 6a. It is observed first that the resistivity increases with temperature in all the ferrite samples; then it decreases continuously with the increasing temperature. The decreasing in resistivity with temperature reveals the semiconducting nature of the prepared samples. On the other hand, the increasing of resistivity with temperature (metal-like behavior) is observed in other ferrites such as Al–Cr substituted and NiSbx Fe2−x O4 ferrites [24, 25]. The authors claim that such behavior at low temperature (343–360 K) is probably due to the evaporation of absorbed humidity; ferrites are hygroscopic in nature [26]. At higher temperature, the plot is divided into two distinct regions corresponding to the ferrimagnetic and paramagnetic regions. The slope is observed to change at a particular temperature. The line changes its slope at the Curie temperature being listed in Fig. 6b. The change of slope of temperature vs. resistivity curves is attributed to the change in the conductivity mechanism. The magnitude of this slope depends on the exchange interaction, which determines the Curie point Tc . The conduction at lower temperature range, i.e., below Curie temperature, is due to the hopping of electrons between Fe2+ and Fe3+ ions, whereas at higher temperature, i.e., above Curie temperature, it is due to the polaron hopping [27]. The relationship between the DC electrical resistivity (ρ) and the temperature may be expressed as
18
I
3.5 Dielectric Properties 15 TC(K) 438 455 422 12 2.0
2.2
2.4
x=0.0 x=0.3 x=0.5 2.6
3
10 /T (K) Fig. 6 Variation of a ρ with temperature and b ln ρ with 1000/T for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrites
Figure 7a shows the variation of the dielectric constant (ε ) of our samples as a function of frequency at room temperature. All samples show normal dielectric dispersion behavior, where the dielectric constant decreases with increasing frequency, then becomes almost constant at higher frequencies. It is well known that the variation of dielectric constant with frequency in ferrites is mainly due to the variation of Fe2+ and Fe3+ ion concentration. At low frequencies, ε
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400
(a)
Ni1-xZnxFe1.78Al0.2Gd0.02O4
350
x=0 x=0.3 x=0.5
300
ε
,
250 200 150 100 50 1.2
(b)
1.0
Tan δ
0.8 0.6 0.4 0.2 0.0 -4.8
(c)
σtotal = σ0 (T ) + σ (ω, T ) where σtotal is the total conductivity of the system, σ0 (T ) denotes the DC conductivity which is independent of frequency, and σ (ω, T ) denotes the frequency-dependent part of the AC conductivity. The term σ (ω, T ) can also be expressed as
-5.2
logσa.c
-5.6 -6.0
σAC = Aωs
-6.4 -6.8 1.5
be explained as the interchange of the electrons between the ions; thus, the dipoles align themselves with field. The increase in frequency leads to a decrease in orientational polarization, since the molecular dipoles need time to change their orientation in response to the applied field. This decrease tends to reduce the value of ε with increasing frequency. The imaginary part of the dielectric constant (ε ) and the associated dielectric loss tangent (tan δ) as a function of frequency were studied at room temperature and are depicted in Fig. 7b. Again, the dielectric loss tangent decreases with increasing frequency for each sample. All the samples exhibit dispersion due to the Maxwell–Wagner interfacial type polarization [30–32]. Furthermore, Fig. 7b indicates that the dielectric loss of the prepared nanoparticles also depends upon the composition; it decreases as the amount of Zn increases. The conduction mechanism in ferrites is a result of electron and hole hopping between ions of the same element existing in different valence states on octahedral sites [33]. The variation of AC conductivity with applied frequency for all samples is shown in Fig. 7c. The common feature of semiconductors (and some disordered systems) is that the frequency dependence of conductivity increases approximately linearly [34]. All the samples show an increasing nature in the AC conductivity curve which is consistent with the power law:
2.0
2.5
3.0
3.5
4.0
log (f) ε ,
Fig. 7 Variation of a b tan δ and c ln σ ac with frequency for Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrites
depends on both the deformational and relaxation polarization mechanisms. The deformational polarization depends on the displacement of electrons and ions while the relaxation polarization depends on the orientational or interfacial effects. The presence of Fe2+ and Fe3+ ions at octahedral positions defines ferrites as polar materials (Table 3). Rotational displacements of the dipoles result in the orientational polarization. The rotation or turning of dipoles can
where A is a constant having the units of conductivity, ω is the angular frequency, and s is a temperature-dependent constant. Increasing the applied frequency induces an increase in the charge carrier transfer rate between different localized sites. It also assists liberation of the charge carriers from the trapping centers. It is noticed that AC conductivity decreases with increasing Zn2+ substitution. This can be correlated with the observed increase in jump length (MA − MA and MB − MB ) of the charge carrier (Table 2) as the amount of Zn increases. This implies that charge carriers will need more energy to jump from one cationic site to the other, which causes a decrease in conductivity. In DC measurement, the electrical conductivity is actually the sum of electronic contribution from grains, intergrain boundaries, surface electrodes contacts, etc. The use of AC measurements at different frequencies, however, makes it possible to discriminate the individual contribution from the overall conduction. The Nyquist plot
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25
Z2(Mohm)
20 15 10 5
0 3 5
0 0
2
4
6
8
10
12
Z1 (Mohm) Fig. 8 Nyquist plot of Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 nano ferrite samples
of Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 samples were recorded at room temperature and are shown in Fig. 8. In a complex Nyquist plot, the imaginary part of the impedance Z2 (ω) is plotted against the real part of the impedance Z2 (ω). The plot expresses a response of an ideal parallel circuit of a resistance R and a capacitance C in the form of a semicircle centered on the real axis. It is a powerful technique for separating the complexities of materials. In general, the plot would be composed of three semicircles, depending upon the electrical properties of the material. The semicircle at lower frequency represents the sum of resistance of grains and grain boundaries, while the semicircle at higher frequency corresponds to the resistance of grains only [35]. The third semicircle is also observed in some materials, which could be due to the electrode effect [36, 37]. In the present investigation, it has been observed that the impedance spectra of Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 samples at room temperature take the shape of an incomplete semicircle. This shows that grain boundary impedance is out of measurement scale, suggesting the insulating behavior of the present compositions.
4 Conclusion Single-phase nanocrystalline (About 6 nm) Ni1−x Znx Fe1.78 Al0.2 Gd0.02 O4 ferrites were synthesized applying citrate procedure. Zn replacement for Ni was found to have a real effect on both magnetic and electric properties, which has been attributed to the radical change in cation distribution among the two crystallographically distinct tetrahedral A and octahedral B sites. For Zn content around 0.1, the nonmagnetic ion Zn2+ resides mainly at the A
site on the expense of Ni2+ resulting in an increase in magnetization. As Zn content increases, Zn2+ tends gradually to distribute evenly between the two sites, turning out a decrease in magnetization. Comparing the calculated magnetic moments with the observed ones suggested the existence of canted spin structure in the doped ferrite system, with the Yafet–Kittel canting angle θY−K decreasing with higher content of Zn. DC electrical resistivity increases with the Zn content, and for all samples, it increases with temperature then decreases indicating two different behaviors. Variation of activation energy of electrical conduction was deduced from DC measurements; it lies between 0.490–0.544 eV in the low-temperature and between 0.748–0.958 eV in the high-temperature regions. The effect of varying Zn content on the dielectric properties was also analyzed by the AC measurements at room temperature. All samples showed normal dielectric dispersion behavior, and the dielectric loss of the prepared nanoparticles is found to decrease as the amount of Zn increases.
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