International Journal of Microwave Science and Technology

Volume 2015, Article ID 219195, 8 pages

http://dx.doi.org/10.1155/2015/219195

## Characterization of Ni_{x}Zn_{1−x}Fe_{2}O_{4} and Permittivity of Solid Material of NiO, ZnO, Fe_{2}O_{3}, and Ni_{x}Zn_{1−x}Fe_{2}O_{4} at Microwave Frequency Using Open Ended Coaxial Probe

^{1}Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia^{2}Faculty of Sciences, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Malaysia^{3}Advanced Materials and Nanotechnology Laboratory, Institute of Advanced Technology, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 10 May 2015; Accepted 28 September 2015

Academic Editor: Samir Trabelsi

Copyright © 2015 Fahmiruddin Esa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper describes a detailed study on the application of an open ended coaxial probe technique to determine the permittivity of in the frequency range between 1 GHz and 10 GHz. The compositions of the spinel ferrite were 0.1, 0.3, 0.5, 0.7, and 0.9. The 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 on the bulk permittivity values . Vector Network Analyzer 8720B (VNA) was connected via coaxial cable to the Agilent Dielectric Probe Kit 85070B.

#### 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 with 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 permittivity :where is the permittivity of free space ( F/m) and the real part and the imaginary part 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 of where is the aperture admittance of the probe [8]:where is the characteristic admittance of the coaxial line and 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:where is the complex relative permittivity of the material under test, is the relative permittivity of the coaxial line, and are the inner and outer radii of the coaxial line, respectively, is the absolute value of the propagation constant in free space, and and 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:where and are the values of the real part of the complex relative permittivity at low and high frequency, respectively, is the relaxation time, and and are positive real constants . From this model, the Cole-Cole equation can be derived setting ; the Debye equation is obtained with and . 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 preparing 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.