Calculations of microwave permeability, permittivity and absorption properties of magnetic particle composites

CALCULATIONS OF MICROWAVE PERMEABILITY, PERMITTIVITY AND ABSORPTION PROPERTIES OF MAGNETIC PARTICLE COMPOSITES NEO CHYE POH B.Eng (Hons), M.Eng, NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 ACKNOWLEDGMENTS I wish to thank my main supervisor, Assoc. Prof. Ding Jun, for his kindness and patience through the years of undertaking this research work. I wish to thank my co-supervisors, Prof. Ong Chong Kim and Dr. S. Matitsine, for their patience and understanding of the difficulties that led to the delay of the completion of this work. I wish to thank Mr. Wu Lezhong, Ms. Yang Yang and Dr. Chen Linfeng for helping me with sample preparation and characterisations. I wish to thank my company, DSO National Laboratories, for co-sponsoring my graduate program. Lastly, I wish to thank my family and friends for bearing with me when I needed time to this project. ii TABLE OF CONTENTS Page Acknowledgment . ii Table of Contents . iii Summary vi List of figures .viii List of tables xii List of symbols .xiii List of acronyms .xvii List of publications . xviii Chapter 1: Introduction 1.1 Background . 1.2 Literature Survey 1.2.1 Fundamentals for microwave absorption 1.2.2 Skin effect 10 1.2.3 Simulation models for calculation of microwave properties . 11 1.2.4 Fe- based metallic magnetic materials . 16 1.3 Problem to be Solved and Motivation . 20 1.4 Organisation of the Thesis 24 1.5 References 26 Chapter 2: Intrinsic permeability of ferromagnetic materials . 29 2.1 Introduction . 29 2.2 Theory 30 2.3 Results and Discussion . 35 2.4 Concluding Remarks . 44 2.5 References . 45 Chapter 3: Permeability of Fe and Fe3O4 composites materials . 47 3.1 Introduction . 47 3.2 Sample Preparation 48 3.3 Characterisation of Samples . 50 3.4 Theoretical Formulation 54 3.5 Results and Discussion . 55 3.5.1 Calculation of magnetic permeability for HQ carbonyl iron 55 3.5.2 Calculation of magnetic permeability for magnetite . 62 3.6 Concluding Remarks . 68 3.7 References . 68 iii Chapter 4: Permeability of Fe/Fe3O4 and Fe-Fe3O4(core-shell) composites 70 4.1 Introduction . 70 4.2 Theory 71 4.2.1 Formulation of the effective permeability of two-phase composite . 71 4.2.2 Formulation of the effective permeability of core-shell composite . 75 4.3 Results and Discussion . 76 4.3.1 Effective permeability of two-phase system 76 4.3.2 Effective permeability of core-shell system . 84 4.4 Concluding Remarks . 92 4.5 References . 92 Chapter 5: Calculation of microwave permeability and absorption property of particle composite . 93 5.1 Introduction . 93 5.2 Theory . 94 5.2.1 Formulation of the effective permittivity of composite 94 5.2.2 Formulation of volume fraction dependable effective permittivity of composite . 94 5.3 Results and Discussion . 95 5.3.1 Permittivity of Fe and Fe3O4 composites 95 5.3.2 Volume fraction dependable effective permeability and permittivity 100 5.3.3 Calculation of microwave absorption property of particle composite. . 103 5.3.3.1 Microwave dallenbach absorber (dielectric). . 103 5.3.3.2 Microwave absorber consisting of multi-layer resistive sheet. . 108 5.4 Concluding Remarks . 117 5.5 References 117 Chapter 6: Calculation of permeability of magnetic material using modified Landau Lifshitz ferromagnetic resonance model 119 6.1 Introduction . 119 6.2 Theory . 120 6.2.1 Calculation of Permeability of Magnetic Thin Film 120 6.2.2 Calculation of Permeability of Particle Composite Material . 125 6.3 Results and Discussion . 126 6.3.1 Magnetic Thin Film. 126 6.3.1.1 Comparison with results obtained using LL-G . 126 6.3.1.2 Extraction of magnetic parameters from measured permeability. . 127 6.3.2 Magnetic Particle Composite. . 132 6.3.2.1 Calculations for arbitrary alignment of single magnetic domain (bcc-Fe) with respect to incident wave. . 132 6.3.2.2 Calculations for average permeability of an isotropic magnetic iv particle (bcc-Fe) without the consideration of skin effect. 132 6.3.2.3 Calculations of effective permeability and absorption property of bcc-Fe particles embedded in an insulting matrix with skin effect. 133 6.3.2.4 Calculation of effective permeability and absorption property of Fe3O4 particles composite . 135 6.4 Concluding Remarks . 141 6.5 References 143 Chapter 7: Conclusions . 144 v SUMMARY This thesis presents a general approach in the design of magnetic absorber through the calculations of magnetic permeability and electric permittivity. The emphasis of this thesis is to calculate and design the intrinsic and extrinsic materials property of particle composite materials. The intrinsic materials property of particle composite materials refers to its effective permeability or permittivity, while the extrinsic materials property of composite materials refers its power reflection coefficient. The first step of the design of magnetic absorber is to select good magnetic filler(s) for the magnetic absorber. The intrinsic permeability of several magnetic metallic materials is investigated using a model developed from the Landau-Lifshitz-Gilbert (LL-G) equation. In this study, we are able to answer why Fe is used to make the magnetic RAM from L to X band (1-12 GHz). The effect of saturation magnetisation, anisotropy field, damping coefficient, particle size and conductivity are studied. The importance of the spatial orientation of the magnetic domain on its intrinsic permeability is demonstrated. The second step is to compute the effective permeability and permittivity of the composite containing the magnetic fillers. This is to check if our results obtained in first step matches well with microwave measurements, and therefore to validate the models used. vi The calculation of materials property of particle composite in the second step is meant for design purpose as some of the composite processing parameters could be unidentified in practice. Thus, there will be some discrepancies in the calculated and measured permeability and permittivity. Consequently, the measured permeability and permittivity are used to design the microwave absorber. The third step is to develop a model to extrapolate or interpolate the measured permeability or permittivity for other volume fractions, and this makes establishing a huge database of permeability and permittivity for different volume fraction unnecessary. The last step is to design the microwave absorber using the Dallenbach or the Salisbury Screens. At the end of the thesis, a new approach to calculate the effective permeability of carbonyl iron and magnetite composite and in general, magnetic material composite has been developed. The approach uses Landau-Lifshitz ferromagnetic resonance (LL FMR) equation to derive an analytical formula. With the understanding of LL FMR equation, an algorithm to extract the effective magnetic parameters of magnetic thin films has been formulated and validated. vii LIST OF FIGURES Number Page 1.1: A schematic representation of radar system 1.2: A schematic diagram for the definition of microwave absorption ability 1.3: A schematic representation of particles embedded in matrix . 14 2.1: (a) Multigrain structure of a spherical magnetic particle. (b) Coordinate system for microwave propagation in a single grain in the spherical magnetic particle . 31 2.2 (a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe. 38 2.3(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Ni 39 2.4(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Co 40 2.5: fmax vs angle of incidence for Fe, Ni and Co. . 42 2.6: i,max vs angle of incidence for Fe, Ni and Co 42 2.7(a)-(b): Real and imaginary part of relative isotropic permeability vs frequency (GHz) for Fe, Ni and Co 43 3.1: (a) SEM image of carbonyl iron, (b) SEM image of magnetite particles and (c) fabricated sample . 50 3.2: (a) XRD of the carbonyl Fe powder; (b) VSM hysteresis loop of the carbonyl iron powder . 52 3.3:(a) XRD of the Fe3O4 powder; (b) VSM hysteresis loop of the powder . 53 3.4(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe (HQ carbonyl iron) . 58 3.5(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe for different d (particle diameters) 59 3.6(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe for different ζ (particle conductivities) 60 3.1(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe (carbonyl iron), for different β (interaction factors) 61 3.8(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe3O4 (magnetite) 64 3.9(a)-(b) : Real and imaginary parts of effective permeability vs frequency (GHz) for Fe3O4 for different d (particle diameters) . 65 3.10(a)-(b): Real and imaginary parts of effective permeability vs frequency (GHz) for Fe3O4 for different ζ (particle conductivities) . 66 3.11(a)-(b) : Real and imaginary parts of effective permeability vs frequency (GHz) for Fe3O4 (magnetite) for different β (interaction factors) 67 4.1: Schematic diagram of the Fe/Fe3O4 (two-phase) system 72 viii 4.2: The effective conductivity of a material having a layered structure. (a) Along a direction perpendicular to the layers. (b) Along a direction parallel to the plane of layers. (c) Material with a dispersed phase in a continuous matrix (adopted from [4.2]) . 74 4.3: Effective conductivities obtained from figure 4.2 (ζ1=1 × 107 S/m and ζ2=2.5× 104 S/m) . 74 4.4: A dielectrically inhomogeneous sphere consisting layers in a static field 76 4.5(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for Fe/Fe3O4 (d=0.25 μm) for different v1 (vol% of Fe in Fe/Fe3O4) 78 4.6(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for Fe/Fe3O4 (d=2 μm) for different v1 (vol% of Fe in Fe/Fe3O4) 79 4.7(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for Fe/Fe3O4 (d=5 μm) for different v1 (vol% of Fe in Fe/Fe3O4) 80 4.8(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for Fe/Fe3O4 (d=10 μm) for different v1 (vol% of Fe in Fe/Fe3O4) . 81 4.9: (a) XRD of the Fe/Fe3O4 powder and its SEM image in the insert; (b) VSM hysteresis loop of the powder 82 4.10(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for Fe/Fe3O4 (d=0.25 μm) for different v1 (vol% of Fe in Fe/Fe3O4) 83 4.11(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe-Fe3O4 (core-shell) for different r (core-shell radius ratio), for M=0 . 86 4.12(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe-Fe3O4 (core-shell) for different r (core-shell radius ratio), for M=1 . 87 4.13(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe-Fe3O4 (core-shell) for different r (core-shell radius ratio), for M=2 . 88 4.14(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe-Fe3O4 (core-shell) for different r (core-shell radius ratio), for M =2 and particle=2 μm . 89 4.15(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for FeFe3O4 (core-shell) for different r (core-shell radius ratio), for M=2 and particle=5 μm . 90 4.16(a)-(b): Real and imaginary part of permeability vs frequency (GHz) for FeFe3O4 (core-shell) for different r (core-shell radius ratio), for M =2 and particle=10 μm . 91 5.1(a)-(b) : Real and imaginary parts of permeability vs frequency (GHz) for Fe for different M 97 5.2: Calculated (c) and measured (m) power reflection coefficient vs frequency (GHz) of Fe using the calculated and the measured permeabilities and permittivities respectively, for (a) M=0 and (b) M=1 98 5.3(a)-(b): Real and imaginary parts of permeability vs frequency (GHz) for Fe3O4 for different M 99 ix 5.4: Calculated (c) and measured (m) power reflection coefficients vs frequency (GHz) of Fe3O4 using M=0 . 100 5.5: Measured and linearly fitted ln ε vs m (mass of paste) . 101 5.6: Measured and linearly fitted tanδe vs m (mass of paste) . 102 5.7: Measured permeability and permittivity from [5.1] vs volume fraction, together with its linearly fitted lines . 103 5.8: Flowchart for the design of a microwave absorber [5.2] . 106 5.9: Predicted and measured power reflection coefficient, plotted against frequency, for the single-layer mm optimized carbon fiber composite (m = 9.68 g) [5.2]. 107 5.10: Predicted and measured power reflection coefficient, plotted against frequency, for the two-layer mm optimized carbon fiber composite (m = g and d = 3.35 mm for first layer, m = 11.1 g and d = 0.65 mm for second layer) [5.2] . 107 5.11: Multilayer resistive sheet . 113 5.12: An example to obtain zero reflectivity at frequency f0 f or one-layer resistive sheet . 114 5.13: R1 = 200 Ω/and R = 700 Ω/for a two-layer resistive sheet (1 denotes impedance curve for first layer and denotes impedance curve for second layer) . 114 5.14: R1 = 250 Ω/and R = 700 Ω/for a two-layer resistive sheet (1 denotes impedance curve for first layer and denotes impedance curve for second layer). 115 5.15: Optimized R1 and R to obtain bandwidth of 0.86 115 5.16: R1 = 330 Ω/, R = 670 Ω/and R = 1560 Ω/for a three-layer resistive sheet . 116 5.17: Optimized R and R 3,max when R1 = 330 Ω/to obtain bandwidth of 1.20 116 6.1: Schematic diagram of a magnetic film serving as a basis for eddy current calculation with d=thickness «Lx, d«Ly, Hk and Ms in y-direction, and h0 and mx are the incident magnetic field and small magnetisation disturbance in xdirection respectively . 123 6.2: Comparison of complex permeability computed using equations (6.3) and (6.6) (Ms , Hk , α, ρ and d are 1.2 T, 1.13 mT, 0.06, 2.7 μΩm and 1500 nm respectively). . 129 6.3: Computed results using (a) equation (6.5) and (b) equation (6.6) vs the experimental data (see figure 6.3 in [6.6]) and LL-G* model (*with skin depth effect) 130 6.4: Computed results using (a) equation (6.5) and (b) equation (6.6) vs the experimental data (see figure 6.3 in [6.7]) and LL-G* model (*with skin depth effect) 131 x 6.3.2 Magnetic Particle Composite 6.3.2.1 Calculations for arbitrary alignment of single magnetic domain (bcc-Fe) with respect to incident wave The magnetic permeability is calculated using the LL-G model for bcc-Fe with 4πMs =21500 G, Hk = 584 Oe and damping coefficient,  = 0.1 (interaction faction, β=-0.02). The solid lines in Figure 6.5(a) and 6.5(b) present the real part and imaginary part of permeability of a single domain with alignments of  = 0, 30, 60 or 90 degree from the LL-G model (equation 2.12). It can be seen that the intensity decreases and the resonance peak shifts to higher frequency, as alignment angle increases from to 90 degree. In figures 6.5(a) and 6.5(b), the corresponding curves are plotted with the permeability calculated from the LL-FMR model (equation (6.7)). These curves are fitted to match the permeability calculated with the LL-G model (solid lines). The fitted curves agree relatively well with the LL-G model. This shows that we can use the LL-FMR model in the calculation of magnetic domains with different orientations. 6.3.2.2 Calculations of the average permeability of an isotropic magnetic particle (bcc-Fe) without the consideration of skin effect 132 The permeability of an isotropic bcc-Fe particle without the consideration of skin effect is first calculated. The solid lines in Figure 6.6(a) and 6.6(b) show the permeability from the LL-G model using the equation (2.13). Equation (6.8) is used for the calculation of the isotropic permeability from the LL-FMR model. The fr,min and fr,max are 1.75 and 10.5 GHz respectively, which are also the resonance frequencies obtained from figure 6.5(b), for  = and  = 90 degrees. As shown in figures 6.6(a) and 6.6(b), the curves of the permeability form the LL-FMR model have the similar shapes of those calculated from the LL-G model. There are two peaks (one maximum and one minimum) in the real part for the both curves for the LL-G and LL-FMR models. For the imaginary part, the curve obtained from the LL-G model shows two peaks. The curve derived from the LL-FMR model has a similar trend, but only one broad peak with a shoulder appears. 6.3.2.3 Calculations of effective permeability and absorption property of bcc-Fe particles embedded in an insulating matrix with skin effect The analytical-form isotropic permeability with skin effect is computed for powdered materials. The calculated results are compared with experimental results for two commercial powders - carbonyl iron and magnetite. 133 The carbonyl iron (HQ) has an average size, d, of µm and electric resistivity of ρ= 0.1 µΩm, saturation magnetization 4πMs =21500 G, and anisotropy field Hk = 584 Oe. 23 vol% of carbonyl Fe particles are mixed with epoxy resin and the sample is characterized using the coaxial air-line method [3.6]. The measured permeabilities are plotted in figures 6.7(a) and 6.7(b). Using the calculated average permeability from equation (2.13) (LL-G model), the effective permeability of the 23 vol% of Fe/epoxy resin composite is calculated using equation (3.1). The calculated permeabilities derived from the LL-G model are plotted in Figure 6.7(a) and figure 6.7(b). Similarly, the permeabilities from the LL-FMR model using equation (6.8) are calculated. Comparing the measured and calculated results shows that the both the LL-G model and the LL-FMR models are able to model the permeability, which agrees with the measurements well. Figure 6.8 shows the calculated power reflection coefficient (labelled as “c”), and the measured value using measured permeability and permittivity (labelled as “m”). As shown in the plot, they also agree well. 134 6.3.2.4 Calculation of effective permeability and absorption property of Fe3O4 particles composite As another example, the results for Fe3O4 particles are presented. The permeability is measured using the sample of 17 vol% Fe3O4 particles, embedded in epoxy resin. Here, the permeability, using the parameters of Fe3O4 magnetite (4πMs =5700 G, HK = 595 Oe, ρ = 40 µΩm, α=0.8 and β=-0.001), is calculated. For the calculated permeability, the average particle size of 0.25 µm is used. The calculation process is similar to the one described for bcc-Fe. As shown in Figure 6.9, the calculated results from our new model agree quite well with measurements. Figure 6.10 shows the calculated power reflection coefficient (labelled as “c”), and the measured value using measured permeability and permittivity (labelled as “m”). As shown in the plot, they also agree quite well. 135 (a) (b) Figure 6.5: (a) Real part of permeability, (b) Imaginary part of permeability vs frequency (GHz) with different θ for bcc Fe (* : LL-FMR model, otherwise : LLG model). 136 (a) (b) Figure 6.6: (a) Real part of permeability, (b) Imaginary part of permeability vs frequency (GHz) for bcc Fe (isotropic case). 137 (a) (b) Figure 6.7: (a) Real part of permeability, (b) Imaginary part of permeability vs frequency (GHz) for carbonyl iron composite (v=23 vol%). 138 Figure 6.8: Calculated (c) and measured (m) power reflection coefficient vs frequency (GHz) for carbonyl Fe (23 vol%) composite using the calculated and the measured permeabilities and permittivities respectively. 139 (a) (b) Figure 6.9: (a) Real part of permeability, (b) Imaginary part of permeability vs frequency (GHz) for magnetite composite (v=17 vol%). 140 Figure 6.10: Calculated (c) and measured (m) power reflection coefficient vs frequency (GHz) for magnetite (17 vol%) composite using the calculated and the measured permeabilities and permittivities respectively. 6.4 Concluding Remarks An algorithm using the LL FMR model with and without skin depth effect, to extract the effective magnetic parameters of thin film with in-plane uniaxial magnetic anisotropy, has been established. The LL FMR model with skin effect has been verified with published theoretical results [6.1] and the algorithm has been used to extract the effective Ms , Hk and α of Si/NiFe/FeCoB and CoZrRe [6.6]-[6.7]. The skin depth effect is found to be important samples with low electrical resistivity, but it is not significant if electrical resistivity is high. The high permeability arising from the anisotropic property of magnetic thin film, is potentially useful for microwave absorbers. 141 A multi-domain structure with a random distribution of the orientations of magnetic domains has been considered (for isotropic cases). From the calculated permeability of a magnetic domain with an orientation of  to the incident microwave, using the Landau-Lifshitz-Gilbert (LL-G) model, the resonance frequency required in LL FMR model is obtained. Upper and lower limits of the resonance frequency are required in the LL FMR model. The integration over the whole range of resonance frequency gives the average (isotropic) permeability of a magnetic particle. Using the extended effective medium theory, the effective permeability is obtained. Comparison between the calculated results from the LL-G and the LL-FMR models has shown that the LL-FMR model can be also used for powered magnetic materials. The permeabilities of two magnetic materials (bcc-Fe and Fe3O4) have been calculated. The calculated permeability and power reflection coefficient agree well with the experimental results. 142 6.5 References [6.1] K. Seemann, H. Leiste, and V. Bekker, J. Magn. Magn. Mater. 278, 200 (2004). [6.2] I.T. Iakubov, A.N. Lagarkov, S.A. Maklakov, A.V. Osipov, K.N. Rozanov, I.A. Ryzhikov, N.A. Simonov, S.N. Starostenko, J. Magn. Magn. Mater., 258259, 195 (2003). [6.3] E. Vanderiet, and R. Roozeboom, J. Appl. Phys. 81, 350 (1997). [6.4] D. Spenato, A. Fessant, J. Gieraltowski, J. Loaec, and H.Le Gall, J. Appl. D. 26, 1736 (1993). [6.5] A. Aharoni, J. Appl. Phys. 83, 3432 (1998). [6.6] A. Hashimoto, S. Nakagawa, and M. Yamaguchi, IEEE Trans. Magn. 41, 2627 (2007). [6.7] D. Spenato, A. Fessant, J. Gieraltowski, H.Le Gall, and C. Tannous, J. Appl. Phys. 85, 6010 (1999). [6.8] C.P. Neo and J. Ding, J. Appl. Phys. 107, 09C507 (2010). [6.9] C.P. Neo, Y. Yang and J. Ding, J. Appl. Phys. 107, 083906 (2010). 143 Chapter CONCLUSIONS I have shown how magnetic anisotropy, saturation magnetization and spatial orientation (  ) affect the microwave magnetic permeability. The magnetic permeability for different metallic magnetic metals (Fe, Ni and Co), assuming zero magnetic interactions, is calculated first. The selection of the metallic magnetic materials covers a wide range of saturation magnetization and magneto-crystalline anisotropy. The result shows that the peak i occurs at a higher frequency but has a lower value and broader peak I, for higher  (  is the angle between the incident magnetic field and the magnetization vector). When the isotropic permeability, 𝜇𝑖 , is calculated for the materials, two peaks in imaginary part of 𝜇𝑖 are observed. The second peak is due to the contributions from  of higher values. Of the metals Fe, Ni and Cu, Ni and Co are shown to have peak 𝜇𝑖 in lowest and highest frequency respectively. The investigation has provided an insight in selecting the correct magnetic material and  for practical application in the desired frequency range. Because our focus is in the choosing of good fillers for the design of microwave absorber in the L to X band, Fe based particles, like carbonyl iron and magnetite, are evaluated. 144 Thereafter, the LL-G model presented is used to predict complex permeability of Fe and Fe3O4 particles composites. The average diameters of Fe and Fe 3O4 particle are and 0.25 μm respectively, while their conductivities used in the simulation are 107 and 25000 S/m. As shown in the simulations, the damping factors of 0.1 and 1.1 produce reasonably good matches with the measurement data. Finally, our simulation results suggest that the interaction factor is -0.002 and -0.01 respectively for the composites of Fe and Fe3O4. The simulation parameters are tabulated below: Table 7.1: Simulation parameters for Fe and Fe3O4. Average diameter (μm) Conductivity (S/m) Damping factor Interaction factor Fe 107 0.1 -0.002 Fe3O4 0.25 25000 1.1 -0.01 The simulation models for the two-phase and core-shell particle composites are proposed in this thesis. As shown in our simulations for the two-phase and core-shell particle composites, the permeability curves obtained are bounded by the permeability curves of the Fe and Fe3O4 composites. The new permeability curves make it possible to design composites with the specific requirements. Moreover, the two-phase and core-shell particle composites 145 could increase the percolation threshold by breaking the conducting chains in the composites with particles of low conductivity. In addition, the core-shell particle composite offers a way to create relatively high permeability with Fe, and yet achieve chemical stability. The calculated permeability of the twophase particle composite agrees quite well with the measured data. A model to calculate the permittivity of composites comprising Fe or Fe 3O4 is presented, and the calculated results compare relatively well with the measurement results. Both calculated permeabilities and permittivities are used to calculate the reflection coefficients which compare well with coefficients calculated using the measured permeabilities and permittivities. The method of extrapolating the permeability and permittivity with different volume fraction is presented and validated. Furthermore, the design of the Dallenbach and Salisbury absorbers are discussed and validated with experimental and published data. The proposed LL FMR with skin effect has been verified with other theoretical results, and the algorithm has been used to extract the effective 𝑀𝑠 , 𝐻𝑘 and 𝛼 of Si/NiFe/FeCoB and CoZrRe. It shows that the skin effect must be considered in the LL FMR model, for samples with low electrical resistivities. It is not necessary if the electrical resistivity is high. The high permeability arising from the anisotropic magnetic property of magnetic thin film offers the potential of making of microwave absorbers. Lastly, we have considered a multi-domain 146 structure with a random distribution of the orientations of the magnetic domains. The LL-G model is used to calculate the permeability of a magnetic domain, oriented at angle  to the incident microwave. The resonance frequency for the LL-FMR model is then obtained, after fitting its permeability curve to that of the LL-G. Integration over the whole range of resonance frequency gives the isotropic complex permeability of a magnetic particle. Using the extended effective medium theory, the effective complex permeability is obtained. The comparison between the calculated results from the LL-G model and LL-FMR model, shows that the LL-FMR model can be also used to calculate the permeability for magnetic particles composites. In this thesis, calculation of the permeabilities of two magnetic materials (bcc-Fe and Fe3O4) using the LL-FMR model has been presented. The calculated permeability agrees well with the experimental results. Thus, it is demonstrated that the microwave permeability of magnetic thin films and particle composites can be calculated using the modified LL-FMR model. 147 [...]... permeability of composite εr Relative permittivity of composite μeff Effective permeability of composite εeff Effective permittivity of composite μm Permeability of host material εm Permittivity of host material μ1 Permeability of Fe phase µ2 Permeability of Fe3O4 phase ε1 Permittivity of Fe phase ε2 Permittivity of Fe3O4 phase v1 Volume fraction of Fe phase v2 Volume fraction of of Fe3O4 phase... high Curie temperature, and large magnetic permeability at microwave frequency Wen et al [1.19] have studied the effect of the shape of carbonyl iron particles on the microwave permeability, and found that the permeability can be enhanced by changing the shapes of particles from spherical to thin flake (disc), because of the reduction of eddy loss, orientation of magnetic moment and space-charge polarization... Frequency range Letter Frequency range Designation L band 1 to 2GHz Designation Q band 30 to 50GHz S band 2 to 4GHz U band 40 to 60GHz C band 4 to 8GHz V band 50 to 75GHz X band 8 to 12GHz E band 60 to 90GHz Ku band 12 to 18GHz W band 75 to 110GHz K band 18 to 26.5GHz F band 90 to 140GHz Ka band 26.5 to 40 GHz D band 110 to 170GHz A schematic representation of radar system is shown in figure 1.1 When the... polarisability a1 Radius of scatterer M Fitting parameter of effective permittivity of core-shell composite xv r Ratio of radius of core to radius of shell tanδe Loss tangent of the effective permittivity Y0 Free-space admittance R i Surface resistivity of the ith layer w Bandwidth ρ Resistivity of the material xvi LIST OF ACRONYMS EM Electromagnetic RAM Radar absorbing material EMI Electromagnetic interference... calculated intrinsic permeability of the magnetic particles, the effective permeability of the composite consisting of the magnetic particles and embedded in a nonmagnetic matrix can be further calculated by using the effective medium theory (EMT) The schematic representation of magnetic particles embedded in non -magnetic matrix is shown in figure 1.3 The microstructure of the composite has been shown... (1.13) where Nk is the shape factor of the particles along the direction of the magnetic field µi µm Figure 1.3: A schematic representation of particles embedded in matrix As a matter of fact, this Bruggeman theory is not fully applicable to particles studied here as the particle size d is of the same order of magnitude of skin effect Indeed, eddy currents can be generated and affect μeff In order to 14... assumption that the dielectric permittivity and magnetic permeability are effective properties of the absorber The absorber consists of inclusions and matrix The permittivity and permeability are influenced by magnetic and structural parameters, such as saturation magnetization, magnetocrystalline anisotropy, electrical resistivity, 11 grain size (domain structure), and particle size In order to know... accuracy of the simulation models 15 1.2.4 Fe- based metallic magnetic materials Magnetic materials with high permeability are utilized in numerous microwave devices For example, fine magnetic particles embedded in a nonmagnetic medium are widely used as microwave absorbers Among different metallic magnetic materials, nanocrystalline carbonyl iron is a very promising microwave absorption material because of. .. magnetite (17 vol%) composite using the calculated and the measured permeabilities and permittivities respectively 141 xi LIST OF TABLES Number 1.1: 2.1: 2.2: 3.1: 3.2: 3.3: 3.4: 3.5: 5.1: 7.1: Page Microwave frequency bands 6 Magnetic Properties of Ni, Fe and Co [2.12] 36 Resonant frequency and peak i for different  for Ni, Fe and Co 37 Errors obtained for different damping factors... πf μi ρε0 c 2 1 2 , (1.16) where d is the particle size (diameter of a spherical particle) , ρ the electrical resistivity, and f the microwave frequency The above EMTs are widely used to predict the influence of microstructural, electrical and magnetic parameters (such as particle size, electrical resistivity, saturation magnetization and anisotropy field) on microwave performance Experimental data are . CALCULATIONS OF MICROWAVE PERMEABILITY, PERMITTIVITY AND ABSORPTION PROPERTIES OF MAGNETIC PARTICLE COMPOSITES NEO CHYE POH B.Eng (Hons), M.Eng,. the design of magnetic absorber through the calculations of magnetic permeability and electric permittivity. The emphasis of this thesis is to calculate and design the intrinsic and extrinsic. permeability and permittivity 100 5.3.3 Calculation of microwave absorption property of particle composite. 103 5.3.3.1 Microwave dallenbach absorber (dielectric). 103 5.3.3.2 Microwave