Proceedings of the Symposium R
ELECTROMAGNETlC MATERIALS
This page intentionally left blank
ICMAT 2 0 0 5
International Conference on Materials for Advanced Technologies (ICMAT 2005)
9th International Conference on Advanced Materials (ICAMS 2005)
3rd
Proceedings of the Symposium R
ELECTROMAGNETlC MATERIALS 3-8 July 2005 Suntec Singapore International Convention and Exhibition Centre
edited by
Lim Hock, Serguei Matitsine 8 Gan Yeow Beng Temasek Laboratories National University of Singapore, Singapore
Symposium R Organiser
Te m a se k Labor a t o r ies
NUS Ndf,onai Unlverrlt”
“I 5ingaporc
Unleashing Minds
Transforming Lives
N E W JERSEY
-
Scientific 1:6World -
LONDON * SINGAPORE
BEIJING
*
SHANGHAI
H O N G KONG * TAIPEI * C H E N N A I
Published by World Scientific Publishing Co. Re. Ltd.
5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library.
ELECTROMAGNETIC MATERIALS Proceedings of the Symposium R, ICMAT 2005 Copyright 0 2005 by World Scientific Publishing Co. Pte. Ltd
All rights reserved. This book, or parts thereoJ may not be reproduced in any form or by any means, electronic or mechanical, including photocopying. recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN 981-256-41I-X (pbk)
Printed by FuIsland Offset Printing (S) Pte Ltd, Singapore
FORE WORD
International Conference on Materials for Advanced Technologies (ICMAT) is a biannual conference jointly launched by the National University of Singapore and the Materials Research Society (Singapore) in 2001. The first two conferences held in July 2001 and December 2003 were great successes, attracting about 1,500 international delegates each. Nobel Laureates actively participated in the programmes, and presented plenary and public lectures. At ICMAT 2003, Temasek Laboratories at National University of Singapore organized Symposium F on Electromagnetic Materials, which attracted wide international attendance. National University of Singapore celebrates its centennial anniversary in 2005. ICMAT 2005 will be the flag-ship event to launch this year-long celebration. Nearly 3,000 papers will be presented at 25 parallel symposia. Again the conference will be graced by four Nobel Laureates. We are pleased to host again, at ICMAT 2005, a Symposium R on Electromagnetic Materials. This Symposium is dedicated to the studies of materials/structures that exhibit electromagnetic effects theoretical understanding of their properties, characterization and measurement techniques, design and fabrication methods, and special applications. Despite the long history of this line of study, the complex phenomena of materials-electromagnetic field interactions continue to provide fertile ground for basic research and technology innovations. Materials with unique properties are synthesized to meet the increasingly demanding specifications of modem technologies, and scientists and engineers are becoming very skillful in precision control of their performance.
~
On behalf of the Organizing Committee of this Symposium, I wish to thank the ICMAT 2005 Conference Committee for setting up the stage on which this Symposium has the privilege to play a supporting role in a niche area. The Scientific Programme Committee must take the credit for the excellent programme of the Symposium. World Scientific Publishing Co. Pte. Ltd., in its usual professional manner, has published with great efficiency, and at a cost within our budget, this handsome volume of the proceedings ready for our participants at the opening of ICMAT 2005. I wish all participants an exciting and fruitful conference, and our guests from overseas a pleasant and enjoyable visit to Singapore.
priofessor limflock Chair Symposium R (Electromagnetic Materials) ICMAT 2005
V
Symposium R: ELECTROMAGNETIC MATERIALS Chair: LIM Hock Temasek Laboratories, National University of Singapore, Singapore Co-Chair: Amar S. BHALLA Pennsylvania State University, United States of America Co-Chair: CAN Yeow Beng Temasek Laboratories, National University of Singapore, Singapore
SCOPE OF SYMPOSIUM The Symposium on Electromagnetic Materials aims to provide an international forum for scientists and engineers to report latest research findings, to exchange ideas and information, and to establish research links. EM materials have both civilian and defence applications, such as novel antenna designs, protection against high power transients in densely packed printed circuits, special frequency response or polarization response to meet component or system specifications. An indepth understanding of the responses of materials to electromagnetic waves may even enable us to design and fabricate materials with properties not found in nature. Researchers in the areas of design and analysis of EM properties of materials, microwave processing of materials, etc, should be interested in the topics covered in the Symposium. Main Topics of Interest: Dielectric and Magnetic Composites with Inclusions Metamaterials (Left-Hand or Double Negative Materials) Smart Materials (includes thin films, tunable dielectrics, etc) Periodic Structures Material Processing and Fabrication Techniques Characterization of Electromagnetic Properties of Materials
vi
INVITED SPEAKERS
0
Masanori ABE, Tokyo Institute of Technology, Japan Olivier ACHER, CEA Le Ripault, France Luk ARNAUT, National Physical Laboratory, UK Amar BHALLA, Pennsylvania State University, USA Jin Au KONG, Massachusetts Institute of Technology, USA Andrei N. LAGARKOV, Institute for Theoretical and Applied Electromagnetics, Russia Akhlesh LAKHTAKIA, Pennsylvania State University, USA Herbert 0. MOSER, Singapore Synchrotron Light Source, National University of Singapore Sergey A. NIKITOV, Institute of Radioengineering and Electronics, Russia Alan TENNANT, The University of Sheffeld, UK Sergei A. TRETYAKOV, Helsinki University of Technology, Finland Victor G. VESELAGO, Moscow Institute of Physics and Technology, Russia YAO Xi, Tongji University, Shanghai, China
SCIENTIFIC PROGRAMME COMMITTEE
0
0
0
Luk ARNAUT, National Physical Laboratory, UK Amar S. BHALLA, Pennsylvania State University, USA DENG Chaoran, DSO National Laboratories, Singapore DING Jun, National University of Singapore, Singapore CAN Yeow Beng, National University of Singapore, Singapore LEE Kim Seng, DSO National Laboratories, Singapore LEE Nam Sua, Defence Science and Technology Agency, Singapore LIM Hock, National University of Singapore, Singapore Serguei MATITSINE, National University of Singapore, Singapore ONG Chong Kim, National University of Singapore, Singapore Konstantin N. ROZANOV, Institute for Theoretical and Applied Electromagnetics, Russia
PUBLICATION AND LIAISON COMMITTEE
0
Karrie CHAN, Temasek Laboratories, NUS, Singapore CAN Yeow Beng, Temasek Laboratories, NUS, Singapore Suhana HANAN, Temasek Laboratories, NUS, Singapore Irene LEOW, Temasek Laboratories, NUS, Singapore Maryate MUHAMAD, Temasek Laboratories, NUS, Singapore
ACKNOWLEDGEMENT ARUMUGAM Sundaram, Temasek Laboratories, NUS, Singapore LUM Kai Yew, Temasek Laboratories, NUS, Singapore
vii
This page intentionally left blank
CONTENTS Session R1
Chair: A.N. Lagarkov
R- 1-IN 1
Metamaterials: From Averaging to Detailed Electrodynamic Description A.N. Lugarkov* and V.N. Kissel
R- 1-IN2
Electromagnetic Field Energy Density in Dispersive and Lossy Metamaterials S.A. Tretyakov
10
R- 1-IN3
Electromagnetic Metamaterials over the Whole THz Range - Achievements and Perspectives H.O. Maser*, B.D.F. Casse, 0. Wilhelmi and B.T. Saw
18
Session R2
3
Chair: J.A. Kong
R-2-IN4
Superlens as Matching Device V.G. Veselago
29
R-2-INS
Theory of Negative Refraction and Left-Handed Metamaterials (LHM) J.A. Kong*, T.M. Grzegorczyk, H. Chen, L. Ran,J. Lu, X . Chen, Q. Jiang and X. Zhang
33
R-2-OR1
The Role of Phase Shift at Energy Transport by Evanescent Waves A.P. Vinogradov* and A.V. Dorofeenko
41
R-2-OR2
Image Oscillations in the Meta-Material Lens Focusing Lei Zhou and C.T. Chan *
44
R-2-OR3
Superprism Effect in 1D Photonic Crystal A.M. Merzlikin * and A.P. Vinogradov
48
R-2-OR4
Cluster Effects of Composites with Long Conductive Fibers L. Liu*, S.M. Matitsine and Y.B. Gun
51
R-2-OR5
Micro- and Nano-Fabrication of Electromagnetic Metamaterials for the Terahertz Range B.D.F. Casse*, H.O. Moser, 0. Wilhelmi and B.T. Saw
55
Sidelobe Suppression of Cellular Base Station Antenna Due to Application of Metamaterials A.N. Lugarkov, V.N. Semenenko*, V.A. Chistyaev, A.I. Fedorenko, N. P. Balabuha and V.P. Moiseev
59
R-2-OR6
Session R3
Chair: S.A. Nikitov
R-3-IN6
Thin Ferromagnetic Film-Based Two-Dimensional Magnonic Crystals S.A. Nikitov, Yu.V. Gulyaev, Yu.A. Filimonov, A.I. Volkov, S.L. Vysotskii, Ph. Tailhades and C.S. Tsai
R-3-IN7
Giga-Hertz Conducted Noise Suppressors of Ferrite Films Prepared from Aqueous Solution M. Abe*, M. Tada, N. Matsushita, K. Kondo, H. OnoandS. Yoshida
ix
65
73
X
R-3-OR7
Microwave Composites Filled with Thin Ferromagnetic Films. Part I. Theory A.N. Lagarkov, A.V. Osipov, K.N. Rozanov* and S.N. Starostenko
R-3-OR8
Microwave Composites Filled with Thin Ferromagnetic Films. Part 11. Experiment 78 I.T. Iakubov, A.N. Lagarkov, S.A. Maklakov, A.V. Osipov, K.N. Rozanov* and I.A. Ryzhikov
R-3-OR9
GHz Permeability of (100) Orientated Fe304+,,Films Prepared from an Aqueous Solution M. Tada*, J. Miyasaka, N. Matsushita and M. Abe
R-3-OR10
Giant Photonic Hall Effect in Magneto-Photonic Crystals A.M. Merzlikin, A. P. Vinogradov *, M. Inoue and A. B. Granovsky
Session R4 R-4-IN8
74
82
83
Chair: A S . Bhalla Recent Developments in the Field of Frequencym-field Agile Microwave Electronics (FAME) A.S. Bhalla
89
R-4-IN9
Tunable Microwave Ceramic Thick Films Yao Xi
90
R-4-IN10
Sculptured Thin Films A. Lakhtakia
97
R-4-OR11
Phase Field Simulations of Hysteresis and Butterfly Loops in Ferroelectrics Subjected to Electro-Mechanical Coupled Loading Y.C. Song and A. K. Soh *
R-4-OR 12
Intrinsic Limit of Dielectric Loss in Ba(MglnTaz13)03and Ba(Mgl/3Nbzn)0,Ceramics T. Kolodiazhnyi*, G. Annino and T. Shimada
R-4-OR13
Ferroelectric (Pb,Sr)Ti03Epitaxial Thin Films on (001) MgO for Room Temperature High-Frequency Tunable Microwave Elements C.L. Chen*, S.W. Liu, J. Weaver, W. Donner, J.C. Jiang, E.I. Meletis, W. Chang, S. W. Kirchoefer, J. Honvitz and A.S. Bhalla
Session R5
103
107
111
Chair: 0. Acher
R-5-IN11
Recent Advances in Microwave Magnetic Materials 0. Acher
I I5
R-5-OR14
Microwave Permeability and Snoek’s Law in Co2ZComposites K.N. Rozanov*, L.F. Chen, Z. W. Li and M.Y. Koledintseva
121
R-5-OR15
Effects of Doping on the High-Frequency Magnetic Properties of Barium Ferrite Composites G. Q. Lin *, Z. W. Li, L. F. Chen, Y. Wu and C.K. Ong
125
R-5-OR16
High Frequency Magnetic Properties of Iron Based Magnetic Particulate Powders L.Z. Wu*, J. Ding, H.B. Jiang, L. F. Chen, C.K. Ong, C.P. Neo, S. Y. Lim and C.R. Deng
129
R-5-OR17
Structural, Electrical and Magnetic Properties of Ca2ZnLio.5Alo.SFe120zz P.R. Arjunwadkar and M.Y. Salunkhe*
133
xi
R-5-OR18
R-5-OR19
Spinel Ferrite Based Composites with Permeability and Permittivity of Almost Equal Values L.B. Kong*, Z.W. Li, L.F. Chen, G.Q. Lin, Y.B. GanandC.K. Ong Electric and Magnetic Studies on CopperKobalt Substituted Ni-Zn Ferrites B. Parvatheeswara Rao, K.H. Rao, P.S.V. Subba Rao, S. Pallam Setty, N.S. Gajbhiye and O.F. Caltun
136 140
Session R6 (Poster Session)
R-6-PO1
Microwave Tunable Dielectric Ba&ro.STi03:Mg0 Composites Prepared from the Nan0 Size Particles S. Agrawal, R. Guo, D.K. Agrawal andA.S. Bhalla
147
R-6-PO2
Preparation and Main Properties of Nd, Pr, and Sm-Doped Bi4Ti3OI2Thin Films J. Han*, C. Yang and Zhuo Wang
R-6-PO3
Influence of Nanoscale Distribution of Magneli’s Phases on the Dielectric Properties of Niobate Oxides H. Manuspiya*, A.S. Bhalla and R. Guo
152
Radiation Characteristics of Circular Disc Microstrip Array Antenna on NiCoAl Ferrite Substrate D. Kumar and P. K.S. Pourush
153
R-6-PO4
151
R-6-PO5
Wide-Band Microstrip Antennas with an Organic Magnetic Material Substrate Wei Huang* and Tao Yu
157
R-6-PO6
Detailed Study of Magnetic Properties of Off-Stoichiometric Ni-Mn-A1 Heusler Alloy V.K. Srivastava, A. Singh, A. Pathak, R. Chatterjee* and A. K. Nigam
158
R-6-PO7
Local Structural Distortions and Mn Random Distributions in (Ga, Mn)As: A First-Principles Study X.S. Chen*. X.G. Guo and W. Lu
162
The Temperature Anomalies of Light Scattering in Ionic Conductor Li2B407 Crystals M.P. Dergachov*, V.N. Moiseyenko and Ya.V. Burak
166
Structural and Electrical Characterization of Bi2V,.,ME,0~S.5.9,,,2(ME = Cu, Ni) Systems S.M. Desai* and G.K. Bichile
167
Electro-Optical Characteristics of Inductively Coupled Plasma by Ar Gas Pressure and RF Power Y.-S. Choi*, J.-C. Lee, S.-H. Lee and D.-H. Park
168
Electromagnetic Field Distribution of Electrodeless Fluorescent Lamps and Analysis of Electrical Properties for Solenoidal Induction Coil Y.4. Choi*, J.-C. Lee, S.-H. Lee and D.-H, Park
171
R-6-PO8
R-6-PO9
R-6-PO 10
R-6-PO 11
R-6-PO 12
Electric Field Generated Stress on PolythiophenePolyisoprene Elastomer Blends T. Puvanawattana, A. Sirivat and D. Chotpattananont*
175
xii
R-6-PO13
Study on Electrorheological Characteristics of Polythiophene-Based Electrorheological Fluid D. Chotpattananont*, A. Sirivat and A.M. Jamieson
Session R7
179
Chair: L.R. Arnaut
R-7-IN12
Active Absorber Research a t The University of Sheffield A. Tennant* and B. Chambers
R-7-ml3
Correcting for Imperfections in the Experimental Characterization of Dielectric Media for High-Precision Metrology L.R. Arnaut
193
Design of a n Isotropic Microwave Screen from Dipole Arrays Using Genetic Algorithm K.M. Hock, P.-M. Jacquart*, Y.B. Gan, L. Liu and K.Y. Lum
200
R-7-OR20
185
R-7-OR2 1
Vector Spectral-Domain Method for the Analysis of Frequency Selective Surfaces Anyong Qing* and Xin X u
R-7-OR22
Frequency-Dependent Permittivity of Carbon Nanotube Composites from 0.01 to 10 GHz L. Liu*, L.F. Chen, S. Matitsine, L.B. Kong, Y.B. Gan and K.N. Rozanov
R-7-OR23
A Numerical Issue in the Modeling of Composites with Randomly Distributed Fibers Xin Xu*, Anyong Qing, Y.B. Gan and Y.P. Feng
R-7-OR24
Study on the Mechanical and Dielectric Properties of LDPElEVA Composites Filled with Carbon Fiber Z.-M. Dang
Session RS
R-%OR25
204
208 212
216
Chair: A. Lakhtakia Experimental Method and Software for Complex Characterization of Magnetic Materials O.F. Caltun*, A. Stancu and P. Andrei
R-%OR26
Effective Permeability of 2D-Lattice of Dielectric Resonators G.V. Belokopytov, A.N. Lugarkov, V.N. Semenenko*, V.A. Chistyaev and A. V. Zhuravlev
R-8-OR27
Carbon-Encapsulated Magnetic Metal Nanoparticles by Arc-Discharge in Organic Solvent N. Sugiyama, T. Watanabe, Y. Yamakawa and M. Yoshimura*
223 227
23 1 234
R-%OR28
FTIR Study of Ni, Cu, Zn Substituted MgFe204Nano-Ferrite A. Pradeep and G. Chandrasekaran*
R-8-OR29
Comparison of Magnetic Properties of Metallic Glasses Fe75B10Si15, Fe72Co$10Si15,Fe74C01,,B16 and Fe67C018B14Sil by Mossbauer Spectroscopy B. Bhanu Prasad* and A.R. Subrahmanynm
238
Effect of A-Site Ionic Radii on the Magneto-Transport Properties in (La,Sml.,)2nSrIBMnO3 (x = 1/3,1/2 and 2/3) Manganites S. Asthma*, A.K. Nigam and D. Bahadur
242
R-%OR30
xiii
R-%OR31
R-8-OR32
Miniaturization of a Microstrip Y-Isolator Utilizing a Large peaand Ip+-p-l of a YIG Ferrite Single Crystal K. Oshiro*, T. Tanaka, H. Kurisu, H. Fujimori, M . Matsuura and S. Yamamoto
246
The Microwave Absorbed Property is Affected by the Shape of Nanometric Crystal y-Fez03 Huang Yunxia*, Cao Quanxi, Wang Yupeng, Yang Peng and Wei Yunge
250
Session R10
Chair: S.M. Matitsine
R-10-OR33 Fabrication and Characterization of Polycrystalline Samples and Tape of Superconducting MgB, - A Future Prospect for an Electromagnet S. Rajput, S. Chaudhary *, D. K. Pandya and S. C. Kashyap
253
R- 10-OR34 Electrorheological Response of Cross-Linked Poly(Dimethy1Siloxane) Containing Polyaniline Particles P. Hiamtup, A. Sirivat* and A.M. Jamieson
257
R- 10-OR35 Microwave Attenuation Measurements on Tetrahedral Amorphous Carbon Coatings for TWT Applications V. Kumar*, A. Vohra and V. Srivastava
26 1
R- 10-OR36 A Novel Electrochemical Sensor for Monitoring Localized Corrosion N.N. Aung and Y.-J. Tan* R- 10-OR37 Electrorheological Properties of Poly(p-phenylene viny1ene)Polydimethylsiloxane Blends S. Naimlang and A. Sirivat*
265
269
R-10-OR38 FEA for SMD Type Piezoelectric Resonator J.-I.Im* and K.-M. Park
273
R-10-OR39 Ab Initio Calculations of V and Ge-Doped Ti02 H.-H. Cao* and Qiang Chen
274
Author Index
275
This page intentionally left blank
Session R l
Chair: A.N. Lagarkov
This page intentionally left blank
Metamaterials: From Averaging to Detailed Electrodynamic Description
A. N. Lagar’kov and V. N. Kissel Institute for Theoretical and Applied Electromagnetics, Russian Academy of Sciences, Moscow, Russia Considerable interest is observed during the last decade in composite materials of unusual radiophysical and optical properties, the so-called metamaterials. This wide range of artificial dielectrics and magnetodielectrics is not yet clearly defined. Many of the researchers apply the term “metamaterials” to composites which contain inclusions of certain resonance properties and characteristic sizes of less than the wavelength, such as highly conducting needles, split rings, spirals, Q-inclusions, and so on. Also classed with metamaterials in some cases are photon crystals which are ordered composite structures characterized by the dependence of the wave vector k on frequency w ,which is typical of periodic structures. One of the objectives of theoretical description of metamaterials is to determine their effective parameters, namely, permittivity E, magnetic permeability p, and the chirality factor, using the results of studies of the properties of individual inclusions (conductivity, magnetic permeability, and shape), as well as their concentration. Even the well-known monograph by Schelkunoff and Friis [ l ] gives expressions which describe an artificial magnet of positive or negative magnetic permeability arising owing to the introduction into the composite of capacitance-loaded split rings. Numerous papers published later were devoted to the study of the effective parameters of composites containing needles (see, for example, [2] and references cited there), rings and spirals [3,4], Q-inclusions, and so on. The use of effective parameters in electrodynamic equations for a continuous medium when studying the electromagnetic wave transmission in metamaterials made it possible to predict a number of surprising effects. In our opinion, the most spectacular of these effects is that of “superresolution” of a focusing system based on the plane-parallel Veselago lens [5] with E = p = -1, which was predicted by Pendry in [6] and confirmed experimentally [7]. Note, however, that the use of effective parameters to describe rather complex systems such as materials with negative E and p is hardly self-evident (though it is efficient) as a tool for studying the wave propagation in metamaterials. For example, it was shown in [S] that, in the case of composites containing extended resonant inclusions, the effective permittivity may be introduced only for sheet materials whose thickness exceeds some critical value and, generally speaking, the value of permittivity may differ depending on the experimental conditions (see also the discussion in [9]). The experimental determination of the effective parameters of composites containing resonant inclusions is based, as a rule, on the results of measurements under incidence of a wave with a plane front. We will demonstrate some characteristic features of electromagnetic wave propagation in a real composite and expose the aspects which turn out to be hidden when the effective parameters are used in Maxwell equations. This could be done by applying a rigorous approach (integral equation method) to obtain a hll-wave solution for the electromagnetic fields. By way of example, we will give the results of a computational experiment which repeats the conditions of real experimental investigations [7]. This latter study involved the use of a plate of a composite with inclusions of resonant elements in the form of spirals with a small pitch and half-wave rods, excited by the magnetic and electric components, respectively, of a field radiated by two linear radiators. The experimental setup is shown schematically in Fig. 1 ( I and 2, linear radiators; 3, probe; 4, plate), and the results of field measurements by the probe are given in Fig. 2.
3
4
No plate
Metarnaterial
Y, mm
30 15
0 -15
-30
1.5
1.6
1.7
a)
Fig. 1
1.8 1.5
LGHz
1.6
1.7
b)
1.8
LGHz
Fig. 2
The microwave image of the sources (half-wave radiators 1 and 2 spaced from each other at a distance that is much less than the wavelength) was recorded by the receiving probe antenna 3 in the process of its displacement parallel to the plate surface, as is shown in Fig. 1. The results of field measurements in the absence of a plate between the antennas, as well as when the plate is introduced, are given in Figs. 2a and 2b, respectively. In the latter case, the frequency range (1.65 to 1.8 GHz) is clearly registered in which a separate image of two closely spaced sources is observed. Therefore, theoretical predictions of the possibility of overcoming the “diffraction limit” in systems with double-negative materials were used to develop some passive device which indeed helped to obtain the expected superresolution. However, it would be rather doubtful to identify the electromagnetic processes occurring in an experimental composite plate with the electromagnetic wave transmission through a layer of homogeneous (ideal) metamatter with E < 0 and p < 0. One of the obvious reasons for this is the discrete structure of the composite. It is known [lo] that, in regular structures, the value of the lattice spacing constrains the limiting resolution of the system. In this case, however, one more fact is worthy of note. According to [7], one can count on the manifestation of the effect of “superresolution” only when thin plates with low loss are employed; therefore, in the setup described above, the plate consisted of only one layer of resonators (see Fig. 1). It is hard to set up a correspondence between this structure and a plate of homogeneous material, even if because of the absence of clearly defined boundaries of the composite in the transverse direction. One can assume that the location of these (conventional) boundaries must depend on the characteristic features of distribution of the electromagnetic field in the vicinity of inclusions. Finally, one must not rule out the possibility that the electromagnetic process in a thinlayer composite plate differs significantly from phenomena occurring in a homogeneous material; as a result, the usage of the effective parameters of the medium E and p will turn out to be invalid. In order to construct the computational model, an equation of the Pocklington type is used, which is based on a thin-wire approximation with regard for the capacitive load of elements (the two-turn spirals with a small pitch and significant inter-turn capacitance could be treated with a high degree of accuracy as rings with a narrow split into which lumped capacitors are introduced). The finite conductivity of the wire metal was also taken into account including the skin effect. Algorithms and computational programs were developed for the calculation of fields of different sources in the presence of both systems of a finite number of elements and infinite structures (twodimensional periodic lattices). Discussed below are the results of numerical simulation obtained for a composite plate with a finite number of elements which corresponds to that of a real experimental sample [7]. The calculation results both reproduced the observed effect of “superresolution” in the presence of a complex composite medium and made it possible to compare the phenomena
5 occurring in real samples of composites (periodic systems of resonant elements) to phenomena occurring in homogeneous media with negative electrodynamic parameters which exist only theoretically (in what follows, we will refer to such media for simplicity as metamatter). It has been demonstrated that a plate of a composite exhibits some properties typical of a plate of metamatter. For example, a frequency band exists (as predicted by theory, it is located in the vicinity of and a little higher than the resonance frequency of inclusions) in which the effect of superresolution shows up. It is well seen in Fig. 3, in whose top part the surface relief is shown, and in the bottom part - the isolines of intensity of an electric field calculated in the plane of the central cross section of the plate and in its neighborhood. For comparison, Fig. 3b gives analogous patterns in the absence of a plate (all geometrical dimensions along the graph axes are expressed in electrical units, i.e., are multiplied by k = 27d2, where /z is the wavelength in free space).
1
kY 05 0
-0.5 -1
plane
4
b)
Fig. 3
The composite plate proper may be by and large characterized as a device in which a backward wave exists, i.e., there is a zone of space in the vicinity of resonators in which the phase and group velocities are opposite to each other. Figure 4 shows (see from the top down) the distributions of the amplitude, phase, and vector of phase velocity of total field (E,-component) in the vicinity of the composite plate, when a plane wave propagating in the direction of the Y-axis is incident on this plate.
6
-1
Fig. 4
-0.5
0
0.5
1
Fig. 5
However, one can readily see the differences in the field distribution between a thin composite plate and a plate of metamatter. For example, in a system with a homogeneous plate with E = p = -1, the phase and group velocities bear different signs only within the plate, and a strong excitation of the linear wires of the composite plate leads to the emergence of a zone with negative phase velocity outside of the geometric bounds of the structure (see Fig. 4). It is further known (e.g. [ 11,7]; see also Fig. 5 ) that, when a plane-parallel plate of metamatter is excited, the reactive energy of evanescent modes accumulates in the vicinity of the interfaces (first of all, in the neighborhood of the non-illuminated face of the plate), owing to which the "superresolution" may be realized. No such interfaces exist in the experimental plate; however, resonance phenomena are present, and the field energy accumulates within and in the vicinity of individual resonators (a maximum of the accumulated reactive energy is attained in the central part of the composite plate in the vicinity of the axial lines of inclusions). The fields of propagating harmonics and evanescent modes, which make up the spatial spectrum of radiation of the filamentary source, excite the resonators of the composite differently. This difference is largely due to the fact that, in the incident field of propagating harmonics (plane waves), the vectors E and E f are in-phase, while the evanescent modes are characterized by a phase shift of 90" between the vectors E and E f . At the same time, it is known that the phase and amplitude patterns of a system consisting of crossed magnetic and electric dipoles (models of resonators of composite) are defined by the relation of the phases of currents of these dipoles. Investigations reveal that the realization of suitable phase relations in the electric and magnetic resonators of the plate results in such an interference of the field of their radiation with the incident wave field that the propagating harmonics (in contrast to the evanescent modes) experience a significant attenuation, and specific sub-wavelength maxima of field intensity arise in the vicinity of the non-illuminated face of the plate. One can use these maxima for registering the location of sources with "superresolution", as was done in the experiment.
7
This is confirmed by the graphs which show the distribution of the E,-component of the amplitudes and phases of the total E, incident E‘, and scattered E“ fields calculated along the characteristic directions (cross sections) in the space in the vicinity of the plate (sections 1,2, and 3 - see Fig. 3a). Figures 6 and 7 give the results of calculations on frequencies f = 1.05fo and f = 0.95fo cfO is the resonance frequency of inclusions of composite) in section I extending normally to the plate through one of the filamentary sources. The region of space Ikyl< 0.1 1 taken up by the plate is also shown in these drawings. One can see that, in the first case, a field maximum is formed on a frequency a little higher than the resonance frequency (see Fig. 6a) in the vicinity of the rear (with respect to the sources) face of the plate. This maximum corresponds to one of the peaks of separate images of radiators (see Fig. 8a which shows the field amplitude in the plane of motion of the measuring probe, i.e., in section 2; curve I corresponds to the calculation of the total field in the presence of a plate, and curve 2 - to the calculation of the incident field, i.e., to the absence of a plate in which the sources are not observed separately). As to the second case, no such peaks are formed on a frequency a little below the resonance frequency, and no “superresolution” is observed (see Figs. 7a and 8b; designations are the same); the low level of the field in section 2 is due to the fact that the incident and scattered fields have close amplitudes and are in fact out of phase (see Figs. 7b and 7c; curves I and 2 correspond to the scattered and incident fields, and curve 3 indicates the phase difference between the scattered and incident fields). When tuning to the frequency f = l . O S f , the field amplitudes vary little (Fig. 6b, designations are the same) unlike the phase relations (Fig. 6c); in this case, it was the excitation of resonators by the evanescent modes that produced the main effect on the variation of the phase of the scattered field, which caused the manifestation of the “superresolution” effect. Note further that a partial compensation of the source field occurs in the vicinity of the “illuminated” face of the plate as well, in particular, in the plane of location of radiators, i.e., in section 3 (Fig. 8c,f= 1.05fo, 1 indicates the total field, and 2 indicates the incident field; a similar pattern is observed in this dane at f = 0.95fo); as a result, their images in this plane become “sharper”. IEl
arg(E), arg(ES)
2
225
180
1.5
135 1
90
45
0.5
0
n -1
-0.5
0
0.5
kY
45
1
-1
-05
0
05
-1
-0.5
0
0.5
kY
1
(b) Fig. 6 PI1 P I
IEl 2
3 25
15
2
1
15 1
05
05
n
0
-1
-0.5
0
1
0.5
kY
-1
-05
0
(b) Fig. 7
05
kY1
(c)
kY
1
a IEL IE’l
IEL IE’l
image plane
image plane
3
2
IEl, IE’l
source plane
2.5
1.5
2 1.5
1
1
0.5
0.5 0
0
kX
kX1’5
(c)
(b) Fig. 8
It is interesting that, when the “superresolution” is realized (in our case - at f = l.O5f), a characteristic field minimum arises in the vicinity of the “illuminated” boundary; this is again due to interference (see Fig. 6a). Therefore, it is to be expected that, as the resonator sizes are reduced and the number of their layers is increased, the layers which are farther away from the illuminated face will be excited more than the front layers; this will result in the known pattern of “rise” of amplitudes of evanescent modes, which is typical of the field in a plate of metamatter. Note finally that, when either magnetic or electric resonators are left out of the composite, the “superresolution” effect will naturally disappear (Figs. 9a and 9b, respectively, f = l.05fo). Nevertheless, it is confirmed by the calculation results that the resolution may be improved somewhat (see Fig. 9a) in extremely thin nonresonance systems of, for example, parallel metal conductors (analogs of thin films with E < 0).
1
05
0
-6 5
1
5
-1.5
-1
4 5
0
05
1
15
Therefore, the main differences in the pictures of field distribution, which are registered in composite materials and in plates of homogeneous metamatter, are defined by the characteristic features of the employed resonators, in particular, by the degree of their electromagnetic coupling with the environment, by the number of layers in the transverse direction of the plate, and (to a
9
lesser extent) by the discrete structure of the composite. Because the field of resonators extends significantly beyond the geometric bounds of the sample (including the zone of location of radiators and the zone of measurements), there is no point in using the effective values of the parameters E and p in this case. Despite the usefulness of the models based on the introducing effective E and p , the hrther improvements in the design of the focusing metamaterial structures are likely to be achieved through using full-wave solution of the electromagnetic boundary problem. Acknowledgements The study was supported in part by President Program on Support of Leading Scientific Schools, grant no. 1694.2003.8. References 1. Schelkunoff S.A., Friis H.T., Antennas: Theory and Practice, New York: John Wiley & Sons,
1952. 2. A.N. Lagarkov, A.K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev. B, 1992, V.53, Nc 10, pp. 6318-6336. 3. A.N. Lagarkov, V.N. Semenenko, V.A. Chistyaev, D.E. Ryabov, S.A. Tretyakov, C.R. Simovski, “Resonance properties of bi-helix media at microwaves,” Electromagnetics, 1997, V.17, NC3, pp. 213-237. 4. J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. MTT., 1999, V.41, pp. 2075-2084. 5. V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of E and p,” Sov. Phys. Usp., 1968, V.10, p.509 6. J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., 2000, V.85, No.18, pp. 3966-3969 7. A.N. Lagarkov, V.N. Kissel, “Near-Perfect imaging in a focusing system based on a lefthanded-material plate,” Physical Review Letters, vol. 92, 077401, 2004. 8. A.P. Vinogradov, D.P. Makhnovsii, K.N. Rozanov, “Effective boundary layer in composite materials,” Journal of Communications Technology and Electronics, 1999. V.44. No.3. pp. 317-322. 9. L. Liu, S.M. Matitsine, Y.B. Gan, K.N. Rozanov, “The thickness dependence of resonance frequency in anisotropic composites with long conductive fibers,” Electromagnetics, 2005, V.25, pp. 69-79. 10. D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna, J.B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Applied Physics Letters, 2003, V.82, No.10, pp. 1506-1508. 11. T.J. Cui, Z.-C. Hao, X.X. Yin, W. Hong, J.A. Kong, “Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials,” Physics Letters A, 2004, V.323, pp. 484-494.
Electromagnetic Field Energy Density in Dispersive and Lossy Metamaterials S.A. Tretyakov Radio Laboratory I SMARAD, Helsinki University of Technology P.O. Box 3000, FI-02015 TKK, Finland
[email protected] Abstract General relations for the stored reactive field energy density in passive linear artificial microwave materials are established. These relations account for dispersion and absorption effects in these materials, and they are valid also in the regions where the real parts of the material parameters are negative. These relations always give physically sound positive values for the energy density in passive metamaterials.
Introduction During a few recent years, interest in artificial electromagnetic materials has been very high. In particular, artificial media with negative real parts of material parameters (called Veselago media, backward-wave media, double negative media) have attracted much attention in view of the first experimental realizations of such media and because of potential applications in sub-wavelength imaging. Some other applications have been proposed, including improvement of antenna performance. In paper [l], radiation from a small electric dipole inside a spherical shell of such material has been considered, with some conclusions regarding the antenna bandwidth. A twodimensional model of an antenna coated by a dispersive material shell has been considered in [2]. These and many other issues involve considerations of the reactive energy stored in complex dispersive and lossy materials, and in this paper we present a new method for calculation of the stored energy density in general isotropic linear materials. A general approach that we describe here allows us to determine the time-averaged energy density of time-harmonic electromagnetic fields in dispersive and lossy materials with various dispersion laws. It is well known that the field energy density in materials can be uniquely defined in terms of the effective material parameters only in case of small (negligible) losses (e.g. [ 3 ] ) . This is because in the general case when absorption cannot be neglected, the terms dD dB E.-+H.at
at
describe both the rate of changing the stored energy and the absorption rate. Only if the absorption is negligible, we can write
E.!!!+H.dR=r?M',+(?W,, at
at
at
at
where we and w,,, are the energy densities of the electric and magnetic fields, respectively. For artificial materials based on metal or dielectric inclusions of various shapes absorption can be neglected when the operational frequency is far from the resonant frequencies of the inclusions and from the lattice resonances, if the material is periodical. For electromagnetic fields whose spectrum is concentrated near a certain frequency w,, , the time-averaged energy density in a material with scalar frequency-dispersive parameters E ( W ) and p ( w ) reads (e.g. [3,4])
10
11
If in the vicinity of the operating frequency w,,the frequency dispersion can be neglected and E and y can be assumed to be independent from the frequency, ( 3 ) simplifies to 1 2 1 2 w=-&IEI +-plHI . (4) 2 2 The validity of this formula is restricted to positive values of E and p , because no passive media in thermodynamic equilibrium can store negative reactive energy, as this is forbidden by the thermodynamics (the second principle) [3,5]. In thermodynamically non-equilibrium states, e.g. in non-uniform magnetized plasmas, the field energy may take negative values [6] leading to power amplification and instabilities, but we do not consider such situations here. Actually, this means that frequency dispersion cannot be neglected when estimating the stored energy in the frequency regions where the material parameters are negative. If the material has considerable losses near the frequency of interest, it is not possible to define the stored energy density in a general way (more precisely, it is not possible to express that in terms of the material permittivity and permeability fimctions) [ 3 ] .Knowledge about the material microstructure is necessary to find the energy density, and this problem is far from trivial. Attempts to derive a general expression in terms of the effective parameters (e.g. [7])may give negative values of the stored energy [8]. In the literature, the energy density expressions for lossy and dispersive media have been derived only for a special case of an absorbing classical dielectric (Lorentz dispersion) with a single resonant frequency [9] and for the case where also the permeability obeys the same dispersion law as the permittivity [lo]. The known artificial materials with negative real parts of the material parameters have different and more general dispersion laws, which means that we need to develop a more general approach suitable for calculations of the stored energy density in general dispersive and lossy materials. Such method will be presented here.
Field energy in passive dispersive and lossy materials For media without magnetoelectric interactions that can be adequately characterized by two materials parameters: the permittivity and permeability, it is possible to consider energies stored in the electric and magnetic fields separately. Indeed, the properties of linear media do not depend on what particular external field we apply. Having the full freedom to choose the external sources, we can always realize a situation where in a certain (small) volume only electric or magnetic field is non-zero. Because we deal with eflective materiak, the period of the microstructure or the average distance between inclusions is considerably smaller than the wavelength, otherwise one cannot introduce effective permittivity and permeability. Thus, we can take a representative sample of the material that contains many inclusions but whose size is still much smaller than the wavelength, and probe its properties in (nearly) uniform electric and magnetic fields. The new general approach to the definition and estimation of the stored energy we will develop using particular examples of metamaterials, starting from the wire medium. Field energy densitv in wire media Negative effective permittivity is most often realized by dense arrays of parallel thin metal wires. For plane electromagnetic waves whose wave vector is orthogonal to the wires, the effective permittivity for electric fields directed along the wires can be modeled by the plasma permittivity function
12
There exist several models for the equivalent plasma frequency u p ,and here we will use the quasistatic model [ 111 that is not limited to the case of small wire radius and allows to estimate the loss factor. For example, if the skin effect in the wires can be neglected (uniform current distribution over the wire cross section), the effective parameters read [ 111
Here a is the array period, ro is the wire radius, D is the conductivity of the wire material, and E~ and po are the parameters of the matrix. The matrix is assumed to be a lossless magnetodielectric, so soand pa are real numbers. To determine the stored field energy density in this material, we position a small (in terms of the wavelength or the decay factor in the effective medium) piece of this material in a parallelplate capacitor. If we fill a capacitor with a medium described by (5), its admittance becomes
where C, is the capacitance of the capacitor filled with the matrix material (permittivity so),and L =l/(~;c,), R =r/(@;Co). (8) Obviously, the equivalent circuit is a parallel connection of a capacitor and an inductor with a loss resistor, Figure 1.
tcoI -
L= l/(G4)
L Figure 1. Equivalent circuit of a capacitor filled by a wire medium sample with lossy wires. This circuit has the same input impedance as the actual capacitor filled by a material sample. However, before using this circuit in order to calculate the stored reactive energy in the medium, we must ensure that the circuit structure indeed corresponds to the microstructure of the material under study. It is well known that from the input impedance of a circuit it is impossible to uniquely determine the circuit structure. In other words, different circuits can have the same input impedance at all frequencies (e.g., [6]). In the context of this study this means that our circuit model correctly describes the input impedance of the material-loaded capacitor, but it may fail to properly model the material microstructure. In our particular case the material is realized as an array of wires along the electric field direction (that is, running from one plate of the capacitor to the other). Apparently, this array of wires possesses some inductance and resistance connected in series, so we see that our model indeed corresponds to the microstructure of the medium, and we can use it. In the time-harmonic regime the time-averaged stored reactive energy is L
13
where V, is the voltage amplitude on the capacitor and ZL is the amplitude of the current through the inductor (see the equivalent circuit in Figure -1). This can be written - as
Co(w2L2+ R 2 ) For a parallel-plate capacitor (the plate area S, the distance between the plates d), we have C, = E,S/d and V, = Ed . The total energy is the energy density we multiplied by the capacitor volume S d -
Co(w2L2+ R 2 )
2 d
Thus, the energy density reads
(
w , = o l+-
)El2.
2 w2+r2 where we have substituted the values of the circuit parameters from (8). If the losses can be neglected (I- 0 w ), the same result follows from (3). Let us next consider a wire medium where the matrix is a lossy dielectric, with the permittivity E = go - jo,/ w , where o, is the conductivity of the matrix material. Following the approach of [ 1 I], we find that the effective permittivity is
where the plasma parameters up and r remain the same as for wires in a lossless matrix (the physical reason for this is that the negative permittivity appears due to the inductance of the wire array, and that inductance does not depend on the dielectric loss). In the equivalent circuit shown in Figure I , the matrix loss will be reflected by an additional loss resistance Rd = d l(o,S) connected in parallel with the capacitor C, . This means that the expression for the stored energy density (12) does not change if the matrix has some non-zero conductivity: dielectric losses in the matrix have no effect on the stored energy density function, while losses in the wires have a strong effect. Let us assume next that the matrix has no conductivity, but there are some magnetic losses: the matrix parameters are so and p = pa- jp'"/po, where S, and po are real. The effective permittivity of the wire medium in this matrix can be found using formulas of [ 1 I] with substitution L + L(l- j p " / p,) , where L is the inductance per unit length of the wire array in the matrix with the permeability p, . The result is the same as (5), where the plasma frequency does not depend on p" and is given by (6), but the loss factor r is different: 2 Y"
r=
fW-.
In addition to the loss factor due to resistive wires, there is a factor measuring magnetic losses in the background medium. The structure of the equivalent circuit in Figure 1 does not change, but the resistance R = r /(mica) is now frequency-dependent. However, the stored energy density can be still calculated using formula (12). Field energy density in artificial Lorentzian dielectrics Negative permittivity can be alternatively realized using artificial dielectrics with resonant inclusions. Frequency dispersion in such materials is described by the Lorentz formula
14
which is widely used as a model of natural materials in solid state physics. We will consider microwave materials designed as a collection of short metal needles, although the inclusion shape is actually not critical for the validity of the model relation (15). If the length of the needles is much smaller than the wavelength and the distance between the needles is much larger than the needle length but much smaller than the wavelength, formula (15) gives a good estimate for the effective permittivity. Parameters up,w, , and r can be estimated in terms of the particle dimensions and the inclusion concentration using the antenna model of an individual inclusion [12] and an appropriate mixing rule (e.g., [12,13]). Making use of the same approach as above, we consider a capacitor filled with a material having this dispersion law. Its admittance is (16) Apparently, this is the admittance of a parallel connection of a capacitor C, and a series resonant circuit with the elements C=C,,W:/W~, L=l/(w:C,), R=TI(CD;C,). (17) It differs from the equivalent circuit for wire media (Figure 1) by the additional capacitance C in series with L and R. This equivalent circuit is a valid model for the microstructure of this material because currents along needles are modeled by inductance L and charges at the ends of the needles by capacitance C. The loss is due to non-ideally conducting material of the needles (the matrix material is assumed to be lossless), so it is appropriately modeled by resistor R in series with the inductance. The stored reactive energy is the sum of the energies stored in all reactive elements:
where Vc0 and V, are the voltages at the respective elements. Solving for I , and V, and substituting the equivalent circuit parameters (17) we find
This result coincides with that obtained earlier in [lo], where the motion equation for the electric polarization was directly solved. For the case of negligible losses ( r + 0 ), the same result follows from (3). The present method extends to the case of many resonant frequencies (multi-phase mixtures of inclusions of several different sizes) by simply adding more parallel LCR branches to the equivalent circuit. Field energy density in dense arrays of split rings Dense arrays of split rings and other similar structures can be modeled in the quasi-static regime by the following effective permeability (e.g. [14, 151):
where the magnitude factor A and the loss factor r do not depend on the frequency. Similarly to the approach introduced above for artificial dielectrics, we position a small (in terms of the wavelength or the decay length in the effective medium) sample in the magnetic field of a solenoid with inductance L o . The impedance becomes
jw’ LoA
Z(w) = jwLop,(w) = jwLo + 0 :
-w2
+j w r
I
Figure 2. Magnetic material sample in the probe magnetic field of a solenoid (left) and the equivalent circuit (right). An equivalent circuit with the same impedance is shown in Figure 2 on the right. Indeed, the input impedance seen by the source is j w ’ t~L ~ Z = jwLo + 1/(LC)-w2+j o R I L ’ This is the same as (2 1) if M’ 1 R -=LoA, -=@’ o , -=r. L LC L This is a correct equivalent representation from the microscopic point of view, because the material which we model is a collection of capacitively loaded loops magnetically coupled with the incident magnetic field. The total stored reactive energy is the sum of the energies stored in all the reactive elements: 1 w =-(Lo I I12 +L 1 I , 1’ +cI Vc 1’). (24) 2 Expressing I, and V, in terms of I, we get, similarly to the derivations in [2], w’M2C(l+ U2LC) (1-w2LC)’ +w2R’C2 Rearranging terms and substituting the equivalent parameters (23), this can be written as Aw’ (mi + w ’ ) 2 (0,- 0)’ + w 2 r 2 ’ Considering the stored energy in one unit-length section of the solenoid, we have
1
lH12[1+ Aw2(w:+w2) W = w,S =-,uon 1 S(27) 2 n’ (w,’ - O)’ + w 2 r 2 where S is the solenoid cross section area and n is the number of turns per unit length. We have substituted the solenoid inductance per unit length (a tightly wound long solenoid) Lo = pon2S and used the relation I=Hln between the current I and the magnetic field inside the solenoid H. Finally, the stored field energy density is found to be ,uo Aw2(w;+ w ’ ) (28) w,=- 2 1+ ( W , ’ - W ) ~ + W 2 r
[
’1’.
It is important to note that in this particular case formula (3) leads to an incorrect expression even if the losses are negligible (I- + 0). For w > &ma the stored energy density obtained from (3) is less
16
than the energy stored in vacuum. This is a manifestation of the failure of the quasistatic permeability model. The dispersion model (20) has a physically sound behavior at low frequencies [ p ( w ) = O(w2) ] and near the resonance, but in the limit w + co it does not tend to pa.However, in the limit of extremely high frequencies materials cannot be polarized at all because of inertia of electrons, so the parameters must tend to E, and pa.Formula (28) should be used.even in the case of small losses. Conclusion A general approach that allows to determine the stored energy density in complex composite microwave materials has been been presented. The method is based on an equivalent circuit representation of small material samples excited by electric and magnetic fields. Introduction of equivalent circuit parameters for specific microstructures of media is physically equivalent to an appropriate averaging procedure, needed to determine the properties of the effective medium. Particular examples of wire media (negative-epsilon material) and arrays of split-rings (negativemu material) have been considered, as well as the usual Lorentzian dielectrics with losses. The last case has been considered in the literature using a different approach, and the present result agrees with the known formula. The above derivations show how the energy density can be found for any passive and lossy composite, if its microstructure is known. The energy density is determined in terms of the energy stored in the reactive elements of the equivalent circuits. Naturally, in all cases the stored energy is positive, as it should be in all passive materials in thermodynamic equilibrium. This conclusion appears to be very natural if one remembers that passive metamaterials exhibiting negative material parameters are anyway made from usual materials like metals or dielectrics. On the microscopic level, the stored energy is the electromagnetic field energy in the matrix material (normally a dielectric) and in the inclusions (normally a metal of another dielectric). This energy is a strictly non-negative definite function. The energy stored in a sample of the effective medium is the average of the corresponding microscopic quantity, and there is no reason to expect that for some specific shapes of metal inclusions the effective material will store negative energy. For example, the use of passive metamaterials in the design of antennas basically means adding some extra metal or dielectric elements like metal wires or split-ring resonators to a simpler antenna. On the fundamental level, this means only changing the antenna shape. Acknowledgement This work has been partially fimded by the Academy of Finland and TEKES through the Center-ofExcellence program. Helpful discussions with Prof. I.S. Nefedov, Dr. S.I. Maslovski, and Prof. C.R. Simovski are very much appreciated. References R.W. Ziolkowski and A.D. Kipple, Application of double negative materials to increase the power radiated by electrically small antennas, IEEE Trans. Antennas Propag., vol. 51, 2626 (2003). [2] S.A. Tretyakov, S.I. Maslovski, A.A. Sochava, and C.R. Simovski, The influence of complex material coverings on the bandwidth of antennas, to appear in IEEE Trans. Antennas Propagation. Preprint available at http:/lantiv.org/pdf/physics/040 1144. L.D. Landau and E.M. Lifshits, Electrodynamics of Continuous Media, 2nd edition, Oxford, [3] England: Pergamon Press, 1984. [4] J.D. Jackson, Classical Electrodynamics, 3rd edition, N.Y.: J. Wiley & Sons, 1999.
[l]
17
[5] B.B. Kadomtsev, A.B. Mikhailovski, A.V. Timofeyev, Negative energy waves in dispersive media, Zhurnal Teoretich. and Experim. Fiziki, vol. 47, 2266 (1964), (in Russian. English translation in Sov. Phys. ZETF). [6] L.A. Vainstein, Electromagnetic Waves, 2nd edition, Moscow: Radio i Sviaz, 1988 (in Russian). [7] J. Askne, B. Lind, Energy of electromagnetic waves in the presence of absorption and dispersion, Phys. Rev. A, vol. 2,2335 (1970). [8] R.W. Ziolkowski, Superluminal transmission of information through an electromagnetic metamaterial, Phys. Rev. E, vol. 63, 046604 (2001). [9] R. Loudon, The propagation of electromagnetic energy through an absorbing dielectric, J. of Physics A: General Physics, vol. 3,233 (1970) (corrigendum, p. 450). [ 101 R. Ruppin, Electromagnetic energy density in a dispersive and absorptive material, Phys. Lett. A, vol. 299,309 (2002). [l 11 S.I. Maslovski, S.A. Tretyakov, and P.A. Belov, Wire media with negative effective permittivity: a quasi-static model, Microwave and Optical Technology Letters, vol. 35, 47 (2002). [ 121 S. Tretyakov, Analytical Modeling in Applied Electromagnetics, Nonvood, MA: Artech House, 2003. [ 131 A. Sihvola, Electromagnetic Mixing Formulas and Applications, London, UK: The Institute of Electrical Engineers, 1999. [I41 M.V. Kostin and V.V. Shevchenko, Theory of artificial magnetic substances based on ring currents, Sov. J. Communic. Technology and Electronics, vol. 38, 78 (1993). [15] J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwave Theory Tech., vol. 47,2075 (1999).
Electromagnetic metamaterials over the whole THz range achievements and perspectives H.O. Moser, B.D.F. Casse, 0. Wilhelmi’, B.T. Saw Singapore Synchrotron Light Source, National University of Singapore 5 Research Link, Singapore 117603 ‘Present address: FEI Electron Optics BV, Achtseweg Noord 5, 562 1 GG Eindhoven, The Netherlands
Abstract Using modem micro and nanofabrication techniques, the manufacturing of electromagnetic metamaterials (EM3) with structure sizes < 100 pm and critical dimensions < 100 nm has become possible. At this size scale, the resonance frequencies of the structures lie in the THz spectral range. We give an overview of the achievements in and the potential of this field, and discuss new developments towards the microhanofabrication of EM3 with nanoscale dimensions and achievable resonance frequencies accordingly higher in the THz range. We then address ways to produce 3D EM3 which derive from stacking, eventually combined with tilted and rotated exposure during Xray lithography. Finally, we address “foundry” services offered by the LiMiNT facility at SSLS (Lithography for Microhianotechnology) to customers seeking to have their own microhanoscale EM3 manufactured. 1. Introduction In 1964, V.G. Veselago theoretically studied the electrodynamics of materials with simultaneously negative values of their electrical permittivity as well as their magnetic permeability [l]. He showed that the arrangement of the electrical and the magnetic field with respect to the wave vector would have to be described by a left-handed Cartesian co-ordinate frame and described a plethora of unusual consequences such as the inversion of the Doppler and Cerenkov effects, Snell’s law as well as the radiation pressure. Moreover, he described the image-formation of a parallel slab of such material and discussed the change of role of bi-convex and bi-concave lenses. About 30 years later, J.B. Pendry and co-workers showed in 1996 [2] and 1999 [3] how practical structures might be built to exhibit this left-handed property. As these structures were simple and feasible, they marked the onset for a quest to experimentally demonstrate left-handed materials, then also called electromagnetic metamaterials (EM3). First EM3 structures based on the nested split-ring design [3] were built using a shadow maswetching technique on printed circuit boards [4]. The outer diameter or width was 6.6 mm [4] and 2.62 mm [5], respectively, leading to a resonance frequency of 4.8 GHz and 11.2 GHz. The EM3 property of this material was shown first in a transmission-type experiment [5], [6], later followed by the demonstration of the negative refraction
~71. As for the application to imaging, a review by J.B. Pendry and co-workers had revealed that the resolution that could be achieved with EM3 may well be much better than the usual diffractionlimited resolution achievable with classical optics, eventually leading to the notion of the perfect lens [S], [9]. Continuing on earlier work [6], [7], C.G. Parazzoli et al. soon after demonstrated a plano-concave lens at 14.7 GHz [lo]. A further reduction of size to an outer SRR width of 2.22 mm was achieved by D.R. Smith and coworkers [ 1 I] who used transmission and refraction experiments to determine the EM3 behaviour between 13 and 14 GHz. The material was produced by milling of a Cu clad printed circuit board
18
19
on an automated numerically controlled micro-milling machine as it is in use for the rapid prototyping of printed circuit boards. While the work reported so far was all done using structures of the split-ring resonator type, H.S. Chen et al. [12] pursued another approach which they called the extended S-geometry SRR which provided multiple passbands due to multiple sizes of the split rings in a frequency range extending from 10.5 to 18 GHz. J.D. Baena et al. analysed [13] spiral-type split-ring resonators with resonance frequencies around 5 GHz that were seemingly similar to Pendry’s Swiss roll structure. Simplified split-ring resonators, also called deformed SRR, were studied by Y.J. Hsu et al. in the 11 to 12 GHz range [ 141 in view of minimising the attainable size of the unit cell of an EM3. Since Veselago’s paper, the issue of potential applications of EM3 has challenged the imagination of researchers. The concept of the perfect lens is certainly a very attractive one that is vigourously pursued. Other ideas may be found in work by N. Engheta [15]. Recent short reviews of the field were given by Pendry, Smith and others [ 161, [ 171. Meanwhile, micro- and nano-fabrication have been introduced to manufacture the next generations of smaller and higher frequency structures [18], [19], [20]. Thereby, dimensions can be extended down to the pm and nm scales, thus opening up the terahertz range for experiments and applications. Putting in enough development effort may even give access to the petahertz range. In the following, achievements, expectations, and perspectives will be discussed in more detail. 2. Review of existing work on microhanofabricated EM3 During the past year, microhanofabrication was increasingly used to manufacture EM3 structures in the THz range. T.J. Yen et al. [ 181 built an array of square nested split-ring resonators from Cu with an outer edge length of 26, 32, and 36 pm, respectively, on a 400 pm thick quartz substrate, 8%8 mm2 large. They used photolithography enhanced by the photo proliferated process to achieve 3 pm thick structures at a good spatial resolution and were able to show the magnetic response of their samples at about 0.8, 0.95, and 1.25 THz by means of frequency-dependent ellipsometry. S. Linden et al. [19] produced square single split-ring resonators from Au with an edge length of 320 nm, gap of 70 nm, 90 nm width of the ring, and 20 nm thickness. The rings were patterned by means of electron beam lithography into PMMA resist spun on an I T 0 coated glass substrate. The patterned area was 25%25 pm2. They measured transmission and reflection spectra for two directions of polarization in the spectral range from 1 to 4 pm. When the electric field vector pointed from one gap side to the other they obtained electric coupling of the incoming radiation to the gap and excited oscillations at about 3.2 pm wavelength which corresponds to about 95 THz.
At SSLS, H.O. Moser et al. [20] manufactured 2.1%2.1 mm2 chips of Ni and Au nested rod-splitring resonators embedded in a matrix of AZ P4620 photoresist. Their structures had metal rods integrated into the design such as to create negative electrical permittivity and to enable the material to become left-handed in the appropriate frequency range given by the negative magnetic permeability. Samples were produced in various sizes, the inner radius of the inner ring ranging from 8.4 to 14 pm. Using Fourier transform interferometry, far infrared transmission measurements were performed which showed that transmission peaks occurred close to the spectral location expected from Pendry’s formula and from numerical simulation. Fig. 1 shows some of these structures. On the left, there is a close-up of nested circular rod-split-ring structures made of Au electroplated into an AZ P4620 photoresist template. Their resonances were measured to occur in the lower THz range (1-2.5 THz). On the right, PMMA resist was
20
Fig. I : Left: Nested circular split-rings with rods made ofAu electroplated into an AZ P4620photoresist template for the lower THz range (1-2.5 THz) (scale bar 20 pm). Right: Patterned and developed PMMA resist with nested circular rod-split-ring structures for the higher THz range beyond 50 THz (scale bar 500 nm). The smallest gap ridge measures about 40 nm.
patterned to form about 40 times smaller rod-split-ring structures expected to have their resonances at about 51 THz. 3. Development and perspectives Obviously, further development in the field will aim at structures with higher frequency such as to cover a spectral range as large as possible for experimentation and applications. This will require manufacturing of even smaller structures. Fortunately, all structures discussed so far are amenable to microhanofabrication including rod-split-rings, nested split-rings, single split rings, deformed split-rings, spiral split-rings, and extended S-structures. Fig. 2 summarises some of the results that were achieved, of work in progress, and of the perspectives for future development. Pendry’s curve for the resonance frequency of a nested circular split-ring resonator shows that inner radii of 30 to 40 nm must be achieved to bring the resonance in the centre of the visible spectral range. The resonance frequencies of the EM3 samples by Moser et al. [20] match Pendry’s curve satisfactorily. In the cases of Yen et al. [ 181 and Linden et a1 [19], deviations from Pendry’s curve do not come unexpected as their geometry differs from the circular nested split-rings. The lower frequency of the structures by Yen et a1 [18] may be understood by the higher capacitance and inductance of square nested split-rings with other parameters kept constant. In the case of the structures by Linden et al. [ 191, a simple estimate of the resonance frequency leads to a much higher value than given, so that it may be necessary to consider the interaction with the substrate in order to understand their comparably low resonance frequency. Finally, the open triangles mark structures that are under development at SSLS [21]. 3.1 Fabrication techniques In microhanofabrication, the primary pattern generation is done mostly by laser beam or electron beam direct writing depending on required resolution. Typical values of the spatial resolution of a laser writer are 0.8 pm, and for an e beam 30 nm. More rarely, but increasingly, ion beam direct writing is used promising both, a better resolution and substantially larger penetration depth than the e beam [22]. All these writing pattern generators enable almost arbitrary shapes of the structures to be written, i.e., there is a lot of freedom to design resonators such as the nested split-ring [18], the rod-split-ring [20], the deformed SRR [ 141, spirals [ 131, the extended S resonator [ 121, and more.
21
0
Fig. 2: Inner radius of (inner) ring versusfrequency for split-ring resonators over the spectral range from I THz to I PHz. Symbols mark measured results exceptfor the triangles which belong to structures in progress. The straight line is Pendiy 's formula for the resonancefrequency of a circular nested split-ring resonator.
To produce small quantities of experimental test structures the primary pattern generation might be adequate. However, for larger quantities needed for extended experiments and for applications, the parallel-processing lithography with masks, and further replication techniques with metals and polymers come into play. Typically, the structures are produced in a plastic matrix by creating voids, filling them with metal, and releasing the metal-filled matrix from the substrate. The materials may also be produced on a substrate foil in which case the matrix could be removed by subsequent plasma treatment. Unidirectional structures that are topologically sets of cylinders with a common direction of the axis can be mass produced by hot embossing or injection moulding of the matrix followed by metal deposition into the voids. 3.2 3 0 concepts Presently, the basic building blocks of EM3 structures are more or less flat metal structures in a plane. Obviously, they are highly anisotropic, and ways of assembling flat EM3 structures such that they offer full coupling for the incident electric and magnetic fields in two or three orthogonal directions have been devised in the GHz range such as examples [4] - [6] are showing. This usually involves either building a basic unit cell and then repeatedly accumulating it, or cutting, folding, piling or stacking larger parts from an array of EM3 structures such as to reach the 3-dimensionality. We want to address an alternative way, namely, to make 3D orthogonal structures within the same matrix. Usually, when doing lithographic exposure, the photon beam impinges on the masksubstrate stack perpendicularly. However, the angle of incidence can be varied so that inclined exposure results. Moreover, the stack can be rotated to different positions between exposures, and it may even be rotated continuously during exposure. This tilting, rotating, and even wobbling in lithographic exposures was proposed many years ago [23], [24]. Fig. 3 shows a few implementations and the resulting structures, and, obviously, the variety of 3D structures that can be produced in this way is large. Applied to the microhanofabrication of EM3, this method could be used to build structures in the same matrix layer in which the axes of the resonators cover two or even three perpendicular directions so that the incident field always can couple efficiently to the resonators. The need for stacking would then be reduced to a simple piling up of the matrix layers one by one.
22
Fig. 3: Illustration of the plethora of structures that can be achieved using tilting, rotating, and wobbling between or during exposures.
Fig. 4 shows a simple example of a double-angle inclined exposure into SU-8 negative resist.
Fig. 4: Double-angle tilted exposure in SU-8. The tilt angle is 30 (scale bar SO p)
Figs. 5 and 6 illustrate concepts of building inclined structures based on multiply inclined and rotated deep X-ray lithography. Piling up matrix foils with the embedded metal structures would lead to volume EM3.
Fig. 5: Left: Schematic perspective view of a single square split ring with a double-angle tilted exposure. The split-ring at the top is the gold absorber on the mask membrane. Dashed lines are the projection lines for two subsequent tilted exposures. The inclined cylindrical split rings indicate the metal structures obtained from metal deposition into the developed resist structures. Right: Schematic top view of a single square split-ring with three subsequent exposures featuring triple angle rotation plus single angle tilt. The picture shows again the gold absorber on the mask membrane in the centre, and three inclined cylindrical split-rings obtained from metal deposition into the developed resist structures.
23
Fig. 6: Schematic view of a one-layer array of double-angle tilted cylindrical split-rings. Piling up such layers on top of each other creates three-dimensional EM3. Adjacent layers may be arranged such that the split-rings are parallel or they might be crossed for reduced anisotropy.
Such 3D structures are favourably produced by parallel-processing lithography as hot embossing or injection moulding is no longer possible because these structures cannot be de-moulded. These examples show that there is significant freedom in designing the shape of EM3 if lithography is used for manufacturing them. This may lead to entirely new geometries.
4. SSLS' LiMiNT as a foundry and research facility SSLS has installed a complete microhanofabrication facility that is effectively a one-stop shop for microhanofabrication based on the LIGA process (LIGA is a German acronym and stands for Lithography, Electroplating (Galvanoformung), and Plastic Moulding (Abformung))[25], [26], [27]. The facility is open to users, preferably in a service mode. SSLS is offering to fabricate customerdefined structures on a contractual basis and is teaching users to reach autonomy as well.
Fig. 7: At SSLS, the LiMiNTfacility is set up in a class 1000 cleanroom and represents a one-stop - shop for micro / nanornanufacturing based on the LIGA process. _
"
5. Conclusions Construction of electromagnetic metamaterials by means of microhanofabrication techniques is in full swing. As the minimum structural dimensions can be expected to reach 10 nm and below, in the future, the frequency range of EM3 is likely to extend to the near infrared and even to the visible. Mass production methods such as parallel processing lithography and replication techniques such as hot embossing and electroplating promise quantities of EM3 sufficient for ample experimentation
24
and the development and marketing of devices. The LiMiNT facility at SSLS offers its services to broaden and speed up this development. Acknowledgment The authors thank Professor Lim Hock and Gan Yeow Beng of the Temasek Laboratories, NUS, for stimulating discussions. They also thank SSLS LiMiNT staff J.R. Kong and Shahrain bin Mahmood for process development and optimization as well as J.H.W. Wong for help in preparing illustrations. The work was performed at SSLS under A*STAR/MOE RP3979908M, A*STAR 0121050038, and NUS Core Support C-380-003-003-001 grants. References V.G. Veselago, The Electrodynamics of Substances with Simultaneously Negative Values of E and p, Sov. Phys. Uspekhi 10(4), 509(1968) (Usp. Fiz. Nauk 92,517(1964)). J.B. Pendry, A.J. Holden, W.J. Stewart, I. Youngs, Extremely low frequency plasmons in metallic meso structures, Phys. Rev. Lett. 76,4773(1996). J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, Magnetism from Conductors, and Enhanced Non-linear Phenomena, IEEE Trans. on Microwave Theory and Tech. 47(1 I), 2075( 1999). D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite Medium with Simultaneously Negative Permeability and Permittivity, Phys. Rev. Lett. 84( 18), 41 84(2000). R.A. Shelby, D.R. Smith, S.C. Nemat-Nasser, S. Schultz, Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial, Appl. Phys. Lett. 78(4), 489(2001). K. Li, S.J. McLean, R.B. Greegor, C.G. Parazzoli, M.H. Tanielian, Free-space focused-beam characterisation of left-handed materials, Appl. Phys. Lett. 82( 15), 2535(2003) C.G. Parazzoli, R.B. Greegor, K. Li, B.E.C. Koltenbah, M. Tanielian, Experimental Verification and Simulation of Negative Index of Refraction Using Snell’s Law, Phys. Rev. Lett. 90, 107401(2003). J.B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 183966(2000) J.B. Pendry, S.A. Ramakrishna, Focusing light using negative refraction, J. Phys.: Condens. Matter 15,6345(2003) [lo] C.G. Parazzoli, R.B. Greegor, J.A. Nielsen, M.A. Thompson, K. Li, M.H. Tanielian, Performance of a negative index of refraction lens, Appl. Phys. Lett. 84( 17), 3232(2004). [ l l ] D.R. Smith, P. Rye, D.C. Vier, A.F. Starr, J.J. Mock, T. Perram, Design and Measurement of Anisotropic Metamaterials that Exhibit Negative Refraction, IEICE Trans. Electron. E87-C, 359(2004) [ 121 H.S. Chen, L.X. Ran, J.T. Huangfu, X.M. Zhang, K.S. Chen, T.M. Grzegorczyk, J.A. Kong, Metamaterial exhibiting left-handed properties over multiple frequency, J. Appl. Phys. 96, 5338(2004). [13] J.D. Baena, R. Marques, F. Medina, J. Martel, Artificial magnetic metamaterial design by using spiral resonators, Phys. Rev. B 69, 014402(2004) [14] Y.J. Hsu, Y.C. Huang, J.S. Lih, J.L. Chern, Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials, J. Appl. Phys. 96(4), 1979(2004). [ 151 N. Engheta, in “Advances in Electromagnetics of Complex Media and Metamaterials”, Kluwer Academic, Dordrecht, London, 2003 [16] J.B. Pendry, D.R. Smith, Reversing Light with Negative Refraction, Physics Today 57(6), 37(2004) [ 171 D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Metamaterials and Negative Refractive Index, Science 305,788(2004) [I81 T. J. Yen, W.J. Padilla, N. Fang, D.C. Vier, D.R. Smith, J.B. Pendry, D.N. Basov, X. Zhang, Terahertz Magnetic Response from Artificial Materials, Science 303, 1494(2004).
25
[19] S. Linden, C. Enkrich, M. Wegener, J.F. Zhou, T. Koschny, C.M. Soukoulis, Magnetic Response of Metamaterials at 100 THz, Science 306, 135l(2004). [20] H.O. Moser, B.D.F. Casse, 0. Wilhelmi, B.T. Saw, Terahertz Response of a Microfabricated Rod-Split-Ring-Resonator Electromagnetic Metamaterial, Phys. Rev. Lett., 94,06390 1, 2005 [21] B.D.F. Casse, H.O. Moser, 0. Wilhelmi, B.T. Saw, Micro- and Nano-Fabrication of Electromagnetic Metamaterials for the Terahertz Range, this conference. [22] Th. Osipowicz, H.O. Moser, Proton beam direct writing of advanced high-aspect-ratio masks for deep X-ray lithography, Grant ARF R-144-000-130-112, Ministry of Education, Singapore, 2005. [23] H.O. Moser, W. Ehrfeld, M. Lacher, H. Lehr, Fabrication of Three-dimensional Microdevices fvom Metals, Plastics, and Ceramics, Proceedings 1St Japanese-French Congress on Mechatronics, Besanqon, Oct. 20-22, 1992, Institut des Microtechniques de Franche-Comti. [24] W. Bacher, P. Bley, H.O. Moser, Potential of LIGA technology for optoelectronic interconnects, in Optoelectronic Interconnects and Packaging, SPIE Critical Reviews of Optical Science and Technology, Vol. CR62, pp. 442-460, 1996. [25] H.O. Moser et al., Status of and materials research at SSLS, Nucl. Instrum. and Meth. B , (2005), in press. [26] E.W. Becker, W. Ehrfeld, D. Muenchmeyer, H. Betz, A. Heuberger, S. Pongratz, W. Glashauser, H.J. Michel, R.v. Siemens, Production of Separation-Nozzle Systems for Uranium Enrichment by a Combination of X-ray Lithography and Galvanoplastics, Natunvissenschaften 69,520( 1982). [27] E.W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, D. Muenchmeyer, Fabrication of microstructures with high aspect ratios and great structural heights by synchrotron radiation lithography, galvanoforming, and plastic moulding (LIGA process), Microelectron. Eng. 4, 35(1986)
This page intentionally left blank
Session R2
Chair: J.A. Kong
This page intentionally left blank
Superlens as Matching Device V.G.Veselago Moscow Institute of Physics and Technology, Moscow district, Russia Institute of General Physics, Moscow, Russia v.veselago@relcom. ru The appearance of a new class of material - material with negative refraction, which shows many unusual electrodynamic properties, has brought about an intensive search for their new characteristics and possible practical applications. Herewith, some statements appear in the literature, which has given rise to objections. In [l], it was shown that negative refraction exists for phase velocity only, but the group velocity obeys the usual law of refraction with positive refraction index y1. The authors of this work are not embarrassed by the fact that difference in directions of phase and group velocity is a typical property of optical anisotropic media, which cannot be characterized by a scalar y1. The mistake of authors [ 11 can be explained by the fact that the authors confused the direction of group velocity with the direction of the normal to surfaces of constant amplitude for modulated waves. This mistake is considered in detail and explained in [2]. There is one more problem which is closely related to the appearance of materials with negative refraction. This is the problem of “overcoming the diffraction limit”, or in another terminology, the problem of amplifying the so-called evanescent modes. This problem was first discussed by J.B. Pendry in [ 3 ] ,where he showed that material with negative refraction index can successfully propagate waves, of which the wave vector component propagation has imaginary value
k,
along the direction of
This inequality is valid for very large kx, that is, for very short waves. In material with positive value of I?, the amplitude of such waves (the evanescent modes) in accordance with (1) will decrease exponentially along the Z axis. This is exactly the explanation for the impossibility of forming image by optical systems of objects, with sizes noticeably smaller than wavelength. However, in [3] and in many following articles, the authors suggest that in material with negative refraction index, the amplitude of waves with large values of k, do not decrease, but increase. Hence, the authors suggested the possibility to transfer images with sizes much less than wavelength from one point of space to another. This suggestion was motivated by the possibility of resonance due to surface modes in material with negative refraction. The author [3] proposed the notion ”superlens” for the device shown in Fig. 1, confirming that for this type of device, the classical restriction on diffraction limit is not valid. The author of [ 3 ] ,and many other recent authors, drew a veil over the fact that overcoming of the diffraction limit automatically meant a breach of the uncertainty principle. In our case, the uncertainty equation can be written as follows
k,d 2 2z Here,
k, is component of the wave vector orthogonal to the z 29
axis which is the wave propagation
30
d is the transverse size of focused spot of light. The value of k, than wave vector ko in free space: direction, while
cannot be larger
It follows immediately from (2) and (3) that
d2;l
(4)
The possibility to overcome the diffraction limit is equivalent to a rejection of equation (4), or, more exactly, that equation (4) is not an essential result. This is an exceedingly strong statement, and is indeed much stronger than all other possible statements on other characteristics of material with negative refraction. In our opinion, the fact that this sort of statement appeared is due to not very exact use of some terms, the first of which is the main term - "lens". The word "lens" characterizes the optical instrument, as shown in Fig. 1, with the work founded on geometrical optics laws. However, a planar slab of material with negative refraction, as shown on Fig.1, can be considered as a lens only if its transverse size a , wavelength of radiation 2 and the period of the internal structure 6 satisfy the following inequality: (5)
Fig. 1. The flat lens produced by material with refraction index
n = -1
Further, correlation must be imposed on such lens
Only in this case can the lens really work as an optical instrument, complying with the geometrical optics laws. This was exactly the situation meant in our paper [4], though it was not indicated in a straightforward manner.
31
However, in 131 and the following works, the situation was considered without correlation ( 5 ) , since the transverse size of the lens was on the order of the wavelength, and so are the distances from lens to the object and to the image planes. Such a system is not a lens, but some sort of matching device, which does not work on the basis of geometrical optics laws. As is well known, it is possible by means of matching devices to concentrate the flows of energy into a spot that is undoubtedly smaller than the wavelength. To clarify this situation, let us consider the propagation of electromagnetic wave in conventional metallic waveguide. It is well known that electromagnetic wave could propagate in a hollow rectangular waveguide with broad wall of size a , under the following condition:
A22a
(7)
If this condition is satisfied, the wave propagates in the waveguide with small attenuation, and the field at the output end of such a waveguide could be considered as some rectangular image formed by the cross-section of the waveguide. The sizes of this rectangular image are on order of the size
a. To detect radiation and propagation of electromagnetic waves in a waveguide, one usually uses detectors of sizes significantly less than the transverse dimensions of the waveguide. If such a detector is located at the output end of the waveguide, it will receive only a small part of the radiation, with bulk of the radiation passing by the detector. If a higher level of power is desired to be received by the detector, we can reduce the width of the waveguide. However, the wave will be strongly attenuated since correlation (7) is violated. Nevertheless, it is possible to increase the power incident on the detector if appropriate matching devices can be placed in the waveguide in close proximity to the detector. Such matching elements are typically various types of screws and slots. The increase in the power incident on the detector can possibly be considered as the focusing of the radiation to a spot beam whose transverse dimension is of the size of the detector, and hence, greatly less than the wavelength. From this point of view, the diffraction limit is undoubtedly broken in a waveguide with matching device. However, the waves that are incident on the detector are due not only to the plane waves propagating in the long waveguide. There are also plane waves generated by the elements of the matching devices, which form evanescent waves incident on the detector, since these elements are of sizes less than the wavelength and are placed at short distances from the detector. These evanescent waves are the re-radiation of the plane waves propagating in the waveguide due to scattering from the detail structures of the matching devices. In principle, the same process exists in the superlens, as shown in Fig. 1. In essence, this lens will match the source of the radiation to the receiver. However, correlations (5) and (6) are not included here. Hence, the lens can indeed transfer without distortion the object to image with small sizes, but regrettably at short distances comparable to the wavelength [51. In all works dedicated to the problem of overcoming the diffraction limit, starting with [3], it was not directly established as to what would be the exact thickness of the slab of material with negative refraction for undistorted transfer of the object to image with sizes much smaller than the wavelength. However, in most of these works, the slabs were considered to have thicknesses comparable to or less than the wavelength. Accordingly, the distances from source of radiation in front of the slab and that from the slab to the image were also comparable or less than the wavelength. These can be observed in Fig.2, taken from [5].
32
1
E 0.1
I
I
I
2
4
I
4&
I
8
I I I0
Fig.2 Transfer function for LHM slabs of different thicknesses as a function of normalized transverse wave number kv/ k,,. The thicknesses are in arbitrary units A X ,the wavelength is
A = 566hX, value
y is the loss term in
E ( W ) = p(W) = -1 - iy . (From Rao XS., Ong
C.K. cond-mat/0304474.)
This work is supported by the Russian Foundation for Fundamental Research, project #04-0216460-a. References
1. 2. 3. 4. 5.
Valanju P.M., Walser R.M., Valanju A.P., Phys.Rev.Lett., 88, 187401 (2002) Pendry J.B., Smith D.R. cond-mat/0206563 Pendry J.B Phys.Rev.Lett, 85 3966 (2000) Veselago V.G. Sov.Phys. Uspekhi, 10, 509 (1968) Rao X.S., Ong C.K. cond-mati0304474
Theory of negatix refraction and left-handed metamaterials
(LHW J. A. Kong, T. M. Grzegorczyk, H. Chen, L. Ran, J. Lu, X. Chen, Q. Jiang, X. Zhang
Massachusetts Institute of Technology, Cambridge, USA. The Electromagnetic Academy at Zhejiang University, China.
1
Introduction
Current left-handed metamaterials (LHM) are composite structures made of metallic inclusions such as rods and split rings resonators properly arranged in space in order to achieve negative values of the permittivity and the permeability [l, 2, 31. Predicting the behavior of an LHM requires its proper characterization. Such characterization has often been done through the numerical modeling of a unit cell containing the metallic inclusions and the application of a properly designed retrieval algorithm. In this case, an electromagnetic wave is propagated through the structure and the reflection and transmission coefficients are recorded as function of frequency. The application of the retrieval algorithm yields the bulk permittivity and permeability, which are subsequently used in the effective medium theory, from which the properties of the metamaterial can be directly predicted. In this paper, we shall briefly present a generalization of the existing methods [4, 51 to anisotropic and bianisotropic media. Using this method, we show that some ring designs present bianisotropy while other do not. These subtle characteristics are not only revealed but also quantified by the improved retrieval algorithm, which makes them directly usable in the design of LHMs. Having at hand the effective bulk properties of the metamaterial, we proceed by studying some fundamental properties of media in which the permittivity and the permeability can take negative values. These properties include negative refraction, dispersion relations, and focusing. Finally, some characterizations and applications are presented using new rings designs.
2
Ring characterization
Various retrieval algorithms have been proposed so far for the extraction of the effective permittivity and permeability of metamaterials [4, 51. Yet, in most of the cases, these methods are limited to isotropic media, while it is now well-accepted that LHM are anisotropic and possibly bianisotropic [6]. The algorithm we propose is an extension of our previous work for isotropic media [5] to media governed by the following constitutive relations
D ( r ) = 7 . E(F) + {. H(r), B(r) = ,z H ( r ) + 1 E(r), '
'
33
34
Figure 1: First ring design. Figure 2: Second ring design. where 0 0 Ey 0 0 0 0 0 0 0 -i& €z
0 0 €&-
0 0 0
With seven complex unknowns to retrieve, we resort to multiple incidences on the unit cell of the metamaterial. For each incidence, we compute analytically the reflection and transmission coefficients, and unify all the formulae through the redefinition of the impedance and index of refraction. The proper completion of this retrieval process, which we also assimilate to an inverse problem, requires the forward problem to be solved entirely: the reflection and transmission matrices have to be obtained for all the cases considered here, namely anisotropic biaxial and bianisotropic [7]. For the sake of completeness, we have developed a general method to obtain these matrices in layered media as presented in [8] but where the constitutive parameters (?, ,E, can be described by arbitrary fully populated tensors. The method requires to split the fields into their transverse and longitudinal components, and build an eigenvalue systems as described in [9]. The solution of the systems yields the wave-vectors and polarization states in each layer which, along with the application of the boundary conditions, yield the reflection and transmission matrices via a simple mathematical formulation [lo]. Once totally described, the electromagnetic field distribution can be studied in each medium. In particular, the reflection at boundaries between free-space and anisotropic or bianisotropic media can be quantified, corroborating the intuitive results obtained from the dispersion diagrams.
z, 1)
Based on this forward model, we proceed with the computation of the special inverses cases, described by Eqs. (2) [ll]. Results are presented for two unit cells. In the first case (Fig. l ) , the retrieved results of Fig. 3 show that if bianisotropy is not considered, the retrieved parameters ( p y in this case) exhibits a spatial dispersion which prevents us from concluding on an effective medium. If bianisotropy is considered, however, spatial dispersion is removed (see Fig. 4) and the medium can be characterized by a unique set of constitutive matrices like shown in Eqs. (2). In addition, the bianisotropic parameter is shown to be frequency dispersive and resonant, as predicted in [6] and shown in Fig. 5. In the case of Fig. 2, Fig. 6 shows that the design does not exhibit a bianisotropic behavior since the retrieved value is significantly lower than the one exhibited by the design of Fig. 1.
3
Theory of LHM
The retrieval algorithm therefore confirms that within a certain frequency range, the metamaterial can be characterized by a negative permittivity and a negative permeability. In such media, unusual electromagnetic phenomena occur such as the negative refraction, the inversion of critical angle as well as the
35
Frequency [GHzl
4
6 8 Frequency [GHz]
Frequency [GHz]
LO
Figure 5: Retrieved real and imaginary parts of to for the ring design of Fig. 1. A strong and resonant bianisotropy is retrieved.
Y
R
Figure 6: Retrieved real and imaginary parts of for the ring design of Fig. 2. A much smaller bianisotropic term is retrieved compared to Fig. 5 .
36 inversion of Brewster angle, the possible inversion of the lateral Goos-Hanchen shift 1121, the appearance of fundamentally new modes [13],or the sub-wavelength focusing. It is, however, important to realize that some of these phenomena are not proper to LHM, and have been observed with standard media already. In particular, a negative refraction can be obtained in many various ways, including rotated right-handed anisotropic media, photonic-band gap materials, or moving media. Yet, it appears that the unique property of LHM compared to these other known phenomena is to yield a negative refraction for both the power and the phase simultaneously (although this may not be true for anisotropic LHM). The understanding of these properties is directly related to the understanding of the dispersion relations of LHMs, which have been shown to be either elliptic or hyperbolic, as well as positive or negative with frequency (by “positive” and “negative” we mean that the dispersion relation in the spectral plane either expands or shrinks). A direct inspection of the dispersion relations reveals not only the negative refraction property but also the inversion of critical and Brewster angle or the necessity of generalizing Snell’s law [14]. While these properties are not necessarily proper to LHM, other are, such as the appearance of new modes and the sub-wavelength focusing. It is in fact fundamental to realize that these two phenomena are closely related to each-other. This connection is revealed here by studying the distribution of the electric field inside a slab of negative permittivity and negative permeability, slightly mismatched to the surrounding free-space. More specifically, if we let 6 be a small parameter, we write
Upon writing the electric field in all three regions, we find that the pole is given by
k,
= mn/d
+ iln(2/6 + l)/d,
(4)
where d is the thickness of the slab and k , is the projection of the wave-vector onto the direction of propagation. The maximum value of this pole can be related to the wavelength in the y direction of the surface plasmon created at both interfaces by
A simulation of a mismatched case is depicted in Fig. 7, where the wavelength of the surface mode is seen to be indeed corresponding to the one predicted by Eq. (5) [15].
4 Experimental measurements of the S-ring design The verification of the properties studied above relies on the realization of stable samples of LH metamaterial. Yet, the main drawbacks of some of the designs achieving left-handed properties are to exhibit these properties over a narrow bandwidth, and to exhibit significant losses. For these reasons, we have proposed various designs recently that improve upon these drawbacks [16, 17, 181. The experimental validation of these designs as LH samples is performed by studying the transmission properties of slabs, the deflection of a Gaussian beam [19, 20, 211, and the deflection by a prism geometry as reported in [22]. Among the various designs, we draw the the attention here to the S-ring design, as shown in Fig. 8. This ring has been extensively studied in [23, 241 both theoretically and numerically, and has been shown to yield interesting properties. In addition to a wider left-handed bandwidth and reduced losses (measured by a higher transmission level), this ring has two important properties worth mentioning. The first property is that this ring does not require the addition of a rod to exhibit a negative permittivity at similar frequencies where it exhibits negative permeability. In fact, all the rings exhibit a frequency dispersive permittivity response, in addition to the required frequency dispersive permeability
37 Real Part of Ex, S =1e-3, slab at dl=0.5h, d2=l.5h
h
Figure 7: Distribution of the electric field for a source located at 15 cm in front of a slab of thickness d = 0.3 m and described by the constitutive parameters of Eq. (3) with 6 =
a
V
Figure 8: Unit cell of the S-ring geometry: e = 0.5 mm, b = 4 mm, c = 2.5 mm.
L1 =
Lz = 2.8 mm, w = 0.4 mm, a = 5.4 mm,
response (see for example [25] for the broadside couple SRR). However, the interesting region of permittivity response where negative values are achieved is usually at much higher frequencies that the region where the permeability is negative, making this effect not usable. The S-ring, on the contrary, exhibits a negative permittivity response at similar frequencies as the negative permeability response. In addition to being a design advantages since a single entity can now control both parameters, it is mostly an experimental advantage since it avoids the necessity of ensuring the electrical contact between the plates of the parallel-plate waveguide and the rod-like structure present in other designs. A prism experiment based on this ring design has been performed, yielding the results shown in Fig. 10. A high transmission peak corresponding to negatively refracted angles can be seen between 10.9 GHz and 13.5 GHz, indicating a bandwidth of operation of 2.6 GHz. In addition, the insertion losses were estimated in the same way as in the solid-state case, revealing losses of about 0.7 dB per unit cell. The S ring therefore yields a low-loss metamaterial where LH properties are obtained over a large bandwidth. The second important feature of this ring is that its shape can be easily modified to achieve desired frequency responses: the two loops in the S pattern need not necessarily be of the same size or, if needed,
Frequency (GHz)
Figure 9: Photograph of an S-based solidstate metamaterial.
Figure 11: Illustration of a modified S-ring resonator.
Power (rnW)
Figure 10: Transmission through a prism of metamaterial as shown in Fig. 9.
Figure 12: Refractive Index as a function of frequency
additional loops can be added. The whole frequency response of the S-ring can be directly predicted from its circuit model, as it has been shown in 1231. The various capacitances and inductances are directly related to the geometry of the ring, and can be modified or new elements can be added in order to achieve new properties. This flexibility has been illustrated in [26], where a modified S-ring design like the one of Fig. 11 has been proposed. Both thc circuit modcl approach [23] and thc retrieval algorithm discussed above predict two frequency bands where the index of refraction is negative, as illustrated in Fig. 12. Such flexibility is of the foremost importance for the use of negative metamaterial in industrial applications.
5
Conclusion
This paper covers various aspects of studies of left-handed metamaterial, from theory and simulation to their physical realization. We have shown that a robust retrieval algorithm can justify the study of LHM as bulk materials, revealing a series of unique characterisitcs such as the subwavelength focusing. In addition, the retrieval algorithm, coupled with a circuit analysis (not shown here), gives the flexibility to design and optmize ring structures for various applications.
39
References [l]V. Veselago, “The electrodynamics of substances with simultaneously negative values o f t and p,” Sov.
Phys. USPEKHI, vol. 10, pp. 509-514, January-February 1968. [2] J. Pendry, A. Holden, W. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett., vol. 76, pp. 4773-4776, 17 June 1996. [3] J. Pendry, A. J. Holden, D. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2075-2084, November 1999. [4] D. R. Smith, S. Shultz, P. MarkoS, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transniission coefficients,” Phys. Rev. B, vol. 65, pp. 195104-1-5, 2002. [5] X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. P. Jr., and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E, vol. 70, no. 016608, pp. 1-7, 2004. [6] R. Marquks, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B, vol. 65, p. 144440, 2002. [7] J. A. Kong, Electromagnetic Wave Theory. EMW, 2000. ISBN 0-9668143-9-8. [8] J. A. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” Progress in Electromagn. Res., vol. 35, pp. 1-52, 2002. [9] W. C. Chew, Waves and Fields i n Inhomogeneous Media. Van Nostrand Reinhold, 1990. ISBN 0-44223816-9. [lo] T. M. Grzegorczyk, X. Chen, J. Pacheco Jr., J. Chen, B.-I. Wu, and J. A. Kong, “Reflection coefficients and Goos-Hanchen shifts in anisotropic and bianisotropic left-handed metamaterials,” Progress i n Electromagnetic Research, vol. 51, pp. 83-113, 2005. [ll] X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E, 2005. submitted to publication.
[l2] J. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Simultaneous positive and negative GoosHanchen shifts with left-handed slabs,” J . Appl. Phys., 2005. submitted to publication.
[13] B.-I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Guided modes with imaginary transverse wavenumber in a slab waveguide with negative permittivity and permeability,” Journal of Applied Physics, vol. 93, pp. 9386-9388, June 2003. [14] T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, “Refraction laws for anisotropic media and their application to left-handed nietamaterials,” IEEE Trans. Microwave Theory Tech., 2005. accepted for publication. [15] J. Lu, T. M. Grzegorczyk, B.-I. Wu, , J. Pacheco, M. Chen, and J. A. Kong, “Effect of poles on the sub-wavelength focusing by an LHM slab,” Microwave Opt. Tech. Lett., 2005. accepted for publication. [16] J. Huangfu, L.Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of R-like metallic patterns,” Appl. Phys. Lett., vol. 84, pp. 1537-1539, 1 March 2004. [17] S. O’Brien and J. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys. Cond. Matter, vol. 14, pp. 6383-6394, 2002.
40 [18] T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. P. Jr., and 3. A. Kong, “Properties of lefthanded metamaterials: transmission, backward phase, negative refraction, and focusing,” IEEE Trans. Microwave Theory Tech., 2005. submitted for publication. [19] J. A. Kong, B.-I. Wu, and Y. Zhang, “Lateral displacement of a gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett., vol. 80, pp. 2084-2086, 22 March 2002. [20] J. A. Kong, B.-I. Wu, and Y . Zhang, “A unique lateral displacement of a gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett., vol. 33, pp. 136-139, 20 April 2002. [21] L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J . Appl. Phys., vol. 95, pp. 2238-2241, 1 March 2004. [22] R. Shelby, D. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, vol. 292, pp. 77-79, April 2001. [23] H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Magnetic properties of S-shaped split-ring resonators,” Progress in. Electromagnetic Research Special issue on Left-Handed Metamaterials, 2005. accepted for publication. [24] H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed metamaterials composed of only S-shaped resonators,” Phys. Rev. E, vol. 70, no. 057605, 2004. [25] A. Ishimaru, S.-W. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static lorentz theory,” IEEE Trans. Antennas Propagat., vol. 51, pp. 2550-2557, October 2003. [26] H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J . Appl. Phys., 2004. accepted for publication.
The role of phase shift at energy transport by evanescent waves A.P. Vinogradov", A. V. Dorofeenko Institute for theoretical and applied electrodynamics, Scientific Association OIVT Russian Academy of Sciences, Russia *a-vinojgf2yandex.m It is well known that a single evanescent wave dose not transports energy in lossless medium whereas a superposition of several evanescent waves does it. Examples are 1) tunneling of the waves through totally reflecting medium [I], 2) tunneling of the waves through single negative medium where permittivity or permeability is negative [2], 3) optical transmission through subwavelength holes [3]. In all these cases the transport is significant at distances shorter than a wavelength. In the current communication we provide examples where the transport takes place at distances comparable or much greater than the wavelength.
1. The Skrotskii example of total internal reflection The key moment of the effect is that in order to evanescent waves can transport energy a nonzero phase shift between the waves is demanded. To illustrate the fact let us consider the wave traveling through the medium of refractive index nhostwith a slit filled with medium of refractive index nrllt< nhort (see Fig. 1). For n:!,,k; < k,' < niostk; the waves inside the slit are of evanescent type.
, / k/ = iK is purely imaginary quantity. Opposite to the case of half space in our
Indeed kz = n k
-
case of slit there are two evanescent waves E2, = e' . e-Kz+ e- .eKz= E' is described by the y-component of the Poynting vector: --Re((E' C 8n
+ E-)(H' *+IT*)) = --Re(E'H' C
+ E- . The energy transport
*+E-H- *+(E+H-*+E-H+*))= cKIm(e+ .e-*) 4nk0
8n
where H , = H' + H - = ( i l k,,)dE,y l d z . Thus, inside the slit there is a phase shift of n12 between electric and magnetic fields. Hence the first two terms corresponding to energy transport of separate evanescent waves are equal to zero. The third term is a nonzero quantity if and only if ' q f 9. .
with ef =(ec ( dp+ ,e- =(e- 1 -e" . Certainly this term is valuable if the slit thickness d is less than the wavelength.
I
Fig. I
41
42
2. Photonic crystal of negative contrast Let us consider a 1D photonic crystal one of the layers in whose elementary cell has negative permittivity. We shall call such PC a PC of negative contrast. The PC of negative contrast can be imagined as an array of resonators coupled through layers with negative permittivity. Like in usual PC there are traveling solutions that correspond to tunneling or jumping of the resonances over forbidden for traveling layers. There are additional traveling waves. To excite them one has to put on the top of PC sample a dense diffraction grating. The evanescent side lobes can generate a Bloch wave E(z) = g(z)exp(ik,z) that in each layer consists of evanescent waves. The function g(z) is periodic with the period of the PC. For bi-layer PC the equation for the Bloch wave number kB is (see also [4]):
The periodic part g(z) of the traveling Bloch wave is presented in Fig. 2. We can see a series of plasmon resonances on the interfaces between layers with positive and negative permittivity. Thus the traveling solutions correspond to jumping the plasmons over the layers of both positive and negative permittivity. Such a wave transport energy in spite of the fact that in each layer it is a sum of two evanescent waves. The demanded phase shift is produced by the Bloch factor exp(ik,z) . We can avoid employing of diffraction grating. For this purpose we have to consider a PC with more complicated elementary cell. Namely, instead of the layer with positive permittivity we can use an elementary cell of auxiliary PC with band gap. On the boundary of this auxiliary elementary cell and layer with negative permittivity the Tamm surface modes can be excited [ 5 ] . It is worth emphasizing that, first, this waves are evanescent on average and, second, the x-component of the Bloch wave vector is equal to zero. These near field waves can be treated as hopping of the Tamm states (Fg. 3). In both the cases we observe energy transport at arbitrary large distance.
Fig. 2. Z-dependence of the periodic part of Bloch’s function representing the electric field. Vertical lines mean layer’s surfaces.
43 H
\
Fig. 3 A snapshot of the Bloch wave. We can consider the wave as a consequence of resonances of the T a m ’ s states.
3. The role of a detector in formation of image in the Pendry lens So far we consider a consequence of presence of phase shift on energy transport. The inverse logical connective is also important. In particular, the energy transfer caused by an attempt to record the image produced by the Pendry lens (a sheet of material with negative permittivity and positive permeability [ 6 ] )results in destruction of the image. Indeed, the appearing due to recording energy transport causes phase shift of evanescent waves. Whereas in the case of the p e r k t Veselago lens ((a sheet of material with negative permittivity and permeability [6]) the phase shift is the same for each evanescent wave for the Pendry lens the phase shift of different evanescent is not the same. As a consequence, at image location, constructing the evanescent wave experiences destructive interference. We model the image recording by placing a half space filled with lossy material (Fig 4).
Fig. 4 The image without detector (red curve ) and with detector (blue curve). References 1. Kolokolov A A, Skrotskii G V Usp. Fiz. Nuuk 162 164 (1992) [Sov.Phys. Usp. 35 1089 (1992)l 2. S . A. Afanas’ev, and D. I. Sementsov-TechnicalPhysics. 42 (lo), pp. 1181-1183 (1997) 3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, Nature, 391, pp. 667-669 (1998) 4. F.G. Bass and A.P. Tetervov, Phys. Rep. 140 (1986) pp. 237-322 5. A. P. Vinogradov, J. P. Clerc, A. V. Dorofeenko, S. G. Erokhin, submitted to Optical Communications 6. J. B. Pendry Phys. Rev. Lett. 85 (18) pp. 3966-3969 (2000)
Image oscillations in the meta-material lens focusing
Lei Zhou Physics Department, Fudan University, Shanghai 200433, P. R. China
C. T. Chan Physics Department, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Abstract We apply a rigorous time-dependent Green's fimction approach to study the transient behaviors in the meta-material lens (with&= p = -1 + 6 ) focusing with a line source [the two-dimensional (2D) geometry] and a point source [the three-dimensional (3D) geometry]. We find image oscillations in the time evolution of the focusing process, which depend on both the dimensionality and6. When Re(6) = 0 , we demonstrate that the image oscillations, observed in many previous simulations in the 2D geometry, are induced a novel vortex-like surface wave, but such oscillations are weak in the 3D geometry. WhenRe(8) + 0 , image oscillations exist even for the 3D geometry, and show many different features with that observed in 2D. Introduction Using a meta-material slab (with&= p = -1) as a lens to focus electromagnetic (EM) waves has attracted much attention recently. The idea originates from a pioneering analysis by Veselago [ 11, and a recent one by Pendry who showed that the resolution could beat the diffraction limit [2]. Many theoretical works were performed to study this effect [3-141. It was gradually realized that a non-zero6is needed [3-9, 11-12] to avoid the field divergence problems [9] encountered in the "perfect lens" situation (i.e. E = p = -1) [2]. Most studies to date considered the 2D models [3-121, and were only interested in the finally stabilized image properties right at the working frequency. The transient behaviors have been neglected in most studies. Although the sources are monochromatic, transient waves are still inevitable if there is a "switch-on" process, and there are non-trivial consequences in such problems. For example, in a 2D model with a purely imaginary 6 , a finite-difference-time-domain simulation showed that the image oscillates dramatically over time [5]. In this talk, we present our systematic studies on the transient behaviors in meta-material focusing in both 2D and 3D configurations. Mathematics We apply a Green's function approach to quantitatively study the time evolutions [14,15]. The r r r r source is taken asJ(r,t) =v~,s(x>s(z)e-'~'B(t)in 2D [14] andJ(r',t') =P,j6(F')e-'q"B(t?in 3D geometry [ 151. The meta-material lens has E = p = 1- 2004f (f + iy)] and a thickness d. The time-dependent E field can be written as r r 1 r r w E(r,t)=- Sdm-'"E(r,w) 2z w-w,,+iq ' A
1
1
where E ( r ,w) is calculated following Ref. [13]. We note that ~ ( f ,=) p(fo) =-1+0.4(fo -1O)+iO.2y in the limit of f , +lO,y-+O . Thus, near the perfect lens condition, Re(6) and Im(6) can be tuned essentially independently by changing the working frequency f, and y . Below we study quantitatively how Re(6) and Im(6) affect the transient behaviors.
44
45 25 20 n
E E
W
= 0.005 d=10
-y
l5 10 0
10
20
40
30
0.2
=
0
10
20
30
40
Tim (ns) Fig. 1 (a) Resolution was a function o f t in the 2D focusing, calculated with only propagating components (circles) and with all components (line). (b) lE/ as function oft for lenses with different parameters.
2D results We consider theRe(6) = 0 case (by setting& = 10GHz) in order to directly compare with previous studies [5-lo]. Ford = lOmm and y = 0.005 GHz, we plotted the calculated image resolutionw(t), defined as the peak width measured at half-maximum, and field amplitude 1 E:” 1 (at the image point) in Fig. l(a) and (b). Results with propagating components only are shown together for comparison. We find that the time evolution is dominated by damped oscillations with a characteristic period, confirming recent FDTD simulation results [7]. A thinner lens yields a higher-frequency oscillation [see the dashed line in Fig. l(b) for d =8mm], and a larger y suppresses the oscillations better (see the dotted line for y = 0.02 GHz). The oscillation is apparently contributed by the evanescent waves since results including only propagating waves (circles) do not show any oscillations. 3D results We allow 6 be complex. Figure 2 compares the calculated field evolutions with different values ofRe(6) , Im(6) and lens thickness d. We find the field oscillation exists whenever Re(6) f 0 . Similar to 2D, the oscillation is caused by the SW’s, since the calculation including only propagating components shows no oscillation (open circles in Fig. 2(c)). 1.8,
I
= : Y 0.0
-
0.6
=0.004 d = 1 0
h
W -
0.4 0.2
0 .o
0.0 0 0
100
200
T i m e (ns )
300
100 200 Time (ns)
300
Fig. 2 Time evolution of I E 1 at the image point using lenses with different values of Re(6) (a,b), Im(6) and d (c) at the working frequency. Circles are obtained without evanescent waves.
46 We find that 1 E ( t ) I can be written approximately as: 1 E(t) I= E, ( t )+ EoScsin(Gt + @)e? (2) where E,,(t) is the averaged evolution part, E,,, the oscillation strength a n d 5 the oscillation frequency. Several features can be summarized from Fig. 2: 1. W is determined solely by Re(6), and has nothing to do with Im(6) and d. 2. The role ojIm(6) is to damp out the oscillation. The oscillation will not stop ifr = 0 as long as Re(6) f 0 . 3. E,,(t) is determined mainly by Re(6). The evolution toward stabilization becomes slower when Re(6 ) + 0. Underlying physics In 3D case, we plot the magnitude of the integrand in Eq. (1) as a finction of frequency in Fig. 3(a) for7 = y = 0.001 andRe(6) = -0.04. In addition to the pole at the working frequency ( f = f,), we
and& ) which contribute appreciably to the integration find two other frequencies (denoted by in Eq. (1). We then plotted the SW spectrum in Fig. 3(b) for comparison. The pole atf; corresponds to the band-edge SW state possessing a zero group velocity. The pole at f , corresponds to the frequency where,$ + m , which is achieved w h e n s = , u u - 1 . In order to avoid the field divergence problems [12], the lens should haves = ,u + -1 at the working frequencyf,. However, the dispersive nature implies that there must be another frequency at which&= p -+ -1, which is the origin of the pole at f , . The strength of the pole at f,is much stronger than that atf; , since the SW’s for different k,, are nearly degenerate at f , and also f, is closer to f , [recalling the factor l l ( w - ~ ,+iq) in Eq. (l)]. At a relatively long time, we expect that only the poles at f , and f,dominate. Neglecting absorption, the total field approximately becomes:
I E(I) I=I
I=I
EoeiWu‘ + Ezeiqt
E, I +E,,, sin(Zt + 4)
(3) where W = w, - w, , and E,,, =I E, 1’ / I E, I in the limit oflE, = IE, . Since the pole at f,is solely determined the intrinsic property (dispersion relation) of the lens material, a different lens thickness does not alter its position, as shown by the open circles in Fig. 3(a, b). This explains feature (1) thatwdoes not depend on d. Since the pole at f,has no external energy input except at the switch-on process, a finite y will eventually damp it out, and in turn, the oscillation will die out. We thus explained the second feature. The averaged evolution part E,,(t) is contributed mainly by the frequency components aroundf, . For this part, the field evolution can be viewed as the “leaking” of those transient waves
I
I
with frequencies around f,. We believe that this process is conducted through lateral SW transport at a speed of group velocityVE= aw/dkl,. To test this picture, we show the calculated V, as a hnction of frequency in Fig. 3(c). It is clear that V, becomes smaller as Re(6) -+ 0 (i.e., approaching the pole at f , ), which explains the third feature shown above.
47
Fig. 3 (a) Calculated values of 1 E(w)w, /(w- w, + iv) las functions offfor different d. The SW spectra and the group velocity are shown in respectively in (b) and ( c ) .
When Re(6) = 0 , the pole at f,merges with that at f ,, and the pole at J; becomes important. This SW state does not transport energy due to its vortex-like flux pattern [ 141. However, its strength is weak in 3D and the resulting oscillation due tofi is almost non-observable (see solid line in Fig. 2(b)). In 2D, this pole has a much bigger strength leading to strong image oscillations (see Fig. 1). Since this state strongly depends on d, the resulting oscillation is also strongly dependent on d (see Fig. 1). The reason accounting for the stark differences between oscillations in 2D (Fig. 1) and 3D (Fig. 2) is that they correspond to beating effects involving different modes, which exist in different situations. Conclusions We show fascinating image oscillations exist in the time evolutions of meta-material focusing processes, which depend on both the dimensionality and material properties. This work was supported by Hong Kong RGC through CA02/03.SCOl and National Basic Research Program of China (No. 2004CB7 19800). References [ l ] V.G. Veselago, Sov. Phys. Usp. 10,509 (1968) [2] J.B. Pendry, Phys. Rev. Lett. 85 3966 (2000) [3] J. B. Pendry Phys. Rev. Lett. 91 099701 (2003) [4] D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82 1506 (2003) [5] R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64 056625 (2001) [6] X. S. Rao and C. K. Ong, Phys. Rev. B 68 113103 (2003) [7] X. S. Rao and C. K. Ong, Phys. Rev. E 68 067601 (2003) [8] S. A. Cummer, Appl. Phys. Lett. 82 1503 (2003) [9] P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, Phys. Rev. E 67 025602(R) (2003) [lo] L. Chen, S. L. He and L. F. Shen, Phys. Rev. Lett. 92 107404 (2004) [ 111 R. Merlin, Appl. Phys. Lett. 84 1290 (2004) [ 121 N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88 207403 (2002) [13] Y. Zhang, T. M. Grzegorczyk and J. A. Kong, Progress in Electromagnetic Research, PIER 35 271 (2002) [14] L. Zhou and C T. Chan, Appl. Phys. Lett., submitted. [15] L. Zhou and C T. Chan, unpublished.
Superprism effect in 1D photonic crystal A. M. Merzlikin*, A. P. Vinogradov Institute of Theoretical and Applied Electromagnetism OIVT, Russian Academy of Sciences, Russia *merzlikin a@,mail.ru
Recent achievements in nano-technology result in the possibility to create photonic crystals (PC) working in optics. The main efforts of researchers have been devoted to manufacture and study 3D PC. As a compromise, one deals with 2D PC and truncated PC. Concerning 1D PC, there is a strong belief that their properties are studied to such a degree that there is nothing new to expect. Nevertheless, contrary to this prejudice, 1D systems are going to give small wonders. It is worth noting the enhancement of magneto-optical properties in 1D PC (1-31, or recent progress in the study of light localization [4, 51. Thus, it is not so simple a system as it seems. The 1D PCs have the advantage of being cheap and easy fabrication. They exhibit one of the most used properties of PC, namely the band gap. Below, we consider a well-known 3D and 2D PCs effect of superprism but observed in 1D PC. The superprism effect consists in significant deflection of the refracted beam at small change in the angle of incidence [6-81. The physical basis of this effect is that at sufficiently high frequencies, the equi-frequency surface lies in different Brillouin zones; by varying the angle of light beam propagation, we should pass from one Brillouin zone to another. Near the boundary of two different zones, there exists a band gap resulting in the prohibition of wave propagation in certain directions. The surface of 2D or 3D PC is really a diffraction grating splitting the incident beam into several lobes. Some of them are travelling waves, the other are evanescent. By proper choice of grating step, angle of incidence and frequency, we can arrive at situation where the grating produces three travelling lobes, namely the central and two side lobes. The role of the bulk part of the PC reduces to placing a band gap in the way of two lobes. Thus, there is only one travelling wave; and the situation resembles refraction in ordinary media. Small change in the angle of incidence varies slightly the angles of the lobes’ propagation. The superprism effect is observed if at the same time one lobe passes from the travelling band into the band gap, whereas the other lobe comes out from the band gap into the travelling band. We still have one travelling wave but due to switching from one lobe to the other, we observe a significant variation of the angle of “refraction”. The band structure of 1D PC possesses the necessary angle band gaps (Fig. 1). To observe the superprism effect in 1D system, we have to turn the boundary surface of 1D PC into diffraction grating. It is possible to cut the 1D PC at some angle to layers forming the PC or deposit a set of strips on the surface (Fig. 1). Below, we produce an illustrative example of the system. For simplicity, we consider a system of layers of identical thickness d . The values of permittivity of the layers are chosen to be equal to 3 II 10 respectively. We consider TE wave (s-polarization) at frequency k,, = w / c . In our simulations, we employ the formalism of equi-frequency-surface (EFS). The EFS is the cross-section of dispersion surface w(k) with a plane k, = o / c = constant . The upper black solid circle in Fig. 2 represents the EFS of vacuum, which corresponds to the dispersion equation of the form k2 = (o/c)2 = k,’ . We consider two different angles of incidence (cases 1 and 2), with the respective vectors coloured in green and red.
48
49 The EFS for ID PC can be calculated employing a well-known dispersion equation [9] cos(kz2d) = cos(k,zd)cos(k2zd)-(kiz+ k ~ z ) s i n ( k , z d ) s i n ( k , z d ) / ( 2 k , z k , z ) where k,, =
Jn, Jw k2z =
are the wave vector's components orthogonal to the
layers, k, is the Bloch wave vector's component. The corresponding EFS is produced in the bottom of Fig. 2.
kY
ad
I
EFS of hddcilt
Fig 1. The scheme of the 1D superprism Fig. 2 The equi-frequency surface for vacuum andforPC k o d / 2 ~ = 0 . 2E,, = 3 , E, =10 The ID PC is translational invariant in x-direction. Hence, the x-component of the wave vector should be the same for the incident and refracted waves. The dashed vertical lines express this conservation law. The diffraction grating breaks the symmetry. Now, the x-component of the wave vector can be equal to k = kox,koxk Gg,.al,,,g.... where G, is the wave vector of reciprocal-grating. The crossing point of the corresponding vertical lines with EFS determines the wave vector of propagating Bloch wave. In the first case (green lines and arrows), only the left side lobe with wave vector k, can propagate. The propagation of the central and right side lobes is forbidden due to the band gap. In the second case (red lines and arrows), the whole pattern shifts to the right. The only lobe that can propagate now is the right side lobe with wave vectork, . Thus, we see that small change in the angle of incidence leads to significant variation in the direction of propagation of the "refracted" ray. This is the 1D analog of a well-known superprism effect.
References M. Inoue, K. Arai, T. Fuji, M. Abe, J. Appl. Phys. 83 (1 l), 6768 (1998) A. P. Vinogradov, S. G. Erokhin, A. B. Granovski, M. Inoue, Journal of Communications Technology and Electronics, 49, 682 (2004) A. P. Vinogradov, S. G. Erokhin, A. B. Granovski, M. Inoue, Journal of Communications Technology and Electronics, 49, 88 (2004) A. P. Vinogradov, A. M. Merzlikin, "On electrodynamics of one-dimensional system beyond homogenization approximation" in "Advanced in Metamaterials" ed. By A. Sikhvola and M. Zouhdi, NATO BOOK series, Kluwer Academic Publishers Dordrecht 2002, 341 (2003)
50 5. 6. 7. 8. 9.
A. P. Vinogradov, A. M. Merzlikin, Phys Rev E 70,026610, (2004) T. Baba, T. Matsumoto, Appl. Phys. Lett. 81,2325 (2002) T. Baba, M. Nakamura, IEEE J. of Quantum Electronics 38,909 (2002) L. Wu, M. Mazilu, T. Karle, T. F. Krauss, IEEE J. of Quantum Electronics 38, 915 (2002) F.G. Bass, A.P. Tetervov, Phys. Rep. 140 (1986) 237-322
Cluster Effect of Composites with Long Conductive Fibers L. Liu', S. M. Matitsine and Y. B. Gan Temasek Laboratories, National University of Singapore, Singapore 1 17508
Abstract: Transmission coefficient and effective permittivity of composites with embedded long conductive fibers was experimentally and numerically investigated at microwave frequencies. Cluster effect due to overlapping of the fibers was used to explain the dispersive microwave properties of composites with randomly distributed fibers. 1. Introduction Microwave properties of composites with embedded long conductive fibers have attracted much attention recently due to various promising applications, such as substrates with high dielectric constant, impedance matching layer, frequency selective surface or left handed materials ([ 1, 21 and references therein). Both randomly and periodically distributed fibers in composites are of interests. In practice, random distribution is more compatible with spray process. The effective medium theory (EMT) is able to predict the microwave properties of heterogeneous materials with conductive inclusions of size much smaller than the wavelength. For long fiber of length comparable to the wavelength, EMT is inaccurate. Hence, the scale dependent effective medium theory (SDEMT) was proposed for fiber-filled composites [ 3 ] . This theory assumed that the effective permittivity of the host matrix is not constant but depends on the distance to the fiber. Qualitative agreement between SDEMT and experiment was obtained [4]. However, the anisotropy of the host matrix could be the cause of the unusual shift in resonance frequency of fiber-filled composite, instead of the renormalized depolarization factor of the fiber inclusions by the variable permittivity of the host matrix [ 11. For fiber composites with inclusions of low volume concentration, the well-known dilute limit approximation given by the Lorentzian dispersion for permittivity is
where &d is the permittivity of the host matrix. Eq. (1) accounts for the resonance of the permittivity due to the dipole resonance of waves scattered from the fibers, a feature of primary importance in most microwave applications. The quantityfo in Eq. (1) is the resonance frequency that determines the location of the resonance peak; f i is the relaxation frequency related to the quality factor, Q=2filfoo; A is the amplitude of the resonance [4]. For volume concentration (V,) of fiber composite close to or larger than the percolation ratio (V,), the fiber inclusions will overlap. The interactions among the fibers are more complicated than the simplistic inductive and capacitive effects found in periodic fiber array and the mutual coupling in randomly distributed non-overlapping fibers at low V, [5].It is difficult to determine the properties of the composite solely from the design parameters of individual fiber (such as aspect ratio and conductivity, etc) without considering the morphology of the fiber clusters. For volume fraction above the percolation threshold, percolation theory was normally used to model the electrical and dielectric properties of metal-filled polymer composite with inclusions much smaller than wavelength [6]. Power law dependence was employed to fit the dispersive permittivity and AC conductivity of carbon nanotube composites with length of a few microns [7]. Therefore, it is very important to study the behavior of fiber clusters formed by overlapping long conductive fibers for volume concentration close to or higher than the percolation threshold.
* Corresponding author, email:
[email protected] 51
52
To clearly understand the behavior of clusters of different configurations, we first consider the random-periodic distribution of fiber cluster in this study. Namely, the fiber composite can be divided into many periodic units, each unit of which contains a fiber cluster formed by a few randomly distributed fibers. The transmission or reflection coefficient of such materials with different kinds of clusters is measured and simulated. Next, the effective permittivity of composites with randomly distributed fibers is measured and curve-fitted using the Lorentzian model. The cluster effect explains the dependence of resonance and relaxation frequencies on concentration of fiber inclusions. 2. Numerical Model The ANSOFT FEM software High Frequency Structure Simulator 9.2 (HFSSTM) is employed in the numerical study. The fibers and Styrofoam substrate are modeled using tetrahedral elements. Typically, the object resides in an unbounded free space. However, FEM requires the meshing of the infinite free space region as well, which must be truncated in actual computations. Hence, the Perfectly Matched Layer (PML), a fictitious anisotropic layer, is applied to reduce the unbounded space to a reasonable size, while emulating the unbounded free space environment. The space between the PML and the composite sheet is filled with air layer of thickness larger than a quarter-wavelength at the frequency of interest. Adaptive meshing technique is built-in to automatically refine the mesh at locations where computational error is large. A convergence condition is defined (for example, the change in electric field strength between the present and the previous iterations is less than a prescribed value) to obtain sufficiently accurate results. Upon satisfying this condition, the computation process will stop. For composites with randomly distributed fibers, a unit cell of the composite sheet comprises a fiber cluster and Styrofoam substrate. Figure 1 shows the schematic diagram of the Periodic BC computational model. A TEM wave with electric field E parallel to the layer and wave vector k perpendicular to the layer surface illuminates the model at normal incidence. The PML boundary conditions are imposed on 71 surfaces that are perpendicular to the wave vector. Due to m the periodic geometry, a linear phase relationship exists 0 between the fields on the surface of the walls of the unit cell. The surface with free variables is commonly known as the “master” boundary, while that with constrained variables is known as the “slave” boundary. The Periodic BC tangential electric field comDonents on the slave ’: Of fiber boundaries are expressed in terms of that on the master boundaries, with the phase between the two boundaries calculated from the incident angle and periodic cell size. The periodic or linked boundary conditions are applied to the surface parallel to the wave vector, as shown in Fig. 1. The coherent transmission of the composite sheet can be obtained from the ratio of the average intensity of transmitted electric field to that of the incident field. The phase of the transmission coefficient can be calculated from the average phase of the total field and incident field. I
3. Experiment The samples under study comprised array of clusters or randomly distributed copper fibers mounted directly on a Styrofoam board (20cm by 20cm by 5mm) using adhesive tape. The periodicity of the cluster array corresponded to that modelled in computation. The fibers are of diameter 0.1 mm and length 10 mm. Since the Styrofoam has very low permittivity (~=1.05)and small thickness, its effect is not significant as compared to that of the metallic fibers. The slab thickness is therefore considered to be that of the fiber’s diameter. The complex reflection and transmission coefficients of the sample were measured using the free-space method at normal incidence [2]. The experimental setup includes a vector network
53
analyzer, with broadband transmit and receive electromagnetic horn antennas mounted vertically. The frequency of interest covers 2 to 18 GHz. To eliminate multiple scattering between the sample and the horns, time-domain gating was applied. Diffraction effects at the edges of the sample are minimized by attaching a piece of ring-shaped high-quality wave absorber of inner diameter 15 cm to the transmit horn. The effective permittivity can be calculated from measured transmission coefficients based on transmission line model [5].
0.4
'
0.4L
'
' 6
4
2
'
'
12 10 F (GHz)
8
'
'
I
14
16
18
'
Figure 3: T of randomly distributed fibers with various V, 120 100
80
$ 40
6o 20 I
0 ' 0
w
-
0.5
-
2
1
.
f
A
1.5 2 vc (%)
2.5
3
Figure 4:Resonance and relaxation frequency from Lorentzian model
between two overlapping fibers, and may not be due only to physical contact and DC current flowing from one fiber to another. If the fiber cluster is replaced by a bended fiber of identical shape and length (15.6mm), multiple resonances are not found, regardless of the polarization of the incident electric field. Therefore, in modelling of randomly distributed fibers, we cannot use long fibers as substitutes for overlapping short fibers, due to the different interactions involved in the two different configurations. Single fiber may have resonance even if it is close to or in physical contact with other fibers. This explains why the observed resonance is close to the resonance frequency of single fiber in a composite with randomly distributed fibers. For three overlapping fibers forming a cluster in a periodic cell, three resonances are observed, corresponding to that of single fiber, clusters of two fibers and clusters of three fibers. The amplitude of the resonance depends on the projection of the effective lengths onto the polarization. Arrays of clusters with more than 3 fibers in each periodic cell (4 to 6 pieces of fibers) are also fabricated and measured. However, only resonances corresponding to 1-, 2- and 3-fiber
54 clusters can be observed. This implies that for clusters of more than 3 fibers with the given dimensions and material properties, the lower order effects due to clustering are dominant while the higher order effects are negligible. Assuming that the cluster is a resonator, the Q factor will decrease since the contact resistance increases due to the larger number of fibers in each cluster. For other fibers with different dimensions and geometry, the effect of contact can be different. In Fig 3, the transmission coefficient of randomly distributed fibers with and without overlapping is plotted. Each sample is measured twice with incident waves of vertical and horizontal polarizations, respectively. It is observed in Fig. 3 that cluster effect can decrease the Q factor, thereby reduces the amplitude. The shallow resonance peak around 1lGHz could have arisen from the cluster effects. Fig. 4 shows the curved-fitted fa and f i for samples with different concentrations using the Lorentzian model. Three samples are measured for each concentration. The error bars are the calculated standard deviations indicating the distribution of the measurement. fo varies from 13.2 to 13.9GHz when V, increases from 0.1% to 3.2%. Although the concentration V, approaches the percolation ratio ( Vp)of the fibers, the resonance peak remains close to the resonance frequency of the single fiber, implying that fibers in contact can still be considered as resonators. The conclusion agrees well with our observations in the cluster array. Below 0.3%, fibers are far from each other without forming any cluster. The interactions among fibers are explained by inductive and capacitive effects which are stronger for fibers close to each other [ 5 ] . The coupling effects cause an upward shift info (about OSGHz) andfi (about 5OGHz). Above 0.3%, the fibers will be in contact and lor overlap. The increasing coupling due to cluster effect shifts thefi to 115 of its peak value. Namely, the width of resonance peak becomes wider as V, increases. The broadband response at high V, is also caused by the distributed resonance frequencies of overlapping fibers. Statistical study is perhaps needed to understand the dependence of microwave properties of such material on the design parameters (such as dimension, conductive and distribution of conductive fibers). 5. Conclusions Transmission coefficient and effective permittivity of fiber composite was investigated with free space and FEM method. It was shown that the cluster formed by overlapping fibers has multiple resonance frequencies, which are related to the lengths of cluster or that of single fiber. Interactions between fibers within cluster are not eliminated by the electrical isolation. Cluster effect can explain why randomly distributed fibers have broad resonance peak, though the resonance frequency remains close to that of a single fiber. References [l] S.M. Matitsine, K.M. Hock, L. Liu, Y.B. Gan, A.N. Lagarkov and K.N. Rozanov, J. Appl. Phys. 94,8979 (2003). [2] L. Liu, S.M. Matitsine, Y.B. Gan, and K.N. Rozanov, Electromagnetics 25 (2005) [3] A.N. Lagarkov and A.K. Sarychev, Phys. Rev. B 53,6318 (1996) [4] A.N. Lagarkov, S.M. Matytsin, K.N. Rozanov, and A.K. Sarychev, J. Appl. Phys. 84, 3806 (1998). [ 5 ] L. Liu, S. M. Matitsine, Y.B. Gan and K. N. Rozanov,,J. Appl. Phys. Submitted in 2004 [6] T. A. Ezquerra, F. Kremer and G. Wegner, Progress in electromagnetic research, PIER6, ~273-301,1992. [7] L. Liu, L.F. Chen, S. Matitsine, L.B. Kong, Y.B. Gan, K.N. Rozanov, ICMAT2005, Submitted.
Micro- and Nano-Fabrication of Electromagnetic Metamaterials for the Terahertz Range
B.D.F. Casse”, H.O. Moser”, 0. Wilhelmia~bb, and B.T. Saw” ”Singapore Synchrotron Light Source (SSLS), National University of Singapore (NUS) 5 Research Link, Singapore, 117603, Singapore bnow at: FEI Electron Optics BV, Achtseweg Noord 5, 5621 GG Eindhoven, The Netherlands Abstract We present the first electromagnetic metamaterials (EM3) produced by microfabrication. EM3 refers to composite materials having both, permittivity and permeability, negative simultaneously which leads to unusual effects such as a negative index of refraction and an inverse Doppler and Cerenkov effect. The gold-plated micro composites, based on the rod-split-ring-resonator design by Pendry and co-workers, are arranged in an array and embedded in a 2 x 2 mm2 plastic chip. Numerical simulations and experimental results from the ISM1 (Infrared Spectro/MIcroscopy) facility at SSLS show that the composite material which has feature sizes down to 5 pm is an EM3 in the range 1-2.7 THz. This extends the frequency range in which EM3 are available by about 3 orders of magnitude as compared to values achieved with microwaves, thereby opening up opportunities for new applications in Terahertz Optics and Imaging. We further report on our latest results on fabrication techniques for nano-EM3 featuring sub 100 nm critical dimensions. To produce these composite materials, we use lithography-based micro- and nanosystems technology including the LIGA process. Besides enabling further size reductions these techniques are also applicable to a broad range of materials, suitable to implement a variety of complex and nearly 3-D designs, and amenable to mass production and stacking. Introduction In 1964, V.G. Veselago [ 11 theoretically investigated electromagnetic waves interacting with materials having simultaneously negative permittivity E and permeability ,u . He predicted that such materials would exhibit exotic properties such as a negative index of refraction and an inverse Doppler and Cerenkov effect. Veselago coined the term “left-handed” materials as the wave vector is anti-parallel to the usual right-handed cross product of the electric and magnetic fields. The field remained dormant for thirty years, since no such materials were found in nature, until J.B. Pendry and co-workers proposed schemes to artificially fabricate them. They are composed of two basic building blocks - one electric ( E < 0) which consists of a wire medium [2], and the other eff
magnetic ( ,uef < 0 ) which comprises loops or tubes of conductors with a gap inserted and known as split ring resonators (SRR) [3]. Following this recipe, D.R. Smith et al. experimentally built the first composite materials which demonstrated electromagnetic metamaterial properties in the microwave region, i.e. in the Gigahertz range [4]. We present the first microfabricated rod-split-ring-resonators (RSR)[5] with overall structure size below 100 pm and with structural details down to 5 pm. Their resonance frequencies are around 3 orders of magnitude higher than the hitherto known values in the microwave range. We have also realized RSR composite materials with overall structure size of less than 1 Om and having critical dimensions down to 70 nm. Design & Simulation Figure 1 shows the planar adaptation of Pendry’s prototype adopted for micr+ and nanofabiication, together with its geometric paramete1. definition and periodic arrangement.
FIG. 1. Geometric parameter definition of the RSR (left). Periodic arrangement of the RSR adopted for micro/ nanofabrication (right). 55
56
While
E~~
< o over a much wider range than pef
< 0 , provided that a small ratio of radius to
distance of the wires is used, the lower and upper limit of the frequency interval over which prfr< 0 was calculated from Pendry's formulae [3]:
Ni slim Ni fat Au 1 Au 2 Au 3
rlpm
clmm
d/mm
dmm
b/mm
10 10 8.4 11 14
10 15 12 12 12
10 10 4.3 4.3 4.3
110 135 95.4 100.6 106.6
90 110 78.4 83.6 89.6
v0/THz 2.63 2.63 2.24 1.50 1.04
rlnm Nano-Au 1 Nano-Au2
300 150
v,, /THz 2.68 2.67 2.28 1.53 1.08
/THz
200 90
100 70
200 90
2 1.03
1.7 0.87
50.66 119.89
52.91 124.91
57
U P 4 6 2 0 (right, scale bar 200pm)
coated with a 100-nm thin film of indium-tin-oxide (ITO). PMMA 950k was spin coated onto the substrate such that a thickness of 200 nm was achieved. The coated I T 0 glass substrate was then softbaked on a hotplate at 160°C for 2 h. Parameters shown in Table I1 were created in Design CAD files and transferred into the PMMA resist by electron beam lithography with the Sirion NPGS-SEM system from FEI company. A beam of 30 keV electrons was used with an exposure dose of 100 pC/cm2 at a current of 25 pA for the nano-patterning. The PMMA was developed using a mixture of MIBK developer and IPA in a ratio of 3: 1 by volume for 70 s, followed by a 20s dip in IPA, and a final rinse in deionised water for another 20s. A 30 nm thick gold film was deposited onto the photoresist template in a UHV chamber by an e-beam evaporator (Fig. 4, left). Lift-off of the PMMA was carried out by dipping the coated glass in acetone for 10 min and using the ultrasonic bath for 30s. Finally, a mild acidic solution was poured on the glass for 1 min, followed by a rinse with DI water to remove the I T 0 in between the structures to avoid short-circuits. The end product is a 2 x 2 mm2 array of 30 nm thick gold RSR, with an I T 0 base, sitting on top of 1 mm-t
FIG. 4 30 nm ofe-beam evaporatcd gold on photoresist tcmplate (left, wale bar 5 prn) and gold RSR. with an IT0 base, sitting on top of 1-mm thick glass. (right, scale bar 5 pm)
FTIR Measurements To prove that the composite materials are EM3, we show that the frequency dependence of the RSR follows both the prediction of Pendry's formulae and the numerical simulation by Microwave Studio (MWS) when the geometric parameters are changed. The spectroscopic measurements for the micro- EM3 were performed using a Bruker IFV 66 v/S Fourier transform interferometer in the far infrared over the range 22 to 400 cm-' with a 4 cm-' and 2 cm-' spectral resolution. The samples were aligned with their surfaces perpendicular to the optical axis and measurements were carried out with an unpolarised beam. The transmission curves observed for the resist slab alone were more or less flat as compared to the RSR resonant peaks. Figure 5 (left) shows the spectral response of the Au RSR sample 2 and its short-circuited version (i.e. with the gap g of the split rings closed, thus removing a decisive structure element of the SRR). We can observe that the wavenumbers at which the maxima occur agree reasonably with the values expected from Pendry's formulae and MWS simulations. The short-circuited rings do not show any prominent spectral response in the relevant frequency range as expected. Figure 5 (right) shows the resonance frequency peaks for all cases versus the inner radius r. Measured and numerically simulated values are always quite close while the analytical formulae led to an up to 17% deviation in the case of Au sample 3.
58
Wavenuniber [cm '1 r Iw1 FIG. 5. Measured spectral response of an Au RSR structure (Au sample 2, solid line) and its short-circuited version (dashed-dotted line). The vertical lines indicate the wave numbers of the maximum as predicted by MWS (numerical simulation) and Pendry's analytical formulae (left). Frequencies of the maxima of the spectral response curves versus the inner radius of the SRR for the measured (FTIR) and numerically simulated (MWS). The solid curve shows vo(r) of Eq. (1) for the Au cases. When the Ni case is scaled to the same d as for Au, it also comes close to the curve ( 0 )
The three Au cases demonstrate a good f 3 I 2dependence when other parameters are kept constant. In the Ni case, the resonant frequency is higher as the annular gap between inner and outer ring, d, is larger by more than a factor of 2, thus reducing capacitance and increasing resonance frequency. However, when it is scaled to the same value of d as for Au it also comes close to the curve.
Conclusion Micro Ni or Au Rod-Split-Ring-Resonators have been embedded in an AZ P4620 resist matrix in a 2 x 2 mm2 array and produced by lithography based microfabrication. With an outer ring diameter of 73.4 - 100 pm, analytical and numerical simulations predict the spectral resonance of the structures to occur between 1-2.7 THz. This extends the frequency range in which EM3 are available by about 3 orders of magnitude higher than the hitherto achieved values in the microwave spectral range. Spectroscopic measurements by a Fourier transform interferometer performed for various geometric variants on the RSR arrays show that resonant frequency peaks correspond closely to analytical and numerical predictions. This is evidence for the conclusion that these composite materials become EM3 at their respective resonance frequency in the 1-2.7 THz spectral range. Nan0 Au RSRs have been produced on 1-mm thick glass substrate coated with ITO. With an outer ring diameter ranging from 0.78 pm to 1.4 pm, analytical and numerical simulations predict the spectral resonance of the structures to occur between 50 to over 100 THz. The present work opens up new ways for building novel electromagnetic and optical devices. Acknowledgments The authors thank Professor Lim Hock and Gan Yeow Beng of the Temasek Laboratories, NUS, for stimulating discussions. They also thank Bruker Optics for providing fast access to one of their FTIR for the Ni RSR measurements and acknowledge the contribution of SSLS LiMiNT staff J.R. Kong and Shahrain bin Mahmood for process development and optimization. The work was performed at SSLS under A*STAR/MOE RP3979908M, A*STAR 0121050038, and NUS Core Support C-380-003-003-001 grants. References [l] V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1964) [SOV.Phys. Usp. 10,509 (1968)l [2] J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, Phys. Rev. Lett. 76,4773 (1996) [3] J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075(1999) [4] D.R.Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, Phys.Rev.Lett. 84,4184 (2000) [5] H.O. Moser, B.D.F. Casse, 0. Wilhelmi, B.T. Saw, Phys. Rev. Lett. 94(6), 063901 (2005) [6] T. Weiland, R. Schuhmann, R.B. Greegor, C. Parazzoli, and A.M. Vetter, J.App1. Phys. 90,5419 (2001)
Sidelobe Suppression of Cellular Base Station Antenna Due to Application of Metamaterials A. N. Lagarkov, V. N. Semenenko*, V. A. Chistyaev, A. I. Fedorenko, N. P. Balabuha, V. P. Moiseev Institute for Theoretical and Applied Problems in Electromagnetics (ITAE) Russian Academy of Sciences (RAS), Russia *
[email protected] Abstract By the example of cellular base station antenna AMPA065-18, operating in 900 MHz frequency band, high efficiency of suppression in unwanted sidelobes is shown due to application of radio absorbers based on metamaterials. More than 10 dB suppression in far sidelobes of the radiation patterns is obtained as for a case co-polarization and cross polarization patterns. The additional attenuation in power gain is found to be less than 0.5 dB due to application of radio absorbers.
1. Introduction In present work the problem of sidelobe suppression of the transmitting base station cellular antenna of CDMA standard (a frequency band is 800 - 900 MHz) is solved with the purpose to prevent electromagnetic interference (EMI) between cellular communication and aviation short range navigation systems. In this case the EM1 problem arises because of the frequency band of transmitting cellular base stations of cellular communication and that of the receiving antenna of the aviation navigation equipment coincide. This is electromagnetic compatibility (EMC) problem as well. The improvement of an antenna pattern is achieved without change of antenna design and only due to installation on antenna of radio absorbing materials (RAM) based on metamaterials. 2. Theoretical results Improvement of antenna patterns is designed for dipole array antenna AMPA065- 18 (COMSAT-RSZ' design). The schematic diagram of the antenna elements is presented in Fig. 1. The antenna length is about 1.8 m. The antenna represents a reflector array antenna, consisting from six strip half-wave radiators ( 2 ) with the metal reflecting screen (1). The antenna works equally well as a receiving antenna (828-837 MHz), or as a transmitting antenna (873-882 MHz). So it is necessary to attenuate antenna sidelobes as much as possible in transmission frequency range and minimize sidelobes dumping in reception frequency range.
The required result in sidelobe suppression is obtained by the installation of special RAM based on the composite metamaterials. Suggested arrangement of the absorbers on the antenna is shown in Fig. 1. The absorbers (4) arranged on a radome in the area of the first and last radiators serve for correction of the field distribution over the antenna aperture and affect the near sidelobes levels. The absorbers ( 3 ) arranged at the faceplates, reduce diffraction from edges of the antenna and, accordingly, suppress the far sidelobes levels. For correct choice of radio absorbers, arranged on the antenna, the theoretical modeling of antenna pattern is made. The antenna pattern is restored from the measured electric field distribution over the aperture: E = E,, cos (.x I l)Eo2cos2 (EX I L ) , where I is length of the radiator, L is the size of the aperture, E,, ,Eo2are the amplitudes of electric fields. The simplified two-dimensional model of a half-dipole array with the reflecting metal screen is considered. The calculation of RAM influence on the antenna patterns is carried out by a method 59
60
of the integral equations numerically. A set of experiments [ 11 revealed that RAM, based on artificial magnetic composite (metamaterial) is more suitable for suppression of antenna sidelobes. The special feature of such a metamaterial is the resonance frequency dispersion of effective permittivity E = E'+ is" and permeability p = p'+ ip" in the same frequency band (see Fig. 2). Experimental data pointed out that those effective material parameters of metamaterial ( E ', p ' < 1) are optimum RAM parameters for effective suppression of antenna sidelobes. In this connection in computer simulation of antenna patterns for operating frequency 874 MHz we choose the following values of permittivity and permeability of metamaterial: E = 0.3+ iO.1, p = 0.3 + i1.4. Computer simulation reveals that arrangement of the RAM on a radome (near edges of the aperture) leads to suppression in near sidelobes and almost does not change far sidelobes (see Fig. 3, a solid line corresponds to initial antenna, a dotted line - the upgraded antenna with RAM). At the same time the arrangement of the RAM at faceplates of antenna leads to considerable suppression in far sidelobes and weakly affects the near ones (Fig. 4). Calculations of antenna patterns demonstrate also, that application of the RAM at both faceplates results in greater more far sidelobes attenuation in comparison with one placed at one faceplate. Calculations give rise to the result that increasing in thickness of faceplate RAM leads to great suppression in far sidelobes. The increase in thickness of faceplate RAM from 30 mm (a dotted line) to 90 mm (a thin solid line) does not lead to saturation in sidelobe suppression (Fig. 4). The increase of RAM permittivity from 0.3 up to 2.0 (it can correspond to increasing in matrix permittivity of a composite) has a negative effect on suppression of far sidelobes. Application of the RAM with artificial magnetic properties in the paramagnetic region (the left slope of a resonant curve of permeability, see Fig. 2) gives rise to the weaker effect of sidelobe suppression in comparison with application of the RAM displayed parameters corresponding to diamagnetic region (the right slope of a resonant curve). 3. Experimental results Previous experimental investigations of effective material properties of composites with artificial magnetic properties at microwaves (for example, wire bi-helix media [2]) demonstrate the fact that inclusions possessing the greatest magnetic losses are spirals with zero steps [3] (wire loops). Therefore in this work the gaped loop made from isolated nichrome wire is used as inclusion of a composite (Fig.5). Diameter of a wire loop is 17 mm. The gaped loop has twisting of wires which allows changing capacity of elementary inclusion in the wide range and, consequently, matching the resonance frequency of a wire gaped loop.
The tuning of separate loops to the transmitting frequency of the antenna is made by means of the controlling the distortion of the signal received by a coaxial loop from transmitting horn radiators. Matrix of a composite is polyurethane foam with low permittivity of E = 1.03 and small dielectric Inclusions are put into foam slots in mutually perpendicular planes of a sheet losses of tg6 2 and are fixed by sealing (Fig.5). Measured values of effective microwave permittivity and permeability of manufactured metamaterial (free space method) and fitting curves of resonant approximation are shown in Fig.2. The functions of frequency dispersion of permittivity and permeability possess strong resonant behavior with identical resonant frequency. The flat isotropic metamaterials are used on antenna elements, because of the necessity of maintenance of RAM efficiency for both antenna polarizations. Wire loops inclusions are inserted in
61 a foam matrix in two orthogonal directions. The specific volume concentration of inclusions is homogeneous and extreme for faceplate RAM (3), while for radome RAM (4) the concentration of inclusions is reducing smoothly in the direction of the antenna center (see Fig.1). The rule to vary inclusions concentration is determined and optimized experimentally. The proper choice of an optimum arrangement, configuration and thickness of RAM based on metamaterials was carried out in experiments to achieve the possibly best suppression of near and far antenna sidelobes. RAM optimization was carried out for both co-polarization and cross-polarization radiation patterns. Measurements of radiation patterns were performed in principal plane (a plane of symmetry) and profile plane of the antenna. Findings of circular radiation patterns of the initial antenna (a thin solid line) and upgraded antenna with RAM (a thick solid line) are shown in Fig.6 (case of co-polarization) and Fig.7 (case of cross-polarization) in principal plane at 874 MHz. Both radiation patterns show essential suppression of sidelobes for upgraded antenna (more than 10 dB in far sidelobes). Undesired attenuation of the power gain of antenna is less than 0.5 dB. 4. Conclusion The developed method of improvement of cellular communication antenna is effective and does not demand any disassembly of the antenna. New type of RAM based on metamaterials and offered for arrangement on antenna possesses small weight and matches the all operational requirements over a long time.
The obtained results for upgraded cellular base station antenna with suppressed sidelobes can be used by the telecommunication companies for the decision of EMUEMC problems. Acknowledgement The authors are grateful to the Russian telecommunication company “Personnel communication” (MTU-INFORM) for the provision of cellular sector antenna AMPA065-18. References [l] A. N. Lagarkov et al, “Development and Simulation of Microwave Artificial Magnetic Composites Utilizing Nonmagnetic Inclusions”, J. Magn. Magnet. Materials, no. 238-239, pp. 161-166,2003 [2] A. N. Lagarkov et al, “Resonance properties of bi-helix media at microwaves”, Electromagnetics, vol. 17, no. 3, pp. 213-237, 1997. [3] V. N. Semenenko et al, “Microwave magnetic properties of bi-helix media in dependence on helix pitch”, in Proc. of the “Bianisotropics‘98“,Braunschweig, Germany, June 1988, pp. 313 - 316.
Fig.5
62 2.5
2.0
-10 -15
1.5
-20
8 -2s
1.o
-30 0.5
-35
-40 0.0
-45 0.80
0.85
090
0.95
100
I -180
-120 -60 0 60 120 Elevation angle, degrees
Fig.3 -20
Fig1
-25 -30
63 -35 0.80
0.85
0.90
0.95
1.00
Frequency (GHz)
-40 -45
Fig.2
Fig.4 90
90
180
0
270
Fig.6
180
270
Fig.7
180
Session R3
Chair: S.A. Nikitov
This page intentionally left blank
Thin Ferromagnetic Film-Based Two-DimensionalMagnonic Crystals S.A.Nikitov', Yu.V.Gulyaev', Yu.A.Filimonov', A.I.Volkov', S.L.Vysotskii I , Ph.Tailhades2, C. S. Tsai3 1
Institute of Radieengineering and Electronics, Russian Academy of Sciences, 11, Mokhovaya St., Moscow, Center, 101999, Russia 'CIRIMAT-UMR CNRS 5085-Universite Paul Sabatier, 118 route de Narbonne, 3 1062 Toulouse, France 3Department of Electrical and Computer Engineering, University of California, Irvine, CA 92697, USA and Institute for Applied Science, Academia Sinica, Taipei, 11529, Taiwan
A new type of photonic crystals entitled "Magnonic Crystals (MC)" that exhibit forbidden gaps in the microwave spectrum of magnetostatic spin waves (MSW) are reported. The topography of the MCs that consist of two-dimensional (2-D) etched holes periodic structure in yttrium iron garnet films was studied by atomic force and magnetic force magnetometry. The propagation characteristics of spin waves in such 2-D MCs was measured and analyzed. 1. Introduction During the last decade considerable efforts have been made in the sciences and technology for controlling or engineering the optical properties of the materials. For example, a number of artificially arranged materials were engineered to facilitate light propagation in particular direction or in specific regions only. Such materials also enable light to be localized in chosen channels or zones, or even prohibit the propagation of light completely. They are now known as photonic crystals [ 11. Generally speaking, the photonic crystal (PC) is a material that possesses periodic index of refraction. A simple example of photonic crystals, also known as one-dimensional (1- D) PC is a multilayered periodic structure [2]. In such structures there exist a range of frequencies for which the light (photon) propagation is prohibited. It was also demonstrated that such crystals can be made in two and three dimensions [3]. Such structures can have a complete photonic band gap, meaning that light is prohibited to propagate in any direction inside such a crystal. To realize a PC with a complete photonic band gap, the material must have both high refractive index and proper three dimensional structure. Similar to PC, another class of crystals known as phononic crystals [4] was also reported. These crystals possess the properties of PC but for acoustic waves (phonons) instead of light. There exists, however, still another possibility to control properties of PC by using the magnetic materials for magneto-photonic crystals [5, 6,]. Moreover, it is possible to engineer magnetic materials where instead of light (or electromagnetic waves) spin waves (SW) are used as the carriers of information. Drawing an analogy from photonic and phononic crystals they may be called rnugnonic crystals (because magnons are the quasi-particles of spin waves). Magnetic 1-D periodic layered structures have also been studied for more than a decade since the giant magnetoresistive effect was discovered in the three-layer system containing the magnetic and non-magnetic layers ([7]). Propagation of spin waves in ferromagnetic films with periodically and weakly varied parameters has been studied extensively [%lo]. On the other hand the spectra of spin waves in multilayered magnetic structures have also been studied for various wave types (dipole and exchange) for magnetic-non-magnetic, all-magnetic, ferro- and antiferromagnetic lattices (see [ 11211 and references therein). In particular, the Green's function formalism was used for description of spin waves spectra in multilayered structures. Barnas [ 161 developed the transfer matrix approach for description of spin waves modes in 1 - D periodic structures. Gorobetz et a1 [ 17, 191 studied spectra in a stack structure with periodically modulated anisotropy. Ferromagnetic resonance and standing spin waves spectra in a multilayered stack consisting of ultra-thin Fe and Ni layers were also studied experimentally [13,20,21]. However, the resonance properties of a traveling spin wave 65
66
in such structure can differ considerably from that of standing spin wave modes. It has been demonstrated that such waves (at the wavelength of submicron) can be excited in inhomogeneous magnetic films at microwave frequencies [22]. Another possibility is to engineer an anisotropic magnetic photonic crystal [23]. A review paper on magnetic photonic crystal containing a detailed list of references was recently published [24]. In this work we treat the problem of spin wave propagation in periodic structures from the point of view different from those previously employed, namely, in the approach used in investigating the properties of photonic and phononic crystals. Therefore, we first review and calculate the spectra of MSW propagation in the 2-D ferromagnetic film periodic structure, and then implement the 2-D MCs and measure its propagation characteristics. 2. Theoretical part
The simplest one-dimensional magnonic crystal is a strictly periodic multilayer structure consisting of magnetic layers with different magnetizations, or a similar structure consisting of magnetic and nonmagnetic layers. The realization of such a structure is rather difficult, because the periodicity of the magnetic properties of layers can be violated in the course of the layer growth, which will break the magnonic crystal structure possessing a magnonic bandgap. From the point of view of application, a two-dimensional magnonic crystal formed on the basis of ferromagnetic films seems to be preferable. This crystal represents a ferromagnetic waveguide with two-dimensional magnetization inhomogeneities. The inhomogeneities can be represented by, e.g., implanted elements of another ferromagnet or holes made in the structure. We consider here properties of magnetostatic spin waves (MSW) propagating in a ferromagnetic film with two-dimensional periodically etched surface. Let us consider the upper surface of a ferromagnetic film described by the following equation x=d+L,(y,z), rne L,(y,z)= ds cos(uQz)(s~eiQY+&l * e-IQY), (1) where d is the film thickness, dlq 1 is the amplitude of the surface non-uniformity in Y direction, his1 is the amplitude of the surface non-uniformity in Z direction, & I * is complex conjugate to E I , Q=2n I A and A is the structure period in Y direction, ), u=A I 121, Al is the structure period in Z direction. In order to find the dispersion relation for MSW propagating in a ferromagnetic film with periodically uneven surface one should solve the set of Maxwell’s equations and Landau-Lifshitz equation for magnetization motion along with the boundary conditions for continuity of normal components of magnetic induction and tangential components of magnetic field at the surfaces of the film. The solution for magnetostatic potential and magnetic field, respectively, is found using the coupled wave method which was previously used for investigating of MSW propagation in 1D magnonic crystal (similar to the model of Kronig-Penney motion of electrons in a periodic potential) [24]. As a result of solution of a boundary problem the dispersion relation for a MSW propagating in a film with 2D non-uniformities was obtained as a function of various parameters (periods of the structure, external bias magnetic field Ho, etc). Most important thing was found that the dispersion of the wave contains forbidden gaps, where the wave propagation is prohibited. These forbidden gaps form zone structure in dependence of the structure parameters. In Figure 1 we show the dispersion of the wave closely to the resonance frequency defined by the so-called Bragg diffraction condition when the MSW wavenumber is
k
z
7T ~~
A ’
(2)
where A is the period of the 2D lattice in the direction of the wave propagation. The following parameters of the film and structure were chosen d = 9 pm, dlsll = djsl = 1 pm, A = 150 pm, HO= 380 Oe, C2 = 2.868 GHz (Bragg resonance frequency), saturation magnetization 4zMo = 1750 G and k, = Pl4, where P = d A and ky and k, are the wavenumbers of the MSW in the Y and Z directions, respectively. The difference between the resonance wavenumber with the smooth surface and the uneven surface is represented by 6. Figure 2 shows variation of the forbidden gaps width as a function of the structure period A, in the Z axis direction. It can be seen that at large structure period
67
(NAI< 0.25) two forbidden gaps are present in the spectrum. The width of the upper zone remains constant as the ratio between the periods varies. The width of the lower zone reduces and approaches to 0 as N A I approaches to 0. Thus, the dispersion of the MSW propagating in a ferromagnetic film with 2-D periodic structures contains forbidden gaps similar to that associated with the conventional photonic crystals. 2,9 , - - - -
Forbidden gaps width ~~~~~
N
2,78
I
(?
5
2,73
2E
2,68
c
x c
2,63
3 U
?!
2,58
LL
-
2,53-
-10
-5
0
5
10
6, 1 I CM (at k,=P 14) Fig. 1. Dispersion of the MSW for 2-D periodic structure for k, = P14.
kz / P
(kz / ky at ky=P=Q/2, 6=0 )
Fig. 2 . Variation of the forbidden zones width as a function of the ratio between the periods of the structure k,/P = MAI.
3. Experimental results
The MCs used in the experimental study was the ferromagnetic YIG film grown epitaxially on a nonmagnetic gadolinium gallium garnet (GGG) substrate. MSW can be easily excited in such films using microstrip transducers. Owing to the high quality of the films, the propagation loss should be fairly small, and the magnetostatic spin waves should propagate in these films without any significant attenuation within distances of many wavelengths. The 2-D periodic structure studied was facilitated with holes formed by etching. The diameter of the holes and their periodicity were taken to be close to a half-wavelength in order to satisfy the Bragg reflection condition. The area of the film was 1.5cm.0.5 cm, and the film thickness was varied from 5 to 16 pm. The 2-D periodic holes structures were formed in the films by the photolithographic technique involving the following procedure. A silicon dioxide layer was first deposited on the YIG film. The structure was then covered by a 1.3-pm-thick photoresist layer, which was insolated through a chromium mask with a periodic holes pattern. Two types of holes patterns were used: a square lattice and a hexagonal lattice. After exposure, silicon dioxide was removed by a mixture of hydrofluoric acid and ammonium fluoride (solution 1). Then, the remaining silicon dioxide lattice was used as a mask for etching of the YIG film in an aqueous solution of phosphoric acid and iron chloride (with a molar proportion of 49.4 : 49.4 : 1.2; solution 2 ) [26]. The etching time and temperature were chosen so as to etch the material through a thickness from 1.0 to 4.5 pm. After the etching step, silicon dioxide was completely removed by solution 1. The holes depth and the surface structure were studied by a three-dimensional optical rugosimeter and an atomic force microscope (D300 Digital Instruments and Solver P47H NT-MDT). Figure 3 shows the microphotographs of square and hexagonal etch patterns in the YIG films.
68
Fig.3. Microphotographs of the surface of 2-D magnonic crystals (MCs). a) Actual YIG sample, b) hexagonal lattice, c) cubic lattice.
Fig.4. Images of 2-D magnonic crystals (hexagonal and cubic lattices) taken with atomic force microscopy. a) hexagonal lattice structure, b) cubic lattice structure. The patterns were obtained using the polarizing optical microscope. The holes depth is about 4 pm, and the holes periodicity is about 50 pm. In addition, the film surface was also analyzed by a polarizing microscope. Figure 4 shows the micrographs of square and hexagonal etch patterns in the YIG films. These patterns were obtained using atomic force microscope. In order to investigate the MSW spectrum in the resulting 2-D MCs delay line devices were made. A typical delay line for the MSW is shown in Figure 5. The amplitude-frequency characteristics curves (AFC) of propagating MSW were measured. The MSW excitation band decreases by one order of magnitude for the wave propagating through the MC. In Figures 6 and 7 are shown the AFC dynamics at various value of bias magnetic field for the hexagonal structure with the holes depth tl=l pm and tl=2 pm. It is seen that as the magnetic field and the holes depths increase, the bandwidth and the amplitude of the MSW propagating through the structure decrease. The increased attenuation in the amplitude with the increase of the bias magnetic field is attributable to a couple of factors.
,
~
L=l-lOmm
-,
HO
1
2
Fig.5. Delay line used for measurement of MSW propagation in the YIG films. (Note that small rectangle designates the etched part of the YIG film, thickness 16 pm.)
69
2.1
2.3
2.5
2.7
2.9
3.1
Frequency. GHz
-10
-20
30
~
~
40
I' 3.3
3.5
3.7
3.9
4.1
20
-30
-40
3r -20
~30
-40
3.1
6:4
6.6
6:s
Frequency (GHz) 515
7
Fig.6. Amplitude-frequency characteristic (AFC) plots of propagating MSW in the YIG film with hexagonal lattice structure of etched holes (the etching depth is 1 pm) with the bias magnetic field Ho as a parameter.
Fig.7. Amplitude-frequency characteristic (AFC) plots of propagating MSW in the YIG film with hexagonal lattice structure of etched holes (the etching depth is 2 pm) with the bias magnetic field Ho as a parameter.
70
First, as the magnetic field increases the dispersion of the propagating MSW also changes, namely, the frequency band narrows and the group velocity decreases. Therefore, the propagation losses increase. The second factor has to do with is scattering of the MSW by the periodic structure at the Bragg reflection condition. In the case of the hexagonal lattice, Ahex= 74 pm, and in the case of the cubic lattice, /Icuh = 37 pm (see Figs. 3b and 3c). The corresponding wave numbers of the MSW that satisfy the conditions Eq. (2) are k,, = 400cm-' and kcub = 800 cm-I, respectively. Using the delay line configuration of Fig. 5 the MSWs with these wave numbers were readily excited (see Fig. 8). The band B2 shown in Figs. 6 and 7 indicates that this condition was fulfilled for the MSW propagating in the structures. Now, let us examine the experimental data for the case of MSW propagation in the cubic structure. Fig. 9 shows the measured AFC and the phase-frequency characteristic (PFC) plots at the bias magnetic field Ho = 800 Oe under different orientations between the antennas and the etched structure. The anglea designates the angle between the MSW wavevector ff and the lattice axis. It can be seen from Fig. 9a that when the pair of antennas were located outside the YIG film with the 2-D lattice neither AFC nor PFC showed any distinct features. The dispersion obtained in this case is typical for the MSW. However, when one or both antennas were located within the YIG film the bands BI and B2 appeared in the spectra (see, e.g. Figs. 9 c, d). A few observations are now in order with respect to the B2 band. 1) The band B2 appeared at some value of the angle a for some range of the ratio G between the areas of the etched and unetched parts of the YIG film located between the antennas. Increase in the portion of the etched area led to increase in the MSW losses within the whole frequency spectrum. This increase in propagation loss has made it impossible to register the band B2 observed previously. 2) When the band B2 was registered at a given angle a and the etched area between the pair of antennas was increased the depth of the band increased as well. This dispersion is most important because it shows that the band B2 is not caused by the interference between the incident and reflected MSWs from the boundary of the YIG film or the 2D periodic structure. It should also be noted that the shapes of the AFC and PFC plots were practically unchanged as the propagation direction of the MSW or the direction of the bias magnetic field was varied. At the placement of the microstrip antennas shown in Fig. 9b, the band B2 appeared in both the AFC and the PFC plots. The B2 band corresponds to the 55-th interference peak of PFC. Based on the first minimum the distance between the antennas 4 mm, and the MSW wavelength, the wave number was calculated to be k=15.7 cm-'. Then for the 55-th minimum the calculated wave number was k=860 cm". As the angle a w a s varied ( a < 15') the band B2 was seen to move to the longer wavelength or the lower frequency of the MSW. As the axis of the 2-D structure was rotated with respect to the MSW propagation direction at the angle a=15" the lower frequency edge of the minimum in the PFC plot corresponding to the 28-th interference minimum or the wave number of 440 cm-I. The measured half-width of the minimum peak is equal to 16 MHz. The location of the minimum and its frequency width changed continuously as the angle a increased. For example, the minima edges at the angles a=5" and 10" occurred at the 46-th (k=720 C M - ~and ) the 39-th (k= 610 cm-') minima in the PFC plot and the half-width of the minima was increased to 20 MHz. The above experimental results can be interpreted most simply for the angles
a = 0 anda = 45'. In these cases due to the symmetry involved the MSW propagates normally to the 2-D periodic structure and the Bragg condition Eq. ( 2 ) was fulfilled. The periodicity of the cubic =37 pm at the angle a=O.The MSW wave number corresponding to Eq. ( 2 ) is lattice is kcub Y 849 cni'. This wave number corresponds to the 55-th minimum in the PFC plot (Fig. 9b). Similar results are obtained with the case in which the MSW propagates at the angle a=45'. In view of the fact that the existence of the band B2 was caused by the Bragg reflection we may conclude that in the vicinity of the Bragg resonance condition frequency bands that forbid propagation of the MSWs can be engineered. Within these forbidden bands, reflection of the microwave power from the input antenna increases.
71
3,2
o
200 400 600
aoo
10001200
Fig.8. Measured (dots) and calculated (continuous curve) dispersion relations of the propagating MSWs in the YIG magnonic crystals.
Wave Number q , cm-'
h
?i
;
-20-
B L
3.9
4 .O
Frequency f (GHz)
4.7
4.3
3.9
4.7
4.3
4.7
4.7
Fig.9. Measured amplitude-frequency and phase-frequency characteristic (AFC and PFC) plots for the YIG film with the cubic lattice structure at different angular orientations between the microstrip antennas and the etched portion of the film (the bias magnetic field was set at 800 Oe). The above property in turn results in weaker MSW excitation and increase in the standing wave ratio. The above dispersive characteristics were clearly observed in our experimental results. Finally, we shall compare the propagation losses of the MSWs in the YIG film with hexagonal and cubic lattices at the same depth of the holes tl=l pm. It is clearly seen that at a bias magnetic field H d l 0 0 0 Oe the cubic lattice incurs a higher propagation loss. This increase can be attributed to the higher non-uniformity of the YIG film surface. As it is seen in Figures 3 and 4 the
72
cubic lattice is more compact and the etched holes are almost adjoined in the directions of the main lattice axes. 4. Conclusion
The propagation characteristics of the MSWs in the YIG film with 2-D periodic holes structures have been studied both theoretically and experimentally. The 2-D periodic structures serve to alter the MSW propagation conditions. The spectra of MSW propagating in the YIG film with 2-D periodic structures of surface non-uniformities are calculated. The degree of alteration in the propagation conditions is determined by the parameters of the 2-D structure: etching depth of the holes, structure type and holes density. The forbidden gaps found in the frequency spectra are attributable to Bragg reflection of the MSW from the surface periodic structures. Such ferromagnetic films with 2-D structures for control and processing of microwave spin waves are direct analog of the conventional photonic crystals for optical waves. They are thus called magnonic crystals (MCs). Further investigations of this new type of photonic crystals are in progress. This work was supported by the Russian Foundation for Basic Research, projects nos. 05-02-17361, 04-02- 17537.
References J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light 1. (Princetone University Press, Princeton, 1995). 2. M. Jacoby, Chem. Eng. News 76 (47) (1998) 38. 3. B. Grant, Photon Spectra 33 (5) (1999) 33. 4. I.E. Psarobas, N. Stefanou, A. Modinos, Phys. Rev. B 62 (2000) 5536. 5. M. Inoue, K.I. Arai, M. Abe, T. Fujii, S. Fan, J.D. Joannopoulos, J. Magn. SOC.Jpn. 23 (1999)1861. 6. M. Inoue, T. Fujii, J. Appl. Phys. 85 (1999) 5768. 7. G.A. Prinz, J. Magn. Magn. Mater. 200 (1999) 57. 8. C.G. Sykes, J.D. Adam, J.H. Collins, Appl. Phys. Lett. 29 (1976) 388. 9. Yu.V. Gulyaev, S.A. Nikitov, V.P. Plesskii, Sov. Phys. Solid State 23 (1981) 724. 10. R.E. Camley, T.S. Rahman, D.L. Mills, Phys. Rev B 27 (1983) 26 1. 11. C. Vittoria, Phys. Rev. B 32 (1985) 1679. 12. R.P. van Stapele, F.J.A.M. Greidanus, J.W. Smith, J. Appl. Phys. 57 (1985) 1282. 13. K. Vaihinger, H. Kronmueller, J. Magn. Magn. Mater. 62 (1986) 159. 14. L. Dobrzynski, B. Djafari-Rouhani, H. Puszkarski, Phys. Rev. B 33 (1986) 3251. 15. R.E. Camley, M.G. Cottam, Phys. Rev. B 35 (1987) 189. 16. J. Barnas, Phys. Rev B 45 (1992) 10427; J. Phys.: Cond. Matter 4 (1992) 4849. 17. Yu. I. Gorobetz, A.E. Zyubanov, A.N. Kuchko, K.D. Shedzhuri, Sov. Phys. Solid State 34 (1 992) 790. 18. M.S. Erukhimov, G.M. Erukhimov, B.E. Berenshtein, Phys. Solid State 36 (1994) 886. 19. Yu. I. Gorobetz, A.N. Kuchko, S.A. Reshetnyak, Phys. Solid State 38 (1996) 315. 20. R. Krishnan, C. Sella, H. Kaabouchi, B.A. Acharaya, S. Prasad, N. Ventkatraman, J. Magn. Magn. Mater. 104-107 (1992) 1882. 21. R. Kordecki, R. Meckenstock, J. Pelzl, H. Muhlbauer, G. Dumpich, S. Nikitov, J. Appl. Phys. 70 (1991) 6418. 22. P.E. Zilberman, A.G. Temiryazev, M.N. Tikhomirova, JEPT 8 1 (1 995) 151. 23. A. Figotin and I. Vitebsky, Phys. Rev. E 63 (2001) 066609. 24. I.L. Lyubchanskii, N.N. Dadoenkova, M.I. Lyubchanskii, E.A. Shapovalov, Th. Rasing, J. Phys. D: Appl. Phys. 36 (2003) R277. 25. S.A. Nikitov, Ph. Tailhades, C.S. Tsai, J. Magn. Magn. Mater. 236 (2001) 320. 26. Yu.V. Gulyaev, S.A. Nikitov, L.V. Zhivotovski, A.A. Klimov, Ph. Tailhades, L. Presmanes, C. Bonningue, C.S. Tsai, S.L. Vysotsky, Yu.A. Filimonov, JETP Lett., 77 (2003) 567.
Giga-Hertz Conducted Noise Suppressors of Ferrite Films Prepared From Aqueous Solution Masanori Abe*, Masaru Tada and Nobuhiro Matsushita Tokyo Institute of Technology, Japan *amasanor@,pe.titech.ac.ip Koichi Kondo, Hiroshi Ono and Shigeyoshi Yoshida NEC Tokin Corporation, Japan
Abstract To secure stable operation of high-speed mobile cellular phones and mobile computers, we have developed novel GHz conducted noise suppressors using Ni-Zn ferrite films. The films are synthesized from an aqueous solution at low temperatures (< 9OOC). The films are deposited directly onto printed circuit boards, which we call “direct deposition type” noise suppressors. Or, they are deposited onto polyimide sheets, which are cut and attached onto noise sources and are called “sheet type” noise suppressors. Noise currents are dissipated due to magnetic losses of the ferrite films, and thus, noise electromagnetic waves are not radiated to the space. The directdeposited type, using Ni-Zn ferrite film of 3pm thickness, exhibited a strong transmission loss of 40 to 70% at 1.5-lOGHz, which far exceeded that obtained for commercial composite sheet type of noise suppressors (50 pm thick), in which fine ferromagnetic flakes are dispersed in a polymer matrix. The sheet type suppressor using Ni-Zn ferrite film of 5pm thickness exhibited stronger transmission loss and weaker reflection loss than those obtained for composite sheet type noise suppressor of50 pm thickness.
73
Microwave composites filled with thin ferromagnetic films. Part I. Theory A. N. Lagarkov, A. V. Osipov, K. N. Rozanov*, and S. N. Starostenko Institute for theoretical and applied electromagnetics, Russian academy of sciences, 13/19 Izhorskaya ul., 125412 Moscow, Russia *email:
[email protected] Abstract. The microwave permeability of composites filled with pieces of film-shaped ferromagnetic inclusions with small thickness and in-plane anisotropy is studied. A rigorous derivation is presented of Acher’s constraint for microwave permeability of composites. The effect of eddy currents on the microwave magnetic performance of ferromagnets is discussed. Simple equations are introduced that are useful for estimating this effect. The composites under consideration are shown to be advantageous magnets for microwave applications. The results obtained are used in Part I1 of the paper where the microwave permeability of composites filled with pieces of thin ferromagnetic films is studied experimentally. 1 Introduction Materials with high microwave permeability and low magnetic loss are needed for many technical applications, such as high-frequency inductors, magneto-dipole antennas, radar absorbers, etc. [l-41. In magnets, complex permeability p=,u’+i,u’’ is close to the static permeability, f i , at frequencies up to the ferromagnetic resonance frequency, f,, which can be considered as the permeability cutoff frequency. Therefore, the microwave permeability is large, when both ,usandf, are high. However, it is well known that these values are related tightly to each other: higher leads to lowerf,, and vice versa. For bulk magnets, the relation is established by Snoek’s law: (1) (,us - f, = (2/31 Y 4 n ~ , with the saturation magnetization 4EMo and p 3 GHzkOe. For thin films with in-plane magnetic anisotropy, an analogueof Eq. (1) governing the largest component of permeability is given by [J, 61: (2) (,us- 11.fr” = (Y47%j>* ’
11.
Equations (1) and (2) relate the microwave performance to the magnetostatic properties of magnets. Since the right parts of both equations depend on 4nM0, ferromagnets are advantageous over ferrites in their microwave performance due to higher saturation magnetization. Equation (2) permits higher static permeability compared to Eq. (1) with the same resonance frequency provided thatf, is not too high. For example, with 4zM0=2.15 T that is typical for Fe andf,= 3 GHz that is suitable for most applications, Eqs. (1) and (2) yield psFZ 14 and ,us= 400, respectively. Therefore, the ferromagnetic films may have the highest microwave permeability values of all magnets. However, most applications require bulk samples. The microwave magnetic performance of bulk ferromagnets is deteriorated by the effect of eddy currents [7], since all ferromagnets are conductors. The effect of eddy currents may be eliminated, when the bulk sample is a composite filled with ferromagnetic film-shaped inclusions, or flakes, of thickness less than the skin depth. The theory of composites filled with ferromagnetic flakes is considered in [5, 6, 81 based on a simple model of single-domain ellipsoidal inclusions in composite. In [9], a generalization of Eq. (2) is proposed to the case of magnetic composites. This equation provides a higher bound for microwave permeability of composites and will be referred to as Acher’s constraint below. In this paper, Acher’s constraint is rigorously derived and the effect of eddy current is considered on the microwave performance of composites filled with ferromagnetic flakes. The results are exploited in Part I1 of the paper, where microwave permeability of such composites is studied experimentally. 2 Acher’s law for composites For a composite comprising thin film-shaped inclusions with in-plane anisotropy, Acher’s constraint
74
75
is given as [9]:
where f is the frequency, p is the volume fraction of the inclusions, and k is a factor accounting for the orientation of magnetic moment in inclusions relatively to the microwave magnetic field. For composites with random orientation of inclusions, k=113. Uniform orientation of film planes and random orientation of easy axes of magnetic anisotropy in the planes yield k=1/2. If all inclusions have collinear easy axes that also implies uniform orientation of inclusions, then k=l. In the last two cases the sample has anisotropic permeability and Eq. (2) governs its largest component. Equation ( 3 ) is a generalization of Eq. (2) to the case of magnetic composites with an arbitrary dispersion law. The same as Eq. (2), it may be used for estimating the microwave magnetic performance of composites. If the thickness of inclusions is not small compared to the in-plane dimensions of these, an additional term is involved in the right part of Eq. ( 3 ) , which is dependent on the demagnetization factors of inclusions [9]. In this case, the actual microwave permeability of composite is lower than it follows from Eq. ( 3 ) and can not be predicted from the magnetostatic properties of inclusions. Equation ( 3 ) has been introduced in [9] by heuristic consideration and has been successfully employed in the analysis of frequency dependencies of microwave permeability [lo]. The rigorous derivation of Eq. ( 3 ) is given below. The derivation is based on the approach discussed in details by Fano [ 111 for obtaining integral relations involving response functions. According to the Cauchy theorem, for any analytic function F,
See [12], where this approach is applied to the derivation of Kramers-Kronig relations. Put F=@l) and assume that the magnetic dispersion of the film fits to the Lorentzian dispersion law,
where the partial static susceptibility xs,i,resonant frequency h,i,and relaxation frequency fd,i are attributed to i-th Lorentzian term. Let the imaginary part of Eq. (4) be considered, then the integrand is an even function of frequency. The high-frequency asymptote of the permeability that is involved in the right part of Eq. (4) follows readily from Eq. ( 5 ) as:
Dispersion law ( 5 ) may include many Lorentzian terms with different parameters due to possible distribution of properties of the magnet, the effect of domain structure, etc. However, Eq. ( 3 ) is valid for each of these with the right part dependent on the saturation magnetization only. Therefore, the right part is the same for all Lorentzian terms and Eq. ( 3 ) is valid for a ferromagnetic film with an arbitrary dispersion law. In composites, if the permeability of inclusions is close to the permeability of the host matrix, the Landau-Lifshitz-Loyenga mixing rule is known to be valid [ 121. Since p+l atf-m, this is the mixing rule governing the high-frequency asymptote of permeability for any composite. For a composite that comprises inclusions with the permeability p, and a non-magnetic host matrix, it reads: p=(i+p(p;/3-1))?= l + p ( p i - 1 ) . (7) Therefore, the high-frequency susceptibility of a composite is just proportional to the susceptibility of inclusions with a factor ofp. By combining this with Eq. (6), we arrive at Eq. (3).
76
The derivation reveals the validity conditions of Eq. (3). First, the application of Eq. (4) implies that the integrand is an even fhction of frequency, has no poles in the lower semi-plane of complex frequencies, and is proportional to llfat f+m. The first two conditions are the consequence of fbndamental properties of permeability; the last one is true only if the permeability is governed by the Lorentzian dispersion law ( 5 ) with finite resonance frequencies. IfJ-m, which results in the Debye dispersion law, the integrand tends to an imaginary constant at f+m and the integral diverges. One more example of the divergence is provided by the dispersion law following from the Landau-Lifshitz-Gilbert equation, which also produces the susceptibility proportional to iif at f+m. In addition, the integral may diverge due to the effect of eddy currents, as is discussed in the next Section. Second, the derivation is based on the Landau-Lifshitz-Loyenga mixing rule. Therefore, the permeability of inclusions is implied to be independent on the morphology of the composite. However, this assumption may be wrong for film-filled composites. Indeed, an increase of p in a film-filled composite up to p=l results in a bulk material, which does not retain the properties of films. The reason is that the concentration and microscopic structure of composite may affect the demagnetization factors of inclusions, which, in turn, has an effect on the ferromagnetic resonance of the inclusions and, therefore, alters the intrinsic permeability [8]. Hence, Eq. (3) holds for diluted film-filled composites only. When the concentration of inclusions is high, the actual microwave performance of the composite must be worse than that predicted by Acher’s constraint due to the effect of demagnetization of inclusions. 3 The effect of eddy currents Let us assume that the intrinsic permeability of the film, pi, is governed by the Lorentzian law ( 5 ) and consider distortion of the magnetic dispersion law due to the effect of eddy currents. It is well known that the effect may be accounted for by the renormaliztion of the permeability. In the case of a film with the microwave magnetic field being parallel and the wave vector being normal to the film plane, the renormalization yields ap arent permeabili p given by [ 131: tank +i l d , , z / J (8) P = Pi (1 + i ) z d m / c ’
where c is the velocity of light, and oand dare the film conductivity and thickness, respectively. The fi-equency-dependent behavior of the permeability is determined by the poles of the Lorentzian dispersion curve (9,?J,i+$,f/(2fd,i). Similarly, the frequency dependence of the renormalized permeability (8) is determined by the poles of the right part of Eq. (8) found as the complex frequencies, at which the argument of tangent is equal to d2. It readily follows that the effect of eddy current transforms each Lorentzian pole of the intrinsic permeability into an infinite set of poles of the apparent permeability, the Lorentzian parameters of which are given by:
where n=1,2, ...,a and the intrinsic permeability is assumed to possess a narrow magnetic absorption band, fr,,'
Fig. 1. Influence of mechanical loading on: (a) Hysteresis loops; (b) Butterfly loops. phenomenon can be explained by the switching criterion proposed by Hwang et al. [8]. o~AE + E~ i q 2 24.Ec
(1) where q and are the stress and strain tensors, respectively; Ei and Pi denote the components of electric field and polarisation in the ith-direction;Pi is the spontaneous polarisation and E, is the coercive field strength. Since the boundary is not clamped and both the mechanical and electric loading are in the x-direction, the criterion can be simplified as follows: o,AE, f E x W x2 24,Ec (2) For 90" switching from negative x to y-direction, A P, = P, is a fixed value and A E, < 0. The external applied compressive loading increases the mechanical work in the switching criterion given by Eq. (2), while the total work needed for polarisation switching is constant. Therefore, the
105
electrical work is decreased and so does the coercive field. The tensile case can also be explained in the similar manner. With reference to Fig. 1, the polarisation switching in the case of compressive loading is composed of two separate 90" switching. In this section, the simulation is repeated but the compressive -16) to study the separation of switching, as loading is increased to a sufficiently high level (o$*= shown in Fig. 2. The domain structures corresponding to points A-F are illustrated in Fig. 3(a-f). The evolution of the hysteresis loop starts from the twin-likes structure Fig. 3(a). At the beginning, since the electric field is very small, the evolution is predominated by the compressive loading. It can be seen from Fig. 3(a, b) that the 90" switching induced by the compressive loading occurs from the x to the y-direction and the domains of horizontal orientation shrink significantly, which leads to the decrease of macroscopic polarisation and strain in the x-direction, as shown in Fig. 2. As the electric field increases, the electric strength prevails over the compressive loading. Therefore, the domains of horizontal orientation begin to recover, as shown in Fig. 3(c, d). This explains the growth of macroscopic polarisation and strain in Fig. 2. As the electric field continues to grow and exceeds the coercive point, the crystal is polarized by the electric field and only uniform polarisations exist, Fig. 3(e). Once the peak point E is reached, the electric field begins to decrease. Due to the compressive loading, the first 90" switching occurs very early in a positive field, after which all the polarisations are in the y-direction, as shown in Fig. 3(f). Hereafter, although the electric field keeps decreasing, the polarisations and strain seem unaffected. This state is maintained till the electric field is increased to the second critical point, which is sufficient to countervail the negative mechanical work and cause the second 90" switching to occur. 006
I0
005 0 04
05 053
Pi
om O0
EX
0 01
45
_......'...-
-1 0
003 -0 0 1
402 -
4
.
3
.
2
-
1
0
':E
1
2
3
4
- 4 - 3 - 2 . 1
0
z
2
Ee.'
Fig. 2. Separation of polarisation switching in: (a) Hysteresis loop; (b) Butterfly loop.
Fig. 3. Domain structures that correspond to points A-F in Fig. 2.
3
4
106
4. Conclusions Two-dimensional phase field simulations of hysteresis and butterfly loops in ferroelectrics subjected to electro-mechanical coupled loading were conducted. The temporal evolutions show that the mechanical loading can influence the symmetry of hysteresis and butterfly loops by the stress-induced 90" switching. Compressive stresses can separate the polarisation switching process into two stages, each of which corresponds to a 90" switching. In the first switching, the compressive stresses do a positive work that leads to the switching. While in the second switching, the compressive stresses do a negative work that retards it. Moreover, due to the eigenstrain induced by polarisation switching and the elastic strain caused by the mechanical loading, the symmetry of butterfly loop can be affected by the coupled electric-mechanical loading. In summary, the phase field simulation method can give insights to the understanding of domain structures and the ferroelectric macroscopic properties. References [l] Lu W, Fang DN, Li CQ, Hwang KC. Acta Mater 1999; 47:2913. [2] Landis CM, McMeeking RM. Ferroelectrics 2001; 255:13 [3] Huber JE,Fleck NA, Landis CM, McMeeking RM. J Mech Phys Solids 1999; 47:1663. [4] Hwang SC, McMeeking RM. Ferroelectrics 1998; 2 11:177. [5] Hwang SC, McMeeking RM. Int J Solids Struct 1999; 36:1541. [6] Li FX, Fang DN. Mech Mater. 2004; 36:959. [7] Sahota H. Continuum Mech Therm2002; 16:163. [8] Hwang SC, Lynch CS. McMeeking RM. Acta Metal1 Mater 1995; 43:2073. [9] Wang J, Shi SQ, Chen LQ, Li Y, Zhang TY. Acta Mater 2004; 52:749. [lo] Chen LQ. Annu Rev Mater Res 2002; 32:113. [ l l ] Nambu S, Sagala DA. Phys Rev B 1994; 50:5838. [ 121 Hu HL, Chen LQ. Mat Sci Eng A 1997; 238: 182. [13] Hu HL, Chen LQ. J Am Ceram Soc 1998; 81:492. [14] Li YL, Hu SY, Liu ZK, Chen LQ. Appl Phys Lett 2001; 78:3878. [ 151 Haun MJ, Furman E, Jang SJ, Mckinstry HA, Cross LE. J Appl Phys 1987; 62:333 1. [16] Pertsev NA, Zembilgotov AG, Tabantev AK. Phys Rev Lett 1998; 80: 1988. [17] Chen LQ, Shen J. Comput Phys Commun 1998; 108:147.
Intrinsic limit of dielectric loss in B a ( M g 1 , ~ T a ~ /and ~ ) 0 Ba(Mg,,3Nbz,3)03 ~ ceramics T. Kolodiazhnyi* Natzonal Instztute for Matenals Sczence, Tsukuba, 305-0044, Japan
G. Annino Istztuto per i Processi Chimico-Fiszci, CNR., Pisa 561 24, Italy
T. Shimada R&D Center, NEOMAX Go., LTD. Osaka, 618-0013, Japan A whispering gallery mode (WGM) spectroscopy is employed here to study the dielectric constant and tan6 of several Ba(Mgl/3Ta2/3)03and Ba(Mgl/,Nh2/3)03ceramics in the frequency range of 10 - 100 GHz and temperature interval of 5 - 295 K. Below SO GHz, the room-temperature extrinsic dielectric losses manifest themselves by a sub-linear tan6 wersus frequency dependence until intrinsic losses start to dominate the spectra above SO-70 GHz. Based on these data we obtained the roomtemperature intrinsic limit of dielectric loss of BMT and BMN at Qxf = 4S0*5 THz and 250*4 THz, respectively. Among the numerous sources of extrinsic dielectric loss, the lattice point defects and second phase are found to be the most detrimental for the Q-factor. In an attempt to gain an insight into a point defect chemistry of these compounds we present first results of electron spin resonance and magnetic susceptibility measurements of Ba(B’1/3B’’2/3)03,where B‘ = Mg, Zn, Ni, Co and B“ = Nh and Ta. Keywords: Dielectric resonators, WGM spectroscopy, lattice defects, magnetic properties
I.
INTRODUCTION
Over the last 30 years, considerable research activity was dedicated to the origin of the dielectric loss in the low-loss microwave dielectrics.’ As revealed by the FIR spectroscopy‘ and latter confirmed by the microwave studies at cryogenic temperature^,^ the major contribution to the dielectric loss of commercial low-loss dielectric ceramics has an extrinsic origin. In other words, in most cases the losses due to the crystal imperfections (e.g., lattice disorder, point defects, dislocations, grain boundaries, second phase) dominate over intrinsic loss due to the two-phonon-difference a b ~ o r p t i o n . ~ Although ,~ preliminary results on the crystal imperfections are traditionally obtained by the standard analytical tools, such as XRD, SEM and TEM, the analysis of the point defects and lattice disorder a t the ppm level in the high-Q dielectric ceramics obviously requires a novel approach. Unlike the simple ternary A2+B4+03perovskites, the point defect chemistry of the complex Ba(B11/3B”2/3)0s perovskites is largely unknown. However, taking into account a densely packed perovskite structure, the Frenkel defects are usually ignored and only Schottky disorder is considered. This assumption is justified by a well established defect model of the A2+B4+03 compounds; in particular SrTiOs and BaTi03, where B-site cation is even smaller than the B‘ and B” cations studied in this paper. The first-principles calculations show that the 1:2 ordering of the B-site cations along the directions minimizes the concentration of the underbounded oxygens in the B’ -0-B‘ environment^.^ The 1:2 ordering also leads to the expansion of the B’Os octahedron and contraction of the B“O6 octahedron.” The calculated density of states (DOS) indicates some degree of cova-
lent bonding between the oxygens and the B” cations whereas the 0-B’ bonds remain purely ionic.” The difference in the effective charges of the B-site cations and their bonding to oxygens in the Ba(B’”3B’‘2p)03 compounds would result in quite different formation energies of the B’ and B“ vacancies. In thermodynamic equilibrium, the concentration of these defects would increase exponentially with temperature.” From a simple defect chemistry consideration, one can expect that in addition to the substitutional defects (i,e., BL,, and B;,) there are 51 type of potential Schottky point defects and binary defect complexes in the Ba(B’lj3B’’2/3)03 compounds. Considering various ionization state, the single point defects will include for example, [VtJ, [VA,], [VjJ, [Vg,],
[VL,], [V;;,], [v;,,], [V&], [v;;,t], [v;;;,];:,], [V$], [v;;:;’], [V,], [lib],[V&].Hereafter a KrOger-Vinkl3 notation for lattice defects is used. It can be expected, based on the defect model of ternary perovskites, that at sufficiently high temperatures, e.g., 1000 “C, single point defects will not interact with each other. However, at lower temperatures a partial association of these defects into binary defect complexes, such as [VtaVg], [VtaVh], [VtaV6], [VA,V,X],etc., must be taken into account. There is a high probability that some of these defects will have an unpaired electron spin, thus making them ESR-active. Hence, by applying spin-sensitive techniques it. would be possible to detect and characterize trace amounts of these lattice defects. In this contribution we outline several methods of analysis of the early stages of the lattice disorder in the Ba(B’”3B’’2/3)03 complex perovskites.
107
108 11.
EXPERIMENT
Samples of compositions given in Table 1 were prepared by a solid-state method from metal oxides and carbonates of 99.99 % purity. The mixtures were calcined at 95s1200 "C in air for 20 h. The obtained powders were milled for 24 h, pressed into pellets and sintered at 12YU - 1700 "C in air or forming gas (7% HS /93% Ar). After synthesis, the obtained samples underwent a standard materials characterization procedure including XRD (Rigaku Ultima 111), SEM (Hitachi equipped with EDS) Dielectric properties were measured at 10 GHz (TE016 mode) using HP 8510 vector network analyzer and at 20 -100 GHz (WGE and WGH whispering gallery modes) using an ABmillimetre vector network analyzer. The whispering gallery modes (WGM) technique employed for the dielectric characterization of the samples is an extension of the approach discussed in Ref.14 A detailed analysis of this millimeter wave WGM spectroscopy will be presented elsewhere. Magnetic susceptibility of selected samples was measured in the 5 - 300 K range by means of superconducting quantum interference device, SQUID (Quantum Design). The electron spin resonance (ESR) studies were performed on Bruker ELEXSYS E580 X-band ESR spectrometer (courtesy of Bruker-Biospin, Tsukuba). For comparative ESR analysis, the weight of the powdered samples waa kept at 5050.1 mg. The measurements were performed in the frequency range of 9.8 - 9.9 GHz at a constant microwave power of 2 mW.
111.
RESULTS AND DISCUSSION
It is accepted that the lowest limit of the dielectric loss at the microwave (MW) frequency (10 GHz) can be estimated from the extrapolation of the tans from the far infrared.I5 It is speculated that this method allows fast screening of the DR candidates bypassing a time consuming optimization of ceramics. However, this approach suffers from the two major drawbacks. First, it appears to he not accurate enough due to the extrapolation over the 2-3 decades of frequency, and second, it still requires well processed ceramics with negligible extrinsic dielectric loss at the far infrared.I6 Fig. 1 shows frequency dependence of the room temperature dielectric properties i.e., E and tan6 of Ba(Mgl/3Taz/3)03(BMT) ceramics. The MW and millimeter data were obtained from the same dielectric material. The SMM data of Murata ceramics at 300 GHz were taken from Ref." As revealed from our millimeter data obtained from the whispering gallery dielectric resonator, the change in the slope of the tan6 versus frequency from 0.49 to 1.0 at ca. 70-80 GHz indicates that intrinsic dielectric loss in the well processed Ba(Mgl/3Ta2/3)03 takes over extrinsic one above 80 GHz. Extrapolation of the FIR data of Sagala" down to the 10-300 GHz seems to agree fairly well with both the sub-millimeter data of
loo 10 r IF
L a
g
SMM (PeQell)
0.1 r
FIR (Swede)
..... 0.01 r
FIR (shimaaa)
. .......
1E-3 r 1 E-4
Frequency, cm'
FIG. 1: RUUIII temperature t' and tan6 of Ba(Mgl /nTaz/3)Os. The SMM data are from Ref.". The FIR d,ta are-from
Petzelt" and our millimeter data of the WGH,,o,o whispering gallery modes, where 3111115. The only disadvantage of the factorized representation of the dielectric function is an erroneous (negative) value of the tan6 that often appears in the part of the extrapolated r e g i ~ n . ~ ' With an exception of the Ni- and Cc-containing dielectric resonators that show strong paramagnetism, the rest of the dielectrics studied here are normally diamagnetic. Any deviation from the temperature independent diamagnetic behavior would indicate that the material contains lattice defects with a non-zero magnetic moment. The effect of sintering temperature on the molar magnetic susceptibility, zrn of Ba(Mgl/3Ta2/3)03is shown in Fig. 2. A strong temperature-dependent contribution to the xrn comes from the paramagnetic lattice defects at the low temperatures. The concentration of the lattice defects increases exponentially with processing temperature and so does the low-temperature xh. At sufficiently high temperatures, xrn levels off at ca. -49.6~ 10W6 cm3/mol. The calculated molar magnetic cm3/mol which is susceptibilityzuof BMT is - 7 8 . 3 10@ ~ significantly lower than the measured value. This result is in accord with the first-principles calculations" showing that the purely ionic picture of BMT is not valid and some covalent bonding between the 0-21, and Ta-Sd orbitals generate additional paramagnetic contribution to the xrn. The room temperature ESR signals associated with the paramagnetic lattice defects were detected in all but Ba(Co1/3Nb2/3)03samples. The BMT and BMN spectra showed a qualitatively similar behavior and only the
109
t 1570 OC (Pxf =280 THz)
t 1600°C (Qxf=l80 THz) t165O0C(Qxf=50THz)
50
0
150
100
200 250
300
Temperature, K
FIG. 2: Effect of processing temperature on the molar magnetic susceptibility of Ba(Mgl/3Ta2/3)03.
of the Mn2+ sextet in the spectra. Mn was present as a trace impurity in the precursors. Annealing of BMN in the forming gas removes the central ESR feature and also significantly enhances the Mn2+ signal. At high oxygen partial pressure, Mn has an oxidation state of +4 and occupies the B" sites of the the Ba(B'1/3B''2/3)03 compounds. An increase in the Mn2+ signal at higher processing temperatures indicates that Mn starts to substitute the B' cation. High-temperature reduction of ceramics at low oxygen partial pressure further increases the concentration of Mn2+ via the formation of the [Mn2N+b V6]complex. The paramagnetic center with g = 1.997 is ascribed to the lattice defect with a trapped hole. Upon reduction of ceramics, the g = 1.997 signal disappears due to the upward shift of the Fermi level. Our preliminary study on the non-stoichiometric BMN indicates that the g = 1.997 signal is associated with a singly ionized barium vacancy. The ESR spectra of the Mott-Hubard insulators, BNT and BNN, revealed somewhat different behavior of the lattice defects. In the case of BNN, strong and broad ESR signal associated with the Ni3+ impurity progressively increases with processing temperature from 800 "C to 1350 "C (Fig. 4). In contrast t o BNN, the rel-
ESR spectra of BMN are discussed here. The effect of processing temperature and the annealing atmosphere on the ESR spectra of the BMN is shown in Fig. 3. There is .
1350°C
BNN 800 OC BNN 1000°C BNN 12OO0C
BMN 1000°C
-BNN
135OoC
BMN 12OO0C BMN 15OO0C
g=1.997
__
x c
w
_
._
tc. v)
w ,
2000
t,
I
2000
.
M"2+ I
.
'
I
4000 Field, Gauss
3000
.
I
5000
,
I
FIG. 3: ESR spectra of Ba(Mgl/3Nb2/3)03 processed at various temperatures. The spectrum of the BMN annealed in the forming gas is shifted down for clarity.
a progressive increase of the ESR singlet with a giromagnetic constant of g = 1.997 as a processing temperature
increases from 1000 "C to 1500 "C. Development of the g = 1.997 signal is also accompanied by the appearance
3000 4000 5000 Field, Gauss
FIG. 4: ESR spectra of Ba(Ni1/3Nb2/3)03 processed at various temperatures.
atively weak Ni3+ signal increases in BNT only up to T = 1400 "C (Fig. 5). At higher processing temperature, the Ni3+ signal decreases which is accompanied by the appearance of a new singlet at g = 2.000. Obviously, the g = 2.000 lattice defect that develops at higher temperatures suppresses the concentration of Ni3+ in BNT. This may partially explain much higher Q-values of the BNT as compared to the BNN.'l More results on the ESR spectroscopy of the Ba(B'1/3B''2/3)03 compounds will appear in a separate publication.
110 IV. CONCLUSIONS
.--.
1200 oc
BNT 800°C
~
BNT 1000 ' C
1000 OC"
BNT 1200°C -BNT
2000
3000
4000
16OO0C
In conclusion, we have demonstrated t h a t t h e early stages of t h e lattice disorder in the Ba(B'1/3B''2/3)03 compounds, where t h e concentration of t h e lattice defects is still at t h e ppm level, can b e detected and characterized by the several highly sensitive techniques including SQUID a n d ESR. We found t h a t all studied compounds contain substantial amount of the lattice vacancy defects, some of them containing unpaired electron spin. T h e absence of the room temperature ESR signal in the Ba(Co1/3Nb2/3)03 compound may be attributed t o the short spin-spin relaxation time.
5000 Acknowledgments
Field, Gauss
P a r t of this study was performed throuch Suecial Coordination Funds for Promoting Science a n d Technology from the Ministry of Education, Culture, Sports, Science and Technology of the Japanese Government. 1
FIG. 5: ESR spectra of Ba(Ni1/3Ta2/3)03 processed at various temperatures.
* Electronic address: k o l o d i a z h y i . t a r a s m n i m s . go. j p
'
Petzelt, J. & Setter, N., Ferroelectrics, 1993, 150, 89.102. Zurmuhlen, R., Petzelt, J., Kamba, S., Voitsekhovskii, V., Colla, E. and Setter, N., J. Appl. Phys., 1995, 77, 5341-50. Templeton, A., Wang, X., Penn, S.J., Webb, S.J., Cohen L.F. and Alford, N.McN., J. Am. Ceram. SOC.,2000, 83, 95-100. Alford, N.McN., Breeze, J., Wang, X., Penn, S.J., Webb, S.J., Ljepojevic, N. and Aupi, X., J. Eur. Ceram. Soc., 2001, 21, 2605-2611. Braginsky, V.B., Ilchenko, V.S. and Bagdassarov, Kh.S., Phys. Lett. A, 1987, 120, 300-305. Gurevich, V.L. & Tagantsev, A.K., Adv. Phys., 1991, 40, 719-767. Seuter, A.M.J.H., Philips Res. Repts. Suppl. 1974, 3, 1-84. Lewis, G.V. & Catlow, C.R.A., J. Phys. Chem. Solids, 1986, 47, 89-97. Burton, B.P., Phys. Rev. B, 1999, 59, 6087-6091. Desu, S.B. & O'Bryan, H.M., J. Am. Ceram. Sac., 1985, 68, 546-51. Takahashi, T., Wu, E.J., Van Der Ven, A., and Ceder, G., Jpn. J. Appl. Phys., 2000, 39, 1241-1248.
12
l3 14
l5
I7
''
_
Kingery, W., Introduction to Ceramics, J. Wiley & Sons. New York, 1976. Kroger, F.A. & Vink, H.J., Solid State Physics, Vol. 3 Academic Press, New York, 1954, p 307. Annino, G.,Bertolini, D., Cassettari, M., Fittipaldi, M., iongo, I., and Martinelli, M., J. Chem. Phys. 2000, 112, 2308-2314. Wakino, K., Murata, M. & Tamura, H., J. Am. Ceram. SOC.,1986, 69, 34-37. Petzelt, J., Kamba, S., Mater. Chem. Phys., 2003, 79, 175180. Sawada, A & Kuwabara, T., Ferroelectrics, 1989, 95, 205208. Sagala, D.A. & Koyasu, S., J. Am. Ceram. Soc., 1993, 76, 2433-2436. Shimada, T., J. Eur. ceram. Soc., 2003, 23, 2647-2651. Selwood, R.W., Magnetochemistry, Interscience Publishers, New York, 1956. Kolodiazhnyi, T., Petric, A . , Belous, A,, V'yunov, O., Yanchevskij, O., J. Mater. Res., 2002, 17, 3182-3189.
Ferroelectric (Pb,Sr)Ti03 Epitaxial Thin Films on (001) MgO for Room Temperature High-Frequency Tunable Microwave Elements
C. L. Chen*, S. W. Liu, J. Weaver, W. Donner, J. C. Jiang, E. I. Meletis, W. Chang, S.W. Kirchoefer, J. Honvitz and A. Bhalla Department of Physics and The Texas Center for Superconductivity and Advanced Materials United States of America *clchen@,uh.edu, clchen@,mail.uh.edu
Abstract Ferroelectric Pb0.35Sr0.65Ti03 (PSTO) thin films were grown on (001) MgO by using pulsed laser deposition. Microstructure studies from X-ray diffraction and electron microscopy indicate that the as-grown PSTO films have excellent single crystal quality and good epitaxial behavior with their caxis oriented perpendicular to the plane of the films. The interface relationships between the PSTO films and MgO were determined to be [1oo]P~~O//[1oo]M~O and (oo1)p~~O//(oo1)MgO. The high frequency dielectric property measurements (up to 20 GHz) reveal that the as-grown films have a high dielectric constant value above 1420 and very large dielectric tunability above 38% at room temperature. These results suggest that the as-grown PSTO thin films on MgO are a good candidate for developing room-temperature high-frequency tunable microwave elements.
111
This page intentionally left blank
Session R5
Chair: 0.Acher
This page intentionally left blank
Recent advances in microwave magnetic materials Olivier ACHER CEA Le Ripault, BP 16, F-37260 France olivier.acher@,cea.fr
Abstract The microwave response of ferromagnetic-based composites can be engineered through the nature and topology of the magnetic inclusions. Powders, wires, flakes or thin films are suitable to manufacture such composites. More recently, works on metamaterials provided new approaches to engineer the permeability response through inductive patterns. These approaches can be combined to make further achievements. Sum rules provide usehl guidelines within this complexity. In particular, we show that at very high frequencies, artificial magnetic materials may be more suitable than conventional magnetic materials. I. Introduction Magnetic materials are widely used for microwave applications. Ferrite materials have been used for a long time, but ferromagnetic-based composites are expanding. Recently, the emergence of metamaterials also made clear that it is possible to obtain composites with a significant permeability without using magnetic materials at all. The aim of this paper is to give on overview of these recent trends in microwave magnetic materials, and to provide guidelines for the engineering of the permeability of materials.
11. Ferromagnetic-based composite materials Since ferromagnetic materials are highly conductive, microwaves penetrate on a very limited depth into ferromagnetic materials. As a consequence, they can not be used under bulk form to interact with microwaves. They are used under composite form, mixed with a dielectric insulating matrix. Several topologies of composite materials have been explored. A common topology is powder dispersion in a dielectric matrix [1,2]. Homogeneization law such as Bruggeman or MaxwellGarnett are generally found suitable to describe the permeability as a function of the ferromagnetic load fraction. In the case the radius of the particles is not small compared to the skin depth, skin effect should be taken into account [3]. The measurement of this type of material is commonly performed using waveguides or coaxial cells. It should be mentioned that recently, a cell has been proposed that allows the determination of the off diagonal elements of the permeability tensor of such material under a magnetic field [4]. Powder-based ferromagnetic composites generally exhibit a broad electromagnetic response. A different behaviour has been observed in the case of small powders (diameter less than 500nm) prepared using the polyol process. This process allows the preparation of large collections of powders with very narrow dispersion (Figla). It has been evidenced that the microwave permeability spectra of composites made from such powders yields some narrow well-defined peaks (Fig. lb). These peaks correspond to the excitation of so-called “exchange resonance modes” in each sphere [5,6]. The positions of these peaks depend on the size and composition of the particles [7]. As a consequence, this behaviour can be observed only on composites made of particles with very limited dispersion.
115
116
Figure 1: a) Scanning Electron Micrography of a collection of CoNi powder prepared using the polyol process; b) Permeability spectra of a composites made of CoNi powders dispersed in a dielectric matrix. Other classes of ferromagnetic-based composite materials include Laminated Insulating Ferromagnetic lighted on the Edge (LIFE) composites [S], and Conducting along One dimension (ClD) composites made from wires [9]. The corresponding topologies are sketched on Fig. 2. These topologies are anisotropic, and yield high impedance characteristics only for one polarisation. They are perfect reflectors for the other polarisation. A typical permeability spectrum is reported on Fig. 3. LIFE Materials can be fabricated using ferromagnetic thin films deposited on flexible thin sheets. Microwave filters manufactured using this type of materials have been demonstrated [lo]. Materials with similar topology, but manufactured from metallic flakes are manufactured by Tokin corporation [l 11. It is aimed at suppressing unwanted high frequency signals propagating in conductors. The use of flakes instead of continuous thin films degrades the permeability spectra but leads to a broader response.
Fig. 2: Sketch of a) Laminated Insulating Ferromagnetic on the Edge (LIFE) composite topology; b) 1D composite topology.
117 200
150
GILBERT’S MODEL
LIFE HOMOGENIZATION
M s = 13000 G a u s s Ha = l 7 Oe
Resistivity = 8 7 p O h m cm T ferromagnetic = z OOpm T insulator = 6 15pm
100
0
p ’ (experiment) model
-
1
a
50
0
-50
F (GHz)
Figure 3: Permeability spectrum of a LIFE material. The microwave properties of such composites are easily measured on samples with toroidal symmetry that are prepared by winding the flexible ribbon or the microwire into a torus [12]. The permeability takes the form: ~ ~ ( 1+- f.A.pferro, 0 where f is the volume fraction of ferromagnetic material, pferroits intrinsic permeability, and A a factor that describes the skin effect [13].
111. New opportunities in permeability response engineering: the metamaterial approach
Recent work by Pendry and Smith [14,15] and others pioneers [16,17] on so-called metamaterials gave a very large impetus to the works on frequency response engineering of materials. In particular, it opened very attractive ways to engineer the permeability of materials using inductive conductive patterns. The driving idea to obtain “artificial” permeability using these non magnetic elements is to design a resonant structure that will enhance the magnetic field inside the structure close to a resonance frequency. Under these conditions, the permeability which is the ratio of the volume average of the B field, over the average of H external to the conductive structure [ 181, may be large. A large variety of inductive resonant structures can be designed, some of them have been represented on Fig. 4.
Figure 4: Sketch of different types of resonant inductive inclusion.
118
Artificial permeability obtained form metallic patterns have a low frequency permeability that is unity. It is possible to obtain higher permeability levels and sharp resonance feature by combining conventional magnetic materials and inductive patterns. The permeability response of an inductive pattern with a magnetic core is represented on Fig. 5.
6 5 4
JH 2 1
0 0
0.2
M
Q6
QR
I
1.2 LA I d 1,U 2 Frequency (GHz)
2.1
2A
16
24
3
Figure 5: Permeability of a resonant inclusion with a magnetic core.
A convenient way to engineer the permeability response is to use a small loop loaded by a capacitor, or a more complex circuit. The analytical expression of the permeability as a fimction of the load impedance has been established [19,20]. This expression allows the design of artificial permeable materials with engineered responses. We demonstrated recently an artificial magnetic material with a response tuneable through a voltage control [19]. The unit cell of this composite material consists of a conventional magnetic core surrounded by a conducting loop connected to a varactor. By adjusting the capacitance of the varactor, we were able to shift the resonance frequency over more than an octave (Fig. 6). While it is very common to change the permeability of a material by applying an external magnetic field, this is not convenient in many applications, and a low-power electrical control of the permeability is very attractive for many applications.
119 5
1
'
1
'
I
'
I
I
1
'
1
'
4
Frequency (GHz)
Figure 6: Metamaterial with a permeability tuned through a control voltage in the 0 to 24V range
IV. Sum rules as guidelines for microwave magnetic material design It has been shown above that composite materials could be engineered through many different ways to obtain original permeability response. The topology of the ferromagnetic inclusions, their intrinsic permeability governed either by uniform resonance or by more complex excitations, and also the presence of inductive patterns, can be used to achieve sophisticated responses. Though this may seem complex, simple guidelines can be provided : the capacitive effects obtained by breaking continuous ferromagnetic patterns into discontinuous patterns tend to increase the resonance frequency, while inductive patterns allow to decrease the resonance frequency. Inductive patterns do not affect the permeability in the low frequency limit. Another type of very usefbl guidelines consists in sum rules. Sum rules have been introduced by Rozanov to assess the possibilities of microwave materials [21]. We have established in a fairly general case that for magnetic bulk or composite materials [22,23]:
"(w) .w.dw=?( (yln-M3y) 0
The brackets correspond to the spatial averaging. y is the gyromagnetic ratio, and 4nMs the saturation magnetisation of each constituent of the composite. This relation holds for materials with negligible skin effect and conduction effects, and as a consequence metamaterials do not verify this sum rule. It is relatively easy to show that in the case of a metamaterial consisting in a volume fraction a of small loops with negligible losses and a resonance at 0 0 : m
~ " ( O I )w.dw=%m2 . 2 0
120
The comparison of the two identities clearly evidences that the integral of p”(a).a may be larger for metamaterials than for conventional magnetic materials in the case of high resonance frequencies. In contrast, a study of the integral of p”(w)/w using Kramers-Kroenig equations indicates that for low frequency aspects, conventional magnetic material shall not be surpassed by metamaterials ~31. V. Conclusion The microwave magnetic permeability of material can be engineered through magnetic constituents, and also inductive elements. Strong theoretical and experimental basis now exist to provide good landmarks for conception.
References
[1] L. Olmedo, G. Chateau, C. Deleuze, J. L. Forveille, J. Appl. Phys. 73,6992 (1993) 12] G. Viau, F. Ravel, 0. Acher, F. FiCvet-Vincent and F. FiCvet, J. Magn. Magn. Mater. 140-144 377 (1995) [3] D. Rousselle, A. Berthault, 0. Acher, J. P. Bouchaud, P. G. ZCrah, J. Appl. Phys. 74, 475 (1993) [4] P. QuCffClec, A-M Konn, P. Gelin and S. MallCgol, Appl. Phys. 93, 7474 (2003) Ph. Toneguzzo, 0. Acher, G. Viau, F. FiCvet-Vincent, F. Fievet, J. Appl. Phys., 81, 5546 (1998) D. Mercier, J. C. S. Levy, G. Viau, F. Fievet-Vincent, Ph. Toneguzzo, 0. Acher, Phys. Rev. B 62, 352 (2000) Ph. Toneguzzo, G. Viau, 0. Acher, F. Guillet, E. Bruneton, F. Fitvet-Vincent, F. Fievet, J. Mat. Sci., 35, 3767 (2000) 0. Acher, P.-M. Jacquart, J.-M. Fontaine, Ph. Baclet and G. Perrin, IEEE Trans. Magn. 30 4533 (1994) P.-M. Jacquart and 0. Acher, IEEE Trans. Microwave Theory Tech. 44 2 116 (1996) E. Salahun, P. Queffelec, G. TannC, A. -L. Adenot, 0.Acher, J. Appl. Phys., 91, 5449 (2002) H. Ono, S. Yoshida, S. Ando, Y. Shimada, J. Appl. Phys. 93, 6662 (2003) M. Ledieu, 0. Acher, J. Magn. Magn. Mater., 258-259, 144 (2003) ~ 3 0. 1 Acher, 0. Reynet, N. Mallejac and J. -M. Lerat, Proc. of SPIE 5379,76 (2004) [14 ] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47,2075 (1999) [15] D. R. Smith, J. B. Pendry and M. C. K. Wiltshire, Science 305,788 (2004) [16] A.N. Lagarkov, V.N. Semenenko, V.A. Chistyaev, D.E. Ryabov, S.A. Tretyakov, and C.R. Simovski, Electromagnetics 17,213 (1997) [17] S.A. Tretyakov, Microwave and Opt. Tech. Lett., 31, 163 (2001) [ 181 0. Acher, A. -L. Adenot, F. Duverger, Phys. Rev. B 62, 13748 (2000) [19] 0. Reynet, 0. Acher, Appl. Phys. Lett., 84, 1198 (2004) [20] S. Tretyakov, Analytical modeling in Applied Electromagnetics, Artech House Publishers (2003) [21] K.N. Rozanov, IEEE Trans. Antennas Propagat, 48,1230 (2000) [22] 0. Acher, A. -L. Adenot, Phys. Rev. B 62, 11324 (2000) [23] A. -L. Adenot, 0. Acher, T. Taffary, L. Longuet, J. Appl. Phys. 91,7601 (2002)
Microwave permeability and Snoek's law in C02Z composites K. N. Rozanov" Institute for Theoretical and Applied Electromagnetics, Moscow, Russia, *
[email protected] L. F. Chen, Z. W. Li, Temasek Laboratories, National University of Singapore, Singapore and M. Y . Koledintseva ECE Department, University of Missouri-Rolla, Rolla, MO, USA Abstract The microwave permittivity and permeability of Co2Z barium ferrite composite samples is measured as a function of frequency and volume fraction of the ferrite. Magnetostatic properties of the bulk ferrite are determined. This allows Snoek's law to be verified by comparing the microwave and magnetostatic Snoek's constants. The modification of Snoek's law for hexagonal ferrites suggested recently by Acher et al. is also verified. Acher's constant is found from microwave measurements to agree with the value calculated from the magnetostatic properties of bulk ferrite. Microwave and magnetostatic Snoek's constants disagree. This may be attributed to the effect of demagnetizing factors of ferrite inclusions. The measured frequency dependences of permeability of composites satisfy the Lorentzian dispersion law and are consistent with the Maxwell Garnet approximation. According to the theoretical analysis based on the Lorentzian dispersion law and the Maxwell Garnet mixing rule, both Snoek's and Acher's constants must be linear functions of the volume fraction independently of whether the microwave values of the constants are in agreement with the magnetostatic values or not. The experiment reveals a steady decrease of both constants with the volume fraction. The disagreement is discussed in terms of influence of effective medium in composite on the inherent permeability of ferrite particles. Introduction Ferrite particles are promising fillers for electromagnetic wave attenuation materials. Ferrite composites provide high magnetic loss, high resistivity, good chemical stability, and their density is lower than that of ferromagnetic metals. Compared to spinel ferrites, hexagonal ferrites, such as CozZ, have a higher resonance frequency and higher microwave permeability, and therefore are more useful in the gigahertz frequency range. Microwave magnetic properties have recently been extensively studied for hexagonal ferrite composites, see [ 1,2] and references therein. For the microwave permeability of ferrites, p=p'-ip", the Lorentzian dispersion law frequently holds:
where f is the frequency, psi the static permeability, and fd and f r the Debye and resonance characteristic frequencies. To model the permeability of ferrite composites, various mixing rules are employed [3]. The most well known mixing rule is the Maxwell Garnet approximation (MGA). If the MGA mixing rule holds for a composite and if the magnetic dispersion of inclusions is of the Lorentzian type, then the dispersion law for the composite will be Lorentzian as well. If any mixing rule other than MGA is valid, the dispersion curve of the composite is distorted as compared to that of the Lorentzian. In ferrites, parameters of the dispersion law relate to each other by Snoek's law [4]. For ferrite composites that exhibit easy c-plane anisotropy, Snoek's law is given by [ 5 ] :
with the gyromagnetic factor ~ 2 . GHzkOe, 8 the saturation magnetization Ms and out-of-plane and in-plane anisotropy fields, He and If+, respectively. The right hand side of Eq. (2) is Snoek's constant for the ferrite, S. For Snoek's constant to be proportional to the volume fraction of ferrite, 121
122
the permeability of the composite must be governed by the MGA mixing law and by the Lorentzian dispersion law. Recently, Acher et al. [6] suggested another form of Snoek‘s law for hexagonal ferrite composites. If the dispersion curve is of the Lorentzian type, it is given by: (pst-l)fr2 = q3y 4 n A 4 , ) 2
[
1+ Equation (3) is referred to as Acher’s law for hexagonal ferrites, by the analogy to Snoek’s law. The right hand side of Eq. (3) is Acher’s constant, A . For Acher’s law ( 3 ) to be valid, the magnetic dispersion curve of the composite must obey the Lorentzian dispersion law and, therefore, the MGA mixing rule as well, because Eq. (3) is written in terms of the Lorentzian parameters, the static permeability and resonance frequency. In general case, the integral formulation of Acher’s law is introduced [6], with Acher’s constant that is proportional to the volume fraction for an arbitrary shape of dispersion curve. =)7
Snoek’s and Acher’s laws relate the microwave permeability of the magnet to its magnetostatic properties and allow constraints on microwave permeability to be established. Namely, larger Snoek’s and Acher’s constants result in larger real and imaginary parts of permeability that can be obtained at higher frequencies. This paper is aimed at the verification of Acher’s and Snoek’s laws in microwave hexagonal ferrite composites. More detailed discussion of the problem can be found in [7]. Experiment C02Z barium ferrite, Ba3Co2Fe24041,is synthesized by conventional ceramic techniques. The size of the ferrite particles is about 10 p.Measurement of magnetostatic properties of the bulk ferrite yields 4nMs=3.3 kGs, He=12 kOe, and the coercivity Hc=23 Oe. The in-plane anisotropy field is known to be HpO.12 kOe for such ferrites [5].
C02Z composites are prepared by mixing fine powders of C02Z ferrite with epoxy resin. The volume fractions of the powders vary from 0.1 to 0.5.The samples are shaped into hollow cylinders of about 2 mm in length for microwave measurements in a 7/3 mm coaxial air-line. The microwave permeability of the samples is measured with a VNA in the frequency range of 0.5 to 16.5 GHz using the RT method [81. The measured microwave permeability for three of the samples under study is shown in Fig. 1. To find the dispersion law from the measured permeability, fitting of the measured magnetic dispersion curves is made by numerical minimization of the RMS difference between the measured permeability and that calculated with Eq. (I). The fitting curves are given in Fig. 1 by dotted lines. Results For all samples under study, the fitting made with Eq. (1) provides agreement with measured data to within measurement uncertainty. The Lorentzian dispersion law is therefore supposed to be valid for the composites under treatment. It follows from the analysis in the Introduction that the MGA mixing rule must govern the properties of the composites, and both Snoek’s and Acher’s constants must be linear hnctions of the volume fractionp.
The fitted parameters of the dispersion law allow Snoek’s and Acher’s constants to be obtained from Eqs. 2 and 3. The linear dependence of Snoek‘s constant onp follows from the MGA mixing rule, the validity of which is evidenced by the fact that all measured dispersion curves are of the Lorentzian type. Therefore, S must be a linear function o f p for the composites under study. This is not the case, as is shown by Fig. 2,where the ratio of Snoek‘s constant to the volume fraction, Slp, is seen to decrease steadily withp.
123
1 .o
0.5
0 0.1
1
10
0.1
1
10
Fig. 1. The measured microwave permeability of Co2Zcomposites with p=O.l% (l), 0.3% (2), and 0.5% (3). The right hand side of Fig. 2 shows Acher's constants obtained with the measured parameters of dispersion curves and normalized to the volume fraction of inclusions, Alp. Again, a decrease in the measured values ofAlp withp is clearly seen from the figure. By extrapolating the data to p= l , Snoek's constant for the bulk ferrite is found to be S=ll.l GHz. According to Eq. 2, this corresponds to H+ = 2.1 kOe, which disagrees with the reference data [5], H+ =0.12 kOe. Therefore, Snoek's law is not valid for the composites under study. The linear extrapolation of A to p = l results in A=120 GHz2, in an agreement with the value of 130 GHz2 yielded by Eq. (3) with He=O. 12 kOe.
Discussion In this paper, the microwave permeability of CozZ barium ferrite composites is measured as a function of frequency and volume fraction of the ferrite. Magnetostatic properties of the bulk ferrite are also determined. This allows Snoek's law and Acher's law to be verified by comparing the microwave and magnetostatic Snoek's and Acher's constants. Acher's constant is found from the microwave measurements to be in agreement with the value calculated from the magnetostatic properties of bulk ferrite. In contrast, microwave and magnetostatic Snoek's constants disagree. The reason for the invalidity of Snoek's law may be that it does not allow for demagnetization in ferrite inclusions. The demagnetizing factors have an effect on the parameters of magnetic dispersion and may therefore affect the microwave Snoek's constant. Another possible reason could be that intrinsic damping (that is true magnetic loss) is dominant over extrinsic damping (that is a spread of the magnetic loss peak due to inhomogeneity of magnet). It is conventional opinion that intrinsic damping and extrinsic damping are indistinguishable from the experimental data [9]. The data obtained reveal that the analysis based on Snoek's law could allow these to be distinguished. The microwave permeability of the composites under study is in agreement with the predictions of the MGA mixing rule. However, determination of Snoek's and Acher's constants from the measured data reveals disagreement with the theory, which are not seen from the comparison of measured and calculated dispersion curves. In theory, both Snoek's and Acher's constants normalized to the volume fraction, must be independent of the volume fraction. In actual composites, a steady decrease in both the normalized constants with volume fraction is observed, which cannot be attributed to the uncertainty of the measurement and to the inaccuracy of the fitting procedure.
124
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
Fig. 2. The measured volume fraction dependence of Snoek's constant (left) and Acher's constant (right) This disagreement may also be attributed to the effect of demagnetizing factors of ferrite inclusions. If a non-spherical magnetic particle is considered as an inclusion in a composite, then the demagnetization fields depend on the permeability of surrounding host medium. Hence, the basic assumption on which all mixing rules are based, namely, the material properties of inclusions do not depend on the surrounding host medium, may not be valid for magnetic composites. Therefore, the theory of magnetic composites must take into account that the intrinsic permeability of inclusions may change with the volume fraction due to variations in demagnetizing fields [ 10, 111. For large multi-domain inclusions, this correction is negligible, since the domain structure reduces demagnetizing fields of the particle. The same is true in cases when the shape of inclusions is close to spherical. In contrast, for fine powders and especially for nanocomposites imbedding nonspherical single-domain inclusions, the correction may drastically change the performance of the composite. Acknowledgement K. Rozanov appreciates the partial support of the work from the Russian Federation President Foundation, Grant no. 1694.2003.2. References [l] T. Nakamura and K. Hatakeyama, ZEEE Trans. Magn., vol. 36, pp. 3415-3417, September 2000. [2] Z. W. Li, L. F. Chen, and C. K. Ong, J. Appl. Phys., vol. 94, pp. 5918-5924, November 2003. [3] A. Sihvola, Electromagnetic mixing formulas and applications. IEEE, 1999. [4] J. L. Snoek, Physica, vol. 14, p. 204, 1948. [5] J. Smit, Magnetic properties of materials, McGraw-Hill, 1972. [6] A. L. Adenot, 0. Acher, T. Taffary, and L. Longuet, J. Appl. Phys., vol. 91, pp. 7601-7603, 2002. [7] K. N. Rozanov, Z. W. Li, L. F. Chen, and M. Y . Koledintseva, J. Appl. Phys., vol. 97, Art.no. 013905,2005. [8] A. M. Nicolson and G. F. Ross, IEEE Trans. Znstr. Measur., vol. 19, p. 377, 1970. [9] J. Huijbregtse, F. Roozeboom, J. Sietsma, J. Donkers, T. Kuiper, E. van de Riet, J. Appl. Phys., vol. 83, p. 1569, 1998. [lo] R. Ramprasad, P. Zurcher, M. Petras, M. Miller, P. Renaud, Phys. Status Solidi (b), vol. 233, p. 3 1,2002. [l I] J.L. Mattei and M. Le Floc'h M, J. Magn. Mag. Muter., vol. 264, pp. 86-94,2003
Effects of Doping on the High-Frequency Magnetic Properties of Barium Ferrite Composites
G. Q. Lin, Z. W. Li, and Chen Linfeng Temasek Laboratories, National University of Singapore, 5, Sports Drive 2, Singapore 117508 Yuping Wu and C. K. Ong Centre for Superconducting and Magnetic Materials, Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 Abstract The effects of doping on the high-frequency magnetic properties of Ba3CozFe24041 and BaCo1.0Znl.oFe16027 barium ferrite composites were investigated. The results show that the barium ferrite powders doped with some oxides are excellent fillers for EM wave attenuation materials with broad bandwidth and low reflectivity. I. Introduction Electromagnetic (EM) materials with small thickness, broad bandwidth, and low reflectivity have attracted much attention due to their extensive applications in commercial and defense sectors. To achieve these electrical properties, potential materials are typical to have -+ 1 and large p". The first condition provides good impedance matching for EM waves to penetrate into the material with minimal reflection, while the second one leads to strong absorption of the EM energy propagating in the material. Further, the optimum thickness can be significantly reduced for materials with high resonance frequencyh. Doping with small amount of oxides is an effective way to optimize the dynamic properties of barium ferrites, such as p', p", E', andfR. In this paper, we present our work [I ,2] on oxide-doped Z- and W-type ferrites. Emphasis is placed on the effects of doping on the dynamic and attenuation properties. 11. Experiment and Results Two series of barium ferrites, CozZ (Ba3CozFe24041) and CoZnW (BaCol .oZnl,oFe16027),doped with 1.O wt% CuO, MgO, A1203, IrOz, RuOz, SiOz, MnO2, Nbz05, V205, or M003, were prepared using conventional double-sintering ceramic techniques.
X-ray diffraction shows that all samples are single phase with hexagonal structure. The microstructures were observed by SEM with a field emission gun. The saturation magnetization Ms and coercivity H,, were obtained from the magnetization curves M(H) and M-€I loops. The complex permeability/permittivity spectra of the composites with 50% volume fraction of barium ferrite powders were measured using coaxial airline and impedance methods. pro is the real permeability at 0.1 GHz and prrmax is the imaginary permeability at resonance. The attenuation is determined from the reflection loss (RL)which, in the case of a metal-backed single layer, is given by RL(dB) = 2010g
, where Z,,/Z,
=m
t a n h
Z,, is the intrinsic impedance of the composites, Zo is the intrinsic impedance of free space, c is the velocity of light, t is the thickness of the composite slab, f is the frequency of the incident EM wave, is . the complex permeability, and E = E' - id' is the complex permittivity. The relative p bandwidth W is defined as W = fudjow,where fup and j & are the band-edge frequencies corresponding to 10 dB attenuation withf,,>jin,. W and the optimum thickness to can be obtained from the RL-f curves based on Eq. ( I ) [2]. x
ipl1
The acquired static magnetic properties (M, and H,), dynamic magnetic properties (p', p", fR, and E'), and the attenuation (Wand to)are listed in Tables I and 11.
125
126
Table I: Static, dynamic, and attenuation properties of C02Z composites doped with various oxides of 1.0 wt% Dopant
Original
IrO,
RnO,
Nb205
MnOz
VzOs
SiOz
AIZO3
MOO3
M , (emu/& Hc (Oe) p' at 0.1 GHz
48.1
46.7
48.0
50.3
46.8
57.1
51.9
44.9
48.3
12.3
13.3
15.0
12.0
13.1
16.2
18.8
14.5
17.1
3.31
2.51
2.73
3.70
3.46
2.87
2.57
3.21
3.16
Pmax
1.70 2.23
1.50
1.80
2.04
1.76
1.46
1.19
1.79
1.67
3.80
4.39
2.29
2.09
2.46
3.08
2.54
2.23
8.618.1
7.316.8
8.117.7
7.817.0
7.717.0
7.316.9
7.717.3
7.417.0
7.216.5
2.66
3.00
3.63
3.39
2.80
2.61
2.26
3.00
2.83
0.34
0.28
0.24
0.30
0.34
0.38
0.40
0.34
0.32
(GHz) €'at 0.5/16.5 GHz Bandwidth W Ootimum t. (cm)
fR
Table 11: Static, dynamic, and attenuation properties of CoZnW composites doped with various oxides of 1.O wt% Dopant M. (emu/d H, (Oe) p' at 0.1 GHz
Original
IrO,
Ru02
NbZOs
MnO,
VzO5
MgO
CuO
IrOI+V20s
84.2
83.45
83.8
84.7
83.2
78.5
81.9
82.8
86.1
19.8
23.8
16.4
19.0
19.9
18.7
24.6
22.1
8.6
4.70
4.08
4.63
4.11
4.86
4.30
3.51
4.18
5.03
@'mar
1.61
1.41
1.63
1.52
1.77
1.67
1.08
1.39
1.88
(GHz) &'at0.5/16.5 GHz Bandwidth W Optimum f (em)
2.33
3.58
3.44
3.27
2.51
3.78
5.36
2.47
2.26
19.119.1
16.018.4
15.818.3
9317.2
15.418.2
7.716.9
17.919.1
18.818.8
7.316.8
1.94
2.05
2.19
3.14
2.24
3.82
1.67
1.92
3.91
0.44
0.38
0.40
0.26
0.44
0.30
0.44
0.40
0.34
fR
111. Discussions 3.1 Effect of Doping on the shape of the grain The original barium ferrite without doping, such as C02Z or CoZnW, has bar-like grains. By doping of Si02 in CozZ or V205 in CoZnW, perfect hexagonal-plate grains are formed, as shown in Fig. 1. In barium ferrites, the grain shape can sometimes affect the static permeability or resonance frequency (due to the inherent demagnetizing field) in their corresponding composites, which will give some discussions later.
3.2 Effect of Doping on E' For original CoZnW, the permittivity E' has a strong dependence on frequency, with a high real permittivity of 19.1 at 0.5 GHz and about 9.1 at 16.5 GHz. The behaviour is related to the formation of Fez+ in the materials, which leads to a decrease in the resistivity due to electronhopping between Fe2+and Fe3'[3]. By doping with V205 or Nb205, E' is decreased to about 7.5 and remained almost constant over 0.5-16.5 GHz, as shown in Fig. 2(b). The results can be explained by the fact that doping of these two oxides prevent the formation of Fe2+ ions or inhibit the movement of electrons. Other dopants in CoZnW, such as CuO, 11-02,Ru02, and Mn02, have no significant influence on E', as shown in Tables I and 11. 3.3 Effects of Doping on ,do, ,u'',,,~~, and f R Some typical complex permittivity and permeability spectra are shown in Figs. 2(c), (d), (e), and (f). The dynamic parameters are also listed in Tables I and 11. In general, two types of resonances are found in ferrites, namely natural resonance and domain-wall resonance. For the CoZnW series, two separated absorption peaks are observed when doped with V2O5 and MgO, natural resonance at high frequency and domain-wall resonance at low frequency. When doped with other oxides, an overlapping broad peak is observed. However, in the C02Z series, only natural resonance occurs.
127
Fig. 1: SEM images of (a) Co2Z,(b) Co2Zdoped with SO2,(c) CoZnW, and (d) CoZnW doped with v205. In the CoZnW series, the original sample has p'o=4.70, y",,,,,=1.61, a n d h = 2.33 GHz. By doping with Ir02+V205,proand p",,,,, can be significantly increased. This can be attributed to both natural and domain-wall resonances. Same effect is also observed in the sample doped with MnOz. In the CozZ series, ph can be significantly increased by 12.0%, from 3.31 in original Co2Z to 3.70 is increased from 1.70 to 2.04. On the in the sample doped with Nb205. Correspondingly, is increased other hand, in the sample doped with RuOz, although p' is decreased by 18.0%, ,dmax to 1.80. The value of ,u'~~,,depends on not only y', but also the damping coefficient for natural resonance. Hence, as compared to the original CozZ sample, doping with RuOz leads to a narrow Meanwhile, doping with IrOz resonance linewidth, as shown in Fig. 2(d), thereby increases p"max. and RuOz shift the resonance frequencyfR to 3.00 GHz and 3.63 GHz, respectively, from 2.23 GHz in original CozZ sample. The natural resonance frequencyh is given by
f,
= 2.n q m
(2)
for c-plane anisotropy [4]. He and Hvare the anisotropy fields along the c-axis and in the c-plane. The large orbital momentum of Ir and Ru ions lead to a high anisotropy field He, which increasesh
90
3 7.5 -
.
-
4.0
3.2
6.0 E 4.5 -
,2
1: c0,z 2: c0;z + Irol 3: CO,Z + sio,
301 1.5
-
2.4
,
-1
-1
1.6 0.8
0.0 2.5
00
2.0 18 15 B 12
p j
1.5 -3
1.a
9 6
0.5
3
nn
n
,I
0
2
4
6 8 10 12 Frequency (CHz)
14
16
0.01
0.I
1 Frequency (GHz)
10
Frequency (GHe)
Fig. 2: Some typical complex permittivity (a and b) and permeability (c, d, e, and f ) spectra of C q Z and CoZnW composites doping with various oxides. 3.4 Effects of Doping on the attenuation The attenuation results are given in Tables I and 11. The RL-f curves at optimum thickness are shown in Figs. 3 (a) and (b) for some typical CozZ and CoZnW series.
In the CozZ series, the relative bandwidth for 10 dB attenuation is W=2.66 with a thickness of t,=0.34 cm. Doping with NbZOs or MnOz increases W to 2.80-3.39, due to the large p'o and p"max.
128
Doping with Ru02 and IrO2 increase Wto 3.0 and 3.63, although , d o =2.51 and 2.73 are lower than , d o =3.3 1 in the original sample. Moreover, the optimum thickness to is reduced to 0.24 cm and 0.28 cm, respectively. The characteristics are attributed to the highfR, 3.80 and 4.39 GHz, as compared to 2.66 GHz in the original C02Z sample, 5
0 h
rn
I!
-5
v) w,
3 C
B
-10
2
d
-15
2
4
-20 6 8 10 12 Frequency (GHz)
14
16
2
4
8 10 12 Frequency (GHz)
6
14
16
Fig. 3: Some typical RL-f curves at the optimum thickness for (a) CozZ and (b) CoZnW composites doped with various oxides.
In the CoZnW series, the high permittivity at low frequency results in lower than 0.5 for the original sample. This impedance mismatching causes strong reflection at the interface between the materials and free space, and degrades the attenuation properties of the materials. The relative bandwidth W is only 1.94, although its permeability is large (pub =4.70 and yffmax=l.61). When doping with V205, Ir02+V205, or Nb205, E‘ decreases to about 7.5 and hence, is larger than 0.75. This improvement of impedance matching, as well as the large y f o and ptfmax, greatly increases W, e g , to 3.91 in sample doping with Ir02+V205. IV. Conclusions Doping with small amount of oxides is an effective way to improve the dynamic magnetic properties of EM composites. It is found that in CoZnW, Nb205 and V205 can stabilize E’ and then, improve corresponding attenuation properties, while in C O ~ ZNb205 , and MnO2 can increase y‘ and p”,and, Ru02 and Ir02 can shift f , to high frequency. C02Z doped with Ru02 and CoZnW doped with Ir02+V205 or V205 are potential candidates for EM composites with broad bandwidth and low reflectivity. References [ l ] Z. W. Li, L. F. Chen, and C. K. Ong, Journal of Applied Physics, 94, 5918 (2003); Y. P. Wu, Z. W. Li, L. F. Chen, S. J. Wang, and C. K. Ong, Journal of Applied Physics, 95,4235 (2004) [2] Z. W. Li, L. F. Chen, Y. P. Wu, and C. K. Ong, Journal of Applied Physics, 96,534 (2004) [3] Y. Purushotham and P. V. Reddy, International Journal of Modern Physics B, 10,3 19 (1 996) [4] J. L. Snoek, Physica XIV, 207 (1948)
High Frequency Magnetic Properties of Iron Based Magnetic Particulate Powders
L.Z. Wu", J. Ding", H.B. Jiang", L.F. Chenb, C.K. Ongb, C.P. Neo', S.Y. Lim', C.R. Deng' aDepartment of Materials Science, National University of Singapore, Singapore b Tamasek Laboratories, National University of Singapore, Singapore "DSO National Laboratories, Singapore Abstract The high frequency magnetic properties (Complex intrinsic permeability pi and effective permeability pe) have been studied for iron based magnetic particulate materials and composite with non-magnetic matrix. The complex relative intrinsic permeability spectra of iron based magnetic particulate powders were calculated with the Soohoo model. Effective permeability of composite consisting of Fe inclusions embedded in a nonmagnetic matrix (epoxy resin) was calculated using Bruggeman's effective medium theory. The theoretically calculated permeability spectra were then compared with experimentally measured permeability spectra of the composite. The measured permeability pmax'and resonant frequency is 2.5-2.8 and around several GHz, respectively, for composites with 30% (by volume) carbonyl iron powders. The parameters indicate that iron based composites possess suitable high frequency magnetic properties for use as electromagnetic materials with low reflectivity at microwave frequencies. The results also showed that the Soohoo model is suitable for simulation of high frequency magnetic properties of ferromagnetic iron based powders. Keywords: High Frequency magnetic properties; Complex Permeability; Carbonyl Iron powder 1. Introduction With the development of radar and microwave communication technology, and especially the need for antielectromagnetic interference coatings, self-concealing technology, the study of electromagnetic (EM) wave absorbing materials has increased in recent years. Electromagnetic (EM) materials have been uscd extensively in defense, industry, and commerce etc. nowadays. In both civil and military applications, it is often important to have strong attenuation of EM waves or suppress reflections from metal structures. Coating of radar absorbing materials (RAMS) offers a possible solution. [ 1-61 Magnetic powder materials with high values of permeability are promising for the application of microwave absorption. As it is well known, finelultrafine magnetic metal particles (e.g. carbonyl Fe and Fe based powders) have been widely used as electromagnetic wave absorption materials, because of its excellent magnetic properties [7]. Metallic magnetic materials can be used to make thinner electromagnetic wave absorbers because of their high saturation magnetization and high relative complex permeability. Several researchers have studied the microwave properties of finehltrafine metallic magnetic powder materials as promising radar absorber candidates. Toneguzzo et al. [8] proposed that ferromagnetic particles may be promising for microwave applications. Bregar [9]showed the advantages of ferromagnetic nanoparticle composite as magnetic microwave absorbers. Wiedwald et al. [ 101 showed the promise of monodispersed Co particles as absorbers. Wu et al. [ 1 11 also showed that microwave properties can be improved when Fe nanoparticles was coated with SiOz. As far as microwave absorbing properties are concerned, metals have to be used as fine particles dispersed in an insulating matrix. The effective microwave properties of the composite depend on both the intrinsic characteristics of the particles and their microstructural, electrical and magnetic parameters. The influence of these properties can be well described by mixture laws derived from the Bruggeman's effective medium theory [12]. Until now, the dependence of microwave properties of composite materials on the intrinsic properties of the magnetic particles has not been well studied. A better understanding of the dynamic properties of fine magnetic particles and a tentative correlation with their static magnetic 129
130 properties is needed [13]. In this paper, we begin with a presentation of theoretical formulation of dynamic frequency dependent intrinsic permeability of magnetic materials and Bmggeman's effective medium theory. The complex relative intrinsic permeability spectra of iron based magnetic particulate powders were calculated with R.F. Soohoo model. Effective permeability of composite consisting of Fe inclusions embedded in a nonmagnetic matrix (epoxy resin) were calculated by using Bruggeman's effective medium theory. In addition, we have performed microwave properties measurements for finehltrafine Fe based powders in order to provide usefbl information for our calculations. 2. Details of Theoretical Model 2.1 Ferromagnetic resonance and Gilbert Equation Some theories were developed to give the dynamic frequency dependent permeability and permittivity of magnetic materials. One of the most commonly used models for ferromagnetic resonance is the Gilbert Equation or equivalent Landau-Lifshitz Equation. The Gilbert Equation provides the change of magnetization M under a magnetic field H expressed as below:
d@
a y(G x H- ) + -A4
- xd a dt M dt Where y is the gyromagnetic ratio and a is damping coefficient. Soohoo derived the microwave susceptibility tensor from Eq. (1) for natural resonance. The equivalent scalar susceptibility and then the complex permeability spectra p(f) were got with the eigenvalue of tensor x. [ 141 --
-
~
x
a=
wowm[w,' - w2(1 - a 2 ) ] w',2-wm2 [w,' -w2(1+a2)]2+4w2w,'a2 w'owrn -
b = -mu,,
w,
2
-
[ma2+ w2(1+ a2)] j[w,' -w2(1+a2)]' +4w2w,2a2
[ma2- w2(1+ a 2J)
[w,'-w2(1+a2)]2+4w2w~a2 +J,w,'
2 w, w 2 woa -w2(1+a2)]2+4w2w;a2
(3)
Where w,,, = -yM, , wo = -yHz , ofo= w, + j w a and a is the damping coefficient. 2.2 Bruggeman's Effective Medium Theory (EMT) For radar-absorption, magnetic particles are embedded in a matrix (e.g., polymer). The effective permeability can be obtained by the Bmggeman's Extended Effective Medium Theory:
Where p is the volume fraction of magnetic particles, pi is the intrinsic permeability of magnetic particles, pe the effective permeability of the composite and p,,, is the permeability of the medium. ~51. 3. Results and Discussion The above outlined theories were now used to investigate the complex intrinsic magnetic permeability pi of Fe-based magnetic powders and the effective permeability pe of composites. Fig. 1 shows the real part and imaginary part of intrinsic magnetic permeability calculated using Eq.
131
(2) for pure Fe powders, values of 20000Gauss and 6000e were used for 4zM, and Ha respectively. In the calculation, damping coefficient ct with 0.4 was used. This value was obtained from experimental results, as calculated permeability by using damping coefficient ct of 0.4 is the most close to the experimental results. It can be seen that the calculated intrinsic permeability spectra shows a resonant frequency around 2.5-3GHz. I'
'
'
'
'
'
'
'
'
I
Frequency (Hz)
Fig. 1 Calculated Real part and Imaginary part of Complex Intrinsic Permeability for pure Fe by using Eq. (2). In order to experimentally evaluate the calculated intrinsic permeability for pure iron, composite samples were prepared by mixing fine powders of widely used commercially available carbonyl iron powders (HQ from Ciba) with epoxy resin. The real and imaginary values of the effective permeability of composite consisting of carbonyl iron powders (HQ) with different volume concentrations below percolation threshold (20% and 30% volume concentrations respectively) were measured over 0.5-16.5 GHz, using transmissiodreflection method by HP Vector Network Analyzer. The measured microwave properties were then compared with the calculated results. Fig. 2 shows the SEM and TEM pictures of commercial carbonyl iron HQ powder. It can be seen that HQ powders have uniform spherical shapes with average particle size about 1pm.
Fig. 2: SEM (Left) and TEM (Right) micrographs of HQ carbonyl iron powders. The above calculated intrinsic permeability was then used to calculate the effective permeability by using effect medium theory Eq. (4). The measured and simulated effective permeability spectra of HQ were shown in Fig. 3. It can be seen that the calculated and measured data of the real part of permeability pew' matched very well. Except the imaginary part of permeability spectra of samples, there is some discrepancy between calculated and experimental results. The discrepancy may be caused by that our samples are not in the ideal form. The real sample supposes to have certain
132 distribution of particle sizes, interaction between magnetic particles and a random distribution of easy axes. Grain boundary and domain structure may affect magnetic permeability.
-%Measured
1.6
Effect $
1.2
I0.8 0.6
c
0.2
0.0
5.UG
10.UG
Frequency (Hz)
15.UG
20.0G U.0UEtUUO
5.00Et009
1.00EtU10
1.50Et010
2,00E+010
Frequency (Hz)
Fig. 3 Measured and predicted permeability spectra for composite with different volume concentration of carbonyl iron HQ powders.
4. Summary In this work, intrinsic high frequency permeability and effective Permeability of spherical iron particles in a non-magnetic matrix were calculated by using the combination of Gilbert equation and effective medium theory. The calculated effective Permeability spectra were compared with experimentally measured results and showed well match. It was found that Soohoo model and Bruggeman's effective medium theory can be well applied to the system of dispersion of Fe-based particles into a non-magnetic matrix.
Acknowledgements This research project was supported by DSTA grant (R152-000-046-422) and MINDEF-NUS grant
(R152-000-072-123/232).
References [l] [2] [3] [4] [5] [6] [7]
[8] [9] [ 101 [ll] [ 121
[13] [I41 [15]
Y. Naito and K. Suetaki, IEEE Trans. Microwave Theory Tech. Vol. MTT-19,65 (1971) G. D. Mahan, Physical Review B Vol. 38,9500 (1988) H. M. Musal and H. T. Hahn, IEEE Transactions on Magnetics Val. 25,3851 (1989) H. M. Musal and S. D. C., IEEE Transactions on Magnetics Vol. 26, 1462 (1990) C. A. Grimes, IEEE, 217 (1993) K. J. Vinoy and R. M. Jha, Sadhana Vol. 20,815 (1995) M. Z. Wu,H. H. He,Z. S. Zhao and X. Yao, Journal of Physics D-Applied Physics Vol. 33,2398 (2000) P. Toneguzzo and G. Viau, Adv. Mater. Vol. 10, 1032 (1998) V. B. Bregar, IEEE Transactions on Magnetics Vol. 40, 1679 (2004) U. Wiedwald, M. Spasova, M. Farle, M. Hilgendorff, and M. Giersig, Journal of Vacuum Science & Technology a-Vacuum Surfaces and Films Vol. 19, 1773 (2001) M. Z. Wu, Y. D. Zhang, S. Hui, T. D. Xiao, S. H. Ge, W. A. Hines, J. I. Budnick, and M. J. Yacaman, Journal of Applied Physics Vol. 92,6809 (2002) A. Berthault,D. Rousselle and G.Zerah, Journal of Magnetism and Magnetic Materials Vol. 112,477 (1992) R. Ramprasad,P. Zurcher,M. Petras and M. Miller, phys. stat. sol.(b) Vol. 233,31 (2002) R. F. Soohoo, Microwave Magnetics (Harper & Row Publishers, New York, 1985) L. Olmedo,G. Chateau,C. Deleuze and J. L. Forveille, J. Appl. Phys. Vol. 73,6992 (1993)
Structural, Electrical and Magnetic Properties of CazZnLio.sAlo.sFe12022
P.R. Arjunwadkar and M.Y.Salunkhe* Physics Department, Institute of Science Nagpur, India
Abstract The possibility of improving the magnetic properties of Y type hexagonal ferrite CaZn2-Y, by partial substitution of Zn2+cations by the scheme 2Zn2+f) Li' + A13+.The new phase obtained by the combination of monovalent, bivalent and trivalent cations leads to a magnetic material, which is better suitable for its use as permanent magnet. Sample exhibit transitions with change in slope of graph logo vs 1/T. Keywords: hexaferrite, magnetic susceptibility. Introduction The hexagonal ferrite Ba2Zn2Fel2022 (Y type ferrite) was discovered by Jonker in 1956 [l]. Due to its magneto-crystalline planer anisotropy and high initial permeability this hexagonal ferrite has been attractive for the applications in microwave devices.
Like ordinary ferrite the kind of cations and the positions occupied by these cations in the Y type ferrite are the dominant factors affecting their magnetic properties. Replacing Zn ions by various other divalent cations (Cu, Ni, Co, Mg, etc) [2] and combinations of these cations will change the magnetic properties and hence choosing the ions properly the properties of the ferrite can be controlled for suitable application. Substitution of mixed valency cations for the divalent zinc is also tried with success. The substitutions of the combination of the monovalent Li along with a trivalent Fe or A1 etc. in place of divalent Zn is interesting to study the distribution of these cations among the various sites and thus controlling the properties of these ferrites. Present study is concerned with the structural, electric and magnetic properties of Ca2ZnLio.sFel2022 ferrite where one of the Zn ions is substituted by Li' together with A13+. Experiment The ferrite was synthesized by using the standard solid state reaction method. This method involves heating of oxides and/or carbonates of various cations mixed in proper molar ratio to very high temperature for long duration. In the present work A.R. grade CaO, ZnO, Li2CO3, A1203and Fez03 was mixed in proper molar ratio and grounded in agate mortar under acetone for several hours. Then the powder was heated in an electric furnace at 1200°C for 120 hours and then cooled at 60°C per hour up to 500°C and allowed to cool naturally up to room temperature.
The sample thus synthesized is then analysed using Philips X-ray diffractometer with Cu-Ka radiation and Ni as filter. The electrical conductivity measurements were done by using two-probe method in the temperature range 50°C to 300°C. The activation energy was calculated by plotting logo vs 1/T. the magnetic susceptibility measurements were carried out on a Gouy's apparatus [3] in the temperature range 175°C to 400°C.
133
134
Table 1: X-ray diffraction results of Ca2ZnLio.sFe12022 dobs
dcal
Relative Intensity
h
k
4.8348 3.6672 2.9665 2.691 1 2.5329 2.5095 2.2013 2.1003 1.8376 1.7164 1.6918
4.8680 3.6897 2.7860 2.691 1 2.5578 2.5095 2.1914 2.1194 1.8448 1.7107 1.6922
5.6 17.4 38.9 53.6 100.0 40.9 11.6 13.8 17.9 9.2 31.6
0 1 1 1 1 2 1 2 2 2 2
0 0 0 1 1 0 0 0 0 1 0
13 11 16 11 19
Results and discussion X-ray diffraction pattern of the sample confirms the formation of single hexagonal phase without the traces of the reacting oxides. Thus the substitution of Li+ with A13+for the divalent zinc is successfully tried. 15
20
illx
lo4
I
25
30
35
-12
e *
30
-13
* e
25
-14
-15
-
-16 -17 -18
e
20 E
,x r 15 10 5
-19 0
-20
Figure 1: Variation of logo with 1/T
150
250
350
450
TOC
Figure 2 : Variation of l/xm with T°C
The lattice parameters were calculated by the usual procedure and are almost matching with the reported values of Y type ferrite a = 5.88 8, and c = 43.6 8, for Zn2Y [4]. The lattice parameters calculated for the prepared sample are a = 5.7954 8, and c = 43.542 8,.Both a and c parameters decreased slightly, while the variation in parameter a is more, which is attributed to the contribution of lithium with aluminum in the structure. The structural data viz observed and calculated d values, relative intensities with hkl plane are given in Table 1. The sample behaves like a semiconductor with very high room temperature resistivity. The plot of logo vs 1/T is shown in figure 1. The activation energy calculated from the graph is Ea = 0.2760 eV, 0.4917 eV and 0.776 eV respectively for low, moderate and high temperature. The results
135
indicate that the electrical conduction is due to “Electron hopping”. The magnetic study with Gouy’s method showed that the sample is ferrimagnetic at room temperature and becomes paramagnetic at temp above 190°C. The Curie molar constant (Cm) is calculated from the plot inverse molar magnetic susceptibility versus temperature (Figure 2) and found to be 22.56. It is seen from the electrical conductivity and magnetic susceptibility results that the activation energy in paramagnetic region is higher than those in ferromagnetic region, which suggest that the magnetic disordering inclines towards higher activation energy side. This is in well agreement with the theory developed by Irkhin and Turov and Satyanarayana. References 1. G. H. Jonker, H. P. J. Wijn and P. B. Braun, Philips Tech. Rev. 18 (1956 / 1957) 145 2 . G. Albanese, A. Deriu and S. Rinaldi, J. Phys. C9 (1972) 1313 3. L.F. Bates, Modern Magnetism (Camb. Univ. Press) 1939 4. M. Mita and Shimizu H., J. Phys. SOC.Japan 35 (1973) 414 5. P. Irkhin Yu and E.A. Turov, Sov. Phys. JETP 33 (1957) 673. 6. R. Satyanmarayana, S.R.Murthy and T.S.Rao, J. less Common Metals 86 (1982) 115. 7. R. Satyanmarayana, S.R.Murthy, T.S.Rao and S.M.D. Rao, J. less Common Metals 90 (1983) 243.
Spinel ferrite based composites with permeability and permittivity of almost equal values L. B. Kong", Z. W. Li", L. F. Chen", G. Q. Lin", Y. B. Gan" and C. K. Ongb aTemasek Laboratories, National University of Singapore bCenter for Superconducting and Magnetic Materials, Department of Physics Faculty of Science, National University of Singapore Abstract This paper reports on our recent attempt to prepare composites with permeability and permittivity of almost equal values for low frequency applications. The composites were based on spinel ferrites with composition of Nio.7~.xCo,Zno.2~Fe~.~~Mn~.~204 (x=O, 0.05, and 0.10). The ferrite powders were synthesized via the conventional solid-state reaction process. The composites were fabricated using epoxy as matrix. For all samples of the fabricated composites, the permittivity remains almost the same, while the permeability can be varied through doping of cobalt in the spinel ferrites. 1. Introduction Materials of high refractive index ( n =
f i ),
impedance-matched to free space
(Z= = 1 , with E' = p' ), with low dielectric and magnetic loss tangent, have many potential electromagnetic applications [ 1, 21. However, such materials are rarely found in nature. Composite materials can be designed to achieve these properties [3-51, comprising several components, one or more of which should have both dielectric and magnetic properties. Composites with metallic alloys usually have very large permittivity due to their high conductivity [6-81. This is undesirable for our requirement. Hence, we have selected ferrites for preparation of the composites. To achieve low loss tangent, the materials selected must have a resonant frequency far beyond the operating frequency band. Three types of ferrites are considered: spinel, garnet and hexaferrite. The resonant frequencies of composites based on spinel and garnet ferrites are several hundreds MHz [9], and that with hexaferrites can operate in the microwave band [lo-121. Hence, it is possible to use spinel or garnet ferrite for low frequency applications, and hexaferrites for microwave requirements. This study aims to develop composite materials with permeability and permittivity of almost equal values, with low dielectric and magnetic loss tangent, over 2-30 MHz, 30-90 MHz and 100300 MHz. In this paper, we report our preliminary experimental results on the dielectric and magnetic properties of composites based spinel ferrites. The spinel ferrite selected has composition of Nio.7~.xCoxZno.2~Fe~.~~Mn~.~~04 (x=O, 0.05, and 0. lo). The basic composition of Ni0.7sZn0.25Fe204 has high permeability and low magnetic loss tangent. Cobalt was introduced to change the magnetic properties of the spinel ferrite, while iron deficiency and doping with manganese reduced the dielectric loss tangent. Our preliminary results showed that composites with 50% volume concentration of spinel ferrite powders are promising materials towards achieving such electromagnetic properties. 2. Experiment (x=O, 0.05, and 0.10) were synthesized Spinel ferrite powders Nio.75-xCo,Zno.~~Fe,,~oMno.o~04 via the conventional solid-state reaction process, using commercially available constituent oxides as the seed materials. The mixtures of oxides were thoroughly mixed and then calcined at 1000°C for 4 h. The calcined powders were compacted and sintered at 12OO0C, 1250°C and 1300°C for 4 h. The sintered samples were pulverized into powders. The powders were mixed with a commercially available epoxy (with a certain amount of hardener) to prepare for composites with volume concentration of about 50%. The permeability and permittivity of the composites were measured using a HP8722D vector
136
137
network analyzer over 0.5-16.5 GHz and a HP4291B impedance analyzer over 0.01-1.8 GHz. Measurement at low frequency uses samples of disk-shape, while measurement at microwaves uses coaxial samples. Phase compositions of the calcined and sintered samples were analyzed using a Philips PW 1729 type X-ray diffractometer (XRD) with Cu K, radiation. Grain size and grain morphology of the sintered samples were examined using a JEOL JSM-6340F type field emission scanning electronic microscope (FESEM). 3. Results and discussions Fig. 1 shows the XRD patterns of the ferrite powders after sintering at 1200°C for 4 h. All three samples are of phase-pure spinel structure, implying that the reaction of the constituent oxides is already complete at this temperature. The XRD results of the sintered samples showed that the spinel phase was retained after sintering at high temperatures.
I
10
x=o
1
1
I
I
I
20
30
40
h
1
50
60
70
20 ("1 Fig. 1: XRD patterns of the Nio.75.xCo,Zno.25Fel.soMno.0204 powders sintered at 1200°C for 4 h.
Fig. 2 shows the surface SEM images of the N ~ o . ~ ~ C O ~ . ~ ~ Z ~ ~ . Zceramics ~F~~. sintered at 1200"C, 1250°C and 1300°C for 4 h. Almost hlly dense (-95% relative density) spinel ferrite ceramic pellet was obtained after sintering at 1200°C. 99% relative density was achieved after sintering at 1300°C. The grain sizes of the ferrite ceramics, sintered at 1200"C, 1250°C and 1300"C, are -2.5 pm, -3.7 pm and -6.3 pm, respectively. Similar microstructures were observed in the samples of Nio.75Zno.25Fel.soMno.o204 and Ni0.~~Co~.~oZno.~~Fel.~0Mn~.~~O~. The grain size of the spinel ferrites has slight effect on the magnetic properties of the final composites. Fig. 3 shows the permeability and permittivity of the composites with 50% volume concentration of spinel ferrite powders sintered at 125OOC for 4h. The real permittivity E' is slightly dependent on frequency for all composites, decreasing from 7 to 5.5 as frequency varies from 40 to 600 MHz. With Co substitution, the real permeability p' at low frequency increases slightly from 9 for x=O to 10 for x=0.05, and then rapidly decreases to 6 for x=O.lO. This characteristic is attributed to two opposing factors of Co ions. First, in spinel ferrites, Fe and Ni ions contribute to positive magnetocrystalline anisotropy, while Co ion provides a negative anisotropy. After doping with Co, the total magnetocrystalline anisotropy decreases, leading to a slight increase in permeability. Second, the permeability of ferrite materials is due to the domain-wall motion and spin rotation [ 13, 141. The Co ions immobilize the domain walls. Consequently, the permeability due to domain-wall motion decreases greatly. Therefore, the total permeability is reduced for composite with x=O. 10. It is concluded that the real permeability p' can be varied to achieve p'=~' through doping with cobalt.
138
Fig. 2 Surface SEM images of Nio.7~Coo.o~Zno.2~Fe,.9oMno.o~04 ceramics sintered for 4 h at (a) 12OO0C,(b) 1250°C and (c) 1300°C. 10
10
3 6
6
4
1
2
2
0
0 10
10
5
E
8
2.
1
6
6
5
'E
E $
.s 'E
a 4 2
2
d
0 10
0 10
4
x=o.10
8
6 4
2
0
10'
10'
10'
Frequency (Hz)
10''
10'
10'
10'
10''
Frequency (Hz)
Fig. 3 Permeability and permittivity of the composites based the N ~ O . ~ ~ . ~ C O.9oMno.0204 ~Z~O. powders sintered at 1250°C for 4 h. It is noted that dispersion of the permeability of the composite has shifted slightly to higher frequency as the sintering temperature is decreased. This is due to the small grain size of the ferrite powder when sintered at low temperature, which led to low fraction of domain-walls. Therefore, powders of small grain size contribute less to the permeability, due to reduced domain wall motion. However, the effect of sintering temperature in the present study is significantly less than that of the composition (Co content).
139
4. Conclusions (x=O, 0.05 and 0.10) powders were synthesized Spinel ferrite via the solid-state reaction process. Composite materials were prepared using ferrite powders as inclusions and epoxy as matrix. For composites with 50% volume concentration of ferrite powders, permeability and permittivity of almost equal values at frequencies below 50 MHz were demonstrated. This was achieved via doping the spinel ferrites with Co to change the permeability. References 1. V. M. Petrov and V. V. Gagulin, Microwave absorbing materials, Inorganic Mater., 37 [2], 9398 (2001). 2. A. N. Yusoff, M. H. Abdullah, S. H. Ahmand, S. F. Jusoh, A. A. Mansor and S. A. A. Hamid, Electromagnetic and absorption properties of some microwave absorbers, J. Appl.Phys., 29 [2], 876-882 (2002). 3. W. Yu, R. Mettra and D. H. Werner, PFTD modeling of an artificially synthesized absorbing medium, ZEEE Microwave Guided Wave Lett., 9 [ 121,496-498 (1999). 4. W. Yu, D. H. Werner and R. Mittra, An artificially-synthesized absorbing medium for the truncation of FDTD lattices, ZEEE Microwave Guided Wave Lett., 10 [4], 128-130 (2000). 5. W. Yu, D. H. Werner and R. Mittra, Reflection characteristic alalysis of an artificially synthesized absorbing medium, IEEE Trans. Mag., 37 [5], 3798-3802 (2001). 6. M. Wu, X. Zhao, H. H and X. Yao, Preparation and microwave characteristics of magnetic iron fibers, J. Mag. Mag. Mater., 217, 89-92 (2000). 7. M. Wu, H. He, Z. Zhao and X. Yao, Preparation of magnetic cobalt fibres and their microwave properties, J. Phys. D: Appl.Phys., 33, 1-4 (2000). 8. C. Sudakar, G. N. Subbanna and T. R. N. Kutty, Hexaferrite-FeCo nanocomposite particles and their electrical and magnetic properties at high frequencies, J. Appl. Phys., 94, 6030-6033 (2003). 9. T. Nakamura, Snoek’s limit in high-frequency permeability of polycrystalline Ni-Zn, Mg-Z, and Ni-Zn-Cu spinel ferrites, J. Appl.Phys., 88 [l], 248-253 (2000). 10. R. C. Pullar, S. G. Appleton and A. K. Bhattacharya, The manufacture, characterization and microwave properties of alingned M ferrite fibres, J. Mag. Mag. Mater., 186,326-332 (1998). 11. P. Singh, V. K. Babbar, A. Razdan, S. L. Srivastava and R. K. Puri, Complex permeability and permittivity, and microwave absorption studies of Ca(CoTi),Fel2.2,019 hexaferrite composites in X-band microwave frequencies, Mater. Sci. Eng. B 67, 132-138 (1 999). 12. Z. W. Li, L. F. Chen and C. K. Ong, Studies of static and high-frequency magnetic properties for M-type ferrite BaFe12.2,Co,ZrxO19, J. Appl.Phys., 92 [7], 3902-3907 (2002). 13. T. Tsutaoka, Frequency dispersion of complex permeability in Mn-Zn and Ni-Zn spinel ferrites and their composite materials, J.Appl.Phys., 93 [5], 2789-2796 (2003). 14. T. Nakamura, T. Tsutaoka and K. Hatakeyama, Frequency dispersion of permeability in ferrite composite materials, J. Mag. Mag. Mater. , 138, 3 19-328 (1994).
Electric and Magnetic Studies on Copper/Cobalt Substituted Ni-Zn Ferrites
B. Parvatheeswara Rao', K.H.Rao', P.S.V. Subba Rao', S. Pallam Setty', N.S. Gajbhiye3and O.F. Caltun4 1 Department of Physics, Andhra University, India 'Department of Engg. Physics, Andhra University, India 3 Department of Chemistry, Indian Institute of Technology, Kanpur, India 4 Department of Electricity and Electronics, A.Z. Cuza University, Romania Abstract Lattice constant, DC resistivity and saturation magnetisation measurements on copper or cobalt substituted Ni-Zn ferrites have been reported in this paper. Cobalt has shown predominant impact on saturation magnetisation where as copper exhibited similar impact on DC resistivity for lower concentrations of dopant ions. The variations in both the parameters have been explained on the basis of their respective ionic radii size, ionic distributions, associated conduction mechanisms and contributions of magnetic exchange interactions. Introduction Ferrites find a large number of applications over a wide frequency range due to their higher electrical resistivities and better magnetic properties. The properties of ferrites are highly sensitive to amount of impurities present in or added to them. There have been many reports on ferrites [ 1-41 on the substitution of ions of different valences to improve the required properties depending on the applications of interest. In power electronics, the devices in the design of inductor and transformer cores make extensive use of ferrites such as Mn-Zn and Ni-Zn systems [5]. Particularly, for the operating frequencies in excess of 1 MHz, NiZn ferrites have an edge [6]. The cores for such applications require high magnetisation and low core losses. Improvements in magnetisation and resistivity as a result of compositional modifications would certainly help these materials to be used as more compact devices in application systems. The present paper reports the variations of lattice constant, DC resistivity and saturation magnetisation of NiZn ferrites doped with ferromagnetic cobalt or diamagnetic copper and discusses the results in terms of conduction processes and magnetic interactions between the cations. Ionic distribution for both the systems has been suggested in the light of the knowledge of site preferences of various cations present.
Experimental Details Polycrystalline Ni-Zn ferrites with the chemical formula Ni0.35 Zn0.65.~ Me, Fez 0 4 where Me being Cu or Co and x values ranging from 0.00 to 0.25 in steps of 0.05 have been prepared by conventional ceramic technique using the procedure described elsewhere [7]. Calcination and sintering of the samples have been carried out at 975OC and 1250°C respectively for 4 hours in air atmosphere followed by natural cooling. X-ray diffraction patterns confirm single phase cubic spinel structure in all the samples. Characterization of the samples was done further by comparing the measured values of lattice constant and Curie temperature of the basic composition with the respective parameters of the same composition reported earlier and these are found to be in good agreement with each other [7]. DC resistivity measurements on the samples have been made by standard two probe method and saturation magnetisation measurements are made using a VSM with fields up to 15 kOe respectively. Sintered density measurements by Archimedes principle are also presented to understand the impact of substitutions of copper and cobalt in these systems. Results & Discussion The observed sintered densities along with lattice constants for both the Cu and Co doped ferrites 140
141
are listed in Table I. Copper containing ferrites have been found to have higher sintered densities as it is known to act as sintering aid by influencing the atomic diffusivity while resulting volumetric shrinkage. Fig.1 shows the variation of lattice constant as a function of Cu or Co concentration. The lattice slightly increases as expected in both the substitutions for initial concentrations as ionic radius of C~~'(0.87nm) or Co2+(0.89 nm) is larger than the ionic radius of Zn2+(0.82nm). The deviation at higher concentrations in both the cases may be due to the presence of Cu and Co in other valence states. If Cu enters the lattice as Cu"(0.97 nm), it distorts the lattice because of its larger ionic radius and causes an indirect reduction in lattice constant.
Table-1 Table-1 2 2 c
2
0 8435 0 8430 0 8425 0 8420
80
i
70
-,
0 8415
2 0 8410
-0 0
2
8405
0 8400 0 8395
__
000
__
~
005
010
015
020
~
025
concentration, x ~
_
_
_
concenlratlon, x _
~
_
~~~~~~
_
Fig 1. Variation of lattice constant with CoICu Fig 2. Variation of saturation magnetisation with concentration in the system Nio 35 Zno 65-x Fe2 M, CoICu concentration in the system Ni0.35 Zno.65.x 0 4 where M=Cu or Co Fez M,04 where M=Cu or Co Fig.2 shows variation of saturation magnetisation as a function of Co or Cu concentration. The saturation magnetisation has been found to increase significantly with substituent's concentration in both the cases. In the present study, the basic composition contains 0.65 mol % zinc content and it is well known that all these zinc ions occupy A-sites only. Therefore, only 0.35 mol Yo trivalent iron ions are likely to occupy A-sites for this composition and the remaining 1.65 mol % Fe3+ions are expected to sit in B-sites along with 0.35 mol % nickel ions [8]. The small amount of iron present in A-sites is observed to be too small to maintain the predominant A-B exchange interaction among A and Bsublattices and hence the B-B exchange interaction is expected to take place. AS a result, the basic composition of the present system provides relatively low magnetisation value. Since both the cobalt and copper ions in their divalent state have marked preference for octahedral sites [9], theirs' incorporation in the basic composition yields higher saturation magnetisations based on the following distribution 4 ( Zn2+0.65.x Fe3+3 ~ + ~[ Ni2+ ) 0.35 Fe3+1.65-x M2+ 02in both the systems through the migration of some of the Fe3+ions from B-sites to A-sites and
142
thereby strengthening the A-B interaction with each step of increased substitution. The observed higher values of magnetisation (fig.2) for cobalt doped system are in accordance with the predictions as ferromagnetic Co2+ions possess magnetic moments of 3 p ~ .Though these Co2+ ions preferentially occupy B-sites and thereby forcing equal number Fe3+ions to migrate into Asites to fill the vacant Zn2+ sites as a result of substitutions, they indirectly strengthen the Asublattice as well as the magnetic interactions between A and B site cations [lo]. This leads to weakening of B-B interaction described above with each step of substitution and causes the magnetisation to increase. The observed variation of magnetisation with cobalt concentration is in accordance with this. The variation of magnetisation (fig.2) for copper doped system can be explained as follows: The Cu2+ions with magnetic moment of 1 p~ in octahedral sites contribute less to the net magnetisation compared to that of Co2+ ions. Further, the incorporation of copper may be forcing parallel formation of Cu2+ions as well as Cul+ions right from x=0.05 [ 1 11. These Cul+ions would prefer to occupy A-sites [ 121 and thus preventing the migration of B-site iron ions into A-sites throughout the range of substitutions. As a result, the weakening of B-B exchange interactions and strengthening of A-B exchange interactions would take place rather slowly and also the increase in magnetisation. Besides, as more and more Cul' ions are formed with increase in substitution, these along with certain quantity of Fe2+ions formed during preparation may be forcing some of the Ni2+ ions to convert into Ni3+ ions to maintain the charge balance and this hrther lowers the net magnetisation as evidenced through out the range of concentrations of copper in these ferrites. Fig. 3 shows the variations in DC resistivity with Co or Cu concentration. The substitutions in both the systems have resulted higher resistivities for lower concentrations though the copper is more effective in increasing the resistivity. Thereafter, at higher concentrations the trend continues in case of cobalt substitutions whereas lower resistivities are observed in case of copper substitutions.
I
3000
1 -i
I
500
,
0 0.00
I
I
* c u l
0.05
0.10
0.15
0.20
0.25
c o n c e n tra tio n , x
Fig 3. Variation of resistivity with CoICu concentration in the system Ni0.35Zn0.65-, Fez M, where M=Cu or Co
0 4
Electronic conduction in ferrites predominantly takes place through hopping of electrons between ions of different valence states within the identical crystallographic positions, the observed higher resistivities at lower concentrations in both the systems can be understood as a consequence of the hindrance of the Venvey mechanism [13] between such ions. Since ferrous ions are essential to realise low magnetic losses [ l 11, the preparation of these ferrites is made in such a way that the final product definitely contains certain quantity of divalent iron. This leads to increased hopping probability between Fe2+- Fe3+ions and the basic composition exhibited resistivity in the order of three. As the cobalt ions are introduced in place of zinc, by sitting in B-sites they force some of the
143 Fe3+ions there to move into A-sites. This reduces the total quantity of iron in B-sites and also the possible formation of Fe2+content as well as the hopping probability between Fe2+a Fe3+.Thus, the resistivity is increased initially. At subsequent concentrations of cobalt, possible formation of Co3+ions in the midst of Co2+ions triggers hopping between Co2+u Co3+ions and also initiates conduction process [I 11 of the type Co2++ Ni3+ e Co3++ Ni2+. The summation of these three conduction mechanisms prevents the resistivity from increasing further in the cobalt doped ferrites. The variation of resistivity in copper doped system can be explained as follows: Even though the formation of small number of CU" ions occurs simultaneously, they sit in A-sites and does not contribute to conduction in B-sites. Substitution of Cu2+ions in B-sites not only causes reduction in B-site iron quantity but also by sitting in between iron ions they contribute to increase the bond length between the iron ions; both these processes invariably reduce the hopping probability between iron ions and increases the resistivity. The observed higher values of resistivity at lower concentrations of copper doped ferrites are in accordance with these considerations. As more and more Cul+ ions are formed with the increase in copper substitution, some of the Cul+ ions may occupy B-sites as well [I21 and lead to conduction process of the type Cul+ u Cu2+.This is in addition to the conduction process of Ni2+ + Fe3+ e Ni3+ + Fe2+ contributing to lower the resistivities as evidenced for higher concentrations of copper doped ferrites. The observed higher values of sintered densities of these ferrites are also responsible for lower resistivities particularly at higher concentrations of copper. However, chemical analyses to determine the valence state of doped cations, Mossbauer studies to estimate the cationic site preferences and densities and microstructures to understand the contributions of grains and grain boundaries to the resistivity would be more helphl to complement the arguments made above in respect of magnetisations and resistivities.
Conclusions The results of the Co or Cu doped NiZn ferrites suggest magnetisation can be better improved with cobalt substitution and similarly resistivity can be better improved with copper substitution at lower concentrations. Improvements in resistivity and magnetisation with copper or cobalt substitution would help to decrease the eddy current losses and increase the operating frequency limit further; thus finding these materials utility for power applications at higher frequencies. However, a complete picture corroborating its usefulness will be made known only after evaluation of all the results for which the measurements are underway. References 1. K.H. Rao and R.G. Mendiratta, J. Appl. Phys. 54 1795 (1983). 2. B.V. Bhise, M.B. Dongare, S.A. Patil and S.R. Sawant, J. Mater. Sci. Letts., 10 922 (1991). 3. J.H. Jean and C.H. Lee, Jpn. J. Appl. Phys. 40 2232 (2001). O.F. Caltun and L. Spinu, IEEE Trans. Magn. 37 2353 (2001). 4. 5. R. Lebourgeois, J. P. Ganne and B. Lloret, J. Phys. IV France 7 Suppl. C1:105 (1997). 6. E.C. Snelling, Advances in ferrites, vol.1, Edited by C.M. Srivastava and M.J. Patni, New Delhi, India, Oxford & IBH, p.579-586 (1989). 7. B. Parvatheeswara Rao, P.S.V. Subba Rao and K.H. Rao, IEEE Trans. Magn. 33 4454 (1997). 8. J.M. Daniels, A. Rosencwaig, Can. J. Phys. 48 (1970) 381. 9. E. Rezlescu, L. Sachelarie, P.D. Popa and N. Rezlescu, IEEE Trans. Magn. 36 3962 (2000). 10. J. Smit and H.P.J. Wijn, Ferrites, Philips Technical Library, Eindhoven (1959). 11. J.G.M. De lau, Philips Res. Repts. Suppl. No. 6 (1975). 12. E. Kester, B.Gillot, P.Perriat, C. Villete, Ph. Tailhades and A. Rousset, J. Phys. IV France 7 Suppl. C1:261 (1997). 13. E.J.W.Venvey and J.H. de Boer, Rec. Trav. Chim. Pays-Bas. 55 531 (1936).
This page intentionally left blank
Session R6
Posters
This page intentionally left blank
Microwave Tunable Dielectric Bao~Sro~Ti03:MgO composites prepared from the nano size particles S. Agrawal, R. Guo, D. K. Agrawal, A. S. Bhalla Materials Research Lab./MRI Pennsylvania State University, University Park, PA 16802, USA
Abstract Ceramic composites of Ba0$3o.~TiO3 (BST) and MgO are prepared by the solid state reaction. The nano-size particles BST and MgO are used for synthesizing the composites with uniform grain distribution and homogenous dielectric properties. Dielectric properties are measured in the temperature range lOOK to 300K in the radio frequency range, while the microwave frequency measurements (3 6 GHz) are carried out at room temperature. By using nano particle size, low dielectric constant and dielectric losses are observed in the resulted composites. Tunable Dielectric characteristics of the composites are studied and compared with the composites prepared by using different sizes grains. SEM studies are carried out to study the grain size and distribution of phases in the composites.
-
Introduction The present demand for the miniaturization of devices for the communication and frequency tunable systems has led researchers to explore new materials with improved properties. The use of ferroelectric material is one of the possible avenues which can be exploited for field dependent electrical and electro-mechanical properties [ 11. Though, these materials have electric field dependence, high dielectric constant and losses in general limit their use in the microwave devices. Invariably, for the field agile applications the high dielectric constant in the ferroelectrics is diluted through the composite route in order to match the device requirement. Thus, by the addition of nonferroelectric low loss material in composite samples the tunability is hampered to a great extent, though the decrease in dielectric loss is observed [2,3]. Bal.,Sr,TiO3 is a well known ferroelectric material and has been extensively used in devices for the past few decades. The non-ferroelectric component was selected with low dielectric permittivity, very low dielectric losses (preferably I and which has low or no chemical reactivity with BST [4, 51. The selected candidate material MgO is mixed with BST in different weight ratios to prepare the tunable dielectric composite with low dielectric permittivity. The composites were prepared by using nano size particles to enhance the overall properties. Experimental Procedure The calcined powders of BST and MgO were mixed in different weight ratios using nano size particles. The powder was ball-milled for 16 - 24 hours in ethyl alcohol. The powder was pressed into pellets and sintered at temperatures between 1400°C and 1650°C. The description of sintering is given elsewhere [6]. The samples (97-99% density) were polished and thinned down to suitable thickness and sputtered with gold electrodes for dielectric measurements. The dielectric measurements in the frequency range of 1 KHz to 1 MHz were carried out using the multi-frequency LCR meter (HP 4284A) in the temperature range of 50K to 300K, in a computer assisted set up. The temperature controller (Lakeshore model 330) and a closed-cycle helium cooled cryostat (Displex DS-202 and HC-2, APD Cryogenics Inc.) were used to make the low temperature measurements. Tunability measurements were conducted with the addition of voltage source (TREK 610, TREK Inc.) and a 2 KV blocking circuit that isolated the LCR meter from the high voltages applied to the sample. These instruments were interfaced with a controlling computer for monitoring and collecting data. High frequency measurements were done using the modified perturbation technique method. The measurements were carried out at 3GHz at room temperature using C-band waveguide connected
-
147
I48
to the network analyzer through cables and adapters as shown in Figure l(a). A rectangular C-band waveguide with inner dimensions of (4.74 cm X 2.21 cm X 18.2 cm) was modified for dielectric Quartz tube Brass tube
Figure 1(a): Setup for microwave frequency measurements Figure 1(b): Graphical representation of modified C-band waveguide measurements as shown in Figure l(b). Two holes were cut through both the walls of the cavity and a quartz tube was inserted. A ceramic sample was put inside the quartz tube and placed at the center of the cavity with maximum electric field intensity. The changes in the resonant frequency and quality factor with the insertion of a sample and quartz tube were observed and the complex dielectric permittivity was calculated. Results and Discussion Table I shows the maximum dielectric temperature and dielectric constant of composites prepared by using the nano particle size BST and MgO. The maximum dielectric peak temperature for all the composites has been shifted to a lower temperature resulting in the low K of the composite near room temperature. The dielectric constant of pure Bao.5Sro.5Ti03 is 4000 at 270 K (phase transition peak). The dielectric properties tailor depending upon the BST:MgO ratio, as shown in Table I.
Table I: Dielectric data for composite of BSTSO,,,, Composition Ba0.&0.5Ti03 (Y) : MgO (1-y) 0:lOO 40:60 50:50 60:40 70:30 80:20 90:lO 1oo:o
Maximum Dielectric Peak Temperature (K) 203 203 205 204 210 212 270
+ MgO,,,, in various weight ratios at 100 KHz Maximum Dielectric Constant -7 86 225 475 640 1600 2710 4000
Dielectric Constant (273 K) -7 70 163 312 486 760 1608 3900
Dielectric Loss (273K) -0.0005 -0.00 15 -0.0024 -0.0017 -0.0026 -0.0020 -0.0039 -0.0323
149 0.10
1600 -1KHz
0.08
0.06 4
.2
4
0.04 .0.02 0.00 3 Temperature (K)
Figure 2: Variation of dielectric constant and loss in various Bao.sSro.sTi03(nano):MgO(nano) (80:20) composite
Figure 3: SEM micrograph of BST,,,, MgO,,,, composite showing the connectivity pattern
+
Table-1 Table-1 Table-1 Table-1 Table-1 Table-1 Table-1 Table-1 Table-1 Table-1 Composition
Maximum Dielectric Temperature (Tm)
BaU.5%.5Ti03inane) + MgO(nano) (40:60) Ba0.5Sr~~Ti03 inane) + MgO,mi,ron, (40: 60)
203
203
Dielectric Constant (* Tm)
(* ---t Tm)
Tunability (%) 40 KV/cm.
K-factor
0.0045 (203 K*) 0.0010 (300 K) 0.005 1 (203 K*) 0.0029 (300 K)
34 10 30 22
75 100 58 75
Dielectric Loss
+
86 (203 K*) 50 (300 K) 105 (203 K*) 79 (300 K)
150
the complex permittivity can be described as equations 1 & 2, where the change in f and Q of a cavity with and without sample are described as,
-------------_-(1)
SE,E2dv
.A
--- f 2
-
-1)
f2
v
2 1E;dV V
-_______________ (2) Q*
Y
f, {I tan6 = 2 ( f c -f,> Q,
l ]
-----------_____ (-3)
Q,
The above expression is based on the assumption that the electric field lines are tangential to the surface of the sample and if there is very little change in the resonant frequency (fr) and Quality factor (Q) of the cavity, above equations can be simplified to calculate tan6 as shown in equation 3, as suggested by Dube and Lanagan [8]. The composites were characterized at 3.249 GHz at 297 K and the microwave frequency losses were calculated. The composite samples gave the typical value of tan6 < 0.01 as compared to -0.09 for pure BST. Detailed studies on the composites in the microwave frequency are in progress. Conclusion
The dielectric and tunable properties of BST/MgO composites depends on the use of nano size particles. Low dielectric constant with high K-factor were observed in BST,,,,+MgO,,n, composites, where as the high tunability with low K-factor was observed in the BST,,,,+MgO,icron composites. At 40 KV/cm. fields, 10 % tunability in BST,a,,+MgOna,, composite and 22 % in BSTnano+MgO,icron composite at 300 K were achieved. Connectivity of the two phases in the composite samples probably played a significant role in the resulted properties of the composites. Acknowledgement
The work is supported by the NSF meta-materials project. S. Agrawal is thankful to Dr. M. T. Lanagan for the guidance in microwave frequency measurements. References 1) A. S. Bhalla, Ruyan Guo, Rustum Roy, The perovskite structure - a review of its role in ceramic science and technology, Materials Research Innovations (2000), 4, 3-26. 2) E. F. Elberta, R. Guo, A. S. Bhalla, Novel BST:MgTi03 composites for frequency Agile Applications, Ferroelectrics (2002), 268, 169-174. 3) Wontue Chang, Louise Sengupta, MgO-mixed Ba0.6Sr0.4Ti03bulk ceramics and thin films for tunable microwave applications, Journal of Applied Physics (2002), 92,3941-3946. 4) S. Agrawal, H. Manuspiya, R. Guo, D. K. Agruwal, A. S. Bhalla, Dielectric tunability of microwave sintered BST:MgO composites, Ceramic Transactions (2004), 15O(Ceramic Materials and Multilayer Electronic Devices), 299-306. 5) S. Agrawal, R. Guo, D. K. Agrawal, A. S. Bhalla, C. B. Murray, R. R. Neurgaonkar, Dielectric tunability of BST:MgO composites prepared by using nano particles, Ferroelectric Letters (2004), 31, 149-156. 6 ) S. Agrawal, R. Guo, D. K. Agrawal, A. S. Bhalla, Tunable BST:MgO dielectric composite by microwave sintering, Ferroelectrics (2004), 306, 155-163. 7) George Birnbaum, Jacques Franeau, Measurement of the dielectric constant and loss of solids and liquids by a cavity perturbation method, Journal of Applied Physics (1949), 20,817-818. 8) D. C. Dube, M. T. Lanagan, J. H. Kim, S. J. Jang, Dielectric measurements on substrate materials at microwave frequencies using a cavity perturbation technique, Journal of Applied Physics (1988), 63 (7), 2466-2468.
Preparation and Main Properties of Nd, Pr, and Sm-doped BhTi3012Thin Films Jianru Han*, Changhong Yang and Zhuo Wang Shandong University, China *jhan@,,sdu,edu.cn
Abstract Nd, Pr, Sm-doped Bi4Ti3012 thin films have been synthesized by metal-organic solution decomposition method and deposited on SiOz/Si substrate by spin coating. The structural characteristic and crystallization of the films are examined by X-ray diffraction. The surface morphology was studied using atomic force microscopy. The films exhibit good insulating property and resistance to breakdown. The clockwise hysteresis curves observed show that the films have a memory effect. The fixed charge density and the surface state density were also calculated. The results show that the films have promising application as the ferroelectrics field effect transistor memories.
151
Influence of Nanoscale Distribution of Magneli's Phases on the Dielectric Properties of Niobate Oxides
Hathaikarn Manuspiya" Chulalongkorn University, Thailand *hathaikarn.m@,chula.ac.th Amar Bhalla and Ruyan Guo Perm State University, United States Abstract A small variation in polar cluster size can lead to a wide dielectric dispersion covering several frequency decades. The dielectric measurements of Nb205 solid solutions show strong frequency dispersion of the dielectric maxima at frequencies 1 kHz to 1 MHz in the temperature range of -150°C to 150°C.
The direct-current (dc) electric field dependence of the dielectric constant has been measured showing significant suppression of the dielectric constant by application of dc bias. The strong dielectric dispersion which exists in a large frequency range implies that the relaxation process involved is not of a Debye type. A relaxation distribution can be therefore expected. The influence of the cluster size dispersion is one assumption. Thus, the data of dc bias field dependence of the dielectric constant has been analyzed by the modified Devonshire relation including a cluster term giving the fitted parameters: cluster sizes distribution and their polar cluster polarization.
152
Radiation Characteristics of Circular Disc Microstrip Array Antenna on NiCoAl Ferrite Substrate Dheeraj Kumar and P.K.S. Pourush Microwave and Antenna System Lab Department of Physics, Agra College Agra dheeraivadav 790yahoo.co.in
Abstract The problem of a 4x4 circular disc array antenna (CDAA) printed on a uniaxially anisotropic ferrite (NiCoAl) substrate is treated. The effect of anisotropy on the resonant frequency of the antenna is investigated. Radiation and scattering characteristics of the antenna with a normal and parallel magnetic bias field to the direction of wave propagation in the plane of ferrite are described. Calculated results for the radar cross section (RCS) of antenna are presented, and it is shown that the peaks in the RCS can be moved with respect to angle of incidence by changing the magnetic bias field. This effect offers a way of minimizing the radar visibility of microstrip antennas and arrays. Results are obtained from cavity modal solutions for a circular patch antenna at its TMll mode. Introduction Recent advancement of thin film technology has motivated the use of ferromagnetic thin films in microwave and millimeter-wave integrated circuits [ 1-21, The integration of ferrite technology in to integrated circuit structures has advantages including possible lower cost, smaller size, and more diversification in monolithic microwave integrated circuits (MMIC). Applications of ferrite technology in millimeter-wave scanning arrays have increasing important [3-41. An attractive feature of biased ferrite is that the material characteristics are nonreciprocal and electronically tunable. The use of biased ferrite layers in printed circuit antenna characteristics has been investigated extensively. Unique antenna characteristics including electronic tenability, RCS control, beam steering, surface wave reduction, and gain enhancement have been derived in [5-71 It has been established that, for a biased ferrite slab, a normal incidents plane waves may excite two types of waves (ordinary and extraordinary wave). In the case of a normal incidents wave, the ordinary wave is the same as the plane wave in a dielectric slab transversely to the biasing direction. On the other hand, the extraordinary wave is a TE mode polarized parallel to the biasing directions with its phase propagation constant Ke. The phase propagation constant Ke and KO of an extraordinary and an ordinary wave, respectively, may be given as follows [l, 81. K,
(-)2
KO
=
+
-wz
(0,
w, (w,
+ w,)
-w2
=”&
KO
C
..l
...2
where 00 = yH0, om= y4nMs, HO is the bias field, 4nMs is the saturation magnetization, y is the gyromagnetic ratio as y = 2.8 MHz/Oe. It is seen that, when peflis negative, the extraordinary wave is decaying even if the material is lossless. The frequency range for negative peffis:
[wo(wo+w,)y2 < w < (0, + w,)
...3
It has been pointed out and experimentally demonstrated that if the normal incident wave is properly polarized, the ferrite radome may cause significant RCS reduction of microstrip patches due to the excitation of a decaying extraordinary wave. The use of biased field to control the properties of the extraordinary wave results in an externally switchable antenna. The antenna is “off’ when an attenuating extraordinary wave in ferrite cover causes large RCS reduction and little radiation, and is “on” when peKis negative. 153
154
On applying a DC magnetic bias parallel to wave propagation in the plane the ferrite substrate the resonance splits in two separate frequency modes one right hand, the other left hand circular polarization. The explicit dependence of propagation constant of the two modes is given as [8] K, w,+w,fw (-)2 = .4 KO w, T w where K+,K. are the propagation constant for right handed and left handed circularly polarized mode (RHCP & LHCP) respectively. It is seen that LHCP mode is practically non dispersive and corresponds to the 0-mode. However, the RHCP mode is strongly dispersive and resembles the E-mode propagating perpendicular to the dc field. It follows from equation [ 11 that LHCP mode propagates at all frequency while there is no propagation of the RHCP mode when u,< w < (w, + w, ) , the cut-off range is larger in this case (i.e. for propagation along Ho) than the preceding case (i.e. for propagation perpendicular to Ho). There is resonance, as expected, at O=OO. Antenna Configuration The geometry and co-ordinates system of CDAA is shown in Fig.1. It comprises 16 circular disc patch elements of radius 5.1 mm printed on ferrite of thickness (h) 1.27mm, substrate permittivity ~ , = l 2 tan6=0.002, , 47cMS=2200Gauss,resonant frequency (f,)=SGHz, element separation dx=d,=3 .O mm, progressive phase excitation difference px=py=!? and applied magnetic field (Ho)=2000 Oe. 2
Results 1. Propagation Perpendicular to Ho By the application of the bias peff is negative for [u,(w, +w,)]”2 < w < (0, + u,) according to which extraordinary wave is decaying in this range. The cutoff and resonace frequency of CDAA for external magnetic field of 2000 Oe are 1.292GHz and 1.872GHz. These limits can be tuned by the optimum variation in the bias field as shown in Table I. It is seen that tuning of 186MHz in resonant frequency of the antenna is possible by the application of DC bias up to 2000 Oe as shown in 1
N
I
a
2
LL
5.2
5.15 5.1 5.05 5
0
500
1000
1500
2000
Magnetic Field (Oe) Fig. 1. Array geometry and co-ordinate system of CDAA on NiCoAl
Fig.2 Variation in resonant frequency with magnetic field
The field patterns and RCS for the antenna are computed and plotted for unbiased and biased case in two different planes (i.e. E-plane and H-plane) and are shown in Figs.3, 4, 5 and 6 respectively. It is observed from the figures that patterns of array antenna are directive in nature and provide limited number of secondary lobes. For E-plane pattern the power of secondary lobe for biased case increased by 70dB with respect to unbiased case [Fig. 31. However, variation in power for biased and unbiased case in H-plane has been observed almost same [Fig. 41. We show the RCS peaks shifts with angle of incidence and it get reduced - 40dB by the application of magnetic bias in Eplane [Fig. 51. The peaks are identical for biased and unbiased case in H-plane [Fig. 61.
155 Table I: Computed values of resonance and cutoff limits for extraordinary wave [ w o (a,,+ w,
)] '/2x < w/2x < ( wo + w,
)/2x (GHz)
0.51% 0 / 2 x 4 . 2 0 3 0.797< w/2x 4 . 4 2 6 1.050< w/2x (b) Fig. 1. (a) Schematic diagram and (b) Mesh Configuration of Electrodeless Fluorescent Lamp. 171
172
3. Results and Discussion 3.1 Magnetic flux and magnetic field strength following the increase in thickness Figure 2 is a graph in which the magnetic flux and magnetic field strength is compared in Line 3 (Q type) and Line 4 (K type). In other words, it shows the characteristics of the electromagnetic field in each lamp’s surface of Q type and K type. In K type, where the thickness has doubled to 3.8 [mm], the magnetic flu in the center had a value of 2 . 9 0 3 ~ 1 0 -[Wb]. ‘~ This value is 1 . 3 7 7 ~ 1 0 - ’ ~ [Wb] increased than 1 . 5 2 6 ~ 1 0 -[Wb] ’ ~ of Q type. The magnetic field strength was 0.059 [Nm], showing that an increase of 0.022 [Nm] was made.
3.2 Electricity loss and energy following the changes in frequency Figure 3 shows the electricity loss and energy following the changes in frequency between the range of 250 [IcHz] - 2.65 [MHz]. As frequency increases, the electricity loss incrcases as well. On the other hand, energy was inversely proportional with frequency increase. At 2.65 [MHz], there was 0.55 [mW] of electricity loss, and 5 . 2 ~ 1 0 - ’[J] ~ of energy. In the Mn-Zn type ferrite core selected for this simulation, the electricity loss and energy had a fair value when the input frequency was about 900 [kHz] while applying a current at 0.05 [A].
Fig. 2. Flux and Mag H as the function of distance on line
Fig. 3 Power loss vs.
a function of frequency.
3,4
3.3 Characteristics of the QL lamp Figure 4 shows the characteristics of frequency, impedance and inductance for the QL-85W antenna. In 2.65[MHz] which is the operation frequency, the impedance and inductance were each 318.7[L2] and 19.13[pH]. Generally, frequency showed stable characteristic. The change of inductance especially showed 16 22.3[H] in 2 - 4[MHz]. For the frequency of the QL-S5W antenna (5OO[kHz] 6[MHz]), the changes of coil resistance and reactance are shown in Figure 5. When the frequency was at 4.8[MHz], high resistance and reactance at around 4000[R] was observed. Before and after 2.65[MHz], where the QL-lamp operates, they were relatively stable against the frequency. At 2.65[MHz], the resistance and reactance were each 4.3[L2] and 318[Q].
-
-
5
u FqW*.iC/
lkuaj
Fig. 4. Impedance [Z], Inductance [L] properties as a function of frequency.(QL-85W Antenna).
1rm
>La’
an
ra,
%liu
Frrguenc~~ {Wzj
Fig. 5. Resistance [R], Reactance [XI properties of QL85W antenna as a function of frequency.
173 3.4 Electrical characteristics of k-Core coil Figure 6 shows the relationship between the frequency of K-type Antenna and the Q-factor. In K-type Antenna, the Q-factor was largest around 1 MHz. Up till 4 MHz, it was decreased drastically as the frequency is increased. For the relationship between the number of coil turns and the Q-factor, the graph shifted to the lower frequency area as the number of coil turns is increased. Based on 2.65 MHz, the Q-factor was highest at 59.72 when the number of coil turns was 9. The Qfactor decreased by 3 as the number of coil turns is increased. When the number of coil turns was 17, the Q-factor was 33.24. In Figure 7, the changes in inductance following the changes in frequency for each coil turns is shown. As the number of coil turns increases, the inductance is increased. Based on 2.65 MHz, the
-
changes were within the range of 9.13 29.17 pH for each coil turns. The resonance frequency decreases as the number of coil turns increases. 4. Conclusions In this paper, the characteristics of the electromagnetic field radiation in electrodeless fluorescent lamp were examined. We have checked that the generation of the electromagnetic field, which generates plasma electric discharging by energizing the gas inside the lamp, is proportional to the size of the ferrite. Also, the electrical characteristics following the increase of frequency for the previous and k-type antenna was examined. By comparing and analyzing the characteristics of the impedance, inductance, reactance and Q-factor following the frequency and the number of coil turns, we have concluded as follows.
t Fig. 6. Frequency VS. Q-Factor as the function of each coil turns.
Fig. 7. Frequency VS. Inductance [L] as a function of each coil turns.
1. When the input electricity is increased, the electricity loss increased drastically. Thus, the electromagnetic field radiation towards the inside of the lamp is dependent on the magnetic permeability value of the ferrite, when the used frequency in limited. Also, the strength of the electromagnetic field radiation towards the inside of the lamp changes as the thickness changes. 2. The electricity loss was proportional to the change in frequency. On the other hand, energy was inversely proportional. When the input frequency was at about 900 kHz, the electricity loss and energy had fair value compared to the values at 2.65 MHz. 3. For the impedance, QL-85 Antenna and K-Antenna had a similar value of 319a and 324a each, when the operation frequency was 2.65 MHz and the number of coil turns was 14. As the number of coil turns is increased, the impedance increases, and when the number of coil turns was 17, the value of impedance went up to 486a. 4. For the inductance, QL-85 Antenna and K-Antenna had a similar value of 19.12pH and 19.45pH each, when the operation frequency was 2.65 MHz and the number of coil turns was 14. As the
174
number of coil turns is increased, the inductance increases, and when the number of coil turns was 17, the value of impedance went up to 29.17pH. 5 . For the resistance elements of the coil, QL-85 Antenna had a value of 4.3952, while K-Antenna had a relatively high value of 7.09L2, when the operation frequency was 2.65 MHz and the number of coil turns was 14. As the number of coil turns is decreased, the resistance decreases, and when the number of coil turns was 11, the value of resistance was 3.7952. Acknowledgement This work was financially supported by MOCIE through EIRC program (1-2004-0-074-0-00).
Electric Field Generated Stress on PolythiophenelPolyisopreneElastomer Blends
Toemphong Puvanatvattana, Anuvat Sirivat, and Datchanee Chotpattananont" The Petroleum and Petrochemical College, Chulalongkorn Universiq, Thailand *datchanee@,yahoo.com Abstract Electrorheological properties of polyisoprene and polythiophene/polyisoprene composites were investigated as potential electroactive actuator applications. Experiments were carried under the oscillatory shear mode and applied electric filed strength varying from 0 to 2 kV/mm. The dynamic moduli, G' and G", of the pure polyisoprene varied with the crosslinking ratio and electric filed strength; the storage modulus (G') increased but the loss modulus (G') decreased with increasing crosslinking ratio. The storage modulus (G') and the loss modulus ( G ' ) of the pure polyisoprene fluid, PI-00, exhibited no value change with increasing electric filed. For PI with the crosslinking ratios of 2, 3, 5 and 7, (PI-02, 03, 05 and 07), the storage modulus sensitivity, AG'/G'o, increases with electric filed strength at lo%, 60%, 25%, and 30% at electric field strength of 2 kV/mm, respectively. For the composite of undoped polythiophene and PI (Pth-U/PI-03 j, with the undoped particle concentrations of 5%, lo%, 20% and 3O%vol., the dynamic moduli, G' and G" of each composite, were generally higher than those of pure crosslinked polyisoprenes (PI-03). Their storage modulus sensitivity, AG'IG',, increased with electric filed strength and attained a maximum value of SO%, 35%, 110% and 45% at the electric field strength of 2 kV/mm, respectively. Introduction Electromechanical energy conversion, which converts the electrical energy into mechanical energy, has been of scientific and technological interests with regards to many applications such as muscle/insect-like actuators, robotic, etc. Electroactive polymers (EAPs), which offer many promising and novel characters such as light-weight, high energy density and high flexibility, are material candidates for muscle-like actuators. Dielectric elastomers are a type of electric-filedactivated electroactive polymer that is capable of demonstrating large strains, fast response, and high efficiency. Polyisoprene or natural rubber is one type of dielectric materials which has many advantageous characters; inexpensive due to its natural source, flexible polymer, low swelling in water, high tensile strength, good resilience, high hot tensile, and well behaved hysteresis. These characteristics generate desirable properties that can be used to induce large actuation strains by subjecting the material to an electrostatic field. Recently, incorporation of a conductive polymer into a dielectric elastomer forming a composite has been of keen interest. Conductive polymers can offer a variety of benefits to the host elastomer: good conductivity, better thermal stability, and mechanical properties. Examples are Polyanilene-polyisoprene composite for biosensor application, Polyanilene-EPDM composite, and Ti02 embedded in PDMS gels for actuators application.
In our work, the aim is to develop a polythiophene/polyisopreneelastomer blends as a substitute for artificial muscles. The mechanical properties, viscoelastic properties and electrical properties will be investigated in the terms of degree of polyisoprene crosslinking, electric field, and polythiophene composition in order to understand its behavior under various conditions. Experiment Preparation of the Pth/Polyisoprene Blends Poly (3-thiopheneacetic acid), Pth, was synthesized by oxidative-coupling polymerization according to the method of Kim et al. The crosslinked polyisoprene matrix was prepared by using dicumyl peroxide as crosslinking agent. Various amounts of dicumyl peroxide were used to vary the degree of crosslinking (crosslinking ratios: 2 , 3, 5 and 7). The crosslinked polyisoprene was fabricated by compression molding at 175"c and 5 MPa for 7 min. 175
176
The PtWPolyisoprene blends were prepared by mechanical blending of undoped synthesized polythiophene particles and polyisoprene with various particle concentrations (5%, lo%, 20% and 3O%vol./vol.). The optimum degree of crosslinking, having the highest rheological sensitivity, was chosen. (crosslinking ratio of about 3). The fabrication of the P3TAAicrosslinked polyisoprenes was done by compression molding at 175°C and 5 MPa for 7min. Electrorheological Properties Measurement A Melt rheometer (Rheometric Scientific, ARES) with parallel plates fixture was used to measure rheological properties. A DC voltage was applied with a DC power supply (Instek, GFG 8216A) which can deliver electric field strength up to 2 kV/mm. In these experiments, the oscillatory shear strain was applied and the dynamic moduli (G' and G") were measured as functions of frequency and electric field strength. Strain sweep tests were first carried out to determine the suitable strain to measure G' and G" in the linear viscoelastic regime. The appropriate strain was determined to be 220% for pure polyisoprene fluid and 1% for these crosslinked polyisoprenes and for these polythiophene/polyisoprene.Then frequency sweep tests were carried out to measure G' and G" of each sample as hnctions of frequency. The deformation frequency was varied from 0.1 to 100 rad/s. Each measurement was carried out at the temperature of 27 OC and repeated at least two or three times.
Results and Discussion Electrorheological Properties of Pure Polyisoprene The effect of crosslinking on the rheological properties of pure polyisoprene (PI) was first investigated. The crosslinking ratios were 0, 2, 3, 5 and 7. Our results clearly suggest that with increasing amount of crosslinking ratio free movements of polymer chains are prohibited and the PI behavior changes from that of a fluid-like structure (PI-00) to that of a solid-like structure (PI-07). The effect of electric field strength on the rheological properties of pure PI, at various crosslinking ratios, was further investigated in the range between 0-2 kV/mm. Figure 2a and 2b show the dynamic moduli G'(a) and G'(a) of various crosslinked PI systems as functions of electric field strength. The G' (a)of each crosslinked PI systems increase only at high electric field strengths (0.5-2 kV/mm); the sensitivity values, defined as AG'/G'o, are lo%, 60%, 25%, and 30% for PI-02, PI-03, PI-05, and PI-07, respectively. The G'(a), of the lightly crosslinked systems (PI-02 and PI-03) increase with increasing electric field strength (Fig. 1b). However, the G"(a) of the higher crosslinked systems (PI-05 and PI-07) decreases with increasing field strength. Our results suggests that the lightly crosslinked systems contain a particular group of chain segments that are capable of moving and generating friction with its environments. For the higher crosslinked systems, they possess the more solid-like structures with increasing field strength; relative motion between chain segments is progressively limited in the presence of electric field. 400
10000
-
u PILOO, G'0 = 1.50 Pa + PI-02, C'o = 4812 Pa PI-03, G'o = 7401 Pa PI-05, G'o = 19155 Pa PI-07, G'o = 27201 Pa
8000 6000
CL
2
4000
200 1 0:
-6
-200
25
-400
2000 -800 0
4
I
~
P1-00, 6 " 0 = 9 2 u PI-00, Pa +PI-02, G"o = 1176 Pa
-Y?
-
PI-03, C"0 = 418 Pa PI-05, G " o = - 7 8 Pa & PI-07, G"0 = -370 Pa A
.inon .... 1 1
10
100
1000
1
10000
E (Vlmm)
(4
10
100
LOO0
10000
E (Vimm)
(b)
Figure 1. Responses of the storage and the loss moduli of the polyisoprenes at various crosslinking ratios vs. electric field strength, at frequency 1.0 rads, strain 1%, (PI-00 system, strain 220%). Moreover, we have found that the sensitivity (AG'/G'o) of the fluid system depends on frequency
177
but those of the crosslinked systems do not. For the fluid system, at low and medium frequencies (0.1 and 1.0 rads) which representing the larger chain segments, high G’ sensitivity can be observed. On the other hand, at high frequencies (10 and 100 rad/s) which representing the smaller chain segments (a group of monomers), low G’ sensitivity can be observed. For the crosslinked systems, the crosslinked PI-03 system has the highest G’ sensitivity (AG’/G’o) at the maximum field strength; this system contains a balance between the solid-like and the fluid-like structures. On the other hand, the lower crosslinked system (PI-02) has more fluid-like structures than other crosslinked systems; free movement of polymer chains and lesser intermolecular interactions occur. The higher crosslinked systems (PI-05 and PI-07) contain relatively more solid-like structures. The polymer segments and chains are quite rigid and fixed; they simply cannot response under the same electric field or the induced dipole moment strength. Electrorheological Properties of Polythiophene/PolyisopreneBlends (PTh/PI) Effect of Polythiophene Composition The PI-03 system was picked out to blend with poly(3-thiopheneacetic acid) because it exhibits the maximum G’ sensitivity at about 0.6. Figure 2a and 2b show the storage modulus (G’) and the loss modulus (G”) vs. frequency in the absence of electric field at various Pth particle concentrations of 0%, 5%, lo%, 20% and 30%vol (PI-03, PthUS/PIO3, Pth-UlO/PI-03, PthU20/PIO3 and Pth-U30/PI-03). We found that G’ and G ’ increase with Pth particles concentration. The G’(w) and the G”(w) of each polymer blends systems are higher than PI-03 system in the absence of electric field. Close inspection of these results indicates that Pth particles in polymer blends act as filler in matrix, which can store or absorb the forces/stresses within the matrix. The polymer blends system with a higher particle concentration will generate a higher internal stress response than that of pure PI-03 system so the G’(o) and the G’(o) of polymer blends system are higher than those of PI-03 system. --(t
le+6
PI-03
* Pth-U5/PIL03 PthLU10/PI_03
-
* Pth
le+5
-
U30/P1-03
t
le+4
7
le+3 -
b
b + PILO3
* Pth-UYPILO3
1e+4
le+Z
1
A
Pth-U10/PIL03
--ct
Pth-U30/PIL03
i le+3
le+l .01
1
1
10
100
1000
.01
freq (radls)
(a)
1
1
10
100
1000
freq (radls)
(b)
Figure 2. Comparison of the storage (G’) and the loss moduli (G”) of polyisoprene and Polythiophen/polyisoprne composites (PtWPI-03) at various particle concentrations, strain 1%, 27OC, electric field strength 0 Vimm. Effect of Electric Field Strength The effect of electric field strength on the rheological properties of PthPI blends at various Pth particle compositions was investigated in the range between 0-2 kV/mm. Figure 3a and 3b show the dynamic moduli AG’(o) and AG”(o) response of various polymer blend systems as fimction of electric field strength. The AG’(o) response of these systems monotonically increase with increasing field strength; the sensitivity values, defined as AG’/G’o, are 50%, 35%, 110% and 45% for Pth-U5P-03, Pth-U1 O/PI-O3, PthU20/PI-03 and PthU30/PI-03, respectively. Our results clearly suggest that as the electrical field is applied; both molecules of PI and Pth particles become polarized creating induced dipole moments, leading to intermolecular and inter-particle interactions. Higher field strength induces higher dipole moment strength along field direction, and stronger intermolecular inter-particle interactions are generated. These stronger intermolecular
178
interactions result in the loss of chain free movements, stronger agglomerates between Pth particles, and in higher chain rigidity as indicated by a higher AG’(w).
-P
PthLU5m103, G‘o 11085 Pa Pth_U2OmIL03, G’o 19428 Pa
u Pth-U30iPIL03,
1
10
100
1000
1
10000
E (Vlmm)
(4
10
G”0 10822 Pa
100
I000
10000
E (Vlmrn)
(b)
Figure 3. Responses of the storage and the loss moduli of the polythiophedpolyisoprene composites at various particle compositions vs. electric field strength, at frequency 1.O rads, strain 1%, at 27’C: (a) AG’(w); (b) AG’(w). In addition, the Pth-U2O/PI-O3 system shows the highest G’ sensitivity at the maximum field strength. This system shows that it contains relatively more solid-like structure than PI-03 system due to the additional undoped polythiophene particles interactions. However, it also contains optimum polythiophene particles concentration in P I 0 3 matrix and it also possesses the highest interaction between polythiophene particles within matrix. For lower Pth particle concentrations (Pth-U5/PI-03 and PthUlO/PI-03), they have a bit lower G’ sensitivity (AG’/G’,,) than that of the crosslinked polyisoprene system P I 0 3 system, which contains a balance between the solid-like and the fluid-like structures. Comparison between Pth-USPI-03 and PthUlO/PI_03 system show that Pth-UIOPI-03 system has a lower G’ sensitivity than that of PthU5PI-03 because of the Pth segments and chains possesses a higher rigidity than that of PthU5PI-03 system; they simply have lower response under the same electric field or the induced dipole moment strength. For the higher particle concentration Pth-U3O/PI-O3 system, it contains not only the most solid-like structure but also the highest interaction between polythiophene particles. Thus, the polymer segments and chains are the highest rigidity than those of other systems; they simply have a lower response, under the same electric field or the induced dipole moment strength than, those of P I 0 3 and Pth-USPI-03, and a higher response than that of PthUlO/PI-03 due to higher interaction between polythiophene particles. Conclusions Electrorheological properties of polyisoprene were measured under the oscillatory shear mode at applied electric filed strength varying from 0 to 2kV/mm. The G’ sensitivity of the pure polyisoprene varies with electric field depending on frequency: large vs. small scales. The maximum G’ sensitivity is found at about 0.6 for the PI-03 system; it is frequency independent. For the composite of undoped polythiophene and PI (Pth/PI-O3), with the undoped particle concentrations of 5%, lo%, 20% and 30 %vol., the dynamic moduli, G’ and G ’ of each composite, were generally higher than those of pure polyisoprene due to polythiophene particles within the matrix acting as fillers; they can store or absorb the forces/stresses within the matrix. The storage modulus sensitivity, AG’/G’o, increased with electric filed strength and attained a maximum value of 50%, 35%, 110% and 45% at the electric field strength of 2 kV/mm, respectively. References 1. Faez, R., Schuster, R-H., and De Paoli, M-A. (2002). European Polymer Journal, 38,2459-2463. 2. Shen, Z., Xue, H., and Li, Y. (2001). Svnthetic Metals, 124,345-349. 3. Kumar, D., and Sharma, R.C. (1998). European Polymer Journal, 34, 1053-1060 4. Zrinyi, M., Feher, J., and Filipcsei, G. (2000). Macromolecules, 33, 5751-5753.
Study on Electrorheological Characteristics of Polythiophene-basedElectrorheological Fluid
Datchanee Chotpattananont'*, Anuvat Sirivat', and Alexander M. Jamieson2 1
The Petroleum and Petrochemical College, Chulalongkorn University, Thailand 2 Department of Macromolecular Science, Case Western Reserve University Cleveland, OH 44106-7202, U.S.A *
[email protected] Abstract Electrorheological (ER) fluids are typically composed of polarizable particles dispersed in a nonconducting fluid. Upon the application of an electric field, chain-like or fibrillar aggregates of the suspended particles are oriented along the direction of the electric field, thereby inducing viscoelasticity and a drastic increase in viscosity. In our study, Poly(3-thiophene acetic acid), PTAA, has been developed for using as ER material. The rheological properties of this PTAA suspension upon the application of electric field are investigated under various deformations; oscillatory shear flow, steady shear, and creep. PTAA based ER fluid exhibits viscoelastic behaviors and shows excellent responses under an applied electric field. Moreover, the ER response of this PTAA fluid increases with increasing electric field strength, particle concentration, and particle conductivity. Under the oscillatory shear, the dynamic moduli, G' and G", increase dramatically by 10 orders of magnitude, when the field strength is increased to 2 kV/mm. The suspensions exhibit a transition from fluid-like to solid-like behavior as the field strength increases. Under the steady shear flow, the yield stress increases with electric field strength, E, and particle volume fraction, $, according to a scaling law of the form, T~ cc Ea$y. Furthermore, the creep curves of this ER fluid consists of both elastic and viscous responses and the fluid exhibits a partially elastic recovery after the removal of applied stress. The creep properties strongly depend on the magnitude of the applied stress. Introduction Electrorheological (ER) fluids are suspensions that exhibit a dramatic change in rheological properties in the presence of AC or DC electric fields. Commonly, they are composed of polarizable particles dispersed in a non-conducting fluid. Upon the application of an electric field, chain-like or fibrillar aggregates of the suspended particles are oriented along the direction of the electric field, thereby inducing viscoelasticity and a drastic increase in viscosity [I]. ER fluids have attracted considerable recently because their mechanical properties can be electrically controlled. Many applications based on ER technology have been developed, including the active elements of clutches, breaks, shock absorbers, engine mounts, valves, and flow pumps. There are many ER applications which are operated under the various types of loading conditions. However, the ER responses under various loading conditions have been thoroughly studied and are still not well understood. Therefore, it is interesting and important to systematically investigate the rheological properties of ER fluids under various conditions, i.e. oscillatory shear, steady shear, creep.
In this study, we hence investigated the ER behaviors under various types of shearing of Poly (3thiophene acetic acid) or PTAA, doped with perchloric acid (HC104), suspensions with a control the PTAA particle conductivity. The rheological properties of the PTAA suspensions were investigated under the application of electric field. The effects of electric field strength, particle concentration, and particle conductivity were then observed. Experiment Preparation of PTAA-ER Fluids Poly (3-thiopheneacetic acid), PTAA was synthesized by the oxidative-coupling polymerization 179
180
according to the method of Kim et al. [2]. The PTAA particles were then doped with perchloric acid to control the particle conductivity [3]. The electrorheological, ER, fluids were prepared by dispersing HC104 doped PTAA particles in a silicone oil (density 0.96 g/cm3 and kinematic viscosity 100 cSt) with an ultrasonicator for 30 minutes at 25°C. ER Properties Measurement under Oscillatory Shear A fluids rheometer (Rheometrics, ARES) was used to investigate the rheological properties. It is fitted with a custom-built copper parallel plates fixture (diameter of 25 mm) attached to insulating plexiglass sheets. A DC voltage was applied with a DC power supply (Tektronic, PS280) and a custom-built DC power supply, which can deliver an electric field strength to 2 kV/mm. A digital multi-meter (Tektronic, CDM250) was used to monitor voltage and current. When evaluating the steady state ER response, the electric field was applied for 10 minutes to ensure formation of an equilibrium agglomerate structure before measurements was taken. Each measurement were carried out at a temperature of 25 k 0.1"C. and repeated at least two or three times. In these experiments, G' and G" were determined as a function of frequency and electric field strength. ER Properties Measurement under Steady Shear and Creep Measurement Rheological properties were carried out using a rotational rheometer (Carrimed, CR50) with 4 cm diameter parallel plate geometry at 25 k 0.1"C. The gap for the geometry used was 0.1 mm for each measurement. A DC voltage was applied during the rheological measurements using a high voltage power supply (Bertan Associates Inc., Model 215). The electric field was applied for 10 minutes to ensure the formation of equilibrium agglomerate structure before a measurement was taken. Each measurement was carried out at the temperature of 25 k 0.1"C and repeated at least two or three times. The static yield stress was measured using the controlled shear stress mode (CSS) as the highest stress value prior to the onset of flow in the presence of an electric field of a specified magnitude. In the CSS experiments, the shear rate sweep was always applied at a sweep rate of 40 Pdmin. The creep and recovery behaviors were carried out using a stress-controlled rheometer (Carrimed, CR50) with 4 cm diameter parallel plate geometry at 25 f 0.1"C. The gap for the geometry used was 0.1 mm for each measurement. A DC voltage was applied during the measurements using a high voltage power supply (Bertan Associates Inc., Model 2 15). For initial conditioning, the suspensions were subjected to steady shearing at 300s.' and then electrified in a quiescent state for 5 min to ensure the formation of equilibrium agglomerate structure before a measurement was taken. A constant stress was then instantaneously applied, maintained for 180s, and suddenly removed. The time dependent of strain was measured at various electric field strengths. Each measurement was carried out at the temperature of 25 f 0.1"C and repeated at least two or three times.
Results and Discussion ER Properties of PTAA Suspension under Oscillatory Shear The PTAA based ER fluids were found to exhibit a viscoelastic behavior under an applied electric field and the ER response enhanced with increasing electric field strength. The dynamic moduli, G' and G", dramatically increased by 10 orders of magnitude when the electric field strength was increased to 2 kV/mm as shown in Fig. 1. Effect of particle concentration and particle conductivity were apparent at moderate electric field strengths and the suspensions show saturated ER properties at electric field strength of 1 kV/mm. Moreover, the suspensions exhibited transition from the fluidlike to the solid-like behavior as electric field strength increased. Higher particle concentration and higher particle conductivity induced a lower transition electric field strength.
181
I
I
I
500
0
I
nio
2?
5 n 05
n no n
ion
zoo
300
Time (s)
400
inn
300
200
Time
400
500
(8)
Figure 3. Creep and recovery curves of the 20 wt% highly doped PTAA suspension under the electric field strength of 1 kV/mm at various applied stress values.
Creep and Recovery Behaviors of PTAA Suspension Furthermore, the creep and recovery behaviors of poly(3-thiopheneacetic acid) suspension were investigated. The results indicated that this ER suspension behaved like a viscoelastic solid under the electric field with a combination of elasticity, plasticity, and viscosity behaviors. With increasing stress, the fluid showed instantaneous elastic response whereas the retarded elastic and the viscous response decreased. After the removal of the applied stress, the strain decreased but did not completely relax to original value. This indicates that this fluid exhibited a partially elastic recovery. When the stress was increased above the yield stress, the fluid exhibited purely liquid response in which the strain continuously increased with time. Moreover, the compliance parameters, J, and J,, the equilibrium and the recovery compliance, were found to be decrease with increasing particle concentration and particle conductivity. The parameters J, and J, exhibit a power-law dependence on the electric field strength, J, a E" and J, a EY,respectively.In addition, the recovery increased with the increasing of the electric field strength, particle concentration, and particle conductivity. Conclusions In our work, Poly(3-thiophene acetic acid), PTAA, has been developed for using as ER material. The PTAA was synthesized by the oxidative-coupling polymerization and the obtained PTAA particles were then doped with perchloric acid, HC104 to control the particle conductivity. The rheological properties of this PTAA suspension upon the application of electric field were investigated under various deformations; oscillatory shear flow, steady shear, and creep. The results show that PTAA based ER fluid exhibits the viscoelastic behavior and shows dramatic responses under an applied electric field. Moreover, the ER response of this PTAA fluid can be amplified with increasing electric field strength, particle concentration, and particle conductivity. Under the oscillatory shear, the dynamic moduli, G' and G", increase dramatically by 10 orders of magnitude, when the field strength is increased to 2 kV/mm. The suspensions exhibit a transition from fluidlike to solid-like behavior as the field strength increases. While under steady shear flow, the yield stress increases with electric field strength, E, and particle volume fraction, I$, according to a scaling law of the form, zy cc EVY. Furthermore, the creep curves of this ER fluid consists of both elastic and viscous responses and this fluid exhibits a partially elastic recovery after the removal of applied stress. The creep properties strongly depend on the magnitude of an applied stress. References 1 . R. Sakurai, H. See, T. Saito, S. Asai, M. Sumita. Rheol. Acta. 1999, 38,478. 2. B. Kim, L. Chen, J. Gong, Y. Osada. Macromolecules. 1999, 32,3964. 3. L. Chen, B. Kim, M. Nishino, J. Gong, Y. Osada. Macromolecules. 2000,33, 1232. 4. M. Parthasarathy, K.H. Ahn, and D.J. Klingenberg. International J. Modern Physics. 1994, B 8: 2789.
This page intentionally left blank
Session R7
Chair: L.R. Arnaut
This page intentionally left blank
Active Absorber Research at The University of Sheffield A Tennant and B Chambers The University of Sheffield Department of Electronic and Electrical Engineering Mappin Street, Sheffield S1 3JD, UK (
[email protected],
[email protected])
Abstract In this paper we present an overview of recent research into active radar absorber design being carried out at The University of Sheffield. A brief outline of the theory of operation of an active absorber based on the concept of a phase-switched screen (PSS) is presented followed by a description of an experimental prototype. Measured data is presented to show that the absorber can be configured to operate in several different modes and can provide variable reflectivity control, including reflectivity enhancement, over a frequency range of 8GHz to 12GHz.
Introduction Active radar absorbers may be described as structures that can modify their electromagnetic scattering properties in response to an applied control signal. Unlike passive radar absorbers, whose characteristics are fixed at the time of design and manufacture, an active radar absorber has the ability to reconfigure its reflectivity characteristics to adapt to a given operating situation. This may simply mean switching from a high reflectivity state (used for example in routine operations) to a low reflectivity state during threat situations, or the absorber may adapt its reflectivity performance to operate at several different frequencies. Research into various types of active radar absorbing materials has been carried out at The University of Sheffield since 1992 [l], when work concentrated on the development of electroactive conducing polymers. Although this work is still progressing, in recent years we have concentrated our research effort into structures controlled by active semiconductor devices typically pin diodes. In previous publications we have reported a new concept in active absorber design called the phase-switched screen (PSS) [2-81. The PSS differs from conventional radar absorbers in that an ‘ideal’ PSS does not absorb incident electromagnetic energy but redistributes it in the frequency domain so that it is undetectable by interrogating radar systems. The PSS achieves this translation in frequency by imposing phase modulation onto the energy scattered from its surface to produce a signal with a low time-average energy spectral density. In addition, the form of the modulation applied to the PSS can be chosen to provide adaptive radar signatures such as a variable time-average radar cross section (RCS). In this contribution we present an introduction to the basic operating principles of a PSS and describe details of recent developments in active absorber research at The University of Sheffield.
Theoretical background A detailed analysis of the design and operating principles of generic, single-layer, planar PSS can be found in [6], and so here we present only a brief introduction. The simplest form of PSS consists of a single active layer placed in front of, and at a distance d, from a conducting back plane, as shown in Figure 1. The active layer takes the form of a thin sheet of material that can be switched rapidly between very high and very low resistance states. Consider first the case of an ideal screen 185
186
incident wave
2
reflected wave
conducting back-plane Figure 1. Details of the PSS construction in which the active layer can be switched between totally transparent (OFF, ROFF= m R) and totally reflecting (ON, RON= 0 0) states. If the screen is illuminated at normal incidence by a unit amplitude plane wave of frequency f,, the reflected field may be described by cos(2nfct) when the screen is ON, and by cos(2nfct + 2 p ) when the screen is OFF. Here p is the wave propagation constant in the spacer between the active layer and the back plane and is defined as
2z p = -. A
/I 4
When d = - , the reflected signals produced by the ON and OFF states are 180" out of phase and the resultant signal is binary phase modulated. If the active layer is switched between these two states by a periodic square wave with an equal mark-space ratio and period T, the normalised frequency spectrum of the reflected field is given by
sin(x) The spectrum consists of discrete sidebands whose amplitudes follow a -envelope centred on X
the illuminating frequency. Crucially however, the spectrum has no component at f , and so the time-averaged reflected energy at the illuminating frequency is zero. To exploit this property in a practical application, for example that of radar signature reduction, the frequency at which the screen is modulated,f,, must be sufficiently high to move all the sidebands in the reflected spectrum outside the bandwidth of the receiving system. The active layer in a practical PSS will not exhibit ideal switching characteristics but instead may be characterised by an ON resistance, RON> 0 , and an OFF resistance, R , < m . The non-ideal screen is conveniently analysed in terms of a switched reflection coefficient which may be derived using a transmission line analogue. Assuming a planar structure of infinite transverse dimensions and normal plane wave incidence, the reflection coefficients of the ON and OFF states are given by
187
Where ZLN and ZAFFrepresent the input impedances at the front face of the structure and are given by
The time-averaged reflection coefficient of the screen, assuming a symmetrical square-wave switching function, is given by
(4) il Solving ( 5 ) for zero reflectivity when d = - leads to the result 4
(5) This condition may be difficult to achieve in practice, but zero reflectivity may still be obtained by adjusting the mark-space ratio of the switching waveform. This case may be analysed by letting the active layer be switched on for a time z , and off for T - z , where T represents the period of the modulating waveform. The time-averaged reflection coefficient is now given by
Solving (6) for p,,,( f )= 0 and considering only valid solutions for z (i.e. 0 I z I T ) leads to the conditions RONI Z , and R ,
2 Z,
(7)
Hence, provided that the resistance of the active layer can be switched between values that are above and below the impedance of free space, the zero reflectivity condition can be obtained by adjusting the mark-space ratio of the modulating signal. The reflectivity versus frequency performance of a PSS designed according to (7) are similar to those of a conventional Salisbury screen, and for the limiting condition when RON= RoFF= Z, the PSS becomes a single layer Salisbury screen. A detailed discussion of the bandwidth performance of a PSS can be found in [6].
Experimental Screen design To realise a practical PSS we need a surface that can be rapidly switched between two or more impedance states. Potentially this could be achieved using some type of hnctional material such as an active conducting polymer [ 11, but to date we have concentrated on the development of layers comprised of a two-dimensional grid of half-wavelength dipoles that are loaded at their centres with pin diodes. Under no-bias conditions the pin diodes present a high microwave impedance and
188
the dipoles may be considered open circuit. Hence the grid of dipoles is non-resonant and represents a high impedance equivalent surface. When the diodes are biased 'on', however, their microwave impedance becomes low and the dipoles are resonant at the half wavelength frequency. Then the grid of shorted dipoles becomes a strong scatter and represents a low impedance surface. The basic geometry of the active layer in our PSS is shown in Figure 2. The layer is based on a unit cell containing a bow-tie dipolc which is loaded at its centre by apin diode contained in a SOD323
15mm
~
diode loading points
!
i
'w
dc bias l i n e d Figure 2. Layout of the PSS active layer package. The use of bow-tie dipoles provides greater bandwidth than linear dipoles and also provides a reactive component to the effective sheet impedance. Figure 2 also shows a close-up view of part of an active layer containing 400 elements. The active layer was used to form a PSS by combining 6.0mm thick loos-loss dielectric spacer (Rhoacel foam E,. = 1.05, tan6 = 0.0017) and a conducting back-plane in the form of a fine copper mesh embedded in a GRP substrate. The three layers of the absorber were bonded together, with the diode surface of the FSS layer in direct contact with the foam spacer, to form a rigid square panel. The final structure measures 300mm by 300mm in area and is approximately 8.0mm thick. Measured Performance of the screen
Firstly we present the reflectivity tuning properties of the experimental screen when configured to operate as a conventional PSS. The reflectivity characteristics of the panel were measured between 7GHz and I2GHz in a calibrated NRL arch using an Agilent 8510C vector network analyser. The active panel was modulated by a lOMHz square-wave signal with a constant drive current of 4mA. The duty cycle of the modulating signal was varied to produce various reflectivity responses and these results are given in Figure 3.
189
-5 1
.-> ~
-10
CI
.c
p
-15
E
2
-20
-25
~
-30
a
7
+
9
10
9
12
11
Frequency (GHz)
t=0.34
t=O
A
t = o. 38
t=o.4
Ot=0.5
0 t =0. 68
Figure 3. Reflectivity characteristics produced by modulating the screen with a 4 . W variable mark-space ratio square-wave with relative ON time t. Next we show the frequency domain response of the PSS. For these measurements an Agilent E8257C signal generator was used as a source in conjunction with an Agilent E4407B spectrum analyser to record the spectrum of the scattered signal from the PSS. The frequency spectrum of the signal reflected by the PSS was recorded over a frequency span of lOOMHz for the screen in its ‘off-state’, i.e. with no applied modulation, and also with a 20MHz square-wave signal applied to the PSS. These data are shown in Figure 4 where it is observed that the energy level at the carrier frequency has been reduced by over 55dB and redistributed into multiple sidebands with 20MHz separation.
{ -c $5
-50
-60
-70 -80 -90 -100
L
10.95
I____.-
10.96
10.97
10.98
10.99
11.00
11.01
11.02
11.03 11.04
I 11.05
frequency c+lz
Figure 4. Measured frequency spectrum of the reflected signal from the PSS with CW illumination (grey trace - unmodulated PSS; black trace - PSS modulated with a 20MHz square-wave)
190
The above two results are examples of the active panel operating as a conventional PSS in that scattered energy is redistributed into sidebands in the frequency domain. Recently however, we have discovered that the active panel can also be configured to operate as an adaptive absorber using dc current control as oposed to modulated current current control [9]. To illustrate this property the reflectivity characteristics of the active panel were measured for various values of applied dc bias current ranging from OmA to 9.7mA, and these results are presented in Figure 5. For zero applied bias current the panel is strongly reflecting, but as the diode bias current is increased the reflectivity level decreases between 8 GHz and 1lGHz with deep reflectivity nulls forming at spot frequencies within the band. Further increases in diode bias current causes the reflectivity response of the panel to increase until in the saturated state (bias current greater than 1OmA) the screen becomes strongly reflecting again.
0 -5
P
s -10 .->I > CI
=
-15
Q
0
-20 -25
-30 7
8
9
10
9
11
12
Frequency (GHz)
+
O ~ A 4 1.6mA
A
2.2m~0 3 m ~
03 . 7 m ~
4 m ~
A
9.7m~
Figure 5. Reflectivity characteristics produced by varying the applied dc bias current level. The results we have shown so far have demonstrated that the PSS can provide a time-averaged reduction in reflectivity at the frequency of illumination, but in a final example we demonstrate that the PSS is also capable of providing reflectivity enhancement and operation against broadband, modulated incident waveforms [lo]. In this experiment the PSS was illuminated by a frequency modulated signal with a 1OMHz bandwidth centred on a 7.85GHz carrier. The spectrum of the signal scattered from the PSS was recorded for various values of mark-space ratio of the squarewave used to modulate the screen. The results are presented in Figure 6 and show that as the value of ?QE is decreased the screen reflectivity reduces and reaches a minimum when ?QE = 0.6 ; ‘ON
‘ON
=0
then produce a gradual rise in reflectivity until when
further decreases in ‘ON
(i.e. the
‘ON
screen is switched fully ON) there is an increase in reflectivity of approximately 6dB compared to the screen in its OFF state.
191 0
-100 7.80
7.81
7.82
7.83
7.84
7.85
7.86
7.87
7.88
7.89
7.90
frequency GHz
Figure 6. Measured frequency spectrum of the reflected signal from the PSS due to illumination by an FM signal with lOMHz bandwidth. The various traces show the change in reflectivity (including enhancement) due to changes in the mark-space ratio of the PSS modulating waveform
Conclusions In this paper we have presented an overview of some of the research being carried out into active electromagnetic absorbers at The University of Sheffeld. Our active absorber designs are based on structures that contain planar arrays of periodic conducting elements controlled by semiconductor pin diodes. Experimental results have been presented that show that the active absorber can operate in different modes. Firstly, the absorber can be configured to act as a PSS; in this mode the active panel of the absorber is modulated by a periodic control signal. This causes the energy scattered from the PSS surface is to be phase modulated and redistributed in the frequency domain. We have also shown that the active absorber can operate as a conventional absorber in which a variable dc bias current is applied to the active panel to control its reflectivity characteristics. Finally experimental results have been presented to show that the absorber is effective against broadband modulated incident energy and can also be used to provide reflectivity enhancement.
References [l]
[2] [3]
[4] [5] [6]
Wong P.T.C., Chambers B., Anderson A. P. and Wright P.V., “Large area conducting polymer composites and their utilisation in microwave absorbing material”, Electronics Letters, vol28, No 17, pp 1651-1653, 1992 A. Tennant, “Reflection properties of a phase modulating planar screen”, Electronics Letters, V O ~33, . pp 1768-1769, 1997 B. Chambers, “Characteristics of modulated planar radar absorbers”, Electronics Letters, vol. 33, pp 2073-2074, 1997 A. Tennant and B. Chambers, “Experimental phase modulating planar screen”, Electronics Letters, vol. 34, pp 1143-1144, 1998 A. Tennant and B. Chambers, “Experimental two-layer adaptive phase-switched screen”, Electronics Letters, vol. 37, pp 1379-1380,2001 B. Chambers and A. Tennant, “General analysis of the Phase-Switched Screen, Part 1: The
192
[7]
[8]
[9] [ 101
single layer case”, IEE Proc- Radar Sonar and Navigation, vol. 149, no 5 , pp243-247,2002 B. Chambers and A. Tennant, “Influence of switching waveform characteristics on the performance of a single layer phase-switched screen”, IEEE Trans. Electromug Compat., vol EMC-44, NO 3, pp. 434-44 1, Aug 2002 A. Tennant and B. Chambers, “Experimental broadband single layer PSS using reactive impedance switching”, Electronics Letters, vol. 39, pp 121-122, 2003. P N Kaleeba, A Tennant and B Chambers, “Measured performance of an active radar absorber with either DC or modulated current control”, submitted to Electronics Letters, 2004 A. Tennant and B. Chambers, “Experimental Performance Of A Phase-Switched Screen Against Modulated Microwave Signals”, accepted for publication, IEE Proc- Radar Sonar and Navigation, 2004
Correcting for Imperfections in the Experimental Characterization of Dielectric Media for High-Precision Metrology L. R. Arnaut Division of Enabling Metrology National Physical Laboratory Teddington, Great Britain
Introduction
The National Physical Laboratory (NPL) is the U.K.’s national measurement institute providing national standards for most physical quantities and for numerous technical applications. NPL has developed and maintains one of the most comprehensive ranges of measurement techniques and equipment for radio-frequency & microwave (RF&MW) characterization. The facilities for measurement of electromagnetic materials cover high-, medium- and low-loss dielectrics, solids and liquids, magnetic and anisotropic media. Frequency coverage is from below 1 kHz to 100 GHz; higher frequencies are covered in NPL’s terahertz and infrared laboratories. The facilities are used in research programmes for the Department of Trade and Industry (DTI), in national and international collaborations and intercomparisons (including EU Framework activity), and in measurements for various external customers (academic, governmental and industrial). Experience in RF&MW metrology at NPL dates back over many decades. At NPL, characterization techniques for low-loss dielectric materials are based on resonators or cavities and cater typically for laminar specimens (e.g., substrates) and discs (Figure 1).
(c)
(b)
Figure 1: Some resonators used at NPL: (a) parallel-plate resonator, (b) split-post resonator, (c) open resonator.
193
194
Medium- and high-loss materials measurements are performed in cells based on waveguides or coaxial lines. Alternatively, reflectometric probes are used. Specimens of largely different shapes can be handled, including thin films. Measurement techniques for experimental characterization of anisotropy include open resonators (for millimeter-wave measurements), waveguide cells (including magnetic materials) and waveguide and TEM probes (for RF), coaxial and waveguide probes and tunable dielectrics (e.g. ferroelectrics). Several of these methods have been recently described and discussed in a Good Practice Guide [ 11. Aside from practical metrology activity, a team of specialists in electromagnetic modeling is involved in parallel and supporting theoretical studies relating to statistical and numerical characterization of advanced composite magneto-dielectrics, including adaptive materials and structured metamaterials. The dielectric measurement facilities have been modelled by a range of analytical and numerical methods, including modal analysis, FDTD, FEM, PMM, etc., also for validating and improving the accuracy of the measurements.
Modelling of measurement imperfections
A realistic measurement set-up involves finite tolerances and uncertainties, either by design or as a result of wear or environmental effects. In specifying and maintaining uncertainty limits and confidence intervals for constitutive parameters obtained in a particular fixture, it is important to account and, if possible, correct for the resulting errors. Most of these imperfections are caused by relatively small mechanical changes to nominal dimensions of the fixture or specimen (typically less than one percent). Therefore, efficient numerical modeling of such cases typically requires very fine meshing, and must be performed on a case-by-case basis (e.g., a different simulation for each new material specimen). Furthermore, one wishes to obtain physical insight into the effect of specific imperfections and parametric dependencies. For this reason, advanced analytical modelling techniques have been found to be useful in extending the use and practicality of measurement systems. Below we describe three examples of such modelling, aimed at increasing the accuracy of the complex permittivity estimated from resonance or reflectiodtransmission measurements.
Nonuniform gap effects in parallel-plate resonators The Courtney parallel-plate resonator (Hakki-Coleman method) is widely used for characterization of high-permittivity low-loss cylindrical dielectric samples. The method is most accurate for large diameter-to-height ratios of specimens. A major source of uncertainty is the occurrence of air gaps between the interfaces of the specimen and the resonator plates. These gaps may be due to imperfections as a result of machining of specimen andor plates, or may have been introduced deliberately to avoid direct abrasive contact between plates and the specimen or to achieve higher quality factors (e.g., using a low-permittivity spacer). Small uniform, i.e., constant-width gaps can be corrected for using simplified models (Itoh-Rudokas method) or rigorous axial or radial modematching for an axially symmetric configuration. The latter are computationally more demanding when the top and bottom surfaces are no longer perpendicular to the cylindrical axis, in which case the integrations must be calculated numerically. A full-wave numerical analysis is generally required for more complicated gap profiles, but contains an inherent accuracy as a result of ‘staircasing’ (discretization) errors for non-uniform gap widths (caused by slanted or curved sample edges).
195
An extended perturbation method avoids these difficulties and can be used in conjunction with standard methods to yield relatively high accuracy for relatively complicated gap profiles. Correction formulas have been derived to account for the effect of small non-uniform gaps in a parallel-plate dielectric resonator configuration. A polynomial expansion of the gap profile hnctions is used to characterize the effect, allowing for gap profiles of algebraic nature but otherwise arbitrary complexity. A procedure for replacing the simple geometrically averaged gap width by an electromagnetically (EM) weighted gap has been outlined and applied to the practically important TE,, modes. Several important classes of gap profiles can be described using a polynomial expansion of a gap profile with azimuthal symmetry and variable radial height: N,
Zr/(r)=&kra,,
(i=o,l)...; j = O , 1 )
where a v k = 0, 1, 2, 3, . .. correspond, respectively, to parallel, linearly, parabolically, cubically, etc., tapered interface j of gap i. These coefficients are obtainable from Nu gauge measurements of the specimen and plates, relative to a reference plane, along a radius a. The EM weighted azimuthal field for TE,, modes for a single interface is
where J1(.)is a Bessel function of the first kind of order one. The EM weighted gap width is
where, in this case, wm(kpr ) = Jl(kpr). For example, for TEonpmodes and integer auk, the corrected coefficients for the linear and parabolic terms are
a@= 1 :
a, +a,
a,. =2: ‘ik
a2 + a2
x2Jo(x)-2xJ,(x)
XI,(XI - xo x3J0(x)- 3 x 2 J , ( x )- 3xT0(x) + 3x0
xl,(XI - x0
etc., with x = kp r and &(x) = bo(y)dy. More elaborate closed-form expressions for the higher-order mode coefficients have also been obtained [2]. Figure 2 shows the effect of nonuniform air gaps on the measured permittivity and variations in the axial mode number p in parallel-plate measurements of an actual dielectric puck with nominal real permittivity E = 36.48~0(the effect of the line broadening as a result of the air gap is neglected here).
196 Effect of gap weighting on calculated permittivity
1oo
I
10” I
1o-2
I
I
I
I
I
10.-
1on 100*A/L(pct)
10‘
1o2
*-
A*---=
lo3 1041
lo2
-
I
I
I
10.’
1on 100 * s I L (pct)
10’
1
1o2
Figure 2: Effect of air gaps on parallel-plate resonator measurement of real part permittivity of dielectric specimens: comparison of geometrical vs. electromagneticweighting of air gaps on estimated permittivity and on axial mode numberp for TE,., resonator modes.
Gap effects in waveguide measurement of dielectric samples
Gap effects occur a fortiori in measurement of dielectric samples in waveguide and transmissionline methods (Figure 3). The dimensions of such samples need to be machined to high precision in order to fit tightly and evenly. In practice there is always a residual gap, and the cost of machining to a precision better than about 10 pm increases dramatically. Typically, the samples can be machined such that the gap in the longitudinal direction can be assumed to be constant. In this case, gaps give rise to mode hybridization (LSEILSM modes). For a 2-term LSEiLSM modal expansion, the measured permittivity for a specimen with nominal permittivity E with an air gap of width & in the E-plane of a waveguide is obtained as
where
+,/($I
k: = kcz
--1 --,4
P
2P
k,
=z l a
,
k,’ = W
~ , ~ , E ~ ,
197
Figure 3: Waveguide fixture at NPL for measurement of dielectric samples at 900 MHz.
in which the pii and tq are functions of k,, ko, &I@and &lb [3]. A similar analysis has been performed for H-plane gaps & and are found to produce a much smaller effect than E-plane gaps. Simpler, but less accurate corrections are obtained when using a capacitor model, for which the estimated measured permittivity is bE Em =
(b-
+ (&)&
A comparison between both correction models (Figure 4) demonstrates that the capacitor model tends to overestimate the gap effect on the measure E in all cases, compared to the LSEILSM expansion. The results are used in an inversion scheme that yields the true value of E.
Higher-order modes in coaxial waveguide measurement of high-permittivity beads Typical waveguide characterization of dielectric samples is based on transmission-line theory of a single propagating mode. However, if the relative permittivity of the sample is sufficiently large, higher-order modes may be excited inside the sample by the incident wave. Since the cut-off wavelength of such modes is too low to allow for propagation outside the sample in the air-line, towards the transmitting or receiving port, these modes give rise to energy being trapped inside the sample, resulting in distorted values of the measured complex permittivity which show up as ‘bumps’ near their resonance frequencies, when plotting the permittivity as a fimction of frequency by inversion. The effect has been calculated based on cut-off wavenumbers of higher-order modes in coaxial waveguides (Figure 4). The results were successfdly verified against measured data [4].
198 Effect of E-plane air gap on measured 8(
Effect of E-plane air gap on measured E"
2-term LSERSM expansion capacitor model
---
E 8' 0
,
I . ,. ,
-. 0.002 0.004 0.006 0.008 Relative gap width 6b/b
l
capacitor model
1.7' 0
0.01
0.002 0.004 0.006 0.008 Relative gap width 6b/b
I
0.01
(4 Effect of H-plane air gap on measured 8('
Effect of H-plane air gap on measured E' 8.6005
-
. f wo
I
B
,
8.5995 8.599 -
7
8.5985/1~ L;~/Ls~,emansi! - - - capacitor model 8.598 0 0.002 0.004 0.006 0.008 Relative gap width Sa/a
1.~1
- 2-term LSE/LSM expansion - - - capacitor model
0.01 Relative gap width 6a/a
(b)
Figure 4: Effect of air gaps on X-band waveguide measurement of complex permittivity of dielectric specimens: comparison of modal expansion and capacitor models for (a) E-plane and (b) H-plane air gaps.
Conclusions
The accurate measurement of dielectric samples in waveguide or resonator involves the issue of imperfections caused by inherent mechanical inaccuracies in the measurement set-up. For highprecision characterization, these effects need to be accounted for by modifying simplified models for ideal configurations. In order for this more sophisticated model to be still practically useful, the extension of analytical models is often preferred over full-wave numerical modeling. The examples listed in this paper constitute only a selection of work performed at NPL in this area. Several other issues have been addressed, e.g., the effect of ohmic contact loss on permittivity measurements in low-frequency circular or interdigital capacitance cells.
Acknowledgements
This work has been supported by the Electrical Programme of the National Measurement System Policy Unit. Stimulating discussions with A.P. Gregory, R. N. Clarke, P. D. West, and G. J. Hill in the course of this work are gratefully appreciated.
199
,001
1on
10’
Sample length (mrn)
Figure 4: Resonance frequencies for higher-order modes in coaxial waveguide characterization of highpermittivity specimens with outer diameter a = 7.002 mm and inner diameter 6 = 3.040 mm.
References [l] Various, ‘A Guide to the Characterisation of Dielectric Materials at RF and Microwave Frequencies’, Institute of Measurement and Control, ISBN 0 904457 38 9, Sep. 2003. [2] Amaut, L. R., ‘Correction model for nonuniform gap distributions in precision parallel-plate dielectric resonator measurements’, NPL Report R000203, Feb. 2000. [3] Arnaut, L. R., ‘Correction model for uniform gap distributions in precision waveguide measurements of dielectric specimens’, NPL Report R98 1026, Oct. 1998. [4] Amaut, L. R., ‘Higher-order mode excitations in coaxial waveguides with high-permittivity dielectric inserts’, NPL Report R970129, Jan. 1997.
Design of an Isotropic Microwave Screen from Dipole Arrays using Genetic Algorithm
a
Hock K. M.”, P.-M. Jacquartb*, Can Y. B.a, Liu L.”, Lum K. Y .a Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508 Dassault Aviation, DTIAEIEMIR, 78 quai Marcel Dassault, 92552 Saint-Cloud, France *email :
[email protected] Abstract-In this paper, we discuss the design of a multilayered Frequency Selective Surface (FSS) with low transmission coefficient, for two principal polarisations, via application of a genetic algorithm (GA). A very simple two-step approach is considered by first studying the scattering of a single dipole array in dielectric layers, then optimising a multiple FSS screen comprising several such dipole arrays. Numerical results are compared to the experimental data. Index Terms-Frequency
Selective Surface (FSS), Genetic Algorithm (GA), multilayered media
I. INTRODUCTION The objective of this work is to design a band-pass or band-stop screen for microwave applications exhibiting isotropic behaviour with very simple designs for the Frequency Selective Surfaces (FSSs). Starting with the study of a single FSS screen made of a dipole array embedded in dielectric layers, we focus on the reflection and transmission coefficients of a multiple FSS screen and apply a Genetic Algorithm (GA) approach to optimise some parameters, e.g. spacer thicknesses. The GAbased combinatorial optimisation technique offers many advantages, succeeds in designing broadband absorbers comprising only a few layers [l], [ 2 ] and has been widely applied in the design of FSS [3]. In practice, GAS are computationally expensive due to the significant amount of computation time required for each design evaluation. Moreover, having more design parameters will require longer iterations to reach the optimal design. To reduce the computation time, reduction techniques can be suitably used to design practical devices. Some authors employ hybrid GAS, which involve domain decomposition [3] and are applied to the optimisation technique itself; others resort to the scattering matrix technique [4] for each FSS making up the more complex screen. In this work, we adopt a very simple approach consisting of two steps. First, we consider a FSS with a very simple design, such as a dipole array made of long and very thin wires of copper located on a square array. For realistic applications and mechanical considerations, the FSS is embedded in a dielectric slab comprising several layers of Kevlar pre-preg fabrics. The thickness of the slab is minimized numerically (using a simple search) to such value that the resonance frequency of the planar structure remains close to that of the FSS in a bulk dielectric material [5, 61. Reflection and transmission coefficients are then computed using several methods, based on the Method of Moments (MOM), and compared to experimental results performed using a free-space facility. In this preliminary step, design parameters, such as the discretisation parameter, are dispensed with to minimise the computation time. Next, we consider the complete screen that comprises a stack of similarly designed FSSs that are shifted or rotated from one to another. The set of design parameters for the stack is thus reduced to the thicknesses of the dielectric spacers between adjacent layers. GA is then used to design a multilayer composite structure with minimum reflection for both transverse electric (TE) and transverse magnetic (TM) waves simultaneously over a prescribed range of frequency. Numerical results are compared to experimental data for verifications. APPROACH 11. NUMEFUCAL 1I.a. ANALYSIS OF FREQUENCY SELECTIVE SURFACES A conventional MOM-based computer code is used. The numerical analysis follows the wellestablished procedure of solving the Electric Field Integral Equation (EFIE) for the current distribution on perfectly conducting patches, derived by enforcing Floquet periodic boundary condition in an elementary cell. Boundary integral equation with rooftop functions and Galerkin
200
201
integration process are used. An adapted Green's hnction that takes into account the case of a FSS structure with dielectric superstrate and substrate is employed. The incident plane wave is defined by the angle $, and 8,,,, as shown in Figure 1. Two polarisations of the incident electric field, parallel (W)and perpendicular (BH), are considered with respect to the plane of incidence. Both and frequencyj reflection R and transmission T coefficients are computed as functions of O,,,,
(a) Parallel incidence (b) Perpendicular incidence Figure 1: Convention of incidence and polarisation 1I.b. GENETIC ALGORITHM FORMULATION We employ for the design of multilayered structures a basic form of genetic algorithms [2] with fixed-size populations, Gray binary coding, stochastic tournament selection and crossover and mutation operators for binary strings. The objective is to minimize, over the vector h of spacer thicknesses, the following function of reflection coefficients: f
1
where A and B are constant penalty coefficients and f the frequency. A and B are judiciously chosen so as to lead to a feasible design of an anti-reflection screen with isotropic properties. Binary codes define an inherent parameter precision that corresponds to a spacer thickness of 0. lmm. 111. EXPENMENTAL METHOD
1II.a. SAMPLE PREPARATION Dipole arrays are produced using standard fabrication process of printed circuit board (PCB). The dipoles are copper strips arranged in a square array. To reduce the effects of eddy currents, the width of the strip is taken to be the minimum value that the process offers, i.e. about 80 pm f 10%. The copper strips, on a kapton PCB of thickness 40 pm, are 17.5 pm thick. An assembly of four kevlar pre-preg fabrics on each side supports each FSS screen, with dimensions of 424x424 mm2 (see Figure 2a). All samples are vacuum bagged and cured at 195°C at 7 bars for 1 hour. The overall thickness after curing is 1.7 mm. Three FSS designs are discussed in this paper: configurations #1 and #2 are single-screen FSS comprising the PCBs in Figures 2b and2c, respectively. Configuration #3 comprises four FSS screens separated by polystyrene spacers. These are, from top to bottom, #1, #2, #2 rotated by 90 deg, and #1 rotated by 90 deg (see Figure 4). To ensure good alignment among copper strips on different screens, the pre-pregs and PCBs were all cut and cured using the same steel frame. 1II.b. MEASUREMENT PROCEDURE The measurement setup consists of two broadband horn antennas with the sample located in between. The antennas are separated at a distance of 1 m, to each side of the sample, and are clamped to a wooden arch. The sample is supported on a polystyrene platform. Measurements are performed using HP 8720 Vector Network Analyzer. Response & Isolation calibration is used, so that error correction can be done in two measurements - with and without a metal plate of the same size as the FSS. Time gating is used to filter out multiple scattering from the antennas. As the time domain response of #3 is found to last for 3 ns, a time gate of 6 ns centred at the main response
202
peak is selected. The antennas could be clamped at any position on the wooden arch such that they always lie on a plane through the sample, for convenience in measuring bistatic transmission and reflection. For this set-up and calibration method, however, it is found that measurement results for incidence angles more than 60" give unphysical results of greater that 0 dB at certain frequencies.
IV. RESULTS AND DISCUSSION We first evaluated the scattering from single FSS for two preliminary designs. The first design (configuration #1) comprises a square array of perfectly conducting dipoles, oriented along the yaxis (see Figure 2b). The second design (configuration #2) has the dipoles rotated by 45" with respect to the x-axis (Figure 2c).
L = S mm
L=8mm y = 4 5 O
(a) Single FSS screen (b) Configuration #1 (c) Configuration #2 Figure 2: Definition of square arrays of conducting dipoles in single-layer FSS The algorithm described in Section 1I.a. was used to compute reflection and transmission coefficients of an incident plane wave illuminating the single FSS in kapton slabs. Simulation and measurement results are plotted in Figure 3a and 3b, for configurations #1 and #2 respectively, at normal incidence (€tinc. = 0"). 2
4
6
8
10
12
14
16
2
18
0
4
6
8
10
12
14
16
18
0
5
-s
s-lo q-15 +
-5
I
,& -20
& -10
E -25
t
8
I-" -30
-15
P -35
-T.
Q
cc -40
-20
-45 -50
-25 Frequency (GHz)
1
R polar H. FSS16x16 polar H, FSS16x16
x Tmes (dB) A R polarH FSS128x128 0
T palarH FSS128x128
Frequency (GHz)
(b) #2, $, = 0", HH (or VV) polarisation (a) #I, $in=. = O", HH polarisation Figure 3: Reflection and transmission coefficients vs. frequency for configuration #1 and #2 Assuming that the permittivities of the kapton PCB and kevlar fabric are 3.5 -j.O and 3.1 -j.O, respectively, Figure 3 shows a good agreement between numerical and experimental results, with a narrow-band transmission coefficient centred at 10 GHz and highly anisotropic properties for configuration #1. In contrast, configuration #2 exhibits isotropic properties, with poor performance, as the dipoles are rotated by 45" with respect to the plane of incidence. In both cases, a good agreement between numerical and experimental results is obtained, thanks to a refined selective grid. Next, we considered the multilayered screen, as illustrated in Figure 4, comprising single FSS of configurations #1 and #2. GA was applied to optimise the thicknesses of the foam spacers (hl, h2 and h3 with Efoam = 1.04 - j.0) for isotropic frequency response with respect to the two orthogonal polarisations at normal incidence, with a population size of 15, a frequency resolution
203
Top view
Figure 4: Multilayered FSSs screen made by stacking #1 and #2 fixed at 0.25 GHz, a 16x16-grid FSS model, to satisfy relation ( I ) in the frequency range [2-8; 1218 GHz]. The isotropic response is expected to be maintained for the same geometry but with thinner printed dipoles, which was implemented in the experimental samples. Hence, the R and T are recomputed subsequently with a 128x128 refined grid (thinner dipoles), are plotted vs. frequency in Figure 5 for $inc. = 0", with the experimental results. It is obvious that the screen designed showed almost isotropic performances for both polarisations at oblique incidence. Similar results were obtained for $inc. = 90". Good agreement was obtained for the transmission coefficients from numerical simulations and experiment, with a very well defined resonance frequency at 10 GHz. However, comparisons of the reflection coefficients suggest that a refined 128x128 grid may not be adequate to account for the coupling between the layers of dipoles. 2
4
6
8
12
10
14
16
18
2
4
6
8
10
12
14
16
18
0
-
-
-35 40
I
=
F R h h incidence 20' incidence 20'. 1 0 Rhhlncidence20" x Thh incidence 20'
~1 -Thh
fh th
rnes
~~
~
-~ rnes
Frequency (GHz)
~
I
Frequency (GHr)
(b) $inc. = 0", f3inc.= 20", W polarisation (a) $inc. 0", Oinc. = 20", HH polarisation Figure 5 : Reflection and transmission coefficients vs. frequency for the multilayered FSSs screen with hl = h3 = 1.0 mm, hz = 1.5 mm The good agreement between numerical and experimental results highlights the relevance of the two-step approach to the design of a multilayered FSS. Extension of the simple element used in single layer FSS to more sophisticated geometry, e.g. tripole or square spiral, is possible but should be kept simple in the interest of the computation time needed for multilayered design optimisation. This approach can also be enlarged to a multi-objective optimisation [2] in screen synthesis.
ACKNOWLEDGEMENTS: The authors gratefully acknowledge the support from the French Embassy and the Defence Science and Technology Agency (DSTA) in Singapore. They are also grateful to Qing A. and Xu X. of Temasek Laboratories for contributing ideas and computational results to this work, G. Sola and D. Guiard of Dassault Aviation for their help in manufacturing the samples and N. Ribikre-Tharaud from SupClec for the technical support with the free-space facility at SONDRA Laboratory.
REFERENCES [1] E. Michielssen and al., ZEEE Trans. MTT, vol. 41, n06/7 (1993) 1024. [2] K.-Y. Lum and al., in Recent Advances in Simulated Evolution and Learning, K. C. Tan and al. (eds.), World Scientific, (2004) 603. [3] D. S. Weile and al., Comput. Methods Appl. Mech. Eng. 186 (2000) 439. [4] S. Chakravarty and al., ZEEE Trans. Antennas Propagat., vol. 50, n"3 (2002) 284. [5] B. A. Murk, "FSS:Theory and design", John Wiley & Sons, Inc. Ed. (2000). [6] L. Liu and al., Electromagnetics, 25 (2005) 69.
Vector Spectral-domain Method for the Analysis of Frequency Selective Surfaces Anyong Qing* and Xin Xu Temasek Laboratories, National University of Singapore 5 Sports Drive 2, Singapore 117508 *Email: tslqav0,nus.edu.sq
Abstract-The original scalar spectral-domain method for the analysis of frequency selective surfaces (FSS) is inherently limited in its formulation. A vector spectral-domain method is presented in this paper. It has been applied to analyze some interesting FSS. Results agree well with experimental data. I. Introduction FSS have been widely employed in various engineering applications. Hence, the analysis of FSS is of great interests to both design and application engineers.
0
Figure 1: An FSS Structure
Figure 2: A Type-2 Gangbuster
A FSS structure comprises one or more periodic arrays embedded in multilayered medium, as shown in Fig. 1. A type-2 gangbuster array is depicted in Fig. 2. The array is generated by repeating its reference element along two non-trivial directions with periodicity T , , and Sb with periodicity q . n,,,is the domain in which element (m,n) is embedded. Alternatively, the array is generated by repeating its reference unit cell, as described above. The unit cell is a parallelogram with side vectors S, = S,T, and S, = S,T,, and the domain of the unit cell (m,n) is RU,, . Generally speaking, Szt,
f
Szi,
. In addition, the following relationship holds for unit cells:
n
RU,~ wmt, = smm,snn,wm, , where S,n, is the Kronecker symbol. Similar relationship may not exist for element domains Rmn and Sztfn,. The (scalar) spectral-domain Galerkin's method [1][2] is widely applied to analyze FSS. In our study, we have noticed that: (a) The method cannot handle normal incidence. Instead, a very small incident elevation angle [ 1][2] is chosen to approximate normal incidence. (b) This method is formulated using the unit cell concept with the non-overlapping property as stated in (l), with the assumption that an element must reside within a unit cell. However, for the gangbuster array shown in Fig. 2, an array element cannot be confined by a unit cell. (c) In [1][2], the transmission and reflection coefficients are defined based on vector electric and magnetic potentials. The formulation appears to be unnecessarily complicated. The amplitude could exceed 1 in certain cases. Recently, we have developed a vector spectral-domain method following the basic idea of the 204
205
scalar spectral-domain method to overcome the above shortcomings. The following sections discussed the formulation and comparisons with experimental data. 11. Scattering from FSS The FSS is assumed to be illuminated by a plane wave (time factor of e'm is assumed and suppressed) as depicted in Fig. 3, E,nC(,) = EFe-/k'"r , (2) where k'"' = k r + k;; is the propagation vector, k r = k F 2 + k y j , k: = -kh sin8'"' COSY,
k y = -k, sin 0'"'sin yY", k; = -kh cos8" , k,' = w2ph.zh,k,, is the wave number in host medium,
B" and f" are the elevation and azimuth angles of incidence, ph and
&h
are the permeability and
permittivity of the host medium. The plane of incidence is defined by k'"' and the normal i to the interface.
Figure 3 Plane of Incidence and Polarization of Incident Field (Left: parallel, right: perpendicular) Accordingly, the incident field is decomposed into components parallel and perpendicular to the plane of incidence, as follows: EZC = E i n C E b t C (3) Oil 01 The induced current on element (m,n) is J:zn(rE SZ.,,). The induced current on unit cell (m, n ) is +
7
J::,,(r E
These currents are related as follows:
Following the basic idea of the original scalar spectral-domain method, the scattered field from multiple FSS embedded in the multilayered medium is given by
where p = xi + ~, k:
Y
N
+ q S , + k:
-
= apq2+flpqj, So and
-
S, are the reciprocal lattice spacing of a unit cell [3] in spectral domain. It is noted that the reciprocal lattice spacing is related to the spatial periodicity by eq. (6), =pS,
Y
si.s; = 2n-4,
(6)
where L is the total number of FSS, E ( k r , z , z ' ) is the dyadic Green's function, I , is the index of the interface on which the Zth FSS lies, iY(k?,z,)) is the spectral-domain current on arbitrary unit cell, and is related to its spatial domain counterpart as follows:
where
206
i; (kr , z ) = jjJ; (r)e'pk7dp,
(9)
%"I
Applying (4) and (6) to (9), the spectral-domain unit cell current and spectral-domain element current are found to be equivalent:
i; ( k r ,z)= $(kF, z), Accordingly,
(10)
Obviously, (1 1) is numerically more convenient since it is more natural to define spatial current over a physical element. 111. Reflection and Transmission Coefficients
The total reflected and transmitted field of mode (p,q) is E'(k:, z)= 6,,6,,$,(kT, z)+ E""(kF,z)= E'(k7, zo).-Jk&(z-zo)
) -
-q
(12)
9
E'(kr,z)=Gp,~qoEb(kT,z +E" (kpq,z ) = E kpq,zN) / & ( z - z J
(13)
where Ei(ky,z) and Ei(k7,z) are the spatial-domain reflected and transmitted fields from the multilayered structure without FSS embedded, k:'q is the wave number in the ground layer, k,'
,-/,
k&
=
= w ' , u ~ E ~pg ,
and
E~
,-/
k,
=
are the permeability and
permittivity of the ground layer. The plane of reflection of mode (p,q) is defined by the reflection propagation vector kLq = k r + i k k q and the normal 2 to the interface, while the plane of transmission of mode (p,q) is defined by the transmission propagation vector kbq= k:
-
2k& and the normal 2 .
y,
Accordingly, E'(k z o ) is decomposed into components parallel and perpendicular to the plane of reflection of mode (p,q),
Er (ka, zo)= (ELq),/+ (ELq)L, Similarly, k'(kr, z N ) is decomposed into components parallel and perpendicular to the plane of
-
transmission of mode (p,q) as Ef(k;>zN)=(E;q)/,+(E;,), The reflection and transmission coefficients are therefore defined as
(ELM)p,.. i::/Eyi, .j p , TLf = .i::/E:i, .j p ,
Rp4T
=
(16)
(17) where the subscripts p r , p t and subscriptisuperscript pi are the polarization (parallel, 11, or perpendicular, I)of the reflected, transmitted and incident fields, respectively. j;:, j;: and j: are the corresponding polarization unit vectors IV. Numerical Results The vector spectral-domain method is first applied to analyze a FSS comprising 45O-rotated dipole array, as shown in Fig. 4. The metal thickness is 17.5pm. Galerkin's method with piecewise sinusoidal basis and testing fimctions are used. The co-polarization reflection coefficient with parallel incidence is shown in Fig. 4. We have also fabricated the structure and measured its reflection coefficient which is also shown in Fig. 4. The simulation result agrees well with the experimental result.
207 Ol
y
Cross section
-y/-, ,
,
,
,
,
,
,
,
spectral-domain Galerkin's method
1,
,
,
,
,
..... measurement
-60
~70 2
Array Pattern
4
6
8
10
12
14
16
18
frequency (GHz)
Figure 4: An FSS with 45O-rotated Dipole Array Next, consider a FSS with type-2 Gangbuster as shown in Fig. 2.3 of [4]. Again, piecewise sinusoidal basis and testing hnctions are used. Results obtained by the vector spectral domain method are shown in Fig. 5 (symbols), along with that obtained in [4] (solid lines). The agreement is excellent. 0-
5-
-
-10 -
-15-
-
I
u --20
-25
-
-30-0
Frequency(GHz)
Figure 5 An Frequency Selective Surface with Type-2 Gangbuster V. Conclusions and Future Works Analysis of FSS using vector spectral-domain method is presented in this paper. The equivalence of the spectral-domain unit cell current and element current is shown. Comparisons with experimental results on FSS with 45O-rotated dipole array, and with type-2 Gangbuster array showed excellent agreement.
Acknowledgement The authors would like to thank Hock Kai Meng for providing experimental results, Lum Kai Yew, Liu Lie, Gan Yeow Beng, and Prof. C. H. Chan of City University of Hong Kong, for their fmitfd discussions. References [ l ] R. Mittra, C. H. Chan, and T. Cwik, Techniques for analyzing frequency selective surfaces-a review, IEEE Proc., vol. 76, no. 12, pp. 1593-1614, 1988 [2] C. H. Chan, Analysis of frequency selective surfaces, in T. K. Wu, Ed., Frequency Selective Surface and GridArray, New York: Wiley, chap. 2, 1995 131 R. E. Jorgenson, Electromagnetic Scattering from a Structured Slab Comprised of Periodically Placed Resistive Cards, Ph. D. dissertation, University of Illinois at Urbana-Champaign, 1989 [4] B. A. Mu&, Frequency Selective Surfaces: Theory and Design, New York: Wiley, 2000
Frequency-dependent permittivity of carbon nanotube composites from 0.01 to 10 GHz L. Liu'*, L. F. Chen', S. Matitsine', L. B. Kongl, Y. B. Gan', K. N. Rozanov2 'Temasek Laboratories, National University of Singapore, Singapore 'Institute for Theoretical and Applied Electromagnetics, Moscow, Russia "email:
[email protected] Abstract Dependence of the permittivity of carbon nanotube composites on frequency and concentration was investigated experimentally using the coaxial air-line method (0.5 to 10 GHz) and the impedance method (0.01 to 1.8GHz). Measured results from both methods showed good agreement. The effective permittivity of the composites was modeled using percolation theory. It was found that scaling law based on the percolation theory is able to provide a good description of the frequencydependent permittivity of CNT composites. 1. Introduction Carbon black (CB) has been used as filers in microwave composites for several decades, since CB composites have low weight, high permittivity, and good chemical stability in comparison to composites with metal powders. The materials are widely used in numerous applications [ 11. In many cases, the permittivity of CB composites is frequency dependent, which can be usehl to obtain broadband microwave response. Another type of carbon fillers for composites is carbon fibers (CF). The elongated shape of the inclusions in CF composites gives rise to special microwave properties, such as high permittivity at low fiber concentrations. As the frequency dispersion is determined by individual fibers, it is more pronounced in CF composites than in CB composites. Due to desired microwave properties, CF composites have been extensively studied [2] and used [3]. Recently, a new type of carbon particles - carbon nanotube (CNT) - has been developed. As in the case of carbon fibers, CNT exhibits high permittivity and dielectric frequency dispersion in composites at low concentrations. Special features have been reported for CNT, such as excitation of localized electronic states, which results in high intrinsic permittivity [4]. In CNT composites, a resonance dielectric absorption has been observed [4,5] that leads to negative microwave permittivity [5]. In other studies, the microwave permittivity is positive and exhibits smooth frequency dependence [6,7]. These features raise the possibility to obtain, in CNT composites, a variety of properties that is much richer than that achievable with other carbon inclusions. For this reason, CNT composites have attracted considerable attention for microwave applications [8,9]. However, the properties of CNT composites have not been full understood yet. In this paper, microwave permittivity of CNT composites is studied as a fimction of frequency and concentration. After brief review of theoretical approaches, the experimental data are presented and discussed in terms of percolation theory. The discussion is aimed at revealing the peculiarities of CNT composites, which are of importance in development of a model for the microwave behavior.
2 Theory In CB composites, the dielectric properties are typically due to agglomerates of carbon particles. Therefore, the percolation theory is appropriate that accounts for the statistical properties of clusters composed of many contacting inclusions in the composite. The theory depends on two parameters, the percolation thresholdp, and the correlation length 6. Both are empirical, i.e., can not be derived within the scope of the theory. The percolation threshold is the least concentration, at which a composite with conducting inclusions is able to conduct DC current. The correlation length is an average inhomogeneity size of the composite. The percolation theory predicts scaling laws for the permittivity et'+iE''as a hnction of frequencyj" 101: & " = Af x - ' , & ' = Bf - ' , (1) where A and B are proportionality factors, and x and y are critical exponents. The critical exponents 208
209
are believed to be universal, i.e., independent of the type and properties of inclusions comprising the composite. Law (1) is valid at concentrationsnear pc and at wavelengths that are small compared to 5 and large compared to the size of inclusions. The theory accounting for inter-cluster polarization effects yields ~ 0 . 7 andy0.27 3 that agrees well with the experimental data for many composites. In contrast, the microwave properties of CF composites are mostly due to individual properties of fibers. Therefore, scale dependent effective media theory (SDEMT) has been used for modeling of such composites [11, 121. At low concentrations,the resonance frequencyfdof the dispersion region is characterizedby:
where a, b, and D are the length, thickness, and conductivity of the fibers, respectively, and Q is the permittivity of the host matrix. SDEMT has been used for analysis of microwave behavior of CF composites [2] and CNT composites [ 5 ] . The further discussion focus on which of the above approaches is more appropriate for modeling of the microwave properties of CNT composites.
3 Experiment Single-wall CNT produced by metal carbon arc method were supplied by Sigma-Aldrich.The purity of CNT is about 40%, with length of 2 to 20 pm and diameter of 0.7 to 1.2 nm. The CNT form bundles of about 20 tubes each. The main impurities are carbon-coated nickel and m u m nano-particles, and amorphous carbon nano-powders. Commercial epoxy resin was used as host matrix to prepare composites. The CNT was manually mixed with the epoxy for 15 minutes, and was subsequently poured into the model before curing in thermal oven at 100°C. In this paper, weight concentration of CNT in composites is used. The conductivity of CNT composites was calculated from the resistance measured by a multi-meter with samples of 12.7~12.7~1.5 mm3 in size. The same samples were used for the permittivity measurement from 0.01 to 1 GHz frequency band with Agilent 4291B impedance analyzer. The coaxial air-line method is used to measure the permittivity from 1 to 10 GHz using a HP8722D vector network analyzer. Ring-shaped samples were produced with an inner radius of 3 mm, outer radius of 7 mm, and thickness of 2mm. Due to the shrinkage of the sample after curing, the outer diameter of the sample could be slightly smaller than the inner diameter of the fixture. Hence, the measured data were recalibrated using the actual diameter of the samples. Results Figure 1 gives a micrograph of a CNT composite. ARer mixing with the epoxy host matrix, the tubes intermingled with each other to form a complex noodle-like morphology. The diameter of the CNT bundles in the figure is about 10 to 20 nm, which is larger than the specificationsfrom the supplier. This could be due to possible formation of larger bundles during fabrication or the presence of multi-wall tubes. DC conductivity shows that the percolation threshold in the CNT composites under the study is about 5%. Above p,, the dependence of conductivity on the concentration is governed by a scaling law, in agreement with the percolation theory. The real part of permittivity,$, is shown by the solid lines Figure 2. The small discrepancy between the two results can be attributed to the imperfect shape of the coaxial samples, and possibly due to the effect of the conductivity of samples on the accuracy of both methods. The measured d are fitted by the scaling law (l), as shown in Fig.2 (dotted lines). The fitting Fig. 1 A micrograph of CNT composite, p=33 %. curves agree very well with the measurement results. 4
210
i..../
10 10
05
001
01
1
00
10
01
Fig. 2. The real permittivity of CNT composites for different LJ
02
r.
concentration
Freauency (GHz)
Fig. 3. Dependence of B on the concentration
10
i ,
I
0 01
01
1
10
Frequency ( G H L )
Fig. 4. Dependence ofy on the concentration
Fig. 5 . Imaginary permittivity of CNT composites for differentp
The factor B and exponent y from curve-fitting depend on the concentration, as shown in Fig. 3 and 4, respectively. B increases steadily with p , while y has a peak at certain concentration value. The inflection in Fig. 3 and the peak in Fig. 4 appeared around the concentration of 5%, which corresponds to the percolation threshold from the conductivity measurements. Hence, these peculiarities are attributed to the percolation behavior of the composites. Fig. 5 shows the measured imaginary permittivity &’’of CNT composites. The results showed higher noise and poorer agreement between the two measurement methods, as compared to that for d. For the samples under study, the dielectric loss tangent is less than unity. Hence, the effect of uncertainties in the measurement techniques for &“is more severe than that for 2. A significant discrepancy between the imaginary permittivity measured by the two methods is noted. A resonance peak is observed at about 10 GHz for large concentrations of CNT, and can be attributed to the excitation of higher order modes in the coaxial line. The frequency dependence of 6’ follows the power law as before. However, parameters of the law are difficult to extract from the experimental data due to inaccuracy in the measurement. 5 Discussion The measured percolation threshold, 5%, is noticeably higher than that of CF composites reported by [2]. This can be attributed to the impurity of CNT, and possibly the difference in the morphology between CF composites and CNT composite. Both result in an increased percolation threshold. The value ofp, obtained in this study is close to 3% observed in [S]. However, the percolation has not been found in [4] at the CNT concentrations as high as 25%. Therefore, the percolation threshold is greatly dependent on the preparation conditions of the samples and hence must be included as an empirical parameter in the theory. For the measured frequency dependence of permittivity, Eq. (1) is valid even at low p , the same as in CB composites. This shows that the dielectric response of CNT composites is due to clusters rather
21 1
than individual inclusions. The conductivity of CNT is known to be about ~ 1 S/m0 [14].~ Assuming a=10 pm, b=l nm, and &=3, the resonance frequency of individual fiber calculated by Eq. ( 2 ) is about 6 GHz. This is the high-frequency limit according to SDEMT. Therefore, the observed dispersion in permittivity must be attributed to the effect of clusters. The dependence of parameters of scaling law (1) on concentration is similar to that of CB composites [14]. However, different values of B are obtained in [14]. This implies different morphology of CB and CNT clusters, such as, different shape, size, and interaction among the particles. The value o f y is universal and must not be dependent on the morphology, at least near the percolation threshold. The values o f y obtained here are between 0.1 and 0.18, which are slightly larger than the range of 0.06 to 0.15 obtained from CB composites [14]. Nevertheless, these values are lower than 0.27 obtained from percolation theory. Lower critical exponent can be attributed to the effect of imperfect electrical contacts of inclusions. In fact, the scope of dispersion curve is due to size distribution of clusters. The dispersive microwave properties of a cluster are determined by its size and resistance. If contacts between inclusions are imperfect, the dispersive range is shifted to larger wavelength and the distribution becomes wider. Both of them lead to dispersion curves with smaller critical exponent.
6 Conclusions The microwave permittivity and specific conductivity of CNT composites obtained from the impedance analyzer and the coaxial air line method are found to be in good agreement. The frequency dependence of the permittivity is well described by the scaling law based on the percolation theory. This is also applicable to the dependence of conductivity on concentration. Therefore, tt is concluded that CNT composite is a percolation system comprising clusters and conducting networks. The microwave behavior is dependent on the cluster formation. The performance is affected slightly by individual properties of fibers. The deviations from the percolation theory can be attributed to the imperfect electrical contacts inside clusters. The CNT composites have large real part of permittivity, reasonable dielectric loss tangent, and noticeable frequency dispersion of permittivity, even for concentrations above the percolation threshold. The effect of DC conductivity to the microwave permittivity appears to be negligible. For this reason, CNT composites with p>pc can be successfully used in the microwave technique as microwave dielectrics and dispersive materials. Acknowledgements The authors appreciate the kindness of Prof. C.K. Ong in granting the use of the measurement facilities, Dr. Li Zheng Wen and Mr. Lin Guo Qing for help in the preparation of the samples. The research was supported by Defense Science and Technology Agency (DSTA), Singapore under project PODO103671. K. Rozanov is grateful to the Russian Federation President Foundation for partial support of the work according to Grant no. 1694.2003.2. References [I] J.B. Donnet, R. C. Bansal, M. J. Wang, Eds. Carbon Black: Science and Technology, M. Dekker, NY, 1993. [2] A.N. Lagarkov, S.M. Matytsin, K.N. Rozanov, and A.K. Sarychev,J. Appl. Phys. 84,3806 (1998). [3] C.P. Neo, V.K. Varadan, IEEE Trans. Electromugn. Compat., 46, 102 (2004). [4] P.C.P. Watts, D.R. Ponnampalam, W.K. Hsu, A. Barnes, B. Chambers, Chem. Phys. Lett. 378,609 (2003). [S] C.A. Grimes, C. Mungle, D. Kouzoudis, S. Fang, andP.C. Eklund, Chem. Phys. Lett. 319,460 (2000). [6] S.L. Browning, J. Lodge, R.R. Price, J. Schelleng, P.E. Schoen, D. Zabetakis, J. Appl. Phys. 84, 6109 (1998). [7] J.K.W. Sandler, J.E. Kirk, I.A. Kinloch, M.S.P. Shaffer, andA.H. Windle, Polymer44, 5893 (2003). [8] B.K. Kim, J. Lee, and 1. Yu, J. Appl. Phyx 94,6724 (2003). [9] B.E. Kilbrdge, J.N. Coleman, J. Fraysse et al., J. Appl. Phyx 92,4024 (2002). [lo] Y. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett. 50,77, (1983). [l 11 L. Liu, S.M. Matitsine, Y.B. Gan, and K.N. Rozanov, Electromagnetics 25 69 (2005). [12] A.N. Lagrkov and A.K. Sarychev, Phys. Rev. B 53,6318 (1996). [13] 0.Cauvet, L. Forro, W. Basca, D. Ugarte, B. Doudin, and W.A. de Heer, Phys. Rev. B 52, R6963 (1995). [I41 C. Brosseau, F. Boulic, P. Queffelec et ul.,J. Appl. Phys. 81,882 (1997).
A Numerical Issue in the Modeling of Composites with Randomly Distributed Fibers Xin
Anyong Qing', Yeow Beng Gan' and Yuan Ping Feng2 'Temasek Laboratories, National University of Singapore *Dept. of Physics, National University of Singapore *Email: tslxuxin@,nus.edu.sq
Abstract The optimal sample size for the numerical simulation of composites with randomly distributed fiber is critical to obtaining accurate results with minimal computational resources. The effects of the inclusion's concentration and frequency on the optimal sample size are studied via numerical modeling. A larger optimal sample size is required for higher concentration and resonance frequency. The underlying reason is due to stronger interactions among the inclusions. 1. Introduction Electromagnetic (EM) composite materials are of great interests in practice. Fiber-filled composites are particularly useful due to their unique properties, such as high permittivity with inclusions of low concentration, distinct and controllable microwave dielectric dispersion. In an earlier paper [ 11, a semi-analytical-numerical method is proposed to study the effective properties of fiber-filled composite slabs. This method involves two steps: (1) configurational average technique [ 2 ] and stationary phase integral method [3] are applied to obtain the field transmitted through a thin composite slab in terms of the averaged forward scattering amplitude (AFSA) of the fibers; (2) method of moment (MOM) [4] and Monte Carlo method (MC) are used to obtain the numerical values of the AFSA. The transmission coefficients and thus, the effective properties of the composite slab, can be obtained. In this method, the propagation of an EM wave through a slab of infinite extent is approximated by a slab of finite transverse extent. Correspondingly, the interactions among inclusions in an infinite slab are approximated by that in a finite slab. As the transverse dimension of the finite slab increases, the result is expected to approach that of the infinite slab. However, a larger slab requires significantly more computational resources. In addition, computation time grows rapidly as the slab size (i.e. number of inclusions) increases. Therefore, it is important to find an optimal size in order to reduce computation time without compromising on accuracy. The optimal sample size used in simulation is dependant on many factors, such as the type of inclusion and concentration, frequency, host materials, etc. In this paper, we focus on the effects of concentration of inclusions and frequency. 2. Theory Consider a collection of fibers in a slab of thickness h . The fibers are randomly but uniformly distributed in planes parallel to the slab surface. An incident plane wave polarized along the x direction (time factor eiwi is used and suppressed) is assumed: EinC (.) = & - i k . r (1) where k = k,:
is the free space wave vector. The configurationally averaged scattered field
(Esca(r)) at any observation point r = xi + y$ (E""(r)) = (E""(z2))
= -j-e
2nnh
+ 22 can be written as [ 11:
-iL,z
F,(O,i)
ko where n = N/VI is the number density of the inclusions, and the minimum
V,
must be able to
accommodate N fibers.
F, (0,); = jdsp(sP(O,.r,2)
(3)
212
213
F ( O , ~ , ; ) = F , (=o,s, ~ ~ =S,R, = i A
)
is the conditionally averaged far-field scattering amplitude of the j th scatterer located at ri with scattering parameter s j in the presence of all other scatterers,
(.) .
is the first order conditional
configurational average. s is the scattering parameter characterizing the scattering behaviour of each scatterer. For identical fibers, s is simply represented by the orientation of the fibers. p ( s ) is the probability that a scatterer has the scattering parameter s . Detailed derivation is given in [ 11. The configurationally averaged forward scattering amplitude Fc(0,z^) will be determined numerically via the Monte Carlo method. With the scattered field given by (2),the effective transmission coefficient of a composite slab of thickness h can be obtained from E'"'(hi)+ (E""(hi))/, T= (5) E""(0) where (E"'"(hi))/,is the component of (E"""(h2))parallel to E'""(r).Since the fibers are randomly distributed in the slab, the scattered field will inevitably have a component perpendicular to E"' (r). As the magnitude of the cross polarized scattered field is significantly weaker than the co-polarized scattered field, it will not be considered hrther in this paper. The effective permittivity of the composite slab can be obtained by comparing its transmission coefficients to that of a homogeneous slab of the same shape. The permittivity of the homogeneous slab that produces the same transmission coefficient as that from the composite slab will be taken as the effective permittivity of the composite slab. 3. Numerical Results and Discussions Identical fibers are randomly distributed in a finite slab at a preset volume concentration (or number concentration). All fibers are of length 1 = 1Omm and diameter a = 0. Imm , and lie parallel to the slab surface (see Fig. 1). The MOM is applied to obtain the forward scattering amplitude of the composite slab. Since the forward scattering amplitude depends on the configuration of the fibers, a MC simulation is carried out in order to determine the most probable value of the forward scattering amplitude. This is finally used to compute the transmission coefficients of the composite slab. Figs. 2 and 3 show the simulated transmission coefficients of a composite material with low fiber concentration, and different sample sizes. The inclusion's concentration is 1.2725~m-~ . No electrical contacts are allowed in the simulation. It is noted that physical contacts are rarely found for this concentration. The computed transmission coefficients are found to be unstable in the frequency range of interest as the number of fibers increases from 1 to 30 (see Fig. 2). Increasing the number of fibers from 15 to 200, the transmission Coefficients tend to be stable (see Fig. 3). The numerical results are reliable only when the number of fibers considered are more than 10 for inclusion concentration of 1.2725cm-* . Hence, the optimal Figure 1: Slab with randomly distributed fibers sample size is 3.5x3.5cm2 (with 15 fibers). Each
214
c
b
li
10
f (GHz)
20
f (GHz)
Figure 2: T-f relation for different number of fibers ( from 1 to 30)
Figure 3: T-f relation for different number of fibers ( from 15 to 200)
data point is a converged result of the MC simulation. The convergence behavior of the MC simulations with 40 fibers is shown in Fig. 4. A minimum of 50 MC Steps are required for all frequencies. Another example is shown in Figs. 5 and 1 GHz 6 for a composite slab with a high 4 GHz concentration of 5 c K 2 . Many physical 20 GHz r contacts are noted in this case, but electrical 10 GHz 09 18 GHz contact can always be avoided through using 3 insulator coatings on the fibers. In the p 0s simulation, it is assumed that no electrical -cE contact exists, even for fibers in physical 07 15 GHz contact. It is obvious that composites with high 13 GHz concentration require a larger number of fibers 06 in the simulation to obtain reliable results. This 20 40 so so 100 120 No. of M C Steps can be guaranteed if the number of fibers exceed 150, corresponding to a sample size of Figure 4: Convergence with respect to Monte 5.5 x 5.5cm2, which is therefore the optimal Carlo Steps size. In both examples, the inclusions are identical and resonate at about 14GHz. The transmission coefficient drops significantly as this frequency is approached. It is observed that the transmission coefficient curves differ significantly in the vicinity of the resonant frequency for sample smaller than the optimal size. The variation in the numerical results is very small at frequencies far from the 10
-150 03
~
~
001
0.0
, 5
10
15
20
f (GHz)
Figure 5 : T-f relation for different number of fibers ( from 5 to 130)
'
170 190
. 5
10
15
20
f (GHz)
Figure 6: T-f relation for different number of fibers (from 150 to 190)
215
resonance frequency. As shown in Fig. 4, the MC simulation also converges slower around the resonance frequency than at other frequencies. It is found that higher concentration and resonance frequency result in stronger interactions among fibers. The optimal size is directly proportional to the strength of the interaction. The interactions among fibers can be completely ignored only when 1 fiber is used. The results for sample with one fiber are in agreement with the converged results at frequency far from the resonance frequency of the fibers (see Fig. 2), implying that interactions among fibers can be neglected. However, near resonance, the interactions among fibers are so strong that more fibers must be used for accurate modeling. This implies that strong interactions among inclusions are important for high concentration. The shape of the transmission curve can also be changed by the strong interactions. In Fig. 3, the dip in the transmission curve is due mainly to the resonance of identical fiber inclusions, since the concentration is low. From Figs. 3 and 6, it is obvious that the bandwidth of the sample with high concentration is broader than that with low concentration.
4. Conclusions The effects of frequency and the concentration of the inclusions on the optimal sample size are studied via numerical modeling. A larger optimal sample size is required for higher concentration and resonance frequency. This is due to the stronger interactions among the inclusions. Other factors that will affect the interactions, such as electrical contacts and types of element, have not been considered in this paper. In the case with electrical contacts, the interaction mechanism among fibers is more complex. This complexity is hrther enhanced when percolation is involved. These are problems that will be considered in the future. Acknowledgement The authors would like to thank Dr. Chao-Fu Wang of Temasek Laboratories for his discussion on the Moment Method. References [ l ] X. Xu, A. Qing, Y. B. Gan, and Y. P. Feng, Effective properties of fiber composite materials, J. Electromag. Waves Appli., Vol. 18, No. 5, pp649-662,2004 [2] L. L. Foldy, The multiple scattering of waves, Phys. Rev.Vo1. 67. No. 3. pp.107-119, 1945. [3] C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles, New York: Wiley. 1998 [4] J. H. Richmond, Radiation and scattering by thin-wire structures in the complex frequency domain, in E. K. Miller, L. Medgyesi-Mitschang, and E. H. Newman, Ed., Computational Electromagnetics, New York: IEEE Press, 1992, pp. 156-169
Study on the mechanical and dielectric properties of LDPEIEVA composites Filled with carbon fiber Zhi-Min Dang Key Laboratory of the Ministry of Education Nanomaterials Beijing University of Chemical Technology Beijing 100029, P. R. China
[email protected] Abstract Low-density polyethylene/ethylene vinyl acetate (LDPE/EVA) composites filled with carbon fiber (CF) were prepared using simple blending and hot-molding technique. Mechanical and dielectric properties of the LDPE/EVA/CF composites were investigated here. The results show that the elasticity of LDPE-based materials could be improved by adding the rubber-like EVA copolymer. The CF in the LDPE/EVA composites may improve the mechanical property of the materials. And the CF plays an important role on deciding the dielectric properties of the LDPE/EVA/CF composites. The LDPE/EVA composites filled with suitable amount of CF have good mechanical and dielectric properties, which are very important for the potential application of the LDPE/EVA/CF composites in the integrated circuit and packaging fields. Keywords: Mechanical property; Dielectric property; LDPE; EVA: CF; Percolation
1. Introduction The study on the improvement of mechanical property in polyolefin, such as low-density polyethylene (LDPE) with excellent impact strength, is always attracting much attention [ 1-21. By blending LDPE with the rubber-like particles, such as ethylene vinyl acetate (EVA) copolymer, the impact property of LDPE material can be improved significantly due to the elasticity of EVA. Very recently, melt elasticity behavior and extrudate characteristics of LLDPE/EVA blends have been reported [3]. Sharifet al has already studied the effect of radiation on LDPE/EVA blends [4]. In addition, the electrical properties of LDPE filled with the conductive fillers have been studied intensively in past years [5-71. Some physical phenomenon, such as electrical percolation, can be observed in polymer-based composites as the concentration of electrical conductive fillers is close to the critical value [8-91. The electrical properties and morphology of polymer-based composites are mainly dependence on the architecture of polymers and the size, shape and volume fraction of electrical conductive fillers employed and the interaction at interfaces between polymers and fillers. Further, the fracture of CF during heat blending would play an important role on deciding the mechanical and electrical properties of LDPE-based composites as reported in reference [8-91. In a viewpoint of application, the LDPE-based composites can be widely used in an integrated circuit field, which field needs the materials with low dielectric constant and good mechanical properties. But some static charges (namely space charges) would be formed at the sites of charge traps in the LDPE material when it is used as electric and electronic devices [lo]. And finally, the devices could be damaged due to a release of static charges in the course of application.
As mentioned above, though some studies have already been carried on the properties of LDPE-based composites, the mechanical and dielectric properties of LDPE/EVA composites filled with CF are still rare in the previous work. The objective of this study is reporting the results of the mechanical and dielectric properties of LDPE/EVA/CF composites and making the composites with good mechanical and electrical properties to be used in the integrated circuit and packaging fields.
2. Materials and experimental procedures LDPE of density 0.922 g/cm3 and melt flow index 2 g/10 min was from China and EVA with 15 % vinly acetate (VA) content and melt index 1.5 g/ 10 min was from Dupont Corporation. The CF 216
217
was a few microns in diameter and -100 microns in average length (Mitsubishi Rayon Company).The LDPE and EVA (LDPE/EVA=70/30) were blended together with CF (the content varies from 0 to 25 phr (per hundred parts)) using a Haake mixer at 120°C with a mixing speed of 40 rpm for 10 min. The processing condition was selected in terms of the rheological property of LDPE material. Subsequently, the mixtures were hot-pressed at 120°C under 10 MPa for 10 min. The mould with hot mixtures was then carried to a cold press and the mixtures were cooled at the same pressure. Disk-samples of 30 mm in diameter and 1 mm in thickness were produced. The disk-samples can be tailored in order to carrying out the different measurements.
-
-
The mechanical strength of the composites was measured from stress-strain tests on dumbbell shaped specimens using Shimadzu AGS-1OKNG instrument with the tensile speed of 1 mm/min. Dynamic mechanical measurements were carried out on a DMA 2980 Dynamic Mechanical Analyzer (TA instruments) from -70 to 70°C. For electrical measurement, alternating current (AC) dielectric properties of the samples were measured using a HP 4194A impedance analyzer in the frequency ranges of 1 kHz - 40 MHz at room temperature. The electrodes were painted with silver paste before the measurement. The morphologies of fracture cross-section broken in stress-strain test and in low temperature supplied by liquid N2 of the LDPE/EVA composite filled with 5 phr CF were observed by SEM (Hitachi model S-450) technique.
Results and discussion The stress-strain curves for pure LDPE, LDPE/EVA (70/30), and the LDPE/EVA composites filled with CF at 5 and 10 phr are shown in Fig. la. The pure LDPE polymer displays a critical stress of 9 MPa with an elongation-at-break value of 500%. Then the stress of the LDPE/EVA (70/30) at same strain is smaller than that of pure LDPE. And the LDPE/EVA composite has a greater strain at elongation-at-break. The great strain of the LDPEiEVA composite would be attributed to the contribution of elastic EVA material. The inset in Fig. l a shows the surface morphology of the LDPEEVA composite, where sphere and agglomeration EVA phase can be observed. Therefore, the structure of LDPEIEVA composite is typical as a sea-island, which the LDPE is sea and EVA, island as referred in the past references. At the same time, the strain of the composites with CF fillers is very high at elongation-at-break, which the value of elongation-at-break is -900%. Such a high value would be attributed to CF effect on the mechanical properties of the LDPEIEVA composites. And, the stress and strain also increase slightly with increasing the concentration of CF fillers. The CF at the fracture-upcoming interfaces would play an important role to keep the elongation-at-break value. With increasing of the content of CF fillers, the critical stress increases, which is -1 1 MPa with the elongation-at-break value of 900%. Fig. l b and l c show the morphologies of the LDPE/EVA/CF composite with 5 phr CF at the different of fractured ways, respectively. One is fractured in the stress-strain test at room temperature (Fig. lb) and the other is broken at low temperature supplied by liquid N2 (Fig. lc). Compared to the morphology of the composite fractured at low temperature, the morphology fractured in the stress-strain test at room temperature shows a lot of LDPEEVA phase as silk-like at the fractured interfaces and CF are orientated along the strain direction, just which the orientation increases the stress strength and elongation-at-break value as shown in Fig. la. The CF orientation here includes two aspects. One is that CF is arrayed in parallel way within the plane, which plane is upright with the direction of press force. The other is that CF has an orientation along the strain direction when the composite is stretched during the stress-strain test.
3.
218
'
-0
200
400
600
800
I
I
1000
Strain / %
(4 (b) (c) Fig. 1. (a) Stress-strain curves of four materials and the inset photo is the surface morphology of LDPEEVA (70/30) composite. The morphology of fracture cross-section broken (b) in stress-strain test and (c) in low temperature supplied by liquid NZof the LDPEIEVA composite with 5 phr CF fillers. 2000
$
0 25
0.20 1500
4
3
015
g
010
n
I :
c 500
0.05
w -60
~ 4 0 -20
0
20
40
60
-60
-40
-20
0
20
40
60
0 00
-60
-40
~20
0
20
10
60
Fig. 2. Dependence of (a) storage modulus, (b) loss modulus and (c) loss Tans of the materials tested on temperature.
Fig. 2a shows the storage modulus (E') of pure LDPE, LDPE/EVA (70/30), and the LDPE/EVA composites filled with CF fillers as a function of temperature. In all cases E'decrease basically with increasing temperatures from -70 to 70°C. Here, it should noted especially that the LDPE/EVA composite with 10 phr CF shows high E' at all temperature ranges. However, the E' of the composites with lower and higher CF contents have almost same E' as pure LDPE and LDPE/EVA (70/30). The result would be explained due to a suitable content of CF in the LDPEIEVA composites. Fig. 2b and 2c show the loss modulus (E") and the loss tangent (tan 6) for the composites, respectively. Two parameters, E"and tan 6 , increase with increasing temperature and arrive peak maximum with increasing temperature further. The LDPEIEVA composite with 10 phr CF shows a great E" in all samples studied as shown in Fig. 2b. The peak maximum of tan 6 shows a slight shift towards higher temperature, which is due to an enhancement in the concentration of CF fillers. Incidentally, with increasing CF content, the peak maximum of tan 6 decreases. This is due to the poor elasticity modulus of the LDPE/EVA composite and the effect of interfaces among LDPE and EVA phases and CF fillers. The dependence of the dielectric constant and electrical conductivity of pure LDPE, LDPE/EVA (70/30), and the LDPE/EVA/CF composites on frequency are shown in Fig. 3a and 3b, respectively. As shown in Fig. 3a, the dielectric constant of the materials investigated increases with increasing the CF concentration. There is a great value in the dielectric constant of the LDPE/EVA composite with 25 phr CF, which can be explained due to the upcoming percolation in vicinity of the volume fraction of conductive CF fillers as reported in much previous works [8-91. The dielectric constants of all LDPE/EVA/CF composites are less than 7 over the broad frequencies. Therefore, the LDPE/EVA/CF composites are still the materials with low dielectric constant. However, the conductivity of this kind of composites with CF fillers is higher than that of pure LDPE over the broad frequencies, which characteristic is very useful to release the static charges in the materials. In addition, Fig. 3a also shows that the dielectric constants of the composites are slightly dependent on frequency, which is often observed in the polymer-based composites filled with electrical
219
conductive fiber-shape fillers with high aspect ratio [6].Accordingly, the effective conductivity *-LOPE
+LUPE/EVA=70/30 -A-
103
104
lo5
LUPE/EVA+ P p h r CF
+InPFIFVAt
ilnhr r'F
lo6
lo7
Frequency I Hz
I
1 0 " ~,03,
I"
1o5
1o6
1o7
Frequency /Hz Fig. 3. Dependence of (a) dielectric constant and (b) conductivity of the materials studied on frequency. The best fit of the conductivity values for the LDPE/EVA composite with 25 phr CF fillers to Equation is shown in the inset of (b).
ueffincreases with frequency (Fig. 3b). According to the percolation theory [8-91, as f,, + f,, ceff l x w1(,Een-lx wll-L, where w = 2m, f,, is the volume fraction of CF fillers, f, is the percolation threshold and u is a critical exponent. The data for the composite with 25 phr CF yields u = 1.09 as shown in the inset of Fig. 3b. The parameter, u , is fitted using the experimental data. In fact, u is always close to 1. Therefore, all LDPE/EVA/CF composites with low dielectric constant and appropriate conductivity would have a potential application in the integrated circuit and packaging fields. 4. Conclusions The mechanical and dielectric properties of the LDPEIEVNCF composites have been studied. The results show that an introduction both of EVA and CF would improve the elasticity and mechanical property of the LDPE-based materials. With increasing the CF concentration in the LDPE/EVA composites, both of the dielectric constant and electrical conductivity increase slightly. And the dielectric constant is almost a constant value over wide frequency range, which is very important for the LDPE/EVNCF composites employed in the integrated circuit and packaging fields. In a word, the LDPE/EVA composite with suitable content of CF fillers has a potential application due to good mechanical and dielectric properties in this study.
Acknowledgements We would like to express our great thanks to Foundation of Education Ministry of China for the support of this study (2005). References [l] [2] [3] [4] [5] [6] [7] [8] [9] [101
Y. Yokoyama, T. Ricco, Polymer 39 (1998) 3675. T. Nomura, Nishio, et al, Polymer 55 (1995) 1307. K. A. Moly, S. S. Bhagawan and S. Thomas, Mater. Lett. 53 (2000) 346. J. Sharif, K. Hashim, et al, Radiation Phys. Chem. 58 (2000) 191. R. Taipalus, T. Harmia, et al, Comp. Sci. Tech. 61 (2001) 801. Z. M. Dang, C. W. Nan, J. Appl. Phys. 93 (2003) 5543. Z. M. Dang, Z. Y. Zhang, S. C. Tjong, Synthetic Metals 146 (2004) 79. Z. M. Dang, Y. Shen and C. W. Nan, Appl. Phys. Lett. 81 (2002) 4814. Z. M. Dang, Y. H. Lin and C. W. Nan, Advanced Materials 15 (2003) 1625. K. Kaneko, IEEE Trans. Dielect. Elect. Insul. 6 (1999) 152.
This page intentionally left blank
Session R8
Chair: A. Lakhtakia
This page intentionally left blank
Experimental Method and Software for Complex Characterization of Magnetic Materials Ovidiu CALTUN and Alexandru STANCU Department of Physics, “Alexandru I. Cuza” University, Iasi, Romania Petru ANDRE1 Electrical and Computer Engineering, Florida State University and Florida A&M University, Tallahassee, FL 323 10, USA
Abstract The experimental set-up and software dedicated to measure and characterize the magnetic properties of magnetic materials are presented. Various magnetization curves are measured efficiently by using a resistor-inductor circuit, in which the inductor contains nonlinear magnetic core. These curves can be readily used for magnetic characterization of the core. The experimental set-up and the software developed for this purpose are presented in detail. 1. Introduction Inductors and transformers are needed in many engineering applications and the desired performances of these devices should be higher and higher. The operating frequency is increasing and the expected values of the permeability are higher and higher. The electrical and magnetic properties of the magnetic materials depend on the microstructure of the magnetic cores resulting from the manufacturing process. The magnetization processes depend on frequency, temperature, as well as the past and current values (history) of the applied magnetic field. Current developments in the field of characterization of magnetic materials lead to new experimental set-ups and upgrade of the well-known hysteresisgraph apparatus. One of the challenges is the development of different methods, which is a complex task. For users, such as engineers and physicists, a compact and manoeuvrable measurement system is very useful. This paper presents a PC-assisted measurement system with the capability to plot various magnetization and hysteresis curves. Parameters such as saturation, remanence magnetic flux density, coercive magnetic field strength, initial permeability, and hysteresis and power losses can be easily extracted easily.
2. Experimental set-up There are two ways to measure hysteresis curves. The magnetic quantities can be determined either directly by using sensors (Hall probe for field strength meters, coils for flux meter) [ 11 or indirectly by measuring the current-voltage characteristics [ 2 , 3 ] .In this paper, we present a technique based on the second approach. This technique has been introduced previously by us in [4], and has been subsequently upgraded and improved in [5,6]. Figure 1 shows the experimental set-up. The test core, part of an RL circuit, is driven by a voltage applied to the primary winding. The induced voltage u,(t) is measured on the secondary winding The magnetic induction b(t) can be determined by using the following equation:
where us(t) is the induced voltage on the secondary coil, N, is the number of turns in the secondary coil and A is the cross-sectional area of the coil.
223
224
If the value of the current in the secondary winding is equal to zero (e.g. open circuit measurement), the total current flowing in the primary winding is the magnetizing current. This current is measured by using a current sensing resistor. From Ampere's low the magnetic field strength h(t) is: (t>.Np
- ' R M ( ~ ) 'N p
h(t) = p -
(2) ' where ip(t) is the primary current, Np is the number of primary turns, 1, is the magnetic path length, and u~,(t) is the voltage drop across the current-sensing resistor R,. The plot of b(t) versus h(t) represents the dynamic hysteresis loop. The dissipated power P , in the core during a period T is related to the primary current and secondary voltage as shown in (3).
lm
4.L
The wave generator is a Stanford Research System Model DS 345. The waveforms are generated by using the Direct Digital Synthesis (DDS) method. The method gives good frequency resolution, low frequency switching time, and crystal clock-like phase noise. The DDS is interconnected with a computer and assisted by a program generating all the waveforms desired by the user. These waveforms are then amplified by the Power Amplifier and applied to the primary (excitation) coil.
Generator
Aquisition
Computer
Fig. 1 The diagram of the experimental set-up A digital storage oscilloscope (Tektronix TDS 3000B) is used to digitize the secondary voltage and primary current (voltage drop across the current-sensing resistor R,) and to transfer the data via Internet. All hrther calculations, such as numerical integrations and scaling, are carried out on the personal computer.
3. Software presentation One of the most difficult problems in the computation of dynamic hysteresis loops is to find the exact phase relationship between the primary current referred and the induced voltage. Any additional phase shifts induce deformations of the hysteresis loop [4].
225
Fig. 2 The front screen of the software allowing the experimental data downloading The front screen of the magnetic hysteresis measurement software is presented in Fig. 2. The experimental data are loaded by clicking on the “Load Data” button. A second window allows setting the number of the turns in the primary and secondary coils and the value of the current sensing resistor in ohms. The inner and the outer radius, as well as the height of the core are used to scale the magnetic field and magnetic flux density. By clicking on the H(t), dBidt, B(t) or B(H) buttons one can display the experimental curves. In Fig. 2, we show the applied magnetic field in our experiment. The primary coil was excited by using a triangular wave modulated in amplitude. By integrating the magnetic flux density rate one can obtain the magnetic flux density versus time. If active current probes are used, the phase error caused by the current probe amplitude must be considered in representing the hysteresis loops [4]. The measurement of the voltage across the secondary winding allows a better matching of the core to the measuring device by varying the number of turns accordingly. [NU INTELEG CE INSEAMNA MATCH INTRE MIEZUL MAGNETIC SI APARATUL DE MASURATE] The voltage measurement should not introduce any phase error. It should be noted that the total measurement time is relatively small, which prevent heating the core. Measurement of several different toroidal cores was carried out. Figure 3 shows the hysteresis loops for the commercial Mn-Zn ferrite core under triangular wave modulated in amplitude.
226
- ARer FFT Interpolation ot integrated raw data Integrated raw data
Fig. 3. The hysterezis loops under the complex triangular wave modulated in amplitude 4. Conclusions An experimental set-up used to measure the magnetic properties of soft magnetic materials as a function of the waveform voltage drive was designed. The magnetization curves and the hysteresis loops measured in various experimental conditions can be obtained. The data can be formatted in the ASCII format plotted easily. Several waveforms can be compared in the same time by loading them in the same or separate windows.
References [l] V. J. Thottuvelil Th. G. Wilson and H.A. Owen Jr., “High- Frequency Measurement Techniques for Magnetic Cores,” IEEE Trans. Power Electron, 5 (1) (1990) 41. [2] N. Schmidt and H. Giildner, “A simple method to determine dynamic hysteresis loops of soft magnetic materials,” IEEE Trans. on Magn., vol. 33, no. 2, pp. 489-496, 1996. [3] J.H.B. Deane, “Modeling the dynamics of nonlinear inductor circuits,” IEEE Trans. on Magn., vol. 30, no. 5 , pp. 2795-2901, 1994. [4] Stancu, 0. Caltun, P. Andrei, J. Phys. IV France, Collq. C1, Suppl. J. Phys. 111, (1997) 209. [5] 0. Caltun, C. Papusoi, Al. Stancu, P. Andrei, W. Kappel, “Magnetic cores diagnosis,” ZOS Series “Studies in Applied Electromagnetics and Mechanics“, editors V. Kose and J. Sieved, pp. 594-597. 1998.
Effective Permeability of 2D-Lattice of Dielectric Resonators G. V. Belokopytov', A. N. Lagarkov', V. N. Semenenko', V. A. Chistyaev2, A. V. Zhuravlev'
'
Department of Physics, Lomonosov Moscow State University, Leninskie Gory, Moscow, 119992, Moscow, Russia, email:
[email protected] Institute for Theoretical and Applied Problems in Electromagnetics (ITAE), Russian Academy of Sciences, Izhorskaya Street, 13119, 125412, Moscow, Russia, email:
[email protected] Abstract The model of microwave magnetic response of periodical two-dimensional lattice of dielectric particles is presented. The model takes into account the excitation of magnetic dipole resonances corresponding to eigenmodes of the dielectric resonators. Electromagnetic response of the lattice is considered as the radiation field of the system of oscillators which are coupled through mutual magnetic field. The transmission and reflection coefficients of the lattice are calculated as the functions of partial resonator parameters and normalized lattice constant. Calculations of effective permeability have been compared with experimental results obtained with lattice of (Ba,Sr)TiO, ceramic particles. 1. Introduction
The excitation of dielectric microwave resonator by an electromagnetic wave induces a magnetic moment in the particle. It has been proposed in [l-31 to use periodical lattices of ferroelectric particles, each acting as dielectric resonator, to build up artificial magnetics. Even when such structure includes only one layer, its electromagnetic behaviour could be described by introducing the effective complex permittivity E and permeability p [4]. A number of measurements of effective E and p for 2D-lattices of ferroelectric resonators have been presented earlier in [2]. The resonance in magnetic response of ferroelectric resonator takes place when the dimensions of the particle are much smaller compared with the incident wavelength. It makes possible to calculate the transmission and reflection coefficients of the lattice in the framework of the model [ 5 ] , which represents the excitation of the resonators as the system of oscillators possessing dipole moments and being coupled due to mutual magnetic field. 2. Transmission and reflection coefficients
For the lattice of identical oscillators with magnetic dipoles which are coupled by magnetic induction we have deduced a convenient expression of the complex amplitude reflection coefficient V as a function of the frequencyw , dimensions and equivalent network parameters of the resonator:
where k = w I c is a wave number, s is a square of lattice elementary cell, 5= w I w, -anI w is detuning factor, and w, is natural frequency of the partial resonator. A term 6, = ( 3 I 2)Ci / Q,) describes the additional detuning of the resonances due to electromagnetic coupling of partial oscillators, and a number r, = Q, /en is the ratio of the quality factors of the resonator which correspond to radiation losses (Q,) and internal dissipation(Q,) . At last, Ci is the lattice sum which takes into account the coupling of resonators because of magnetic flux.
(cp
227
228
In the case of rectangular lattice of resonators, with the distance a between neighbors in x - direction and b in y - direction, the lattice sum Z, is defined as follow:
where: Y = ((ma)' +(nb>')''', sin' 9 = (ma)' lr' . The summation in (2) should be performed in infinite limits ( m and n both positive and negative) except the point m = 0 . The convergence and calculation details related with (2) are discussed in [5].Worthwhile to note, that a similar approach to take into account interactions of particles in composite media was applied in [6, 71. The authors of cited works used integrals instead of lattice sums, which is correct when the distance between neighbors is much less than wavelength. The lattice sums approach is free of this restriction. For 2D-lattices of magnetic dipoles the transmission coefficient T is connected with V by simple relation: T=l-V. (3) For ferroelectric resonator, E >> 1, the factor Q, is merely inverse loss tangent of the material. However, to find the value of radiation loss factor Q, is more complicated problem. It is possible to solve it for spherical particle by application of Mie scattering theory [8] with account the relation between Q-factors and cross sections of scattering (Csco)and absorption (C,,) for corresponding mode of oscillations: Qx 1Qo = Csca 1 Cobs.
(4)
3. Model calculations and comparison with experiment.
Frequency dependencies of amplitude and energy coefficients of transmission, reflection and dissipation were calculated for different combinations of lattice and resonators parameters. The dependencies of energy coefficients of reflection( In the case of ~ K M=, 850 G, KH= 2 Oe, and Hi, = 500 Oe, the frequency dependence of the real part of permeability p,Kand the difference between these real parts ~ + K KpKKareshown in Fig. 1. The above-resonance regime is lower than 1.4 GHz and the below-resonance regime is higher than 3.7 GHz. It is clearly shown that W+KK pKwinabove-resonance is much larger than W+KK p , ~ i n below-resonance. A longer distance is needed with a smaller W+KK ppc Therefore lumped-element isolators are much smaller than distributed-element isolators. In Fig. 1, there is a region of which *+KK p Kis large ~ and p + ~ 0. < This region is not used because p+Kisnegative. If this region can be used for distributed-element isolators the miniaturization of the distributed-element isolator may be possible. If Hi, is transverse to the propagation direction of electromagnetic waves, the effective permeability of ferrite pefis written by[8]
Since p+ and p, are complex, pef is complex and written as pef = pefi- i pefi The frequency dependence of pefi pefi and p+Kare shown in Fig. 2. In the range of 1.4 GHz to 2.7 GHz pe@s positive although p+Kk negative. This indicates that the propagation of electromagnetic waves can be possible with p + ~ 0O. However, the value of pefi in the range of 1.4 GHz to 2.7 GHz is larger than that in both the above-resonance regime and the below-resonance regime. The value of pefi is almost proportional to KH.Thus, in order to use the regime with p + ~ 0< and pefi>O, a ferrite with small KHbecome necessary. In another word, if the KHis small enough, the microstrip Y-isolator can be used within the range of 1.5 GHz to 2.5 GHz, that is, a miniaturization of the microstrip Y-isolator might be possible.
Design of microstrip Y-isolator Figure 3 shows the newly designed microstrip Y-isolator, which has very simple structure. The isolator consists of a SiOz substrate, copper transmission line, and a YIG ferrite single crystal disk, which are enclosed by a ground (GND) plane except for two ports to transmit the electromagnetic wave. The thickness and the radius of the YIG ferrite single crystal disk are 0.2 mm and 1.1 mm, respectively. The dimensions of the SiOz substrate with a patterned silver transmission line, which consists of a Y-junction and three feeder parts, are 3.0 mm K 3.0 mm K 0.51 mm. The line width of feeder parts W, was set at 0.6 mm as the characteristic impedance of these feeder parts is 50 B . The isolator part itself has the horizontal size of 2.2 mm K 2.2 111111, which is smaller than the horizontal size of the smallest current isolator products. There is 90-pm-gap between line and YIG ferrite single crystal disk. Thus the designed isolator has the dimensions of 3.0 mm K 3.0 mm K 0.81 mm. The radius of the center circle D and the line width W of the Y-junction were optimized with a magnetic bias field in YIG ferrite disk of 500 Oe using 3D finite-element method (3D-FEM) for high frequency electromagnetic waves. Results and Discussions The designed isolator in Fig. 2 was analyzed using Ansoft HFSS based on a 3D-FEM for high frequency electromagnetic waves. In this analysis, physical parameters were used as follows: For
248
the transmission line, the conductivity o = 6.1 x lo7 Sim as a typical value of a silver line. For SiOz substrate, the dielectric constant is set at E = 4. For the YIG ferrite single crystal, the dielectric constant E, the saturation magnetization 4rr;Ms,and the FMR linewidth AH are set at F = 15, 4xMs = 850 Oe, and AH = 2 Oe as typical values of a YIG ferrite single crystal. The dielectric loss tangent tan 6, and the conductivity o for the YIG ferrite and the SiOz are set at zero. In this analysis, the permeability of the femte was treated as tensor, which is given by p,
-iKr
0
where pr and K~ are defined by
The transmission characteristics of the designed isolator with the magnetic bias field of 500 Oe are shown in Fig. 4. The nonreciprocal transmission characteristic appears at around 1.9 GHz with an insertion loss of 0.7 dB and an isolation of 28 dB. A narrow bandwidth of 13 MHz with isolation and return loss over 20 dB was obtained. As shown in Fig. 2, it is clear that p,’ is negative at around 1.9 GHz in the case of 4xMS= 850 G, AH = 2 Oe, and Hi, = 500 Oe. Thus this analysis shows that electromagnetic waves can be transmitted with positive p& although p,‘ is negative. Thus, by using the regime of large p e iand I p,’ - p_’I of a YIG ferrite single crystal, a drastic miniaturization of a microstrip Y-isolator could be possible. Figure 5 shows the frequency characteristics of the insertion loss S21 and the isolation S12 changing the value of AH. Insertion loss decreased and isolation increased with decreasing AH. An insertion loss was 0.4 dB with AH= 1.O Oe. The bandwidth broadened by 30 % when AHdecreased to 1 Oe from 3 Oe. The transmission characteristic of the isolator is sensitive to the value of AH because the operating frequency is close to the peak frequency of p,/. Conclusion A small microstrip Y-isolator with dimensions of 3 mm x 3 mm x 0.8 mm was designed by using the regime of p,’ < 0 and pe/ > 0 of a YIG single crystal. The transmission characteristics of the isolator were analyzed using 3D finite-element method. In the analysis a non-reciprocal transmission characteristic with an insertion loss of 0.7 dB and an isolation of 28 dB was obtained at 1.89 GHz. Thus, the possibility of the miniaturization of the microstrip Y-isolator has been proven. Reference [l] H. Bosma, Proc. IEE 109, pt B, suppl21, 137 (1962). [2] H. Bosma, IEEE Trans. Microwave Theory and Tech. MTT-12,61 (1964). [3] J. W. Simon, IEEE Trans. Microwave Theory Tech. MTT-13, 335 (1965). [4] L. K. Anderson, IEEE Trans. Microwave Theory Tech. MTT-15,42 (1967). [ 5 ] E. Schwartz, IEEE Trans. Microwave Theory Tech. MTT-16, 158 (1968). [6] K. Oshiro, et aZ., Trans. Magn. SOC.Japan 4, 60 (2004). [7] S. Yamamoto, et al., J. Magn. SOC.Japan 29,66 (2005). [8] R. F. Soohoo, Microwave Magnetics, (Harper & Row, New York, 1985), pp. 163-187.
249 30 25
20 15
10
5
0
Fig. 1 Permeability of positive and negative circularly polarized electromagnetic waves.
0
1
2
3
4
1.9
1.92
1.94
Fig. 4 Transmission microstrip Y-isolator.
characteristics
of
5
Frequency [GHz]
Frequency [GHz]
Fig. 2 Effective permeability of ferrite.
0.2 mm
Ferrite single crystal disk
Silver h e
Resistor 50 Ohm
SiOzsubstrate
E
S
1.88
Frequency [GHz]
Frequency [GHz]
-20
1.86
3.0mm
Fig. 3 Designed microstrip Y-isolator.
Fig. 5 Insertion loss and isolation changing values of KH.
The Microwave absorbed Property is affected by the Shape of Nanometric Crystal y-FezO3 Huang Yunxia*, Cao Quanxi, Wang Yupeng, Yang Peng and Wei Yunge Xidian University, China *yxhuana@,mail.xidian.edu.cn, h yunxiam, 163.com Abstract y-type ferric trioxide (y-FezO3) is a kind of the important magnetic materials used widely and practically. For the magnetic and dielectric wastage properties, it is widely used in the field of microwave absorbent. In this paper, we introduced the preparation of the nanometric crystal yFez03 in different processes with different shape, which depends on chemical precipitation. In the result of the analysis of transmission electron microscope (TEM) and X-ray diffraction (XRD), we obtained the spherical and the acicular y-FezO3 respectively by sintering product after chemical coprecipitation. Finally, we tested the microwave absorbed property of both of them on lOGHz frequency by the method of wave-guide. We found that the microwave absorbed property of the acicular y-FezO3 is better than that of the spherical y-PezO3.
250
Session R10
Chair: S.M. Matitsine
This page intentionally left blank
Fabrication and characterization of polycrystalline samples and tape of superconducting MgB2 -a future prospect for an electromagnet Suchitra Rajput, Sujeet Chaudhary, Dinesh K. Pandya and Subhash C. Kashyap Thin Film Laboratory, Physics Department, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016 INDIA
Introduction MgB2 is an intermetallic compound with a hexagonal AlBZ type structure consisting of alternate layers of Mg atoms 11, 21. Although known since 1950, the MgB2 was discovered to be superconducting below 40K in January 2001 131. The absence of weak-link effects in MgB2 [4] makes it a promising candidate for engineering applications in the temperature range of 20-35K. Along with this, the metallic nature of MgB2 [5] can reduce the manufacturing and operating cost down to very low values compared to the present day Nb-based devices. For large-scale commercialization, it is necessary to fabricate MgB2 into wires or tapes possessing high critical current density (Jc). It is well established that MgB2 itself does not have weak-link problem but its contamination may lead to the appearance of weak-link effect 141. So, the choice of the cladding material for tapes becomes a very important issue. Among all the available materials, iron (Fe) and its alloys can be the most suitable material 14, 61 due to their ductile nature and little solubility with Mg 171. Although there are some papers reporting on synthesis of tapes, but the issue of whether Fe reacted with boron (B) or not when Fe or the stainless steel sheathed tapes were heated is yet to be resolved. Apart from this, the Jc-enhancement is also an important issue. Regardless of the little anisotropy [S] in electronic properties of MgB2 compared to high Tc superconductors, the uniaxial texturing of the MgB2 can be efficacious in the enhancement of the Jc. In the present work, we have followed the strategy of first optimizing the synthesis parameters for bulk MgB2 samples, and then stainless steel sheathed MgB2 tapes have been formed considering these optimized parameters. For optimization, the effect of starting composition of Mg and B, the sintering temperature, sintering duration, the particle size of raw Mg, and the quenching of the samples after the solid-state reaction have been considered.
Experimental Details Four sets Bulk samples were prepared to optimize the synthesis conditions for bulk MgB2 samples. Three batches were prepared by mixing appropriate amount of pure Mg (99.8%, STREM Chemicals, particle sizeS400pm) and B(99.9%, Cerac) powders in Mg:B ratio of2:2, 1.5:2 and 1.25:2,and the respective batch of samples are named as MB3, MB2 and MB1. In the fourth batch MB4, Mg powder with small particle sizeS60pm was employed, with Mg:B=2:2, to study the effect of particle size. The powder mixture in each set was grounded thoroughly and compressed at 750MPa to form the pellets (5mm diameter). These pellets were kept over alumina plate and simultaneously buried under the heap of Mg in order to compensate for the excessive loss of Mg at the surface. The pellets were heat treated at various temperatures under the Ar-ambient. Three stages of heating consisted of, heating of the pellets at 5”C/min, followed by holding the sample at reaction temperature (sintering temperature) for certain duration, and finally followed by their quenching to RT in air (for MB1, MB2 and MB3) and in LN2 (batch MB4). The MgB2 tape was synthesized by encapsulating the grounded mixture of raw Mg and B in the optimized composition of Mg:B=2:2 followed by the heat treatment in Ar atmosphere and then quenching in LN2. The samples have been characterized by resistivity [p-TI, magnetic ac-susceptibility [X(T)=X’(T)ix”(T)], scanning electron microscopy (SEM) and X-Ray diffraction measurements. A home-made ac-susceptometer was employed to record X-T data. The peak temperature in the f(T) data was utilized to evaluate the Jc by employing Bean’s critical state model. 253
254
Result and Discussion In view of the high volatility of the Mg (melting point ~ 6 5 0 ° C ) and the fact that among the known compounds of the Mg-B system (viz., MgB2, MgB4, MgB6 and MgB12), MgB2 is the most Mg rich binary compound 171, excess Mg in the initial powder mixture of pure Mg and B (Mg: B =1.25:2, 1.5:2 and 2:2) was taken as against the nominal composition of Mg: B=1:2. When the question of optimization comes the various physical parameters (viz., - 23 500 600 400 800 transition temperature, transition width, Jc, resistivity) Sintering- emperature ?E! . j, can be studied to compare the behavior of various Fig. 1. Variation of transition temperature Tc, as inferred from the samples. Let us start with electrical properties [p-T dp/dT-T plots, with sintering (K)]. Figure 1 shows the results of resistivity (p(T)) temperature for various samples from measurements for MB3 batch. It can be clearly seen MB3 batch. that the samples synthesized at the reaction temperature ranging from 750 to 800°C exhibits higher transition temperature. In this MB3 batch, when the sintering temperature was kept below 550"C, there was no superconductivity signature observed down to the lowest investigated temperature. At the higher sintering temperature side i.e., T?900"C, the sintered pellets were too mechanically crumbly to make electrical connections. This is in agreement with the observation of Slusky et al., [9] and Jin et al., reporting the loss of 60% of Mg and very porous samples at 900°C [lo]. According to the studies by P. Duhart 1111, Mg sublimation is expected to start -800°C. Also, Liu et al., in their study on Mg-B phase diagram, have shown that MgB2 decomposes into MgB4 and Mg vapors at a wide range of temperatures, and that the pressure also plays significant role on the decomposition temperature.
341
Under MB1 and MB2 batch, when sintering temperature was scanned over a wide range of sintering temperature from 650°C to 770°C no sign of superconductivity was observed. On the other hand, we could achieve the superconducting MgB2 samples even at 550°C in MB3 batch, which is comparable to the lowest reported [I21 sintering temperature range of 530-610°C for MgB2 when synthesized using micro meter range-size raw Mg powder. Figure 2 shows the SEM images of the three samples. First image (Fig, 2a) presents the as compressed sample and the other two (Fig 2b and 2c) are from MB3 batch synthesized at 550°C and 790°C. As sintering temperature was varied from 550 toward 790"C, the increase in grain growth is observed (Fig. 2c). The bigger grains of MgB2 have thus resulted in the higher transition temperature (-40K) along with the sharp transition (transition width-AT (90%-10%)
Fig. 2 SEM images of (a) as-compressed Mg-B pellet, (b) & (c) MgBz samples (MB3 batch) synthesized at 550OC & 790"C, respectively.
(a)
(b)
(c)
(4
Fig. 3. SEM images of bulk MgB2 samples (MB4 batch) synthesized at (a) 750"C, (b) 790"C, and (c) MgB2 tape. The optical micrograph shows the elongated structure formed in the tape sample (d). (The horizontal bar in the SEM images is of 10pm length.)
Figure 4 shows the comparatively clean XRD pattern for these bulk MgB2 samples with small MgO peaks. Sample synthesized at 750°C exhibited comparatively sharp fall in JCwith temperature (Fig. 5). The X-ray diffractogram for this sample shows broader FWHM compared to that for 790°C. This could be ascribed to comparatively smaller grain size of MgBz at lower sintering temperature i.e., 750°C (Fig. 3a) obtained because of much smaller particle size of the raw Mg powder used in these LN2 quenched samples. Considering high transition temperature -40K with sharp transition width-0.4K observed in the samples synthesized at 790°C from MB4 batch, we synthesized stainless (SS) sheathed tape of MgB2 sticking to these optimized conditions. In view of small, but finite, solubility of Mg with Fe, the hold time of sintering was desirably reduced from lhr to 45min (Here, it should be mentioned that when the MgB2 sample was synthesized for half an hour with Mg:B=2:2 as starting composition it did not exhibit superconductivity). A small piece of MgB2 was taken by mechanically removing from the SS sheath for X-ray analysis and other electrical and magnetic measurements. In X-ray diffractogram, apart from main peaks of MgB2, other small peaks of Mg, MgO and MgBs are also observed. This is similar to the observation of B-rich MgB4 phase in MgB2 tapes reported by Xu at e1.[15]. Another important result is that there is no peak (Fig. 4) corresponding to any Mg-Fe system under these synthesis conditions. The portion of unsheathed tape has also been analyzed for isothermal M-H measurements at RT by employing a VSM. The presence of small hysteresis in M-H measurements confirms the incorporation of the ferromagnetic material from the sheath material. But the absence of relevant peak in XRD indicates that the contamination from the sheath material is very meager and below the detection limit of the diffratometer. Figure 5 shows that comparable JCvalues are exhibited by tapes and bulk samples. It is known that the texturing normally helps in enhancing Jc. The optical micrograph for the tape (Fig. 3d) shows
256
some sort of texturing in the sample. This is indeed expected due to high strain applied during the sheathing of the tape. This has also been confirmed by the XRD analysis showing the 7.1% texturing in the tape. We believe that the finite suppression of superconductivity in tape due to the traces of the ferromagnetic impurity (as observed in VSM measurements) is outbalanced by the enhanced Jc due to the observed texturing effect. The lattice parameters for the tape are a=3.0892&0.00368, and c=3.5285f0.00568,. The better mechanical properties, lower p(RT) and p(42K) values of 0.88pClm and 0.32pClm, high T p 4 0 K (compared to Nb based wires) along with moderately higher Jc, with sharp transition width AT=0.3K, the shorter processing time and the relatively low synthesis temperature in the MgB2 tapes (compared to YBCO), can be viewed as motivating feature for manufacturing MgB2-based magnets. 1
*-MgBI Q-MgB,
Fig. 4.
i
Bulk,75O0C lo8/
A
A
A
“E & c-,l O . f Bulk, sintered at 750°C
3 9 37 20
30
40
50
60
70
80
38
39 T (K)
40
90
20 Fig. 4. X-ray diffractogram for the bulk and tape MgB2 samples. (The calculated lattice parameters ‘a’ and ‘c’ for 750°C and 790°C sintered samples are 3.0862fO.O036A, 3.527 lk0.0056A and 3.0839fO.O036A, 3.5292fO.O056A, respectively.)
Fig. 5. Jc(T) behaviour for bulk and tape samples of MgBz.
Conclusion In conclusion, we have optimized the synthesis parameters for bulk MgB2, and successfully synthesized the SS sheathed tape of MgB2 exhibiting comparable transition temperature and critical current density. These tapes did not show any detectable trace of impurities corresponding to MgFe system. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
T. Yildirim, Materials Today. April 2002 40. R.J. Cava, H.W. Zandbergen, K. Inumaru, Physica C 385(2003) 8-15. Jun Nagamatsu, Norimasa Nakagawa, Takahiro Muranaka, Yuji Zenitani, and Jun Akimitsu, Nature 410(2001) 63. S. Jin, H. Mavoori, C. Bower, and R.B. van Dove, Nature, 41 1 (2001) 563. S.L. Bud’ko, C. Petrovic, G. Lapertot, C.E. Cunningham, P.C. Canfield, M.H. Jung, A.H. Lacerda, condmat10102413 v2 (preprint). H.L. Xu, Y. Feng, Z. Xu, C.S. Li, G. Yan, E. Mossang and A. Sulpice, Physica C (in press) “Binary alloyphase diagrams ”, edited by T. Massalski (ASM International, OH, 1990) Ind. ed. C. Buzea, T. Yamashita, Supercond. Sci. and Techno. 14 (2001) R115. J.S. Slusky et al., Nature 410 (2001) 343-345. P. Duhart, Ann. Chim. 7 (1962) 339. C. Chen, Z-jun Zhou, X-guo Li, J Xu, Y-hao Wang, Z-xiang Gao, Q-rong Feng, Solid State Comm.. 131 (2004) 275-278. J-qin Shen, M-hu Feng, H-tao Wang, Y. Lu, Z-an Xu, Physica C 386 (2003) 663-666. C.U. Jung, M . A . Park, W.N. Kang, M.-S. Kim, S.Y. Lee, S.-I. Lee, Physica C 353 (2001) 162. P.C. Canfield, S.L. Bud’ko, D.K. Finnemore, Physica C 385 (2003) 1-7. H.L. Xu, Y. Feng, Z. Xu, C.S. Li, G. Yan, E. Mossang, A. Sulpice, Physica C (2005) (in press).
Electrorheological Response of Cross-Linked Poly(Dimethy1 Siloxane) containing Polyaniline Particles
Piyanoot Hiamtup', Anuvat Sirivatt*, Alexander M. Jamiesod +ThePetroleum and Petrochemical College, Chulalongkorn University, Bangkok 10330 - Thailand $Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106 - USA *
[email protected] .th
Abstract Electrorheological characteristics of poly (dimethyl siloxane) (PDMS) networks containing camphorsulfonic acid (CSA) doped-polyaniline (PANI) particles were investigated. Samples were prepared by dispersing fine polyaniline particles into cross-linked PDMS. Rheological properties of the PANI/PDMS composites were studied in the oscillatory shear mode in order to study the effects of electric field strength, crosslink density of the matrices, particle concentration, and operating temperature on their electromechanical response. The electrostriction of the composites were observed as a result of an attractive force among polarized particles embedded in the network. The sensitivity values of composites which are defined as storage moduli at any applied electric field subtracted by those values at zero electric field, all divided by moduli at zero field are found to increase about 10-50% when electric field strength are increased to 2 kV/mm. These moduli values increase with particle concentration and temperature but they decrease with crosslink density of the matrices. Introduction The exchange of electrical energy for mechanical energy has long been of both theoretical and practical interests [l]. Electromechanical energy conversion are needed for a wide range of demanding applications such as mini- and micro-robots, biomorphic robots, automobiles, and, in progress, mammalian striated skeletal muscle. Certain polymer gels represent one class of actuators that have the unique ability to change elastic and swelling properties in a reversible manner [2]. Gels consisting of ionic polymers which deform when an electric field is applied have been intensively during the past decades. However, utilization of these kinds of gels in practical applications is still complicated by the fact that structural changes are kinetically restricted by difhsion of liquid molecules into or from the polymer matrix. Another attempt has been proposed in order to solve this problem by using of electrorheological (ER) effect to speed up the response as addressed in several reviews; silicone elastomers containing semi-conducting polymer particles undergo the storage modulus change under dc electric field [3], silicone elastomers blending with ER fluids have been shown to displace flexible electrodes under dc and ac electric fields [4].
In this study, we shall report the electromechanical response of PANI/ PDMS composites, investigated under the oscillatory deformation mode. We are interested in the effects of electric field strength, particle concentration, matrix elasticity, and operating on the storage modulus. Experiment Materials Aniline, C6H7N (AR grade, Merck) was vacuum-distilled and used as the monomer. Ammonium peroxydisulphate, (NH&S208 (AR grade, Merck) was used as the oxidant. (f) - Camphor-lOsulfonic acid, C10H1604S (AR grade, Fluka); 37 YOof Hydrochloric acid, HCI (AR grade, Labscan); 257
258
25 % of ammonium solution, NH40H (AR grade, Merck) and methanol, CH30H (AR grade, Labscan) were used as received. Poly(diniethylsiloxane), hydroxy terminated, HO-[Si(CH3)20],-H ( viscosity 3,500 cSt, Aldrich) was used as a precursors of cross-linked elastomeric matrix. Tetraethyl orthosilicate (TEOS), Si(OCzH5)4 (AR grade, Aldrich) and Dibutyltin diluarate (2EHSn), CH3[(CH2)&02]2Sn[(CH2)&H3]2 (AR grade, Aldrich) were used as a crosslinking agent and a catalyst, respectively. Synthesis of PANI and sample preparation PANI was synthesized via an oxidative coupling polymerization [ 5 ] . 20.4 g of distilled aniline was added to 250 ml of 1.5M HCl aqueous solution and the mixture was vigorously stirred and cooled to 0-5°C in a 3-necked round bottom flask. 250 ml of 1.5M HC1 solution of 25.5 g (NH4)&08 was then added drop-wise into the flask within an hour. After all of the oxidant was added, the reaction mixture was left stirring at 0-5°C for 4 hours. The precipitated polyaniline was then washed with CH30H/H20 mixture until the washing liquid was completely colorless. It was then de-doped by immersion in 3% NH40H, washed and dried at room temperature for 48 hours in vacuum. The emeraldine base was then suspended in the solution of CSA in water for 24 hrs at 40°C in order to increase its conductivity. The doping level was controlled by fixing NCSA/NEB (molar ratio) at 5 [6]. The filtrate was dried at room temperature for 48 hours in an vacuum oven, before passing through a 38 pm sieve shaker to control the particle size and its distribution. Samples were prepared by blending PANI particles with HO-PDMS and TEOS at various mole crosslinking agent to mole monomer ratio (C/M), using 2EHSn as catalyst. The mixtures were poured in mold and allowed to cure under vacuum for 24 hrs [I]. Rheological measurements Rheological properties of the composites were investigated by using a modified melt rheometer (ARES, Rheometric Scientific Inc.) with parallel plates geometry (diameter of 25 mm) attached to insulating spacers where they connect to a transducer or motor. The electric field for rheological measurement was applied by a function generator (GFG-8216A, Instek) and a high voltage amplifier (Model 609E-6, Trek). The samples were firstly checked for viscoelastic linearity by the strain sweep mode tests. They were then pre-sheared until their moduli reached equilibrium values. An electric field was initially applied for 20 minutes to obtain an equilibrium polarization state before each measurement was taken. The experiments were carried out under the frequency sweep mode ranging from 0.1 to 100 rad/s in order to investigate the effect of electric field strength on G' and G ' for the composites. The resulting stress was decomposed into an in-phase and out-of-phase contributions, the storage and loss moduli, G' and G". All experiments were repeated two times at each applied electric field strength to ensure reproducibility.
Results and Discussion Electromechanical Response of PANI / PDMS Composites The effects of electric field strength, crosslink density of the matrices, particle concentration, and operating temperature on electromechanical response of the composites were investigated. Particle concentrations investigated were at volume fractions of 0.05, 0.10, and 0.20 and crosslink density of the matrices was varied at C/M = 0.027, 0.036, and 0.053. Operating temperatures were 27,40, and 60°C. The mean diameter of PANI particles was found to be 23.51 pm with the standard deviation of2.37 pm, and a specific conductivity of 1.2 S/cm.
259
0
5% PANI-CSA
o
20% PANI-CSA
105 1 -
c , a
0
m
B
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
b
0
8
m
I
B
8
P
I ’
01 -
9 :x 1
I 0
20%
001 4
104
1
.1
10
100
Frequency (radls)
Figure 1: (a) Frequency dependence of PANI /PDMS composites of different particle concentrations; and (b) electric field strength dependence of G’ sensitivity at frequency 0.1 rads for composites of different particle concentrations, measured at T = 27OC, C/M = 0.053 1
1
ZEZ m
CIM-0053
0
1
.I
.I 0
0
9
8
2 8
-
Q .01
m
A
.01
0
,001
,001 1
10
100
Electric Field (Vlmm)
1000
1
10
100
1000
Electric Field (Vlmm)
Figure 2: Electric field strength dependence of G’ sensitivity at frequency 0.1 rad/s: (a) for composites with different matrix elasticity, particle concentration is fixed at 10% v/v measured at T = 27OC; (b) for composites with particle concentration of 20% v/v, C/M = 0.053, measured at various temperatures. Effect of Electric Field Strength and Particle Concentration Figures la and Ib show the effects of electric field strength and particle concentration to storage modulus of the composites. As shown in Figure la, the modulus in the absence of an electric field increases with increasing particle concentration as the PANI particles act as filler particles; G’of the composites at C/M = 0.053 increases from 41,924 to 93,124 Pa (122%) when the PANI concentration is increased from 0 to 20 % v/v. Figure I b shows the characteristic value of G’ at each applied electric field strength, obtained at w = 0.1 rad/s. It shows dramatic increases of G’ with increasing electric field strength where the higher particle loading composites shows a greater electromechanical response; the sensitivity is 13% when particle concentration is 5% vol and it increases to 25% at particle concentration of 20% vol. The interaction between the induced electric dipoles causes changes in the overall mechanical properties even though the particles are embedded in the elastomer and are restricted in their movement. The higher volume fraction has the stronger electrostatic interactions since average distance between particles is small and these forces are short range by nature [7]. Effect of Crosslink Density of the Matrices Figure 2a shows the effect of matrix elasticity on the electromechanical response of the composites.
260
It shows that the electromechanical response decreases with increasing C/M ratio or, in the other word, it decreases with increasing elasticity of the matrix. Composites containing PANI particles at 10% vlv possesses the sensitivity of 45% when C/M = 0.027 but it decreases to 12% when C/M = 0.053. When an electric field is applied to an ER elastomer, there is no gross structural change such as the chaidcolumn formation as observed in ER fluids. Nonetheless, it is expected that there is a slight rearrangement of the particle positions to a configuration with lower electrostatic energy causing a reduction of the average particle-particle distance along the electric field direction. The behavior of the ER elastomer can be consequently explained by considering the competition between electrostatic and elasticity forces in which the lower matrix elasticity should reasonably shows the larger electromechanical response [7]. Effect of Operating Temperature The effect of operating temperature on electromechanical response of the composites is shown in Figure 2b. It is observed that the composites tend to show larger responses at higher operating temperature; composites at C/M = 0.053 containing PANI particles at 20% v/v show the sensitivity of 25% at 27OC and it increases to 55% at 55°C. The possible reasons are the matrix elasticity and the particle conductivity [8] which change with temperature.
Conclusion The composites of poly (dimethyl siloxane) (PDMS) networks containing camphorsulfonic acid (CSA) doped-polyaniline (PANI) particles were prepared and their electromechanical responses was investigated by examining the effects of electric field strength, crosslink density of the matrices, particle concentration, and operating temperature. The results show that the response can be enhanced with increasing electric field strength, particle concentration, and operating temperature but it is deteriorated by the matrix elasticity. References [I] Krause, S.; Bohon, K. Macromolecules, 2001,34,7179. [2] Zrinyi, M.; Feher, J.; Filipcsei, G. Macromolecules, 2000,33( 16), 575 1. [3] Shiga, Y.; Okada, A.; Kurauchi, T. Macromolecules, 1993,26,6958. [4] Bohon, K.; Krause, S. J. Polym. Sci.: B Polym. Phys., 1998, 36, 1091 [5] Cao, Y., Andreatta A., Heeger A.J., Smith P., Polymer, 1989,30,2305. [6] Koul, S.; Chandra, R.; Dhawan, S.K. Polymer, 2000,41,9305-9310. [7] Sakurai, R.; See, H.; Saito, T; Sumita, M. J. Non-Newtonian Fluid Mech., 1999, 81, 235. [8] Mzenda, V.M.; Goodman, S.A.; Auret, F.D.; Prinsloo, L.C. Synt. Met., 2002, 127,279.
Microwave Attenuation Measurements on Tetrahedral amorphous Carbon coatings for TWT Applications Vikas Kumar*, Anil Vohra* and Vishnu Srivastava+ *Electronic Sc. Department, Kurukshetra University, Kurukshetra, Haryana- 136119, India +Microwave Tubes Area, CEERI, Pilani, Rajasthan-33303 1, India Emai1:
[email protected],
[email protected] Abstract In the helix TWT amplifier, a coating of lossy material is done on the helix support rods to absorb reflections and hence to improve the stability of the device. Carbon is a very commonly used material for this type of coating, and is commonly deposited by the pyrolytic deposition method of hydrocarbon cracking. In the present work, coatings of tetrahedrally bonded amorphous carbon (taC) have been done on the helix su port rods of alumina using the filtered cathodic vacuum arc system. This is a predominantly sp bonded material and a E-electron semiconductor (due to the residual sp2 bonds). An experimental set up involving a narrow-height wave-guide with a hole was used to measure the attenuation of the coated rods at 6.0GHz frequency. Measurements have been done for the five rods coated with different thicknesses of ta-C. On the basis of the experimental study, it is concluded that ta-C coated rods does not provide significant attenuation and also the thickness of the films that can be achieved with proper adhesion properties is less than that suitable for the significant absorption. Hence, the method and material is not much suitable for this particular application of the microwave absorption.
P
1. Introduction The travelling wave tube (TWT) [1-21, as shown in Fig.1, is a high gain and broadband microwave amplifier, which is commonly used in a communication system. It works on the principle of continuous interaction between the electric field and the electron beam. The major components of a TWT are electron gun, Slow Wave Structure, PPM focusing system, 110 couplers and the collector for collecting the spent beam. A special type of RF circuit known as the slow - wave structure (SWS) is employed for this purpose. Helix, made from the metallic tape or wire, is a commonlyused SWS for extremely wide-band applications. In the analysis of travelling wave amplification, an amount of power is reflected back from the output due to mismatch through the slow wave structure. If there is a mismatch at the input also, a portion of the signal will be reflected back towards the output and this may provide oscillation caused by feedback signal [3] when the following condition is satisfied:
( G - L - R , -R,)>O where G = Gain of the device in dB L = Cold loss in dB pi = Reflection coefficient at input p,, = Reflection coefficient at output
Thus, in order to avoid this problem, coating of a lossy material is done at the helix support rods. Helix is supported by three dielectric rods normally APBN (Anisotropic Pyrolytically deposited Boron Nitride) or Alumina which have high thermal conductivity. The coating on helix support rods forms an attenuator and is most widely used in low power tubes where gain is the important factor. Such coating has significant effects on the characteristics of the device by improving the stability [4]. Helix with support rods having attenuator coating is shown in Fig 2 and a cross sectional view of helix with support rods is shown in Fig.3. 26 1
262 Magnetic Focusing Field
RF Input b
\
Electron Gun
Attenuator
Electron Beam
RF output
/
Helix
Collector
Fig. 1. Schematic Diagram of TWT
Support rod Helix
\
/
Attenuator Coating
Fig. 2. Coating on Support Rods Fig. 3. Cross Sectional View
2. The Attenuator Coatings Carbon is a widely used material for the attenuator coatings and the coating is popularly done using the pyrolytic deposition method [5] in which hydrocarbon cracks at elevated temperatures, as a result of thermal decomposition and carbon deposits over the support rods. In present work, coating of tetrahedral amorphous carbon has been done (ta-C) on the helix support rods to evaluate their performance as microwave attenuators. This is a predominantly sp3 bonded material and a .n-electron semiconductor (due to the residual sp2 bonds). The ta-C films were deposited using a filtered cathodic vacuum arc (FCVA) system that uses either a 90" bend or a double bend ('S' bend) ton during ton that increases to magnetic Filters[6,7].The base pressure taken was deposition. Five alumina rods (cylindrical with 1.4 mm diameter and 60 mm length) have been coated with this method for different thickness by varying the deposition time from 2 to 15 minutes. 3. RF measurement set-up The complete measurement set-up to measure the return loss has been shown in Fig.4. It consists of a sweeper signal source (model 837528) of Agilent Corporation capable of providing signal up to 20 GHz. The input signal is fed through a coaxial cable to a narrow height rectangular wave-guide (34.78mm x 4.96mm) using a coaxial to wave-guide adaptor and normal to narrow wall transition. The wave-guide consists of a hole of diameter 2mm at the center in which the coated rod is to be placed. The Scalar Network Analyzer (HP8757D) provides the reflected power through a 20 dB
263
coupler and a standard matched load has been connected at the other extreme end. Measurements were done at 6.0GHz frequency by varying the position of maximum attenuation of the rod.
AIR
I
%irk
/i
CoatedRod
Signal
Narrow Wave-guide (with hole)
Fig.4 Set-up for return loss (A/R) measurement The measurement set-up used to measure insertion loss (B/R) is shown in Fig.3 in which the SNA is connected in place of a matched load. Also, a power meter has been connected at the coupler end to get a perfect termination. 4. Results and discussion
The measurements have been done to measure the loss in terms of Insertion Loss and the Return Loss for the different samples. The results as obtained for different samples are shown in the Table 1. It is clear from the results that the insertion loss is negligible for all the samples and also the return loss is very small (1 .O dB approx.).The loss characteristics shown are independent of the film thicknesses from 35 to 200 nm. Thus, it is evident that ta-C coated rods do not provide significant attenuation at the microwave frequency of interest and also the thickness of the films that can be achieved with proper adhesion properties is less than the skin depth of the carbon. Hence, the film deposited with this particular method is not much suitable for this microwave absorption application of TWT. The deposition technique may be improved to get the thickness of the films in the order of skin depth with good adhesion and properties may be investigated.
Power Meter
Coated Rod
Network
Narrow Wave-guide (with hole)
Fig.5 Set-up for transmission loss (B/R) measurement Table I
Table-1
264
References
1. A. S. Gilmour Jr., Principles of Travelling Wave Tube, Artech House, Boston, London, 1994. 2. B. N. Basu, Electromagnetic Theory and Applications in Beam Wave Electronics, World Scientific, 1996. 3. J.F. Gittins, Power Travelling Wave Tubes, New York: Elsevier, 1965. 4. Dan M. Goebel, John G. Keller, Willam L. Menninger and Steven T. Blunk, Gain Stability of Travelling Wave Tubes, IEEE Transactions on Electron Devices, Vo1.46, No. 1 1, November 1999, pp.2235-2243. 5. SM Sharma, SK Sharma, RK Gupta, RS Raju, L Kumar & SN Joshi, Development of Pyrolytic Carbon Coated Attenuators for Helix Travelling Wave Tubes, National Symposium of Vacuum Science and Technology, CAT Indore, Nov. 13-15, 1991. 6. M. Chhowalla, M. Weiler, C. A. Davis, B. Kleinsorge, G. A. J. Amaratunga, Appl. Phys. Lett. 67, (1995) 894. 7. P. J. Fallon, V. S. Veerasamy, C. A. Davis, J. Robertson, G. A. J. Amaratunga, W. I. Milne, Phys. Rev. B 81 (1997).
A Novel Electrochemical Sensor for Monitoring Localized Corrosion Naing Naing Aung and Yong-Jun Tan* Corrosion Laboratory School of Materials Science Engineering Nanyang Technological University Nanyang Avenue, Singapore 639798 (*Fax: 65 67909081; e-mail: asyitan@,ntu.edu.s@
Abstract The objective of this research work is to study the initiation, the propagation and growth stages of localized corrosion using an electrochemical sensor namely the wire beam electrode (WBE), in combination with noise signatures analysis (ENA). A novel sensor has been designed to monitor serious localized corrosion process such as pitting corrosion of stainless steel based on the direct correlation of electrochemical potential noise signatures and WBE galvanic current distribution maps. During pitting processes, two characteristic noise patterns have been observed: (i) the characteristic sharp peaks in potential noise data was found to correlate with a sudden disappearance of pits in the initiation and repassivation stage, and (ii) the characteristic pattern of quick potential changes followed by no recovery was found to correspond with stable pits formation during propagation stage in the galvanic current distribution maps. The results suggest that the proposed novel electrochemical sensor is effective and capable of monitoring localized corrosion processes.
Keywords: electrochemical sensor, electrochemical noise, localized corrosion Introduction Almost all conventional electrochemical techniques, which are widely used to determine localized corrosion rates and patterns, have limitations in determining the kinetics of heterogeneous electrode processes. Among the existing methods, the electrochemical noise method is the most promising for monitoring localized corrosion [ 1, 21 and thus noise signatures have attracted the most interests due to its possibility of localized corrosion identification and quantification. However the practical application of noise signatures still remains a rather controversial issue, although many researchers have attempted to use it for understanding the localized corrosion mechanism during the past several decades [3-51. The objectives of this research work are, (i) to address some of the unanswered questions regarding the determination of instantaneous localized corrosion rates and patterns using the novel electrochemically integrated multi-electrode array namely the wire beam electrode (WBE) and electrochemical noise analysis (ENA); and (ii) to achieve a better understanding on the breakdown of the passive film, pit nucleation, pit growth, growth termination and repassivation.
Experimental The WBE sensor was fabricated from 100 metal wires by embedding wires in epoxy resin. The WBE acts both as the mini-electrodes and as the corrosion substrates [6, 71. The stainless steel wire had a diameter of 0.15 cm and the working area was approximately 2.25 cm2 (1.5 cm x 1.5 cm). The total metallic area was approximately 1.77 cm2. The terminals of 100 wires were 265
266
connected to the computer cables in order to measure potential and current distribution over the WBE surface using an AutoAC and computer controlled automatic switch device (Autoswitch) instruments. WBE could enable the direct correlation of noise activities to a specific location of the WBE surface. Combination of WBE and noise signatures could directly correlate noise signatures to localized corrosion activities occurring at a specific location of an electrode surface. The experimental design is illustrated in Figure 1. The working surfaces of the WBE were polished with 400, 800 and 1000 grit silicon carbide paper and cleaned with deionised water and ethanol. The freshly polished WBE was positioned horizontal facing-up position. The working surface was totally immersed in a 6% Ferric chloride corrosive solution at room temperature. The potential noise was obtained by measuring the open circuit potential of each wire of a WBE against an SCE reference electrode using the AutoAC and Auto-switch. The WBE current distribution measurement over the WBE surfaces was done while concurrently monitoring potential noise of the electrodes. The maximum anodic current density (imM), which has the largest positive current density value, the total anodic current density (it& which is the sum of all the anodic current densities, and the number of anodes (No)can be obtained from in WBE current distribution map by registering in a data table for a WBE consisting of 100 wires.
y-. Wire Be-
rc
Elm=
Local Galvanic C u m : &%=W0M&
PotentialNDirs MsermFRurt
-
1
Figure 1. Schematic diagram showing an experimental set-up for detecting potential noise over a WBE and for mapping galvanic currents flowing in the WBE from pitting corrosion system.
Results and Discussion The monitoring of pitting corrosion was carried out using SS316L WBE sensor for 240 hours. From a series of electrode potential-time sequences and the corresponding WBE current distribution maps, three typical stages were observed before occurring stable pit formation. The first stage of pitting was characterised by gradual potential shifting towards negative direction. This stage was featured with corrosion anodic sites existed at the very beginning of electrode exposure to the corrosion environment. WBE The maximum anodic current density increased significantly from 0.94 - 2.166 mA/cm2 during 3 hours exposure. In the second stage, the characteristic 'peak' of rapid potential transient, toward less negative direction, followed by quick or slow recovery was observed after 6 hours exposure. This noise behaviour occurred most
267
frequently during 3-9 hours of exposure. The correlation between this noise signature and WBE current distribution maps clearly suggests that the noise signature of the second stage was due to the disappearance of an unstable anode which leads to the reduction in anodic area or anodic current density and sudden potential change to less negative direction as shown in Figure 2(a). In the third stage, the characteristic pattern of rapid potential transient also toward less negative direction followed by no recovery was correlated with the massive disappearance of anodes over the WBE surface after 22 hours exposure in WBE current distribution maps as shown in Figure 2(b). This noise behaviour occurred seven times during 22-100 hours. The maximum anodic current density of WBE significantly increased to 3.418 mA/cm2. It is generally agreed that the higher the current density at a metastable pit, the higher is the probability of its transition to a stable pit. As expected, the stainless steel major anode at wire no. 35 became the stable anode.
Rapid potential changes followed by quick or slow recovery
Disannearance of unstable anode Galvanic current distribution [After 6:40 hrs]
~
~
distribution l ~ [*fter ~7 hrs] ~
Time (Sec)
Massive disappearance of anodes Rapid potential changes followed by no recovery Galvanic current distribution [&kf'?%hrs]
'
\
,~-'GalvaAc c u m t distribution [After 96 hrsl
Figure 2 Correlation of potential noise signature and WBE current ( d c m 2 ) distribution maps obtained from a stainless steel WBE showing (a) pitting initiation and repassivation stage and (b) stable pit formation stage after exposure to 6% FeCl, solution.
The prediction of the degree of localized corrosion can be achieved by the analysis of maximum anodic current densities (imax),total anodic current densities (itat) and the number of anodes (No)with immersion time. In order to describe the degree of localization, a new parameter namely the localization parameter (LP) can be written as,
i
268
Figure 3 shows the LP significantly decreased in the pit initiation and repassivation stage and it increased again in the stable pit formation and accelerated stable pit growth stages.
&
c
10
E
E
Q
-.Bm
Pitting propagation
Pitting initiation
c
._ 5
x
1
Stable pit formation
0
Local thinning stage
0
50
100
150
200
250
Time (hours)
Figure 3 Change of the localization parameter showing different stages of stainless steel pitting for 240 hours immersion time in 6% FeC13solution.
Conclusions The electrochemical sensor, WBE, has been applied for the first time to monitor stainless steel pitting corrosion in combination with noise signature analysis. The correlation between noise signatures and WBE corrosion patterns change suggests that the noise signatures are indicators of different stages of localized corrosion. The prediction of the degree of localization can be carried out the determination of the localization parameter which was obtained from the i,,,, itotand N, distribution of WBE sensor.
References [ l ] Hladky, K. and Dawson, J. L., The measurement of localized corrosion using electrochemical noise, Corrosion Science, 2 1, 3 17 (198 1). [2] Smulko, J., Darowicki, K., Zielinski, A., Detection of random transients caused by pitting corrosion, Electrochimica Acta, 47, 1297 (2002). [3] Okada, T., A two-step initiation hypothesis of pitting corrosion in passive metals. Corrosion Science, 3 1,453 (1990).
[4] Frankel, G. S., Pitting corrosion of metals: a review of the critical factors. Journal of the Electrochemical Society, 145,2186 (1998). [5] Szklarska-Smialowska, Z., Mechanism of pit nucleation by electrical breakdown of the passive film. Corrosion Science, 44, 1143 (2002). [6] Tan, Y.J. Wire Beam Electrode: A new tool for studying localized corrosion and other heterogeneous electrochemical process, Corrosion Science, 41,229 (1999). [7] Tan,Y. J. U.S.A. Pat.No. 6132593 (2000).
Electrorheological Properties of Poly(p-phenylene vinylene)/PolydimethylsiloxaneBlends Sumonman Naimlang, Anuvat Sirivat* The Petroleum and Petrochemical College, Chulalongkorn University, Bangkok 10330, Thailand * anuvat.s@,chula.ac.th
Abstract Electrorheological properties of PDMS gel and PPV/PDMS blend were investigated experimentally under an oscillatory shear mode at the temperature of 27’C to determine the effects of crosslink ratio, electric field strength and doping level. For the pure PDMS gels, the storage modulus, G’, increases with increasing crosslinking ratio and electric field at all frequencies between 0.1 - 100 rads. When an electric field is applied, the polymer molecules become polarized resulting in the interaction through the electrostatic force between the polarized PDMS molecules. The PDMS gel system with the crosslink ratio of 0.01 possesses the highest G sensitivity to electric field. For the PPViPDMS blends (PPVIPDMS-lo), the dynamic moduli, G’ and G”, are higher than those of pure PDMS in the absence of electric field because PPV particles act as a filler in PDMS matrix. The G’ sensitivity of PDMS increases up to 50% at the electric filed strength of 2kV/mm. The G’ sensitivity PPV/PDMS-10 gels reaches around 45%, comparable to that of the pure PDMS system. Moreover, the doped PPV/PDMS blend (doped PPV (1: 10)/PDMS-10) shows the highest G’ sensitivity (200%) due to interacting electrostatic forces between electric field induced dipole moments of the conductive molecules.
1. Introduction Electroactive polymers (EAP) have emerged in the last decade as promising actuation materials in the field of muscle/insect-like actuators, robotics, etc. The novel characters EAP are light-weight, high energy density, and high flexibility; all are suitable properties for an artificial muscle [2]. EAP can be divided into two major categories based on their activation mechanisms: electronic and ionic. Coulomb forces dominate the electronic EAP, inducing an electrostrictive, electrostatic, piezoelectric or ferroelectric behavior. This type of EAP materials can be made to withstand a large induced displacement while they are activated under DC voltage. In contrast to the electronic EAP, ionic EAPs are materials that involve mobility or diffusion of ions and they operate between two electrodes immersed in an electrolyte [ 11. Dielectric EAP is the one of electronic EAP in which an electric field can be applied to induce a large actuation strain while possessing low elastic stiffness and high dielectric constant. It has been reported that polydimethylsiloxane, PDMS, elastomer can easily bend under an applied electric field [3]. Conductive Polymer is the one of electronic EAP which can be synthesized to produce strong actuators having the potential that matches or is comparable to the force and energy density of biological muscles. Recently, incorporation of a conductive polymer into a dielectric elastomer forming a composite has been interest towards a high efficiency actuator. In our work, we are interested in the rheological behavior of PPV/PDMS blends, under electric field for potential EAP actuator applications. 2. Experiment 2.1 Materials a,a’-dichloro-p-xylene and tetrahydrothiophene,THT (AR grade, Aldrich) were used to synthesized poly(p-xylylene-bis-tetrahydrothiophenium chloride). Acotone, methanol and the sulphuric acid, HzS04 dopant were as received. The matrix phase was hydroxyl terminated polydimethylsiloxane, PDMS (AR grade, Aldrich) with density 1.96g/cm3 and kinematics viscosity 18,000 - 20,000 cSt. Tetraethyl orthosilicated (AR grade, Aldrich) and dibutyl thin dilaurate (AR grade, Aldrich) were used as the initiator and the catalyst, respectively.
269
270
2.2 Polymerization Procedure To a suspension of log of a,a’-dichloro-p-xylene in 150ml of methanol was added 15ml of tetrahydrothiophene, THT. The resulting mixture was heated in a 50°C oil bath overnight, after which the solution was concentrated, and 250ml of acetone was poured in to precipitate the salt p-phenylene dimethylene bis tetramethylene sulfonium chloride. The mixture was stirred in an ice-bath for 0.5h before filtration. The white solid of the salt obtained was washed with acetone and dried under vacuum at room temperature until two sequential weighting were consistent. The yield was approximately 85% [3]. For a salt solution, 1.Og in methanol 7.5cm3 cooled to 0°C was added drowned into an aqueous sodium hydroxide 6.3cm3(0.4M). The reaction mixture was stirred for a further 120 min at 0°C and slightly acidified with hydrochloric acid 1 cm3 (0.4M). The solution 14.8cm3 was then dialyzed against a water-ethanol mixture (1:1, 3x1000cm3) over 3 days after which the solvent was completely removed. The residue was redissolved in methanol. After cooling, the aqueous solution of poly [@-phenylene) bis(tetrahydrothiophenech1oride)l was poured onto glass and allowed to evaporate at room temperature in a free air steam. After 24 hours the yellowish-green precursor films were heated at 200°C for 16 hr. in vacuum over to form PPV. To obtained PPV powder, the PPV film was ground by jar mill for 2 days.
2.3 Doping Process To examine the effect of PPV conductivity on the electrorheological properties, PPV particles having different conductivity values were prepared by doping with sulphuric acid. The H2S04doped PPV was prepared by dispersing the ground PPV powder into a H2S04 aqueous solution at room temperature for 24 hrs. The amounts of acid used were 99,9.9,1.9 and 0 ml of 2 M aqueous acid for doping ratio of mol H2s04: mol ppv 100:1, 10:1, 1:1 and 0: 1 respectively. The H2S04-doped PPV particles were filtered and vacuum dried for 24 h before grinding with a mortar and a pestle and then passed through a 63-ym sieve shaker to control the particle size distribution. 2.4 Preparation of PDMS gels Electrorheogical properties of PDMS under oscillatory shear at fixed temperature of 27°C were measured to determine the effect of $ ratio and electric field. To study the effect of crosslinking ratio, PDMS at various crosslink ratios (0.005, 0.1 and 0.05) were prepared by mixing high molecular weight hydroxyl terminated PDMS, tetraethyl orthosilicate, and dibutyl thin dilaurate at various initiator moles. The mixture was cast in the mold (diameter = 25mm) for 4 hr under 0.6atm.
2.5 Preparation of PPV/PDMS blends The blends were prepared by mechanical blending of doped synthesized PPV particles, which various doping ratio of mol H2S04: mol PPV 100:1, l O : l , 1:l and 0:l respectively, with PDMS. The optimum degree of crosslinking, having the highest rheological sensitivity, was used. (crosslinking ratio of 0.01). The fabrication of the PPVicrosslinked PDMS was cast in the mold (diameter = 25mm) for 4 hr under 0.4atm.
2.5 Electrorheological Properties Measurements Electrorheological properties of PDMS and PPViPDMS gel under an oscillatory shear at fixed temperatured of 27°C were measured (Rheometric Scientific Inc., ARES). The dynamic moduli, G’ and G”, were measured as a function of frequency and electric field strength. First, the linear viscoelastic regime was determined by the strain sweep test to determine the appropriate stain to be used to measured G’ and G”. Frequency sweep test was then carried out measure G’ and G ’ as hnction of frequency (0.1-loorads) at fixed strains of 700% and 1% for pure PDMS fluid and for the PDMS gel, PPV/PDMS gel system, respectively. Pre-oscillatory shear at frequency of lrads and fixed strained at 700% and 1% for pure PDMS fluid and for the PDMS gel, PPViPDMS gel under electric field (-lOmin) was applied to the sample to reach an equilibrium polarization before each measurement was taken.
271
3. Results and Discussion 3.1 Electrorheological Properties of PDMS Gel 3.1.1 Effect of Electric Field Strength The effect of electric field strength on the rheological properties of the PDMS's of various crosslink ratios was investigated under electric field strength between 0 - 2 kV/mm. Figure 1 (a) shows that the storage modulus increases with increasing electric field strength, but the effect of electric field on storage modulus can only be clearly observed at high electric field strength. The pure PDMS fluid has negligible G' response towards the electric field. Figure 1 (b) shows that the loss modulus of the low crasslinking system (0.005) increases slightly only at high electric field strength. On the other hand, G ' the loss modulus of high crosslinking systems (0.01 and 0.05) decreases with increasing electric field strength. The results suggest that the low crosslinking system still retains some fluid behavior as molecules can easily move and align with electric field. As molecules move and slide past each other, they generate energy dissipation resulting in the increase in the loss modulus. We next investigated the maximum sensitivity of PDMS systems. The sensitivity can be defined as AG'/Go = (G'E-G',)/G', where G'E is the G' value of system under electric field, and G', is the G' value of system without electric field. The G' sensitivity of the PDMS systems with the crosslink ratios of 0.005, 0.01, and 0.05 are 35%, 40%, and lo%, respectively as shown in Fig.2. In particular, the system with the crosslink ratio of 0.01 possess the highest G' sensitivity.
-' 60000-
:M
-
n40000-
2
c
v
?-'
"m-
&
lo00 -
-:
1001
i
c?
+"m-0
0
--b m = a 0 1
.-
&
+m = a
um = a m
0;
um - 0 . W s
10 -
11
+" m = R M
&
,
-~~
3 3 . .
. , ..
, ,
,
,
,
.
. , , . ,,,
"m-0.01
-b- " l F o . 6 5
,
. .
, , ,,,,
.
Table-1 Table-1 Y
2 U NclNm
= 0.01
+NrlNm
s 0.05
loooo E (V)
Figure 2: The G' sensitivity of PDMS's at various crosslink ratios as a function of electric field strength at 27OC and frequency of O.lrad/s. The strain of 1% and 700% were applied for the crosslinked PDMS's and the pure PDMS fluid, respectively.
272
3.2 Electrorheological Properties of PPV/PDMS Gel 3.2.1 Effect of Doping Level The effect of electric field strength on the rheological properties of the PPVIPDMS at various doping level was investigated under electric field strength between 0-2 kVlmm. The maximum sensitivity of doped PPVIPDMS system was investigated. The G’ sensitivity of the PPVIPDMS blend system with doping ratio of mol H2S04: mol PPV 100:1, 10: 1, 1:1 and 0: 1 are 45, 3, 200, 5, and -5 respectively as shown in Fig. 3. In particular, the system with doping level of 10:1 possess the highest G’ sensitivity. 250
+PPV/PDMS-10,
-
gap =0.864 mm (l:l), gap =0.997mm Doped PPVPDMS-10 (1:10), gap =0.897mm Doped PPVPDMS-10
+Doped PPVPDMS-10 200
d
3 150
P 0
!2
100
5
50
h
I I I
0
-50 1
10
100
1000
Figure 3: The G’ sensitivity of PPVIPDMS’s at various doping ratios as a function of electric field strength at 27OC and frequency of O.lrad/s. The strain of 1% was applied for the PPVIPDMS blend.
E (V/mm)
4. Conclusion For PDMS system, the storage modulus increases with crosslink ratio due to the increase in the number of junction points between chains where the polymer systems change their behavior from a fluid-like behavior to a solid-like behavior. As sufficiently high electric field strength is applied, storage modulus slightly increases, due the induced electrostatic force set up by the induced dipole moments. G ’ of the low crosslink ratio system increases slightly, while G” of high crosslink ratio systems decreases with increasing electric field strength. At low crosslink ratio, the system appears to retain the fluid like behavior. For the G’ sensitivity, the crosslink ratio system of 0.01 possesses the highest sensitivity.
For PPVIPDMS system, we found that the system of the doped PPVIPDMS blend (doped PPV (1 :10)lPDMS-10) possesses the highest G’ sensitivity. This is caused by the higher electrostatic forces between the polarized molecules. This system will be selected for further study to investigate the effects of blend ratio and temperature on the actuation response. References 1. Cohen Y., Biologically Inspired Reports as Artificial Inspectors. The e- Journal of Nondestructive Testing, vol. 7, p. 1. 2. Gobin, P.F., Goujon, L., Morin, M., Salvia, M. (2002). Brief Overview and Trends about the Use of Inorganic Materials as Artificial Muscles. Proceeding of the First World Congress on Biomimetics. 3. Zrinyl M., Fesher, J., Filipcsei, G. (2000), Novel Gel Actuator Containing Ti02 Particles Operated under Static Electric Field. Macromolecules, 33, 575 1-5753.
FEA for SMD type Piezoelectric Resonator Jong-In lm* and Kyung-Mi Park Korea Institute of Ceramic Engineering & Technology (KICET), Korea *jonain@,kicet.re.kr Abstract This paper describes finite element analysis for surface mounted device (SMD) type piezoelectric resonator. The resonant frequency and impedance characteristics were analyzed and the design was optimized. Studies parameters are the geometry of the resonator, the overlap length of the electrode, and the poling direction of the piezoelectric material. To verify the simulated results, we manufactured the resonator having the optimized geometry and the impedance was measured. The resonant frequency decreased with both the length of the device and the overlap length of the electrode. And the resonant frequency was changed largely with the poling direction of the materials.
273
Ab Initio Calculations of V and Ge-doped Ti02 Hong-Hong Cao" and Qiang Chen Beijing University of Aeronautics and Astronautics, China *buaachh@,sohu.com,buaachhm,163.com Abstract Diluted magnetic semiconductors (DMS) have attracted many attentions since their high Curie temperatures (T,) are greatly in demand for the development of spintronics. Among hole-doped DMS's, Co:Ti02 and Fe:Ti02 thin films have been rather more attentively investigated due to their rather high T, [1,2]. Other dopants such as V, Cr and Ni were predicted theoretically to introduce ferromagnetic ordering into an oxide semiconductor host such as ZnO [3]. Nguyen Hoa Hong et al. [4] reported room temperature FM in V-doped Ti02 thin films fabricated by laser ablation on LaA103 substrates, which showed a good crystallinity and are strong ferromagnetic semiconductors, which certainly are potential candidates for applications. In addition, being a widegap semiconductor, TiOz is mainly activated by ultraviolet (UV) lights. Many studies [5-81 such as cation-doped Ti02 have been carried out in the attempt to shift the absorption edge to a lower energy, thereby increasing the photo-reactivity in the visible-light region. In this paper, we report ab initio density-functional theory investigations on the local structure and magnetization of V ions doped in Ti02 and the electronic structure of the Ge doped TiO2. The calculations were performed using the full potential-linearized augmented plane wave method (FPLAPW) with the generalized gradient approximation (GGA). References [ 11 Y. Matumoto, M. Murakami, T. Shono, T. Hasegawa, T. Fukumura, M. Kawasaki, P. Ahmet, T. Chikyow, S. Koshihara, H. Koinuma, Science 291 (2001) 854. [2] Z. Wang, W. Wang, J. Tang, L.D. Tung, L. Spinu, W. Zhou, Appl. Phys. Lett. 83 (2003) 5 18 [3] K. Sato, H. Katayama-Yoshida, Jpn. J. Appl. Phys., Part 2 (39) (2000) L555 [4] Nguyen Hoa Hong, Joe Sakai, W. Prellier, Antoine Ruyter, Surface and coatings Technology 158-159 (2002) 552 [5] Anpo M, Ichihashi Y and Takauchi M, Res. Chem. Intermed, 24 (1998) 143 [6] Morris D, Dou Y, Rebane J, Mitchell C E J, Egdell R G, Law D S L, Vittadini A and Casarin M, Phys. Rev. B, 61 (2000) 13445 [7] Umebayashi T, Yamaki T, Itoh H and Asai K, Appl. Phys. Lett., 81 (2002) 454. [8] Umebayashi T, Yamaki T, Sumita T, Yamamoto S, Tanaka S and Asai K, Nuclear Instruments and Methods in Physics Research B, 206 (2003) 264.
274
AUTHOR INDEX Abe,M. 73,82 Acher,O. 115 Agrawal, D.K. 147 Agrawal, S. 147 Andrei, P. 223 Annino, G. 107 Ajunwadkar, P.R. 133 Amaut, L.R. 193 Asthana, S. 242 Aung, N.N. 265
Gan,Y.B. 51, 136,200,208,212 Granovsky, A.B. 83 Grzegorczyk, T.M. 33 Gulyaev, Yu.V. 65 Guo, R. 147, 152 Gu0,X.G. 162 Han,J. 151 Hiamtup, P. 257 Hock, K.M. 200 Honvitz, J. 111 Huang, Wei 157 Huang Yunxia 250
Bahadur, D. 242 Balabuha, N.P. 59 Belokopytov, G.V. 227 Bhalla, A S . 89, 111, 147, 152 Bhanu Prasad, B. 238 Bichile, G.K. 167 Burak, Ya.V. 166
Iakubov, I.T. 78 Im, J.-I. 273 Inoue,M. 83 Jacquart, P.-M. 200 Jamieson, A.M. 179,257 Jiang, H.B. I29 Jiang, J.C. 111 Jiang, Q. 33
Caltun, O.F. 140,223 Cao Quanxi 250 Cao, H.-H. 274 Casse, B.D.F. 18,55 Chambers, B. 185 Chan,C.T. 44 Chandrasekaran, G. 234 Chang, W. 111 Chatterjee, R. 158 Chaudhary, S . 253 Chen, C.L. 1 1 1 Chen,H. 33 Chen, L.F. 121, 125, 129, 136,208 Chen, Qiang 274 Chen,X. 33 Chen, X.S. 162 Chistyaev, V.A. 59, 227 Choi, Y.-S. 168, 171 Chotpattananont, D. 175, 179
Kashyap, S.C. 253 Kirchoefer, S.W. 1 1 1 Kissel, V.N. 3 Koledintseva, M.Y. 121 Kolodiazhnyi, T. 107 Kondo,K. 73 Kong, J.A. 33 Kong, L.B. 136,208 Kumar,D. 153 Kumar,V. 261 Kurisu,H. 246 Lagarkov, A.N. 3, 59,74, 78,227 Lakhtakia, A. 97 Lee, J.-C. 168, 171 Lee, S.-H. 168, 171 Li, Z.W. 121, 125, 136 Lim,S.Y. 129 Lin, G.Q. 125, 136 Liu, L. 5 1,200,208 Liu, S.W. 111 Lu, J. 33 Lu,W. 162 Lum, K.Y. 200
Dang, Z.-M. 216 Deng, C.R. 129 Dergachov, M.P. 166 Desai, S.M. 167 Ding, J. 129 Donner, W. 11 1 Dorofeenko, A.V. 41 Fedorenko, A.I. 59 Feng, Y.P. 212 Filimonov, Yu.A. 65 Fujimori, H. 246 Gajbhiye, N.S.
Maklakov, S.A. 78 Manuspiya, H. 152 Matitsine, S. 51, 208 Matsushita, N. 73, 82
140
275
276
Matsuura, M. 246 Meletis, E.I. 11 1 Merzlikin, A.M. 48, 83 Miyasaka, J. 82 Moiseev, V.P. 59 Moiseyenko, V.N. 166 Moser, H.O. 18,55 Naimlang, S. 269 Neo, C.P. 129 Nigam, A.K. 158,242 Nikitov, S.A. 65
Ong, C.K. 125, 129, 136 Ono,H. 73 Oshiro, K. 246 Osipov, A.V. 74,78 Pallam Setty, S. 140 Pandya, D.K. 253 Park, D.-H. 168, 171 Park, K.-M. 273 Parvatheeswara Rao, B. 140 Pathak, A. 158 Pourush, P.K.S. 153 Pradeep, A. 234 Puvanatvattana, T. 175 Qing, Anyong
Srivastava, V.K. 158 Stancu, A. 223 Starostenko, S.N. 74 Subba Rao, P.S.V. 140 Subrahmanyam, A.R. 238 Sugiyama, N. 23 1 Tada, M. 73,82 Tailhades, Ph. 65 Tan, Y.-J. 265 Tanaka, T. 246 Tennant, A. 185 Tretyakov, S.A. 10 Tsai, C.S. 65 Veselago, V.G. 29 Vinogradov, A.P. 41,48, 83 Vohra,A. 261 Volkov, A.I. 65 Vysotskii, S.L. 65 Wang Yupeng 250 Watanabe, T. 23 1 Weaver, J. 11 1 Wei Yunge 250 Wilhelmi, 0. 18, 55 Wu, L.Z. 129 Wu, Y. 125
204,212 Xu, Xin
Rajput, S. 253 Ran,L. 33 Ra0,K.H. 140 Rozanov, K.N. 74,78,121,208 Ryzhikov, I.A. 78 Salunkhe, M.Y. 133 Saw, B.T. 18,55 Semenenko, V.N. 59,227 Shimada, T. 107 Singh,A. 158 Sirivat, A. 175, 179,257,269 Soh,A.K. 103 Song, Y.C. 103 Srivastava. V. 261
204,212
Yamakawa, Y. 23 1 Yamamoto, S. 246 YangPeng 250 Yang,C. 151 YaoXi 90 Yoshida, S. 73 Yoshimura, M. 231 Yu.Tao 157 Zhang,X. 33 Zhou,Lei 44 ZhuoWang 151 Zhuravlev, A.V. 227
This page intentionally left blank
