# Characterization of NixZn1−xFe2O4 and Permittivity of Solid Material of NiO, ZnO, Fe2O3, and NixZn1−xFe2O4 at Microwave Frequency Using Open Ended Coaxial Probe

Authors: Fahmiruddin Esa; Zulkifly Abbas; Fadzidah Mohd Idris; Mansor Hashim
Journal: International Journal of Microwave Science and Technology
 (2015)

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## Abstract

This paper describes a detailed study on the application of an open ended coaxial probe technique to determine the permittivity ofNixZn1-xFe2O4 in the frequency range between 1 GHz and 10 GHz. The x compositions of the spinel ferrite were 0.1, 0.3, 0.5, 0.7, and 0.9. The NixZn1-xFe2O4 samples were prepared by 10-hour sintering at 900°C with 4°C/min increment from room temperature. Particles showed phase purity and crystallinity in powder X-ray diffraction (XRD) analysis. Surface morphology measurement of scanning electron microscopy (SEM) was conducted on the plane surfaces of the molded samples which gave information about grain morphology, boundaries, and porosity. The tabulated grain size for all samples was in the range of 62 nm–175 nm. The complex permittivity of Ni-Zn ferrite samples was determined using the Agilent Dielectric Probe Kit 85070B. The probe assumed the samples were nonmagnetic homogeneous materials. The permittivity values also provide insights into the effect of the fractional composition of x on the bulk permittivity values NixZn1-xFe2O4. Vector Network Analyzer 8720B (VNA) was connected via coaxial cable to the Agilent Dielectric Probe Kit 85070B.


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## Body

## 1. Introduction

Electromagnetic (EM) waves at microwave frequencies have many applications in various fields such as wireless telecommunication system, radar, local area network, electronic devices, mobile phones, laptops, and medical equipment [1, 2]. The effect of growth in various applications has led to electromagnetic interference (EMI) problems that have to be suppressed to acceptable limits. EMI reducing materials (absorbers) may be dielectric or magnetic [3] and the design depends on the frequency range, the desired quantity of shielding, and the physical characteristics of the devices being shielded. Thus it is important to determine their high frequency characteristics for the applications of EM in the high GHz ranges [4, 5]. Ni-Zn ferrite ceramics are the preferred ceramic material for high frequency applications in order to suppress generation of Eddy current [6]. Although Ni-Zn ferrite ceramics have high electrical resistivity to prevent Eddy current generation, they have moderate magnetic permeability compared to Mn-Zn ferrites. However, the electrical and magnetic properties of these ferrite ceramics are heavily influenced by its microstructural features such as grain size, nature of grain boundaries, nature of porosity, and crystalline structure. The microstructural features of interest could be attained via chemical composition and high temperature processing [7]. However, the detailed electrical properties of Ni-Zn ferrite at different Ni-Zn ratio in a wideband frequency using open ended coaxial probe have not been studied yet. Thus, the aim of this work is to determine electrical properties of Ni-Zn ferrites prepared at different chemical composition based on chemical formula NixZn1-xFe2O4 with 0.1≤x≤0.9 that sintered at constant temperature. The variations in the microstructures, surface morphology, and alterations in reflection coefficient as well as their electrical properties of the Ni-Zn ferrites are the concern of this study.


## 2. Basic Principle

### 2.1. Loss Mechanism by Oscillating Electric Field

Materials can be categorized into two types which are the nonmagnetic materials and the magnetic materials. The core loss mechanisms for nonmagnetic materials are dielectric (dipolar) loss and conduction loss. The conduction and dipolar losses usually occur in metallic, high conductivity materials and dielectric insulators, respectively. The loss mechanisms for magnetic materials are also the conductive loss with addition magnetic loss such as hysteresis, eddy current, and the resonance losses (domain wall and electron spin). Loss condition of the materials is greatly influenced by microwave absorption.The microwave absorption is caused by external electrical field and related to the material’s complex permittivityε:(1)ε∗=εoε′-jε′′,where εo is the permittivity of free space (εo=8.86×10-12 F/m) and the real part ε′ and the imaginary part ε′′ are the relative dielectric constant and the effective relative dielectric loss factor, respectively. The real part of permittivity controls the amount of electrostatic energy stored per unit volume for a given applied field in a material. The imaginary part defines the energy loss caused by the lag in the polarization upon wave propagation when it passes through a material.The translational motions of free or bound charges and rotating charge complexes are induced by the internal field generated when the microwaves penetrate and propagate through a material. These induced motions are resisted by inertial, elastic, and frictional forces, thus causing energy losses.


### 2.2. Open Ended Coaxial Probe

For the open ended coaxial probe measurement technique the complex relative permittivity is determined by inverting the expression ofYε∗ where Y is the aperture admittance of the probe [8]:(2)Y=Yo1-Γ1+Γ,where Yo is the characteristic admittance of the coaxial line and Γ is the reflection coefficient at the aperture. The aperture admittance of open ended coaxial probes has several analytical expressions which contains the complex permittivity and can be compared to the measured admittance [9–12]. Some are from the computational points which may contribute to convergence problems because of the presence of multiple integrals, Bessel functions, and sine integrals when numerically solved. The expression for the aperture admittance is given by [13], found by matching the electromagnetic field around the probe aperture, and can be adopted:(3)Y=εr∗γoεcl⁡∗ln⁡b/a∫0π/2Joγoaεr∗sin⁡θ-Joγobεr∗sin⁡θ2dθsin⁡θ+jπ∫0π2Siγoaεr∗1+b2a2-2bacos⁡θ-Si2γoaεr∗sin⁡θ2-Si2γobεr∗sin⁡θ2dθ,where εr∗ is the complex relative permittivity of the material under test, εcl∗ is the relative permittivity of the coaxial line, a and b are the inner and outer radii of the coaxial line, respectively, γo is the absolute value of the propagation constant in free space, and Si and Jo are the sine integral and the Bessel function of zero order, respectively. This integral expression can be evaluated numerically by series expansion as in [10, 11] or numerical integration.A different procedure for the extraction of material parameters involves minimizing the distance between the calculated aperture admittance (3) and the corresponding measured quantities through fitting algorithms, which may be based on either deterministic or stochastic optimization procedures. The minimization can be performed over the whole frequency range or on a point-by-point basis (i.e., at individual frequency points). Optimization procedure is needed to determine parameters for the point-by-point basis since it consists of modelling the complex relative permittivity and magnetic permeability with a prespecified functional form. Laurent series can be used for complex relative permittivity and magnetic permeability models [14], as well as dispersive laws, such as Havriliak-Negami and its special cases Cole-Cole and Debye to model dielectric relaxation [15], or the Lorentz model for both dielectric and magnetic dispersion [16]. The Havriliak-Negami model is an empirical modification of the single-pole Debye relaxation model:(4)εr∗=ε∞+εs-ε∞1+jωτ1-αβ,where εs and ε∞ are the values of the real part of the complex relative permittivity at low and high frequency, respectively, τ is the relaxation time, and α and β are positive real constants 0≤α,β≤1. From this model, the Cole-Cole equation can be derived setting β=1; the Debye equation is obtained with α=1 and β=1. This empirical model has the ability to give a better fit to the behaviour of dispersive materials over a wide frequency range.


## 2.1. Loss Mechanism by Oscillating Electric Field

Materials can be categorized into two types which are the nonmagnetic materials and the magnetic materials. The core loss mechanisms for nonmagnetic materials are dielectric (dipolar) loss and conduction loss. The conduction and dipolar losses usually occur in metallic, high conductivity materials and dielectric insulators, respectively. The loss mechanisms for magnetic materials are also the conductive loss with addition magnetic loss such as hysteresis, eddy current, and the resonance losses (domain wall and electron spin). Loss condition of the materials is greatly influenced by microwave absorption.The microwave absorption is caused by external electrical field and related to the material’s complex permittivityε:(1)ε∗=εoε′-jε′′,where εo is the permittivity of free space (εo=8.86×10-12 F/m) and the real part ε′ and the imaginary part ε′′ are the relative dielectric constant and the effective relative dielectric loss factor, respectively. The real part of permittivity controls the amount of electrostatic energy stored per unit volume for a given applied field in a material. The imaginary part defines the energy loss caused by the lag in the polarization upon wave propagation when it passes through a material.The translational motions of free or bound charges and rotating charge complexes are induced by the internal field generated when the microwaves penetrate and propagate through a material. These induced motions are resisted by inertial, elastic, and frictional forces, thus causing energy losses.


## 2.2. Open Ended Coaxial Probe

For the open ended coaxial probe measurement technique the complex relative permittivity is determined by inverting the expression ofYε∗ where Y is the aperture admittance of the probe [8]:(2)Y=Yo1-Γ1+Γ,where Yo is the characteristic admittance of the coaxial line and Γ is the reflection coefficient at the aperture. The aperture admittance of open ended coaxial probes has several analytical expressions which contains the complex permittivity and can be compared to the measured admittance [9–12]. Some are from the computational points which may contribute to convergence problems because of the presence of multiple integrals, Bessel functions, and sine integrals when numerically solved. The expression for the aperture admittance is given by [13], found by matching the electromagnetic field around the probe aperture, and can be adopted:(3)Y=εr∗γoεcl⁡∗ln⁡b/a∫0π/2Joγoaεr∗sin⁡θ-Joγobεr∗sin⁡θ2dθsin⁡θ+jπ∫0π2Siγoaεr∗1+b2a2-2bacos⁡θ-Si2γoaεr∗sin⁡θ2-Si2γobεr∗sin⁡θ2dθ,where εr∗ is the complex relative permittivity of the material under test, εcl∗ is the relative permittivity of the coaxial line, a and b are the inner and outer radii of the coaxial line, respectively, γo is the absolute value of the propagation constant in free space, and Si and Jo are the sine integral and the Bessel function of zero order, respectively. This integral expression can be evaluated numerically by series expansion as in [10, 11] or numerical integration.A different procedure for the extraction of material parameters involves minimizing the distance between the calculated aperture admittance (3) and the corresponding measured quantities through fitting algorithms, which may be based on either deterministic or stochastic optimization procedures. The minimization can be performed over the whole frequency range or on a point-by-point basis (i.e., at individual frequency points). Optimization procedure is needed to determine parameters for the point-by-point basis since it consists of modelling the complex relative permittivity and magnetic permeability with a prespecified functional form. Laurent series can be used for complex relative permittivity and magnetic permeability models [14], as well as dispersive laws, such as Havriliak-Negami and its special cases Cole-Cole and Debye to model dielectric relaxation [15], or the Lorentz model for both dielectric and magnetic dispersion [16]. The Havriliak-Negami model is an empirical modification of the single-pole Debye relaxation model:(4)εr∗=ε∞+εs-ε∞1+jωτ1-αβ,where εs and ε∞ are the values of the real part of the complex relative permittivity at low and high frequency, respectively, τ is the relaxation time, and α and β are positive real constants 0≤α,β≤1. From this model, the Cole-Cole equation can be derived setting β=1; the Debye equation is obtained with α=1 and β=1. This empirical model has the ability to give a better fit to the behaviour of dispersive materials over a wide frequency range.


## 3. Method

### 3.1. Sample Preparation and Structural and Morphological Characterization

The materials required for preparingNixZn1-xFe2O4 samples were obtained from Alfa Aesar: Iron(III) Oxide (99.500%), Nickel(II) Oxide (99.000%), and Zinc Oxide (99.900%). The sample preparation procedures are roughly illustrated in the flowchart as in Figure 1.Figure 1
Flowchart of sample preparation to characterization.


### 3.2. Complex Permittivity Measurement

In this work, the permittivities of the samples were measured using Agilent 85070B Dielectric Probe Kit. Air and short and distilled water were used as standard materials for calibration as recommended by the manufacturer. The Dielectric Probe Kit automatically determined the complex permittivity of the materials under test by measuring both the magnitude and phase of the reflection coefficients. The measurement was started with the standard test materials which consist of air, Teflon, RT-duroid 5880, and Perspex. Then, the measurement continued with the Iron(III) Oxide (Fe2O3), Nickel(II) Oxide (NiO), and Zinc Oxide (ZnO) materials. The materials already prepared by the manufacturer (Alfa Aesar) in powder form were pressed into cylindrical mold at 4 tons using mechanical pressing machine. The measurement was continued with NixZn1-xFe2O4 samples that have different fractional compositions of x. The sintered mixture powder of NixZn1-xFe2O4 samples was pressed into cylindrical mold at 4 tons using mechanical pressing machine as well.


## 3.1. Sample Preparation and Structural and Morphological Characterization

The materials required for preparingNixZn1-xFe2O4 samples were obtained from Alfa Aesar: Iron(III) Oxide (99.500%), Nickel(II) Oxide (99.000%), and Zinc Oxide (99.900%). The sample preparation procedures are roughly illustrated in the flowchart as in Figure 1.Figure 1
Flowchart of sample preparation to characterization.


## 3.2. Complex Permittivity Measurement

In this work, the permittivities of the samples were measured using Agilent 85070B Dielectric Probe Kit. Air and short and distilled water were used as standard materials for calibration as recommended by the manufacturer. The Dielectric Probe Kit automatically determined the complex permittivity of the materials under test by measuring both the magnitude and phase of the reflection coefficients. The measurement was started with the standard test materials which consist of air, Teflon, RT-duroid 5880, and Perspex. Then, the measurement continued with the Iron(III) Oxide (Fe2O3), Nickel(II) Oxide (NiO), and Zinc Oxide (ZnO) materials. The materials already prepared by the manufacturer (Alfa Aesar) in powder form were pressed into cylindrical mold at 4 tons using mechanical pressing machine. The measurement was continued with NixZn1-xFe2O4 samples that have different fractional compositions of x. The sintered mixture powder of NixZn1-xFe2O4 samples was pressed into cylindrical mold at 4 tons using mechanical pressing machine as well.


## 4. Results and Discussion

### 4.1. Structure Characterization and Morphology of NixZn1–xFe2O4

#### 4.1.1. XRD Profiles

Figure2 presents the XRD patterns of NixZn1-xFe2O4 samples after sintering at 900°C for 10 hours with heating rate of 4°C/min. The patterns showed distinct diffraction lines with the highest peaks at 35.317, 35.319, 35.412, 35.426, and 35.778 of the 2θ (°) for all samples with an increment of x which in turn decrease the d-spacing accordingly (Table 1). The d-spacing was linearly decreased as the fractional composition of x increased as shown in Figure 3. The distinct diffraction lines could be observed for the powders sintered at 900°C meaning that the intensity of XRD peaks increased as the amorphous phase transformed into the crystalline phase for Ni0.1Zn0.9Fe2O4 sample. This could be related to the development of crystal growth of the entire particles. The peaks for 220, 311, 222, 400, 422, 511, and 440 occurred at the reflections planes originated at the 2θ (°) values 30.003, 35.317, 36.931, 42.905, 53.172, 56.680, and 62.228, yielding to the d-spacing [Å] values of 2.978, 2.543, 2.434, 2.108, 1.723, 1.624, and 1.492 consecutively thus indicating that a pure cubic ferrite phase formed according to the reference spectrum of Ni-Zn ferrite (Joint Committee of Powder Diffraction Standards). The XRD profiles of different x are also presented in Figure 2 that showed the same behaviors as described above for Ni0.1Zn0.9Fe2O4 sample with slight difference in the intensity of 2θ (°) and decreased pattern for d-spacing [Å] as x increased in the fractional composition.Table 1
d-spacing for NixZn1-xFe2O4 samples at the main (3 1 1) hkl plane.
x
2
θ (°)
d-spacing (Å)
0.1
35.317
2.543
0.3
35.319
2.536
0.5
35.412
2.526
0.7
35.426
2.518
0.9
35.778
2.511Figure 2
XRD profile ofNixZn1-xFe2O4 samples sintered at 900°C.Figure 3
d-spacing against fractional composition of x for NixZn1-xFe2O4.


#### 4.1.2. Lattice Constant

The lattice constanta was obtained as a function of fractional composition of x substitution in NixZn1-xFe2O4 calculated from the combination of Bragg’s equation and d-spacing expression:(5)1dhkl2=h2a2+k2a2+l2a2for cubic system equation. The calculation of lattice constant for all samples was considered at the single phase crystallite 311  hkl planes and thus the value of lattice constant was established. A linear relationship with negative sensitivity could be obtained between lattice constant and x for NixZn1-xFe2O4 sample as shown in Figure 4. Other studies also found that the lattice constant a decreased with the increasing of x concentration [17, 18].Figure 4
Lattice constant against fractional composition ofx for NixZn1-xFe2O4.


#### 4.1.3. Density

The X-ray densities(Dx) of the NixZn1-xFe2O4 samples were calculated using(6)Dx=8×MN×a3g·cm-3.It was found that the density of the NixZn1-xFe2O4 samples increased linearly with increasing of the substituted amount of x inside the Ni-Zn ferrite sample (Figure 5). Every reduction in number of molecular masses for all compositions gave a higher density value (Table 2).Table 2
Calculated true X-ray density of NixZn1-xFe2O4 samples.
Composition (x)
Molecular mass (g/mole)
Lattice constanta (Å)
X-ray density (g/cm3)
0.1
240.4234
8.4334
5.3250
0.3
239.0802
8.4105
5.3386
0.5
237.7370
8.3789
5.3689
0.7
236.3938
8.3500
5.3942
0.9
235.0506
8.3280
5.4062Figure 5
X-ray densities against fractional composition ofx for NixZn1-xFe2O4.


#### 4.1.4. SEM Morphologies

The microstructural properties of the moldedNixZn1-xFe2O4 samples were obtained by scanning electron microscope as in Figure 6. The raw mixture in the form of powder was first sintered at 900°C for 10 hours before being poured into mold and compacted using mechanical pressing machine. The measurement was conducted on the plane surfaces of the molded samples which gave information in terms of grain morphology, grain boundaries, and porosity. The grain size of each sample was randomly selected through 60000 magnifications from the morphology picture so that the grain size could be seen clearly. The tabulated grain size for all samples was in the range of 62 nm–175 nm. Lots of pores could be seen from the morphology and that was probably due to inhomogeneous size of particle; thus there would be air gaps between the particles. If the sintering time is increased, the pores will reduce because of the formation of strong bonds between the adjacent particles [19].Figure 6
SEM micrograph of (a) Ni0.1Zn0.9Fe2O4, (b) Ni0.3Zn0.7Fe2O4, (c) Ni0.5Zn0.5Fe2O4, (d) Ni0.7Zn0.3Fe2O4, and (e) Ni0.9Zn0.1Fe2O4 sample at 60000 magnifications.
(a)
(b)
(c)
(d)
(e)


### 4.2. Permittivity Results

#### 4.2.1. Standard Material

The measurement procedure to determine complex permittivity using the Agilent Dielectric Probe Kit 85070B was described above. The permittivity values also provide insights into the effect of the fractional composition ofx on the bulk permittivity values NixZn1-xFe2O4. Vector Network Analyzer 8720B (VNA) was connected via coaxial cable to the Agilent Dielectric Probe Kit 85070B. The technique was done by pressing the dielectric probe against the sample material. The microwave signal launched by the VNA was reflected by the sample. The reflected wave was received by the VNA which then used the wave to calculate the dielectric constant and loss factor.The dielectric constant and loss factor of air and several standard materials including Teflon, RT-duroid 5880, and Perspex with thickness of 20 mm, 19.05 mm, and 20 mm were measured in the frequency range between 1 GHz and 10 GHz as shown in Figure7. The dielectric constant values for all the samples were almost constant for the whole frequency range with slight dispersion toward the higher end of the frequency range except for air which was lossless. The slight dispersion for all the samples at the higher frequency end was due to the increase of the loss factor because of higher absorption loss. The dielectric constants of air, Teflon, RT-duroid 5880, and Perspex at 105 Hz to 1 MHz were found to be 1, 2.1 (Tecaflon PTFE, Technical Datasheet), 2.2 (Rogers Corporation, Technical Datasheet), and 2.6 (Goodfellow Group, Technical Information-Polymethylmethacrylate) which were in very good agreement with available data.Figure 7
Complex permittivity of standard samples measured with Agilent 85070B Dielectric Probe Kit.The slight dispersion for all the samples at the higher frequency end was probably due to several factors. Firstly, the minimum sample thickness recommended by the manufacturer (d=30mm/ε′) for the 85070B Dielectric Probe Kit should be more than 20 mm for ε′=2.05. The higher the dielectric constant is, the lower the required minimum thickness shall be based on the higher dielectric. Small errors could be attributed to the fact that Dielectric Probe Kit 85070B was designed for liquid materials. The permittivity computation for the Dielectric Probe Kit 85070B was a simplified version of Debye model obtained from empirical fitting of several known liquids [20]; thus the permittivity calculations were less accurate for solid materials.


#### 4.2.2. Pure NiO, ZnO, and Fe2O3

The dielectric constant and loss factor consisting of Nickel(II) Oxide (NiO), Zinc Oxide (ZnO), and Iron(III) Oxide (Fe2O3) are shown in Figure 8. It could be clearly observed from the graph that NiO had both higher dielectric constant and loss factor compared to ZnO and Fe2O3. The dielectric constants for both ZnO and Fe2O3 were almost stable for the whole frequency range. However the dielectric constant of NiO was gradually decreased from 5.5 at 1 GHz to 4 at 10 GHz. Interestingly, it could be observed clearly that NiO had loss factor approximately 5 times larger than ZnO and Fe2O3 thus qualifying it to be categorized as a highly loss material.Figure 8
Complex permittivity of raw materials measured with Agilent 85070B Dielectric Probe Kit.


#### 4.2.3. NixZn1–xFe2O4

The measurement of complex permittivity ofNixZn1-xFe2O4 samples using open ended coaxial probe with different fractional composition of x was also performed. The thickness of the all samples was 8 mm. Figure 9 shows the results for each NixZn1-xFe2O4 sample, where x=0.1, 0.3, 0.5, 0.7, and 0.9.Figure 9
Complex permittivity ofNixZn1-xFe2O4 samples measured with Agilent 85070B Dielectric Probe Kit.The high uncertainties in bothε′ and ε′′ at frequencies below 2 GHz were due to multiple reflection effect within the sample. The samples must be infinitely thick to avoid reflection from the end face of the sample. The lower the operating frequencies, the longer the wavelengths and thus the higher the uncertainties due to incident wave reflected at the end surface of the sample. These effects were reduced at higher frequencies especially beyond 3 GHz due to shorter probing wavelength. Generally Figure 9 suggests higher fractional composition of x would result in higher values of the dielectric constant of NixZn1-xFe2O4. At 5 GHz, the value of ε′ increased from approximately 3.1 to 3.8 for x=0.1 to 0.9. This was expected as Figure 8 showed the dielectric constant of NiO was much higher than both ZnO and Fe2O3. Similarly, the loss factor ε′′ values for all NixZn1-xFe2O4 samples increased with increasing values of fractional composition of x especially at frequencies above 3 GHz.The effect of fractional composition ofx on the dielectric constant in the frequency range between 3 GHz and 10 GHz can be observed clearly in Figure 10 by defining the change in dielectric constant: (7)Δε′=εxi′-εx=0.1′,where εx(i)′ is the dielectric constant of NixZn1-xFe2O4 with xi=0.3, 0.5, 0.7, and 0.9.Figure 10
Variation inΔε′ with frequency for various fractional composition values of x.The mean valuesΔε′ for the whole frequency range from 3 GHz to 10 GHz are summarized in Table 3. A slight change from x=0.1 to 0.3 would give a change of approximately 0.11 in the value of ε′ and could be as high as 0.70 if x increased from 0.1 to 0.9. The higher the NiO content is, the higher the dielectric constant and loss factor of NixZn1-xFe2O4 will be.Table 3
Mean value of dielectric constantΔε′ in the frequency range from 3 GHz to 10 GHz.
Symbol,x
Mean value ofΔε′
0.2
0.1145
0.4
0.3332
0.6
0.4395
0.8
0.7020


## 4.1. Structure Characterization and Morphology of NixZn1–xFe2O4

### 4.1.1. XRD Profiles

Figure2 presents the XRD patterns of NixZn1-xFe2O4 samples after sintering at 900°C for 10 hours with heating rate of 4°C/min. The patterns showed distinct diffraction lines with the highest peaks at 35.317, 35.319, 35.412, 35.426, and 35.778 of the 2θ (°) for all samples with an increment of x which in turn decrease the d-spacing accordingly (Table 1). The d-spacing was linearly decreased as the fractional composition of x increased as shown in Figure 3. The distinct diffraction lines could be observed for the powders sintered at 900°C meaning that the intensity of XRD peaks increased as the amorphous phase transformed into the crystalline phase for Ni0.1Zn0.9Fe2O4 sample. This could be related to the development of crystal growth of the entire particles. The peaks for 220, 311, 222, 400, 422, 511, and 440 occurred at the reflections planes originated at the 2θ (°) values 30.003, 35.317, 36.931, 42.905, 53.172, 56.680, and 62.228, yielding to the d-spacing [Å] values of 2.978, 2.543, 2.434, 2.108, 1.723, 1.624, and 1.492 consecutively thus indicating that a pure cubic ferrite phase formed according to the reference spectrum of Ni-Zn ferrite (Joint Committee of Powder Diffraction Standards). The XRD profiles of different x are also presented in Figure 2 that showed the same behaviors as described above for Ni0.1Zn0.9Fe2O4 sample with slight difference in the intensity of 2θ (°) and decreased pattern for d-spacing [Å] as x increased in the fractional composition.Table 1
d-spacing for NixZn1-xFe2O4 samples at the main (3 1 1) hkl plane.
x
2
θ (°)
d-spacing (Å)
0.1
35.317
2.543
0.3
35.319
2.536
0.5
35.412
2.526
0.7
35.426
2.518
0.9
35.778
2.511Figure 2
XRD profile ofNixZn1-xFe2O4 samples sintered at 900°C.Figure 3
d-spacing against fractional composition of x for NixZn1-xFe2O4.


### 4.1.2. Lattice Constant

The lattice constanta was obtained as a function of fractional composition of x substitution in NixZn1-xFe2O4 calculated from the combination of Bragg’s equation and d-spacing expression:(5)1dhkl2=h2a2+k2a2+l2a2for cubic system equation. The calculation of lattice constant for all samples was considered at the single phase crystallite 311  hkl planes and thus the value of lattice constant was established. A linear relationship with negative sensitivity could be obtained between lattice constant and x for NixZn1-xFe2O4 sample as shown in Figure 4. Other studies also found that the lattice constant a decreased with the increasing of x concentration [17, 18].Figure 4
Lattice constant against fractional composition ofx for NixZn1-xFe2O4.


### 4.1.3. Density

The X-ray densities(Dx) of the NixZn1-xFe2O4 samples were calculated using(6)Dx=8×MN×a3g·cm-3.It was found that the density of the NixZn1-xFe2O4 samples increased linearly with increasing of the substituted amount of x inside the Ni-Zn ferrite sample (Figure 5). Every reduction in number of molecular masses for all compositions gave a higher density value (Table 2).Table 2
Calculated true X-ray density of NixZn1-xFe2O4 samples.
Composition (x)
Molecular mass (g/mole)
Lattice constanta (Å)
X-ray density (g/cm3)
0.1
240.4234
8.4334
5.3250
0.3
239.0802
8.4105
5.3386
0.5
237.7370
8.3789
5.3689
0.7
236.3938
8.3500
5.3942
0.9
235.0506
8.3280
5.4062Figure 5
X-ray densities against fractional composition ofx for NixZn1-xFe2O4.


### 4.1.4. SEM Morphologies

The microstructural properties of the moldedNixZn1-xFe2O4 samples were obtained by scanning electron microscope as in Figure 6. The raw mixture in the form of powder was first sintered at 900°C for 10 hours before being poured into mold and compacted using mechanical pressing machine. The measurement was conducted on the plane surfaces of the molded samples which gave information in terms of grain morphology, grain boundaries, and porosity. The grain size of each sample was randomly selected through 60000 magnifications from the morphology picture so that the grain size could be seen clearly. The tabulated grain size for all samples was in the range of 62 nm–175 nm. Lots of pores could be seen from the morphology and that was probably due to inhomogeneous size of particle; thus there would be air gaps between the particles. If the sintering time is increased, the pores will reduce because of the formation of strong bonds between the adjacent particles [19].Figure 6
SEM micrograph of (a) Ni0.1Zn0.9Fe2O4, (b) Ni0.3Zn0.7Fe2O4, (c) Ni0.5Zn0.5Fe2O4, (d) Ni0.7Zn0.3Fe2O4, and (e) Ni0.9Zn0.1Fe2O4 sample at 60000 magnifications.
(a)
(b)
(c)
(d)
(e)


## 4.1.1. XRD Profiles

Figure2 presents the XRD patterns of NixZn1-xFe2O4 samples after sintering at 900°C for 10 hours with heating rate of 4°C/min. The patterns showed distinct diffraction lines with the highest peaks at 35.317, 35.319, 35.412, 35.426, and 35.778 of the 2θ (°) for all samples with an increment of x which in turn decrease the d-spacing accordingly (Table 1). The d-spacing was linearly decreased as the fractional composition of x increased as shown in Figure 3. The distinct diffraction lines could be observed for the powders sintered at 900°C meaning that the intensity of XRD peaks increased as the amorphous phase transformed into the crystalline phase for Ni0.1Zn0.9Fe2O4 sample. This could be related to the development of crystal growth of the entire particles. The peaks for 220, 311, 222, 400, 422, 511, and 440 occurred at the reflections planes originated at the 2θ (°) values 30.003, 35.317, 36.931, 42.905, 53.172, 56.680, and 62.228, yielding to the d-spacing [Å] values of 2.978, 2.543, 2.434, 2.108, 1.723, 1.624, and 1.492 consecutively thus indicating that a pure cubic ferrite phase formed according to the reference spectrum of Ni-Zn ferrite (Joint Committee of Powder Diffraction Standards). The XRD profiles of different x are also presented in Figure 2 that showed the same behaviors as described above for Ni0.1Zn0.9Fe2O4 sample with slight difference in the intensity of 2θ (°) and decreased pattern for d-spacing [Å] as x increased in the fractional composition.Table 1
d-spacing for NixZn1-xFe2O4 samples at the main (3 1 1) hkl plane.
x
2
θ (°)
d-spacing (Å)
0.1
35.317
2.543
0.3
35.319
2.536
0.5
35.412
2.526
0.7
35.426
2.518
0.9
35.778
2.511Figure 2
XRD profile ofNixZn1-xFe2O4 samples sintered at 900°C.Figure 3
d-spacing against fractional composition of x for NixZn1-xFe2O4.


## 4.1.2. Lattice Constant

The lattice constanta was obtained as a function of fractional composition of x substitution in NixZn1-xFe2O4 calculated from the combination of Bragg’s equation and d-spacing expression:(5)1dhkl2=h2a2+k2a2+l2a2for cubic system equation. The calculation of lattice constant for all samples was considered at the single phase crystallite 311  hkl planes and thus the value of lattice constant was established. A linear relationship with negative sensitivity could be obtained between lattice constant and x for NixZn1-xFe2O4 sample as shown in Figure 4. Other studies also found that the lattice constant a decreased with the increasing of x concentration [17, 18].Figure 4
Lattice constant against fractional composition ofx for NixZn1-xFe2O4.


## 4.1.3. Density

The X-ray densities(Dx) of the NixZn1-xFe2O4 samples were calculated using(6)Dx=8×MN×a3g·cm-3.It was found that the density of the NixZn1-xFe2O4 samples increased linearly with increasing of the substituted amount of x inside the Ni-Zn ferrite sample (Figure 5). Every reduction in number of molecular masses for all compositions gave a higher density value (Table 2).Table 2
Calculated true X-ray density of NixZn1-xFe2O4 samples.
Composition (x)
Molecular mass (g/mole)
Lattice constanta (Å)
X-ray density (g/cm3)
0.1
240.4234
8.4334
5.3250
0.3
239.0802
8.4105
5.3386
0.5
237.7370
8.3789
5.3689
0.7
236.3938
8.3500
5.3942
0.9
235.0506
8.3280
5.4062Figure 5
X-ray densities against fractional composition ofx for NixZn1-xFe2O4.


## 4.1.4. SEM Morphologies

The microstructural properties of the moldedNixZn1-xFe2O4 samples were obtained by scanning electron microscope as in Figure 6. The raw mixture in the form of powder was first sintered at 900°C for 10 hours before being poured into mold and compacted using mechanical pressing machine. The measurement was conducted on the plane surfaces of the molded samples which gave information in terms of grain morphology, grain boundaries, and porosity. The grain size of each sample was randomly selected through 60000 magnifications from the morphology picture so that the grain size could be seen clearly. The tabulated grain size for all samples was in the range of 62 nm–175 nm. Lots of pores could be seen from the morphology and that was probably due to inhomogeneous size of particle; thus there would be air gaps between the particles. If the sintering time is increased, the pores will reduce because of the formation of strong bonds between the adjacent particles [19].Figure 6
SEM micrograph of (a) Ni0.1Zn0.9Fe2O4, (b) Ni0.3Zn0.7Fe2O4, (c) Ni0.5Zn0.5Fe2O4, (d) Ni0.7Zn0.3Fe2O4, and (e) Ni0.9Zn0.1Fe2O4 sample at 60000 magnifications.
(a)
(b)
(c)
(d)
(e)


## 4.2. Permittivity Results

### 4.2.1. Standard Material

The measurement procedure to determine complex permittivity using the Agilent Dielectric Probe Kit 85070B was described above. The permittivity values also provide insights into the effect of the fractional composition ofx on the bulk permittivity values NixZn1-xFe2O4. Vector Network Analyzer 8720B (VNA) was connected via coaxial cable to the Agilent Dielectric Probe Kit 85070B. The technique was done by pressing the dielectric probe against the sample material. The microwave signal launched by the VNA was reflected by the sample. The reflected wave was received by the VNA which then used the wave to calculate the dielectric constant and loss factor.The dielectric constant and loss factor of air and several standard materials including Teflon, RT-duroid 5880, and Perspex with thickness of 20 mm, 19.05 mm, and 20 mm were measured in the frequency range between 1 GHz and 10 GHz as shown in Figure7. The dielectric constant values for all the samples were almost constant for the whole frequency range with slight dispersion toward the higher end of the frequency range except for air which was lossless. The slight dispersion for all the samples at the higher frequency end was due to the increase of the loss factor because of higher absorption loss. The dielectric constants of air, Teflon, RT-duroid 5880, and Perspex at 105 Hz to 1 MHz were found to be 1, 2.1 (Tecaflon PTFE, Technical Datasheet), 2.2 (Rogers Corporation, Technical Datasheet), and 2.6 (Goodfellow Group, Technical Information-Polymethylmethacrylate) which were in very good agreement with available data.Figure 7
Complex permittivity of standard samples measured with Agilent 85070B Dielectric Probe Kit.The slight dispersion for all the samples at the higher frequency end was probably due to several factors. Firstly, the minimum sample thickness recommended by the manufacturer (d=30mm/ε′) for the 85070B Dielectric Probe Kit should be more than 20 mm for ε′=2.05. The higher the dielectric constant is, the lower the required minimum thickness shall be based on the higher dielectric. Small errors could be attributed to the fact that Dielectric Probe Kit 85070B was designed for liquid materials. The permittivity computation for the Dielectric Probe Kit 85070B was a simplified version of Debye model obtained from empirical fitting of several known liquids [20]; thus the permittivity calculations were less accurate for solid materials.


### 4.2.2. Pure NiO, ZnO, and Fe2O3

The dielectric constant and loss factor consisting of Nickel(II) Oxide (NiO), Zinc Oxide (ZnO), and Iron(III) Oxide (Fe2O3) are shown in Figure 8. It could be clearly observed from the graph that NiO had both higher dielectric constant and loss factor compared to ZnO and Fe2O3. The dielectric constants for both ZnO and Fe2O3 were almost stable for the whole frequency range. However the dielectric constant of NiO was gradually decreased from 5.5 at 1 GHz to 4 at 10 GHz. Interestingly, it could be observed clearly that NiO had loss factor approximately 5 times larger than ZnO and Fe2O3 thus qualifying it to be categorized as a highly loss material.Figure 8
Complex permittivity of raw materials measured with Agilent 85070B Dielectric Probe Kit.


### 4.2.3. NixZn1–xFe2O4

The measurement of complex permittivity ofNixZn1-xFe2O4 samples using open ended coaxial probe with different fractional composition of x was also performed. The thickness of the all samples was 8 mm. Figure 9 shows the results for each NixZn1-xFe2O4 sample, where x=0.1, 0.3, 0.5, 0.7, and 0.9.Figure 9
Complex permittivity ofNixZn1-xFe2O4 samples measured with Agilent 85070B Dielectric Probe Kit.The high uncertainties in bothε′ and ε′′ at frequencies below 2 GHz were due to multiple reflection effect within the sample. The samples must be infinitely thick to avoid reflection from the end face of the sample. The lower the operating frequencies, the longer the wavelengths and thus the higher the uncertainties due to incident wave reflected at the end surface of the sample. These effects were reduced at higher frequencies especially beyond 3 GHz due to shorter probing wavelength. Generally Figure 9 suggests higher fractional composition of x would result in higher values of the dielectric constant of NixZn1-xFe2O4. At 5 GHz, the value of ε′ increased from approximately 3.1 to 3.8 for x=0.1 to 0.9. This was expected as Figure 8 showed the dielectric constant of NiO was much higher than both ZnO and Fe2O3. Similarly, the loss factor ε′′ values for all NixZn1-xFe2O4 samples increased with increasing values of fractional composition of x especially at frequencies above 3 GHz.The effect of fractional composition ofx on the dielectric constant in the frequency range between 3 GHz and 10 GHz can be observed clearly in Figure 10 by defining the change in dielectric constant: (7)Δε′=εxi′-εx=0.1′,where εx(i)′ is the dielectric constant of NixZn1-xFe2O4 with xi=0.3, 0.5, 0.7, and 0.9.Figure 10
Variation inΔε′ with frequency for various fractional composition values of x.The mean valuesΔε′ for the whole frequency range from 3 GHz to 10 GHz are summarized in Table 3. A slight change from x=0.1 to 0.3 would give a change of approximately 0.11 in the value of ε′ and could be as high as 0.70 if x increased from 0.1 to 0.9. The higher the NiO content is, the higher the dielectric constant and loss factor of NixZn1-xFe2O4 will be.Table 3
Mean value of dielectric constantΔε′ in the frequency range from 3 GHz to 10 GHz.
Symbol,x
Mean value ofΔε′
0.2
0.1145
0.4
0.3332
0.6
0.4395
0.8
0.7020


## 4.2.1. Standard Material

The measurement procedure to determine complex permittivity using the Agilent Dielectric Probe Kit 85070B was described above. The permittivity values also provide insights into the effect of the fractional composition ofx on the bulk permittivity values NixZn1-xFe2O4. Vector Network Analyzer 8720B (VNA) was connected via coaxial cable to the Agilent Dielectric Probe Kit 85070B. The technique was done by pressing the dielectric probe against the sample material. The microwave signal launched by the VNA was reflected by the sample. The reflected wave was received by the VNA which then used the wave to calculate the dielectric constant and loss factor.The dielectric constant and loss factor of air and several standard materials including Teflon, RT-duroid 5880, and Perspex with thickness of 20 mm, 19.05 mm, and 20 mm were measured in the frequency range between 1 GHz and 10 GHz as shown in Figure7. The dielectric constant values for all the samples were almost constant for the whole frequency range with slight dispersion toward the higher end of the frequency range except for air which was lossless. The slight dispersion for all the samples at the higher frequency end was due to the increase of the loss factor because of higher absorption loss. The dielectric constants of air, Teflon, RT-duroid 5880, and Perspex at 105 Hz to 1 MHz were found to be 1, 2.1 (Tecaflon PTFE, Technical Datasheet), 2.2 (Rogers Corporation, Technical Datasheet), and 2.6 (Goodfellow Group, Technical Information-Polymethylmethacrylate) which were in very good agreement with available data.Figure 7
Complex permittivity of standard samples measured with Agilent 85070B Dielectric Probe Kit.The slight dispersion for all the samples at the higher frequency end was probably due to several factors. Firstly, the minimum sample thickness recommended by the manufacturer (d=30mm/ε′) for the 85070B Dielectric Probe Kit should be more than 20 mm for ε′=2.05. The higher the dielectric constant is, the lower the required minimum thickness shall be based on the higher dielectric. Small errors could be attributed to the fact that Dielectric Probe Kit 85070B was designed for liquid materials. The permittivity computation for the Dielectric Probe Kit 85070B was a simplified version of Debye model obtained from empirical fitting of several known liquids [20]; thus the permittivity calculations were less accurate for solid materials.


## 4.2.2. Pure NiO, ZnO, and Fe2O3

The dielectric constant and loss factor consisting of Nickel(II) Oxide (NiO), Zinc Oxide (ZnO), and Iron(III) Oxide (Fe2O3) are shown in Figure 8. It could be clearly observed from the graph that NiO had both higher dielectric constant and loss factor compared to ZnO and Fe2O3. The dielectric constants for both ZnO and Fe2O3 were almost stable for the whole frequency range. However the dielectric constant of NiO was gradually decreased from 5.5 at 1 GHz to 4 at 10 GHz. Interestingly, it could be observed clearly that NiO had loss factor approximately 5 times larger than ZnO and Fe2O3 thus qualifying it to be categorized as a highly loss material.Figure 8
Complex permittivity of raw materials measured with Agilent 85070B Dielectric Probe Kit.


## 4.2.3. NixZn1–xFe2O4

The measurement of complex permittivity ofNixZn1-xFe2O4 samples using open ended coaxial probe with different fractional composition of x was also performed. The thickness of the all samples was 8 mm. Figure 9 shows the results for each NixZn1-xFe2O4 sample, where x=0.1, 0.3, 0.5, 0.7, and 0.9.Figure 9
Complex permittivity ofNixZn1-xFe2O4 samples measured with Agilent 85070B Dielectric Probe Kit.The high uncertainties in bothε′ and ε′′ at frequencies below 2 GHz were due to multiple reflection effect within the sample. The samples must be infinitely thick to avoid reflection from the end face of the sample. The lower the operating frequencies, the longer the wavelengths and thus the higher the uncertainties due to incident wave reflected at the end surface of the sample. These effects were reduced at higher frequencies especially beyond 3 GHz due to shorter probing wavelength. Generally Figure 9 suggests higher fractional composition of x would result in higher values of the dielectric constant of NixZn1-xFe2O4. At 5 GHz, the value of ε′ increased from approximately 3.1 to 3.8 for x=0.1 to 0.9. This was expected as Figure 8 showed the dielectric constant of NiO was much higher than both ZnO and Fe2O3. Similarly, the loss factor ε′′ values for all NixZn1-xFe2O4 samples increased with increasing values of fractional composition of x especially at frequencies above 3 GHz.The effect of fractional composition ofx on the dielectric constant in the frequency range between 3 GHz and 10 GHz can be observed clearly in Figure 10 by defining the change in dielectric constant: (7)Δε′=εxi′-εx=0.1′,where εx(i)′ is the dielectric constant of NixZn1-xFe2O4 with xi=0.3, 0.5, 0.7, and 0.9.Figure 10
Variation inΔε′ with frequency for various fractional composition values of x.The mean valuesΔε′ for the whole frequency range from 3 GHz to 10 GHz are summarized in Table 3. A slight change from x=0.1 to 0.3 would give a change of approximately 0.11 in the value of ε′ and could be as high as 0.70 if x increased from 0.1 to 0.9. The higher the NiO content is, the higher the dielectric constant and loss factor of NixZn1-xFe2O4 will be.Table 3
Mean value of dielectric constantΔε′ in the frequency range from 3 GHz to 10 GHz.
Symbol,x
Mean value ofΔε′
0.2
0.1145
0.4
0.3332
0.6
0.4395
0.8
0.7020


## 5. Conclusion

The permittivity ofNixZn1-xFe2O4 in the frequency range between 1 GHz and 10 GHz was successfully determined using an open ended coaxial probe technique as higher fractional composition of x would result in higher values of the dielectric constant of NixZn1-xFe2O4. It was found that the lattice constant of the NixZn1-xFe2O4 samples decreased linearly with increasing of the substituted amount of x inside the Ni-Zn ferrite sample. The tabulated grain size for all samples was in the range of 62 nm–175 nm.



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*Source: 219195-2015-11-29.xml*