# Characterization and Study of Ferromagnetic Resonance of Micro and Nano Ferrites at Microwave and Millimeter waves

код для вставкиСкачатьCharacterization and Study of Ferromagnetic Resonance of Micro and Nano Ferrites at Microwave and Millimeter waves A dissertation submitted by Anjali Sharma In partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering TUFTS UNIVERSITY February, 2014 ADVISER: Dr. M.N. Afsar UMI Number: 3612824 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3612824 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Abstract Ferrites have been used in magnetic recording devices, isolators, circulators and as permanent magnets for a long time. However, the recent developments in semiconductor technology and nanoelectronics have led to a significant growth in high frequency applications. As the device size becomes smaller and applications shift towards millimeter wavelengths, the need for novel materials capable of handling high frequencies has increased. This has generated interest in the study of materials in the nanoscale domain. Nanoferrites are being extensively studied for their potential application as high frequency absorbers, information storage media, circulators, isolators, etc. Other areas of growing interest for these materials include biomedical engineering, alternate energy, aerospace engineering and defense applications. Nanoferrites consist of metal substituted iron oxide nanopowders that have average particle size below 100 nm. At these dimensions the domain wall resonance can be avoided since materials can exist in single domain state and thus such materials prove useful for high frequency applications. Nano-size materials have unique mechanical, electrical and magnetic properties. The unique properties of nanomaterials could be attributed to their structure which is close to that of an isolated atom or molecule. The properties of nanomaterials may not necessarily be predicted from those observed at larger scales. In fact, the electromagnetic properties of materials are known to change as particle sizes are reduced to the nanoscale. Consequently, it is necessary to characterize these materials in order to understand their behavior and better predict their potential use in high frequency applications. A waveguide based set-up has been used here to perform transmission and reflection measurements on powdered nano-ferrite samples at microwave frequencies using a vector network analyzer. This measurement set-up is capable of accurately measuring the material 1 properties in terms of s-parameters in the frequency range from 2 GHz to 40 GHz. The electromagnetic properties, namely, magnetic permeability and electric permittivity are derived from these parameters. The algorithm has been specifically written to calculate the real and imaginary parts of permittivity and permeability of the powdered nano-ferrite samples. The measurements were also performed on micro-size samples to understand the dependence of material properties on particle dimensions. In order to verify the observed difference in the micro- and nano-size samples, the same powders were also analyzed by another technique at higher frequencies. Transmittance measurements were performed in the millimeter wave frequency range from 40 GHz to 120 GHz using a free-space quasi-optical millimeter wave spectrometer. The set-up is equipped with high-power backward wave oscillators. The complex permittivity for both micro- and nano-ferrites has been calculated from the measured transmittance spectrum. It was observed that the constitutive material properties, namely permittivity and permeability, as well as the ferromagnetic resonance frequency of the samples vary with the change in particle dimensions. Based on the results of these measurements, a model for calculating the ferromagnetic resonance frequency of ferrite powders has been derived, which takes into account the size and shape of the particles in the sample. It can be concluded from the size-dependent absorption properties observed in this study that these materials show promise as tunable millimeter wave absorbers. 2 Acknowledgement I am grateful to my advisor, Dr. Mohammed Nurul Afsar for his continuous guidance and support during my research. He provided me with the great opportunity to work in his High Frequency Material Measurement and Information Center Laboratory at Tufts University. His advice and ideas have been a source of great motivation for my work. I am also thankful to the committee members, Prof D. Preis, Prof. X and Prof. X for serving in my defense committee and providing useful review of my work. I would like to thank Dr. Mahmut Obol and Dr. Konstantin A. Korolev for their assistance with the instruments in the laboratory and fruitful discussions about the experimental results. I am also thankful to other members of Prof. Afsar’s research group. I am extremely grateful to Dr. John McCloy at Pacific Northwest National Laboratory for his support with this research. I would especially like to thank my parents and siblings for their constant love and care. This thesis would not have been possible without their support. I am also grateful to all my friends at Tufts University. 3 Table of Contents Abstract ........................................................................................................................................... 0 Acknowledgement .......................................................................................................................... 3 1. Introduction ............................................................................................................................... 14 1.1 Background ......................................................................................................................... 14 1.2 Motivation for the study of nanoferrites ............................................................................. 18 1.3 Problem Statement .............................................................................................................. 22 1.4 Thesis Objective.................................................................................................................. 23 1.5 Thesis Organization ............................................................................................................ 25 2. Theoretical Background ............................................................................................................ 26 2.1 Origin of magnetism in materials ...................................................................................... 26 2.1.1 Diamagnetic materials ............................................................................................. 27 2.1.2 Paramagnetic materials ............................................................................................ 28 2.1.3 Ferromagnetic materials........................................................................................... 29 2.1.4 Anti-ferromagnetic materials ................................................................................... 30 2.1.5 Ferrimagnetic materials ........................................................................................... 30 2.2 Neel’s model of ferrimagnetism ........................................................................................ 34 2.3 Interaction between electromagnetic fields and materials ................................................. 35 2.3.1 Constitutive material properties ................................................................................ 37 2.3.2 Absorption of electromagnetic energy ...................................................................... 39 3. Microwave Measurement Techniques ...................................................................................... 45 3.1 Introduction ......................................................................................................................... 45 3.2 Brief Review of Microwave Techniques ............................................................................ 46 3.3 Two port network ................................................................................................................ 49 3.4 Wave Propagation in a Rectangular Waveguide ................................................................ 52 3.5 Experimental Set up ............................................................................................................ 57 3.5.1 Transmission Unit ...................................................................................................... 57 3.5.2 Measurement Unit ...................................................................................................... 58 3.6 Reflection and Transmission Coefficient............................................................................ 63 3.7 Determination of Permittivity and Permeability ................................................................. 67 4. Measurement Results at Microwave Frequencies..................................................................... 74 4.1 Introduction ......................................................................................................................... 74 4 4.2 Teflon Results ..................................................................................................................... 76 4.3 Nano-size hexagonal ferrites............................................................................................... 79 4.4 Nano-size spinel ferrites ..................................................................................................... 89 4.5 Nano-size Rare Earth Ferrites ............................................................................................. 97 5. Measurement results at millimeter frequencies ...................................................................... 103 5.1 Introduction ....................................................................................................................... 103 5.2 Theoretical Background .................................................................................................... 104 5.3 Experimental Details......................................................................................................... 105 5.4 Results ............................................................................................................................... 110 6. Size effect on ferromagnetic resonance in ferrites .................................................................. 121 6.1 Introduction ....................................................................................................................... 121 6.2 Properties of nano- and micro-size ferrite powders .......................................................... 122 6.3 Structural analysis of ferrite powders ............................................................................... 127 6.4 Ferromagnetic resonance .................................................................................................. 136 6.5 FMR Calculations ............................................................................................................. 142 6.6 Quality Control ................................................................................................................. 146 7. Error Analysis ......................................................................................................................... 150 7.1 Introduction ....................................................................................................................... 150 7.2 Systematic errors in microwave measurements ................................................................ 151 7.3 Random errors in microwave measurements .................................................................... 159 7.4 Uncertainty in millimeter wave measurements................................................................. 166 Conclusion .................................................................................................................................. 170 List of publications ..................................................................................................................... 172 References ................................................................................................................................... 175 5 List of Figures Figure 2.1 Dipole orientation in (a) diamagnetic and (b) paramagnetic materials with and without an external field………………………………………………….......... 29 Figure 2.2 (a) Atomic magnetic dipoles align in parallel directions in a ferromagnetic material, (b) adjacent dipoles align in opposite directions with no net dipole moment in anti-ferromagnetic materials, (c) in ferrimagnetic materials, adjacent dipoles align in opposite directions but with a net dipole moment. ..............31 Figure 2.3 Dipoles are aligned in certain regions of the material called domains. A material may consist of several domains, oriented in mutually random directions. ... 32 Figure 2.4 The electric and magnetic fields are perpendicular to each other and to the direction of wave propagation. Such a wave is incident on the front end of a material with intrinsic properties ε and µ. .................................................................. 40 Figure 2.5 The incident wave (I) is partly reflected (R) at the air-material interface. The wave propagating inside the material attenuates depending in the absorption properties of the material. The remaining energy is transmitted out of the material (T). ............................................................................................................... 41 Figure 2.6 A multilayer structure formed by stacking two materials in medium 1, and (b) the equivalent transmission line model, where the impedance of each component is equal to the equivalent impedance seen at the interface of the corresponding layer. .................................................................................................... 43 Figure 3.1 Schematic representation of a two-port network showing the incident and reflected wave at each port. Hollow rectangular metallic waveguides were used as transmission lines that guide the EM wave between the sample and 6 network analyzer. ........................................................................................................ 49 Figure 3.2 Geometry of a rectangular waveguide ......................................................................... 52 Figure 3.3 Block diagram of the measurement setup ................................................................... 58 Figure 3.4 The energy incident on the material under test is partially reflected at the first material interface and the rest of the energy is transmitted through the material. ...... 59 Figure 3.5 Schematic diagram of the internal components of the network analyzer. ................... 60 Figure 3.6 Measurement set-up for measurement in X band. The network analyzer, coaxial cables, waveguide flanges and adapters are shown. ................................................... 61 Figure 3.7 Standard waveguides used for each band are shown. The largest waveguide is for R band and the smallest one is for Ka band. ........................................................ 62 Figure 3.8 Electromagnetic waves transmitting through and reflected from a sample in a transmission line. ........................................................................................................ 63 Figure 4.1 Empty sample holders used for the measurement of G, C and Ku frequency bands. .......................................................................................................................... 76 Figure 4.2 Variation of permeability and permittivity of barium hexaferrite nano-powder with frequency. The average values of the imaginary permittivity and permeability are 0.0516 and 0.0706, respectively. ..................................................... 81 Figure 4.3 Variation of front-end impedance of barium hexaferrite nano-powder with frequency ............................................................................................................ 83 Figure 4.4 Variation of reflectance of 2cm thick sample of barium hexaferrite nanopowder with frequency. .............................................................................................. 84 Figure 4.5 Variations of permittivity and permeability of strontium hexaferrite nanopowder with frequency. .............................................................................................. 85 7 Figure 4.6 Variation of front-end impedance of strontium hexaferrite nano-powder with frequency..................................................................................................................... 86 Figure 4.7 Variation of reflectance of 2cm thick sample of barium hexaferrite nanopowder with frequency .............................................................................................. 87 Figure 4.8 Material properties of Barium ferrite micro-powders are shown. The average value of real and imaginary parts of permittivity is observed to be 3.065 and 0.0559 whereas real and imaginary parts of permeability are 1.1069 and 0.0536, respectively. ................................................................................................... 88 Figure 4.9 Variations of permittivity and permeability of Copper Iron Oxide nanopowder with frequency. ........................................................................................................... 90 Figure 4.10 Variation of front-end impedance of Copper Iron Oxide nano-powder with frequency.................................................................................................................. 91 Figure 4.11 Variation of reflectance of 2 cm thick sample of Copper Iron oide nanopowder with frequency ............................................................................................ 91 Figure 4.12 Variation of permittivity and permeability of Copper Iron Oxide nanopowder with frequency ............................................................................................ 92 Figure 4.13 Variation of front-end impedance of Copper Zinc Iron Oxide nanopowder with frequency ............................................................................................ 93 Figure 4.14 Variation of reflectance of 2 cm thick sample of Copper Iron oxide nanopowder with frequency ............................................................................................ 93 Figure 4.15 Variation of permittivity and permeability of Nickel Zinc Iron Oxide nanopowder with frequency bands .................................................................................. 94 Figure 4.16 Variation of front-end impedance of Copper Zinc Iron Oxide nano-powder 8 with frequency ......................................................................................................... 95 Figure 4.17 Variations of reflectance of 2 cm thick sample of Copper Iron oxide nanopowder with frequency ............................................................................................ 96 Figure 4.18 (a) Variations of permittivity and permeability of LSCF nanopowder with frequency................................................................................................................. 98 Figure 4.18 (b) Variation of permittivity and permeability of LSM nanopowder with frequency.................................................................................................................. 99 Figure 4.18 (c) Variation of permittivity and permeability of YSZ nanopowder with frequency. ............................................................................................................ 99 Figure 4.19 (a) Variations of impedance of YSZ nanopowder with frequency.......................... 100 Figure 4.19 (b) Variations of impedance of LSM nanopowder with frequency ......................... 101 Figure 4.19 (c) Variations of impedance of LSCF nanopowder with frequency........................ 101 Figure 5.1 Horn antennas used for transmitting the incident signal at Q, V and W bands. ........ 106 Figure 5.2 Experimental set-up for measurement at millimeter wave frequencies .................... 107 Figure 5.3 Experimental set-up for millimeter wave measurements. ........................................ 108 Figure 5.4 Specially designed sample holders for BWO based spectrometer. The thickness of the sample holder used here is 12mm. .................................................. 109 Figure 5.5 Transmitance variations of micro- and nano-size strontium ferrite powders in the millimeter wave range..................................................................................... 113 Figure 5.6 Real (a) and imaginary (b) parts of permeability for Strontium nano-ferrite powder measured in the millimeter wave frequency range. ..................................... 116 Figure 5.7 Real (a) and imaginary (b) parts of permeability for Strontium micro-ferrite powder measured in the millimeter wave frequency range. ..................................... 116 9 Figure 5.8 Real (a) and imaginary (b) parts of permeability for Barium nano-ferrite powder measured in the millimeter wave frequency range. ..................................... 118 Figure 5.9 Real (a) and imaginary (b) parts of permeability for Barium micro-ferrite powder measured in the millimeter wave frequency range. .................................. 119 Fig. 6.1 The transmittance spectrum for micro- and nano-size strontium ferrite powders measured using the BWO technique at Q, V and W bands. ........................................ 124 Figure 6.2 Transmittance spectrum recorded for two slightly different densities of strontium hexaferrite ............................................................................................... 126 Figure 6.3 X-ray diffraction spectra of (a) strontium hexaferrite and (b) barium hexaferrite. ................................................................................................................ 128 Figure 6.4 Scanning electron micrographs of barium hexaferrite nano-powder for different resolutions can be seen. The magnification level for the images shown here are (a) 5,000, (b) 10,000, (c) 20,000, (d) 40,000. The particle size is much smaller than the 1 µm mark indicated in the third inset. ...................... 132 Figure 6.5 The micro-size powder of barium hexaferrite consisted of agglomerates in the size range from 3 to 15 µm. It can be seen in inset C that the primary particle size lies between 0.5 to 1 µm. .................................................................... 135 Figure 6.6 Several lots of samples contained incomplete phases or impurities such as Fe2O3. X-ray studies of a few samples are shown here. ........................................... 147 Figure 6.7 Transmittance spectrum for different lots of barium hexaferrite samples. The hexaferrite phase ....................................................................................................... 149 was missing in lots 2 and 3. This can also be concluded from this data due to the missing resonance. .......................................................................................... 149 10 Figure 7.1. Network analyzer measurement set-up is shown with the sources of errors marked in the red boxes........................................................................................... 153 Figure 7.2 Block diagram of the waveguide set-up. Port1 and port 2 indicate the location of the network analyzer ports while the desired measurement port is at the interface of the material under test. .................................................... 153 Figure 7.3 Thru connection for calibration procedure. ............................................................... 155 Figure 7.4 Block diagram of the reflect connection. .................................................................. 157 Figure 7.5 Block diagram of the line connection. ....................................................................... 158 Figure 7.6 Experimental uncertainty and standard deviations for the transmittance spectra. ... 167 Figure 7.7 Experimental uncertainty and standard deviations for the reflectance spectra. ....... 168 11 List of Tables TABLE 3.1 Cut-off frequency for different modes inside the waveguide ................................... 56 TABLE 3.2 Cut-off frequency for higher order modes for X band .............................................. 57 TABLE 3.3 Properties of rectangular waveguides used in material characterization measurements ........................................................................................................... 62 TABLE 4.1 List of nano-size powders investigated ..................................................................... 75 TABLE 4.2 Dielectric properties of solid Teflon samples ........................................................... 78 TABLE 4.3 Dielectric and magnetic properties of hexaferrite nanopowder ................................ 87 TABLE 4.4 Dielectric ad magnetic properties of spinel ferrites .................................................. 96 TABLE 4.5 Dielectric and magnetic properties of rare earth perovskite nanopowders ............. 100 TABLE 5.1 Investigated millimeter wave frequency bands ....................................................... 106 TABLE 5.2 Best fit value of permittivity for hexaferrite samples ............................................. 114 TABLE 5.3 Resonance frequency of ferrite powders at different sizes ..................................... 120 TABLE 6.1 Electro-Magnetic Properties Measured At Microwave Frequencies ...................... 122 TABLE 6.2 Electro-Magnetic Properties Measured At Millimeter wave Frequencies .............. 123 TABLE 6.3 Particle size determination of barium and strontium ferrite ................................... 129 TABLE 6.4 Calculated values of resonance frequencies of Barium and Strontium hexaferrite nanopowders without demagnetization effects. ..................................................... 143 TABLE 6.5 Calculation of demagnetization factor for different particle shapes in barium hexaferrite nano-powder....................................................................................... 144 TABLE 6.6 Calculated value of resonance requency in the millimeter wave range .................. 145 TABLE 6.7 XRD study of micro and nano hexaferrite powders ............................................... 148 TABLE 7.1 Standard Deviation in the Derived Parameter Values for barium hexaferrite ........ 159 12 TABLE 7.2 Standard deviation in the measurement of s-parameters at each frequency band for barium hexaferrite nanopowder ............................................................................ 162 TABLE 7.3 Average error percentage in dielectric properties of solid and powdered samples 164 TABLE 7.4 Average error percentage in dielectric properties of solid and powdered samples 165 TABLE 7.5 Results of repeated reference scans at each frequency band .................................. 166 TABLE 7.6 Standard deviation in the measured transmittance and reflectance spectrum for millimeter wave frequency bands ............................................................................... 168 13 Chapter 1 Introduction 1.1 Background With rapid developments occurring in the field of wireless communication and high frequency devices, the use of magnetic and dielectric materials finds wider applicability, not necessarily restricted to military and stealth applications only. The ever increasing growth of commercial applications in the higher frequency range of the radio wave spectrum has augmented the need to find materials that can support these applications. This radio frequency (RF) range is viewed as an important area of development due to broader bandwidths and reduction in device size at these frequencies. In addition, the high frequency range is of great interest due to lower propagation losses and reduced fabrication costs of the devices at these frequencies [1]. In the electromagnetic spectrum, the radio frequency spectrum covers frequencies from a few megahertz to several hundreds of gigahertz. The higher frequency range of this spectrum can be further divided into the microwave and millimeter wave frequency bands. The term microwave refers to the frequency region from 300 MHz to 30 GHz. This corresponds to the wavelengths from 1 meter to 1 centimeter. Numerous applications in this frequency range 14 include, for example, cell phones, air traffic control radars and global positioning systems, etc. The higher end of the radio frequency region from 30 GHz to 300 GHz is often referred to as millimeter waves since these frequencies correspond to wavelengths in the millimeter range. This frequency range supports a wide variety of applications such as bio-medical applications, remote sensing and as absorbers for high frequency devices [1-2]. During the last four decades, the smallest feature of a transistor has shrunk from 10 um down to 30 nm. Rapid developments in the semiconductor industry has led to the shrinking of device size which in turn has triggered the development of material preparation techniques in the micrometer to nanometer domains as well as material characterization techniques for these particle sizes and frequency domains. As an example, consider the development of electromagnetic absorbers. Radar absorbing materials have been in use for a long time now to reduce the radar cross section (RCS) in military applications. The first electromagnetic wave absorber came into light in the mid 1930s to improve the front to back ratio of a 4GHz antenna [3]. But nowadays there is broader area of applications for absorbing materials. The extensive use of wireless technology in commercial products has made electromagnetic interference a serious concern for the designers. Absorbing materials are used to eliminate the unwanted electromagnetic leakages and to reduce interference among wireless devices. Since many different types of wireless devices are being used currently, application specific absorbers are desired. Depending on the application, the absorbers can be extremely light weight, narrowband or wideband and thin or multi-layered. As a result, several types of absorbers have been developed over the years [4]. The design of absorbers not only requires the ability to fabricate special materials but also the ability to study their constitutive electromagnetic properties and 15 tailor them to provide custom solutions for various applications [5]. This is true for other applications of electromagnetic materials as well. Several materials with desirable magnetic and dielectric properties have been developed for the high frequency applications. The class of materials consisting of oxides and semiconductors doped with transition metal elements or rare earth metals have been used for the design of devices in the microwave and millimeter wave frequency ranges. Oxides of iron have substantial technological value largely because they possess the combined properties of a magnetic material and an electric insulator. Materials formed with iron (III) oxide, Fe2O3, as the principal constituent are referred to as ferrites. The basic formula for ferrites was identified by Hilppert in 1909 as MeO.Fe2O3, where Me is a divalent metal ion [6]. These are compounds of metals with iron oxide. However, in contrast to metals, ferrites are non-conducting oxides which allow total penetration of electromagnetic fields. Ferrites were initially used as magnetic cores. Over the years, ferrites have proved to be versatile magnetic materials since they are relatively inexpensive, stable and have a wide range of applications [6]. Ferrite materials have been under intense research for several years due to their favorable electromagnetic properties [7]. They are in use in many industries such as automobile, telecommunication, data processing, electronics and instrumentation [8]. This can be attributed to suitable properties of ferrites such as high saturation magnetization and electrical resistivity, good chemical stability and low electrical losses. Ferrites have been used in information storage media such as magnetic tapes and floppy disks, in transformer cores and high frequency circuits [9]. More recently, ferrites are also used in millimeter wave ICs and power handling devices. Lower RF loss makes these materials useful in the design of microwave devices such as isolators and phase shifters. Resonance isolators can require up to 30-35 kOe magnetic fields, which require more space and increased cost. By 16 utilizing the high internal anisotropy of hexaferrites, isolation levels of up to 20 dB can be achieved by using external field as small as 500 Oe [10]. Ferrites are also used as inductive components in low noise amplifiers, voltage-controlled oscillators and impedance matching networks [11]. The performance of these materials in their bulk form is limited upto a few megahertz due to their higher electrical conductivity and domain wall resonance [12]. However, the recent technological advances in electronics industry demand ever more compact devices for work at higher frequencies [14-15]. One way to solve this problem is by synthesizing the ferrite particles in the nanometric scale. When the size of the magnetic particle is smaller than the critical size, the particle is in a single domain state, thus avoiding domain wall resonances. Such materials can work at higher frequencies. The recent developments in fabrication techniques have opened the possibility to manufacture ferrites in nano-scale domain. This has given way to new research areas and fields of application for the ferrites. The term, nano, is commonly used to refer to one-billionth (10-9) of a unit. In the context of nanomaterials, this refers to materials that are composed of particles with at least one dimension in the nanoscale range. Dimensions up to 100 nm, sometimes even 1000 nm, fall in the nanometer range [16]. Nanoferrites are ferrite compounds consisting of particles with the smallest dimension in the nanoscale region. These materials are of great interest since their dimensions approach that of an individual atom or molecule. As a result, the properties of nanoferrites are significantly different from those of the materials in bulk [17]. While bulk ferrites still remain important magnetic materials, the nanomaterials have emerged as strong candidates for electronics as well as medical applications [18, 19]. These are discussed in the next section. 17 1.2 Motivation for the study of nanoferrites In the past, the applications of magnetic and dielectric materials in permanent magnets for frequency tuning of microwave devices or in electromagnetic absorbers employed materials in the bulk form. However, as the device size is shrinking, smaller magnets and absorbers are needed. Study of nanoparticles is currently an area of intense scientific research not only to support electronic applications with modern IC revolution but also to help develop potential applications in the field of biomedical engineering. In the context of biomedical engineering nanoparticles play the role of a bridge between bulk materials and atomic structures. The properties of a material change as its physical size shrinks, due to the increased percentage of atoms on the surface of the material. For a given amount of material, the surface area compared to the volume increases as the particle size decreases. Thus the proportion of constituent atoms on or near the surface increases. For instance, consider a microparticle with a radius of 30 µm and surface area of 0.01 mm2. The same mass of this material in nanoparticulate form, with each particle having a radius of 30 nm will consist of 1 billion nanoparticles, with a total surface area of 11.3 mm2. Thus compared to microparticles, nanoparticles have a very large surface area and higher number of particles per unit mass [16]. This feature is important because many reactions occur on the surfaces of materials. The small particle form of a material may have properties quite different from its properties in bulk form. For example, zinc oxide particles have been found to have superior UV blocking properties compared to the bulk substitute. This is one of the reasons why zinc oxide particles are often used in the preparation of sunscreen lotions [20]. Gold nanoparticles melt at much lower temperature (~ 3000C) than gold slabs (10640C) [21]. Absorption of solar radiation in photovoltaic cells is much higher in nanoparticles than it is in thin films of continuous sheets of a bulk material because of the enhanced effective surface 18 area in the former case. Particles in smaller size domain extend the range of applications of their bulk counterparts. Microwave ferrite devices are used to control energy propagation by a static or switchable dc magnetic field [9]. Another application of ferrites is in frequency tuning of electronic components, which has traditionally required external magnets. However, at high frequencies, the magnetic bias required increases the size and cost of the components. This can be avoided by using self-biased hexaferrites that have high effective internal magnetic anisotropy that can provide the permanent magnetic bias [22], thus eliminating the need for bulky external magnets. Electromagnetic interference (EMI) suppression is needed for radar targets and in electronic devices that are densely packed. Factors such as thickness, weight, mechanical strength and environmental conditions limit the choice of available absorbing materials. As the clock speeds of electronic devices approach microwave frequencies, it has become essential to study the high frequency properties of the materials used in electronics devices and components. Reduction in component size would result in faster speed and higher density of logic on processors and circuit boards. Further, due to the significant increase in the density of components in electronic systems such as high-speed digital interfaces in computers, digital cameras, scanners, and so forth electromagnetic interference becomes a serious issue. Special materials are used in the design of circuits and packaging applications to ensure electromagnetic compatibility in the smaller designs [23]. For the case of narrow-band absorbers, an optimum solution would require a compromise between absorber thickness and absorption characteristics. Material parameters can be optimized once the intrinsic material properties are known. In the case of wide band absorbers the number of parameters increases and optimization becomes a 19 complex task. Such a design can be greatly simplified by using electromagnetic simulation tools. But the accuracy of the results from such simulations is determined by the accuracy with which the material properties are known. In the development of computer aided design circuit simulation programs, both magnitude and phase data are required for accurate models. Therefore if the exact dependence of material properties on frequency is known, application specific absorbing materials can be designed. The intrinsic material properties have been used to study the microwave power absorption of ferrites [24] and magnetic loss in microwave heating [25]. Microwave remote sensing is another field where material characterization plays an important role. In remote sensing, materials are identified by studying the reflection and scattering of microwave signals by the target specimens [26], which in turn depend on the constitutive properties of the target material. Thus by characterizing materials and creating a database, identification of materials by remote sensing can be done more efficiently. Nanomaterials are also proving useful in the field of biomedical engineering. Due to their small size, nanopoarticles are valuable in investigating cells since their size is comparable to the size of important biological constituents of the body. For instance, viruses are 20-400nm, cell 10100 um, proteins 5-50 nm, antibodies 10 nm, bacteria 100nm-10um and red blood cells are 10 um. The small size allows the nanoparticles to penetrate physiological barriers and travel within the circulatory system to perform functions such as the magnetic resonance enhancement, iron delivery for the production of RBCs and drug delivery to improve the availability of seruminsoluble drugs. Nanomaterials with particle size upto 50nm can travel the circulatory system of the body and thus provide drugs to desired cells. These nanoparticles can be manipulated by an external magnetic field. This means that the particles can be guided using an external field for targeted drug delivery inside the body. They can also be coated with biological molecules to bind 20 them to a biological entity [16]. They can also resonantly respond to time varying magnetic field. Thus energy can be transferred from external field to the biological systems by tagging them with magnetic nanoparticles. Magnetic nanoparticles have recently been used to treat bone diseases by using surface modified magnetic nanoparticles [27]. These are also being used in cancer treatment. Unlike the conventional cancer treatment methods, the affected cells can be targeted exclusively and the healthy cells close to an infected one can be saved by using magnetic nanoparticles. Magnetic nanoparticles can also be used in hyperthermia treatment. Due to small size, the particles can produce a more localized and effective solution. Ferrite nanoparticles have wide range of sizes, diversity and chemical stability as compared to metal nanoparticles [28]. The nanoparticles have beneficial properties such as magnetic guidance and induction heating in AC magnetic fields. Another novel application of nanoferrites is in magnetic resonance imaging. In MRI, the person under examination is exposed to a RF pulse in the presence of an external magnetic field. The resulting changes in the spin of the protons in water molecules are used to construct a three dimensional image of the subject. Use of the magnetic nanoparticles in biological systems can enhance the detection sensitivity [29]. Nanomaterial tubes are ideal probe tips for scanning microscopy due to their small diameter which maximizes the resolution and high aspect ratio [30]. With further improvement in imaging technology, magnetic nanoparticles exhibiting strong resonances can be used to perform localized imaging. The scope of applications for nanopowders has driven the need for extensive research in this field. A thorough review of the applications of nano-ferrites in RF and microwave applications has been presented [31]. In order to use materials in applications listed above and beyond, precise characterization of materials is a necessary requirement. Thus the knowledge of intrinsic 21 material properties is essential to understand and predict the behavior of magnetic and dielectric materials and thus utilize them to their full potential in electromagnetic applications. 1.3 Problem Statement Over the last 50 years, many devices have been developed across the microwave spectrum. However, many challenges remain to be addressed to meet the demands for miniaturization, broader bandwidths, higher operating frequencies and reduced costs [9]. From the discussion in the previous section it is evident that the knowledge of material properties is indispensable for the development of novel applications in the fields of electronic and biomedical engineering. Characterization of constitutive material properties allows scientists to understand, analyze and modify the behavior of the materials. This also provides the flexibility to tailor the material properties according to the application. However, higher frequencies of operation and smaller sizes of the samples make characterization challenging. The measurement methodology is limited by the size of components needed to make measurements at such high frequencies and also by the sensitivity of the measurement set-up to interference from other sources. Any additional length of cables or connectors adds significant delay and phase change at high frequencies. The properties of materials depend on the frequency of the application, size and composition of the sample. Controlled growth of powdered ferrites is difficult and as a result the final size and shape of the particles may be different from what was intended. Physical properties of nanoparticles are influenced significantly by the manufacturing technique [32]. The preparation conditions such as chemical composition, sintering temperature and amount of substitutions have been known to affect the physical properties of the fabricated material. 22 Therefore, in materials research and engineering, microwave techniques for the characterization of material properties can be used as nondestructive testing tools to check if the final products match the specifications that they were designed for. Distribution of particle sizes and inter particle spacing affect the magnetic properties. Therefore, it is important to know the effect of particle size on the material properties. In order to do so, it is necessary to collect data for nanopowders of different sizes and analyze the relationship between their size, composition, morphology and their electromagnetic responses. One of the critical challenges faced currently by researchers in the field of nanotechnology is the lack of instruments to characterize and manipulate the materials prepared at the nanometer level. Needless to say that characterization of nanopowders requires extreme sensitivity and accuracy. Furthermore, the particles in the powdered samples tend to form aggregates. These aggregates can vary in size from a few nanometers to micrometer. It may not always be possible to avoid aggregate formation. Therefore it is essential to check the state of the sample during measurement and perform controlled measurements. 1.4 Thesis Objective Constitutive material properties of powdered ferrite samples are studied in this work. Materials have been studied in solid form in the past. However, here the samples are studied as pure powders, without the need to form solid samples by diluting them with epoxy or other forms of conductive binder. Two different measurement techniques have been applied to characterize the samples in the broad frequency range from 1.7 GHz to 120 GHz. For microwave measurements, covering frequencies between 1.7 GHz to 40 GHz, a transmission/reflection based measurement technique has been used to obtain the intrinsic material properties. A vector network analyzer is 23 employed to measure the s-parameters of the material under study. Rectangular waveguides are used to connect the sample to the measurement ports of the network analyzer. The measured data is used to calculate the complex dielectric permittivity and magnetic permeability of the samples. For the millimeter wave measurements, a quasi-optical high frequency spectrometer is used. Backward wave oscillators are used as the high frequency power sources. The signal propagates through two channels. The optical path, consisting of horn antennas and lenses to guide the Gaussian beam, is used for the measurement and the other channel made up of high frequency components such as directional couplers and attenuators acts as the reference path. Power is divided between these two arms by using a waveguide-based directional coupler. The permittivity and permeability values are derived from the transmission data of the sample using curve fitting functions. A thorough error analysis has been attempted to identify the possible sources of errors. The samples investigated in this work include M-type hexaferrites, spinels and perovskite ferrites. Hexaferrite samples with identical material composition but different particle sizes are used. The study revealed a dependence of material properties of hexagonal ferrites on the morphology of the particles in the powdered sample. The morphology of the samples was studied using scanning electron micrographs (SEM) and their compositions were verified using X-ray diffraction. The possible reasons for the difference in behavior of nano-powder and micropowder samples are suggested. A calculation model has been defined to determine the resonance frequency for such samples. The proposed model takes into account the structural properties of the particles in the sample. The results indicate that it is possible to use the hexaferrites as high frequency tunable absorbers. 24 1.5 Thesis Organization The first part of the thesis is an introduction to ferrite materials and the measurement techniques employed for measuring dielectric and magnetic properties at the microwave and millimeter wave frequencies. The measurement results are presented in the later sections of the thesis. The basic principles needed to understand the properties of ferrites are discussed in chapter 2. The measurement technique used in the microwave measurements and the modified algorithm to interpret the data are presented in chapter 3. The limitations of the existing material characterization techniques are also discussed here. The results for microwave and millimeter wave measurements of ferrite samples are analyzed in chapters 4 and 5, respectively. The dependence of material properties on the size of the particles is discussed in chapter 6. Chapter 7 provides an analysis of the possible errors in the results. The relevance and future scope of this work is discussed in the conclusion. 25 Chapter 2 Theoretical Background Extensive use of the iron based compounds including the ferrites in traditional and innovative technologies has been mentioned in chapter 1. Magnetically anisotropic materials such as the hexagonal ferrites hold special promise to realize these and other applications. Micro- and nanosize particles of these materials further extend the scope of such applications, particularly so in the microwave and millimeter spectral regions. In this chapter, a brief introduction to the different types of magnetic materials and their interaction with the external electromagnetic fields is provided. The role of permeability and permittivity of these materials in this process is crucial. Their suitability or otherwise to various applications critically depend on these material properties. 2.1 Origin of magnetism in materials In order to comprehend the electromagnetic behavior of a material, it is important to understand how the electromagnetic fields interact with its fundamental units, that is, the electrons present in the atoms (molecules) and the associated magnetic moment of the atoms (molecules). An 26 electron is a charged body that exerts a force on other charged bodies. A stationary charge is considered a source of electric field and the charges present in this field experience a force. On the other hand, a moving charge (current) creates a magnetic field. Inside a material, the atoms consist of electrons that orbit around the nucleus, generating current loops and thus the atom has a magnetic dipole moment associated with it. This magnetic moment is along its axis of rotation. Additionally, the electron also spins around its own axis. The net magnetic moment of an atom is the vector sum of the magnetic moments of each electron. The magnetic properties of a material are mainly determined by these magnetic moments which result from the orbiting and spinning of electrons in the atom. Net magnetic moment present in unit volume of the material defines its magnetization. In the presence of an external magnetic field, the force of the field exerts a torque that tends to align these dipoles. The magnetic behavior of a material in the presence of an external field can be understood by studying the interaction between the magnetization of the material and the external field. Materials are classified based on the response of their magnetic dipoles to an external field. The different types of magnetic materials are briefly described here. 2.1.1 Diamagnetic materials In the absence of an external field, diamagnetic materials do not have a net magnetic moment since the electrons in such a material are paired up with anti-parallel spins. When an external field is applied, the orbits of the electron change such that the net induced magnetic moment is in a direction opposite to the direction of the applied magnetic field. The magnitude of this induced magnetic moment is extremely small. 27 2.1.2 Paramagnetic materials Some materials possess an unpaired electron spin in the atom and due to the incomplete cancelation of the electron spins the atoms possess a net magnetic moment. However, in the absence of an external magnetic field, the atomic moments are randomly oriented and the material does not exhibit any magnetization. In the presence of an external field, the magnetic moments get aligned along the direction of the external field. As soon as the applied field is removed, the alignment and thus the magnetization is lost. The behavior of the dipoles in diamagnetic and paramagnetic materials, with and without an external field is shown in figure 2.1. On the left side, the behavior of the dipoles is shown in the absence of external field and on the right side an external field, field direction indicated by the arrow, is applied. In case of figure 2.1 (a) diamagnetic materials, the atoms do not possess any net moment because all the spins are paired in opposite directions. In the presence of an external field, the induced dipoles point opposite to the applied field and the material possesses a weak net magnetization. In case of figure 2.1 (b) paramagnetic materials the atoms possess a net dipole moment but these are randomly oriented in the absence of external field. (a) Diamagnetic material 28 (b) Paramagnetic material Figure 2.1 Dipole orientation in (a) diamagnetic and (b) paramagnetic materials with and without an external field. 2.1.3 Ferromagnetic materials Both diamagnetic and paramagnetic materials are considered non-magnetic materials since they do not possess any net magnetization in the absence of an external field. There are certain metallic materials, like transition elements, which have permanent magnetic moment and exhibit magnetism even without any external field. In a ferromagnetic material the permanent magnetic moments result from unbalanced electron spins in the atom. The coupling interaction, commonly called the exchange interaction among atoms, tends to align the magnetic dipoles in neighboring atoms along the same direction. In the process a ferromagnetic material attains what is called the spontaneous magnetization, i.e., the material gets magnetized without the help of an external magnetic field. Therefore these materials possess net magnetic moment even in the absence of an external field. This phenomenon is shown in figure 2.2 (a). Examples of ferromagnetic materials include iron, cobalt and nickel. 29 2.1.4 Anti-ferromagnetic materials There are certain materials other than ferromagnetic materials which show different kind of coupling among the magnetic moments in adjacent atoms. Unlike ferromagnetic materials the neighboring dipoles tend to align in an antiparallel manner. If the magnetic dipoles are arranged such that half of the dipoles align themselves in the direction opposite to that of the rest of the dipoles, then they cancel out each other’s effect and there is no net magnetic moment in the material. It should be noted that the dipoles are assumed to be of the same strength in this case. Such a material is called anti-ferromagnetic material. Examples of anti-ferromagnetic material are chromium and manganese. Neel proposed the two sublattice model to explain antiferromagnetism. This is discussed in section 2.2. 2.1.5 Ferrimagnetic materials Ferrimagnetic materials have similar behavior as anti-ferromagnetic materials except that the neighboring dipoles in these materials have unequal strengths and hence they do not completely cancel each other’s effect. Thus the materials possess a net magnetization. These materials are sometimes also called ferrites. The typical examples of ferrites are magnetite (Fe3O4) and barium ferrite (BaFe12O19). Magnetite is a good example to understand the unequal moments. The chemical formula for Fe3O4 can be re-written as, Fe2+O2- (Fe3+)2 (O2-)3. Thus Fe exists in both Fe2+ and Fe3+ states. The net spin magnetic moment for each of these ions is different and they are present in a 1:2 ratio in the compound. This results in a net magnetic moment in magnetite. This example is discussed in more detail in section 2.2 30 (a) (b) (c) Figure 2.2 (a) Atomic magnetic dipoles align in parallel directions in a ferromagnetic material, (b) adjacent dipoles align in opposite directions with no net dipole moment in anti-ferromagnetic materials, (c) in ferrimagnetic materials, adjacent dipoles align in opposite directions but with a net dipole moment. Figure 2.2 shows the arrangement of dipoles in the three categories of magnetic materials described in section 1.1.3 to 1.1.5. However, the arrangement of dipoles in various magnetic materials can be more complicated than what is shown in this figure. The dipoles may not be arranged in the same direction over the entire extent of the material. The mutual spin alignment (parallel or anti-parallel) may exist over the entire volume of the material or over certain regions of the crystal. In general, at a macroscopic level, a material is composed of several regions of aligned dipoles but the alignment direction can vary from one region to the other. Each small volume region consisting of mutually aligned dipoles is called a domain. An example of a material containing several domains is shown in figure 2.3. The boundaries of the domains are commonly called domain walls. Although these are just shown as lines in figure 2.3, it should be realized that these basically represent areas along which the dipole orientation direction changes gradually. 31 Figure 2.3 Dipoles are aligned in certain regions of the material called domains. A material may consist of several domains, oriented in mutually random directions. Thus a material can have several domains and each domain can have a different orientation of the magnetic dipoles and hence magnetization. For a polycrystalline material, each grain may consist of more than a single domain. The net magnetic field for such a material is the vector sum of the magnetizations of all the domains. Of course, larger domain volumes would have a more significant contribution towards the net magnetization. In case of single domain, all the dipoles are aligned. Thus materials with single domain would have a higher magnetization as compared to polycrystalline materials consisting of several randomly oriented domains. The value of magnetization when all the magnetic dipoles present in the material are aligned with the external field is referred to as the saturation magnetization. Another important feature of polycrystalline materials is that they may have preferred orientation directions for the grains. Even for a single crystal ferromagnetic material, the magnetization depends on its crystallographic orientation relative to the direction of the applied magnetic field. It is easier to achieve higher values of magnetization if the field is applied along certain preferred directions. For instance, the effect of applied field direction on the 32 magnetization has been studied for nickel and cobalt single crystals [33-34]. It was observed that in these materials there is one crystallographic direction in which magnetization is the easiest. This direction is termed as the easy magnetization axis. If the field is applied along this direction, then very small value of magnetic field is required to achieve saturation magnetization. This is often the lowest energy state for the dipoles. The dipoles in a domain also tend to align along the easy axis. The reason for a material to form multiple domains is to achieve a state of minimum internal energy. The size of a domain depends on the overall balance of energy in the material. In a single domain ferromagnetic material, the magnetization does not vary across the material. The size range over which a ferromagnet exists as a single domain is generally quite narrow. There is a critical radius for a material such that for particle or grain size less than the critical radius, the ferromagnetic particles stay uniformly magnetized as single domain [35]. Ferromagnets tend to be in a state of uniform magnetization when the diameter of the particles is between 10 nm and 100 nm [36]. The dependence of the magnetic behavior on crystallographic orientation is termed as magnetic anisotropy. The origin of this anisotropy goes back to the spin-orbit interaction at the atomic level. The distribution of the orbits of the electrons in a transition metal is anisotropic, which in turn affects the distribution of spins and hence magnetization via the spin-orbit interaction. Magnetic anisotropy follows the crystal symmetry. The advantage of high magnetic anisotropy is that such materials do not easily demagnetize. Such materials find use as permanent magnets. On the other hand, materials with low magnetic anisotropy can easily change their magnetization and are used to make inductors and transformer cores. 33 2.2 Neel’s model of ferrimagnetism L. Neel in 1948 proposed the existence of two magnetic sublattices in an antiferromagnetic substance. The dipoles in each sublattice point in the same direction but the two sublattices have magnetizations in exactly opposite directions. These dipolar orientations are caused by what is called the superexchange interaction. Unlike in a ferromagnetic substance where adjacent dipoles are in close neighborhood (with the resulting tendency to align parallel to each other), the dipoles in an antiferromagnetic substance are rather far apart. The oxygen anions with zero magnetic dipole moments lie between neighboring magnetic cations. It is the super exchange interaction among the magnetic cations mediated by the intervening non-magnetic oxygen anions which lead to dipolar alignment in each sublattice. The interaction among the dipoles belonging to different sublattices is stronger than the interaction among the dipoles belonging to the same sublattice so that the two sublattices can align in opposite directions. The orientation of the dipoles in each sublattice competes with the disorientational tendency due to the thermal energy of the overall lattice. The thermal energy increases with increasing temperature. At a certain critical temperature called Neel temperature, individual sublattices get demagnetized and the material is no longer antiferromagnetic and becomes paramagnetic. Consequently the material is anti-erromagnetic below the Neel temperature and paramagnetic above it. In an antiferromagnetic material, the dipolar moments in the two sublattices are of equal strength but oppositely oriented, leading to zero net magnetization. In ferrimagnetic materials (ferrites), the dipoles on the two sublattices may have unequal strengths but oppositely oriented. Thus the net magnetization in a ferromagnetic substance is small but not zero. However, not all ferrimagnetic materials obey this scheme. It may happen, as in the case of magnetite (Fe 3O4), 34 that interactions within and between the sublattices may be comparable in strength but all cations may not occupy identical crystallographic sites in the unit cell. For instance, for magnetites there are 16 Fe3+ cations and 8 Fe2+ cations in the unit cell. The unit cell has two kinds of sites. Site A has four oxygen anions near neighbors in a tetrahederal orientation and site B has eight oxygen anions near neighbors in octahederal sites. There are 8 A sites and 16 B sites in the unit cell. In normal spinel structure, the divalent cations occupy all 8 A sites and trivalent cations occupy all 16 B sites. But in magnetite (FeO.Fe2O3) with inverted spinel structure, 8 trivalent cations occupy all 8 A sites and the remaining 8 trivalent cations and all 8 divalent cations occupy the 16 B sites. Sites A and B belong to different sublattices. All dipoles on A site are oriented oppositely to dipoles on the B sites. The trivalent cations in the two sublattices yield zero magnetic moment because of their oppositely oriented dipoles. The net reduced magnetization in magnetite is due to the 8 divalent cations in the unit cell. 2.3 Interaction between electromagnetic fields and materials A TEM electromagnetic wave is composed of perpendicular electric and magnetic fields. The time-varying electric and magnetic fields can mutually sustain each other. The direction of propagation of the wave is perpendicular to the direction of either field. Maxwell’s equations describe the propagation of the electromagnetic wave in a material. During propagation, the electric and magnetic fields associated with the wave interact with the electric and magnetic constituents of the material. The electric and magnetic phenomena have been known for a long time but the connection between the two was established much later. James C. Maxwell was the first to formalize the missing link between the electrical and magnetic effects. He gave a 35 mathematical formulation known as Maxwell’s equations which describe the interrelated behavior of electric and magnetic fields inside a medium. Maxwell’s equations have the form, ⃗ (2.1) ⃗ ⃗ ⃗ ⃗ ⃗ where D is the electric displacement vector, E is the electric field strength, B is the magnetic flux density, H is the magnetic field strength, and J is the current density. These are all vector quantities, ρ is the charge density. These quantities are related by the following constituting relations, ⃗ ⃗ ⃗ ⃗ ⃗ Here, σ is the conductivity of the material, and ε and µ are the permittivity and permeability of the material. Permittivity and permeability are complex quantities and are explained in more detail in the following section. These equations indicate that the response of a material to electromagnetic fields is determined essentially by three constitutive parameters, namely, permittivity, permeability and conductivity. These parameters also determine the spatial extent to which the electromagnetic field can penetrate into the material at a given frequency. 36 Thus the knowledge of these parameters is crucial to develop and utilize these materials for specific applications at a given frequency. 2.3.1 Constitutive material properties As mentioned earlier permittivity and permeability are important material properties that describe the behavior of the material in the presence of an external field and can be used to predict the interaction of the material with electromagnetic waves. Being complex quantities, the permittivity and permeability can be expressed as, where ε’ and µ’ are the real parts of permittivity and permeability and ε” and µ” are the imaginary parts of permittivity and permeability, respectively. However, the terms most commonly used to define a material property are relative permittivity and relative permeability, defined as where ( ) is the relative permittivity (permeability), (permeability) of a medium and ( ) is the complex permittivity ( ) is the permittivity (permeability) of free space. Combining equations (2.10) and (2.11) gives 37 where we have used . The complex index of refraction N is defined as, ⁄ ⁄ Defining, And using equations (2.7) and (2.8) gives, ( ( ) ) where n is the real part of the complex index of refractions and is usually referred to as index of refraction or refractive index. K is called the absorption coefficient. It should be noted that the index of refraction n and absorption coefficient K depend on the dielectric (ε) and magnetic (µ) properties of the medium. Thus we have only two equations to derive the four unknowns. In the past, two approaches have been used to extract the permittivity and permeability values. The first method is used for dielectric samples. For such materials, the real part of permeability is taken as unity and the imaginary part is neglected (assuming no magnetic losses). Now there are only two unknowns and these can be easily evaluated using Eqs. (2.15) and (2.16). For more complicated materials, such as ferrites, the evaluation of material properties is not as direct. In such materials, the permeability values cannot be assumed to be unity since the permeability changes near the resonance frequency. The calculations are performed in two steps. First, the dielectric properties are determined at frequencies outside the ferromagnetic resonance region, assuming the real and imaginary part of permeability to be unity and zero, respectively. This assumption may not 38 always hold as for example for some of the rare earth ferrites discussed in chapter 4. However, ignoring such complications, we may use these values of the dielectric parameters to extract the values of permeability in the resonance region. These methods may suffice is some situations for estimating the material parameters but they are not very accurate. A more precise method to calculate permeability in the ferromagnetic resonance region is based on Schloemann’s equation [37], [ ⁄ ⁄ ] The values of Ms, and Ha are also evaluated from the curve fitting program by using the known values of real and imaginary parts of the permittivity. 2.3.2 Absorption of electromagnetic energy An electromagnetic wave interacts with a material in two ways, which are, energy storage and energy dissipation [38]. The real parts of these parameters determine the amount of energy from an external field that can be stored in the material. The permittivity is associated with the energy stored in terms of the electric field and permeability is associated with the energy stored in terms of the magnetic field. The imaginary parts of these parameters are associated with the loss of energy. They indicate how dissipative a material is to an external field. The conductivity of the material is, in fact, related to the imaginary part of permittivity. 39 where σ is the electric conductivity and ω is the angular frequency. Another important property of materials is the loss tangent. The dielectric loss tangent describes the energy dissipation of a dielectric material and is defined as the ratio of the imaginary part of permittivity to real part of permittivity. The loss tangent is an indicator of the extent of energy being absorbed by the medium. Thus for the medium to be an effective absorber, the loss tangent should be as large as possible. In a similar way, the magnetic loss tangent can be defined as, Now that all the important material parameters have been defined, consider an electromagnetic wave propagating inside a material. This is shown in figure 2.4. Figure 2.4 The electric and magnetic fields are perpendicular to each other and to the direction of wave propagation. Such a wave is incident on the front end of a material with intrinsic properties ε and µ. 40 T I R Figure 2.5 The incident wave (I) is partly reflected (R) at the air-material interface. The wave propagating inside the material attenuates depending in the absorption properties of the material. The remaining energy is transmitted out of the material (T). Figure 2.5 shows the side view of a material as a wave is incident on it. The incident wave (I) can be completely or partially reflected at the air-material interface, depending on the constitutive material properties. As the wave propagates through the material it loses some of its energy and finally the transmitted wave comes out of the material. Now the amount of signal coming out of the material depends on losses suffered in the material in addition to the relection losses at the interfaces. First consider the interaction of the wave with the material at the front end. The amount of energy reflected from the front surface of the material depends on the impedance seen by the incident wave. The reason for reflection of the wave is the impedance mismatch. The impedance of a material is defined as, √ The characteristic impedance of a material is defined in terms of its permittivity and permeability. The characteristic impedance of a medium can be re-written as, √ √ 41 where Z0 is the impedance of free space which can be calculated by using the values of free space permittivity and permeability, √ Thus in order to minimize the front end reflection the impedance of the material, as seen by the incident wave, should be as close to 377 ohm as possible. This impedance match and hence minimization of reflection at the air-material interface is the first condition that has to be satisfied in order to design an absorber. A good absorber would minimize the reflected energy and make sure that the entire energy incident at the boundary enters the material. The transmitted wave as it propagates in the medium continuously keeps storing the energy of the wave by establishing electric and magnetic fields within the medium. At the same time the energy is getting dissipated in the medium in the form of heat, which is desirable for absorbing materials. The material should be lossy enough to completely terminate the wave inside it so that nothing is transmitted. This is the second condition in the design of absorbers [39]. As discussed earlier, the loss properties of a material are captured in the permittivity and permeability of the material. For several applications, several layers of different materials are used to achieve strong broadband absorption. A two-layer structure is shown in figure 2.6 (a). The equivalent transmission line model used to analyze such structures is shown in figure 2.6 (b). Each layer in this structure is characterized by its characteristics impedance and represented as the circuit components of a transmission line. 42 1 Ei 2 Er 3 Z2 Et Z3 Zin d (a) (b) Figure 2.6 A multilayer structure formed by stacking two materials in medium 1, and (b) the equivalent transmission line model, where the impedance of each component is equal to the equivalent impedance seen at the interface of the corresponding layer. In this figure, Zin represents the input impedance seen into the transmission line which is the impedance seen by the incident wave. For multilayered structures, Zin is determined by taking all the successive layers into account. Using the transmission line analysis, the input impedance can be calculated as, where d is the thickness of the absorber and γ is the propagation constant of the wave given by, √ This is the effective impedance as seen by the incident wave at the interface between media 1 and 2. The overall power reflection coefficient is given by, 43 Multilayer absorbing material is often coated over a metallic body to reduce its backscatter. It therefore becomes essential to include a metal backing when analyzing these absorbers. In the above example if we consider medium 3 as metallic in nature, the power reflection coefficient at the interface of medium 1 and 2 becomes, Theoretically, the condition for zero reflection can be derived by substituting the right hand side of equation (2.27) with zero to get, In practice it is not possible to get a zero reflection off the front surface. In this work, front-end reflection less than -15 dB is considered satisfactory. 44 Chapter 3 Microwave Measurement Techniques 3.1 Introduction It was mentioned in the previous chapter that nanoferrites hold great potential for applications in a wide variety of fields. This is more so for devices working in the higher frequency range. However, the pre-requisite for all such developments is a detailed knowledge of the intrinsic properties of these materials. Unfortunately, this knowledge is lacking, particularly so in the higher frequency range. In fact most of the existing experimental techniques for the measurement of intrinsic properties of the promising materials have limitations. Furthermore, for designing materials for high frequency or wide bandwidth applications, it is necessary to measure material properties over the entire operational frequency range. The high performance commercial electromagnetic simulation tools also require accurate data of the material properties to replicate the behavior of the material and provide results that match the actual behavior of the material very closely. Needless to say that precise material characterization techniques are needed. The two properties of interest here are the permittivity and permeability of the samples under investigation. Complete information on the permittivity and permeability of a medium can 45 be obtained from the scattering parameters or s-parameters measured at the material boundaries. We have used a transmission-reflection (T/R) based waveguide technique that employs a vector network analyzer to measure the scattering parameters in the microwave frequency range from 2 GHz to 40GHz. Using this technique, one can generate both the reflection and transmission spectra when the frequency of an electromagnetic wave traveling through the material under study is changed in a continuous fashion. Based on the reflection and transmission spectra obtained from these measurements, the frequency interval over which the sample exhibits strong absorption can also be determined. The algorithm used to determine the permittivity and permeability from the measured data has been modified over the years to improve accuracy. Since the measurements are being carried out over a wide range of frequencies, the size of the measurement components, which include rectangular waveguides and sample holder, must be changed for each frequency band. Therefore multiple adapters and connectors have to be used. This necessitates frequent instrument calibration which adds to the error involved in the measurement process. The test methodology and calculation algorithms have to be modified to compensate for these errors and provide accurate data on the properties of the materials. The theoretical and experimental details of the technique employed in this study are discussed in this chapter. We begin by reviewing the existing techniques available for these measurement and their limitations. 3.2 Brief Review of Microwave Techniques Several microwave techniques have been introduced to characterize the electrical and magnetic properties of materials [40]. On a broad scale, these techniques can be divided into two categories, namely, resonant and non-resonant methods. Resonant methods are based on the fact 46 that the resonance frequency and Q-factor of a dielectric resonator depend on the permittivity and permeability values. The changes in the resonance frequency and Q-factor values with the introduction of the sample in the resonator are used to determine the properties of the sample [41]. The sample either forms the resonator or a part of it in the measurement circuit. Although resonant methods provide accurate values of the material properties, their application is limited by the fact that they can provide data only at a single frequency or at a few discrete frequency points. Non-resonant methods, on the other hand, are applied to measure material properties over a wider range of frequencies. The resonance method also restricts the sample size that can be used for measurement. The resonance method is one of the several rigorous techniques used in measuring magnetic properties of ferrites. Other proposed methods have been found to be inefficient due to complicated experimental configurations or redundant measurement repetitions. Other measurement techniques include free-space methods, open-ended coaxial probe techniques, cavity resonators, full body resonance techniques and transmission line techniques. Although these measurements are quite reliable, the minimum diameter requirement for the Gaussian beam in free space measurement limits the operational frequency range. The errors in free-space measurement are primarily due to diffraction effects at the edges of the sample and multiple reflections between the horn antennas [42]. The errors due to diffraction can be avoided by keeping the target material diameter at least three times the diameter of the Gaussian beam. The disadvantage of this is the large amount of sample needed at lower frequencies. This is especially undesirable for the measurement of nano-ferrites since the fabrication is a complex process and the samples are relatively more expensive. 47 The fundamental idea in non-resonant techniques is to let the incident wave propagate towards the material and measure the reflected and transmitted wave amplitudes. Different types of transmission lines can be used to direct the energy, such as, coaxial lines or metallic waveguides. Non resonant methods are based on either reflection measurements alone or on transmission and reflection measurements together. As the name suggests, in reflection method, only the reflected wave is studied whereas in transmission/reflection (T/R) method, both reflected and transmitted waves are studied. In the former case only one parameter is measured, either the permittivity or permeability. For permittivity measurements, the material is assumed to be non-magnetic and the thickness of the sample is chosen to be much larger than the aperture diameter of the open-ended coaxial line used for the measurement. Shorted reflection method is used for the measurement of permeability, assuming the permittivity to be same as the free space permittivity. Thus this methodology is limited in its application. The transmission/reflection method is used to measure both permittivity and permeability values. In the T/R method, the sample is inserted inside a section of the transmission line and the permittivity and permeability of the sample are derived from the analysis of the reflected and transmitted waves from the two port network thus formed. Several algorithms exist to derive the permittivity and permeability of the material from the measured transmission and reflection coefficients [43-45]. These will be discussed in a subsequent section. The first step is to measure the reflection and transmission coefficients of the two port system containing the sample. A vector network analyzer is employed for this purpose. By measuring the amplitudes and phases of the transmission and reflection coefficients of the system, a network analyzer reveals all the network characteristics of that system. The transmission lines used for these measurements can be in the form of hollow rectangular waveguides. One can also apply the free space measurement 48 technique instead. In free space measurement, a set of horn antennas is used to provide the incident electromagnetic wave and detect the transmitted signal. The advantage of this technique is that the sample can be of any convenient shape and the temperature of the sample can be varied easily for low or high temperature measurements. However, multiple reflections between the horn antennas and diffraction effects at sample edges lead to inaccurate results. The set-up also becomes bulky when measuring over a wide frequency range. Here, a waveguide based T/R measurement technique has been used to measure the parameters of the network. 3.3 Two port network The measurement of current or voltage for rectangular waveguides is difficult at microwave or higher frequencies [46]. At these frequencies, the network is characterized in terms of the transmitted and reflected waves at each port. Consider a general two port network as shown in figure 3.1. Figure 3.1 Schematic representation of a two-port network showing the incident and reflected wave at each port. Hollow rectangular metallic waveguides were used as transmission lines that guide the EM wave between the sample and network analyzer. 49 An electromagnetic wave is assumed to be incident on the device under test (DUT) at port 1. Here, the device under test can be a solid or powdered sample or a device such as amplifier. The two ports represent the input to the DUT and the output from the DUT. Depending on the properties of the DUT, a part of this wave is reflected at the first air-DUT interface and the rest of the wave enters the DUT. The propagation of wave inside the DUT is governed by the properties of the medium inside the DUT. In the network shown here, and represent the incident waves and and represent the reflected waves at ports 1 and 2, respectively. These can also be thought of as input and output ports of the network. The scattering parameters or s-parameters relate the incident and reflected wave at each port. The scattering matrix (S) can be expressed as, ( ) ( )( ) (3.1) The equations relating the incident and reflected waves for the two port network are given by, (3.2) Where S11 = input reflection coefficient S12 = reverse transmission coefficient S21 = forward transmission coefficient S22 = output reflection coefficient and are the square roots of the incident and reflected powers at port i. The input power reflection coefficient is calculated as the ratio of the power of the reflected wave at the input port to the power of the incident wave at the input port, with the output incident wave set to be zero. It represents the amount of incident power that is reflected 50 back at the input port and does not reach the output port. Thus, in a well matched network, the value of would be close to zero. | (3.3) The forward transmission coefficient is computed by taking the ratio of the output reflected power and the input incident power with the output incident wave set to zero, | (3.4) This parameter measures the amount of incident power that reaches the output port. It is sometimes also referred to as the gain of the device under test. In a similar manner, the rest of the parameters can be expressed as, | (3.5) | For a symmetric system, and are equal. As described in chapter 2, the reflected power would be minimum when there is no impedance mismatch. Thus and would be equal to zero for a well matched network. Another important property of two port networks is reciprocity. A two-port system is said to be reciprocal if the S matrix and its transpose are equal. In other words, the forward and reverse transmission coefficients are equal for a reciprocal network. The condition for reciprocity can be expressed as, (3.7) If in addition to the condition described above, the input and output power reflection coefficients are also identical then the system is said to be reciprocal. 51 For the measurement of powdered samples, the objective is to measure the s-parameters of the two port network formed by placing the sample under study between the two ports. A vector network analyzer is used to measure the s-parameters. A network analyzer measures the wave reflected from and transmitted through the material under test. The sample is loaded in a waveguide between the ports of the network analyzer and an electromagnetic wave is incident on this material. The reflected and transmitted waves are analyzed to calculate the intrinsic material properties. Propagation of an EM wave in a rectangular waveguide is described in the next section. 3.4 Wave Propagation in a Rectangular Waveguide Waveguides, in general, have high power handling capability and low loss as compared to other forms of transmission lines. Waveguides provide a restricted guided path for electromagnetic waves to propagate. Coaxial cables, hollow or dielectric metal pipes and fiber optical cables are all waveguides. For the measurements in this work, hollow rectangular waveguides are used. Figure 3.2 Geometry of a rectangular waveguide 52 Fig. 3.2 shows the geometry of a rectangular waveguide. For the purpose of the analysis, the waveguide is considered to be homogeneous and infinitely long in the z direction. The wave, is assumed to propagate along the z-direction, (α=0 for lossless line). Expanding the curl equation, ⃗ ⃗ (3.8) as ̂ ̂ ̂ | ⃗ | (3.9) (3.10) ( ) and The spatial variation in z can be calculated, ( ) ( Using this value to simplify the curl equations, 53 ) A similar expansion can also be ⃗ performed on Ampere’s equation, ⃗ To give, These six equations can be manipulated to produce equations for the transverse components of electric and magnetic fields yielding, ( ) ( ) ( ) ( where and ) . In these equations, kc is the cut-off wavenumber and k is the wavenumber in the material. These equations are used to analyze the waves traveling inside a waveguide structure. For a rectangular waveguide, the waves propagate in transverse electric or TE mode ( transverse magnetic or TM ( ) or ) mode inside the waveguide [39]. In rectangular waveguides we assume TE mode propagation only. For TE modes these equations reduce to, 54 ( ) ( ) ( ) ( ) The z-component of the magnetic field component must satisfy the Helmholtz wave equation, ( ) where , These equations can be solved by the method of separation of variables. The propagation constant is, √ where m, n = 0,1….( ( ) ( ) ) represent the mode of the propagating wave. This equation would yield real results when . This condition provides the condition for wave propagation and defines the cutoff wavenumber as, √( ) ( ) The cutoff frequency for any mode is given by, 55 √ √ √( ) ( ) Waves will propagate inside the waveguide when the frequency exceeds . The mode with the lowest cutoff frequency will therefore be the dominant mode. For TE mode, TE10 mode has the lowest cutoff frequency given by, √ For X-band waveguide, the cross-sectional dimensions are a = 2.286cm and b = 1.016cm. The cut-off frequencies for different modes are calculated in Table 3.1. TABLE 3.1 CUT-OFF FREQUENCY FOR DIFFERENT MODES INSIDE THE WAVEGUIDE (GHz) m n 1 0 6.562 2 0 13.123 0 1 14.764 1 1 16.156 In the X-band region (8.2-12.4 GHz) only the TE10 mode can propagate in the waveguide regardless of how it is excited. This is called single mode operation and is most often used as the preferred mode for hollow waveguides. It can be shown that no TM mode can propagate in the X band waveguide either. For TM modes, if either m or n is zero, then E field = H field = 0. This means that no TM modes with m = 0 or n = 0 are allowable in a rectangular waveguide. 56 TABLE 3.2 CUT-OFF FREQUENCY FOR HIGHER ORDER MODES FOR X BAND (GHz) m n 1 1 16.156 1 2 30.248 2 1 19.753 Rectangular, circular, elliptical and all hollow, metallic waveguides cannot support TEM waves. Two separate conductors are required for TEM waves [39]. 3.5 Experimental Set up The block diagram in figure 3.3 is a simplified representation of the measurement set up, excluding the internal intricacies of the devices or components, used by us to investigate the dielectric and magnetic properties of ferrites at the microwave frequencies. It can be divided into two main blocks, namely, the transmission unit and measurement unit. We now briefly discuss the contents and roles of these blocks. 3.5.1 Transmission Unit The transmission unit consists of the transmission medium used to carry signals between the measurement planes and the sample. Rectangular waveguides are employed for this purpose. The theory of the wave propagation in rectangular waveguides has been discussed in section 3.4. 57 Figure 3.3 Block diagram of the measurement setup 3.5.2 Measurement Unit The heart of the measurement unit is the network analyzer used to measure the amplitudes and phases of the transmitted and reflected waves at the two measurement ports. The high frequency network analysis involves incident, reflected and transmitted waves traveling along the transmission lines- waveguides in the present case. Network analysis is concerned with the accurate measurement of the ratios of the reflected signal to the incident signal, and the transmitted signal to the incident signal. Theory of the network analyzer has already been discussed in section 3.3. 58 Figure 3.4 The energy incident on the material under test is partially reflected at the first material interface and the rest of the energy is transmitted through the material. The automatic vector network analyzer can characterize the sample material primarily in the microwave range. It has limitation in the higher frequency range. The input signal is a frequency swept sinusoid. A source supplies the stimulus for the test system with variable frequency and power levels. The components of the network analyzer are discussed next. Signal separator: It measures a portion of the incident signal to provide a reference. This is done by using splitters or directional couplers. The second function of the signal splitting hardware is to separate the incident and reflected waves at the input of the DUT. Couplers and bridges are used for this purpose. The reference channel provides the reference signal against which test channel readings are compared for making phase measurements. This two channel scheme serves another purpose. Taking the ratio of test channel to reference channel results in considerable cancellation of amplitude and phase noise variation that might be present on the microwave source or receiver LO. Detector: Scalar network analyzers use diode detectors. For both magnitude and phase detection, the tuned receiver uses a local oscillator to mix the RF signal down to a lower intermediate frequency. The LO is either locked to the RF or the IF signal so that the receivers in the network analyzer are always tuned to the RF signal present at the input. The IF signal is bandpass filtered, which narrows the receiver bandwidth and greatly improves sensitivity and 59 dynamic range. Modern analyzers use ADC and DSP to extract magnitude and phase information from the IF signal. Tuned receivers provide the best sensitivity and dynamic range, and also provide harmonic and spurious signal rejection. The narrow IF filter produces a considerably lower noise floor, resulting in a significant sensitivity improvement. Processor/Display: This is where the reflection and transmission data is formatted in ways that make it easy to interpret the measurement results. Most network analyzers have similar features such as linear and logarithmic sweeps, linear and log formats, Smith charts, etc. A simplified block diagram of the network analyzer is shown in figure 3.5. Figure 3.5 Schematic diagram of the internal components of the network analyzer. A photograph of the set-up used to measure the powdered samples is shown in figure 3.6. The sample is placed between the two waveguide flanges. These are connected to the ports of the 60 network analyzer via connectors and cables. A 2.4mm coaxial cable is used to connect the network analyzer ports to waveguide ports. A 2.4mm connector is good for measurements up to 50 GHz. Since the measurements were carried out across eight different frequency bands, the inner dimensions of the waveguides used varied between 109.22 x 54.61 mm for R band to 7.112 x 3.556 mm for Ka band. Figure 3.7 shows all the waveguides that were used in the study. In order to match the different waveguide adapters to the coaxial cable on the network analyzer, additional connectors had to be used. Figure 3.6 Measurement set-up for measurement in X band. The network analyzer, coaxial cables, waveguide flanges and adapters are shown. 61 Figure 3.7 Standard waveguides used for each band are shown. The largest waveguide is for R band and the smallest one is for Ka band. The dimensions of the waveguide and sample holder used for each frequency band are summarized in table 3.3. TABLE 3.3 PROPERTIES OF RECTANGULAR WAVEGUIDES USED IN MATERIAL CHARACTERIZATION MEASUREMENTS Frequency Frequency Cut-off Dimensions Sample holder Band (GHz) Frequency (inches) thickness (GHz) (cm) R band 1.70-2.60 1.37 4.30x2.15 4.52 S band 2.60-3.95 2.08 2.84x1.34 2.82 G band 3.95-5.85 3.15 1.87x0.87 1.27 C band 5.85-8.20 4.37 1.37x0.62 1.25 X band 8.20-12.4 6.52 0.90x0.40 0.50 Ku band 12.4-18.0 9.49 0.62x0.31 0.64 K band 18.0-26.5 14.06 0.42x0.17 0.45 62 Ka band 26.5-40.0 21.09 0.28x0.14 0.30 3.6 Reflection and Transmission Coefficient The s-parameters are calculated by applying boundary conditions to the two-port network formed with the sample. Consider a schematic representation of the two-port network as shown in figure 3.8. Here, the material under test is placed between two transmission lines. The thickness of the sample is L2 and the length of the transmission lines on either side of the sample are L1 and L3. Ports 1 and 2 represent the measurement ports for the network analyzer. It is clear from this figure that the actual measurement ports are not at the DUT interfaces. This should be taken into account when analyzing the measured parameters. The desired measurement would be at the sample holder walls but instead the measurement system consists of sections of transmission lines filled with air and the material under test. To calculate the precise sample properties, the set-up shown in figure 3.8 can therefore be divided into three regions. Figure 3.8 Electromagnetic waves transmitting through and reflected from a sample in a transmission line. 63 The first region consists of an empty transmission line (air-filled/free space) of length . The electromagnetic wave is assumed to be incident at this port. This is followed by a piece of transmission line filled with the material under study ( ) and another piece of air-filled transmission line ( ). Region 1 consists of the wave incident on the material and the wave reflected from the air-material interface. The electric field in this region can be expressed as, where represents the net electric field in the transmission line region 1, is the propagation constant in the transmission line filled with free space, x represents the location of a point in region 1 and and are the constants to be determined by applying boundary conditions on the fields. In this expression, the first term represents the incident wave and the second term is for the reflected wave. Proceeding in a similar manner, the equations for regions 2 and 3 can also be written. The second region represents the waves travelling inside the material. The third region consists of the transmitted wave which is measured at port 2. The electric fields for these regions ( and ) can be written as, where, γ is the propagation constant inside the sample and the rest of the quantities are as defined above. The wave gets reflected inside the material as well and therefore the expression for electric field in region 2 represents two waves travelling in the opposite directions. As can be seen in the figure, the third region consists of the transmitted wave only. The propagation constant inside the material (γ) and in free space ( ) are, 64 √ ( √( ) ( ) ) where ω is the angular frequency, c is the speed of light in vacuum and is the cutoff wavelength of the transmission line. The constants Ci mentioned in equations (3.35) – (3.37) can be determined by applying the boundary conditions at the interface. The continuity of the tangential components of the electric field at the two interfaces give, | | | | The lengths L1 and L2 are indicated in figure 3.8. The boundary condition on the magnetic field requires an additional assumption that no surface currents are generated so that the tangential component of magnetic field is continuous across the interface giving, | | | | Applying these boundary conditions the solution for the s-parameters of the two-port network for the case of the symmetric scattering matrix, S12 = S21 gives, 65 where R1 and R2 are the reference plane transformations at the two ports, given by: here, L1 and L3 are the lengths of the air line between the ports and sample interface. Here, z represents the reference plane transformation for the wave being transmitted in the sample of length . Additionally, S21 for the empty sample holder is given as, The reflection coefficient can also be expressed in terms of permeability (µ) and propagation constant (γ), The next step is to calculate the values of permittivity and permeability from the data collected for s-parameters. For the case of non-magnetic materials, the unknown quantities are the real and imaginary parts of permittivity, length of material (L2) and the reference plane transformations, R1 and R2. The length of sample is considered unknown since the position of the sample inside the transmission line may not always be known precisely. However, in some cases it can be a known quantity. Thus the system consists of nine real equations for five unknown quantities. The four complex equations (3.44, 3.45, 3.46, and 3.49) are actually eight real equations. The ninth equation is for the total length of the transmission line, 66 For the case of magnetic materials, the real and imaginary parts of permeability are unknown, making the number of unknown quantities to be seven. Thus the system of equations is over determined and several methods can be used to calculate the unknown parameters. 3.7 Determination of Permittivity and Permeability Several algorithms exist for determining the permittivity and permeability of the sample from the above results. The Millimeter and Sub-Millimeter Waves Laboratory at Tufts University has an improved version to increase the accuracy of the measurements [47]. Nicolson and Ross [43] developed a broadband simultaneous measurement technique using coaxial transmission line. In their algorithm, they combined the equations for S11 and S21 and derived explicit formulas for the calculation of permittivity and permeability. Nicolson and Ross derived S21 and S11 from time domain measurements using Fourier transform. This method had two major shortcomings. First, the determination of permeability and permittivity is bandlimited, depending on the time response of the pulse and its repetition frequency. Secondly, in using discrete Fourier transform, errors arise due to truncation and aliasing. According to their algorithm, the power reflection coefficient was calculated as: √ where, The reflection coefficient is defined as the ratio of the reflected signal to the incident signal. Therefore, the value of reflection coefficient is always less than unity. It is equal to unity 67 in case of completely reflective surfaces. The positive or negative sign in equation (3.51) is chosen such that the condition,| | Here, , is satisfied. The transmission parameter is calculated as: is the free space permeability and µ is the permeability of the sample. Using these values the permittivity and permeability are calculated as, √( ) [( ) ( [ ( )] ( ) )] where It should be noted here that the argument of the natural logarithm function in Eq. (3.56) consists of a complex number. The phase factor of 1/z in Eq. (3.56) repeats its value after a phase change of 2πn. Therefore the phase of the transmission coefficient does not change when the sample length increases by multiple of wavelength. To overcome this ambiguity, Weir introduced the use of group delay to accurately determine permeability and permittivity. The measured value of group delay is compared to the calculated value in order to find the correct root. Group delay through the material is strictly a function of the total length of the material. Therefore phase ambiguity can be resolved by calculating the value of group delay using the derived permittivity and permeability values, 68 √ The value of group delay thus computed is compared with the measured value of group delay, which is determined from the slope of the phase of the transmission coefficient ( ) versus frequency using the following equation, The correct root should satisfy, g ,n g 0 . Thus phase ambiguity can be resolved by matching the calculated and measured group delay. But this is not a very consistent method. Another limitation of the existing methods is that the solution becomes divergent at frequencies corresponding to half-wavelength in the sample [45]. At these frequency points, the magnitude of S11 becomes very small and the uncertainty in the phase becomes very large. Since the solution is proportional to , the equations become algebraically unstable as S11 0. Many researchers use samples that have a length less than nλ/2 at the highest measurement frequency to resolve this issue. But the use of thin samples lowers the measurement sensitivity due to uncertainty in reference plain positions [48]. Therefore, a major limitation of Nicolson-RossWeir algorithm is that the results are unstable at certain frequencies. James Baker-Jarvis developed an iterative method to calculate the value of the permittivity. This proposed method minimizes the instability of the equations used by NicolsonRoss-Weir and allows measurements to be taken on samples of arbitrary length. Sample length and air length are treated as unknowns in this system of equations. The solution is therefore 69 independent of reference plane position and sample length. For example, one useful combination that was proposed is shown below, {[ ] [ ]} here, β is a function of sample length, uncertainty in s-parameter values and loss characteristics of material. For low loss materials, S21 is strong and β is zero whereas for high loss materials S11 dominates, so large value of β is appropriate. In general, β is given by ratio of the uncertainties in S21 and S11. Since this is an iterative procedure, an initial value is required to start the calculations. The solution for permittivity obtained from Nicolson-Ross-Weir algorithm can be used as a starting point. All the modifications suggested so far either need an initial guess parameter or choice of appropriate integer values of phase. A novel technique for the measurement of samples with arbitrary length was developed at the Tufts Millimeter and Sub-Millimeter Waves laboratory. This technique allows the simultaneous calculation of the permittivity and permeability of the sample by using a modified value of the transmission coefficient. This method does not require initial guess parameters, thus making the measurement set up more accurate. The first advantage of this algorithm is that it allows the measurement of different thickness values of the sample. In previous work, the sample is required to completely fill the sample holder. However, the proposed algorithm corrects for the presence of air between the sample and waveguide interfaces, in case the sample does not occupy the entire volume of the sample. It should be noted that this still requires that the surface of the powder inside the sample holder is smooth and flat. This is especially helpful when measuring across various frequency bands since it allows to minimize the variation in the density of the sample. In other methods, the air gap between the sample and sample holder edges is corrected by filling it up with a conducting material [49]. But 70 this affects the calculated parameter values as well and the sample dilution must be accounted for. The modified s-parameters used in the measurements in our work are given below, ( ̃ √ ( ̃ ) √ ) where, l is the quarter wavelength difference between thru and line in air, d is the thickness of the sample inside the waveguide, k0 is the wavenumber in the sample and kc is the cutoff wavenumber. These equations take into account the effect of using samples with thickness (d) values that are smaller than the waveguide shim used in the experimental setup. In the measurements performed in this study, a phase unwrapping technique was used to resolve this phase ambiguity. Whenever the jump in the value of the phase from one measurement frequency to the next is more than π, all subsequent phases are shifted by 2π in the opposite direction. It was also noticed that the permeability and permittivity of the loaded sample affect the cut-off frequency for the waveguide band. This was accounted for in the calculations by including the cut-off frequency for each band in the derivation of permeability and permittivity from the data for s-parameters. The propagation constant inside the waveguide can be calculated as, | | Considering the effect of loaded material’s magnetic and dielectric properties in the calculation of the cutoff wavelength of the propagation constant, we get 71 (√( ) √ ( ) ) ( ) Using this, we can write the equations for the determination of permittivity and permeability as [50], ( )( | | ) √( ) ( ( ) ( )( )( ( ) ) (√( ) | | ) ( ) ) where, Г is the reflection coefficient, T is the transmission coefficient, propagation constant for the and are mode with and without the material inserted in the waveguide, a is the longer dimension of the rectangular waveguide, is the phase of the transmission coefficient and d is the material thickness. In case of rectangular waveguide measurements, the permittivity and permeability can also be expressed in terms of the equivalent impedance and refractive index as [51], ⁄ ( ) ⁄ ( where ) ( ) is the wave impedance and N is the complex refractive index, already defined in chapter 2. The permittivity and permeability can now be defined in terms of the equivalent impedance ( ) and equivalent refractive index ( 72 ) as, The experiments carried out in the lab suggest that these modifications are necessary and known materials were measured to confirm the accuracy of the measurement technique. The derived permeability and permittivity data is very reliable and not effected by the scattering voltage ratios of the vector network analyzer. This method is also applicable to non-reciprocal circuits. Previous methods depend on the values of all four S parameters and required that S11 = S22 and S21 = S12. Since the proposed method uses only the values of parameters S11 and S21, it can be used to calculate the permittivity and permeability for non-reciprocal networks as well. Finally the relative permittivity of the material is calculated as, ( here, ) , a is the longer dimensions of the rectangular waveguide. 73 Chapter 4 Measurement Results at Microwave Frequencies 4.1 Introduction The results of the measurements described in the previous chapter are presented and discussed in this chapter. A considerable amount of useful information can be derived from these results. In addition to the permittivity and permeability values of a number of ferrite materials, the loss factor and reflection coefficient of the samples are also obtained. These characteristics help predict the possible use of these materials in different applications such as the radar absorbing materials and microwave filters. Wherever published data is available in literature, the properties of the nano-powders have been compared with the properties for the same composition of samples in bulk form. A few deviations from the expected results have been observed and these have been discussed in the following chapters. By controlling the material type (dielectric or magnetic) and its thickness, loss factor, impedance and internal design, the performance of a microwave absorbing material can be optimized for a single narrow band frequency, multiple frequencies, or over a broad frequency spectrum. 74 A brief description of the nanopowders analyzed in the microwave and millimeter wave frequency ranges is enumerated in Table 4.1. The particle sizes mentioned in this table are as per the manufacturer’s data sheets. In addition to these samples, a solid sample of Teflon was also studied using the waveguide technique in each frequency band. This is used as a reference material to validate the ability of the proposed algorithm for determining the permittivity and permeability values from the measured s-parameters. Powders of barium ferrite and strontium ferrite consisting of micro-size particles were also studied to observe if the differences in the properties of the nano- and micro-size ferrites can be detected using the proposed measurement technique. TABLE 4.1 Sample LIST OF NANO-SIZE POWDERS INVESTIGATED Chemical Formula Sample Description Barium nano-ferrite BaFe12O19 Avg. particle size 50-100 nm Barium micro-ferrite BaFe12O19 Avg. particle size 5-50 µm Strontium nano-ferrite SrFe12O19 Avg. particle size 50-100 nm Strontium micro-ferrite SrFe12O19 Avg. particle size 5-50 µm Copper Iron Oxide CuFe2O4 Avg. particle size 50-100 nm Copper Zinc Iron Oxide CuFe2O4Zn Avg. particle size 50-100 nm Nickel Zinc Iron Oxide Fe2NiO3Zn Avg. particle size 50-100 nm La0.6Sr0.4Co0.2 Fe0.8O3-δ Avg. granular size 30 – 40 µm La0.8Sr0.2MnO3 Avg. granular size 40 µm (ZrO2)92(Y2O3)8 Avg. granular size 0.5 µm Lanthanum Strontium Cobalt Ferrite (LSCF) Lanthanum Strontium Manganite (LSM) Yttrium Stabilized Zirconia 75 Lanthanum Strontium Cobalt Ferrite, Lanthanum Strontium Manganite, Yttrium Stabilized Zirconia and micro-size Barium and Strontium ferrite samples were purchased from Trans-tech, Inc. and the rest of the samples were obtained from Sigma Aldrich. The powders are filled inside the sample holder that is placed between the waveguides. A transparent tape is used on one side of the sample holder to prevent the powdered sample from falling off. The use of tape does not affect the measurement results. This was verified on the solid Teflon sample. The sample holders used in the measurement process are shown in figure 4.1. Sample holders for G, C and Ku frequency bands are shown here. Figure 4.1 Empty sample holders used for the measurement of G, C and Ku frequency bands. 4.2 Teflon Results Teflon has long been used for various household and industrial applications. The small value of the loss tangent at high frequencies makes it useful for applications in electrical engineering. The dielectric constant of Teflon is known to be around 2.1. 76 The complex values of the permittivity and permeability of Teflon have been reported to be ε = 2.045 - j0.00045, and µ = 1 .00 – j0.00, respectively [49]. Since the dielectric constant of Teflon is almost twice the dielectric constant of air, the waves inside this material would cover larger electric lengths than the waves travelling in free space of the same physical extent. Teflon is often used as a substrate in electrical industry, as insulators in the form of spacer or tubing and in the production of discrete electrical components, such as the capacitors. Teflon has been reported to have a stable permittivity value of about 2.03 in X band and loss tangent value of less than 0.0004 [44]. Since it is non-magnetic, the expected value of real permeability is close to unity. The s-parameters of the Teflon samples were measured in each of the eight microwave frequency bands between 2 to 40 GHz. The algorithm presented in chapter 3 was used to derive the permittivity and permeability values from the measured data. Solid samples of teflon that tightly fit the sample holder for each frequency band were used for these measurements. The average values of the real and imaginary parts of the teflon permittivity obtained for each frequency band are listed in table 4.2. These values are in close agreement with the known values for Teflon. The permeability of Teflon samples was also measured but did not show much variation with frequency. The average permeability across the measurement frequency range from 1.77 GHz to 40 GHz was close to 1.032. The close match between the expected and observed permittivity and permeability values of Teflon validates the measurement technique and proposed algorithm. 77 TABLE 4.2 Frequency Band DIELECTRIC PROPERTIES OF SOLID TEFLON SAMPLES Average value Sample Imaginary Thickness (cm) Real Permittivity Permittivity Dielectric Loss Tangent R 10.9 2.0628 0.000571 0.000277 S 7.241 2.0577 0.000519 0.000252 G 1.27 2.0497 0.000484 0.000236 C 1.25 2.0423 0.000416 0.000204 X 0.50 2.0375 0.000402 0.000198 Ku 0.64 2.0321 0.000387 0.000191 K 0.45 2.0252 0.000344 0.000169 Ka 0.30 2.0181 0.000315 0.000156 We now present the results for different ferrite powders investigated in this work. The permittivity and permeability values of these samples were obtained using waveguide based transmission/reflection technique described in chapter 3. In preparing samples for measurement, the powders were filled inside the waveguide shim with one end taped to keep the powdered samples in the sample holder. The effect of using an adhesive tape has been discussed in more detail in the error analysis (chapter 7). Sufficient care was taken while loading the samples in the waveguide shim to make sure that the powder is tightly packed, without any air gaps. The powder is added in steps and pressed at every stage to prevent the formation of agglomerates and air gaps inside the sample holder. We expect the samples to maintain uniform density during measurement. 78 4.3 Nano-size hexagonal ferrites The generic formula for M-type ferrites is MO.6Fe2O3, where M can be any divalent ion. The two hexaferrite samples studied here are barium (BaO.6 Fe2O3 or BaFe12O19) and strontium hexaferrites (SrFe12O19). Compared to ferrites with inverted spinel or garnet structures, hexagonal ferrites have larger intrinsic magnetic fields. Due to the hexagonal symmetry of the structure, such ferrites have a major preferred axis, i.e., there are certain preferred directions along which it is easier to magnetize the material. This makes them highly anisotropic. As a consequence of the effectively large internal magnetic anisotropy, these materials remain magnetized even after the external applied field is removed. This diminishes the need for an external magnetic field and makes M-type hexagonal ferrites very useful in the design of high frequency devices. Bulk hexagonal ferrite samples have been extensively used in microwave applications such as transformers and circulators. Due to the growing interest in these materials, the basic characteristics of nano-sized M-type hexaferrite powders have been extensively studied [52]. Recently these materials are also being investigated for use as microwave absorbers [5356] due to their large magnetic losses in the microwave range. The hexagonal ferrites are suitable as radar absorbing materials due to their large permeability values and favorable dielectric properties at microwave frequencies. Several substituted barium hexaferrite samples are being designed for such applications [57-60]. Substitution for the Fe3+ and Ba2+ ions is an effective method to vary the magnetic properties of barium hexaferrite. Common substitutions include ZnTi, Ni-Zr or Ti-Cu. It has been found that the absorption properties can be manipulated by varying the amount of substitution [61]. 79 The permittivity and permeability of these materials have been extensively studied in bulk form [62]. When materials are produced in powder form, depending on the particle size, the microwave behavior may change. However, not much has been reported on these materials in powder form. This could be due to the lack of accurate high frequency characterization techniques suitable for the powder samples. The variation of the real and imaginary parts of the permittivity and permeability of barium hexaferrite nanopowders at microwave frequencies are shown in figure 4.2. It should be noted that the plots shown here are generated from average values over certain frequency points. The data is collected at 201 frequency points for each frequency band. This would result in a total of 1608 frequency points for the entire data. Since it is difficult to show a plot with such a large number of data points, only certain selective data points are marked in the plots. It is immediately clear that the measured values of the real part of the permittivity for nano-powders are much smaller compared to the known values of real part of permittivity of bulk barium hexaferrite, which lie between 13 and 16 [63, 64]. These numbers refer to the real part of the permittivity. The real part of the permeability of barium hexaferrite in bulk form has been reported to be as high as 6 [63]. It should be noted that the bulk properties are reported for solid samples whereas the samples studied here are being measured in powder forms. The permittivities for M-type barium and strontium ferrites in bulk form have been reported in literature to lie between 14 and 16 [64, 65]. These are significantly different from the values measured here for their powder samples. In another study, a different measurement technique, namely, cavity resonator technique was applied to study powder samples of barium and strontium hexaferrites [62]. The particle sizes were much bigger than the samples studied here. The important point to note, however, is that the parameter values reported by them differ 80 significantly from the values for bulk samples. For an approximate powder size of 100µm, the average real parts of the permittivity for barium and strontium ferrite at microwave frequencies were reported to be 2.5 and 2.6, respectively. The magnetic and dielectric properties of the sample are affected by the state of the sample, i.e., whether bulk or particulate form. The reasons for the difference between bulk properties and micro- or nano-size powder samples is further investigated in chapter 6. 1.6 1.4 Parameter Value 1.2 1 0.8 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 0.6 0.4 0.2 0 2 5 8 11 14 17 20 23 26 29 32 35 38 Frequency (GHz) Figure 4.2 Variation of permeability and permittivity of barium hexaferrite nano-powder with frequency. The average values of the imaginary permittivity and permeability are 0.0516 and 0.0706, respectively. For sample density of 0.4004 g/cm3, the average values of the real and imaginary parts of the permeability of barium ferrite are 1.0642 and 0.0706 while the average permittivity values are 1.4647 and 0.0516, respectively. The value of real part of permittivity shows slight variation with frequency. The real part of permeability is fairly constant over the measured frequency range, except for the drop at the end of Ka band. For some of the bands, a trivial variation in the 81 parameter value at the band extremities is observed during measurements. This manifests into a discontinuity in the data plots at frequencies that correspond to the end of one band and beginning of the successive band. As can be seen in figure 4.2, this difference in values from one frequency band to the next is very small. Since the same density of the sample was used for measurement at each frequency band the data continuity is good. The non-zero values of the imaginary parts of permittivity and permeability suggest that the ferrites are lossy in nature. This means that an electromagnetic wave propagating through these materials would lose energy. This is an essential property for absorbing materials. The dielectric and magnetic loss tangent values for each sample are listed in Table 4.3. Another important observation here is that the permittivity and permeability values are very close to each other. This means that the impedance seen at the front end of the material would be close to the free space impedance (377 ohm) and hence there will be very little reflection at the air-ferrite interface. This satisfies the first condition for the absorbing materials described in chapter 2 and thus these powders may be useful as non-reflecting coatings for microwaves. The impedance values shown here have been calculated from the permittivity and permeability values using the following equation, √ √ The frequency dependence of impedance thus obtained is shown in figure 4.3. It can be observed that the front end impedance of barium ferrite nanopowder approaches the free space impedance value of 377 ohm towards the high end of microwave frequencies. 82 340 Impedance 335 330 325 320 315 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.3 Variation of front-end impedance of barium hexaferrite nano-powder with frequency Bulk barium hexaferrite is known to have resonance frequency around 48 – 50 GHz [64]. Results of our measurement on ferromagnetic resonance frequency of Barium hexaferrite powder are presented in chapter 5. It suffices here to state that resonance reqeuncy of barium hexaferrite powder also falls within the above range. The resonance corresponds to the maximum absorption frequency of the sample. From the data presented here, it can be predicted that nano size-barium ferrite should be an excellent microwave absorbing material at relatively lower frequencies, near the higher end of Ka band. In order to better understand the performance of the sample as an absorber, we calculate the front end reflectance. In chapter 2 the front end reflectance has been shown to have the form, Here, medium1 is air and medium 2 is nano-size barium ferrite powder. The power reflection coefficient Γ, when multiplied by the incident energy gives the amount of energy that gets reflected from the air-sample interface due to impedance mismatch between the two media. 83 Figure 4.4 gives the frequency dependence of Γ. This behavior is as expected. As the front end impedance becomes close to 377 ohm, the reflected energy decreases considerably. At frequencies higher than 34 GHz, the reflectance is less than -10dB, which is a practical value for an absorber. The performance improves significantly beyond 38 GHz with power reflection coefficient touching -25 dB at 38 GHz. Plots 4.3 and 4.4 are mutually consistent and suggest that Barium hexaferrite nanopowder should have excellent non-reflecting properties at higher frequencies. The magnetic loss shows an increase. The real part of permittivity decreases in magnitude, becoming closer to the permeability value near the frequency of resonance. The reflectivity results shown below are for a sample of thickness of 2 cm. Frequency (GHz) 2 6 10 14 18 22 26 30 34 38 Reflection Coeeficient (dB) 0 -5 -10 -15 -20 -25 -30 Figure 4.4 Variation of reflectance of 2cm thick sample of barium hexaferrite nano-powder with frequency. The properties of strontium hexaferrite nanopowder are discussed next. Figure 4.5 shows the variation of permeability and permittivity of strontium hexaferrite nanopowder with frequency. The overall variation pattern in this case is quite similar to the one found for the 84 corresponding barium based nanopowder (figure 4.2). The values of the permittivity and permeability are somewhat higher for the strontium nanopowder than for the barium nanopowder. The average values of real parts of permittivity and permeability obtained for strontium hexaferrite are 1.689 and 1.088, respectively. Further, the real part of the permeability of strontium hexaferrite nanopowder does not vary much with frequency except perhaps towards the higher end of frequencies used in our measurements. The magnetic loss factor for the strontium nanopowder shows a minor increase towards the higher end of the frequency range. The imaginary part of permittivity is very small and would not contribute much towards absorption in this case for the strontium nanopowder. However, the magnetic loss is considerably higher. We can therefore expect significant energy attenuation during propagation in strontium hexaferrite nanopowder. 2 1.8 Parameter Value 1.6 1.4 1.2 1 0.8 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 0.6 0.4 0.2 0 2 . 6 10 14 18 22 26 30 34 38 Frequnecy (GHz) Figure 4.5 Variations of permittivity and permeability of strontium hexaferrite nano-powder with frequency. 85 Characteristic Impedance 312 310 308 306 304 302 300 298 296 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.6 Variation of front-end impedance of strontium hexaferrite nano-powder with frequency. The difference between real parts of permittivity and permeability of Strontium hexaferrite nanopowder is small but somewhat larger than what was observed for barium hexaferrite nano-powder. As a result, its characteristic impedance in this frequency range is not as close to the free space impedance value of 377 ohm as it was in the case of barium hexaferrite nanopowder. The variation of impedance of strontium hexaferrite nano-powder with frequency is shown in figure 4.6. In this frequency range, the highest impedance value is 310 ohm at about 30 GHz. The fluctuation in values after that frequency could be due to measurement inaccuracies. But it can be concluded that the impedance rises towards the end of the frequency range investigated here, just as in the case of Barium hexaferrite nanopowder. The variation of power reflection coefficient for Strontium hexaferrite nanopowder shown in figure 4.7 is in general agreement with its impedance values. The impedance was observed to be best matched at 30 GHz and this corresponds to the sharp -16 dB minimum in reflectance observed in figure 4.7. 86 Frequency (GHz) 2 6 10 14 18 22 26 30 34 38 Reflection Coefficient (dB) 0 -4 -8 -12 -16 -20 Figure 4.7 Variation of reflectance of 2cm thick sample of barium hexaferrite nano-powder with frequency The results of measurement for the two nano-size hexaferrites are summarized in table 4.3. The data in this table provide only the average value of each parameter across the wide frequency range from 2 to 40 GHz. Material TABLE 4.3 DIELECTRIC AND MAGNETIC PROPERTIES OF HEXAFERRITE NANOPOWDER Dielectric Permittivity Magnetic Permeability Density Real Imaginary Loss Real ImaginLoss (g/cc) Part Part Tangent Part ary Part Tangent Bulk Permitti vity Barium 1.464 0.052 0.016 1.064 0.071 0.041 0.4004 16 [64] 1.689 0.030 0.018 1.088 0.0658 0.060 0.3531 14[65] Hexaferrite Strontium Hexaferrite 87 It is clear from figures 4.2 and 4.5 that the parameter values are somewhat frequency dependent. For instance, the dielectric loss tangent value is very small at lower frequencies but increases steadily with frequency. This behavioral phenomenon cannot be captured in average values and thus the frequency dependent analysis is essential. A single average value for any parameter undermines the fact that the value is high at certain frequencies and falls at others. For comparison, micro-size samples of Barium hexaferrite were also studied. The frequency dependence of real and imaginary parts of permittivity and permeability for this powder is shown in fig 4.8. The average value of real parts of permittivity and permeability for the micro-size sample were found to be 3.065 and 1.1069, respectively. An interesting observation here is that the values for the micro-size powders are different from those measured for the nano-size powder. This is explored in more detail in chapter 6. 3.5 Measured Value 3 2.5 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 2 1.5 1 0.5 0 2 8 14 20 26 Frequency (GHz) 32 38 Figure 4.8 Material properties of Barium ferrite micro-powders are shown. The average value of real and imaginary parts of permittivity is observed to be 3.065 and 0.0559 whereas real and imaginary parts of permeability are 1.1069 and 0.0536, respectively. 88 4.4 Nano-size spinel ferrites Spinel ferrites generally have a cubic crystal structure. Their general formula is MFe2O4, where M is a divalent cation. Common examples of divalent cations include manganese, zinc, nickel and copper. Spinel ferrites have been utilized as absorbing materials in various forms for many years due to their large magnetic losses and large resistivity [66-67]. Nickel-zinc spinel ferrites have been prepared with different amounts of substitution for use as absorbers in the ISM band (at a frequency of 2.4 GHz) for mobile devices [68]. As was seen in the case of hexaferrites, within the GHz range, the permittivity of a ferrite is almost constant with its imaginary part close to 0. Therefore, the dielectric loss is negligible and its absorbing performance mainly depends on the magnetic loss. However, in the microwave region, the application of spinel ferrites are limited at the lower end of the microwave frequency 1-3 GHz because of their lower natural resonance frequencies in comparison with those of other types of ferrites, such as hexaferrites [66-67]. One of the frequently used methods to tune the complex permeability of spinel ferrites is to dope the ferrites with many metallic ions, such as copper, zinc, cobalt or manganese. In order to do this, it is necessary to know the precise values of permittivity and permeability and the relation between material properties and microwave absorption. For instance, Co-doped NiZn spinel ferrite or multilayer copper substituted nickel-zinc spinel ferrite have been used for absorption in the microwave region [69]. Thus the performance of spinel ferrites can be extended to microwave region by substituting them with metallic ions such as copper, zinc, cobalt, lithium or manganese. In order to do this in an efficient way and get desired performance, it is important to know the constitutive properties of the spinel material first. A remarkable characteristic of spinel structure is that it is able to form an extremely wide variety of solid solutions [70]. This means that the composition of a given ferrite can be easily 89 modified, without altering the basic crystalline structure. In this work, three spinel ferrite powder samples were studied, each consisting of particles with sizes in the nanometer domain. The results of our measurements for each sample are presented here. Figure 4.9 shows the permittivity and permeability of copper iron oxide. The average values of the real parts of the permittivity and permeability of this nano-ferrite are obtained to be 1.507 and 1.03, respectively. Real part of the permeability shows only marginal changes with frequency but real part of permittivity undergoes considerable changes over the frequency range investigated here. Unlike the hexaferrite samples, the loss values are observed to be higher at the lower frequency end and decrease in the higher frequency range. 1.8 1.6 Parameter Value 1.4 1.2 1 0.8 0.6 0.4 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 0.2 0 2 6 10 14 18 22 26 Frequency (GHz) 30 34 38 Figure 4.9 Variations of permittivity and permeability of Copper Iron Oxide nanopowder with frequency. The impedance values for copper iron oxide are shown in figure 4.10. The characteristic impedance is closest (though not very close) to free space impedance at low frequencies and then seems to fall with frequency but not so smoothly. This is generally consistent with the 90 reflectance variations obtained for the air-sample interface (Fig. 4.11). The reflectance characteristic reaches -20 dB at low frequencies and subsequently worsens as the frequency increases. Characteristic Impedance 320 316 312 308 304 300 296 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.10 Variation of front-end impedance of Copper Iron Oxide nano-powder with frequency Frequency (GHz) 2 6 10 14 18 22 26 30 34 38 0 Reflectance (dB) -5 -10 -15 -20 -25 Figure 4.11 Variation of reflectance of 2 cm thick sample of Copper Iron oide nano-powder with frequency 91 Next, the results for Copper Zinc Iron Oxide are presented. Fig. 4.12 shows that the addition of zinc results in a higher value of the real part of the permittivity and substantially higher magnetic loss. The real part of the permeability is still close to unity but since the real part of the permittivity is considerably higher than that of copper iron oxide, the characteristic impedance of copper zinc iron oxide sample is farther removed from free space value. As a result, it shows poor front end reflection performance. The front end impedance and reflectance variations of copper zinc iron oxide are shown in figures 4.13 and 4.14, respectively. The reflectance value does not reach the -10 dB limit. 2 Parameter Value 1.6 1.2 0.8 0.4 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 0 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.12 Variation of permittivity and permeability of Copper Iron Oxide nanopowder with frequency 92 310 Characteristic Impedance 308 306 304 302 300 298 296 294 292 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.13 Variation of front-end impedance of Copper Zinc Iron Oxide nano-powder with frequency Frequency (GHz) 2 6 10 14 18 22 26 30 34 38 0 Parameter Value -1 -2 -3 -4 -5 -6 -7 -8 Figure 4.14 Variation of reflectance of 2 cm thick sample of Copper Iron oxide nano-powder with frequency 93 The third spinel ferrite sample studied by us is the nickel zinc iron oxide. The variations of permittivity and permeability with frequency for this sample are shown in figure 4.15. 1.6 Parameter Value 1.4 1.2 1 0.8 0.6 0.4 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 0.2 0 2 6 10 14 18 22 26 Frequency (GHz) 30 34 38 Figure 4.15 Variation of permittivity and permeability of Nickel Zinc Iron Oxide nanopowder with frequency bands The material properties of nickel zinc iron oxide have been studied in bulk form at lower microwave frequencies in the S band [71]. The permittivity and permeability plots of figure 4.15 show that the nickel zinc iron oxide is expected to perform well at high frequencies due to the close proximity in the values of the real parts of these parameters. The lower value of permittivity results in good impedance matching at the air-sample interface. The loss factors are not very high but compare favorably with barium hexaferrite loss factors. The impedance variations are shown in Fig. 4.16. At higher frequencies, the impedance is fairly close to the free space value. This is reflected in the high reflectance value (nearly -25 dB) at these frequencies (Fig. 4.17). 94 The average values of the real parts of the permeability and permittivity of Copper Zinc Iron Oxide nano-powder in the frequency range explored by us are 1.058 and 1.313, respectively. These are much lower than the values reported for bulk samples. For bulk samples of these ferrite, the real part of the permeability has been reported to be around 18.42 at 2.44 GHz and 15.12 at 3.98 GHz and the imaginary part of permeability has been reported to be 0.825 and 0.615 at 2.44 GHz and 3.98 GHz, respectively. Characteristic Impedance 355 350 345 340 335 330 325 320 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.16 Variation of front-end impedance of Copper Zinc Iron Oxide nano-powder with frequency 95 2 6 10 14 Frequency (GHz) 18 22 26 30 34 38 Reflection Coefficient (dB) 0 -5 -10 -15 -20 -25 -30 Figure 4.17 Variations of reflectance of 2 cm thick sample of Copper Iron oxide nano-powder with frequency Results of measurement on spinel ferrites are summarized in table 4.4. TABLE 4.4 Material DIELECTRIC AD MAGNETIC PROPERTIES OF SPINEL FERRITES Dielectric Permittivity Magnetic Permeability Density Bulk (g/cc) Properties 0.085 0.5204 - 0.150 0.5454 - Real Imaginary Loss Real Imaginary Loss Part Part Tangent Part Part Tangent CIO 1.507 0.075 0.0499 1.03 0.087 CZIO 1.637 0.0618 0.0377 1.037 0.156 µ= 15.12 NZIO 1.313 0.037 0.028 1.058 0.091 0.086 0.2754 [71] 96 4.5 Nano-size Rare Earth Ferrites Oxides of rare earth metals are often classified as orthoferrites. These ferrites, in general, have perovskite crystal structure, with formula MFeO3, where M represents a rare earth trivalent cation such as Yttrium [72]. These materials are classified as ferrites as different cations occupy different sub-lattices. This results in a net magnetic moment, making these materials behave as ferromagnetic materials. Current problems of microelectronics strongly call for materials with large magnetoresistance at room temperature [73]. From this standpoint manganite perovskites with a general formula Ln1-xAxMnO3, where Ln is a trivalent cation like La and A is a divalent alkalineearth cation like Ca, Sr, Ba, are very promising compounds demonstrating colossal magnetoresistance (CMR) effect, by many orders of magnitude exceeding the giant magtoresistance of multilayered films and granulated systems [74]. In addition to CMR, manganite perovskites show a variety of other interesting magnetic and electrical properties, including ferromagnetic and antiferromagnetic ordering of manganese magnetic moments, charge ordering of the Mn3+ and Mn4+ cations and orbital ordering of the manganese 3d orbitals [74-76]. These magnetic nanoparticles have great potential for use in a wide range of applications, including magnetic recording media, sensors, catalysts, magnetic refrigeration, medicine, etc. Lanthanum Strontium Manganite (LSM) nanoparticles have been used as mediators for hyperthermia applications [77]. Thus these materials have generated a lot of interest in the past years. We therefore decided to investigate the magnetic and dielectric properties of nanoparticles of some of manganite perovskites at microwave frequencies. The materials studied by us are Lanthanum Strontium Manganite (LSM), Yttrium stabilized Zirconia (YSZ) and Lanthanum Strontium Cobalt Ferrite (LSCF). 97 Making measurements on the samples of these materials was most challenging. The samples for these powders tend to exist as agglomerates. Thus even after pressing the powder well, the distribution of particles was not uniform in the sample holder. As a result, the powder shifted very easily inside the sample holder. The experiment was very sensitive to any movement of the sample holder. So in order to carry out these measurements, the sample was never completely filled in the sample holder and the sample holder was always kept horizontal once the powder was filled in. The rare earth perovskites investigated by us have already been listed in Table 4.1. They were acquired from Trans-Tech. The variations of the permittivity and permeability of these materials are shown in figure 4.18 (a), (b), (c). 6 Parameter Value 5 4 3 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 2 1 0 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.18 (a) Variations of permittivity and permeability of LSCF nanopowder with frequency 98 5 4.5 Parameter Value 4 3.5 3 2.5 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 2 1.5 1 0.5 0 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.18 (b) Variation of permittivity and permeability of LSM nanopowder with frequency. 3.5 Parameter Value 3 2.5 2 Real Permeability Imaginary Permeability Real Permittivity Imaginary Permittivity 1.5 1 0.5 0 2 6 10 14 18 22 26 Frequency (GHz) 30 34 38 Figure 4.18 (c) Variation of permittivity and permeability of YSZ nanopowder with frequency. Except for the YSZ nanopowder (Fig. 4.18c), other rare earth perovskites show only marginal variations in permeability and permittivity in the microwave frequency range. The real 99 parts of the permittivity and permeability of these rare earth perovskites are considerably higher than the values for other materials studied here. The imaginary parts of the permittivity and permeability of these materials are almost zero, implying that these materials are not lossy. The average parameter values are summarized in table 4.6. TABLE 4.5 DIELECTRIC AND MAGNETIC PROPERTIES OF RARE EARTH PEROVSKITE NANOPOWDERS Material Dielectric Permittivity Magnetic Permeability Real Imaginary Loss Real Imaginary Loss Part Part Tangent Part Part Tangent LSCF 4.7704 0.0513 0.01 2.162 0.021 0.0097 LSM 4.639 0.079 0.017 2.17 0.0176 0.008 YSZ 3.133 0.0089 0.003 1.308 0.0024 0.002 The characteristic impedances of these samples are plotted in figure 4.19 (a)-(c). As expected, the characteristic impedance of these samples substantially differs from the free space impedance value. Characteristic Impedane 250 248 246 244 242 240 238 236 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.19 (a) Variations of impedance of YSZ nanopowder with frequency 100 Characteristic Impedance 261 260 259 258 257 256 255 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.19 (b) Variations of impedance of LSM nanopowder with frequency Characteristic Impedance 268 264 260 256 252 248 244 2 6 10 14 18 22 26 30 34 38 Frequency (GHz) Figure 4.19 (c) Variations of impedance of LSCF nanopowder with frequency 101 Due to the poor impedance matching, it is evident that these samples are not suitable for absorbing applications. However, their loss factors would be a major consideration in devices where higher losses cannot be tolerated. The rare earth perovskites, LSCF and LSM with relatively high permeability of about 2 may find use in other magnetic applications. Frequency (GHz) 0 2 6 10 14 18 22 26 30 34 38 Reflectance (dB) -1 -2 -3 -4 -5 -6 -7 Fig.4.20 Variation of reflectance of LSCF nanopowder with frequency 102 Chapter 5 Measurement results at millimeter frequencies 5.1 Introduction It was mentioned in chapter 4 that the intrinsic material properties of micro- and nano-sized barium and strontium hexaferrite powders are different at microwave frequencies. To further explore the size dependent behavior of these materials we decided to measure their dielectric and magnetic properties at still higher frequencies using a different measurement technique. A quasioptical backward wave oscillator was employed to measure the variation of the power transmittance of Barium and Strontium hexaferrite micro- and nano- powders. These materials show strong ferromagnetic resonances in the millimeter wave frequency range. The permittivity and permeability values are obtained by comparing the measured power transmittance spectra of these samples with the theoretically obtained ones. The measurement results for micro- and nano-sized barium and strontium ferrite powders at the millimeter wave frequency range are presented in this chapter. The results show that the magnetic properties such as the ferromagnetic resonance frequency and effective magnetic anisotropy vary with the particle size in powders. 103 The spectrometer designed here reduces the measurement errors that occur in spectrometers employing pure optical technology by using a combination of guided wave technology and optical technology [78]. 5.2 Theoretical Background By using appropriate BWO source and waveguide elements such as directional couplers, phase shifters and antennas, the power transmittance spectrum of the sample is measured in three frequency bands, namely, Q (34-56 GHz), V (44-76 GHz) and W (70-117 GHz) bands. The wave propagating through the sample under test may undergo several reflections at the ⁄ boundaries of the sample. The sample transmittance T which takes into account the interference among the multiple reflected waves coming out of the sample takes the form [79], where the power reflection coefficient for normal incidence at either surface of the sample is, ( ( ) ) where r is the amplitude transmission coefficient of the sample, d is the sample thickness, n and K are the real and imaginary parts of the complex index of refraction of the sample and intensity of radiation incident on the sample. 104 is the The expression for α in equation 5.5 suggests that this parameter depends on the wavelength inside the medium, which in turn suggests that α would vary with frequency. As a result, the expression for evaluating T (Eq. 5.1) also oscillates as a function of the frequency. Thus the amplitude of the transmittance spectrum is expected to oscillate with frequency. The maxima and minima of the oscillating signal respectively correspond to the constructive and destructive interference among the multiply reflected waves exiting the sample. The location of maxima and minima in the transmittance as a function of the frequency depends on the argument of the sine function in the denominator of Eq. 5.1 and their strengths depend on the reflection coefficient R (Eq. 5.2) of the sample. The maxima in the transmittance spectrum occur when the argument of the sine function in the denominator of Eq. (5.1) is a multiple of π, so that the sinusoidal term is at its minimum value. The reduction in transmittance within the sample described by Eq. 5.3 takes into account the magnetic and dielectric losses suffered by the wave inside the sample. It should be noted that phase φ (Eq. 5.4) vanishes in a lossless material (k = 0). 5.3 Experimental Details The barium and strontium ferrite samples were studied using a quasi-optical millimeter wave technique developed at the High Frequency Materials Measurement and Information Center at Tufts University. The quasi-optical spectrometer has been in use for some time now and the technology has been continually improved over the years [80]. The measurement system employs backward wave oscillators (BWO) as high power sources to observe the transmission of energy through the sample. The BWOs can give about 30 mW of power at each frequency point. The frequency range from 34 to 117 GHz is divided into three bands, shown in Table 5.1. Three different sets of sources, detectors and antennas were used to cover these frequency bands. 105 TABLE 5.1 INVESTIGATED MILLIMETER WAVE FREQUENCY BANDS Frequency band Frequency Range Q 34 – 56 GHz V 44 – 76 GHz W 70 – 117 GHz The horn antennas used for each frequency band in the experimental set-up are shown in figure 5.1. As expected, the size of the antenna depends on the operational frequency band. Figure 5.1 Horn antennas used for transmitting the incident signal at Q, V and W bands. The block diagram of the measurement set-up is shown in figure 5.2. The high power backward wave oscillator source is used to generate the millimeter waves. As seen in the block diagram, the modulated signal is divided into two channels. Instead of using a pure optical technique, which has been reported to have high measurement error [78], the measurement system developed here uses a guided wave technology combined with a quasi-optical millimeter 106 wave system for precision measurements. One of the channels is made up of the waveguide components to serve as a reference for phase information. The other channel consists of an optical transmit and receive system. Horn antennas are used to radiate and receive energy. Figure 5.2 Experimental set-up for measurement at millimeter wave frequencies Waveguide based isolators and directional couplers are used to divide the signal into the two different propagation paths. Isolators are used to prevent the radiated signal from entering the source. The channel made out of the waveguide components is used to provide reference signal for phase measurements. In the optical channel, the transmitted signal propagates along a path consisting of four lenses, placed as shown in the figure. The first two lenses help to effectively expose the sample to the signal radiated by the transmitter antenna. The remaining lenses focus the transmitted Gaussian beam exiting the sample on to the receiver horn. The quasi-optical channel is placed inside the pole pieces of a 1 Tesla magnet to attain partial saturation of the magnetization in the samples. The material under study is placed in the common 107 focal planes of the lenses on its two sides. The signal from the quasi-optical channel, after passing the receiver horn antenna is combined with the signal from the reference channel by the directional coupler similar to the one used for the division of the input signal into the two channels. The two signals are combined at the detector and the interference of the combined waves is recorded with a detector. Specially written Lab View based software is used to automate the spectrometers and process the measured data. Figure 5.3 Experimental set-up for millimeter wave measurements. 108 A photograph of the measurement set-up used in our lab is shown in figure 5.3. The sample is placed between the poles of the electromagnet. First, the reference data is collected by running the set-up without placing any sample in the quasi-optical path. Next, the same procedure is repeated with the sample located in the propagation path of the transmitted wave in the optical channel. The powders were carefully packed inside the sample holder. The volume of the sample used for millimeter wave measurements is much larger than what was used for microwave measurements. The sample containers designed for the experiment are shown in figure 5.4. The sample holder is made out of aluminum frame with mylar films fixed through Teflon strips on either side. The container is about 6 cm high. The thickness of the frame and hence of the sample is 12 mm. The thickness of mylar sheet is 0.05 mm. Prior to filling the sample holder, the powdered samples were manually milled to make sure that the sample does not form agglomerates. The powders were carefully packed inside the sample holder in gradual amounts to make sure that there are no air gaps within the sample. Figure 5.4 Specially designed sample holders for BWO based spectrometer. The thickness of the sample holder used here is 12mm. 109 The computer controlled quasi-optical measurement system records the power transmission spectrum of the sample under test and the permeability and permittivity of the sample are extracted from this spectrum by fitting the theoretical curves to the experimental ones, as explained in the next section. As mentioned earlier, the reference data is collected by running the set-up without placing any sample between the lenses. Next, the same procedure is repeated with the sample located in its position in the optical channel. The power transmittance spectrum is then obtained as the ratio of the measured point to point voltages at the detector with and without the sample. 5.4 Results The power transmittance spectra of micro- and nano-powders of Barium and Strontium hexaferrites were obtained in the millimeter range using the quasi-optical technique described in the previous section. The results in the form of the transmittance plots for the strontium hexaferrite are shown in figure 5.5. The strong dips in the transmittance plots between 50-60 GHz correspond to the ferromagnetic resonances of micro- and nano-powders of Strontium hexaferrite. The ferromagnetic resonance for nano-powders is much sharper than the one for micro-powder. The flattening of ferromagnetic resonance of micropowder is due to power broadening. Ferromagnetic resonance in bulk samples of strontium hexaferrite under similar experimental conditions are known to be even more broad. Next we note that the dips due to ferromagnetic resonances in the transmittance plots are followed by nearly sinusoidal transmittance variations of relatively smaller amplitudes for each of the samples. The small amplitude sinusoidal variations correspond to the oscillations discussed in section 5.2 in the context of Eq. 5.1. The appearance of interference among the 110 multiply reflected waves within the samples is evident. The small amplitude of these oscillations reflects the fact that the sample power reflection coefficient R (Eq. 5.2) is not very large (R<<1) at the millimeter wave frequencies. We now describe how complete information on the permeability and permittivity of the samples can be obtained from the measured variations in the power transmittance of Barium and Strontium hexaferrite powders. At the outset, we note that the transmittance is not significantly affected by the magnetic interaction of the external field with the magnetic dipoles present in the material at frequencies sufficiently away from the natural ferromagnetic resonance of the material. Further, the dielectric behavior of these ceramic type materials has only weak linear dependence on frequency within the millimeter wave frequencies. The dielectric resonances (absorption) take place at much higher frequencies. We shall identify the spectral portions of the transmittance plots where magnetic effects are dominant and where they are weak. The real and imaginary parts of permeability are extracted from the spectral regions where magnetic effects are overwhelmingly high. The permittivity values are extracted where magnetic effects are rather weak. As mentioned earlier, sample transmittance described by Eq. 5.1 oscillates with frequency. The frequency difference of two successive peaks of transmittance when magnetic effects can be ignored is given by , where c is the velocity of light in vacuum, n is the real part of the index of refraction and d is the thickness of the sample. This frequency difference may change somewhat from peak to peak. One can then take the mean value of this frequency difference. The refractive index n of the material can be obtained from the mean frequency difference measured among the transmittance oscillations far removed from the ferromagnetic resonance. The absorption coefficient k can be obtained from the overall decay of the 111 transmittance in the spectral region where the magnetic effects are rather weak. This happens in the spectral range around 90-110 GHz. Similarly the absorption coefficient calculated from the decay of the transmittance in the 90-110 GHz essentially corresponds to the dielectric losses ( ). A curve fitting function is used to match the measured transmittance spectra to the transmittance spectrum calculated theoretically from equation. The transmittance spectrum of the sample is measured by taking the ratio of the detector output with and without the sample placed between the lenses. The values of n and k are optimized such that the experimental and theoretical graphs can be overlaid on each other as closely as possible. The goal is to get the peaks in the two waveforms to line up in position and overlap in magnitude by changing the values of n and k. These parameters are recorded for all peaks and the average value of the real and imaginary parts of the refractive index are determined. An alternative method is to express these parameters in terms of first or higher order equations in frequency and then use frequency dependent parameter values for further calculations. Schloemann’s equation (Eq. 2.17) can be used to obtain the best fit to the transmittance variations in the neighborhood of the ferromagnetic resonances. The permittivity coefficients and obtained from the estimated values of n and K in the high frequency range of the millimeter wave frequencies can be used in this fitting procedure. The transmittance spectra measured for two strontium hexaferrite samples are shown in figure 5.5. These samples consist of different sizes of the particles in the material. The marked dips in the transmittance spectra (figure 5.5) observed around the resonance frequencies indicate that strontium ferrite powders can be used as efficient absorbers in the frequency range of their resonances. 112 Sr Ferrite, Micro, 2.13 g/cc 1 Sr Ferrite, Nano, 0.57 g/cc Transmittance 0.8 0.6 0.4 0.2 0 30 40 50 60 70 80 90 100 110 Frequency (GHz) Figure 5.5 Transmitance variations of micro- and nano-size strontium ferrite powders in the millimeter wave range. Next, the real and imaginary parts of permittivity were determined by the procedure mentioned earlier. The values obtained here are slightly higher than the permittivity values obtained at microwave frequencies using the network analyzer based technique discussed in chapter 4. Since the value of permittivity obtained from this technique is based on curve fitting, it may not be as accurate as the one obtained using the waveguide technique at microwave frequencies. This could be due to different densities of the samples used in the two measurement techniques and accuracy of the algorithms. However, as at microwave frequencies, we find that the permittivity of nano-powder is lower than the permittivity of micro-powders in the millimeter wave range as well. The values of permittivity for nano- and micro-sized powders at millimeter wave frequencies are summarized in table 5.2. 113 TABLE 5.2 BEST FIT VALUE OF PERMITTIVITY FOR HEXAFERRITE SAMPLES Sample Density (g/cc) Millimeter wave Measurements Ɛ’ Ɛ’’ Barium Ferrite Micro 1.83 4.41 0.029 Barium Ferrite Nano 0.59 1.88 0.01 Strontium Ferrite Micro 2.13 5.8 0.057 Strontium Ferrite Nano 0.57 2.15 0.012 Using these values of permittivity, the real and imaginary parts of permeability were calculated by a similar curve fitting procedure. The best fit results for nano- and micro-sized strontium ferrite samples in the millimeter wave frequency range are shown in figure 5.6 and 5.7, respectively. The phenomena of ferromagnetic resonance can be seen more clearly in these plots. It should be noted here that Schloemann’s equation is useful in calculations close to the ferromagnetic resonance frequency. However, as we move away from the resonance frequency, the accuracy of this method decreases. In fact, for frequencies that are distant from the resonance frequency, more accurate calculations can be performed by using Polder’s theory [87]. Therefore, the permeability data that is presented in the following plots is not accurate at higher frequency points. 114 Real Part of Permeability 1.09 Strontium Ferrite, Nano ρ = 0.57 g/cm3 Fres = 48.2 GHz 1.05 1.01 0.97 0.93 0.89 30 40 50 60 70 80 90 100 110 Frequency (GHz) (a) Imaginary part of permeability 0.24 Strontium Ferrite, Nano ρ = 0.57 g/cm3 Fres = 48.2 GHz 0.2 0.16 0.12 0.08 0.04 0 30 40 50 60 70 80 Frequency (GHz) (b) 115 90 100 110 Real part of permeability Figure 5.6 Real (a) and imaginary (b) parts of permeability for Strontium nano-ferrite powder measured in the millimeter wave frequency range. 2 Strontium Ferrite, Micro ρ = 2.13 g/cm3 Fres = 53.1 GHz 1.6 1.2 0.8 0.4 0 30 40 50 60 70 80 90 100 110 Frequency(GHz) Imaginary part of permeability (a) 2 Strontium Ferrite, Micro ρ = 2.13 g/cm3 Fres = 53.1 GHz 1.6 1.2 0.8 0.4 0 30 40 50 60 70 80 90 100 110 Fequency (GHz) (b) Figure 5.7 Real (a) and imaginary (b) parts of permeability for Strontium micro-ferrite powder measured in the millimeter wave frequency range. 116 A careful inspection of the plots in figure 5.6 and 5.7 lead us to conclude the best fit permeability values obtained in the lower frequency range (30 – 40GHz) are in good agreement with the values obtained from the microwave measurements. It is also observed that the microsized powders show higher values of intrinsic material properties as compared to the nano-sized powders in both microwave and millimeter wave frequency ranges. An important observation from these plots concerns the resonance phenomena in these materials. It can be observed that the resonance frequencies are different for the two sizes of the powders. The resonance frequency seems to shift to lower values for nano-powders as compared to micro-sized powders. Resonance is the phenomena by which absorption occurs in ferrite samples. This means that the absorption frequency for a given composition of the ferrite sample can be tuned by changing the size of the particles in the sample. The best fit permeability plots for barium ferrite samples are shown in figures 5.8 and 5.9. The best fit results or barium ferrite powder samples are qualitatively similar to those for strontium ferrite powder. Real part of permeability 1.08 Barium Ferrite, Nano ρ = 0.59 g/cm3 Fres = 42.5 GHz 1.04 1 0.96 0.92 30 40 50 60 70 80 Frequency (GHz) (a) 117 90 100 110 Imaginary part of permeability 0.16 Barium Ferrite, Nano ρ = 0.59 g/cm3 Fres = 42.5 GHz 0.12 0.08 0.04 0 30 40 50 60 70 80 90 100 110 Frequency (GHz) (b) Figure 5.8 Real (a) and imaginary (b) parts of permeability for Barium nano-ferrite powder measured in the millimeter wave frequency range. Real part of permeability 2 Barium Ferrite, Micro ρ = 1.83 g/cc Fres = 49.2 GHz 1.6 1.2 0.8 0.4 0 30 40 50 60 70 80 Frequency (GHz) (a) 118 90 100 110 Imaginary part of permeability 2 1.6 Barium Ferrite, Micro ρ = 1.83 g/cm3 Fres = 49.2 GHz 1.2 0.8 0.4 0 30 40 50 60 70 80 90 100 110 Frequency (GHz) (b) Figure 5.9 Real (a) and imaginary (b) parts of permeability for Barium micro-ferrite powder measured in the millimeter wave frequency range. The best fit values of the resonance frequencies of micro- and nano-powders of strontium and barium hexaferrites are given in table 5.3. From the data shown above, it is clear that the material properties for solid ferrite are different from those of the powdered ferrites. Further, these properties depend on the size of the particles in the powder. The data is also compared to values reported in literature using different techniques. There is no data available to compare the nano-ferrite properties but considerable study has been done on bulk and powdered ferrites with particle size in micrometer or greater size region. For example, the ferromagnetic resonance of barium ferrite pressed-powder sample was studied using optically switched spectrometer [64]. 119 TABLE 5.3 RESONANCE FREQUENCY OF FERRITE POWDERS AT DIFFERENT SIZES Resonance Frequency Material Particle size (GHz) Bulk 50-53 [64] Micro 49.2 Nano 42.5 Bulk 57.0 [81] Micro 53.1 Nano 48.15 Barium Hexaferrite Strontium Hexaferrite It is clear from the measurement procedure described above that the parameter estimation for the BWO based millimeter wave measurement technique is based on trial and error and curve fitting of the expected and measured values. Thus this technique is not as accurate for permittivity and permeability measurements as the transmission/reflection based waveguide technique. However, if the measured transmittance spectrum is accurate, the information derived from these procedures provides a good estimation of the material properties [82]. The material properties for micro- and nano-ferrites at microwave and millimeter wave frequencies have been discussed here. The values from the two measurement techniques are not exactly equal but they both reveal similar trend of material properties in case of micro- and nanopowders. This size dependence of these material properties is further analyzed in the following chapter and the causes for these differences are identified. 120 Chapter 6 Size effect on ferromagnetic resonance in ferrites 6.1 Introduction The intrinsic properties of different sizes of barium and strontium hexaferrite powders at microwave and millimeter wave frequencies were presented in chapters 4 and 5, respectively. Significant differences were observed in the properties of the micro- and nano-size powders of these ferrites at these frequencies. A deeper analysis is needed to understand the origin of these differences. In this chapter, the dependence of the material properties on the size of the particles is investigated. To make further progress, it is necessary to understand the role of the composition and internal morphology of the samples. Therefore, in addition to microwave and millimeter wave characterization, structural analysis of the samples was also performed. The results indicate that properties such as the ferromagnetic resonance frequency and effective magnetic anisotropy vary with the particle size. Barium and strontium hexaferrite show similar behavior with changing particle size. 121 6.2 Properties of nano- and micro-size ferrite powders The frequency dependence of the real and imaginary parts of the permittivity and permeability of barium hexaferrite nano- and micro-powders were discussed in chapter 4 (fig 4.2 and 4.8, respectively). The permittivity of both the nano and micro powders of this ferrite was found to be much smaller compared to the permittivity of bulk barium hexaferrite, which lies between 13 and 16 [63, 64]. It was further observed that the measured permittivity of the micro powder was slightly larger than that of the nano powder. Similar behavior was observed for strontium microand nano-ferrite powders as well. The average values of the permittivity and permeability of the nano and micro-sized powders for each sample, measured in the microwave frequency range are summarized in Table 6.1. TABLE 6.1 ELECTRO-MAGNETIC PROPERTIES MEASURED AT MICROWAVE FREQUENCIES Barium Hexaferrite Frequency (GHz) Nano-sized Powder Strontium Hexaferrite Micron-sized Powder Nano-sized Powder Micron-sized Powder 4 μ' 1.11 ε' 1.43 μ' 1.06 ε' 3.07 μ' 1.09 ε' 1.68 μ' 1.02 ε' 3.83 8 1.14 1.50 1.06 3.05 1.09 1.72 1.03 3.77 12 1.14 1.50 1.10 3.04 1.08 1.74 1.03 3.82 16 1.11 1.45 1.12 3.09 1.09 1.73 1.04 3.91 20 1.06 1.44 1.13 3.06 1.07 1.69 1.06 3.95 24 1.04 1.49 1.13 3.11 1.06 1.68 1.04 3.89 28 1.08 1.48 1.12 3.08 1.11 1.66 1.05 3.74 32 1.10 1.46 1.03 3.06 1.1 1.65 1.08 3.85 36 1.14 1.44 1.08 3.01 1.09 1.69 1.06 3.93 40 1.12 1.42 1.07 3.06 1.07 1.63 1.04 3.98 122 Barium and strontium micro-powders (particle size 50-100 µm) have been studied in the past in the frequency range from 8 GHz to 26.5 GHz using a cavity resonator [62]. Our results for micro-powders of these materials are in close agreement with their published results reported in [62]. The slight differences in the two results could be attributed to the difference in particle size and sample density used in the two measurements. However, only limited literature exists on these materials in the small size range. Therefore, it is difficult to say if these results are indeed typical. But we have observed similar results in the millimeter wave frequency measurements also. At this point, we feel that intrinsic material properties depend on the size of the particles in the powder. For reference, the millimeter wave results are also summarized in Table 6.2. Since the saturation magnetization will be higher for the single domain nano-powders, resonance frequency is expected to be lower for nano-powders. This is in agreement with what was observed in the measurements. The detailed calculations are presented in the next section. TABLE 6.2 ELECTRO-MAGNETIC PROPERTIES MEASURED AT MILLIMETER WAVE FREQUENCIES Sample Density (g/cc) Millimeter wave Measurements Ɛ’ Ɛ’’ Ferromagnetic resonance frequency (GHz) Barium Ferrite Micro 1.83 4.41 0.029 49.2 Barium Ferrite Nano 0.59 1.88 0.01 42.5 Strontium Ferrite Micro 2.13 5.8 0.057 53.1 Strontium Ferrite Nano 0.57 2.15 0.012 48.2 123 As discussed in chapter 5, the values of permittivity and permeability of the samples at millimeter wave frequency range are derived from the observed power transmittance spectrum. The transmittance spectra for strontium ferrite samples are reproduced in figure 6.1. The resonance phenomenon can be clearly seen in the transmittance spectrum. Sr Ferrite, Micro, 2.13 g/cc 1 Sr Ferrite, Nano, 0.57 g/cc Transmittance 0.8 0.6 0.4 0.2 0 30 40 50 60 70 80 Frequency (GHz) 90 100 110 Fig. 6.1 The transmittance spectrum for micro- and nano-size strontium ferrite powders measured using the BWO technique at Q, V and W bands. Under similar conditions, strontium hexaferrite in bulk form is known to have a resonance frequency between 50 – 65 GHz [81], implying strong absorption of electromagnetic energy entering the sample in this frequency range and the material can be used as an absorber. From the transmittance spectrum in figure 6.1, it can be concluded that strontium hexaferrite samples consisting of nano- and micro-size particles exhibit resonance within the frequency range of resonance of bulk strontium hexaferrite. The resonance in the case of micro powder is spread out and therefore the exact value of the resonance frequency cannot be determined from 124 this data alone. The absorption width seen in figure 6.1 for micro-size strontium ferrite may not be the actual width of the ferromagnetic resonance. The visual inspection of the micro-sized samples showed that the particles form aggregates inside the sample holder. Thus the measurement surface was not smooth and formation of cracks and pores was visible. The different crystallites present in the sample tend to orient randomly and form local grain boundaries. All these factors contribute to the broadening of the observed linewidth [83]. However, in the case of nano-size sample, the powder was packed much more smoothly and showed no discernible cracks or discontinuity inside the sample holder. It should also be noted here that the level of transmittance observed in this plot does not represent the maximum amount of absorption possible through the sample. Further study reveals that the strength of absorption depends on the density of the sample packed inside the sample holder. For instance, it cannot be concluded from figure 6.1 that micro-size strontium ferrite powder shows stronger absorption than nano-size strontium ferrite powder. This is because the densities of the samples differ considerably. For reference, the specific gravity of solid ferrite ceramics (for both barium and strontium) is about 4.7 -5.2 g/cm3. However, when used in powdered form, the specific gravity is much lower. The density for micro-powder is about 2 g/cm3, which is about 2.5 times lower than the usual solid ferrite samples. The density for nanopowder is about 0.57 g/cm3, which is almost 9 times lower. In order to better understand the effect of density on the measured transmittance levels two different densities of the same powder were used for the measurement. The difference in density was achieved by gradually increasing the amount of pressure applied during the packing of the sample. Figure 6.2 shows the transmittance spectrum recorded for two different densities of the nano-size strontium hexaferrite sample. In one case, the powder was filled in the sample holder without applying any extra 125 pressure. Next, external pressure was applied in order to tightly pack more powder in the same sample holder. The sample can be packed even more tightly inside the sample holder by using special milling techniques to achieve higher density values that are comparable to solid samples. It can be concluded from the results shown in figure 6.2 that higher density of the sample results in stronger absorption at resonance frequency. However, the sample density does not affect the frequency at which the resonance occurs. The weaker absorption observed for lower sample density is due to air dilution in the scarcely packed sample. 1 Transmittance 0.8 0.6 Sr-Fe Nano, 0.52 g/cc Sr-Fe Nano, 0.57 g/cc 0.4 0.2 34 44 54 64 74 84 94 104 114 Frequency (GHz) Figure 6.2 Transmittance spectrum recorded for two slightly different densities of strontium hexaferrite Quantitative differences in the transmittance of micro- and nano-powder samples of strontium hexaferrite shown in figure 6.1 can be summarized as, a. The strength of absorption is different for the two types of powder, b. Wider absorption width is observed for micro-powders as compared to nano-powders, 126 c. Resonance frequency is lower for nano-powders as compared to micro-powders. The first two observations in this list have already been explained. In order to understand the dependence of resonance frequency on the particle size, structural studies were carried out on the samples. The results are presented in the following section. 6.3 Structural analysis of ferrite powders The powders were characterized for their composition and size using the following techniques, scanning electron microscopy (SEM) laser particle size distribution (PSD) X-ray diffraction (XRD) The XRD spectra for the four samples (micro- and nano- size barium and strontium hexaferrite) are shown in figure 6.3 (a)-(b). Single phases without any impurity are observed for each sample. 127 (a) (b) Figure 6.3 X-ray diffraction spectra of strontium hexaferrite (a) and barium hexaferrite (b). 128 The primary particle and agglomerate sizes of barium and strontium hexaferrite were determined using the scanning electron microscopy technique (SEM) and also by the laser particle size distribution technique (PSD). Crystallite sizes in the sample were determined from the x-ray study. There is a good correlation between the data obtained from the different techniques. These measurements were performed at Pacific Northwest National Laboratory (PNNL, WA). The size distribution and average particle as well as agglomerate sizes are presented below, in Table 6.3. TABLE 6.3 PARTICLE SIZE DETERMINATION OF BARIUM AND STRONTIUM FERRITE XRD Particle Diameter (nm) Agglomerate Diameter (nm) Powder Crystallite Size PSD SEM PSD SEM size (nm) Micro 161 1000-2000 500-1000 20000-50000 3000-15000 Nano 60 100-200 20-50 500-600 500-1000 The particle sizes obtained using particle size distribution (PSD) method are higher than the values obtained using other methods. However, it should be noted that the resolution of this technique is limited to these values and so it cannot measure smaller sizes [90]. Thus the SEM results are more reliable. Based on these measurements, it can be concluded that the nano-particles are about 20 50 nm in size whereas the micro-particles are about 0.5 - 2.0 µm. These sizes are lower than what was mentioned in the sample data sheet supplied by the manufacturer. From the average particle size calculated above and the crystallite dimensions obtained from X-ray diffraction, it can be concluded that particles exist as single crystallites in the nano-powder samples. However, 129 in the micro-powder samples, the particles exist in polycrystalline state. This is in agreement with published results [84]. The critical size for particles to exist as single crystallites calculated for these powders using the theory due to Kittel is about 100 nm, which is smaller than the particle size in micro-powders but larger than the particles in the nano-powder [85]. The direct observation of the domain structure of barium hexaferrite small particles at room temperature by Goto, Ito and Sakurai also confirms that the critical size is in the region of 1 um [86]. Therefore, it can be concluded that the nanoparticles definitely exist as single domains whereas the micro particles may exist in polycrystalline state. When the size of the particle is smaller than the critical size for multi-domain formation, it exists in a single-domain, where the domain-wall resonance is avoided, and therefore, the material could be used at higher frequencies [22]. By definition, the magnetic moments in a single domain particle are aligned in the same direction. Therefore single domain material is expected to possess the maximum saturation magnetization for that particular size and composition. However, in reality the alignment may not be completely uniform and the materials are assumed to be in a quasi-uniform magnetization state, when their diameter is a few nanometers. Next, the morphology of the samples was studied using scanning electron micrograph. The images from the high resolution microscope are shown in figures 6.4 and 6.5. The SEM pictures show that the powders consist of agglomerates ranging in size from 3 to 15 um. The high resolution pictures show that individual particles have sizes much below 1 um. It is difficult to ascertain the exact shapes of individual particles from these images. These shapes appear to be in between spherical and hexagonal. Figure 6.4 shows the micrographs obtained for the nanosize barium hexaferrite powder. 130 (a) (b) 131 (c) (d) Figure 6.4 Scanning electron micrographs of barium hexaferrite nano-powder for different resolutions can be seen. The magnification level for the images shown here are (a) 5,000, (b) 10,000, (c) 20,000, (d) 40,000. The particle size is much smaller than the 1 µm mark indicated in the third inset. 132 Each graph (figure 6.4a to 6.4d) shows the sample morphology at a different magnification level. In order to get a visual estimate of the particle size, the scale has been shown in each plot. For instance, in figure 6.4 (a), it can be seen that the particle size is much smaller than the 5um dimension indicated in the image. The individual particle size can be observed to be much smaller than the 0.5um mark indicated in figure 6.4 (d). However, in some cases the agglomerate size can be close to this dimension. Figure 6.5 shows the SEM data obtained for the micro-size powders. The individual particle size was observed to be about 0.5um to 1 um whereas the agglomerate sizes range from 3 um to 15 um. (a) 133 (b) (c) 134 (d) Figure 6.5 The micro-size powder of barium hexaferrite consisted of agglomerates in the size range from 3 to 15 µm. It can be seen in inset C that the primary particle size lies between 0.5 to 1 µm. Based on these images, it can be concluded that the shape of the particles is near spherical in case of nano-powders. For the case, of micro-powders, the shape of the individual particles is not clearly distinguishable but the shape of the agglomerates in each case seems to be close to hexagonal. The resonance frequency is known to depend on the crystallite size and shape [72]. In the next section, we discuss the phenomenon of ferromagnetic resonance and calculate resonance frequencies of hexaferrite nanoparticles using the information gathered so far on the crystal structure and morphology of hexaferrites and see if the calculated results agree with our observations. 135 6.4 Ferromagnetic resonance The phenomenon of ferromagnetic resonance occurs when a ferromagnetic substance is simultaneously subjected to a dc magnetic field and a relatively weak alternating magnetic field, perpendicular to each other, provided the frequency of the alternating magnetic field satisfies what is called the resonance condition. The dc magnetic field includes the externally applied dc field and any fields existing in the medium due to the demagnetization and crystallographic anisotropic effects. The alternating magnetic fields in ferromagnetic resonance are in the radio and microwave frequency regimes. Kittel’s theory of ferromagnetic resonance (1947) was extended by Polder (1949) [87]. Below, we describe Polder’s phenomenological theory of ferromagnetic resonance. 6.4.1 Polder’s Theory of Ferromagnetic Resonance To begin with, ferromagnetic material of arbitrary shape and size is considered. The shape and size of the ferromagnetic material become relevant because of the long range character of the dipolar interaction among its atoms and molecules possessing non-zero magnetic moments. The crystal anisotropy favors orientation of magnetic moments in preferred crystallographic directions. Further, energy dissipation also occurs during the ferromagnetic resonance. These effects, neglected in Polder’s theory, can be subsequently incorporated in a phenomenological manner. A ferromagnetic material acquires a net magnetization in the presence of the external dc magnetic field. The motion of an elementary dipole under these conditions is quite like the motion of a spinning top. The net magnetic field seen by the elementary dipole is, (⃗ ) ⃗ ⃗⃗ 136 where ⃗ is the macroscopic field and ⃗⃗ is the magnetization (dipole moment per unit volume) produced in the ferromagnetic substance. The equation of motion of an elementary dipole of magnetic moment is, (⃗ where gyromagnetic ratio ⃗⃗ ) is the ratio of the dipole moment of the atom and its angular momentum. The magnetization ⃗⃗ is given by ⃗⃗ where is the number of atoms per cc. Combining eq. (6.2) and eq. (6.3) gives ⃗⃗ ⃗⃗ ⃗ In the absence of the alternating magnetic field, the magnetization ⃗⃗⃗⃗⃗ and the dc field ⃗⃗⃗⃗ are parallel. The net magnetic field and magnetization in the presence of the alternating magnetic field are ⃗ ⃗⃗⃗⃗ ⃗ ⃗⃗ ⃗⃗⃗⃗⃗ ⃗⃗ where ⃗⃗⃗⃗⃗ is the saturation magnetization produced by the dc field ⃗ and ⃗⃗ is the ac magnetization produced in the material. On substituting equations (6.5) in eq. (6.4), we obtain, ⃗⃗ (⃗⃗⃗⃗⃗ ⃗⃗⃗⃗ ⃗ ⃗⃗⃗⃗⃗ ⃗⃗ ⃗⃗⃗⃗ ⃗⃗ ⃗) Last term on the RHS being a product of two small quantities may be neglected. Further ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗ ⃗⃗⃗⃗ and ⃗⃗⃗⃗⃗ may be taken along the z-axis and ⃗ to lie in the xy plane. Eq. (6.6), then yields, ( ) 137 Rearranging terms, we obtain the components of the ac magnetization as, where Resonance occurs when the frequency of the alternating magnetic field approaches leading to enhancement in the induced alternating magnetization ⃗⃗ . The magnetic susceptibility is defined by the tensor equation, [ The total magnetization ⃗⃗ , [ ⃗) [ ](⃗⃗⃗⃗ [ where ] ] ][ ] [ ] ⃗ can now be expressed as, [ ][ , Recalling the relationship, 138 ] , ⃗ we can write, ⃗ ⃗ ⃗⃗⃗⃗ ⃗ ⃗⃗ ⃗⃗⃗⃗⃗ ⃗⃗ ⃗⃗⃗⃗ ⃗ ⃗⃗ ⃗ We have for the alternating magnetic field, ⃗ ⃗ ⃗ ⃗⃗ With eq. (6.9), eq. (6.15) yields, where Eq. (6.15) can be written in the tensor notation as ⃗ where [ ] [ [ ]⃗ ] Eq. (6.11) or equivalently eq. (6.16) can easily be extended to incorporate the effects due to crystal anisotropy and energy dissipation. We can require the permeability tensor to be consistent with crystal symmetry. Further, allowing and in the permeability tensor to be complex quantities can account for the energy dissipation in ferromagnetic resonance. 139 From the equations defining the permeability tensor, it is clear that the permeability tensor has a singularity at . This value of ω corresponds to the ferromagnetic resonance. The physical meaning of this expression is that when the operating RF frequency is equal to , the energy from the microwave field is transferred most efficiently to the system of spins. The closer the frequency of the microwave field to the natural precession frequency ( ), the greater the energy absorbed by the spins [22]. In the discussion so far, the medium is assumed to be infinite and the losses associated with dipole motion are not explicitly considered. However, the resonance frequency is affected by the loss mechanisms associated with demagnetization, magnetic anisotropy and crystalline imperfections in polycrystal structures. To consider the finite size of the material, the magnetic field inside the sample should be evaluated by applying electromagnetic boundary conditions. Demagnetization factors can be easily obtained for uniformly shaped samples like sphere, cylinder or a slab. The modification in the magnetic field due to demagnetization can be expressed as, and where N is the demagnetization vector, Hi and hi are the reduced dc and ac fields due to finite size of the sample. The complex susceptibility can be obtained by substituting Eq. (6.18) in Eq. (6.4) and proceeding in a similar way as described above for the case of infinite materials. The final values of the susceptibility tensor thus obtained are, ́ [ ́ ] [ ́ 140 ( ) ] [ ́ ́ ́ ] [ ́ ( ) ́ ] ( [ ́ ) ] where, ́ ][ {[ where , , ( ) ]} ⁄ are the demagnetizing factors applicable for the x, y, z directions. In the presence of demagnetization and anisotropic effects, this expression gets modified. For a ⁄ . For other simple shapes, these factors can be calculated. The sphere, demagnetizing factors so defined satisfy the condition . A method to simplify these equations for further analysis is often used [88]. The solution to the boundary problem to evaluate the magnetic fields inside a ferrite is very difficult. However, these solutions have been worked for certain specific shapes of the ferrite sample. Here the results for hexagonal and spherical ferrites are used to calculate the expected resonance frequency for the micro- and nanoferrites studied here. We next consider the effect of anisotropy on the ferromagnetic resonance frequency. Following Kittel [89], the anisotropic field Hanis can be taken to be in the xy plane of a single crystal. In that case the effect of anisotropy can be described by additional demagnetizing factor and such that 141 so that changes to due to the anisotropic field, and to in Eq. (6.21). For small perturbation takes the value for a uniaxial crystal, so that Values of are tabulated. Since nano-particles generally exist as single domains with larger values of the magnetization as compared to the micro-particles, the anisotropic effects are less prominent for nano-particles in comparison to the micro-powders. 6.5 FMR Calculations Using the theory and equations presented in section 6.4, one can calculate the ferromagnetic resonance (FMR) frequency for the samples. Taking a simpler approach, if the demagnetization and anisotropic effects are neglected, the resonance frequency is given by, or, where, here is the external field (1 kOe in the present case), g is the spectroscopic splitting factor with a value of 2, e is the electron charge (1.6 x 10-19 C) and m is the mass of electron (9.109 x 10-31 kg). Using these values, γ is evaluated to be 1.759 x 108 C/g. 142 Equation (6.26) needs to be modified to incorporate demagnetization and anisotropic effects. First, the ferromagnetic resonance frequency is calculated by neglecting the demagnetizing effects but including the anisotropic effects. The resonance frequency takes the form, where The values for saturation magnetization and anisotropy constant for single crystals of barium and strontium hexaferrites have been calculated by Shirt and Buessen [92]. These are listed in Table 6.4, along with the calculated values of the resonance frequency using Eq. (6.27). TABLE 6.4 CALCULATED VALUES OF RESONANCE FREQUENCIES OF BARIUM AND STRONTIUM HEXAFERRITE NANOPOWDERS WITHOUT DEMAGNETIZATION EFFECTS. Sample K1 (erg/cm2) Ms (G) Hanis H0 Calculated Measured (Oe) (kOe) FMR (GHz) FMR (GHz) Ba-ferrite 3250000 380 17,092 1 50.60 42.50 Sr-ferrite 3570000 380 18,775 1 55.37 48.15 The calculated values of the resonance frequency are much higher than those observed in the measurements. Thus it is clear that the demagnetizing effects cannot be neglected here. We now incorporate the demagnetization effects by modifying Eq. (6.27) to ( ) 143 where, We have used . The value of the demagnetization factor (N) calculated by Glass is about 4 for spherical particles and 8 for hexagonal particles [91]. The effective anisotropy has been measured to be approximately 15.5 kOe for spherical particles and 12.9 kOe for plate-like shape of the particles [84]. This data can be used to calculate the values of N for different shapes of the particles by using the following relationship, where is the effective anisotropy field. The derived values of the demagnetization factor are shown in table 6.5. TABLE 6.5 CALCULATION OF DEMAGNETIZATION FACTOR FOR DIFFERENT PARTICLE SHAPES IN BARIUM HEXAFERRITE NANO-POWDER Particle K1 Demag. Ms (G) shape (erg/cm2) (kOe) Factor (N) Spherical 3250000 380 15.5 8.1 Hexagonal 3250000 380 14 4.2 Plate-like 3250000 380 12.9 11 It was observed earlier in the morphological study of the samples that the nano-powders exist nearly as spherical particles. Assuming the particles to be spherical with N = 4.2 and using 144 ( ) the calculated resonance frequency for barium hexaferrite nano-particles is 46.14 GHz which is on the higher side of the measured value. However, if we use applicable for the hexagonal shape, the calculated value for the resonance frequency for barium hexaferrite nano-particles is 42.15 GHz, which is much closer to the experimental value. As mentioned earlier, the actual particle shape may lie in between spherical and hexagonal, perhaps more towards hexagonal shape. Table 6.6 gives the final results for Barium and Strontium ferrites. The agreement between the calculated and experimental values is quite good. Therefore this model can be used to calculate the ferromagnetic resonance frequency of different sizes of hexaferrite powders. TABLE 6.6 CALCULATED VALUE OF RESONANCE REQUENCY IN THE MILLIMETER WAVE RANGE K1 Hanis Demag. Calculated Measured Sample Ms (G) (erg/cm2) (Oe) (kOe) Factor (N) FMR (GHz) FMR (GHz) Barium 3250000 380 17,092 1 4.2 46.14 42.50 Nano-ferrite 3250000 380 17,092 1 8 42.15 Strontium 3570000 380 18,775 1 4.2 50.90 Nano-ferrite 3570000 380 18,775 1 8 46.89 48.15 It is clear from these measurements that the resonance frequency can be tuned by changing the size and shape of the particles. Nano-ferrites can be used to achieve sharper resonance and hence absorption over specific frequencies in the millimeter wave range. It is not 145 easy to fabricate absorbers at these frequencies but barium and strontium nano-ferrite show promise. 6.6 Quality Control To ensure that the differences observed in the properties of ferrite samples are not due to measurement errors, such as non-uniform packing of powder inside the sample holder, several lots of the same material were studied and measurements were repeated for each sample. An Xray diffraction pattern was taken to confirm the completion of the phase transition to the hexagonal structure of BaFe12O19. The diffractogram indicates that the sample is almost completely transformed to BaFe12O19 and no other phases were detectable. Some interesting results were observed during the measurement of the powdered samples. As mentioned earlier the samples studied here are commercially available powders. The structural results shown in previous sections reveal that the actual particle dimensions may vary from the dimensions reported in the datasheet. The preparation of powders with nano-size particles is challenging. Various techniques have been developed to prepare ultrafine ferrite powders. Some of the commonly used methods are chemical co-precipitation method [93-94], glass crystallization method [95-97], organic resin method [98], and hydrolysis method metalorganic complexes [99]. The advantage of developing small-sized particles is that phase transformations can be achieved at lower temperatures. It has been seen here and other similar studies that the crystallite size, particle size distribution and inter particle spacing significantly influence the behavior of the material [100]. In recent years, significant scientific effort has gone into developing techniques for the controlled growth of nano-powders. The synthesis techniques used for the preparation of nano-powders over the years have been reviewed [101]. 146 Several different lots of barium and strontium hexaferrite nano-powders were purchased to carry out the measurements. However, during millimeter wave characterization, some barium hexaferrite samples did not show any resonance. In order to understand this, all samples were studied with X-ray diffraction. The samples presented here are in addition to the ones that were used for measurement and discussed in this work. X-ray results for these new samples are shown in Fig. 6.5. Figure 6.6 Several lots of samples contained incomplete phases or impurities such as Fe2O3. X-ray studies of a few samples are shown here. The barium hexaferrite nanopowders shown in this figure contained at least 50 volume percent of ε-Fe2O3. These samples are labeled as lot 1 to lot 3. Lot 1 shows 50% barium hexaferrite by volume but lot 2 and lot 3 show almost no traces of barium hexaferrite. However, barium ferrite micro-power shows single phase only. This means that the preparation method is 147 correct but it is not reliable. For the three lots of barium hexaferrite, the percentage of each phase was determined by Rietheld method. These measurements were carried out at PNNL. The results are shown in Table 6.6. TABLE 6.7 XRD STUDY OF MICRO AND NANO HEXAFERRITE POWDERS Sample Nano- Ba ferrite Micro- Ba ferrite Lot Number Phases (vol %) Barium hexaferrite Iron oxides Lot 1 56.2 43.8 Lot 2 - 100 Lot 3 - 100 - 100 - As expected, only the barium hexaferrite micro-powder shows a single phase. The nanosized barium hexaferrite samples were either partially or completely composed of iron oxides. This characterization method does not completely distinguish between γ- Fe2O3 and ε- Fe2O3. So the compositions shown in Table 6.6 might not be exact but the indicated percentage of barium hexaferrite phase is correct. Presumably these iron oxide phases resulted from an incomplete synthesis of barium hexaferrite during the preparation process. Another iron oxide, α- Fe2O3 is known to be used as a precursor for the production of barium hexaferrite. These samples were also characterized at millimeter wave frequency range. Out of the three barium ferrite samples mentioned here, only lot# 1 showed resonance phenomena (millimeter wave absorption) during the characterization process, which could be due to the 148 partial presence of barium hexaferrite phase in the sample. The other two samples did not show any resonance. The transmittance spectra for the three nano-ferrite samples are shown in figure 6.7. Figure 6.7 Transmittance spectrum for different lots of barium hexaferrite samples. The hexaferrite phase was missing in lots 2 and 3. This can also be concluded from this data due to the missing resonance. These results suggest that the BWO based measurement technique used here is sensitive enough to imply the absence of a certain phase and thus millimeter wave absorption could be used as a quality control technique in the manufacture of ferrite nano-powders. The advantage of this technique is that it is non-destructive and quick. It can be concluded from the results shown in section 6.5 that the performance of the samples depends on the morphology of the particles in the sample. But controlled fabrication of powders in this size is not possible. The particle size and shape gets deviated from the intended design. As can be seen in table 6.6, even though the same procedure is used to manufacture several samples of these powders the outcomes can be different. The microwave or millimeter wave properties can be used as an additional check to confirm if the sample constituents and dimensions are correct. 149 Chapter 7 Error Analysis 7.1 Introduction In order to interpret the measured parameter values correctly, it is essential that we identify the possible sources of error and uncertainties in the measurement process and apply the corrective action, wherever possible. The occurrence of experimental uncertainties is inevitable but a good estimate of these uncertainties can help in validating the accuracy of the experiment. The error in any measurement is classified as either random or systematic error. Experimental uncertainties that can be revealed by repeated measurements are called random errors [102]. But all types of experimental uncertainties cannot be assessed by repeated measurements. The repeatable and stable uncertainties in measurement are called systematic errors. Systematic errors are due to imperfections in the network analyzer and the test set up. They are repeatable (therefore predictable) and are assumed to be time invariant. Systematic 150 errors are characterized during the calibration process and mathematically removed during measurements. Random errors, on the other hand, are unpredictable since they vary with time in a random fashion. Therefore, they cannot be removed by calibration. The main sources of random errors are instrument noise. In addition to these errors, the system may also suffer from drift error. Drift errors occur due to change in system performance after calibration. Drift is primarily caused by temperature variation and it can be removed by further calibration. The timeframe over which a calibration remains accurate is dependent on the rate of drift that the test system undergoes in the user’s test environment. Drift can be minimized by providing a stable ambient temperature. The measurements were performed under constant temperature and humidity conditions and so no significant drift errors were observed. The systematic and random errors in the microwave measurement procedure are discussed in the following sections. 7.2 Systematic errors in microwave measurements Systematic errors are caused by imperfections in the test equipment and test set-up. These errors do not vary over time and so they can be characterized through calibration and mathematically removed during the measurement process. The process of removing systematic errors from the network analyzer s-parameter measurement is called measurement calibration. In network analyzer based measurements, the need for calibration arises because of the presence of several physical components between the sample under study and the measurement equipment. These introduce losses and phase delays in the measurement. In our experiments, these components include waveguide adapters, connectors and cables. The measurement set-up described in chapter 3 is shown again in figure 7.1. All the additional components added to connect the sample with the network analyzer have been highlighted in this figure. It should be 151 noted here that the frequency range covered in the frequency band defines the size of the waveguide that can be used for the measurements. Each of the eight frequency bands studied here had a specific rectangular slot dimension associated with them. As a result, in this measurement eight different waveguides were connected to the network analyzer ports. The network analyzer cables are 2.4 mm coaxial cable. But depending on the band, the connectors on the waveguide varied from 2.4 mm (Ka band) to N-type SMA (R band). Thus a variety of adapters were used in the measurement process and each frequency band was calibrated before carrying out the measurements. 152 Figure 7.1. Network analyzer measurement set-up is shown with the sources of errors marked in the red boxes. As seen in figure 7.1, there are several components between the measurement plane of the network analyzer and the desired measurement plane, which is at the sample interface. All these components, including the black coaxial cable shown in the figure, become part of the error box. The presence of special components in the measurement path leads to a difference between the measurement port of the network analyzer and the sample interfaces. These are marked as VNA measurement port and desired measurement port in figure 7.2. VNA Measurement Plane Port 1 VNA Measurement Plane Desired Measurement Plane Material under Test Error Box I [ ] [ [ ] ] Error Box II [ Port 2 ] Figure 7.2 Block diagram of the waveguide set-up. Port1 and port 2 indicate the location of the network analyzer ports while the desired measurement port is at the interface of the material under test. The additional cables and adapters used to connect the sample holder to the network analyzer ports introduce uncertainty in the measurement. These components are considered to be 153 error networks and their impact must be removed from the measured values in order to obtain the actual characteristics of the sample being studied. This is done by calibrating the experimental set-up before each measurement. The idea is to first characterize the error boxes over the entire measurement frequency range and apply this knowledge to obtain actual error-corrected sample measurements. This way the network analyzer’s measurement port is transformed to the desired measurement port. For s-parameter measurements, the reference planes are defined by means of a standard calibration technique such as Short-Open-Load-Thru (SOLT), Line-Reflect-Reflect-Match (LRRM) or Thru-Reflect-Line (TRL). These are all cascade-based two port techniques. These eliminate the need to know the internal structure of the components forming the error network. Here, a TRL calibration technique was applied. TRL technique does not rely on known standard loads, such as matched loads or opens, and so it does not suffer from the errors occurring due to load imperfections at higher frequencies. Each frequency band has a specific calibration kit. The calculations involved with the calibration procedure are implemented via a software package. The TRL calibration procedure consists of three steps. Consider the block diagram of the set-up is shown in figure 7.2. As mentioned earlier, the error box represents all the connectors, cables waveguides and waveguide adapters that are used in the measurement path. Instead of standard loads, the calibration procedure uses three different types of connections to characterize the error boxes. Since the system is considered to be a cascade of three sub-systems, it is better to use ABCD matrix. The overall parameters of a cascade system can be written as the product of the constituent networks, thus simplifying the calculations [46]. For the system shown in figure 7.2, the network equation can be written as, [ ] [ ] [ 154 ] [ ] [ or simply, ] [ ] [ ] [ ] here, [Am] represents the ABCD matrix measured for the overall two port network, [A1] and [A2] are the ABCD matrices of the individual error boxes and [As] corresponds to the ABCD matrix of the material under test. The goal is to determine the accurate parameters for the sample, that is, the [As] matrix. Once [As] is determined, the ABCD matrix can be converted to the sparameter matrix. The first step is to determine the parameters for the error box. The three scenarios used for this purpose are described below. It is assumed that the error network II is the mirror image of error network I and that both networks are uncoupled. The TRL calibration method employs known loads in the form of thru, reflect and line to characterize the network. For thru connection, the two waveguide sections are connected together. This set-up is shown in figure 7.3. VNA Measurement Plane VNA Measurement Plane Port 1 Error Box I Error Box II Figure 7.3 Thru connection for calibration procedure. The s-parameters of error network I can be converted into T-parameters using the wellknown conversion equations [ 39], [ ] 155 For the mirrored network II, the T-parameters can be obtained by simply swapping the ports, [ ] The T-matrix for the THRU set-up is given by the product of TI and TII, [ ] This matrix can be converted back to s-matrix and compared with the measured sparameters for the set-up shown in figure 7.2. Let STHRU represent the overall s-parameters for Thru connection. [ ] [ ] Due to symmetry and reciprocity of the circuit, it is expected to observe and = . By applying these conditions on the symmetric error box matrices, the following relation between the known ( , and = ) quantities for the thru connection is obtained, 156 and ) and unknown ( , It should be noted that for the case of thru connection the system is reciprocal ( ). Next, the reflect measurement is carried out. For reflection measurement, a metallic short is placed at the end of each waveguide. Identical equations are obtained for either port. The block diagram and calculations have only been shown for port 1. VNA Measurement Plane Port 1 Error Box 1 Figure 7.4 Block diagram of the reflect connection. The measured s-parameter matrix is denoted by and by following the similar calculation procedure as above the following equation can be obtained, [ here, ] is the reflection coefficient at the short circuited end of the waveguide. The last connection in the calibration procedure is line. This can be basically seen as inserting a known length of transmission line between the waveguides. It can, however, not be zero since that would be the case for thru connection. In this study, the length used was the same as the thickness of the sample holder (l). 157 Figure 7.5 Block diagram of the line connection. Following the same procedure of calculation as in step 1, the following relations are obtained, [ ] [ ] Equations (7.6) to (7.10) are used to characterize the error boxes. These form a set of five equations with five unknowns, namely, , , , γ and Γ. The derivation of these quantities is complicated [39]. The final form of the s-parameter matrix for the error box is given here in terms of the known measured quantities, √ [ √ ] 158 where, Thus the s-parameters for the error boxes are now determined. These can be converted to ABCD matrix and used in equation x to determine the ABCD matrix for the sample under study, which is converted back to s-parameters for further calculations. We were able to maintain return losses less than -50 dB for all bands. This allows us to neglect any unwanted reflections from the inner walls of the waveguide. 7.3 Random errors in microwave measurements Random error is defined as the result of a measurement minus the mean over a very large number of measurements of the same measurand carried out repeatedly. These can be treated statistically to find the variation in the values and specify the confidence level for the data. For each sample, the measurements were repeated ten times and the result was averaged. The error percentage and standard deviation observed in the measurements at 40 GHz is shown in table 7.1. TABLE 7.1 STANDARD DEVIATION IN THE DERIVED PARAMETER VALUES FOR BARIUM HEXAFERRITE Average Standard Error Material Property Value Deviation Percentage Real Permeability 1.0642 0.0042 5.17 Imaginary Permeability 0.0706 0.0018 2.37 Real Permittivity 1.4647 0.0058 1.56 159 Imaginary Permittivity 0.0516 0.0027 3.21 The reasons for random errors in these measurements can be identified as uncertainty in the experimental setup, including sample preparation and the errors due to the ambient conditions. The network analyzer uses the same coaxial cable for all frequency bands. The size of the waveguides for these bands varies from 4.32 inch to as small as 0.28inch across the 2 to 40 GHz frequency band. Thus several connectors have to be used to connect the different waveguides to the cables of the network analyzer which makes the system more sensitive to noise and drift. The adapters and connectors added to the waveguide were accounted for in the calibration process. In order to minimize these errors, an effort was made to keep the whole setup as stable as possible. Extra care was taken to ensure that the measurement path included minimum number of twists and turns and that the system remains unchanged between calibration and measurement steps. Another major source of random errors is the packing of the sample. The measurement becomes more challenging since the samples are not in solid form but powder form. The sample was manually milled right before filling in the sample holder to prevent the particles from forming agglomerates. The sample surface must be flat and there should not be any air gaps inside the sample holder. Since the sample is in powder form, the particles in the sample holder get displaced easily even with a slight movement and the density becomes non-uniform. It is important to make sure that the same uniform density is maintained when loading the sample as well as at the time of measurement. Proper alignment tools must be used to make sure that the sample holder and waveguides are completely aligned with each other and there is no air gap between the sample holder and the waveguide surfaces. 160 All attempts were made to eliminate these sources of random errors in the measurements. These were minimized by repeating the measurement ten times for each sample. The standard deviation in the values of real part of permittivity and permeability was observed to be +0.0058 and +0.0042, respectively. To keep the density fixed across all frequency bands, different samples had to be repacked for each measurement. A scale was used to weigh the mass of the sample. The variation in values read from the scale is about +0.02%, which can be neglected. The mean value and standard deviation in the measured values of real and imaginary parts of the transmission and reflection s-parameter are shown in table 7.2. Since the reflection and transmission coefficients are used in the calculations, only these parameters have been tabulated. The data presented in this table is the averaged result of ten repeated measurements. The standard deviation (σ) is calculated as, √ ∑ ̅ where, N is the number of experiments (which is 10 in this case), experiment and is the data value at the ̅ is the mean of all the data points. Standard deviation shows how much the measured data values deviate from the average value for that parameter. Sometimes the average value is also referred to as the expected value. Thus calculating the standard deviation is a way of identifying the variation in the measured values. 161 TABLE 7.2 STANDARD DEVIATION IN THE MEASUREMENT OF S-PARAMETERS AT EACH FREQUENCY BAND FOR BARIUM HEXAFERRITE NANOPOWDER Frequency Real Mean Real -0.108+0.0002 -0.365+0.0004 Imaginary Imaginary -0.031+0.0003 -0.693+0.0003 R Correlation C Mean -0.931 -0.119+0.0003 -0.413+0.004 -0.871 -0.026+0.0007 -0.678+0.0005 S Correlation C Mean -0.956 -0.096+0.0005 -0.397+0.0007 -0.755 -0.037+0.0007 -0.763+0.0006 G Correlation C Mean -0.891 -0.081+0.0005 -0.371+0.0008 -0.639 -0.029+0.0006 -0.740+0.0009 C Correlation C Mean -0.902 -0.158+0.0006 -0.427+0.0009 -0.726 0.018+0.0008 -0.825+0.0008 X Correlation C Mean -0.849 -0.132+0.001 -0.459+0.0011 -0.802 -0.042+0.0011 -0.873+0.0013 Ku Correlation C Mean -0.873 -0.162+0.0006 -0.319+0.0009 -0.634 -0.033+0.0007 -0.719+0.0009 K Correlation C Mean -0.981 -0.131+0.009 -0.368+0.013 0.588 0.056+0.016 -0.678+0.012 Ka Correlation C -0.988 -0.419 It can be observed here that the standard deviation increases with frequency. For instance, the standard deviation for all four parameters is observed to be the highest for Ka band. This is because since the size of the waveguides and sample holder becomes too small at this frequency 162 range. The system becomes extremely sensitive to even the slightest variation in the set-up. Even a tiny air gap becomes significant at this frequency. The calibration becomes tougher for the higher frequency bands and the calibration procedure had to be repeated several times before favorable results were achieved. Correlation is another statistical tool that represents the relationship involving dependence in the measured set of data. Correlations are useful since they provide an indication on whether the values of two parameters are related in some way. If this relationship can be predicted, then additional steps can be taken to improve the measurement results. ∑ ∑ ( ̅ ̅ ∑ It can be seen in table 7.2 that the real parts of ̅ ) ̅ and are strongly correlated. This means that the value of one is dependent on the other. The data also indicates that these parameters are negatively correlated. This is expected since energy that is reflected at port 1 or at the input to the sample and is a measure of the amount of is a measure of the amount of energy that reaches port 2 after transmission through the material. Therefore, if is large, it means that less energy will be available for transmission and thus lower amount of energy will reach port 2 as compared to the case when is small. Thus the results obtained here are in agreement with the expectations. The average error percentage in the measurement of samples existing in two different forms is shown in table 7.3. These values are also averaged for ten repeated measurements. The random error percentage is calculated as, 163 | ̅| ̅ In table 7.3, the error percentage has been compared for solid and powdered samples. Measurement of solid samples is relatively easier when compared to the measurement of samples that are in the form of powder. This is because the particles in the powder can shift inside the sample holder and give rise to air gaps. This leads to unexpected measurement results. The powdered samples therefore need extra caution when packing inside the sample holder. Another common source of error is the agglomeration of the particles at the corners of the sample holder which leads to the formation of discontinuity and gaps at the corners. Solid samples, on the other hand, fit perfectly inside the entire sample holder volume, leaving no room for air gaps. The challenge with these samples is to cut them in exact dimensions so that they are neither loose nor tight inside the sample holder. Solid samples of Teflon were especially cut out to the size of each frequency band. These were used for reference. In tables 7.3 and 7.4 the error percentage for samples is compared to that of nano-size barium hexaferrite sample. TABLE7.3 AVERAGE ERROR PERCENTAGE IN DIELECTRIC PROPERTIES OF SOLID AND POWDERED SAMPLES Real Imaginary Dielectric Loss Sample Permittivity Permittivity Tangent Teflon 2.03 + 0.034 0.0005 + 0.041 0.0002 + 0.062 1.47 + 0.053 0.053 + 0.069 0.016 + 0.86 (solid) Ba-ferrite (powder) 164 The error percentage for powdered samples is higher than that for the solid samples. This could be attributed to the challenges in measuring powdered samples that were described above. However, the error percentage is still very small and within acceptable limits. Therefore, it can be concluded that these measurements are reliable. The error percentage for dielectric loss tangent is higher than that for the real and imaginary parts of permittivity. This is because the loss tangent values were derived from the real and imaginary permittivity values and so the error propagates along in the calculations. The error percentage in the calculation of magnetic properties of the samples are summarized in table 7.4 TABLE7.4 AVERAGE ERROR PERCENTAGE IN MAGNETIC PROPERTIES OF SOLID AND POWDERED SAMPLES Real Imaginary Magnetic Loss Sample Permeability Permeability Tangent Teflon 0.26 0.78 1.56 1.064 + 0.015 0.071 + 0.019 0.041 + 0.023 (solid) Ba-ferrite (powder) The major sources of errors in the microwave measurements of the samples have been identified in this section. The error analysis shows that the results are within acceptable tolerances and that this technique can reliably determine the real and imaginary parts of electric permittivity and magnetic permeability for powdered samples. Next, the uncertainties in the measurement of millimeter wave properties are analyzed. 165 7.4 Uncertainty in millimeter wave measurements The experimental set-up for measurements at millimeter wave frequencies is more stable than the waveguide based microwave measurement set-up. This set-up does not have a pre-defined calibration procedure. The uncertainties in the BWO based measurement technique are determined by performing several reference scans before taking the actual measurement. Both transmittance and reflectance modes were scanned for each band while keeping the other conditions unchanged. These scans were performed without any sample in the transmission path. Repeated measurement of the transmittance and reflectance spectra, under constant conditions, should yield identical results. Therefore the ratio of any two measurements of either transmittance spectrum or reflectance spectrum should be unity. The results of the reference measurements are summarized in table 7.5. These values were obtained as the average over several measurements. In each case, the ratio was calculated for consecutive measurements performed under identical conditions. TABLE7.5 RESULTS OF REPEATED REFERENCE SCANS AT EACH FREQUENCY BAND Frequency band Q V W Transmittance spectrum ratio 1.015 1.012 1.01 Reflectance spectrum ratio 1.02 1.018 1.015 The results of the reference scan seem quite good. Although the ratio is not exactly unity, it is still very close. The reason for this variation observed in the test runs is the instability of the electronic devices that constitute the measurement set-up [103]. These include the BWO tubes 166 and high power supply. From the values shown in table 7.5, it can be concluded that the uncertainty in the measurements is about 2%. These measurements have been repeated ten times. As mentioned in the case of microwave measurements, repeated measurements reduce the random uncertainties in the experiment. The average value of these measurements and the variation in the measured transmittance and reflectance spectra are plotted together in figure 7.6. Since the standard deviation is not too large the plots appear to overlap in the figure. The inset in figure 7.6 provides a magnified view of the plots. The slight variation is evident from this plot. It can be concluded from these results that the measured values do not vary significantly. The stability of several transmittance scans show that the systematic errors are also negligible in this case. Figure 7.6 Experimental uncertainty and standard deviations for the transmittance spectra. 167 Figure 7.7 Experimental uncertainty and standard deviations for the reflectance spectra. The standard deviation for each case is also summarized in table 7.6. As discussed in chapter 5, in case of millimeter wave measurements the material properties are derived by curve fitting the calculated transmittance to the measured transmittance spectra. Therefore, it makes sense to identify the uncertainties in the measurement of the transmittance plots alone. The variation in the derived material properties would reflect the same uncertainties. It is not necessary to characterize the curve fitting procedure since it is a manual step and depends on the precision of the operator. TABLE7.6 STANDARD DEVIATION IN THE MEASURED TRANSMITTANCE AND REFLECTANCE SPECTRUM FOR MILLIMETER WAVE FREQUENCY BANDS Frequency band Standard Deviation 168 Transmittance Spectrum Reflectance Spectrum Q + 0.00177 + 0.001 V + 0.00214 + 0.0008 W + 0.00171 + 0.0019 169 Conclusion Microwave and millimeter wave properties of micro- and nano-size ferrite powders have been studied. Ferrites with different crystal structure and particle sizes have been studied. Measurement of samples in powder form is challenging at such high frequencies. Material characterization techniques were developed to accurately determine the intrinsic material properties, namely, permittivity and permeability of the powder samples. The network analyzer based microwave measurement technique has been modified to obtain precise measurements of material properties of powdered samples. Millimeter wave measurements have been performed by a quasi-optical spectrometer. Since the properties have been found to be size dependent, it is important that the measurement set-up is accurate enough to detect these differences. The measurement of samples in powder form is a complex procedure. In the past, the powder samples have been diluted with conductive materials or epoxy to fabricate a solid sample for measurements. The procedure followed in this study does not use any such additive. Therefore the properties of the samples can be determined precisely. This information is useful to understand the behavior of the sample in the presence of electromagnetic energy. This knowledge can also be applied to simulate the material more accurately. Designers can save time and money by simulating their design before fabrication. The results presented here reveal that the ferromagnetic resonance frequency of the ferrite samples vary with the particle size. Therefore the material can be tuned to resonate at different frequencies by changing the size of the particles. This is particularly useful in the design of high frequency tunable absorbers. The resonance observed in the case of nanoparticles is much sharper than that observed for bulk samples or samples containing micro-sized particles. 170 Absolutely no resonance was observed in case of samples that did not contain the proper phase of barium hexaferrite. Preparation of ferrite powders in nano-size is challenging. The preparation procedure and conditions affect the properties of the sample. The techniques developed in this study can be used for non-destructive testing to check if the desired phase has been achieved or not. Accurate characterization would allow scientists to utilize nanomaterials to their full potential and achieve high performance in diverse applications. 171 List of publications Journal Publications 1. A. Sharma, L. Chao, M. N. Afsar, “Microwave and millimeter wave ferromagnetic absorption of nanoferrites,” IEEE Transactions on Magnetics, vol. 48, no. 11, November 2012. 2. Anjali Sharma, M. N. Afsar, “Effects of particle size on magnetic and dielectric properties of ferrites at microwave and millimeterwave frequencies,” accepted at European Microwave Conference’2013 and submitted to IEEE transactions on Magnetics (under review). 3. A.Sharma, M.N. Afsar, “ Measurement Technique for Characterizing Constitutive Material Properties of Thin films,” accepted for oral presentation at International Instrumentation and Measurement Technology Conference (I2MTC), 2013. Journal manuscript has been submitted. 4. N.Rahman, A.Sharma, M.N.Afsar, “Characterization, design and optimization of low-profile cavities for UWB spiral antennas,” International Journal of Electromangetics and Applications, 2012. 5. A. Sharma, M. Obol, M.N. Afsar, “Microwave Complex Permeability and Permittivity Measurements of Commercially Available Nano-ferrites,” IEEE Transactions on Magnetics, vol. 47, No.2, Feb’2011. 6. A. Sharma, M.N. Afsar, “Microwave Complex Permeability and Permittivity of NanoFerrites,” Journal of Applied Physics, vol.109, Issue 7, April’2011. 172 7. Nahid Rahman, Mahumt Obol, Anjali Sharma, Mohammed Afsar, “Determination of Negative Permeability and Permittivity of Metal Strip Coated Ferrite Disks Using the Transmission and Reflection Technique”, Journal of Applied Physics,2010. 8. Zijing Li, Anjali Sharma, Ana M. Ayala, Mohammed Afsar, K.Korolev, “Broadband Dielectric Measurements on Highly Scattering Materials”, IEEE Transactions on Instrumentation and Measurement, Vol. 59, Issue 5, May 2010. Conference Proceedings 1. A.Sharma, M.N.Afsar, “Improved waveguide based technique for measurement of magnetic and electrical properties of powdered ferrite sample at microwave frequencies,” Joint MMM Intermag Conference, 2013. 2. A. Sharma, L.Chao, M.N.Afsar, “Microwave and millimeter wave measurements of electrical and magnetic properties of oxide based nanopowders” Joint MMM Intermag Conference, 2013. 3. John McCloy, A.Sharma, M.N.Afsar, et.al. “Mangetic and Mossbauer studies of unirradiated and gamma ray irradiated barium hexaferrite powders,” submitted to MMM 2010, revised 2012. 4. L.Chao, A.Sharma, B. Yu, M.N.Afsar, “Dielectric permittivity measurements of thin films at microwave and terahertz frequencies,” European Microwave Conference, 2012. 5. A. Sharma,L.Chao, M.N.Afsar, O. Obi, Z. Zhou, N. Sun, “Permittivity and permeability measurement of spin-spray deposited NiZn-ferrite thin film sample from 18 to 40 GHz,” Intermag 2012 Conference. 173 6. A.Sharma, M.N.Afsar, “Accurate permittivity and permeability measurement of composite broadband absorbers at microwave frequencies,” International Instrumentation and Measurement Technology Conference, 2011. 7. Anjali Sharma, Nahid Rahman, Mahmut Obol, Mohammed Afsar, “Precise Characterization and Design of Composite Absorbers for wideband Microwave Applications”, European Microwave Conference’2010. 8. Anjali Sharma, Nahid Rahman, Mohammed Afsar, “Precise Permittivity and Permeability Measurement of Absorbers over Broadband Microwave Frequency Range”, Conference of Precision Electromagnetic Measurements’2010. 9. Nahid Rahman, Anjali Sharma, Mahmut Obol, Mohammed Afsar, Sandeep Palreddy, Rudolf Cheung, “Broadband Absorbing Material Design and Optimization of Cavity-Backed, Twoarm Archimedean Spiral Antennas”, International Symposium on Antennas and Propagation’2010. 10. Nahid Rahman, Anjali Sharma, Mahmut Obol, Mohammed Afsar, Sandeep Palreddy, Rudolf Cheung, “Dielectric Characterization and Optimization of Wide-band, Cavity-backed Spiral Antenna”, Applied Computational Electromagnetics Society’2010. 11. Anjali Sharma, Mahmut Obol, Mohammed Afsar, “Microwave Permittivity and Permeability Properties and Microwave Reflections of Micro/Nano Ferrite Powders”, International Instrumentation and Measurement Technology Conference’2009. 174 References [1] C. Vittoria, “Ferrite uses at millimeter wavelengths,” Journal of Magnetism and Magnetic Materials, vol. 71, pp. 109-118, 1980. [2] Vijay K. Varadan, Linfeng Chen, Jining Xie, “Nanomedicine- Design and applications of magnetic nanomaterials, nanosensors and nanosystems,” Wiley Publications, 2008. [3] W.H.Emerson, “Electro-magnetic wave absorber and anechoic chambers through the years,” IEEE Transactions on Antennas and Propagation, vol. 21, issue 4, pp. 484–490, 1973. [4] Eugene F. Knott, John F. Shaeffer, Michael T. Tuley, “Radar Cross Section,” SciTech Publishing, pp. 248-266, 2004. [5] A. Sharma, N. Rahman, M. Obol, M. N.Afsar, “Precise Characterization and Design of Composite Absorbers for Wideband Microwave Applications,” European Microwave Conference, 2010, Paris. [6] S. Hilpert, “Genetische und konstitutive Zusammenhange in den magnetischen Eigenschaften bei Ferriten und Eisenoxyden,” Ber. Deut. Chem. Ges., vol. 42, p.2248, 1909. [7] M.M. Costa, G.F.M. Pires Junior, A.S.B. Sombra, “Dielectric and impedance properties’ studies of the lead doped (PbO)-Co2Y type hexaferrite,” Intl. Journal of materials chemistry and physics, vol. 123, pp. 35-39, 2010. [8] T. Yamaguchi, M. Abe, “Ferrites: Proceedings of sixth international conference on ferrites (ICF6),” The Japan Society of powder and powder metallurgy, Japan, 1992. [9] J. D. Adam, L. E. Davis, G. F. Dionne, E. Schloemann, S. N. Stitzer,“Ferrite materials and devices,” IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 3, March 2002. [10] A. M. Bhavikatti, S. Kulkarni, A. Lagashetty, “Characterization and electromagnetic studies 175 of nano-sized barium ferrite,” International Journal of Engineering Science and Technology, vol. 2 (11), pp. 6532-6539, 2010. [11] D. R Taft, “Hexagonal Ferrite Isolators,” Journal of Applied Physics, vol. 35, pp. 1776, 1968. [12] R. Valenzuela, “Novel Applications of Ferrites,” Hindawi Publishing Corporation, Physics Research International, vol. 2912, ID 591839, 9 pages [13] S. A. Morrison, C.L. Cahill, E.E Carpernter, S. Calvin, R. Swaminathan, M.E. McHenry, V.G Harris, “Magnetic and structural properties of nickel zinc ferrite nanoparticles synthesized at room temperature,” Journal of Applied Physics, vol. 95, pp. 6392, 2004. [14] J. M. Daniels, A. Rosenwaig, “Mossbauer study of the Ni-Zn ferrite system,” Journal of Applied Physics, vol. 48, issue 4, pp. 381-396, 1970 [15] D. Stopples, “Developments in soft magnetic power ferrites,” Journal of Magnetism and Magnetic Materials, vol. 160, pp.323-328, 1996. [16] C. Buzea, I.I.P. Blandino, K. Robbie, “Nanomaterials and nanoparticles: Sources and toxicity,” Biointerphases, vol. 2, issue 4, pp. MR17-MR17, 2007. [17] A. Lagashetty, S. Kalyani, S. Omprakash, “Combustion Synthesis of Nickel Ferrite,” Material Science Research India, vol. 3, issue 2, pp. 145-148, 2005. [18] D Minoli, “Nanotechnology applications to telecommunications and networking,” John Wiley and Sons, 2006. [19] S. Mornet, et.al. Magnetic Nanoparticle design for medical applications, Progress in Solid State Chemistry, vol. 34, pp 237-247, 2006. [20] M.A Mitchnick, D. Fairhurst, S.R. Pinnell, “Microfine zinc oxide (Z-cote) as a photostable UVA/UVB sunblock agent,” Journal of the American Academy of Dermatology, vol. 40, 176 pp. 85–90, 1999. [21] Ph. Buffat, J-P. Borel, “Size effect on the melting temperature of gold particles,” Physical Review A, vol. 13, issue 6, pp. 2287-2298, 1976. [22] U. Ozgur, Y. Alivov, H. Morkoc, “Microwave ferrites, part 1: Fundamental properties,” Journal of Material Science- Material Electronics, vol. 20, no. 9, pp. 789-834, 2009. [23] M. Montrose, “EMC and printed circuit board- design, theory and layout made simple,” IEEE Press, 1999. [24] Z. Peng, J.Y. Hwang, M. Andriese, “Microwave power absorption characteristics of ferrites,”IEEE Transactions on Magnetics, vol. 49, issue 3, March 2013. [25] Z. Peng, J.Y. Hwang, M. Andriese, “Magnetic Loss in Microwave Heating”, Applied Physics Express, vol. 5, 027304, 2012. [26] J. Thuery, E.H. Grant, “Microwaves: Industrial, scientific and medical applications,” 1992. [27] N. Tran, T.J. Webster, “Magnetic nanoparticles: biomedical applications and challenges,” Journal of Materials Chemistry, 20, pp. 8760-8767, 2010. [28] H. Nathani and R. D. K. Misra, “Surface effects on the magnetic behavior of nanocrystalline nickel ferrites and nickel ferrite-polymer nanocomposites,” Materials Science and Engineering, vol. 94, pp. 228, 2004. [29] L. Babes, B. Denizot, G. Tanguy, J. J. L. Jeune, P. Jallet, “Synthesis of iron oxide nanoparticles used as MRI contrast agents: a parametric study,” Journal of Colloid and Interface Science, vol. 212, pp. 474-482, 1999. [30] J. H. Hafner, C. L. Cheung, A. T. Woolley, C. M. Lieber, “Structural and functional imaging with carbon nanotube AFM probes,” Progress in Biophysics and Molecular Biology, vol. 77, pp. 73-110, 2001. 177 [31] A. M. Attiya, “Nanotechnology in RF and microwave applications: review article”, 29th National Radio Science Conference, NRSC’2012, Egypt. [32] A. M. Bhavikatti, S. Kulkarni, A. Lagashetty, “Characterization and electromagnetic studies of nano-sized barium ferrite,” International Journal of Engineering Science and Technology, vol. 2, issue 11, pp. 6532-6539, 2010. [33] K. Honda, S. Kaya, “On the magnetization of single crystals of iron,” Science Reports of Tohoku University, vol. 15, pp. 721,1926. [34] S. Kaya, “On the magnetization of single crystals of Nickel,” Science Reports of Tohoku University, 17, 639, 1928. [35] W. F. Brown, “The fundamental theorem of fine-ferromagnetic particle theory,” Journal of Applied Physics, vol. 39 (2), pp. 993, 1968. [36] E. S. Murdock, R. F. Simmons, R. Davidson, “Rpadmap for 10 Gbit/in2 Media: Challenges,” IEEE Transactions on Magnetics, vol 28,3078, 1992. [37] E. F. Schloemann, “Microwave behavior of partially magnetized ferrites,” Journal of Applied Physics, vol. 41, pp. 204-214, 1970. [38] K.J.Vinoy, R.M. Jha, “Radar Absorbing Materials: from theory to design and characterization,” Kluwer Academic Publishers, pp.19-48, 1996. [39] A. Sharma, M. N. Afsar, “Accurate permittivity and permeability measurement of composite broadband absorbers at microwave frequencies,” Proceedings of IEEE Transactions on Instrumentation and Measurement Technology Conference, pp. 1-6, 2011. 178 [40] M. N. Afsar, J. R. Birch, R. N. Clarke, “The measurement of the properties of materials,” Proceedings of the IEEE, vol. 74, issue 1, January 1986. [41] R. J. Cook, “Microwave Cavity Methods,” in High Frequency Dielectric Measurement Conference Proceedings, March 1972. [42] D. G. Ghodgaonkar, V. V. Varadan, V. K. Varadan, “Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies,” IEEE Transactions on Instrumentation and Measurement, vol. 39, no. 2, April 1990. [43] A. M. Nicolson, G. F. Ross, “Measurement of Intrinsic Properties of Materials by Time Techniques,” IEEE Transactions on Instrumentation and Measurement, vol. IM-19, pp. 377-382, Nov. 1970. [44] W. B. Weir, “Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies”, Proceedings of the IEEE, vol. 62, pp. 33-36, Jan. 1974. [45] J. Baker-Jarvis, E.J. Venzura, and W.A. Kissick, “Improved Technique for Determining Complex Permittivity with the Transmission/Reflection Method”, IEEE Transactions Microwave Theory Tech., vol. 38, pp. 1096-1103, Aug. 1990. [46] D. M. Pozar, “Microwave Engineering,” Third Edition, John Wiley & Sons, Inc. 2005. [47] Anjali Sharma, Mahmut Obol, Mohammed Afsar, “Microwave Permittivity and Permeability Properties and Microwave Reflections of Micro/Nano Ferrite Powders”, International Instrumentation and Measurement Technology Conference’2009. [48] J. Baker-Jarvis, “Transmission/Reflection and short-circuit line permittivity measurements,” National Institute of Standards and Technology, 1990. [49] K.S. Champlin, G. H.Clover, “Influence of waveguide contact on measured complex permittivity of semiconductors,” Journal of Applied Physics, vol. 37, pp. 2355-2360, 1966. 179 [50] A. Sharma, “Design of broadband microwave absorbers for application in wideband antennas,” MS Thesis, Tufts University, 2010. [51] A.H. Boughriet, C. Legrand, and A. Chapoton. “Noniterative stable transmission/ reflection method for low-loss material complex permittivity determination,” IEEE Transactions on Microwave Theory and Techniques, vol. 45, issue 1, pp.52-57, 1997. [52] T. Koutzarova, S. Kolev, C. Ghelev, K. Grigorov, I. Nedkov, “Structural and magnetic properties and preparation techniques of nanosized M-type hexaferrite powders,” Advances in Nanoscale Magnetism, Springer Proceedings in Physics, vol. 122, pp. 183-203, 2009. [53] N. Dishovski, A. Petkov, I. Nedkov, I. Razkazov, “Hexaferrite contribution to microwave absorber characteristics,” IEEE Transactions on Magnetics, vol. 30, issue 2, pp. 969-971, 1994. [54] S. Sugimoto, S. Kondo, K. Okayama, H. Nakamura, “M-type ferrite composite as a microwave absorber with wide bandwidth in the GHz range,” IEEE Transactions on Magnetics, vol. 35, issue 5, pp. 3154-3156, 1999. [55] M.R. Meshram, Nawal K. Agrawal, Bharoti Sinha, “Characterization of M-type barium hexagonal ferrite base wide band microwave absorber,” Journal of Magnetism and Magnetic Materials, vol. 271, pp. 207, 2004. [56] S.P. Ruan, B.K. Xu, H. Suo, F. Wu, S. Xiang, M. Zhao, “Microwave absorptive behavior of ZnCo-substituted W-type Ba hexaferrite nanocrystalline composite material,” Journal of Magnetism and Magnetic Materials, vol. 212, pp. 175-177, 2000. [57] M. K. Tehrani, A. Ghasemi, M. Moradi, R. S. Alam, “Wideband electromagnetic wave absorber using doped hexaferrite in Ku band,” Journal of Alloys and Compounds, vol. 509, pp. 8398-8400, 2011. 180 [58] R. Sharma, R. C. Agarwala, V. Agarwala, “Development of electroless (NiP)/BaNi0.4Ti0.4Fe11.2O19 nanocomposite powder for enhanced microwave absorption,” Journal of Alloys and Compounds, vol. 467, pp. 357-365, 2009. [59] S. P. Gairola, V. Verma, A. Singh, L. P. Purohit, R. K. Kotnala, “Modified composition of barium ferrite to act as a microwave absorber in X-band frequencies,” Solid State Communications, vol. 150, pp. 147-151, 2010. [60] A. Ghasemi, A. Hossienpour, A. Morisako, A. Saatchi, M. Salehi, “Electromagnetic properties and microwave absorbing characteristics of doped barium hexaferrite,” Journal of Magnetism and Magnetic Materials, vol. 302, pp. 429-435, 2006. [61] R.D.C. Lima, M.S.Pinho, M. L. Gregori, R.C.R. Nunes, T. Ogasawara, “Effect of double substituted m-barium hexaferrites on microwave absorption properties,” Materials SciencePoland, vol. 22, No. 3, 2004. [62] A. Bahadoor, Y. Wang. M N. Afsar, “Complex permittivity and permeability of barium and strontium ferrite powders in X, Ku, and K-band frequency ranges,” Journal of Applied Physics, vol. 97, 2005. [63] D. C. Kulkarni, V. Puri, “Perturbation of EMC microstrip patch antenna for permittivity and permeability measurements,” Progress in Electromagnetics Research Letters, Vol. 8, pp. 6372, 2009. [64] S. W. McKnight, L. Carin, C. Vittoria, S. F. Wahid, K. Agi, D. Kralj, “Picosecond-Pulse and Millimeter-Wave Spectroscopy of Barium Ferrite,” IEEE Transactions on Magnetics, Vol. 32, No. 2, March 1996. [65] N. Zeina, H. How, C. Vittoria, “Self-biasing circulators operating at Ka-band utilizing Mtype hexagonal ferrites,” IEEE Transaction on Magnetics, vol. 28, issue 5, sept 1992. 181 [66] Z. W. Li, L. Chen, C. K. Ong, “High-frequency magnetic properties of W-type barium ferrite BaZn2-xCoxFe16O27 composites,” Journal of Applied Physics, vol. 94, pp. 5918-5921, 2003. [67] P. Lubitz, F. J. Rachford, “Z type Ba hexagonal ferrites with tailored microwave properties,” Journal of Applied Physics, vol. 91, pp. 7613-7616, 2002. [68] A. Kakirde, B. Sinha, S. N. Sinha, “Development and characterization of nickel-zinc spinel ferrite for microwave absorption at 2.4 GHz,” Bulletin of Material Science, vol. 31, no. 5, pp. 767-770, oct 2008. [69] D. L. Zhao, Q. Lv, Z. M. Shen, “Fabrications and microwave absorbing properties of Ni-Zn spinel ferrites,” Journal of Alloys and Compounds, vol. 480, pp. 634-638, 2009. [70] R. Valenzuela, “Novel applications of ferrites,” Physics Research International, article ID 591839, 2012. [71] V. Raveendranath, K. T. Mathew, “New cavity perturbation technique for measuring complex permeability of ferrite materials,” Microwave and optical technology letters, vol. 18, no. 4, July 1998. [72] N. R. Panchal, “Crystal Structure, Preparation techniques and Swift heavy ions irradiation,” chapter 2, pp. 14-42. [73] A. Barthelemy, A. Fert, J. P. Contour, M. Bowen, V. Cros, J.M. De Teresa, A. Hamzic, J.C. Faini, J.M. George, J. Grollier, F. Montaigne, F. Pailloux, F. Petroff and C. Vouille, “Magnetoresistance and spin electronics,” Journal of Magnetism and Magnetic Materials, volumes 242-245, pp. 68-76, 2002. [74] A. P. Ramirez, “Colossal magnetoresistance,” Journal of Physics: Condensed Matter, vol. 9, pp. 8171-8199, 1997. 182 [75] M. B. Salamon, M. Jaime, “The physics of manganites: Structure and transport,” Reviews of Modern Physics, vol. 73, pp. 583-628, 2001. [76] E. L. Nagaev, “Colossal-magnetoresistance materials: manganites and conventional ferromagnetic semiconductors,” Physics Reports, vol. 346, issue 6, pp. 387-531, 2001. [77] A. A. Kuznetsov, O. A. Shlyakhtin, N. A. Brusentsov, O. A. Kuznetsov, “Smart mediators for self-controlled inductive heating,” European Cells and Materials, vol. 3, pp. 75-77, 2002. [78] I. I. Tkachov, “Millimeter wave complex dielectric permittivity and complex magnetic permeability measurements of absorbing materials,” Tufts University, PhD. Dissertation, 2000. [79] A. A. Volkov, Yu. G. Goncharov, G. V. Kozlov, S. P. Lebedev, and A. M. Prokhorov, “Dielectric measurements in the submillimeter wavelength region”, Infrared Physics, vol. 25, issue 1, pp. 369 – 373, 1985. [80] K. A. Korolev, L. Subramanian, M. N. Afsar, “Magnetic properties of diluted ferrites near ferromagnetic resonance in millimeter waves,” IEEE Transactions on Magnetics, vol. 42, no. 10, pp. 2864-286, 2006. [81] M. N. Afsar, K. A. Korolev, L. Subramanian, I. I. Tkachov, “Complex permittivity and permeability measurements of ferrimagnets at millimeter waves with high power sources,” IEEE Transactions on Magnetics, vol. 41, no. 10, 2005. [82] A. A. Volkov, G. V. Kozlov, S. P. Lebedev, “The optimization of dielectric measurements in the submillimeter wave range,” Radiotekh Elecktron, vol. 24, pp. 1405-1408, 1979. 183 [83] Y. Chen, A. L. Geiler, T. Chen, T. Sakai, C. Vittoria, and V. G. Harris, “Low-loss barium ferrite quasi-single-crystals for microwave application,” Journal of Applied Physics, vol. 101, 2007. [84] K. Haneda, A H. Morrish, “Magnetic properties of BaFe12O19 small particles,” IEEE Transactions on Magnetics, vol. 25, no. 3, 1980. [85] C. Kittel, “Physical theory of ferromagnetic domains,” Review of Modern Physics, vol. 21, pp. 54, 1949. [86] K. Goto, M. Ito, T. Sakurai, “Studies on magnetic domains of small particles of barium ferrite by colloid-SEM method,” Japan Journal of Applied Physics, vol. 19, p. 1339, 1980. [87] D. Polder, “On the theory of ferromagnetic resonance,” Phys. Rev. 73 (9), pp. 1120, 1948. [88] B. Lax, K.J. Button, “Microwave Ferrites and Ferrimagnetics,” McGraw-Hill, New York, 1962. [89] C. Kittel, “On the theory of ferromagnetic resonance absorption,” Physical Review, vol. 73, pp. 155, 1948 [90] J. McCloy, R. Kukkadapu, J. Crum, B. Johnson, T. Droubay, “Size effects on gamma radiation response of magnetic properties of barium hexaferrite powders,” Journal of Applied Physics, vol, 110, 2011. [91] H.L. Glass, “Ferrite films for microwave and millimeter-wave devices,” Proceedings of the IEEE, vol 76, issue 2, pp. 151-158, 1988. [92] B. T. Shirk and W. R. Buessem, “Temperature dependence of Ms and K1 of BaFe12O19 and SrFe12O19 single crystals,” Journal of Applied Physics, vol. 40, issue 3, pp. 1294–1296, 1969. 184 [93] C. D. Mee, J. C. Jeschke, “Single-domain properties in hexagonal ferrites,” Journal of Applied Physics, vol. 34, pp.1271, 1963. [94] K. Haneda, C. Miyakawa, and H. Kojima, “Preparation of high coercivity BaFe12O19,” Journal of the American Ceramic Society, vol. 57, pp. 354, 1974. [95] O. Kubo, T. Ido, H. Yokoyama, “Preparation of Ba ferrite for perpendicular magnetic recording media,” IEEE Transactions of Magnetics, vol. MAG-18, pp. 1122, 1982. [96] B. T. Shirk, W. R. Buessem, “Magnetic properties of barium ferrite formed by crystallization of a glass,” Journal of the American Ceramic Society, vol. 53, pp. 192, 1970. [97] K. Oda, T. Yoshio, K. O-oka, F. Kanamaru, “Magnetic properties of SrFe12O19 particles prepared by the glass ceramic method,” Journal of Materials Science Letters, vol 3, pp. 1007, 1984. [98] F. Licci, T. Besagni, “Organic resin method for highly reactive and homogeneous hexaferrite powders,” IEEE Transactions on Magnetics, vol. MAG-20, p. 1639, 1984. [99] K. Haneda, C. Miyakawa, K. Goto, “Preparation of small particles of SrFe12O19 with high coercivity by hydrolysis of metal-organic complexes,” IEEE Transactions on Magnetics, vol. MAG-23, p. 3134, 1987. [100] V. Pillai, P. Kumar, M.J. Hou, P. Ayyub, D.O. Shah, “Preparation of nanoparticles of silver halides, superconductors and magnetic materials using water-in-oil microemulsions as nano-reactors,” Advances in Colloid and Interface Science, vol. 55, pp.241-269, 1995 [101] T. Koutzarova, S. Kolev, C. Ghelev, K. Grigorov, I. Nedkov, “Structural and magnetic properties and preparation techniques of nanosized M-type hexaferrite powders,” Chapter 10, 183-203. 185 [102] John R. Taylor, “An Introduction to Error Analysis,” University Science Books, 1982, pp.81-93. [103] Z. Li, A. Sharma, A. M. Ayala, M. N. Afsar, K. A. Korolev, “Broadband dielectric measurements on highly scattering materials,” IEEE Transactions on Instrumentation and Measurement, vol. 59, issue 5, pp. 1397-1405, 2010. 186 Appendix 187 I2MTC 2009 - International Instrumentation and Measurement Technology Conference Singapore, 5-7 May 2009 Microwave Permittivity and Permeability Properties and Microwave Reflections of Micro/Nano Ferrite Powders M. N. Afsar, IEEE Fellow, A. Sharma, and M. Obol, IEEE Member High Frequency Materials Measurement and Information Center, Department of Electrical Engineering, Tufts University, Medford, Massachusetts, USA Abstract— The application of magnetic powders are becoming attractive in electromagnetic shielding interferences in wireless systems. Magnetic powders such as Fe3O4 are also very important in magnetic resonance imaging as well as drug delivery applications in biomedical researches. Also, some of the special catalyst nano magnetic particles are increasingly useful in the fuel cell applications. Hence, a good understanding of the electromagnetic wave response such as permittivity and permeability of magnetic powders may be important in modern microwave technological applications. In this paper we present broad-band measurements on the real and imaginary parts of permeability and permittivity of micron sized commercial nickel ferrites of Ni1-x-yCoxCuyFe2-zdMnzO4 (TT2) and Ni1-xZnxFe2-yMnyO4 (TT86) in the frequency range from 4 to 40 GHz. We also present broadband permeability and permittivity of some other commercially available nano and micron sized ferrite powders, so that this is a paper that explores microwave properties of nine different nano and micron sized magnetic powders in terms of permittivity and permeability aspects. Keywords-Components— Broadband, permeability, permittivity, TRL calibration and important ferrite powders I. INTRODUCTION It is obvious that the microwave permittivity and permeability of these solid substances are very well known. The partial attempts to measure the permeability and permittivity of these solid and powdered materials were presented in the previous investigations [1, 2, 3, 4, and 5]. The current technology adopts those solid composites in the scheme of nano and micro sizes. The precision measurements [1] showed that nano magnetic powders microwave permittivity and permeability are very different compared to their solid cases. It is our understanding that it may be very useful to extend the work [1] into the broadband microwave regime. As such, the objective of this work is to present the magnetic characteristics of nine different powdered ferrite composite materials. The three different commercially available powdered magnetic composites, purchased from Trans-Tech, are known as TT2, TT86 and Ba2Co2Fe12O22 (99% pure phase hexaferrite). The average particle size of these powders was between 3 and 6 micron. The other six different nano ferrites (average particle sizes were less than 40 nm) used 978-1-4244-3353-7/09/$25.00 ©2009 IEEE in the experiment are purchased from Sigma-Aldrich, Inc. To carry out the powder measurements, the ferrite powders, whose complex permittivity and permeability are to be determined, are loaded inside calibrated waveguide shims and measured with a network analyzer. The measurement procedure is basically similar to the technique in [1]. The difference in this paper is to apply the technique to six different bands. Here, the raw ferrite powders were simply loaded inside waveguides without applying any pressure so that the same density is maintained; perhaps this approach will reduce particles interfering with each other at some degree. The waveguides are different in physical sizes for measurements at different frequency bands. In addition to that this paper extrapolates the continuous scattering parameter of broadband using microwave permittivity and permeability in six different bands. This calculation approach provides broadband reflectivity and transmittance of scattering parameters which is often hard to obtain by using the free space measurements [4]. The method applied here is the usual calibration technique, known as TRL (through-reflect-line). The calibrated parameters help to determine the complex permeability and permittivity of the powdered ferrite composites. II. THEORY OF WAVEGUIDE The permeability and permittivity measurements of various materials were reported in previous work [1], [2], [3], [4] and [5]. The theory of this work is based on paper [1], and each parameter in the equations well corresponds to the work of [1]. In order to expand this to the broadband measurements purposes, in this work, several micro and nano powdered ferrite composites were loaded in the waveguides of six different rectangular waveguides of G (4 to 6 GHz), C (4 to 8 GHz), X (8 to 12.4 GHz), Ku (12.4 to 18 GHz), K (18 to 26.5 GHz) and Ka bands (26.5 to 40 GHz), and were measured with the help of TRL calibration. The Agilent’s 8510C Vector Network Analyzer (VNA) was used to record the scattering parameters from waveguides which were further used to perform transmission and reflection measurements on the powdered ferrite composites. The measurement method in a previous paper [1] was used to obtain the permeability and permittivity of the powders (equations 1, 2 and 3 are from paper [1]) and the BakerJarvis method [3] was used to calculate broadband scattering parameters S11 and S21 (equations 4, 5, and 6 are from paper [3]) using permittivity and permeability in six different waveguides in this paper. The purpose in doing so is to ensure that the derived permeability and permittivity by the waveguide technique [1] has the capability to reproduce the appropriate scattering parameters as obtained by calculation method [3]. It is also a reasonable idea to present broadband scattering parameters for demonstrating purpose. Γ= T =e μr +1 εr ⎛ω ⎞ − j ⎜ ⎟ d μrε r e ⎝c⎠ −γd S11 (ω ) = S 21 (ω ) = Γ = K ± K 2 −1 ~ ~ S 2 − S 2 +1 K = 11 ~ 21 2S11 ~ ~ S +S −Γ T = 11~ 21~ 1 + ( S11 + S 21 )Γ ⎛ ⎞⎜ 1 ⎛ 1 + Γ ⎞⎛ 1 ⎞⎛⎜ μ = − j⎜ ⎟⎜ ⎟⎜ ln( ) + j (2πn − ϕT ) ⎟⎟⎜ ⎝ 1 − Γ ⎠⎝ 2πd ⎠⎝ T ⎠⎜ ⎝ μr −1 εr III. (1) 2 2⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ ⎟ ⎜ ⎟ −⎜ ⎟ ⎟ ⎜λ ⎟ ⎝ 0 ⎠ ⎝ 2a ⎠ ⎟ ⎠ = (1 − T 2 )Γ 1 − T 2Γ 2 (1 − Γ 2 )T (4) (5) (6) 1 − T 2Γ 2 EXPERIMENTAL RESULTS OF NICKEL FERRITES Ni1-x-yCoxCuyFe2-z-dMnzO4 (TT2): Figure 1 represents the real and imaginary parts of the permittivity and permeability of the two different Trans-Techs powdered micron sized Nickel ferrites. −1 (2) ⎛c ⎝ f ε = − j ⎜⎜ ⎞ ⎟⎟ ⎠ 2 ⎞⎛⎜ 1 ⎛ 1 − Γ ⎞⎛ 1 ⎞⎛⎜ ⎜ ⎟⎜ ⎟⎜ ln( ) + j (2πn − ϕT ) ⎟⎟⎜ ⎝ 1 + Γ ⎠⎝ 2πd ⎠⎝ T ⎠⎜⎝ 2 ⎞ ⎛ 1 ⎞ ⎟ 1 ⎜ ⎟ − ⎛⎜ ⎞⎟ ⎟ ⎜λ ⎟ ⎝ 2a ⎠ ⎟ ⎝ 0⎠ ⎠ 2 (3) According to the recorded S parameters from the VNA, the complex permittivity and permeability of the powdered ferrite composite materials were derived for each different band based on the Weir algorithm [2], i.e., equation set (1) ,equation (2) and equation (3). Although the permeability and permittivity could be determined by the scattering parameters through the VNA, the scattering parameters in six different bands are very different. This is due to the geometrical dimensions of calibration standards for each band and the thicknesses of the appropriate loaded powder inside the waveguide as per the recommended phase regime from Agilent. Although the group delays of wave propagation approach would help to load the powders until the shim is filled by powders [5], that group delay approach would also need to know the initial guess to the parameters. Sometime guessing is difficult, especially to the magnetic materials when both permeability and permittivity are unknown [3], for example. In order that this work keeps the tedious and mechanical approach to the measurements, that is, to load powders until we see the reasonable phases of scattering parameters, to the manufacturer (Agilent). As long as we determine the complex permeability and permittivity of magnetic powder materials, we will always be able to regenerate the scattering parameters for those powders in the entire frequency range. The formulations for regenerating scattering parameters may be as follows: Fig. 1 Measured complex permeability and permittivity of TT2. Fig. 2 Measured complex permeability and permittivity of TT86. Figure 3 represents the calculated scattering parameters S11 and S21 of these powders assuming the load (d) thicknesses of each powder equal to 0.5mm for equation (5). Calculated S-parameters of TT2, d = 0.5mm Magnitude (dB) 0 magnitude of S11 -5 magnitude of S21 -10 phase of S11 -15 phase of S21 -20 -25 -30 -35 4 8 12 16 20 24 28 32 36 Phase (degree) 0 -20 -40 -60 -80 -100 -120 -140 -160 -180 5 40 Frequency in GHz Fig. 3 Calculated scattering parameters of TT2, with thickness of loaded powder as 0.5 mm. Calculated S-param eters, TT86, d=0.5m m Magnitudes magnitude of S11 magnitude of S21 phase of S11 phase of S21 -10 -15 Phase (degree) IV. 0 -20 -40 -60 -80 0 -5 -100 -120 -140 -160 -180 -20 -25 -30 -35 4 8 12 16 20 24 28 Frequency in GHz 32 reasonable data in this measurement process. It should be understood that the presented permeability and permittivity at the entire frequency region will be the average complex permeability and permittivity. As for the TT2, that would be the following, μ~r ≈ 1.15 − j 0.1 and ε~r ≈ 2.22 − j 0.2 . Ni1-xZnxFe2-yMnyO4 (TT86): from Figure 2, one can easily note the phenomena we had seen in Fig.1. The average complex permeability and permittivity of TT86 is as follows, μ~r ≈ 1.2 − j 0.1 and ε~r ≈ 2.3 − j 0.2 . One would note that the two different microns sized powdered nickel spinel ferrites have almost similar microwave properties in nature. Experimentally, we were able to obtain complex permittivity and permeability of the powders by using the scattering parameters for different waveguides. The calculated S-parameters of TT86 are presented in Fig. 4. Since we have not seen any unusual S-parameters by inverse calculation it confirms that the measurement and calculation methods used in this article are reliable for the simultaneous permeability and permittivity measurements as well as calculation of scattering parameters for other micron and nano sized magnetic powders. 36 40 EXPERIMENTAL RESULTS OF OTHER FERRITES In section 3, we succeeded to determine the broadband permeability and permittivity of two different technologically important micron sized powdered nickel ferrites. Therefore, in this section, we are simply interested in determining broadband permittivity and permeability of other technologically important nano and micron sized ferrites. It may be important to present the measurements of these powdered ferrites as a purpose of ferrite data library. Figures 5, 6, 7, and 8 are for the available micron sized powdered planar hexaferrite of Co2Y (Ba2Co2Fe12O22) and powdered nano M-type hexaferrites of Ba2M (BaFe12O19) and SrM (SrFe12O19). Fig. 4 Calculated scattering parameters of TT86, with thickness of loaded powder as 0.5mm. We must point out here that the obtained permittivity and permeability in each waveguide has some discrepancies with other waveguides. This is reasonable, because ideally, according to TRL standards of waveguides, the shim thickness should be within quarter wavelengths of central operation frequencies and that standards were usually in air; but this is very hard to maintain for general cases unless each TRL standard shim thickness was specifically reconfigure out to the unknown loading materials. As such a mathematical averaging method (least squares method of polynomials) was applied to show the continuous data in entire frequency range for six different bands. So the following broadband measurements presented in the paper would be able to overwrite the boundaries of waveguides. The estimated errors from the different bands of permittivity and permeability, which are less than 5% would be considered a Fig. 5 Measurements showed that the real permittivity of ferrites depend on the sizes of particles of ferrites. The broadband measurements showed that micron sized hexaferrites have slightly higher permittivity compared to the micron sized nickel ferrites in section 3. However, the nano hexaferrites showed microwave properties that are close to that of air, in showing low permittivity and low permeability with low losses as well. Now, we present the Spinel nano ferrites microwave complex permeability and permittivity starting from Fig.9 to Fig.12 (see figures from 9 to 12). Fig. 6 Measurements showed that the planar micron sized planar hexaferrites dielectric loss is also slightly higher than nano sized M-type hexaferrites. Fig. 9 Measurement showed the nano Spinel ferrites real permittivity, permittivity of nano magnetite (Fe3O4) has exceptional permittivity. Fig. 7 Measuremnts showed that micron sized planar hexaferrite has larger permeability compare to the nano sized M-type hexaferrites. Fig. 10 Measurements showed that Spinel ferrites imaginary permittivity, the magnetite has strong imaginary component. Fig. 8 Measurements showed that the nano and micron sized hexaferrite are in the state of low magnetic losses, the differences probably describes the systematic and human errors in measurements process. Figures 9, 10, 11, and 12 are for the nano sized available powdered spinel ferrites broadband permeability and permittivity measurements. The measured data showed that powdered nano spinel ferrite of Fe3O4 has exceptional properties compared to the other powdered nano spinel ferrites. It may be contributed either to the aggregate properties of magnetite, since it has strong dipoles or to the semiconductor properties in magnetite between Fe2+and Fe3+. Besides that, the other nano ferrite powders showed pretty similar permittivity and permeability behaviors which can be seen in the above figures. Most notable phenomena is that the microwave permittivity of the nano powders hover close to the permittivity of the air, and as expected the microwave permeability of the nano powders are similar to air. These properties of the nano powders may be useful in the technology that looks for materials with properties similar to air. It should also be very interesting that although the microwave permittivity and permeability of those nano materials are close to air, those powders are capable of generating significant reflectivity at the higher frequency region. Fig. 11 Measurements showed that nano Spinel ferrites real permeability is approximately one which is reasonable. matter of magnetic particles. For permittivity measurements alone, we have not seen any difference between TT2 and TT86. Calculating the reflection (S11) of both powders, it has been shown that the powders are capable to generate more reflectivity at higher frequencies compared to their lower frequency bands. This is consistent with what we obtained for scattering parameters using six different waveguides. It is our understanding that it was not necessary to show the calculated scattering parameters for other ferrite powders since the calculation is straightforward now. According to the nano ferrite powders measurements, one would realize that the powdered nano hexaferrites in general would have smaller microwave losses compared to the powdered spinel ferrites at comparable frequencies. Also, relative permittivities for nano spinel ferrites are little higher compared to the relative permittivities of nano hexaferrites. Interestingly, nano ferrite of magnetite is much different from the other nano spinel ferrites which are regarded to their relative real permittivity and imaginary permittivity. In summary, it is obvious now that the relative permittivity of the nano and micron sized ferrites is very different as compared to their solid state relative permittivity. Thus, this paper presents following important concepts. The nano magnetite (Fe3O4) powder is for MRI measurement that has a very high permittivity compared to other nano powders. Perhaps, the permittivity of the magnetite makes it very special in biomedical applications. Besides that micron sized ferrite have generally two to there order higher permittivity compare to the air. Lastly, several other nano powders permittivity and permeability are hovering close to air while they have the capability to generate microwave reflectivity; this will turn out to be useful for non destructive sensor or drug delivery application. Acknowledgment This research is supported by a contract from US Army National Ground Intelligence Center. References Fig. 12 Measurements showed that nano Spinel ferrites imaginary permeability is very small, the differences may describes the systematic and human errors in the measurement process. DISCUSSION AND CONCLUSIONS The complex permittivity and permeability of nine different composite ferrite powders were determined by using six different rectangular waveguides. The obtained results are reasonably good; the measurements showed that permittivity and permeability depend on the density, size, and volume fraction [1] N. N. Al-Moayed, M. N. Afsar, U. A. Khan, S. McCooey, M. Obol, “ Nano Ferrites Microwave Complex Permeability and Permittivity Measurements by T/R Technique in Waveguide”, IEEE, Transactions on Magnetics, Vol.44, No.7, July 2008. [2] W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proceedings of the IEEE, Vol. 62, No.1, pp. 33-36, January 1974. [3] J. Baker-Jarvis, E. J. Venzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microwave Theory Tech., vol. 38, No.8, pp. 1096-1103, August 1990. [4] R. Grignon, M. N. Afsar, Y. Wang and S., Butt, “Microwave broadband free-space complex dielectric permittivity measurements on low loss solids,” IMTC 2003-Instrumentation and Measurement Technology Conference, Vail CO, USA, 20-22 May 2003. [5] A. Bahadoor, Y. Wang and M. N. Afsar, “Complex permittivity and permeability of barium and strontium ferrite powders in X, KU, and Kband frequency ranges”, JOURNAL OF APPLIED PHYSICS 97, 10F105, 2005. 308 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 2, FEBRUARY 2011 Microwave Complex Permeability and Permittivity Measurements of Commercially Available Nano-Ferrites Anjali Sharma and Mohammed N. Afsar High Frequency Material Measurement and Information Laboratory, Tufts University, Boston, MA 02155 USA The dielectric permittivity and magnetic permeability of nano-sized magnetic powders are studied for a wide microwave frequency range from 2 to 40 GHz. These powders are studied for their potential application as soft microwave absorbers in wireless systems as well as for use in the manufacture of small magnetic recording tape, transformers and circulators. A newly developed and precise transmission-reflection based waveguide technique has been used to carry out measurements across the eight frequency bands. These materials have been accurately characterized for the first time across this frequency range. In this paper, we present equations for simultaneous calculation of permittivity and permeability across a wide frequency band using the vector network analyzer. To account for variable sample thickness in the in-waveguide measurements, the algorithm for transmission and reflection calculations has been modified. The results show that the dielectric permittivity depends on the particle size and density of the sample used for measurement. Index Terms—Nano-ferrites, permeability, permittivity, TRL calibration, waveguide technique. I. INTRODUCTION ANO POWDERS are agglomerates of nanoparticles that have an average size between 1 and 100 nm. Iron based nano-powders are spherical metal nanostructure particles, typically 20–40 nm in size. Electromagnetic properties of solid forms of ferrite compounds have been studied in the past [1]. Various sizes of nano-ferrite powders are now commercially available. Measurements carried out on nano-sized powders have shown that the microwave permittivity and permeability of these materials differ from those of the material in solid state [2]. Therefore, there is a growing interest in studying these powders to understand how the material properties are affected by particle size. Nano-powders of metal substituted iron oxide find extensive application in biomedical and integrated circuit technology. These materials prove very useful in biological drug delivery systems, DNA-separators as well as in magnetic recording and information storage [3]. Due to their low conductivity, these materials have also been used in other microwave applications such as transformers and circulators. Recently, these powders are being investigated for their potential as microwave absorbing materials. Microwave absorbers have been in demand for stealth applications. With the use of higher and broader frequency bands for communication and military operations, the need for materials that absorb electromagnetic radiation at these frequencies has increased. To identify the use of nano-ferrites in these applications, it is important to determine their electromagnetic properties. The absorption capability of a material depends on the intrinsic material properties, namely, permittivity and permeability, which may be frequency dependent [4]. The frequency spectra for the complex relative permittivity and magnetic permeability of a material is therefore N Manuscript received July 09, 2010; revised August 10, 2010; accepted August 27, 2010. Date of current version January 26, 2011. Corresponding author: A. Sharma (e-mail: Anjali.sharma@tufts.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2073457 of prime importance to engineers and scientists who deal with applications where large frequency variations are common. Both permittivity and permeability are complex quantities. The extent to which an electromagnetic wave is attenuated and phase shifted depends on the permittivity and permeability of the material at that frequency. The real part of permittivity (permeability) determines the amount of energy that is stored in the material from the external electrical (magnetic) field while the imaginary part determines the amount of energy lost by the wave in traversing through the material [4]. Therefore, a large real permittivity implies that a large phase change occurs as the wave traverses the material and a large imaginary part of permittivity indicates that the magnitude of the wave will be heavily attenuated. This explains why the knowledge of the exact dependence of these parameters on frequency is required to understand the behavior of the material. In this work, five nano-ferrite powders were characterized to determine their electromagnetic properties over a wide frequency range from 2 to 40 GHz. This microwave frequency range is important because of lower propagation loss and cheaper fabrication of microwave devices at these frequencies as compared to the millimeter wave frequency range [5]. A transmission-reflection (T/R) based waveguide technique that employs a vector network analyzer was used to measure the scattering parameters for each sample. Using this technique, one can record both reflection and transmission spectra generated when an electromagnetic wave travels through the material under study. Based on the reflection and transmission spectra obtained from the measurements, the frequency at which the sample exhibits strong absorption can be determined. The algorithm used to determine the permittivity and permeability from the measured data has been modified over the years to improve accuracy [6]–[8]. The algorithm used in this study takes into account the effect of the thickness of the loaded material and its permittivity and permeability on the cutoff wavelength inside the waveguide. Using this technique, precise electromagnetic properties were determined for the commercially available nano-powders. A thorough error analysis is also presented to account for the systematic and random errors in the measurement process. 0018-9464/$26.00 © 2010 IEEE SHARMA AND AFSAR: PERMEABILITY AND PERMITTIVITY MEASUREMENTS OF COMMERCIALLY AVAILABLE NANO-FERRITES TABLE I SAMPLE DESCRIPTION 309 waveguide delay in the vector network analyzer to further remove errors. The modified equations used in the measurements are given below: (1) II. SAMPLE DESCRIPTION The nano-powders studied in this work were purchased from Sigma Aldrich. The powdered samples have a grain size that varies between 40 and 100 nm for different samples. The frequency range from 2 to 40 GHz is divided into eight frequency bands, namely, R (1.70–2.60 GHz), S (2.60–3.95 Ghz), G (3.95–5.85 GHz), C (5.85–8.20 GHz), X (8.20–12.40 GHz), Ku (12.4–18.00 GHz), K (18.00 GHz–26.5 GHz) and Ka (26.50–40.00 GHz). Depending on the covered frequency range, each band corresponds to specific waveguide dimensions. To maintain uniformity in the measurements taken across different bands, the density of each nano-powder was kept constant across all bands. With density and volume fixed for each band, the appropriate weight of the sample to be filled in the waveguide shim was calculated. The weight of the sample holder is measured with and without the powder to ensure that the required density is maintained. To maintain uniform distribution of the powder and avoid the presence of any air gap in the sample holder, the sample was steadily filled in the shim. The density of each sample used in the measurement is summarized in Table I. Strontium and barium ferrite are M-type hexaferrite whereas the rest of the powders are spinel nano ferrites. Lossless transparent tape was used on either sides of the shim to hold the powder inside the shim. It has been shown that the inclusion of tape has negligible effect on the measured S-parameter [9]. where is the quarter wavelength difference between thru and line in air, is the thickness of the sample inside the waveguide, is the wavenumber of the sample, and is the cutoff wavenumber. These equations take into account the effect of values that are smaller than using samples with thickness the waveguide shim used in the experimental setup. Ideally, the shim thickness should be within quarter wavelengths of the central operation frequency. But this is hard to maintain since the thickness used for each sample depends on the density requirement. The difference between the material thickness and sample holder thickness was taken in to account when performing the calculations. Each frequency band was sub-divided into 201 frequency points at which measurement was taken, giving a total of 1206 frequency points. It should be noted that the data at the end of one band may show some discontinuity with the data at the starting frequencies of the successive band. This may be due to experimental errors, depending on how carefully the operator used the instruments. To remove the experimental discrepancies in the data across different bands a mathematical averaging method (least squares method of polynomials) was used. The derived data is very reliable and not effected by the scattering voltage ratios of the network analyzer. The final form of the equations used to determine permittivity and permeability is shown below: (2) (3) III. EXTRACTION OF PERMITTIVITY AND PERMEABILITY The transmission-reflection based waveguide technique has been widely used to determine the properties of solids. It can be further modified for the measurement of soft powders. The basic technique has been explained in [10]. The vector network analyzer measures the scattering parameters of the 2-port network formed by the waveguide shim filled with the sample under study. The algorithm proposed by Baker-Jarvis was then used to derive the permittivity and permeability values from this data [8]. However, this requires an initial guess parameter to remove phase ambiguities. We were able to eliminate this ambiguity by using phase unwrapping technique [10]. Additionally, the cutoff frequency for each frequency band was calculated and set as the where is the reflection coefficient, is the transmission coefand are propagation constant for the ficient, mode with and without the material inserted in the waveguide, is the longer dimension of the rectangular waveguide, is the phase of transmission coefficient, and is the material thickness. IV. RESULTS The accuracy of waveguide based measurements has been validated by measuring the electromagnetic properties of a known material, namely, yttrium iron garnet (YIG) [10]. According to the Pacific Microwave Ceramics Brochure, the 310 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 2, FEBRUARY 2011 Fig. 3. The measurement result for S-parameters for the barium ferrite nanopowder sample. Fig. 1. For a sample thickness of 0.5 mm, the permittivity and permeability of YIG has been measured in X band [10]. TABLE II ELECTROMAGNETIC PROPERTIES MEASURED AT DIFFERENT PARTICLE SIZE Fig. 2. At a density of 0.4004 g/cm , the average value of real and imaginary parts of permeability for barium ferrite is 1.1046 and 0.0706 while for permittivity it is 1.4647 and 0.0516, respectively. permittivity of YIG is around . This value is in close agreement with our results, shown in Fig. 1. The same technique has now been applied to nano-powders and the values of permittivity and permeability thus obtained for barium ferrite nano-powder are shown in Fig. 2. It can be observed that the value of real part of permeability remains stable throughout the frequency range except for a slight dip observed through K band. The real part of permitis close to 1.46 0.02 throughout the range, which is tivity a very small variation. It is also observed here that the imaginary and permeability are very close parts of permittivity to zero. Hence, the loss tangent for this sample is expected to be very small. For example, at 20 GHz, the dielectric loss tangent is 0.0095 whereas the magnetic loss tangent is 0.01. At this freis measured to be 11.61 dB. It can be quency, the value of inferred that reflection occurs from the air-sample interface at this frequency. Thus, it behaves as a weak absorber at this frequency. But as we move towards higher frequencies, the value improves. At 40 GHz, it is measured to be 31.12 dB. of This is expected since barium ferrite has been shown to exhibit strong absorption between 47 and 60 GHz [11]. The measured and are shown in Fig. 3. values of To analyze the effect of particle size on measured electromagnetic property, another set of data was collected for the micron-sized powder of barium ferrite. The grain size of this sample varied from 50–100 m, with a density of 1.3 g/cm . The data obtained for the two samples is compared in Table II. The difference in the observed values of permittivity and permeability can also be attributed to the difference in sample density. There is not much difference in the permeability values, but permittivity shows significant dependence on density of the sample. The density dependence of these parameters has been established at higher frequencies as well [11]. Higher value of permittivity is observed if the particles are more densely packed. It is therefore very important to keep the density constant throughout the measurements. The calculated permittivity and permeability for strontium ferrite nano-powder are shown in Fig. 4. The real part of permittivity falls from 1.49 at 4 GHz to 1.24 at 40 GHz, whereas the real part of permeability remains close to 1. An analysis of the -parameters of strontium ferrite powder shows that the absorption properties improve at higher frequency. Strontium ferrite is known to show strong absorption between 50 and 63 GHz [11]. As in the case of barium ferrite powder, high density strontium ferrite has a higher real part of permittivity. At a density of 1.3 g/cm , the real permittivity varies very little over the entire frequency range and has an average value of 2.633. The real part of permeability varies negligibly over the frequency bands with an average value of 1.063. Based on the study of these two materials, it can be said that real part of permittivity increases with an SHARMA AND AFSAR: PERMEABILITY AND PERMITTIVITY MEASUREMENTS OF COMMERCIALLY AVAILABLE NANO-FERRITES Fig. 4. At a density of 0.3531 g/cm , the average value of real and imaginary parts of permeability for strontium ferrite is 1.0941 and 0.0730 while for permittivity it is 1.4061 and 0.04465, respectively. 311 Fig. 7. At a density of 0.2754 g/cm , the average value of real and imaginary parts of permeability for nickel zinc iron oxide is 1.0797 and 0.2012 while for permittivity it is 1.3132 and 0.1232, respectively. V. ERROR ANALYSIS Fig. 5. At a density of 0.5204 g/cm , the average value of real and imaginary parts of permeability for copper iron oxide is 1.029 and 0.1061 while for permittivity it is 1.5073 and 0.0906, respectively. Fig. 6. At a density of 0.5454 g/cm , the average value of real and imaginary parts of permeability for copper zinc ferrite is 1.0376 and 0.2092 while for permittivity it is 1.5951 and 0.0888, respectively. increase in the density of the powder. A comparison of the properties of these M-type nano-sized hexaferrites to micron sized planar hexaferrite shows that the planar structures have higher dielectric loss [12]. Similar curves obtained for the constitutive properties of the rest of the nano-powders are shown in the following figures. The spinel nano-ferrites are relatively weak absorbers in this for is only 21.27 dB frequency range. The at 40 GHz. A study of these materials in the higher frequency range would give a better picture of their absorption properties. A comparison of the results obtained for the two types of nano-powders shows that the spine-type ferrites have limited use in this high frequency range. The ferrites with hexagonal structure show natural resonance in the GHz range and are therefore more effective as high-frequency absorbers. For the completeness of experimental data obtained from the vector network analyzer, the possible sources of errors and uncertainties in measurement are identified in this section. Experimental uncertainties that can be revealed by repeated measurements are called random errors [13]. These were minimized by repeating the measurement six times for each sample. The standard deviation in the values of real part of permittivity and permeability was observed to be 0.0058 and 0.0042, respectively. To keep the density fixed across all frequency bands, the scale was used to weigh the mass of the sample. The uncertainty in reading the scale correctly is 0.0002 g, which can be neglected. There are several factors that account for the random errors in the measurements. The connectors used between the network analyzer and waveguide make the system sensitive to noise and drift. These errors can be minimized by keeping the whole set-up clean and stable. Since the sample is in powder form, the particles in the sample holder get displaced easily even with a slight movement and the density becomes non-uniform. It is important to make sure that the same uniform density is maintained when loading the sample as well as at the time of measurement. All experimental uncertainties cannot be assessed by repeated measurements. The repeatable and stable uncertainties in measurement are called systematic errors [13]. In this experiment, the systematic errors caused by the imperfections of the system were reduced by careful calibration of the whole measurement system before the actual measurements were taken. TRL (thrureflect-load) calibration procedure was used here. It removes the errors caused by the difference in the location of reference plane and measurements plane arising due to cables and connectors. In all measurements, we were able to maintain return loss less than 50 dB. This allows us to neglect any reflections occurring from the walls of the waveguide. VI. CONCLUSION AND FUTURE WORK The dielectric permittivity and magnetic permeability of several nano-sized ferrite powders were successfully determined by using the waveguide technique across a wide range of frequency. Measurements show that the real part of permittivity of ferrites depends on the size of the particles and the density 312 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 2, FEBRUARY 2011 inside the sample holder. Future work may involve the determination of permittivity and permeability for the same powders packed at different densities. The effect of an external magnetic field should also be studied. The potential of these powders as microwave absorbers can be better analyzed by measuring the reflection spectra of a metal backed sample of the powders. ACKNOWLEDGMENT The authors would like to thank Dr. M. Obol for sharing technical knowledge on the waveguide technique and J. Qui for assistance in the use of vector network analyzer. REFERENCES [1] H. P. J. Wijn, “Hexagon ferrites,” Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology, vol. III/4b, ch. 7. [2] A. Bahadoor, Y. Wang, and M. N. Afsar, “Complex permittivity and permeability of barium and strontium ferrite powders in X, Ku and K-band frequency ranges,” J. Appl. Phys., vol. 97, no. 10, May 2005. [3] J. M. Greneche, “Magnetic properties of nano-ferrites,” in Conf. Int. Espectroscopia, France, 2009. [4] K. Vinoy and R. Jha, Radar Absorbing Material. Norwell, MA: Kluwer, 1996. [5] C. Vittoria, “Ferrite uses at millimeter wavelengths,” J. Magn. Magn. Mater., vol. 71, pp. 109–118, 1980. [6] A. M. Nicolson and G. F. Rossc, “Measurement of intrinsic properties of materials by time techniques,” IEEE Trans. Instrum. Meas., vol. IM-19, pp. 377–382, Nov. 1970. [7] W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE, vol. 62, pp. 33–36, Jan. 1974. [8] J. Baker-Jarvis, E. J. Venzura, and W. A. Kissickc, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech., vol. 38, pp. 1096–1103, Aug. 1990. [9] Y. Wang, M. N. Afsar, and R. Grignon, “Complex permittivity and permeability of carbonyl iron powders at microwave frequencies,” in IEEE Antennas Propag. Soc. Int. Symp., 2003, vol. 4, pp. 619–622. [10] N. Al-Moayed, M. N. Afsar, U. A. Khan, S. McCooey, and M. Obol, “Nano ferrites microwave complex permeability and permittivity measurements by T/R technique in waveguide,” IEEE Trans. Magn., vol. 44, no. 7, pp. 1768–1772, Jul. 2008. [11] K. A. Korolev, L. Subramanium, and M. N. Afsar, “Complex permittivity and permeability measurements of ferrite powders at millimeter waves,” in Eur. Microwave Conf., Oct. 2005. [12] M. N. Afsar, A. Sharma, and M. Obol, “Microwave permittivity and permeability properties and microwave reflections of micro/nano ferrite powders,” in IMTC’2009. [13] J. R. Taylor, An Introduction to Error Analysis. South Orange, NJ: University Science Books, 1982, pp. 81–93. Microwave complex permeability and permittivity of nanoferrites Anjali Sharma and Mohammed N. Afsar Citation: Journal of Applied Physics 109, 07A503 (2011); doi: 10.1063/1.3536659 View online: http://dx.doi.org/10.1063/1.3536659 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/109/7?ver=pdfcov Published by the AIP Publishing [This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.64.22.2 On: Sat, 09 Nov 2013 20:13:02 JOURNAL OF APPLIED PHYSICS 109, 07A503 (2011) Microwave complex permeability and permittivity of nanoferrites Anjali Sharmaa) and Mohammed N. Afsar High Frequency Materials Measurement and Information Center, Department of Electrical Engineering, Tufts University, Medford, Massachusetts 02155, USA (Presented 18 November 2010; received 1 October 2010; accepted 29 October 2010; published online 18 March 2011) Complex permittivity and permeability of nanosized magnetic powders are studied for eight different bands to cover the frequency range from 2–40 GHz. A precise transmission-reflection based waveguide technique has been used to carry out measurements across the frequency bands. The algorithm for transmission and reflection calculations has been modified to account for variable sample thickness in the in-waveguide measurement setup. Diluted nanopowder sample has also been studied. The ferromagnetic resonance in nanoferrites has been observed to be sharper compared to microsized ferrites. Detailed analysis of measurement uncertainties and instrumentation errors has C 2011 American Institute of Physics. [doi:10.1063/1.3536659] been performed. V I. INTRODUCTION Iron based magnetic powders have been studied for several years now.1 The use of ferrites in waveguides for isolator applications is a well-established concept in the field of microwave technology. In this paper, we are presenting the study of nanosized magnetic powders at microwave frequency range. This frequency range is important because of lower loss and cheaper fabrication of microwave devices as compared to millimeter waves.2 Nanopowders consist of particles with an average size between 1–100 nm. Iron based nanopowders are spherical metal nanostructure particles, typically 20–40 nm in size. Measurements carried out on nanosized powders have shown that the microwave permittivity and permeability of these materials differ from those of the material in solid state.3 These powders are useful in biomedical engineering as they serve as good drug deliver solutions and DNA separators. They also find extensive application in magnetic recording and information storage.3 In our investigation, we have discovered that the ferromagnetic resonance for nanoferrite powders becomes sharper compared to micro-sized ferrite powders at microwave and millimeter wave frequencies. Therefore, an important application of these nanoferrite powders is in the design of isolator, modulator, and phase rotator. These ferrite components can be made better tunable by using nanoferrite powders. To identify the use of nanoferrites in common ferrite applications, for example, absorption of electromagnetic energy, it is important to determine their constitutive properties. The absorption capability of a material depends on the intrinsic material properties, namely, permittivity and permeability, which may be frequency dependent.4 Therefore there is a growing interest in studying the properties of these powders. A transmission-reflection based waveguide technique that employs a vector network analyzer was used to measure a) Author to whom correspondence should be addressed. Electronic mail: Anjali.Sharma@tufts.edu. 0021-8979/2011/109(7)/07A503/3/$30.00 the scattering parameters for nanoferrite samples. Using this technique, one can record both reflection and transmission spectra generated when an electromagnetic wave travels through the material under study. Based on the reflection spectrum, the frequency at which the sample exhibits good absorption can be determined. The algorithm used to determine the permittivity and permeability from the measured data has been modified over the years to improve accuracy.5–7 However, the algorithm used in this study takes into account the effect of the thickness of the loaded material and its permittivity and permeability on the cutoff wavelength inside the waveguide. A thorough error analysis is also presented to identify the systematic and random errors in the measurement process. II. SAMPLE DESCRIPTION The three nanopowders studied in this work were purchased from Sigma Aldrich, Milwaukee, WI. The powdered samples have a grain size that varies between 40 and 100 nm for different samples. The sample properties are summarized in Table I. The frequency range from 2 to 40 GHz is divided into eight frequency bands, namely, R (1.70–2.60 GHz), S (2.60– 3.95 GHz), G (3.95–5.85 GHz), C (5.85–8.20 GHz), X (8.20–12.40 GHz), Ku (12.4–18.00 GHz), K (18.00–26.5 GHz), and Ka (26.50–40.00 GHz). Each band corresponds to a different waveguide dimension and therefore the volume of sample used was different in each band. To maintain constant density for each nanopowder, appropriate weight of the sample to be filled in the waveguide shim was calculated. The weight of the sample holder is measured with and without the powder to ensure that the required density is maintained. To load uniform distribution of the powder in the waveguide and avoid the presence of any air gap in the sample holder, the sample was steadily filled in the shim. Lossless transparent tape was used on either sides of the shim to hold the powder inside the shim. It has been shown that the presence of such a tape does not affect the measured s-parameter.8 109, 07A503-1 C 2011 American Institute of Physics V [This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.64.22.2 On: Sat, 09 Nov 2013 20:13:02 07A503-2 Sharma and Afsar J. Appl. Phys. 109, 07A503 (2011) TABLE I. Sample description. Name Barium ferrite Strontium ferrite Iron (II, III) oxide Chemical Formula Density (g/cm3) BaFe12O19 SrFe12O19 Fe3O4 0.4004 0.3531 1.291 III. EXPERIMENTAL SETUP The transmission-reflection based waveguide technique has been used for the measurement of soft powders. The method is based on the transmission and reflection (T/R) technique introduced by Nicolson-Ross5 and Weir, 6 and the widely acclaimed formulations for transmission and reflection coefficients proposed by Baker-Jarvis.7 We were able to reduce the phase ambiguities arising due to initial guess parameter. The details on the accuracy of the method can be found in Ref. 9. Additionally, the cutoff frequency for each frequency band was calculated and set as the waveguide delay in the vector network analyzer to further remove errors. Ideally, the shim thickness should be within quarter wavelengths of the central operation frequency. But this is hard to maintain since the thickness used for each sample depends on the requirement to maintain constant density for all frequency bands. The difference between the material thickness and sample holder thickness was taken in to account when performing the calculations. The modified equations used in the measurements are given below pﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 S~11 ¼ S11 ejð0 k0 kc Þ pﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 S~21 ¼ S21 ejððldÞ k0 kc Þ ; (1) where l is the quarter wavelength difference between thru and line in air, d is the thickness of the sample inside the waveguide, k0 is the wave number of the sample, and kc is the cutoff wave number. These equations take into account the effect of using samples with thickness (d) values that are smaller than the waveguide shim used in the experimental setup. Each frequency band was subdivided into 201 frequency points at which measurement was taken, giving a total of 1206 frequency points. It should be noted that the data at the end of one band may show some deviation from the data at the starting frequencies of the successive band. This may be due to experimental errors, depending on how carefully the operator used the instruments. To remove the experimental discrepancies in the data across different bands, a mathematical averaging method (least squares method of polynomials) was used. The derived data is very reliable and not affected by the scattering voltage ratios of the network analyzer. The final form of the equations used to determine permittivity and permeability is shown below 2 c 1C 1 1 lnð Þ þ jð2pn uT Þ e¼j f 1 þ C 2pd jT j 0sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1 2 2 1 1 A ; (2) @ k0 2a l¼ gcTE10 jc0TE10 0 1 1 lnð T jÞ þ jð2pn uT ÞC 1þC 1 B B jr C ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ j @ 2 ﬃ A; 1 C 2pd 1 1 2 k0 2a (3) where C is the reflection coefficient, T is the transmission coefficient, c0TE10 and cTE10 are propagation constant for the TE10 mode with and without the material inserted in the waveguide, a is the longer dimension of the rectangular waveguide, /T is the phase of transmission coefficient and d is the material thickness. IV. RESULTS To verify the accuracy of the measurement technique we first measured a known sample, Teflon, in X-band. The permittivity of Teflon was measured to be 2.1 throughout the band with an average variation of 60.001. The results therefore agree with the known published value for permittivity of Teflon. Figure 1 shows the measured permeability and permittivity values for iron (II, III) oxide. Permeability of iron (II, III) oxide nanopowder shows very slight variation with frequency whereas permittivity values show dependence on frequency. The permeability and permittivity results for rest of the samples described in Sec. II are summarized in Table II. It has been shown that barium ferrite and strontium ferrite exhibit strong absorption at frequencies between 47–60 GHz and 50–63 GHz, respectively.1 In the microwave frequency range studied here, it was observed that for these samples the s-parameters, namely, S11 and S21, improve at higher frequency. At 40 GHz, S11 for barium ferrite nanopowder was measured to be 31.12 dB. But at lower frequencies, these parameters show poor values, Fig. 2. In order to see if we can improve the low frequency behavior of barium ferrite nanopowder, we prepared a diluted sample of barium ferrite. This sample was made by adding epoxy solution to barium ferrite nanopowder. The density of this sample was measured to be 1.31 g/cm3. The reflection spectrum of this sample was studied in X-band and FIG. 1. (Color online) The average value for the real and imaginary parts of the measured permeability for iron (II, III) oxide are 0.9755 and 0.2266 while for permittivity it is 5.25 and 1.25, respectively. [This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.64.22.2 On: Sat, 09 Nov 2013 20:13:02 07A503-3 Sharma and Afsar J. Appl. Phys. 109, 07A503 (2011) TABLE II. Measured value of real and imaginary permeability and permittivity. Barium Ferrite Frequency (GHz) 4 8 12 16 20 24 28 32 36 40 Strontium Ferrite m0 e0 m0 1.11 1.14 1.14 1.11 1.06 1.04 1.08 1.10 1.14 1.12 1.43 1.50 1.50 1.45 1.44 1.49 1.48 1.46 1.44 1.42 1.10 1.09 1.09 1.09 1.08 1.05 1.12 1.12 1.12 1.09 e0 1.49 1.49 1.5 1.5 1.44 1.397 1.369 1.35 1.287 1.22 FIG. 3. The measurement result for s-parameters for the diluted barium ferrite nanopowder sample in X-band. significant improvement was observed in the S11 and S21 parameter values. The results are shown in Fig. 3. Lower values of S11 are observed for the diluted sample. This is because epoxy improves the absorption rate of the sample, indicated by the lower S11 values. the whole measurement system before the actual measurements were taken. TRL (thru-reflect-load) calibration procedure was used here. In all measurements, we were able to maintain return loss less than 45 dB. This allows us to neglect any reflections occurring from the walls of the waveguide.9 V. UNCERTAINTY AND ERROR ANALYSIS VI. CONCLUSION To completely define the accuracy of the experimental data obtained from the vector network analyzer, the possible sources of errors and uncertainties in measurement are identified. Any experiment consists of two types of errors, namely, random error and systematic error. Experimental uncertainties that can be revealed by repeated measurements are called random errors.10 The main sources of random errors in this experiment were the connectors used between the network analyzer and waveguide, and the nonuniform nanopowder densities. Since the sample is in powder form, the particles in the sample holder get displaced easily and the density becomes nonuniform. It is important to make sure that the same uniform density is maintained when loading the sample as well as at the time of measurement. These errors were accounted for in this study by repeating the measurement five times for each sample. The standard deviation in the values of real part of permittivity and permeability was observed to be 60.005 and 60.003, respectively. The experimental uncertainties that cannot be assessed by repeated measurements are called systematic errors.10 In this experiment, the systematic errors caused by the imperfections of the system were reduced by careful calibration of The magnetic permeability and dielectric permittivity of nanosized ferrite powders were successfully determined by using the transmission/reflection based waveguide technique across a wide range of frequency. The values of S11 and S21 were studied to determine the potential of these materials as absorbers. Barium and Strontium ferrites can be used for making stronger magnets. The ferromagnetic resonance for both barium and strontium nanoferrites appear between 40– 60 GHz, whereas iron oxide is better for microwave frequencies. Our finding reveals that the ferromagnetic resonance for nanoferrite powders is very sharp compared to microsized ferrites. This will allow the use of nanoferrite powders in isolator, modulator, phase rotator and circulator applications for achieving sharper tunability. It has been shown in this study that the absorption properties of these samples can be improved by diluting the sample with epoxy. Further experimentation with different densities of the diluted sample can be carried out to find the most suitable concentrations of the nanopowder and epoxy in the diluted sample. FIG. 2. The measurement result for s-parameters for the barium ferrite nanopowder sample in X-band. 1 K. A. Korolev, L. Subramanium, and M. N. Afsar, “Complex permittivity and permeability measurements of ferrite powders at millimeter waves,” in Proceedings of 35th European Microwave Conference, Paris, France, 3–5 October 2005. 2 C. Vittoria, J. Magn. Magn. Mater. 71, 109 (1980). 3 A. Bahadoor, Y. Wang, and M. N. Afsar, J. Appl. Phys. 97, 28 (2005). 4 K. Vinoy and R. Jha, Radar Absorbing Material (Kluwer Academic, Boston, 1996). 5 A. M. Nicolson and G. F. Ross, IEEE Trans. Instrum. Measur. IM-19, 377 (1970). 6 W. B. Weir, “Proc. IEEE 62, 33 (1974). 7 J. Baker-Jarvis, E. J. Venzura, and W. A. Kissick, IEEE Trans. Microwave Theory Tech. 38, 1096 (1990). 8 Y. Wang, M. N. Afsar, and R. Grignon, IEEE Trans. Antennas Prop. 4, 619 (2003). 9 N. Al-Moayed, M. N. Afsar, U. A. Khan, S. McCooey, M. Obol, IEEE Trans. Magn. 44, 1768 (2008). 10 John R. Taylor, An Introduction to Error Analysis (University Science Books, Sausalito, CA, 1982), pp. 81–93. [This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 130.64.22.2 On: Sat, 09 Nov 2013 20:13:02 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012 2773 Microwave and Millimeter Wave Ferromagnetic Absorption of Nanoferrites Liu Chao, Anjali Sharma, and Mohammed N. Afsar, Fellow, IEEE Department of Electrical and Computer Engineering, Tufts University, Medford, MA 02155 USA Complex dielectric permittivity and magnetic permeability of several commercially available nanoferrites have been studied over a broad microwave and millimeter wave frequency range. Nano-sized barium, strontium, copper, zinc, nickel substituted iron oxide powders with different lattice structures are investigated. A transmission-reflection based in-waveguide technique that employs a vector network analyzer was used to determine the scattering parameters for each sample in two microwave bands (18–40 GHz). A free space quasi-optical spectrometer energized by backward wave oscillators was used to acquire the transmittance spectra in the millimeter wave frequency range (30–120 GHz). Relatively broad and sharp ferromagnetic resonance of hexagonal barium ferrite and strontium ferrite are observed in millimeter wave frequency range. The ferromagnetic resonance peak for nano-sized hexagonal ferrite powder material moves to lower frequencies compared to micro-sized and solid hexagonal ferrites. An X-ray diffraction measurement is performed on these hexagonal ferrites to understand the magnetic behavior and the structure. Index Terms—Dielectric permittivity, ferromagnetic resonance, magnetic domain, magnetic permeability, nanoferrite. I. INTRODUCTION N ANOFERRITES consist of metal substituted iron oxide nanopowders that have average particle size below 100 nm. These nanosize ferrites show different dielectric and magnetic properties in microwave and millimeter wave frequencies compared to micro-size and solid ferrites. Therefore there is a growing interest in studying these powders to understand how the material properties are affected by the particle size. The use of nanoferrites is significant in many aspects, such as biological drug delivery systems, DNA-separators as well as in magnetic recording and information storage [1]. These nanosize ferrites are also useful in other microwave applications such as transformers, absorbers and circulators. It is necessary to investigate their electromagnetic properties and understand their changing magnetic behavior with particle dimension. In the microwave measurement, a vector network analyzer together with waveguides was employed to determine the scattering parameters of the nanoferrites inside the waveguide in K band and Ka band. From the S-parameters, complex permittivity and permeability are evaluated by an improved algorithm. The millimeter wave measurement is based on a free space quasioptical spectrometer powered by backward wave oscillators. Initially precise transmittance spectra over a broad millimeter wave frequency range from 40 GHz to 120 GHz are acquired. Later the transmittance spectra are converted into complex permittivity and permeability spectra. These ferrite powder materials are further characterized by x-ray diffraction (XRD) to understand the crystalline structure relating to the strength and the shift of the ferromagnetic resonance affected by the particle size. vector network analyzer measures the scattering parameters of the 2-port network formed by the waveguide shim filled with the sample under study as shown in Fig. 1. The nanopowders were filled in the sample holder that was placed between the waveguides. It is important to ensure that the sample must fill the entire area of the sample holder so that there are no air gaps at the corners of the shim or between the powders. The sample was packed tight enough such that changing the orientation of the shim does not cause any shift in the particles. The algorithm proposed by Baker-Jarvis was then used to derive the permittivity and permeability values from this data [2]. The phase unwrapping technique was employed to avoid the use of initial guess parameter [3]. Additionally, the cut-off frequency for each frequency band was calculated and set as the waveguide delay in the vector network analyzer to remove errors. The modified equations used in the measurements are given below, where is the quarter wavelength difference between thru and line (in air), is the thickness of the sample inside the waveguide, is the wavenumber of the sample and is the cutoff wavenumber. The final form of the equations used to determine permittivity and permeability is shown below II. MEASUREMENT TECHNIQUE A. Transmission-Reflection Waveguide The transmission-reflection based waveguide technique has been widely used to determine the properties of solids. It can be further modified for the measurement of soft powders. The Manuscript received March 02, 2012; revised April 27, 2012; accepted May 15, 2012. Date of current version October 19, 2012. Corresponding author: L. Chao (e-mail: stream.chao@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2012.2200666 where, is the reflection coefficient, T is the transmission coefand are propagation constant for the ficient, mode with and without the material inserted in the waveguide, 0018-9464/$31.00 © 2012 IEEE 2774 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012 Fig. 1. Schematic diagram of nanoferrites in waveguide. Fig. 2. Schematic diagram of the free-space quasi-optical millimeter-wave spectrometer in the transmittance mode with BWO as radiation source. is the longer dimension of the rectangular waveguide, is the phase of transmission coefficient and is the material thickness. Fig. 3. Complex permittivity and permeability in K and Ka bands of nanopowder. Real permeability is around 1.05 and the real permittivity is around 1.3. The imaginary part of permeability and permittivity are 0 and 0.05, respectively. TABLE I SAMPLE PREPARATION B. Quasi-Optical Spectrometer Free space millimeter wave quasi-optical spectroscopy technique, including technical details and measurement uncertainties analysis, has been successfully employed and presented by several researchers [4]–[7]. This study presents complex dielectric and magnetic measurements at millimeter waves performed by the free space quasi-optical spectrometer in transmittance mode [6], [7]. Three high vacuum, high power backward wave oscillators (also called carcinotrons) (BWO) have been used as sources of coherent radiation continuously tunable in the range from 30 to 120 GHz. A couple of pyramidal horn antennas and a set of polyethylene lenses along the propagation path from the source antenna to the receiver antenna have been adjusted to form a Gaussian beam as well as to focus the beam into the sample. The diameter of the millimeter wave beam focused into the sample has been found to be around a few millimeters. The simplified schematic diagrams of the millimeter wave quasi-optical spectroscopic system are shown in Fig. 2. The mathematical relationships between transmittance and reflectance spectra, and refractive and absorption indexes are presented below where is the speed of light, is the refractive index of the sample material, is the absorption index, is the complex magnetic permeability of the sample material, is the complex dielectric permittivity, is the transmittance, is the reflectance, is the phase of the transmitted wave, and is the phase of reflected wave. III. SAMPLE PREPARATION Five nanoferrites, namely barium ferrite ( , , SrM), copper iron oxide BaM), strontium ferrite ( , CAS-No.12018-79-0), copper zinc iron oxide ( , CAS-No.66402-68-4), nickel zinc iron oxide ( , CAS-No.12645-50-0) examined in this work ( were purchased from Sigma Aldrich. The grain size of the powders varies from 40 nm to 100 nm for different kind of ferrites [8]. Density of the ferrites in the sample holder is determined by weighting from an accurate balance over the dimensions of the sample holders. The density and purity are listed in Table I. IV. RESULTS AND DISCUSSION Complex dielectric permittivity and magnetic permeability spectra obtained in microwave frequency range using transmission-reflection in-waveguide technique are shown below. Transmittance spectra of hexagonal ferrites are acquired in the millimeter wave frequency from 40 GHz to 120 GHz. The angles from 5 to X-ray diffraction data are collected from 70 in 0.015 step size on these hexagonal ferrite nanopowders. The complex dielectric permittivity and magnetic permeability of nickel zinc iron oxide, copper zinc iron oxide and copper iron oxide nanopowder in 18–40 GHz frequency range are shown in Fig. 3, Fig. 4, Fig. 5, respectively. The real parts of these copper, zinc, nickel substituted of permittivity nanopowders are much smaller than their solid form. One can treat these nanopowders as diluted by the air between nano particles. The real part of magnetic permeability value is almost the same as the value for micro size and solid form. The values are close to zero for imaginary parts of permittivity specifying to have high electric resistivity. No ferromagnetic resonance is observed in this frequency region for these samples and the imaginary parts of permeability values are very small (close to 0.01 to 0.05). CHAO et al.: MICROWAVE AND MILLIMETER WAVE FERROMAGNETIC ABSORPTION OF NANOFERRITES Fig. 4. Complex permittivity and permeability in K and Ka bands of nanopowder. Real permeability is around 1.1 and the real permittivity is around 1.5. The imaginary part of permeability and permittivity are 0 and 0.05, respectively. 2775 Fig. 6. Millimeter wave transmittance spectra of barium and strontium nanoferrites. Ferromagnetic resonance peaks are observed at 42.5 GHz and 48.2 GHz, respectively. TABLE III COMPLEX PERMITTIVITY AND RESONANT FREQUENCY TABLE IV ANISOTROPY FIELD AND SATURATION MAGNETIZATION Fig. 5. Complex permittivity and permeability in K and Ka bands of nanopowder. Real permeability is observed in 1.0–1.2 region. The real permittivity varies around 1.5. The imaginary part of permeability and permittivity are 0.1. To evaluate the complex magnetic permeability spectra, Schlömann’s equation [9] for partially magnetized ferrites has been used: TABLE II SAMPLE AVERAGE PERMITTIVITY AND PERMEABILITY Table II shows the average permittivity and permeability of , , nanopowders in K and Ka bands from 18 GHz to 40 GHz. Transmittance spectra of hexagonal barium (BaM) and strontium (SrM) nanoferrites measured by the quasi-optical technique are shown in Fig. 6. A deep and sharp absorption in transmittance spectra has been observed for both barium and strontium nanoferrites in 40–60 GHz frequency range. This deep absorption is the natural ferromagnetic resonance that shifts to millimeter wave range due to the strong magnetic anisotropy of barium and strontium ferrites. The periodic structure observed in all transmittance spectra at the frequencies above zone of deep absorption represents channel fringes. The analysis of channel fringes allows us to determine the complex dielectric permittivity value of materials. where is the frequency, is anisotropy field, is saturation magnetization, is the gyromagnetic ratio. Demagnetizing factors are determined by the theory of Schlömann’s model for nonellipsoidal bodies. The complex permittivity and permeability together with the center of the ferromagnetic resonance are shown in Table III. From the ferromagnetic resonance, the hexagonal barium and strontium nanoferrites show relatively strong anisotropy field of and and weak saturation magand , respecnetization of tively. However, these anisotropy fields and saturation magnetization are smaller comparing to the solid barium and strontium and ferrites which have anisotropy field of , saturation magnetization of and , respectively. Comparison of anisotropy field and saturation magnetization between nano-sized and solid hexagonal ferrite is summarized in Table IV. To understand the weak saturation magnetization is straightforward because the nanoferrites are actually diluted by the air between each particle even though the layer was compressed. The reduced anisotropy field is interesting for it is the intrinsic characteristic affected by the crystal structure. But the physical 2776 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 11, NOVEMBER 2012 resonance completely at room temperature. The size of barium and strontium nanoferrite powders measured in this paper is right between the upper limit of single domain size and the lower limit size of turning into superparamagnetism. V. CONCLUSION Fig. 7. XRD spectra for nanoferrite and micro-ferrite. Fig. 8. XRD spectra for nanoferrite and microferrite. change of the powder size does affect the anisotropy field of these hexagonal ferrites. The X-ray diffraction was then performed on this nanoferrites and the diffraction pattern is compared to micro size barium and strontium ferrites in Fig. 7 and Fig. 8. The x-ray diffraction spectra show that both barium and strontium keep the same crystalline structure in micropowder and nanopowder particle size. This further demonstrates that the shifting of ferromagnetic resonance (towards lower frequency) and reduced anisotropy field are not caused by any crystal structure change. The micro size particle of the hexagonal ferrite has almost the same anisotropy field as the solid ferrite. This is due to the domain size of the hexagonal ferrite. The upper limit of single magnetic domain should have the size of about 100 nanometer. The nanoferrite powder with a physical dimension smaller than this single magnetic domain size will lead to a lower ferromagnetic resonance frequency. At the upper limit of single domain size, all of the particle’s internal magnetization is aligned to reduce the system energy to the lowest [10]. Therefore, at upper limit of single domain size, ferrite has the largest anisotropy field which is the sum of all magnetic moment in the particle. Below this physical upper limit of single domain size, the anisotropy field of the ferrite is determined by the volume of the particle until the dimension drops to a certain size. The spins of the magnetic moment will no longer be aligned without the application of an external magnetic field because of random thermal flips. As the powder dimension turns to even smaller size, the hexagonal ferrite is deduced to lose ferromagnetic The complex dielectric permittivity and magnetic permeability are measured in microwave and millimeter wave frequency range. The improved vector network analyzer based transmission-reflection technique with waveguide is applied to several nanoferrites in microwave frequency. Quasi-optical backward wave oscillator spectrometer was employed to determine the transmittance of these nanoferrite samples. Ferromagnetic resonances on hexagonal barium and strontium nanoferrites are observed in the millimeter wave frequency range by this millimeter wave spectrometer. The ferromagnetic resonance is shifting to the lower frequency and the anisotropy field reduces to lower strength. X-ray diffraction was performed on these hexagonal nanoferrites. The diffraction spectra demonstrate that the crystal structure keeps the same as larger size barium and strontium ferrites. The ferromagnetic resonance moving is caused by magnetic domain size limit. Further research on the detail reasons leading to this phenomenon will be carried through. REFERENCES [1] H. Pfeiffer, R. W. Chantrell, P. Görnert, W. Schüppel, E. Sinn, and M. Rösler, “Properties of barium hexaferrite powders for magnetic recording,” J. Magn. Magn. Mater., vol. 125, pp. 373–376, 1993. [2] J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 10, pp. 1096–1103, Oct. 1990. [3] N. N. Al-Moayed, M. N. Afsar, U. A. Khan, S. McCooey, and M. Obol, “Nano ferrites microwave complex permeability and permittivity measurements by T/R technique waveguide,” IEEE Trans. Magn., vol. 44, no. 10, pp. 1768–1772, Oct. 2008. [4] A. A. Volkov, Y. G. Goncharov, G. V. Kozlov, S. P. Lebedev, and A. M. Prokhorov, “Dielectric measurements the submillimeter wavelength region,” Infrared Phys., vol. 25, pp. 369–373, 1985. [5] G. V. Kozlov, S. P. Lebedev, A. A. Mukhin, A. S. Prokhorov, I. V. Fedorov, A. M. Balbashov, and I. Y. Parsegov, “Submillimeter backward-wave oscillator spectroscopy of the rare-earth orthoferrites,” IEEE Trans. Magn., vol. 29, no. 6, pp. 3443–3445, Nov. 1993. [6] K. N. Kocharyan, M. Afsar, and I. I. Tkachov, “Millimeter-wave magnetooptics: New method for characterization of ferrites the millimeterwave range,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2636–2643, Nov. 1999. [7] K. A. Korolev, C. Shu, L. Zijing, and M. N. Afsar, “Millimeter-wave transmittance and reflectance measurement on pure and diluted carbonyl iron,” IEEE Trans. Instrum. Meas., vol. 59, no. 11, pp. 2198–2203, Nov. 2010. [8] A. Sharma and M. N. Afsar, “Microwave complex permeability and permittivity measurements of commercially available nano-ferrites,” IEEE Trans. Magn., vol. 47, pp. 308–312, 2011. [9] E. Schlomann, “Microwave behavior of partially magnetized ferrites,” J. Appl. Phys., vol. 41, pp. 1350–1350, 1970. [10] E. C. Stoner and E. P. Wohlfarth, “A mechanism of magnetic hysteresis heterogeneous alloys,” Phil. Trans. Roy. Soc. Lond.. A, Math. Phys. Sci., vol. 240, pp. 599–642, 1948.

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