Applied Physics in the 21st Century (Horizons in World Physics)

HORIZONS IN WORLD PHYSICS SERIES

APPLIED PHYSICS IN THE 21ST CENTURY, (HORIZONS IN WORLD PHYSICS, VOLUME 266) No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services.

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Applied Physics in the 21st Century, Edited by Raymond P. Valencia The Physics of Quarks: New Research, Edited by Nicolas L. Watson and Theo M. Grant Lev Davidovich Landau and his Impact on Contemporary Theoretical Physics Edited by Ammar Sakaji and Ignazio Licata New Trends in Quantum Coherence and Nonlinear Optics Edited by Rafael Drampyan Astrophysics and Condensed Matter Edited Thomas G. Hardwell Superconductivity Research Advances Edited by James E. Nolan Instabilities of Relativistic Electron Beam in Plasma, Edited by Valery B. Krasovitskii Self-Focusing of Relativistic Electron Bunches in Plasma, Edited by Valery B. Krasovitskii New Topics in Theoretical Physics, Edited by Henk F. Arnoldus and Thomas George Boson’s Ferromagnetism and Crystal Growth Research, Edited by Emerson D. Seifer Horizons in World Physics, Edited by Victor H. Marselle Frontiers in General Relativity and Quantum Cosmology Research, Edited by Victor H. Marselle Optics and Electro-Optics Research, Edited by Albert V. Berzilla Trends in General Relativity and Quantum Cosmology, Edited by Albert Reimer Chemical Physics Research Trends, Edited by Benjamin V. Arnold Quantum Dots: Research Developments, Edited by Peter A. Ling Quantum Gravity Research Trends, Edited by Albert Reimer General Relativity Research Trends, Edited by Albert Reimer Spacetime Physics Research Trends, Edited by Albert Reimer New Developments in Quantum Cosmology Research, Edited by Albert Reimer Quantum Cosmology Research Trends, Edited by Albert Reimer Horizons in World Physics, Edited by Tori V. Lynch Horizons in World Physics, Edited by Albert Reimer Theoretical Physics 2002, Part 2, Edited by Henk F. Arnoldus and Thomas F. George Models and Methods of High-Tc Superconductivity: Some Frontal Aspects, Volume 2, Edited by J. K. Srivastava and S. M. Rao Models and Methods of High-Tc Superconductivity: Some Frontal Aspects, Volume 1, Edited by J. K. Srivastava and S. M. Rao Horizons in World Physics, Edited by Albert Reimer Theoretical Physics 2002, Part 1, Edited by Henk F. Arnoldus and Thomas F. George Theoretical Physics 2001, Edited by Henk F. Arnoldus and Thomas F. George Generalized functions in mathematical physics: Main ideas and concepts, Edited by A.S. Demidov Edge Excitations of Low-Dimensional Charged Systems, Edited by Oleg Kirichek On the Structure of the Physical Vacuum and a New Interaction in Nature (Theory, Experiment, Applications), Edited by Yu. A. Baurov Electron Scattering on Complex Atoms (Ions), Edited by V. Lengyel, O. Zatsarinny and E. Remeta An Introduction to Hot Laser Plasma Physics, Edited by A.A. Andreev, A.A. Mak and N.A. Solovyev Electron-Atom Scattering: An Introduction, Maurizio Dapor Theory of Structure Transformations in Non-equilibrium Condensed Matter, Edited by Alexander L. Olemskoi Topics in Cosmic-Ray Astrophysics, Edited by M. A. DuVernois Interactions of Ions in Condensed Matter, Edited by A. Galdikas and L. Pranevièius Optical Vortices, Edited by M. Vasnetsov and K. Staliunas Frontiers in Field Theory, Edited by Quantum Gravity and Strings, R.K. Kaul, J. Maharana, S. Mukhi and S. K. Rama Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions, Edited by D. Kastler, M. Russo and T. Schücker Aspects of Gravitational Interactions, Edited by S.K. Srivastava and K.P. Sinha Dynamics of Transition Metals and Alloys, Edited by S. Prakash Fields and Transients in Superhigh Pulse Current Devices Edited by G.A. Shneerson Gaussian Beams and Optical Resonators, Edited by A. N. Oraevsky Laser Cathode-Ray Tubes, Edited by Yu. M. Popov Quantum Electrodynamics with Unstable Vacuum, Edited by V.L. Ginzburg

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The Muon Method in Science, Edited by V.P. Smilga and Yu.M. Belousov Radiative and Collisional Characteristics of Ions in Hot Plasmas, Edited by I.I. Sobel'man Nonlinear and Quantum Optical Phenomena in Nonequilibrium Media , Edited by V.A. Shcheglov Semiconductors and Insulators: Optical and Spectroscopic …, Edited by Yu.I. Koptev Relativistic Theory of Gravity, Edited by A.A. Logunov Research in Quantum Field Theory, Edited by V.I. Man’ko Nonlinear Theory of Strong Electromagnetic Wave-plasma…, Edited by O.N. Krokhin Dynamics of Elementary Atomic-Molecular…, Edited by O. S. Scheglov Optics and Lasers, Edited by G.G. Petrash Theory and Technology of High Temperature Superconductors, Edited by Yu.I. Koptev Theory of Interaction of Multilevel Systems…, Edited by V.I. Man’ko Physical Properties of High Temperature Superconductors, Edited by Yu.I. Koptev Generalized Mayer Series in Classical Statistical Mechanics, Edited by Igor J. Ivanchik Mathematical Physics, Applied Mathematics and Informatics, Edited by Yu.I. Koptev Squeezed and Correlated States of Quantum Systems, Edited by M.A. Markov Sakharov Memorial Lectures in Physics, Edited by L.V. Keldysh and V.Ya. Fainberg Fiber Optics: Research and Development, Edited by Ye.M. Dianov Gas Dynamics, Edited by Yu.I. Koptev Generation of Nonlinear Waves and Quasistationary …, Edited by L.M. Kovrizhnykh Laser Thermonuclear Targets and Superdurable Microballoons, Edited by A.I. Isakov Spatiotemporal Characteristics of Laser Emission, Edited by M.V. Pyatakhin and A.F. Suchkov Theory of Nonstationary Quantum Oscillators, Edited by M.A. Markov Reliability Problems of Semiconductor Lasers, P.G. Eliseev Pulsars, Edited by A.D. Kuzmin Physical Characteristics and Critical Temperature of High Temperature Superconductors, Edited by M.M. Sushchinskiy Biophysical Approach to Complex Biological Phenomena, Edited by E. Volkov Research on Chemical Lasers Edited by A.N. Orayevskiy Atomic and Ionic Spectra and Elementary Processes in Plasma , Edited by I.I. Sobelman Polarization of the Vacuum and a Quantum Relativistic Gas …, A.Ye. Shabad Superconductors with A15 Lattice and Bridge Contacts Based …, Edited by M. M. Sushchinskiy Metal-Optics and Superconductivity, Edited by A.I. Golovashkin Clusters of Galaxies and Extragalactic Radio Sources, Edited by A.D. Kuz'min Integral Systems, Solid State Physics and Theory of Phase Transitions. Pt. 2. Symm. and Alg. Structures in Physics, Edited by V.V. Dodonov and V.I. Man'ko Quantum Field Theory, Quantum Mechanics and Quantum Optics: Pt. 1. Symm. and Alg. Structures in Physics, Edited by V.V. Dodonov and V.I. Man'ko Photoproduction of Pions on Nucleons and Nuclei, Edited by A.A. Komar Injection Lasers in Optical Communication and Information Processing Systems, Edited by Yu. M. Popov Electron Processes in MIS-Structure Memories, Edited by A.F. Plotnikov Invariants and the Evolution of Nonstationary Quantum Systems, Edited by M.A. Markov Luminescence of Wideband Semiconductors, Edited by M.D. Galanin Pulsed Metal and Metal Halogenide Vapor Lasers, Edited by G.G. Petrash Inelastic Light Scattering in Crystals, Edited by M.M. Sushchinskiy Electron-Excited Molecules in Nonequilibrium Plasma, Edited by N.N. Sobolev Interaction of Ultrashort Pulses with Matter , Edited by M.D. Galanin X-Ray Plasma Spectroscopy and the Properties of Multiply-Charged Ions, Edited by I.I. Sobel'man The Delfin Laser Thermonuclear Installation: Operational Complex …, Edited by G.V. Sklizkov Stoichiometry in Crystal Compounds and Its Influence on Their Physical Properties, Edited by Yu. M. Popov Quantization, Gravitation and Group Methods in Physics Edited by A.A. Komar Classical and Quantum Effects in Electrodynamics Edited by A.A. Komar

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Luminescence and Anisotropy of Zinc Sulfide Crystals Edited by M.D. Galanin Luminescence Centers of Rare Earth Ions in Crystal Phosphors, Edited by M.D. Galanin Electron Liquid Theory of Normal Metals Edited by V.P. Silin Nonequilibrium Superconductivity, Edited by V.L. Ginzburg Thermodynamics and Electrodynamics of Superconductors, Edited by V.L. Ginzburg Quantum Mechanics and Statistical Methods , Edited by M.M. Sushchinskiy Phase Conjugation of Laser Emission , Edited by N.G. Basov Research on Laser Theory , Edited by A.N. Orayevskiy The Theory of Target Compression by Longwave Laser Emission , Edited by G.V. Sklizkov The Physical Effects in the Gravitational Field Black Holes, Edited by M.A. Markov Issues in Intense-Field Quantum Electrodynamics, Edited by V.L. Ginzburg Group Theory, Gravitation and Elementary Particle Physics, Edited by A.A. Komar The Nonlinear Optics of Semiconductor Lasers, Edited by N.G. Basov Solitons and Instantons, Operator Quantization, Edited by V.L. Ginzburg

HORIZONS IN WORLD PHYSICS SERIES

APPLIED PHYSICS IN THE 21ST CENTURY, (HORIZONS IN WORLD PHYSICS, VOLUME 266)

RAYMOND P. VALENCIA EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2010 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Available upon request. ISBN: 978-1-61728-139-6 (E-Book)

Published by Nova Science Publishers, Inc.    New York

CONTENTS Preface Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

ix Emerging Concepts and Challenges in Nano Metal Oxide Thin Films A. Subrahmanyam,, T. P. J. Ramesh, A. Karuppasamy, U. K. Barik, K. Jagadeesh Kumar, N. Ravichandra Raju and R. V. Muniswami Naidu Spectroscopic Analysis of Chemical Species in Carbon Plasmas Induced by High-Power IR CO2 Laser J. J. Camacho, J. M. L. Poyato, L. Díaz and M. Santos

1

63

Induction Transformer Coupled Discharges: Investigation and Application I.M. Ulanov and M.V. Isupov

113

Features on the High Frequency Dielectric Response in Ferroelectric Materials J. D. S. Guerra

169

The Principle that Generates Configuration in Animate and Inanimate Systems – A Unified View Antonio F. Miguel

195

Computational Studies on Drag Reduction Effect by Surface Grooves Haosheng Chen and Yongjian Li

217

Chapter 7

Current Limiting in Oxide Ceramic Structures Alexander Bondarchuk

Chapter 8

Characterisation of Silicide Thin Films for Semiconductor and Nanotechnology Electronics Madhu Bhaskaran, Sharath Sriram and David R. G. Mitchell

245

273

viii Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Index

Contents Magnetically Modified Biological Materials as Perspective Adsorbents for Large-Scale Magnetic Separation Processes Ewa Mosiniewicz-Szablewska, Mirka Safarikova, and Ivo Safarik Optimisation of Deposition Conditions for Functional Oxide Thin Films Sharath Sriram and Madhu Bhaskaran Optical Waveguides Produced by Ion Implantation in Oxide Glasses Feng Chen, Xue-Lin Wang, Lei Wang and Ke-Ming Wang

301

319

341

Thin Film Piezoelectric Response Coefficient Estimation Techniques Sharath Sriram, Madhu Bhaskaran and Arnan Mitchell

353

Plasma Technology: An Alternative to Conventional Chemical Processes for Hydrogen Production María Dolores Calzada

365

Target-Plasma-Film Interactions in High Power Pulsed Magnetron Sputtering (HPPMS) K. Sarakinos

373 391

PREFACE Applied physics is rooted in the fundamental truths and basic concepts of the physical sciences but is concerned with the utilization of these scientific principles in practical devices and systems. This new and important book gathers the latest research from around the globe in this dynamic field. Chapter 1 - The metal oxides thin films have created a revolution in technology. The nano metal oxide thin films continue in giving a new dimension to the understanding pushing the frontiers of science with new concepts and advanced applications. The present article is an attempt to compile the emerging concepts and the novel applications in four metal oxide systems; the article also gives the details of the complexities in the understanding of the physical phenomena. The four nano metal oxide systems coverd in this article are : (i) nano titanium oxide thin film photo catalysis in bio-medical (lung assisted) devices, (ii) nano Silver oxide thin film fluorescence in non-volatile optical memories, (iii) Nano Tungsten oxide thin film electro-chromics in efficient and smart windows and (iv) the p- type transparent conducting oxides (TCO) thin films for transparent electronics with a special reference to Zinc oxide thin films. It is interesting to note that the materials described in the four systems even though possessing a good knowledge base, still offer stiff challenges in the basic understanding. The emphasis in the present article is laid on the new applications, the related physics and chemistry. The preparation methods described are limited to those which have a scope for up-scaling (and for possible industrial adoption). This article is not a review of the state of the art for these metal oxide systems. The aim of this article is to introduce the new and emerging applications with the existing concepts. Chapter 2 - This chapter describes some fundamentals of laser-induced breakdown spectroscopy (LIBS) and experimental results obtained from ultraviolet-visible-near infrared (UV-Vis-NIR) spectra induced by laser ablation of a graphite target, developed in our laboratory. Ablation was produced by a high-power IR CO2 pulsed laser using several wavelengths (λ=9.621 and 10.591 µm), power density ranging from 0.22 to 6.31 GW cm-2 and medium-vacuum conditions (typically at 4 Pa). Spatially and time resolved analysis were carried out for the plasma plume. Wavelength-dispersed spectra of the plume reveal the emission of C, C+, C2+, C3+, C4+, N, H, O, N+, O+ and molecular features of C2, CN, OH, CH, N2, N2+ and NH. For the assignment of molecular bands a comparison with conventional emission sources was made. The characteristics of the spectral emission intensities from the different species have been investigated as functions of the ambient pressure, laser irradiance, delay time, and distance from the target. Excitation, vibrational and rotational temperatures,

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ionization degree and electron number density for some species were estimated. Time-gated spectroscopic studies have allowed estimation of time-of-flight (TOF) and propagation velocities for various emission species. Chapter 3 - Researches in the field of low-temperature plasma provide development of devices, which are widely used by the advanced and high-tech industries. Low-temperature plasma is applied by such major industries as microelectronics, semiconductor industry, solar cell production, plasma chemistry, metallurgy, lighting engineering, etc. Among the known methods of production and use of low-temperature plasma (DC and AC arc discharges, RF plasmatrons, microwave plasmatrons) the devices based on application of induction transformer coupled toroidal discharges (TCTD) are the least studied and, thus, rarely used. Simultaneously, these discharges can be used for development of electrodeless generators of low-temperature plasma: transformer plasmatrons and new induction sources of light. The chapter deals with investigation of properties of TCTD, transformer plasmatrons and induction light sources on the basis of TCTD. Investigation results on electrophysical properties of TCTD aimed at development of transformer plasmatrons are presented in the current paper. Dependences between the strengths of TCTD electric field, discharge current and gas flow are obtained for different gases within the pressure range of 10÷105 Pa. The thermophysical characteristics of TCTD were determined: device efficiency, energy balance of a discharge (heat losses to the discharge chamber wall, plasma jet power). The stable TCTD of the atmospheric pressure in argon and in air was firstly obtained and studied by the authors of this chapter. The process of plasmachemical synthesis of NO in air plasma of TCTD was studied. The abnormally high percentage of NO ~7 % was obtained without product quenching. The transformer plasmatrons of the 10÷200 kW power, operating under the pressures of 10÷105 Pa on argon, air and argon+hydrogen, argon+oxygen mixtures, were developed on the basis of the studies performed. The schemes and constructions of these plasmatrons are presented. The electrophysical and spectral characteristics of TCTD were studied in vapors of mercury and neon. The electrodeless sources of visible and UV radiation with the power of 100 W ÷ 100 kW were developed on the basis of this research. Chapter 4 - Single crystal and/or polycrystalline ferroelectric materials show a high frequency dielectric dispersion, which has been attributed as well to a dispersive (relaxation like) as a resonant mechanism. Physical properties such as relaxation and/or resonant motion mechanisms can be investigated by analyzing the complex dielectric permittivity (real, ε’ and imaginary component, ε’’) in a broad spectral frequency range (100 MHz–13 GHz). Especially, for classical (or ‘normal’) and relaxor ferroelectric systems a dielectric response indistinguishable of dispersion or a resonance mechanism has been found in the literature. The occurrence of such common dispersion process in so different kinds of ferroelectric systems has encouraged the development of several mutually excluding models to explain this physical phenomenon. Nevertheless, the reported results are not conclusive enough to clearly distinguish each mechanism. In this work, a detailed study of the dielectric dispersion phenomenon, including the microwave frequencies, carried out in perovskite structure-type ferroelectric systems, for ‘normal’ and/or relaxor compositions, is presented. The dielectric response in “virgin” and poled state have been investigated taking into account the relative direction between the measuring direction and the orientation of the macroscopic polarization. Results revealed that the dielectric response in ferroelectric systems may be described as a

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general mechanism related to an “over-damped” resonant process rather than a simple relaxation-like dielectric behavior. Chapter 5 - The generation of flow configuration (shape, structure, patterns) is a phenomenon that occurs across the board, in animate and inanimate flow systems. Scientists have struggled to understand the origins of this phenomenon. What determines the geometry of natural flow systems? Is geometry a characteristic of natural flow systems? Are they following the rule of any law? Here we show that the emergence of configuration in animate flow systems is analogous to the emergence of configuration in inanimate flow systems, and that features can be put on a unifying theoretical (physics) basis, which is provided by the constructal law. All scientific endeavors are based on the existence of universality, which manifests itself in diverse ways. Here the authors also explore the idea that complex flow systems with similar functions have a propensity to exhibit similar behavior. Based on this thought relationships that characterize animate systems are tested in relation to cities and countries, and some conclusions are drawn. Chapter 6 - The drag reduction effect caused by the periodic surface grooves were studied using computational fluid dynamic method in two different flow conditions: laminar flow in a slide-disk interface, and turbulent flow on the grooved surface immerged in water. In the first part, the drag results by Reynolds equation that is commonly used in lubrication calculation is compared with the CFD result based on Navier-Stokes equation. It was validated that the Reynolds equation is not suitable when the groove depth is higher than 10% of the interface distance. Then, the drag forces on the surface with transverse and longitudinal grooves are calculated using CFD method. It was found that the ‘side wall’ effect causes the drag reduction, which means the drag reduction would appear when the loss of the drag on the groove’s bottom can not be compensated by the pressure drag or the viscous drag on the side walls of the grooves. In the second part, the drag force on the transverse rectangular grooves in turbulent flow is analyzed based on the RANS equations coupled with the RNG k-ε turbulent model. It was found that the pressure drag force makes up a large proportion of the total drag, and the turbulent vortex structure in the grooves affects the drag characteristic of the surface. The ‘side wall’ effect also functions in turbulent flows, and the drag reduction is determined by the synthesized effect of the reduction of viscous drag and the increment of pressure drag. Chapter 7 - The review of physical phenomena which lead to current limiting behavior (current is increased weaker than voltage, saturated and even decrease) in oxide ceramic structures are presented. Particular attention is given to the mechanisms of current limiting in materials whose electrical conductivity is controlled by potential barriers at the grain boundaries. In particular, the current saturation effect in the nano-grained ceramic films is examined. The consideration of physical models describing the current limiting in specific material is followed by the short posing of main experimental data. For some models, the computational modeling has been performed. Chapter 8 - Nanotechnology devices require low resistance contacts, which can be fabricated by the incorporation of silicide thin films This chapter discusses in detail the study of silicide thin films using a suite of materials characterisation tools. The silicides of interest in this study were titanium silicide (TiSi2) and nickel silicide (NiSi), given their low resistivity and low barrier heights to both n-type and p-type silicon. The silicide thin films were formed by vacuum annealing metal thin films on silicon substrates. Silicide thin films

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formed from metal films deposited by DC magnetron sputtering and electron beam evaporation were compared. The composition, crystallographic orientation, and morphology of these thin films were studied using spectroscopy (AES, SIMS, RBS, in situ Raman spectroscopy), diffraction (Bragg-Brentano and glancing angle XRD, RHEED), and microscopy techniques (TEM, SEM, and AFM). Chapter 9 - Novel magnetically modified biological materials, containing magnetic iron oxides nanoparticles as labels, have been successfully developed and applied as magnetic affinity adsorbents for the magnetic separation of various biologically active compounds and xenobiotics. The main attention was focused on cheap and easy to get magnetic adsorbents which could be applied for large-scale processes. Among them magnetically modified plant-based materials (sawdust) and microbial cells (yeast and algae) were taken into consideration. An inexpensive, extremely simple procedure was proposed for the preparation of such magnetic adsorbents using standard water-based ferrofluids containing maghemite nanoparticles with the diameter of about 12 nm. Such ferrofluids can be prepared in a simple way (almost in any lab) and such nanoparticles can be used to prepare biocomposite materials enabling their simple magnetic separation with standard permanent magnets. Both of these properties are important for possible large-scale applications. The structural, adsorption and magnetic properties of the developed materials were studied in detail by means of scanning electron microscopy, transmission electron microscopy, spectrophotometric measurements, ESR spectroscopy and conventional magnetic methods (DC magnetization and AC susceptibility measurements). The prepared materials efficiently adsorbed selected biologically active compounds and xenobiotics (mainly different enzymes, water-soluble organic dyes and heavy metal ions). Their magnetic behavior was dominated by the superparamagnetic relaxation of isolated single domain maghemite nanoparticles, although a little amount of agglomerates was also present. However, these agglomerates were sufficiently small to show at static conditions the superparamagnetic behavior at room temperature which allows to use the developed materials as magnetic adsorbents in the magnetic separation techniques. Moreover, the prepared materials exhibit the peculiar features enabling their rapid and efficient removal not only from solutions, but also from suspensions. Such materials could be efficiently used to isolate rare biologically active compounds from difficult-to-handle materials including raw extracts, blood and other body fluids, cultivation media, environmental samples, etc. Inexpensive raw materials, extremely simple preparation method, affinity to various biologically active compounds and both organic and inorganic xenobiotics, and distinctive magnetic properties make the developed materials greatly suitable as magnetic adsorbents for large-scale magnetic separation processes. Chapter 10 - This chapter describes a systematic approach to determining the optimal conditions required to deposit thin films of complex functional oxides using RF magnetron sputtering. The motivation of this study was to attain films of designed stoichiometry and of preferentially oriented perovskite crystal structure, as the composition and structure of complex oxides determines their functionality (e.g. ferroelectricity, piezoelectricity, etc.) which is exploited by a variety of applications. The process has been demonstrated with strontium-doped lead zirconate titanate (PSZT) thin films using a combination of materials characterisation techniques – X-ray diffraction, X-ray photoelectron spectroscopy, atomic force microscopy, and crystal structure calculations. The major variables in the deposition

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process using RF magnetron sputtering were identified as the deposition substrate temperature, post-deposition thermal processing, oxygen partial pressure during deposition, and the choice of metallisation on silicon substrates. Starting with these variables the influence of each was systematically determined. The results highlighted the advantages of slow cooling to promote perovskite growth, the influence of oxygen on the composition and crystal structure of the thin films, and the presence of modified unit cell structure for the PSZT thin films on gold- and platinum-coated silicon substrates. The combination of these results led to the limiting the variables in deposition to finite values and arriving at two definite sets of deposition conditions for deposition based on the dependence of microstructure on thermal conditions and the choice of substrate. The validity of the conditions chosen is then demonstrated by deposition of PSZT thin films on thermally-grown silicon dioxide and attaining nanocolumnar preferentially oriented thin films. Chapter 11 - Optical waveguides can restrict light propagation in very small size of order of several microns, reaching high optical intensities even at low pumps; consequently, some properties of the bulk materials may be considerably improved in waveguide structures, such as non-linear responses, laser actions and optical signal amplifications. As one mature technique for material property modifications, ion implantation has been applied to construct optical waveguides in many optical materials, including insulating crystals and glasses, semiconductors and organic materials. Oxide glasses receive much attention for various photonic and telecommunication applications for its competitive costs and excellent optical features. In this chapter, the authors reviewed the research results obtained for optical waveguides in oxide glasses produced by ion implantation techniques, by giving a brief introduction of basic fabrication principles and methods and a summary of interesting results obtained in this topic. The prospects of possible practical applications of ion-implanted oxide glass waveguides in photonics are also demonstrated. Chapter 12 - The response of piezoelectric materials is quantified using charge and voltage coefficients. One such coefficient is d33, which numerically describes the resulting effect for an applied cause along the same direction. There is a lack of established techniques for quantitative estimation of d33 for piezoelectric thin films. This initiated an investigation into the development of such techniques, as a consequence of which two new techniques for piezoelectric coefficient estimation, under the inverse piezoelectric effect, have been developed. One technique capitalises on the measurement accuracy of the nanoindenter in following thin film displacement, while the other uses a standard atomic force microscope in contact imaging mode to estimate d33. Both techniques were developed by rigorously testing them against standard materials and avoiding commonly reported sources of error. Full details on the development, scope, and limitations of both techniques are presented in this chapter. Chapter 13 - There is currently a strong debate on the need to look for new alternative energy sources to replace fossil fuels (particularly oil), due to atmospheric pollution derived from their use, probable reserve exhaustion and productive countries’ excessive dependence on future political events. Therefore, many countries are currently giving an incentive to research aimed at the development of new energy sources, among which hydrogen —and its use by means of fuel-cells— is to be included. Within the so-called hydrogen economy, hydrogen production —from different raw materials such as hydrocarbons, alcohols and some others— becomes an important aspect, since hydrogen is not a natural product but is obtained by means of water vapour. However, such process leads to the production of high amounts of CO2. The use of plasma technology allows generating hydrogen by decomposing organic

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compounds (alcohols and methane), so plasma acts as a reactive environment; this way, biogas —which can be easily found in city landfills— can also be used for hydrogen obtention. Thus, the use of plasma with this purpose arises as an alternative process not only to reforming of hydrocarbons and other substances with water vapour but also to other purely chemical processes, avoiding or minimizing CO2 emissions (involving greenhouse effects). A subproduct —obtained with H2 and which also deserves special attention— is solid carbon, which has important added value, since it may work as a base element for chemical industry and other technological fields. Given the foregoing, research in the use of plasma technology for hydrogen production is one of the research lines within Applied Physics with higher applicability potential within the energy sector. Chapter 14 - Growth of films by plasma-assisted physical vapor deposition (PVD) techniques provides means for tailoring their properties and improving their functionality in technological applications. State of the art plasma-assisted PVD techniques, like direct current magnetron sputtering (dcMS), suffer from low degree of ionization and thus, low ionto-neutral ratios in the flux of the deposited material. The implementation of external sources for the enhancement of the ionization is in many cases technically complicated and increases the end-product cost. High power pulsed magnetron sputtering (HPPMS) is a novel sputtering technique that elegantly enables the conversion of conventional sputtering source into an ion source. By applying the power in unipolar pulses of low frequency (30 μs) and (b) 7 successive laser shots (td=4 μs and tw=0.02 μs). The emissions of ionized C2+(1s22s3p 3P02,1,0 → 1s22s3s 3S1) around 4650 Å, and C3+ around 4658.3 Å are considerably higher in the spectrum of Figure 22a, while the C2(d-a) Swan Δv=+1 sequence emission is similar. Figures 23a-b and 24 show the typical temporal sequence of laser-induced carbon plasma. At early times (td≤0.02 μs) emission from C2+ and C3+ is easily detected between 4645-4670 Å (see inset within figure 23-a). As seen in figure 23-b during the initial stages after laser pulse (td≤0.04 μs), C2+ emissions dominate the spectrum. As time evolves (0.04 μs≤td≤1.5 μs), C3+ emission dominate the spectrum. As the delay is increased up to 2.5 μs (1.5 μs≤td≤2.5 μs) again C2+ emission dominates the spectrum. These ionic lines decrease quickly for higher delay times, being detected up to ∼ 3 μs. Some oxygen and nitrogen ionic lines were also observed in the spectra at the gate delay from 0.02 μs to 1 μs and its emission intensities remain approximately constant in this time interval (see Figure 23a). They vanished after the delay of ∼1.5 μs. It shows that the air is ionized by the CO2 laser pulse and by the collisions with the laser induced plasma. During the time period up to ∼ 0.5 μs, no apparent C2 emissions were observed. As can be seen from Figure 24, the C2(d-a; Δv=1 band sequence) emissions were clearly observed from ∼2 μs. The C2 emission intensities increase lightly with increasing td, reach a maximum at ~5 μs, and then decrease as the time is further increased.

Spectroscopic Analysis of Chemical Species in Carbon Plasmas Induced...

105

3+ 2

3 0

2+

2

3

3

3

tw = 0.02 μs

C2: d Πg-a Πu

1-0

8-7

v'-v"

8-7

2-1

3-2

3

7-6

C : 1s 2s3s SJ"

6-5 5-4 7-6 4-3

2+

C

4-3

td = 4 μs J" 1

3

C2: d Πg-a Πu

1-0 v'-v"

2+

C : 1s 2s3p PJ'

0

2-1

2

J' 1

3-2

C

6-5 5-4

2+

C

(b)

(a) 4650

4675

4700

4725

4650

4750

4675

Wavelength / Å

4700

4725

4750

Wavelength / Å

Figure 22 (a)-(b). Measured high-resolution pulsed laser ablation of graphite emission spectra observed in the region 4645-4750 Å region. The data acquisition was performed by averaging the signal over: (a) 20 successive laser shots with td=0 and tw>>30 μs; (b) 7 successive laser shots with td=4 μs and tw=0.02 μs. The assignments of some ionic lines of C2+ and C3+ and molecular bands of C2 are indicated. The insert in (a) illustrates the rotational structure of one triplet of C2+ line.

3+

C

1000

td=0 ; tw=20 ns 100

+

500

7000

td=500 ns

6000

td= 20 ns

4650

4675 4700 Wavelength / Å

+

O

+

O O +

td=100 ns

5000 4000

tw=20 ns

td= 30 ns

200

0

O

3+

C

(b)

Relative Intensity / a. u.

1500

2+ C 2+ td=40 ns; tw=20 ns C

Relative Intensity / a. u.

Relative Intensity / a. u.

2000

2+

C

2+

C

3000 2000 1000 0

0

4650 4660 4670 4680 4690 4700 4710 4720 Wavelength / Å

4645

4650

4655

4660

4665

4670

Wavelength / Å

Figure 23(a)-(b). Time-resolved high-resolution emission spectra from laser-induced carbon plasma observed in the region: (a) 4645-4720 Å region monitored at 40 ns delay time; (b) 4645-4670 Å region monitored at 20, 30, 100, and 500 ns gate delay times for a fixed gate width time of 20 ns. The inset in (a) displays the spectrum the first 20 ns after incidence of the laser pulse.

Space-and-time resolved OESs laser-induced measurements could be used to estimate plasma expansion rate. To obtain additional time resolved information about the optical emission of the plume, wavelength resolved spectra have been recorded at different delay times at a distance of 9 mm. The temporal evolution of spectral atomic, ionic and molecular line intensities at a constant distance from the target can be used to construct the time-offlight (TOF) profile. TOF studies of the emission provide fundamental information regarding the time taken for a particular species to evolve after the laser-induced plasma has formed.

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Specifically, this technique gives an indication of the velocity of the emitted species. A rough estimation of the velocity for the different species in the plume can be inferred from the time resolved spectra by plotting the intensities of selected emission lines versus the delay time, and then calculating the velocity by dividing the distance from the target by the time where the emission peaks. This method for determination of plasma velocity should be used with care due to the superposition of both expansion and forward movements of the plasma plume. 2+

C

3

8-7

1-0

td=10 μs

Relative Intensity / a. u.

30000

v'-v"

2-1

3-2

4-3

2+

C

3

C2:d Πg-a Πu

6-5 5-4

tw=0.02 μs

25000

20000

td=5 μs

3+

C

15000

td=3 μs

10000

2+

C

td=2 μs

5000

0

4640

4660

4680 4700 Wavelength / Å

4720

4740

Figure 24. Time-resolved high-resolution emission spectra from laser-induced carbon plasma observed in the region 4645-4750 Å region monitored at 2, 3, 5, and 10 μs gate delays for a fixed gate width time of 20 ns.

Figure 25 displays the TOF profile, for ablation experiments induced by CO2 laser pulses, of several C, C+ and C3+ lines intensities in UV region and C2+ in the visible as a function of delay time. However, the insert of the figure shows the time dependence of C2+ and C3+ line intensities in the visible region for ablation induced by CO2 laser pulses in which the tail has been eliminated by means of the suppression of the N2 in the gas mixture of the active laser medium. All the data are taken from high-resolution spectra and in the figures the temporal profiles of both kinds of laser pulses are also plotted. In both cases emissions from C3+ are stronger than emissions coming from the other species. All the ionic lines follow the time profile of lasers pulses lasting until four or three microseconds depending on the kind of the laser pulse. These behaviours may be related to the laser absorption processes on the target surface. Thus for “non tailed pulses” the line intensities start to growth at 400 ns while for “tailed pulses” start at 70 ns. Since the energy pumping (rise time) of each kind of pulse is different, the species reach the maximum intensity at different times: ∼1 μs for non tailed pulses and 700 ns for tailed ones, indicating that the graphite target needs some energy threshold to eject the different species. The higher intensity in the 0-400 ns time interval for the C2+ may be due to the higher sensibility of our ICCD camera in the visible region than in the UV one. The different behaviour of atomic C can be also observed in figure 25. Atomic C have a higher rise time and lasting more ( > 15 μs) than ionic species, possibly due to the

Spectroscopic Analysis of Chemical Species in Carbon Plasmas Induced...

107

continuous recombination of ions with electrons to give excited carbon. From these results has not been observed excitation dependence on the pulse tail however the energy of the pulse intensity seems to be the pulse parameter that influence on the graphite ablation process. The peak velocities estimated for C3+, C2+ and C+ species, from figure 25, are about 7x103 m/s.

CO2 laser pulse CO2 laser pulse without tail C2+:4647.42 Å C3+: 4658.3 Å

Intensity / a.u.

Intensity / a. u.

C : 2478.56 Å + C : 2509.12 Å 2+ C : 4647.42 Å 3+ C : 2529.98 Å

0

1

2

3

4

5

Delay time / μs

0

1

2

3

4

16

18

Delay time / μs Figure 25. Emission intensity change of C(2478.56 Å), C+(2509.12 Å), C2+(4647.42 Å) and C3+(2529.98 Å) lines as a function of delay time (fixed gate width time of 20 ns) for a CO2 pulse laser with a tail of about 3 μs. The insert shows the emission intensity change of C2+(4647.42 Å) and C3+(4658.3 Å) lines as a function of delay time (fixed gate width time of 20 ns) for a CO2 pulse laser without tail.

In this section the plasma temperature was determined form the emission line intensities of several C+ lines observed in the laser-induced plasma of carbon target for a delay time of 1 μs and 0.02 μs gate width. The obtained excitation temperature was 26000 ± 3000 K. The carbon ionic multiplet line at ∼3920 Å was identified as candidate for electron-density measurements. Figure 26-a shows, the 3920 Å carbon ionic line with sufficient resolution to measure the full width at half-maximum at 8 different time delays. All the data points were fitted with Lorentzian function to determine the Stark line width. By substituting these values in Eqn. (2.21) and the corresponding value of electron impact parameter W (0.465 Å from Griem [27] at plasma temperature of 26000 K), we obtain the electron density. Figure 26-b gives the time evolution of electron density by setting the gate width of the intensifier at 0.02 μs. The initial electron density at 0.02 μs is approximately 3 1016 cm-3. Afterwards, the density increases over the period of 0.1 μs and reaches a maximum at 0.1 μs (time period of the peak CO2 laser pulse), and then decrease as the time is further increased. At shorter delay times (0.1 μs, the line to continuum ratio is within reasonable limits and the values of electron density shown in figure 26-b should be reliable. Initially the laser-induced plasma expands isothermically within the time of the duration of the laser pulse. After termination of the peak laser pulse (∼0.1 μs) the plasma

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expands adiabatically. During this expansion the thermal energy is converted into kinetic energy and the plasma cools down rapidly. After 4 μs, the electron density is about 1.5 1016 cm-3. For a long time >4 μs, subsequent decreased C+ emission intensities result in poor signal-to-noise ratios, and there exits a limitation in the spectral resolution. The decrease of ne is mainly due to recombination between electrons and ions in the plasma. These processes correspond to the so-called radiative recombination and three-body recombination processes in which a third body may be either a heavy particle or an electron.

2

2 0

C :2s 4s S1/2→2s 3p P3/2 2

+

25000

2

16

4x10

td=3 μs +

2

2

td=1 μs

2 0

td=0.5 μs td=0.1 μs

tw=20 ns

td=0.05 μs

15000

td=0.02 μs td=0

10000

5000

Electron density / cm-3

2

C :2s 4s S1/2→2s 3p P1/2 20000

Relative Intensity / a. u.

td=4 μs

0

16

3x10

16

2x10

16

3917

3918

3919

3920

3921

1x10

3922

-3

10

Wavelength / Å

-2

10

-1

10

0

10

Delay time / μs +

Figure 26 (a). Stark-broadened profiles of the C line at 3920 Å at different delay times for a fixed gate width time of 0.02 μs. (b) Temporal evolution of electron density at different delay times from plasma ignition. In order to further identify properties of the ablation plasma plumes originated from graphite targets, we have estimated the vibrational temperatures of C2 molecule as function of delay time. The emission intensities of the C2 d-a Swan Δv=+1 band sequence were used to estimate these vibrational temperatures Tvib. The estimated vibrational temperatures were Tvib=8000±500, 8300±600, 7500±600, 4500±900 K at 3, 5, 10 and 15 μs after plasma ignition, respectively compatible with a cooling stage. Optical emission accompanying TEA-CO2 nanosecond laser ablation of carbon is very long lived (∼40 μs) relative to the average radiative lifetimes of the excited levels that give rise to the observed emission lines. At distances close to the target surface (1 for ferromagnetic, electric field strength E, required for TCTD glowing, can be reached in a low-frequency discharge. In fact, the TCTD is the most low-frequent of all electrodeless discharges [3, 4]. The minimal value of current frequency, sufficient for induction discharge glowing, is determined by the electric field strength in discharge E. The main criteria for maintenance of TCTD glowing were considered firstly in the paper of Eckert [3], with regard to a particular quasistationary discharge in argon. General relationships can be also used for analysis of criteria of TCTD generation in other plasma-forming media.

1.2. Optimization of the Transformer Coupled Toroidal Discharge The correct choice of ferromagnetic material allows minimization of losses in the magnetic core and significant reduction of core sizes for the transformer gas-discharge device. According to expression 7, the required voltage of discharge glow U can be achieved by an increase in the core cross-section S or in current frequency f or in induction Bm. It is obvious that a significant increase in the core cross-section is unacceptable from the practical point of view. Thus, to achieve the required voltage, it is desirable to increase maximally the value of f·Bm, what can be only done with application of special kinds of magnetic materials. Two groups of materials with minimal volumetric losses at high frequency and induction of the magnetic field can be distinguished: amorphous soft magnetic alloys and special kinds of ferrites. Flat-strip amorphous soft magnetic alloys are characterized by high permeance, low coercitivity (Hc below 1 A/м), high specific electric resistance (ρ ~ 108 Ohm·cm), low losses for hysteresis and eddy currents (3÷5 times less than the best crystalline alloys). Since they are the semiconductors, ferrites have high specific volumetric electric resistance, exceeding the resistance of steels and alloys by factor of 50 and more. This makes it possible to use ferrites for high frequencies without a significant rise of eddy-current losses. Among disadvantages of ferrites there is relatively strong dependence of their magnetic properties on temperature. In contrast to ferrites, amorphous alloys can operate efficiently up to ~ 250–300 ºC. In case of low operation temperatures of the magnetic core, which allow application of both ferrites and amorphous alloys, the choice of the magnetic material will be determined from the condition of maximal Bm at the required current frequency and given threshold level of specific heat losses Pv (W/cm3).

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119

The value of losses in the magnetic core is composed of separate components: eddycurrent losses, hysteresis, and magnetic viscosity (magnetic aftereffect). On the ground of statistical processing of abundant experimental data, the reference literature on electric engineering provides the following dependence of specific losses on frequency and induction of the magnetic field: β α PV ⎛ f ⎞ ⎛ Bm ⎞ ⎟ =⎜ ⎟ ⎜ (9) P* ⎜⎝ f* ⎟⎠ ⎜⎝ Bm* ⎟⎠ where f* = 1 kHz, Bm* = 1 T are the basic values of frequency and induction; P*, α, β are coefficients, obtained by processing of experimental dependences Pv(f, Bm). The typical dependence of specific heat losses PV on the amplitude value of magnetic induction Bm at different current frequencies is shown in Fig. 2 for the strip magnetic cores of amorphous alloy and ferrites of the Philips 3C96 grade. According to the figure, with a rise of Bm heat losses in ferrites increase faster than heat losses in amorphous steel because of lower saturation induction. However, at fixed induction of magnetic field, with a rise of frequency heat losses in amorphous alloys increase faster than in ferrites (Fig. 2). The above differences between ferrites and amorphous alloys are visually demonstrated in Fig. 3. Dependence of f·Bm on frequency f is shown there for the fixed level of specific heat losses in the magnetic core (0.5 W/cm3), for amorphous alloy and different kinds of ferrites.

Specific loss Pv, W/cm

3

Philips 3C96, 25 kHz Philips 3C96, 200 kHz Steel 5BD,25 kHz Steel 5BD,250 kHz 1

0,1

0,01 0,01

0,1

Bm, T Figure 2. Dependence of specific heat losses in the core PV on magnetic induction Bm.

1

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I.M. Ulanov and M.V. Isupov

4

4x10

4

f·Bm, Hz·T

5x10

3x10

4

2x10

4

5BD 3С96 3С94 3С90 3F3 3F4 3F35

4

1x10

0 10

100

1000

f, kHz Figure 3. Dependence of f·Bm on current frequency f at the fixed level of specific heat losses PV =0.5 W/cm3.

According to Fig. 3, there is the optimal value of current frequency, corresponding to the maximal value of f·Bm at a constant level of heat losses, and the maximum achievable value of f·Bm depends essentially on the quality of magnetic material. In the range of low current frequencies (below 20÷30 kHz) the magnetic cores on the basis of amorphous alloys have a definite advantage over the best grades of ferrites because of a weak dependence of specific heat losses on magnetic field induction. At current frequencies above 100 kHz application of ferrites seems to be the most optimal.

1.3. Matching the Power Source and the Transformer Coupled Toroidal Discharge The transformer plasmatron is similar to inductive thermoelectric devices (induction furnaces). Hence, to match the power source with the transformer plasmatron, we can use the known calculation schemes, applied for devices of induction heating. In these devices the oscillating circuit, formed by an inductor and additional capacitor bank, serves as the load. The equivalent scheme of the power source and transformer plasmatron is shown in Fig. 4a. Here Rg and Xg are active resistance and reactance of the generator, Rtr and Xtr are active resistance and reactance of the transformer, XC1 and XC2 are capacitances for matching. Under the steady state it is convenient to present the oscillating circuit, formed by the transformer and matching vessels, as a parallel equivalent circuit, including equivalent active resistance Req and reactance Xeq (Fig. 4b). At this, Req and Xeq are determined by the following formulas [6]: Rtr ⋅ BC21 Req = (B12 + X tr ⋅ BC1 ⋅ BC 2 )2 + (Rtr ⋅ BC1 ⋅ BC 2 )2

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( B12 + X tr ⋅ BC1 ⋅ BC 2 ) ⋅ ( X tr ⋅ BC1 − 1) + (Rtr ⋅ BC1 ⋅ BC 2 )2 X eq = (B12 + X tr ⋅ BC1 ⋅ BC 2 )2 + (Rtr ⋅ BC1 ⋅ BC 2 )2 B12 = BC1 − BC 2 X eq tgϕ = Req Z eq =

(10)

Req 1 + (tgϕ )2

where BC1, BC2 are capacitive susceptances; ϕ is phase angle, Zeq is total resistance of the circuit. The value of Zeq should correspond to the inner resistance of generator, and tgϕ of the load should fit the ratings of generator to provide the transfer of maximal active power to the transformer plasmatron.

a) ~ Ig

Rg

b)

X g X C1 X tr R tr

X C2

X eq

R eq

Figure 4. Equivalent schemes:a) Transformer plasmatron; b) Parallel equivalent circuit.

Thus, calculations are reduced to determination of Req and Xeq and, hence, XC1 and XC2 for every specific operating condition (idle running – before discharge ignition; operating condition – for specific gas and pressure). Besides, it is necessary to determine Rtr, and Xtr (active resistance and inductance of the transformer plasmatron). The equivalent circuit of the plasmatron, required for determination of Rtr and Xtr, is the equivalent circuit of the conventional transformer with active-inductive loading. This circuit is widely spread and described in electric engineering. In conclusion it should be noted once more: various electrodeless gas-discharge devices of the high and low pressure can be developed on the basis of transformer coupled toroidal discharges for efficient plasma generation with a high density of charged particles of any chemical composition. Therefore, the transformer coupled toroidal discharges can be used successfully by many practical applications, which require the use of low-temperature plasma.

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2. TRANSFORMER PLASMATRONS 2.1. Experimental Setup Initially experiments on generation and investigation of transformer coupled toroidal discharges in inert and molecular gases were carried out at setup No. 1, shown in Fig. 5a. The picture of this setup is shown in Fig. 5b.

Figure 5a. Experimental setup No. 1. 1 – primary winding; 2 – sections of magnetic core; 3 – discharge chamber; 4 – heat exchanger; 5 –main gas feed; 6 – secondary gas feed; 7 – probe No.1; 8 – probe No.2; 9 – probe No.3; 10 – spectrophotometer; 11 – mass-spectrometer.

Figure 5b. Transformer plasmatron for current frequency of 10 kHz.

The total power of setup No.1 was 180 kW. The magnetic core consisted of 8 separate sections made of cold-rolled electric sheet steel 3425 of the 80-µm thickness. The outer diameter of each section was 420 mm, the inner diameter was 160 mm, and the height was 70 mm. Each section had the own system of primary coils. The number of primary coils is 4. All primary coils were connected either in-parallel or in-series to the machine generator (10 kHz) depending on the experimental conditions. The discharge chamber was of the closed

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“toroidal” shape. The perimeter of discharge chamber along the mean line was L=1.8 m. The chamber consisted of the metal, water-cooled, mutually insulated sections with the inner diameter Dint=(80÷100) mm and length (20÷60) mm. The plasma gas was fed to the discharge chamber through two tangential holes with the diameter of 6 mm and the swirl angle of 20°. The gas flow was controlled by rotameters. Experiments on thermal synthesis of ozone from oxygen and natural gas conversion in the presence of СО2 were carried out in the mixture with argon. For these purposes two experimental methods were used. By the first method a mixture with the known percentage of the studied gas in argon was fed into the main feed chamber. By the second method the feed of argon and required reagents was separated. Oxygen, natural gas and carbon dioxide were fed through additional vortex chamber 6, located at distance L=60 cm from the point of the main argon supply. This allowed operation in mixtures of the studied gas and argon within a small region of the discharge chamber at relatively high concentration of products in discharge. Total induced discharge voltage Udisch was measured by an additional insulated coil of wire, enveloping the magnetic core. The mean mass temperature of gas at discharge chamber outlet was measured by calorimetric study of heat exchanger 4. Distribution of the mean mass temperature of gas in the discharge chamber was measured by calorimetric (enthalpy) probe [24], whose scheme is shown in Fig. 6. The gas temperature at the outlet as well as the water temperature at the probe inlet and outlet was determined by a chromel-coppel thermocouple. The gas flow through the probe was determined by accumulation in a diaphragm evacuated volume. During the experiment the volume was evacuated constantly, and the pressure drop on the diaphragm was supersonic always. When measuring the gas flow, buffer volume evacuation was stopped, and the flow rate was determined by the time of pressure alteration in this volume. The time range was chosen to obtain a constant supersonic drop on the diaphragm, corresponding to a constant flow rate. A relative error of mean mass temperature measurements by this method depends on the ratio of the inlet velocity of the sampling gas to the velocity of the incident flow and makes up from 3% to 17%.

Figure 6. The scheme of calorimetric probe with the system of sampling and analysis

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I.M. Ulanov and M.V. Isupov

Radial distributions of mean mass temperature of gas in the discharge chamber were measured for two distances from the point of plasma gas supply: l=60 mm (probe No.1); and l=800 mm (probe No.2). A gas sample was analyzed by spectrophotometer CF–26 and mass-spectrometer Quadrovak. Preliminary, the mass-spectrometer and spectrophotometer were calibrated by the gas mixtures with given concentrations of substances. This method of experiments allowed determination of radial distributions of product concentrations in the discharge chamber together with measurement of temperature distributions. Both tubular probes and probes with rectangular cross-section were used in the experiments. The typical rate of high-temperature gas cooling was estimated by the formulas, suggested in [25]:

(

w ⋅ T f − Tw dT = 0.107 ⋅ dt d ⋅ Re0.2

)

(11)

(where w is average gas velocity, Tf, Tw are mean mass temperatures of the flow and probe wall, d is efficient diameter of the gas-sampling channel); for initial temperature Tw 3000÷6000 K this rate was about 106÷107 К/s for the probe with d = 1.5 mm. Samples for analysis of product concentration at plasmatron gas outlet were taken by probe No.3. Probe No.З was located near the heat exchanger (Fig. 5a). The heat exchanger consisted of the water-cooled tubes with diameters of 8 and 15 cm and lengths of 1 and 1.5 m, correspondingly. According to the estimate by formula (11), the maximal average rate of gas cooling in this heat exchanger is dT/dt≈103÷104 К/s. A disadvantage of the transformer plasmatron (рис. 5b) was the fact that magnetic cores were made of ordinary transformer steel 3425 and the machine generator with current frequency of 10 kHz was used as the power source. Therefore, the magnetic cores of the transformer plasmatron were heavy (~300 kg), and the plasmatron itself was too bulky. Now it is possible to make more compact transformer plasmatrons because of development of new high-quality ferrites for power electronics and design of compact and cheap power sources with current frequency of ~100÷400 kHz [26]. The further works were aimed at reduction of transformer plasmatron sizes with preservation of high productivity. The works performed allowed development of a compact transformer plasmatron with the power of 20 kW and current frequency of 100 kHz (Fig. 7a, 7b). The magnetic cores of plasmatron 1 were assembled of EPCOS ferrite bars of N 87 grade (the analog of ferrite 3F3, Fig. 3). The total cross-section of magnetic core was 100 cm2, and the mass was ~ 20 kg. Water-cooled gas-discharge chamber 2 was made of 12 sections, mutually insulated by silastic gaskets 4. The inner diameter of gas discharge chamber was D = 45 mm and the gas discharge perimeter along the mean line was L = 1 m. To stabilize a plasma discharge, the transformer plasmatron was mounted vertically with argon input via vortex chamber 3. Plasma went out from the opposite side to the chamber of chemical reactor 6. To perform various plasma-chemical reactions, the inlet for chemical reagents 5 was made in the lower part of the discharge chamber, and branch pipes were provided below for the input of additional chemical reagents and plasma observations through a window. The

Induction Transformer Coupled Discharges: Investigation and Application

125

chamber of chemical reactor can be used both for accumulation of reaction products and allocation of items for plasma processing.

Figure 7a. The scheme of transformer plasmatron with ferrite cores.1 – ferrite cores; 2 – water-cooled chamber; 3 – vortex tangential input of argon; 4 – silastic gaskets; 5 – reagent input; 6 – outlet to chemical reactor.

Figure 7b. Transformer plasmatron with ferrite cores of the 20-kW power.

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To ignite a discharge, air was evacuated from the plasmatron and chamber to the pressure of about 10–20 Pa. After powering-on the system, argon was fed into the discharge chamber, and discharge was ignited. When the atmospheric pressure was reached, a damper was open to let argon into the atmosphere. The voltage of discharge glow was measured by an additional coil, enveloping magnetic cores 1; the discharge current was measured by the current transformer. The thermophysical characteristics of discharge were determined by calorimetric measurement of water-cooled chamber 2. The main achievement of the chapter authors should be marked out specially: for the first time the stable transformer coupled toroidal discharge of atmospheric pressure was obtained in argon, air, and argon mixtures with molecular gases (oxygen, hydrogen, carbon dioxide, and natural gas).

2.2. Electric-Physical and Thermal-Physical Characteristics of Transformer Plasmatrons The electric-physical and thermal-physical characteristics of transformer coupled toroidal discharges were studied in argon, air, and mixtures of argon with natural gas and carbon dioxide at atmospheric and reduced pressures. Experiments were carried out at setup No.1. The effect of “glow” conditions on the electric field strength of a discharge in argon was studied within the range of pressures of 10÷105 Pa; currents of 90÷450 А; and argon flow rate of 1÷30 g/s. The thermal-physical and electric-physical characteristics of the transformer coupled toroidal discharge were also studied at atmospheric pressure in the mixture of argon and hydrogen in the transformer plasmatron with ferrite cores (Fig. 7а). The effect of argon flow rate on the electric field strength in a discharge at atmospheric pressure is shown in Fig. 8.

Electric field strength, V/cm

1,5 1,4 1,3 1,2 1,1 1,0 0,9 0,8

0

5

10 15 20 Ar flow rate, g/s.

25

Figure 8. Electric field strength vs. argon flow rate.I=200 А, p=1 atm.

30

Induction Transformer Coupled Discharges: Investigation and Application

127

Electric field strength, V/cm

1,2

1,1

1,0

0,9

0,8 50

100 150 200 250 300 350 400 450 TCTD current, A

Figure 9. Current-voltage characteristic of transformer coupled toroidal discharge in argon. Argon flow rate is 4 g/s.

The initial incident region of the curve corresponds to unsteady operation, when gasvortex arc stabilization is insignificant because of a low gas flow rate. Therefore, a discharge is spatially unstable (because of development of current-convective instability), what increases heat transfer between the arc and discharge chamber wall, and, hence, this leads to a rise of applied power required for stationary discharge maintenance. At a given current this increases the electric field strength. The second constant region of the curve corresponds to stable arc “glow”. A following increase in the electric field strength relates to an increase in a degree of flow turbulence and increase in heat losses to the plasmatron wall as well as to a rise of energy, “carried out” by a gas flow. In general, this increases the power required for discharge maintenance. The current-voltage characteristic of a discharge in argon was studied for TCTD currents of 90÷450 А. The typical current-voltage characteristic of the TCTD is shown in Fig. 9 for argon flow rate G=4 g/s. According to the diagram, at the initial stage (at low currents) the current-voltage characteristic is descending. Then, after a small region of constant Е(I) there is an ascending part of the curve. This dependence E(I) is also characteristic for the DC arc discharges. Dependence of the electric field strength on the argon pressure is shown in Fig. 10. The diagram represents the experimental results both with and without vortex gas supply. According to this diagram, at low pressure (diffusion discharge) the electric field strength decreases with a rise of pressure. This is caused by the fact that the free path of electrons decreases with a rise of pressure, and this provides less electron losses to the wall of discharge chamber; on the other hand, electron concentration increases. This reduces the electric field strength in a discharge at a given current density. With the following rise of pressure the discharge contraction occurs, and current-convective instability increases. A discharge takes a wavy shape, the arc length increase, and heat transfer between the arc and the wall becomes more intensive. This increases the electric field strength, required for discharge maintenance. With the following rise of pressure considerable voltage pulsations occur in a discharge and the instantaneous voltage can exceed the maximal voltage, induced by the magnetic core.

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If the vortex supply of plasma gas is used, current-convective instability of discharge is expressed weakly. This allows a pressure increase in the discharge chamber of up to the atmospheric one and higher without significant fluctuations of the discharge voltage. 1,2

Electric field, V/cm

1,0 0,8 0,6 0,4 0,2 0,0

2

3

10

4

5

10 10 Argon pressure, Pa

10

Figure 10. Electric field strength vs. argon pressure. ■ – Without vortex supply of argon (I=100 A). + – With vortex supply of argon (I=100 A).G=3÷5 l/s 2

8

Electric field, V/cm

7 6 5 4

1

3 2 0

2

4

6 8 10 12 Air flow rate, g/s.

14

16

18

Figure 11. Average electric field strength E vs. air flow rate. Discharge current I=125 А. 1 – E at initial arc region in electric-arc plasmatron; 2 – E at developed turbulent region in electric-arc plasmatron.

Dependence of the electric field strength in air flow rate (Fig. 11) has been studied. The behavior of E=f(G) function in air is similar to the experiments with argon. It is obvious that the electric field strength in air is 4÷6 times higher than in argon. In the same diagram empirical dependences of electric field strength on air flow rate are shown at the initial region (curve No.1) and at the developed turbulent region (curve No. 2); they were derived in [27] at processing of data on the electric field strength in electric-arc plasmatrons.

Induction Transformer Coupled Discharges: Investigation and Application

129

Since there are no electrodes we could work with aggressive gas mixtures both at a reduced and atmospheric pressures. There was no any destruction of discharge chamber walls, and plasma was not contaminated by admixtures. Dependence of electric field strength in [Аг + O2] mixture on oxygen content in this mixture is shown in Fig. 12. According to the diagram, even at low oxygen concentrations in the mixture the electric field strength increases significantly. For instance, at oxygen content in argon of ~ 1 % the electric field strength increases almost twice. Dependences of electric field strength in [Аг + СО2], [Аr + СН4] and [Ar + H2O] mixtures on their percentage in argon are shown in Fig. 13. It is clear that for these gases the electric field strength is relatively high, therefore, a more powerful and efficient setup with a perfect magnetic core and power source of increased frequency (~100 kHz) is required for the work with such pure gases. 12

Electric field, V/cm

10 8 6 4 2 0

10

20 30 40 O2 concentration, vol. %

50

Electric field, V/cm

Figure 12. Electric field strength in [Ar + O2] mixture vs. oxygen content. Discharge current I=125 А, argon flow rate G=4 g/s. 12 11 10 9 8 7 6 5 4 3 2 1 0

H 2O

CO2

CH4

0

10

20

30

40

50

60

Concentration, vol. %

Figure 13. Electric field strength in [Ar + H2O, Ar + CO2, Ar + CH4] mixtures vs. substance concentration in argon. I=125 А, argon flow rate G=4 g/s

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Dependence of argon plasma temperature at the atmospheric pressure on argon flow rate is shown in Fig. 14 for the distance from the axis of discharge chamber r/R=0.3 and discharge current I=125 А. According to the diagram, with a rise of argon flow rate the hightemperature zone is localized in the center of discharge chamber, i.e., with a rise of the flow rate the mean mass temperature of gas decreases within the given radius at the same discharge current. Temperature distribution in the discharge chamber is shown in Fig. 15 for two distances from the point of gas supply and different air flow rates. According to the diagrams, temperature distributions are subjected to two main factors: the flow rate of plasma gas and the distance from the point of gas supply. A rise of the gas flow localizes the hightemperature zone in the center of discharge chamber, and the temperature gradient becomes higher with a rise of the flow rate. With an increase in the distance from the point of gas supply the temperature profile becomes smoother. 5000 4500

Temperature, K

4000 3500 3000 2500 2000 1500 1000 500 1,0

1,5

2,0

2,5

3,0

3,5

4,0

Ar flow rate, g/s.

Figure 14. Temperature of argon plasma at atmospheric pressure vs. argon flow rate for r/R=0.3, z/R=1 (probe No.1). Discharge current I=125 A 7000 6000 Temperature, K

5000 4000 3000 2000 1000 0

0

10

20

30

40

50

Distance from discharge axis, mm

Figure 15a. Temperature distributions in the discharge chamber for two distances from the point of air input into the chamber: I=125 A. L =60 mm (probe No.1).• 3.7 g/s; ■ 6.8 g/s * 12.6 g/s

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6000

Temperature, K

5000 4000 3000 2000 1000 0

5

10 15 20 25 30 35 40 45 50 55 Distance from discharge axis, mm

Figure 15b. Temperature distributions in discharge chamber for two points of air input into the chamber: I=125 A.L =800 mm (probe No.2).• 3.7 g/s; ■ 6.8 g/s * 12.6 g/s

Power, kW

20

Discharge power Plasma Jet power Heat Losses

efficiency, %

40

15

30

10

20

5

10

0 0,0

0,1

0,2 0,3 H2 flow rate, g/s.

0 0,4

Figure 16. Thermal-physical characteristics of transformer plasmatron with ferrite cores. I=65 А, GAr=4 g/s.■ – discharge power;• – power in plasma jet, flowing into plasmachemical reactor;▲ – heat flux to water-cooled wall of plasmatron;♦ – plasmatron efficiency.

Then, the results of experimental investigations have been used for development of a compact transformer plasmatron with ferrite cores (рис. 7а, b) for plasmachemical reactions in a plasma jet [Ar+H2] leaving the plasmatron. Hydrogen was fed to the lower section of the gas-discharge chamber. Dependence of plasmatron efficiency, heat losses and power in the leaving plasma jet on hydrogen flow rate is shown in Fig. 16. According to the diagram, the maximal plasmatron efficiency is ~ 35%, and it can be achieved at hydrogen flow of 0.1 g/s. The following decrease in plasmatron efficiency is explained by a rise of gas flow turbulence and enlargement of heat losses to the plasmatron walls (Fig. 16).

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Dependence of the power of argon-hydrogen plasma jet on hydrogen flow rate was determined as the difference between discharge power and heat losses. According to the diagram, the maximal power was obtained at hydrogen flow rate of about 0.1 g/s, with the following increase in the flow rate the jet power decreased slightly. Analysis of thermal-physical and electric-physical characteristics of the TCTD allows us to make a conclusion that characteristics of the transformer coupled toroidal discharge are similar to characteristics of a positive DC arc column. It is shown that without vortex stabilization of a discharge current-convective discharge instability starts developing from the pressures in discharge chamber of 104 Pa, what leads to significant voltage fluctuations, providing TCTD “extinction”. If there is the vortex gas flow in the discharge chamber, the described instabilities do not develop, what allows a stable TCTD at the pressures above the atmospheric one.

2.3. Thermal Production of Ozone in Plasma of Transformer Coupled

Toroidal Discharge By now the most common plasma chemical method of ozone production is its synthesis in a barrier discharge. Ozone is produced directly in the zone of a discharge in one stage. Another plasmachemical method of ozone production is the thermal method. In this case ozone is produced in two stages. The first stage is oxygen “heating” up to the temperatures of dissociation. The second stage is the process of fast cooling of dissociated oxygen. In this process ozone is synthesized at the stage of non-equilibrium cooling of gas, consisting of oxygen atoms, molecules and radicals. Let’s consider the main processes occurring at thermal production of ozone. At the first high-temperature stage ozone concentration under the conditions of thermodynamic equilibrium is negligibly small, and ozone production by the considered method is possible only at the stage of non-equilibrium gas cooling, when ozone is formed by recombination of atomic and molecular oxygen. Let’s estimate the typical rate of cooling of dissociated oxygen (at the temperatures of 3500÷4500 К), when atomic oxygen turns mainly into ozone, but not into molecular oxygen: 1. Transition of O–atoms into molecular oxygen and ozone at cooling of dissociated gas occurs by the following main reactions: (R1) O+O2+M Æ K1 O3 + M (R2) O+O3 Æ K2 O2 + O2

(12)

(R3) O+O+M Æ K3 O2 + M 2. A change in the density of atoms, radicals and molecular oxygen in the considered processes equals:

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d [O ] = − K1 ⋅ [O ] ⋅ [O2 ] ⋅ [M ] − K 2 ⋅ [O ] ⋅ [O3 ] − K 3 ⋅ [O ]2 ⋅ [M ] dt

(13)

d [O3 ] = K1 ⋅ [O ] ⋅ [O2 ] ⋅ [M ] − K 2 ⋅ [O ] ⋅ [O3 ] dt

(14)

d [O2 ] = − K1 ⋅ [O ] ⋅ [O2 ] ⋅ [M ] + K 2 ⋅ [O ] ⋅ [O3 ] + K 3 ⋅ [O ]2 ⋅ [M ] dt

(15)

Thus,

d ([O ] + [O3 ]) = −2 K 2 ⋅ [O ] ⋅ [O3 ] − K 3 ⋅ [O ]2 ⋅ [M ] dt

(16)

3. A relative change in concentration of oxygen atoms and radicals during the processes of cooling equals:

1 d ([O ] + [O3 ]) K 2 ⋅ [O ] ⋅ [O3 ] K 3 ⋅ [O ]2 ⋅ [M ] 2 dt = − dt − ∫ ([O ] + [O ]) ∫ ([O ] + [O ]) ∫ ([O ] + [O ]) dt dt 3 3 3

(17)

The expression in the left part is a relative portion of atomic oxygen, converted into molecular oxygen at cooling [28]. Let’s determine the condition, when it is assumed that concentration of molecular oxygen at quenching is not changed, i.e., this is the condition, when almost all atomic oxygen turns to ozone. With this assumption we can consider that the left part of equation (17) is a small value. Considering the rate of gas mixture cooling constant (dT/dt = const), we obtain the following condition:

⎡ K 3 ⋅ [O ]2 ⋅ [M ] ⎤ dT K 2 ⋅ [O ] ⋅ [O3 ] dT ⎥ dT − ∫ >> ⎢− 2∫ ([O] + [O3 ]) ([O] + [O3 ]) ⎦⎥ dt ⎢⎣

(18)

Integrands (18) include equilibrium values of densities, determined by relationships:

[O] + [O3 ] ≈ C [O] = K (T ) [O ] [O ] [M ] 3

(19)

where С[O] is concentration of oxygen atoms at the initial temperature, K(T) is the constant of equilibrium between atomic oxygen and ozone. Integrals converge within the temperature area, where atomic oxygen turns into ozone. The sought temperature area is determined by the following condition: K(T) ~ 1, which is satisfied at T ~ 800 K. Integrals should be taken at the temperatures of 3500÷4500 K, when concentration of atomic oxygen is high. After substitution of values for T=4500 K, we obtain dT/dt>>108 K/s. It should be noted that this condition determines ozone formation in assumption of almost all transition of atomic oxygen into ozone, but not into molecular oxygen. In case of partial transition of О–atoms into ozone we can expect that formation of not-zero ozone concentration in the process of dissociated oxygen cooling is possible at dT/dt ~ 107÷108 K/s.

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Quenching with the given rates is easy to organize by the recuperative methods because the process of gas cooling in a heat exchanger is well studied, and this allows us to study experimentally the effect of the rate of “hot” oxygen cooling on kinetics of the considered reaction and final output of the product. Experiments on investigation of thermal synthesis of ozone from the mixture of argon and oxygen were carried out at setup No. 1. The power of this setup did not allowed operation with pure oxygen; therefore, the experiments were carried out in the mixture of argon and oxygen. Two methods of experiment implementation were used. In the first case, the mixture with given concentration of oxygen was fed into the discharge chamber through the main section of gas supply. In the second case argon was fed into the main section of gas supply, and oxygen was fed into the secondary section (see Fig. 6). All experiments were carried out for the discharge current I = 125A. To study experimentally the effect of dissociated oxygen quenching on ozone production, the water-cooled quenching probes of the slot type were made. These probes had the rectangular cross-sections of the gas sampling channel with the sizes of 0.2х10 and 0.5х10 mm. The geometrical scheme of this probe is shown in Fig. 17. The probes were located at the distance of 100 mm from the heat exchanger (Probe No. 2 – Fig. 6). The inlet sampling slot of the probe was at distance r/R=0.5. Visually this position of the probe corresponded to the boundary of the “glowing” conducting channel. Thus, it can be assumed that the initial temperature of gas was not lower than 4000 К (in these experiments the initial temperature of a sample was not measured).

Figure 17. Quenching probe of the slot type.

The probes were located at the distance of 100 mm from the heat exchanger (Probe No. 2 – Fig. 6). The inlet sampling slot of the probe was at distance r/R=0.5. Visually this position of the probe corresponded to the boundary of the “glowing” conducting channel. Thus, it can be assumed that the initial temperature of gas was not lower than 4000 К (in these experiments the initial temperature of a sample was not measured). Experimental results in Fig. 18 are shown for two probes, providing different rates of high-temperature gas quenching. In the diagram there are the values of volumetric ozone concentrations, which can be reached at cooling of oxygen-argon plasma in probes, depending on oxygen concentration in argon.

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7

probe 0.2x10 mm, dT/dt~2*10 K/s. 7 probe 0.5x10 mm, dT/dt~10 K/s)

0,55 0,50 0,45 O3, Vol. %

0,40 0,35 0,30 0,25 0,20 0,15 2

4

6

8

10

12

14

O2, vol. %

Figure 18. Dependence of ozone concentration on oxygen concentration in initial mixture [Ar + O2].

According to the diagram, ozone concentration increases with a rise of gas cooling rate and with an increase in oxygen concentration in the initial mixture. At that it can be seen that ozone concentration depends non-linearly on oxygen concentration. In other words, initial concentration of atomic oxygen influences directly the kinetic processes at quenching. According to investigation of thermal synthesis of ozone in the transformer coupled toroidal discharge with the use of recuperation quenching devices, at cooling rates of ~107 K/s, from 5 to 10% of oxygen turn into ozone at oxygen content in mixture [Ar+O2] from 15 to 3%, respectively.

2.4. Synthesis of Nitrogen Monoxide in Plasma of the Transformer Coupled Toroidal Discharge One of the most examined gas-phase plasmachemical processes is synthesis of nitrogen monoxide from air. There are many publications dealt with kinetics and thermodynamics of nitrogen oxide formation in low-temperature plasma. The first detailed investigation of this plasmachemical process is the research of Ya.B. Zeldovich, P.Ya. Sadovnikov, and D.A. Frank-Kamenetsky [29], where it is shown that the bimolecular mechanism of nitrogen oxide formation and decay, used before this research, does not explain the measured times of reaction. The cited paper suggests the chain mechanism, which disposes the contradiction. This mechanism includes the following elementary reactions: 1) 2) 3) 4) 5)

O2 + M ÆK1 O + O + M…O + O + M ÆK1’ O2 + M O + N2 ÆK2 NO + N……..NO + N ÆK2’ O + N2 N + O2 ÆK3 NO + O……..NO + O ÆK3’ N + O2 N2 + M ÆK4 N + N + M….N + N + M ÆK4’ N2 + M NO + M ÆK5 N + O + M…N + O + M ÆK5’ NO + M

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In assumption of atomic oxygen stationarity (concentration of atomic oxygen is determined by equilibrium of reaction (1)), Zeldovich [29] has derived the following expression for the total rate of nitrogen monoxide formation:

⎛ 86000 ⎞ exp⎜ − ⎟ d ( NO ) RT ⎠ ⎝ = 1.5 ⋅ 1013 ⋅ ⋅ [NO ]2 − ( NO )2 mole/cm3/s dt (O2 )

{

}

(20)

where [NO] is equilibrium concentration at estimated temperature. On this basis the optimal rate of air quenching was determined in [30] within the temperature range of 3300÷1800 K; at this rate total decay of nitrogen monoxide equals 5% of the initial equilibrium value:

{

}

2 2 dT ⎛ 86000 ⎞ [NO ] − (NO ) ⋅ (T1 − T2 ) = 1.5 ⋅ 1013 ⋅ exp⎜ − ⋅ ⎟ dt RT ⎠ (O2 ) ⋅ 0.05 ⋅ (NO )1 ⎝

(21)

where T1 – initial temperature, T2 – final temperature, (NO)1 – initial concentration of NO. According to this expression, to get the maximal output of NO, it is necessary first to “set” the gas temperature, corresponding to the maximal equilibrium content of the product (T ~ 3400 K), then quenching should be carried out with the rate of ~5·106 К/s, with this rate reduction to 104 К/s (at the final temperature of ~ 1800 К). It should be noted that the described process of nitrogen oxide formation by cooling of quasi-equilibrium air within the temperature range of 1000÷4000 K is proved well by the experimental data [30]. If air is cooled from the higher temperatures (> 5000 K) there is divergence between experimental and calculation data: at air cooling from the temperatures above 5000 К, super-equilibrium concentration of nitrogen monoxide is formed (~6÷7 %) [31]. Together with a practical interest to NO production, abundance of experimental and theoretical works in this field also seemed very attractive. This allowed us to use this process as the ‘model’ one for understanding of the features of the transformer coupled toroidal discharge with regard to plasmachemical technologies. Experiments on investigation of NO synthesis from air were carried out at setup No. 1. The plasma-forming gas (air) was fed into the main vortex chamber. Temperature and concentration distributions over the discharge chamber were measured in these experiments at different distances from the point of air input into the chamber. The water-cooled tubular probes-samplers were used for this purpose (Fig. 6). Radial distributions of product temperature and concentration were studied in two different zones of the discharge chamber (Fig. 5a): Concentration of NO after the heat exchanger was also measured in these experiments (probe No.3). The mean mass temperature of gas at the discharge chamber outlet was measured via heat exchanger calorimetry. Distributions of NO concentration over the radius of discharge chamber, obtained by probes No.1 and No.2 are shown in Fig. 19(a,b) (temperature distributions under the same conditions are shown in Fig. 15(a,b)). It can be seen that near the point of air input (probe No.1) distribution of nitrogen monoxide concentration is similar to temperature distribution.

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Far from the input point (probe No.2) distribution of nitrogen monoxide concentration does not depend on the gas temperature. It attracts attention that near the wall of discharge chamber, where the level of temperature is relatively low (Т ~ 300÷2000 К) NO concentrations, measured by probes No.1 and No.2, differ significantly. At high temperatures (Т>5000 К), NO concentrations, measured by probes No.1 and No.2 are close to each other. 8 7

NO, vol. %

6 5 4 3 2 1 0

0

10

20

30

40

50

Distance from discharge axis, mm

Figure 19а. Distribution of NO concentration over the chamber of transformer plasmatron, L =60 mm (probe No.1), I=125 A.Air flow rate.• 3.7 g/s; ■ 6.8 g/s * 12.6 g/s

8 7

NO, vol. %

6 5 4 3 2 1 0

0

10 20 30 40 50 Distance from discharge axis, mm

Figure 19b. Distribution of NO concentration over the chamber of transformer plasmatron, L =800 mm (probe No.2). I=125 A.Air flow rate. • 3.7 g/s; ■ 6.8 g/s * 12.6 g/s

Values of NO concentration vs. the temperature of a gas sample are shown in Fig. 20(a,b) by circles and squares for probes No. 1 and 2, respectively. The solid line shows the temperature dependence of equilibrium concentrations of NO. In the same diagram the heavy

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line indicates calculated values of NO concentration, obtained in assumption of thermodynamic equilibrium of gas before quenching. 8 7

NO, vol. %

6 5 4 3 2 1 0

0

1000 2000 3000 4000 5000 6000 7000 Temperature, K

Figure 20a. NO concentration vs. air temperature.L =60 mm (probe No.1), I=125 A. Air flow rate:• 3.7 g/s; ■ 6.8 g/s * 12.6 g/s 8 7

NO, vol. %

6 5 4 3 2 1 0

0

1000

2000

3000

4000

5000

6000

Temperature, K

Figure 20b. NO concentration vs. air temperature.L =800 mm (probe No.2). I=125 A. Air flow rate:• 3.7 g/s; ■ 6.8 g/s * 12.6 g/s The equilibrium curve of NO content in air depending on T.

It can be seen in Fig. 20(a,b) that NO content, measured at low (Т ~ 300÷2000 К) and high temperatures (Т > 4000 К), is significantly higher than the corresponding equilibrium NO content in air. The difference between experimental and calculated concentrations of nitrogen monoxide, obtained at air cooling from the temperatures of above 5000 К, is the known fact. The explanations of this phenomenon were discussed actively in [32, 33]. According to one of these explanations [32], the additional production of NO occurs at quenching of the hightemperature gas (>4000÷5000 К) due to divergence of oscillating and translation temperatures at the initial moment of cooling. This phenomenon is not discussed in the

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current work, but an attempt to explain a high content of NO in the peripheral gas at temperatures below 2000 К is emphasized. Dependence of NO concentrations on the mean mass temperature of gas at the outlet of a transformer plasmatron (probe No. 3) is shown in Fig. 21(a) by dots. The values of NO concentrations, obtained by the authors of [30, 34, 35] vs. the mean mass temperature of gas before the quenching devices are also shown there by the shaded area. It is necessary to note that in experiments of these authors NO was synthesized in two stages: in the first stage the air in plasmatron was heated up to some certain temperature, then high-temperature air was quenched (the cooling rate was ~ 106÷107 К/s). The calculated value of NO, reached at cooling of thermodynamically equilibrium air with experimentally determined initial temperature, is shown by the corresponding curve. 1

7 6

3

NO, vol. %

5 4 3 2 2

1 0

2000

3000 Tenperature, K

4000

Figure 21.a. Concentration of nitrogen monoxide at the heat exchanger outlet (probe No. 3) depending on the mean mass temperature of gas at the heat exchanger inlet.1 – experimental data (probe No. 3).2 – calculated value of NO concentration at the equilibrium state of air before cooling in heat exchanger;3 – the area of experimental data of different authors [30, 34, 35], obtained at the use of equilibrium gas quenching. 7,0

1

6,5 6,0 NO, vol. %

5,5 5,0 2

4,5 4,0 3,5 3,0 2,5

0

2

4

6

8

10

12

14

16

Air flow rate, g/s.

Figure 21.b. Concentration of nitrogen monoxide at the heat exchanger outlet (probe No. 3) depending on the air flow rate. 1 – experimental data (probe No. 3).2 – calculation by the model.

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Dependence of NO concentration on the air flow rate, measured at plasmatron outlet (probe No. 3), is shown in Fig. 21.b by dots. According to the diagram, at low flow rates (1÷5 g/sс) NO concentration increases almost linearly. With the following increase in the air flow, NO concentration depends on the flow rate weakly and tends to ~ 7%. Thus, a high (superequilibrium) content of nitrogen monoxide at the gas outlet from the plasmatron was determined experimentally at synthesis of nitrogen monoxide in the transformer coupled toroidal discharge at vortex arc stabilization without application of the quenching devices, which provide high rates of gas cooling. After measurements of plasma temperature and NO concentration profiles, it was determined that in the low-temperature peripheral zone of a vortex flow, which stabilizes the transformer discharge, the NO content exceeds significantly the thermodynamically equilibrium values. Let’s estimate the typical times of molecular diffusion under the considered conditions and show that the diffusion processes cannot provide significant concentration of NO at the periphery of discharge chamber. We consider a cylindrical chamber with radial temperature distribution, determined experimentally. The typical time of diffusion can be estimated as:

τ diff =

[r (T1 ) − r (T2 )]2

(22)

D

As initial temperature Т1 we will take the temperature corresponding to the maximal thermodynamic-equilibrium concentration of nitrogen monoxide (Т1 ~ 3500 К), and as final temperature Т2 we will take the temperature, when product stability is provided by a low decomposition rate of NO (Тк ~ 2000 К). It follows from experimental temperature distributions (Fig. 15a) that r(T1)-r(T2) ~ 1 cm. Taking into account that in the considered temperature range (3500÷2000 К) coefficient of diffusion is D ~ 50÷20 cm2/s, we obtain τdiff≈0.02÷0.05 s

(23)

For comparison we should indicate that time τ of nitrogen monoxide decomposition in the considered temperature range under the atmospheric pressure is [35]: T, К τ, s

3500 ~10-6

3000 8·10-5

2300 5·10-3

2000 1

Hence, at diffusion of NO molecules from the high-temperature zone (Т ~ 3500 К with equilibrium NO content of ~ 5%) to the zone with a lower temperature (to 2000 К), in every considered point gas will be in the state close to thermodynamic equilibrium. Within gas layers with the temperature below 2000 К, the time of NO decomposition is comparable or exceeds the typical times of diffusion, and concentration of NO there can correspond to the equilibrium value for Т ~ 2000 К (NO ~ 0.5 %). Therefore, at the chamber periphery, where the temperature is below 2000 К, nitrogen monoxide concentration because of diffusion should be, at its best, about 0.5%. To explain a high content of NO at Т70 ◦C), and the temperature range corresponding to the maximal efficiency of resonance line 253.7 nm becomes significantly wider (70÷120 ◦C). The unique samples of mercury high-intensity discharge lamps of the 3÷100-kW power with efficiency of ~60 lm/W were developed on the basis of investigations of the TCTD in mercury vapors (Fig. 37, 38). On the basis of experimental studies of the TCTD with amalgam filling, the pilot samples of bactericidal induction UV lamps with the power of 50, 100, 200 and 500W and current frequency f = 150 kHz (Fig. 39) were constructed; their emission yield to line 253.7 nm is ~30÷35% of consumed electric power. 1,0 0,8 0,6 150 0,4 0,2 0,0 180 0,2 0,4 0,6 210 0,8 1,0

90 120

60

1 2 3 4 5 6 7

30

0

330

240

300 270

Figure 40. Corner diagram of directivity of the 50Wlamp.1–253.7 nm, 2–312.6/313.2 nm, 3– 365.0/366.3 nm, 4–404.7 nm, 5–435.8 nm, 6–546.1 nm, 7–577.0/9.0 nm. 90

1,0 0,8 0,6 150 0,4 0,2 0,0 180 0,2 0,4 0,6 210 0,8 1,0

120

60

30

0

1 2 3 4 5 6

330

240

300 270

Figure 41. Corner diagram of directivity of the 100W lamp. 1–253.7 nm, 2–312.6/313.2 nm, 3– 365.0/366.3 nm, 4–404.7 nm, 5–435.8 nm, 6–546.1 nm.

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The measured corner diagrams of emission directivity of different spectral lines are shown in Figs. 40 and 41 for developed lamps with the power of 50 and 100 W (in the reduced form, the lamp position is schematically shown in the figure (vertical one), the axis of spectral characteristic measurements passes the centre of the lamp). According to Figs. 40 and 41, the corner diagram of radiation directivity of resonance line 253.7 nm differs maximally from the round one, what is possibly caused both by its intensive absorption in discharge plasma and partial absorption by the chamber walls. Before discussing the experimental results, first of all, it is necessary to emphasize the fact that in contrast to RF induction discharges, the TCTD can be considered as the analogue of an arc discharge with electrodes, combined in one plane [10]. Therefore, it is interesting to apply the standard models of arc discharges for the description of TCTD. However, it should be noted that the most standard models of arc discharges are developed for description of DC discharges in long cylindrical tubes. As a result, the question arises: whether these models are applicable for TCTD description. Nevertheless, it can be assumed that for some cases, the standard models of axisymmetric DC arc discharges will satisfactorily describe the TCTD characteristics. Let us consider the main conditions, when the TCTD can be described by the standard models: (a.) A small curvature radius of the toroidal gas-discharge chamber. Apparently, in this case deviations from cylindrical symmetry in a discharge are minimal, and the discharge itself can be shown as a discharge in a straight cylindrical tube with length L, where L is the perimeter of the gas-discharge chamber over its middle line. (b.) Fulfillment of condition f · τ > 1, where f is the current frequency and τ is the typical time of plasma “damping”. In this case, the parameters of discharge plasma (conductivity, electron temperature, concentration of excited and metastable atoms) do not change during discharge current passing through zero, and the TCTD can be considered and used as the analogue of a DC discharge. (c.) An absence of the skin-effect on the electrical characteristics of a discharge. The analysis of experimental data shown in Figs. 33–35 demonstrates that dependences of the optical characteristics of TCTD on the mercury vapour pressure, discharge current strength and diameter of the gas-discharge tube correspond qualitatively to similar dependences for the arc mercury discharges (excluding the abovementioned effect of the luminous efficiency reduction to a visible triplet with an excitation potential of 7.73 eV with an increase in discharge power). However, for some cases, there are significant quantitative differences between the radiation characteristics of TCTD and arc mercury discharges, which are possibly caused by different “glow” conditions. Thus, even for the pressure of ~ 20 kPa, the light efficiency of TCTD with D = 75mm is ~ 70 lm/W (Fig. 33), what is relatively close to the known limit of light efficiency of the arc mercury discharges with a tube diameter of 20÷30 mm ( ~ 80÷85 lm/W), obtained if the pressure of mercury vapour equals several atmospheres. The authors of the current paper consider the possibility of using the standard “channel” model of axisymmetric DC arc discharges [37], based on the assumption of LTE presence in discharge plasma, for the calculation of the TCTD parameters in mercury vapour. According to this model, electric field strength E in a mercury discharge is determined by expressions

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E=

C1 p 7 / 12 P1 / 2

(26)

C2m7 / 12 P1 / 2

(27)

(P − PT )1 / 3 D1 / 3

Or

E=

(P − PT )1 / 3 D3 / 2

where C1, C2 are constants, PT is the value of specific heat losses of discharge, P is specific discharge power, m is the specific amount of evaporated mercury and D is the tube diameter. Additionally, it is assumed by this model that PT does not depend on the discharge power and diameter of the discharge tube. In this case, minimal E is reached, if the following condition is satisfied: P = 3PT

(28)

The analysis of TCTD voltage–current characteristic (Fig. 28) with criterion (28) provides the following values of specific heat losses: PT = 16 W/cm for p ≈ 10 kPa; 7.9 W/cm for p ≈ 22 kPa and 7.5 W/cm for p ≈ 35 kPa, what coincides with the results of Elenbaas [37] (PT = 9÷10 W/cm), obtained similarly for the arc mercury lamps of high pressure in the following range of discharge parameters: P 15÷60 W/cm, D 12÷38 mm. For the pressures of mercury vapour below 10 kPa, the VCC of TCTD has no the expressed minimum, what proves the fact that formulae (26) and (27) can have high errors for calculation of electrical characteristics of the TCTD. According to formula (26), field strength E for the fixed pressure of mercury vapour depends on the tube diameter as E ~ D−1/3. The analysis of data in Fig. 29 demonstrates that an increase in the tube diameter from 35 to 75 mm really provides the reduction of the field strength by a factor of 1.3, whereas for the TCTD with a tube diameter of 20 mm, the experiment gives an excessive value of the field strength. However, it should be noted that in this experiment the ratio of perimeter and diameter L/D for the toroidal chamber was ~10, whereas, for the lamps with the tube diameter of 35÷75 mm, parameter L/D varied from 15 to 25. It can be assumed that for L/D ~ 10, the condition of axial symmetry is disturbed considerably (visually, the discharge was significantly “pressed” into the inner wall of the toroidal chamber), therefore, the standard models of axisymmetric gas discharges cannot be applied for this situation. As it can be seen from Fig. 30, for the TCTD with the chamber diameter of 35÷75 mm and fixed discharge power P ≈ 40W/cm, product E · D1/3 can be perfectly described by formula (25) with constants, obtained by Elenbaas via the analysis of characteristics of the arc axisymmetric mercury discharges. Therefore, for the pressures of mercury vapor above 10 kPa and ratio L/D > 15, the TCTD in mercury vapour can be approximately considered as the axisymmetric, and the “channel” model of axisymmetric discharges can be used for calculation and analysis of discharge parameters.

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3.2. Transformer Coupled Toroidal Discharge in Neon

E, V/cm

Dependence of electric field strength of the TCTD on neon pressure is shown in Fig. 42. Dependence of electric field strength on discharge current is shown in Fig. 43.

D, mm; I, A 20 ; 1 [39]

2,0 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 10

20 ; 5 [39] 20 ; 10 35 ; 1 35 ; 8 51 ; 1 [40] 51 ; 10 [40] 58 ; 20

100061 ; 10 [39]

100 p Ne, Pa

E, V/cm

Figure 42. TCTD electric field strength vs. neon pressure.[39] – Published data, DC arc discharge.[40] – Published data, TCTD at current frequency of 450 kHz.

1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2

35 mm; 25 kHz 35 mm; 250 kHz 61 mm; [39]

1

I, А

10

Figure 43. TCTD electric field strength vs. discharge current. Neon pressure of 1 torr.

According to analysis of data, shown in Figs. 42, 43, dependences E(p, D, I), observed for the TCTD in neon coincide qualitatively with similar dependences for the positive column of a gas discharge in neon. However, it was determined that the field strength increases with a rise of current frequency (Fig. 43). To analyze the observed increase in the field strength with a rise of current frequency, let’s estimate the influence of skin-effect on electric-physical characteristics of a discharge. To simplify calculations, we will represent the studied discharge as a uniform cylindrical conductor with radius r, with specific electric conductivity σ. In this case efficient depth of skin layer δ is calculated by formula

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δ=

2

(29)

2 μ0ωσ

where μ0 is magnetic constant, σ is conductivity of TCTD plasma. Plasma conductivity, averaged by the discharge cross-section, can be determined from relationship j=σE. Dependence of skin layer thickness for TCTD in neon on discharge current strength is shown in Fig. 44. Conductivity is calculated by the voltage-current characteristic, shown in Fig. 43. According to the figure, the minimal thickness of the skin layer almost twice exceeds the radius of a gas-discharge tube. In this case, the influence of skin-effect on electric-kinetic characteristics of a discharge can be described by approximated formula Rω/R0=1+k4/3 (at k 15, the electrical characteristics of TCTD can be approximately calculated by the standard “channel” model of the DC arc discharges [23]. However, the range of the middle pressures of mercury vapor demonstrates the unknown effect of decreasing emission to the triplet with a potential of 7.73 eV for increasing discharge power. The qualitative hypothesis, explaining this effect, is suggested. Based on the obtained experimental results, we have developed and made the pilot samples of electrodeless lamps: electrodeless mercury high intensity discharge lamps with an luminous efficiency of 60 lm/W, and power of 3÷100 kW; germicide UV induction lamps of a low pressure with the power of 50,100, 200 and 500W and luminous efficiency to the resonant line 253.7 nm at the level of ~30–35% of consumed power, neon induction lamps with the power of 100÷2000 W and luminous efficiency of 20÷30 lm/W.

REFERENCES [1] [2] [3] [4] [5]

Heinrich, F. B.; Shevel’ko, V. P. Introduction to Physics of Highly Charged Ions.CRC Press, 2003. Bell, W.E. Applied Physics Letters. 1965, Vol. 7, 190–191. Eckert, H. U. AIAA Journal. 1971, Vol. 9, 1452–1456. Eckert, H. U. IEEE Transactions on Plasma Science. 1974,Vol. PS–2, 308–309. Goldfarb, V. M.; Donskoy, A.V.; Dresvin, S.V.; Rezvov, V.A. High Temperature. 1979, Vol. 17, 698–702.

166 [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

[27] [28] [29] [30] [31] [32] [33] [34]

I.M. Ulanov and M.V. Isupov Kogan, V. A.; Ulanov, I. M. High Temperature. 1993, Vol. 31, 129–135. Kolmakov, K.N.; Ulanov, I. M.; Predtechensky, M. R.; Prikhodko, V. G. Thermophysics and Aeromechanics. 2000, Vol. 7, 419–427. Shabalin, A. Plasma Sources Sci Technol. 2004, Vol. 13, 588–593. Kulumbaev, E. B.; Lelevkin, V. M. High Temperature. 1997, Vol. 35, 351–356. Kulumbaev, E. B.; Lelevkin, V. M. High Temperature. 1999, Vol. 37, 187–193. Gonzales, J. J.; Shabalin, A. Plasma Sources Sci. Technol. 2003, Vol. 12, 317–323. Reinberg, A. R. Inductively Coupled Discharge for Plasma Etching and Resist Stripping. 1984. US patent 4.431.898. Cox, M. S. Toroidal plasma source for plasma processing. 2002. US patent 6.418.874. Zhang, B. C.; Cross, R. C. J. Vac. Sci. Technol. A. 1998, Vol. 16, 2016–2020. Anderson, J. M. Illuminating Engineering. 1969, Vol. 64, 236–244. Anderson, J. M. Electrodeless Gaseous Electric Discharge Devices Utilizing Ferrite Cores. 1970. US Patent 3.500.118. Anderson, J. M. High Intensity Discharge Lamp Geometries. 1979. US patent 4.180.763. Godyak, V. A. High intensity electrodeless low pressure light source driven by a transformer core arrangement. 1998. US patent 5.834.905. Curry, J. J.; Lister, G. G.; J.E. Lawler. J. Phys. D.: Appl. Phys. 2002. Vol. 35, 2945– 2953. Didenko, A. N.; Ulanov, I. M.; Predtechensky, M. R.; Kolmakov, K. N. Phys.—Dok., 2000. Vol. 45, 155–157. Isupov, M. V.; Ulanov, I. M.; Litvintsev, A.Yu. High Temperature. 2004, Vol. 42, 682– 688. Isupov, M. V.; Ulanov, I. M. High Temperature. 2005. Vol. 43, 169–176. Ulanov, I. M.; Isupov, M. V.; Litvinsev, A. Yu. J. Phys. D.: Appl. Phys. 2007, Vol. 40, 4561–4567. Grey, J.; Jacobs, P. F.; Sherman, M. P. Rev. Sci. Instr. 1962. Vol 33, 738–741. Ambrazyavichus. Heat Transfer at Gas Quenching. Vilnius: Nauka, 1983 (in Russian). Ulanov, I. M.; Litvinsev, A. Yu.; Mischenko, P. A.; Krotov, S. V. Proc. of the Russian (International) Conference “Physics of Low-Temperature Plasma–2007”. Petrozavodsk. 2007, Vol. 1, 240–245. (in Russian). M. F. Zhukov and A.S. Anshakov. Electric-Arc Generators with Inter-Electrode Insertions. Novosibirsk: Nauka, 1981. (in Russian). O.E. Skadchenko. Investigation of Ozone Formation in a Jet of Low-Temperature Plasma. Thesis. Moscow, 1972. (in Russian). Zeldovich, Ya. B.; Sadovnikov, P.Ya.; Frank-Kamenetsky, D. A. Oxidation of Nitrogen at Combustion. Moscow. Izd. AN SSSR, 1947. (in Russian). Polak, L. S. Kinetics and Thermodynamics of Chemical Reactions in Low-Temperature Plasma. Moscow: Nauka, 1965. (in Russian). P.R. Ammann, R.S. Timmins. A. I. Ch. E. Journal. 1966, Vol. 12, 956–963. Zhivotov, V. K.; Rusanov, V. D.; Fridman, A. A. Diagnostics of Non-Equilibrium Chemically Active Plasma. Moscow: Energoatomizdat, 1985. (in Russian). Potapkin, B.V. Chemistry of High Energies. 1983, Vol. 17. 524–530. (in Russian). Polak, L. S. Application of Plasma in Chemical Reactions. Moscow: Nauka, 1970. (in Russian).

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[35] Parkhomenko, V. D.; Soroka, P. I.; Krasnoutsky, Yu. I. Plasmachemical Technology. Vol. 4. Low-Temperature Plasma. Novosibirsk: Nauka, 1991. (in Russian). [36] Klarfeld, B. N. Zh. Tekh. Fiz. 1937, Vol. 7, 1017–1038. (in Russian). [37] Elenbaas, W. The High Pressure Mercury Vapor Discharge. Amsterdam: NorthHolland, 1951. [38] Rokhlin, G. N. Discharge Light Sources. Moscow: Energoatomizdat, 1991. (in Russian). [39] Klarfeld, B. N.; Taraskov, I. M. Technical Physics. 1934. Vol. 4, 504–514. [40] Piejak, R.; Godyak, V.; Alexandrovich, B. J. Appl. Phys. 2001, Vol. 89, 3590–3593.

In: Applied Physics in the 21st Century… Editor: Raymond P. Valencia, pp. 169-194

ISBN: 978-1-60876-074-9 © 2010 Nova Science Publishers, Inc.

Chapter 4

FEATURES ON THE HIGH FREQUENCY DIELECTRIC RESPONSE IN FERROELECTRIC MATERIALS J. D. S. Guerra* Grupo de Ferroelétricos e Materiais Multifuncionais, Instituto de Física, Universidade Federal de Uberlândia, 38400-902 Uberlândia-MG, Brazil.

Single crystal and/or polycrystalline ferroelectric materials show a high frequency dielectric dispersion, which has been attributed as well to a dispersive (relaxation like) as a resonant mechanism. Physical properties such as relaxation and/or resonant motion mechanisms can be investigated by analyzing the complex dielectric permittivity (real, ε’ and imaginary component, ε’’) in a broad spectral frequency range (100 MHz–13 GHz). Especially, for classical (or ‘normal’) and relaxor ferroelectric systems a dielectric response indistinguishable of dispersion or a resonance mechanism has been found in the literature. The occurrence of such common dispersion process in so different kinds of ferroelectric systems has encouraged the development of several mutually excluding models to explain this physical phenomenon. Nevertheless, the reported results are not conclusive enough to clearly distinguish each mechanism. In this work, a detailed study of the dielectric dispersion phenomenon, including the microwave frequencies, carried out in perovskite structure-type ferroelectric systems, for ‘normal’ and/or relaxor compositions, is presented. The dielectric response in “virgin” and poled state have been investigated taking into account the relative direction between the measuring direction and the orientation of the macroscopic polarization. Results revealed that the dielectric response in ferroelectric systems may be described as a general mechanism related to an “over-damped” resonant process rather than a simple relaxation-like dielectric behavior.

1. INTRODUCTION Since the late 1950s decade [1], the investigation of the high frequency dielectric properties of dielectric materials has been one of the most challenging tasks in the field of the

*

Corresponding author: E-mail: [email protected]

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Physics Condensed Matter [1]. Microwave measurements of high dielectric permittivity materials (> 100) will certainly assist in materials selection for high frequencies applications such as high-speed data transmission and dielectric resonators devices [2]. Specifically ferroelectric materials, which have relatively high dielectric permittivity, have led to a rising interest in the gigahertz region and have prompted research for microwave range application due to its excellent ferroelectric and piezoelectric properties [3]. The dielectric dispersion (frequency dependence of the dielectric parameters, such as, real, ε’ and imaginary component, ε’’ of the dielectric permittivity), as shown in the schematic representation of the Figure 1, can provide information on the dynamics of the mechanism of phase transitions and shows the frequency region where the ferroelectrics are useful for practical applications [4, 5]. The parameters εs and ε∞ in Figure 1 are the static (high frequency) and optical (high frequency) dielectric permittivities, respectively.

Figure 1. Representative curves for the high frequency dielectric response, showing the frequency dependence of the real (ε’) and imaginary (ε’’) component of the dielectric permittivity.

The study of the polarization mechanisms related to the observed behavior requires the ability to work over both large frequency and temperature ranges, were coaxial cells and network analyzers are commonly used [6]. Thus, for the study of orientation and relaxation polarization effects, automated measuring equipments are usually applied and commercially available today, using the reflectometric method by coaxial technique [7]. Most of the microwave dielectric studies have been performed in a wide temperature range from room temperature up to 900 K by using a coaxial line and a discrete varying frequency (resonant cavity-RC) and/or continuously varying frequency (CVF) method as the principal techniques [7, 8]. For instance, in the case of incipient ferroelectric materials, like Ca modified SrTiO3 [9, 10], for which a clear interpretation of the dielectric results [11] it is believed is lacking, it is interesting to investigate the dielectric relaxation mechanisms mainly at low temperatures (below room temperature) and high frequencies. However, for high permittivity and high dielectric loss materials, which is the case of ferroelectrics, the dielectric coefficients become difficult to be measured [12]. For temperature-dependent measurements, specifically at low temperature region (T < 300 K), the coaxial line of the high frequency analyzer and the sample holder must be thermally decoupled because of the thermal contraction/expansion effects of the coaxial line-sample

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system. Thus, the dielectric response may result mainly from spurious resonance effects of the system when CVF methods are used, which may often to mask the true dielectric behavior of the sample under test. In this way, the best control of the dielectric measurements may be obtained by adjusting the pressure on the sample. Adjusting the pressure it is possible to guarantee measurement of the true dielectric response of the material under test when decreasing temperature. Within the most commonly used ferroelectric materials, the barium titanate (BaTiO3 BT) system and others perovskite-type structure ferroelectric materials have been distinguished because they presented intrinsic dispersion phenomenon near 1 GHz [3, 13]. This behavior can limit their use specifically in communication systems and electrically controlled devices, such as, phase shifters [2]. In this context, such dielectric dispersions were firstly observed in the so-called ‘normal’ ferroelectrics [14], being characterized later in relaxor ferroelectrics (frequently named as relaxors) [15] and more recently in antiferroelectrics [16] and incipient ferroelectrics [17]. However, it is well known that ‘normal’ ferroelectrics have micro-sized polar regions (domains) with long-range order [18], while relaxors and doped-incipient ferroelectrics have nanometric polar regions (nanodomains) distributed in a non-polar matrix, in which a short-range order prevails [19]. Therefore, the occurrence of such common dispersion process in so different kinds of ferroelectric systems has encouraged the development of several mutually-excluding models to explain this physical phenomenon [15, 20, 21-23], in terms of either a grain or ferroelectric domain resonance [24, 25], as well as the correlation between the ferroelectric polar structures and their respective dynamical response [26]. Previous investigations on both ceramics and single crystals of BaTiO3 [14] and others perovskite-type structure ferroelectric materials [27] suggest the presence of a large dielectric dispersion in the gigahertz region, which was reported to be close to a dipolar character (that is to say, like a Debye-type relaxation). In spite of not being still clarified, several theoretical attempts have been proposed to explain the origin of this effect. The relation between the high frequency dielectric dispersion and the microstructure of ceramics was expressed by Von Hippel [28], who attributed the piezoelectric resonance of the grain as the principal cause of the observed microwave anomalies. Kittel [29] suggested that the domain walls motion have an inertial component. He attributed the decrease of the dielectric permittivity at the microwave region to the resonance of the domain walls in ceramics. Some others models based on piezoelectric resonance of individual domains [30] or on correlated hopping of offcentered ferroelectric active ions between several potential wells [23] have been proposed in more recent years. In all the cases, the structural disorder on the atomic scale, assuming the two-minimum potential relief for some lattice ions, was used as the principal cause for the high frequency dielectric dispersion. As observed, the dielectric dispersion in ferroelectric materials has been a well investigated subject. However, more recent experimental results [31] showed evidences of a resonant dielectric behavior, rather than the previous observed dielectric dispersion. It has been shown, that the resonant behavior may coexist, in the same studied systems, together with the dispersion behavior, under certain conditions. Therefore, it seems that the high frequency dielectric response in ferroelectric materials, observed near to 1 GHz, is dictated by a universal mechanism involving a resonant response (damped or overdamped), which is until now a not fully clarified matter. The objective of the present work is to show a detailed review concerning the high frequency dielectric dispersion in ferroelectric systems, by considering the obtained results

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for ‘normal’ and relaxor ferroelectric ceramic compositions with perovskite type structure. A measuring system suitable for investigation of the high frequency dielectric dispersion, over a wide temperature range from 90 K to 450 K, is presented. Construction and correct calibration procedures are also described, including a brief description of the experimental setup. On the other hand, the present work proposes the fulfillment of the nature of the microwave dielectric dispersion in ferroelectrics materials viewing a better understanding of the dispersion and/or resonant behavior verified in ‘normal’ ferroelectric systems at high frequencies.

2. EXPERIMENTAL DESCRIPTION Dielectric measurements can be commonly carried out by using high frequency impedance analyzers. Here, will be described measurements carried out using a Network Analyzer HP-8719C in the frequency range of 50 MHz to 2 GHz. Technical reasons associated to the system configuration limited accurate measurements above the mentioned frequency range. Indeed, at higher frequencies (> 2 GHz), due to natural resonance of the experimental setup, only measurements at discrete frequencies can be obtained, although the signal in the analyzer can be generated up to higher frequencies. The dielectric response is obtained by the reflectometric method where the reflection coefficients (real and imaginary components: Γ’ and Γ’’, respectively) versus frequency are measured. The setup, currently known by coaxial probe method, is shown in the Figure 2.

Figure 2. Experimental diagram for dielectric characterization using the reflectometric technique by the coaxial probe method.

The sample is kept at rest on the end of the probe. However, in the case of very high dielectric permittivity (ε’ > 100) materials this method presents some disadvantages: a- with the increase of the frequency the modulus of the reflection coefficient ⏐Γ⏐ becomes close to 1 and its phase φ close to zero. Therefore, such materials are difficult to be measured and the

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quality of the results largely depends on the initial calibration of the analyzer; b- air gaps formed between the sample and the inner/outer conductors cause very large measurement errors when the sample is badly tooled and c- for high temperatures different thermal expansions of the sample and inner/outer conductors also can bring errors generated by the air gaps formation. Thus, for reducing these limitations and successful characterize high dielectric permittivity materials, as is the case of ferroelectrics, an alternative coaxial line method has been considered. In order to explore a large frequency spectrum of dielectric properties of ceramic materials, CVF measurements involving the case of a coaxial line and the reflectometric technique are appropriate [7]. The coaxial line, including commercial coaxial semi-rigid connectors, provides a suitable link between the measuring port of the network analyzer and the temperature-controlled sample holder, as shown in Figure 3.

Figure 3. Experimental diagram for dielectric characterization using the reflectometric technique by the coaxial line method.

The coaxial line method can be schematically presented by a simple configuration as shown in Figure 4a. The system is based on a microwave generator signal, a signal detector and a divider system located into the network analyzer and a 50 Ω coaxial connector coupled to the coaxial line being terminated by the capacitance of a cylindrical sample. By using the reflectometric method, the coaxial line (see Figure 3) can be characterized in terms of the network theory as a terminated two-part network as shown in Figure 4b. The measured reflection coefficient Γ* (=Γ’ + jΓ’’) is fundamentally affected by the absorption and phase shift of the signal inside the line, and can be described by the S parameters (S11, S22, S12 and S21) of the network. Therefore, in order to determine the frequency dependence of the reflection coefficient of a sample, the coaxial line has to be previously calibrated. Thus, careful compensation procedures have to be carried out to (i) eliminate spurious reflections that may result by transmission line discontinuities, and also (ii)

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reduces stray resistances and stray capacitances in the sample holder. Standard terminations (open, short and 50 Ω) were used over all the operating frequency range at room temperature. Because of the special construction of the system, the calibration performed at room temperature was assumed to be valid over the whole temperature range. It is important to point out that identical dimensions of the sample and standard terminations are necessary to avoid faults by different measuring planes and different stray fields. Thus, reflection coefficients data corrected for the line effects can be frequency scanned and automatically transferred from the network analyzer to the computer. By using the relation between the reflection coefficient and the admittance at the line Y = Yo

1 − Γ* (where Υo=1/Zo) and 1 + Γ*

taking into account the complex dielectric permittivity (ε=ε’–jε’’), the real and imaginary component of dielectric permittivity are obtained by using the Eqs. (1) and (2) [12], respectively,

Figure 4. Experimental diagram of reflectometric method used by the network analyzer.

ε'=

⎤ 1 ⎡ − 2Γ ' ' ⎢ 2 2⎥ Af ⎣ (1 + Γ') + Γ' ' ⎦

(1)

ε''=

1 ⎡ 1 − Γ ' 2 − Γ ' '2 ⎤ ⎢ ⎥ Af ⎣ (1 + Γ')2 + Γ' '2 ⎦

(2)

where f is the measuring frequency; A is determined by the characteristic impedance Zo of the analyzer ( A = 2ε o

π 2r 2 t

Z o ); r and t are the radius and thickness of the sample,

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respectively, and εo is the dielectric permittivity of the free space. To obtain more precise measurements, the sample dimensions should have (preferably) cylindrical symmetry with a diameter smaller than the diameter of the central conductor of the coaxial line, in order to avoid border effects and to ensure the electric field only in axial direction inside the sample. Heating of the sample can be achieved by a conventional resistive heater, which can be screwed onto the top of the coaxial line and coupled to a temperature control Flyever FE50RP, as shown in Figure 3. Finally, this measurement system can be inserted into a cryogenic system, which allows to perform experiments under either high vacuum level or nitrogen atmosphere to covers the low temperature ranges. The coaxial line can be inserted inside a silicate boron tube, in order to isolate the line of the liquid nitrogen. Gassy nitrogen can be placed inside the silicate boron tube by a gassy nitrogen input to account for a best good control of the cooling and heating processes. Air gaps at the interface between the coaxial line and the sample were avoided by an optimal sample polishing process, in order to guarantee parallel and flat faces. Alumina powder of 1 μm was used in this polishing process. Gold electrodes were sputtered on the faces of the discs with 2.0 mm in diameter and 0.5 mm in thickness to insure good electrical contacts, for all the investigated samples.

3. HIGH FREQUENCY DIELECTRIC MEASUREMENTS 3.1. Microwave Dielectric Characterization in Low Permittivity Materials (Al2O3)

40.0

90 K 150 K 200 K 300 K Ref. [32] Ref. [33]

20.0

1.0

40 30 20 10 0

300 K

2x10

9

4x10

9

6x10

9

0.5 ε''

ε'

30.0

ε'

Firstly, an alumina (Al2O3) ceramic disk (2.0 mm diameter and 0.5 mm thickness) was used for the dielectric characterization in the range of 50 Hz to 2 GHz at low temperatures. The Al2O3 ceramic was chosen as reference material for the measurements to successfully check the correct calibration of the experimental set-up in the low temperature region. Figure 5 shows the dielectric response of the alumina ceramic obtained at four selected temperatures (90 K, 150 K, 200 K and 300 K). As can be seen, the obtained data were characterized by a high stability of the dielectric parameters in the whole frequency interval. Also, the real component of the dielectric permittivity was found to be around 9.5, in agreement with previously reported results in the literature (ε’ ≈ 9) [32, 33].

0.0

10.0 HF

LF 4

10

5

10

6

7

8

10 10 10 10 Frequency (Hz)

9

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Figure 5. Dielectric response for alumina ceramic including the low (LF) and high frequency (HF) range (100 Hz–2 GHz), at room temperature.

For comparison, low frequency dielectric data were measured using an HP-4194A Impedance/Gain-Phase Analyzer (100 Hz–10 MHz), and the results have been added to microwave properties as shown in the same Figure 5. Since Al2O3 ceramic materials do not display a dielectric dispersion phenomenon [34] (frequency independent dielectric permittivity), the smooth continuity in the values of real and imaginary component of dielectric permittivity for low and high frequency ranges confirms the accuracy of the results obtained at the microwave frequency range. The ε’ and ε’’ values are again in agreement with those found in the literature [32, 33].

3.2. Microwave Dielectric Characterization in High Dielectric Permittivity Materials In order to demonstrate the range of applicability of the experimental setup and to illustrate its capabilities when investigating high dielectric permittivity materials, dielectric measurements were carried out in Sr1-xCaxTiO3 (x=0.1) quantum paraelectric ceramic samples, hereafter labeled as SCT–90/10, as a function of the frequency (50 MHz–2 GHz) and temperature (90 K–450 K).

10.0

90 K 150 K 200 K 250 K 300 K 360 K 430 K

2

ε' ( 10 )

8.0 6.0 4.0 2.0 0.0 2.0

SCT-90/10

2

ε'' ( 10 )

1.5 1.0 0.5 0.0 8

10

9

10

Frequency (Hz)

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Figure 6. High frequency dependence of the real and imaginary component of dielectric permittivity (ε’ and ε’’, respectively) for the SCT quantum paraelectric system, at several temperatures above the transition temperature.

In this case, due to additional effects, related to the piezoelectric phenomenon characteristic in ferroelectric systems, a careful control of the pressure on the sample should be taken into account. The adjustment and control of the pressure on the sample was made when decreasing temperature because loss of contacts between the line and the sample holder originated by the thermal contraction of the different elements. Thus, the dielectric response of the sample was obtained at each measured temperature for a critical pressure level on the sample, sufficient to guarantee the electrical contacts. In this case, the frequency dependence of the dielectric properties (ε’ and ε’’) was carried out at various temperatures. Figure 6 shows such dependences for the temperature and frequency range of 90 K–450 K and 50 MHz–2 GHz, respectively. As can be observed, the frequency dependence of ε’ and ε’’ revealed the characteristic behavior of a dielectric dispersion, i.e., a decrease in the real component of the dielectric permittivity and a maximum in the imaginary one at the characteristic frequency (fR). The fR value lies in the order of 700 MHz, in agreement with the reported values obtained for some perovskite-type structure materials [15, 24]. Similarly to the BaTiO3 type ferroelectric system [35], the dielectric dispersion does exist for temperatures above the transition temperature, which suggests the existence of polar regions in the paraelectric state [36], and will be discussed in the next sections. Parallely, low frequency dielectric measurements were performed at the frequencies of 10 kHz, 100 kHz and 1 MHz, in the same temperature interval. The results, shown in Figure 7, do not present any dielectric dispersion in this low frequency range, evidencing a good agreement between the low and high frequency results.

3.3. Microwave Dielectric Characterization in ‘Normal’ and Relaxor Ferroelectrics The present section treats about the investigation of the high frequency dielectric dispersion processes in Pb1-xLaxTiO3 ferroelectrics ceramics for ‘normal’ (x=0.15) and relaxor (x=0.27) compositions (hereafter labeled as PLT–15 and PLT–27, respectively), in order to better understand the occurrence of such common dielectric dispersion process in so different kinds of ferroelectric systems. 16.0 90 K 200 K 300 K

2

ε' ( 10 )

12.0 8.0

LF

HF

4.0 0.0 10

4

10

5

10

6

10

7

10

8

Frequency (Hz)

10

9

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Figure 7. Low and high frequency dielectric dispersion for the SCT system for temperatures of 90 K, 200 K and 300 K, respectively.

Figure 8 shows the frequency dependence of the real, ε’ and imaginary, ε’’ component of the dielectric permittivity for the PLT–15 ceramics, at different temperatures. The Curie temperature of the samples, TC~393 K, was determined by the dielectric measurements of ε’ at low frequencies (1 kHz). A dielectric response indistinguishable from a dispersive behavior was observed in the whole analyzed temperature interval. As can be seen, for a fixed temperature (i.e. at 300 K) and in the frequency range of 70–400 MHz, ε’ decreases slightly as the frequency increases. Above 400 MHz, ε’ decreases quickly, whereas ε’’ passes through its maximum value. The frequency corresponding to the maximum of imaginary component of the dielectric permittivity (fR=700 MHz) is known as the characteristic frequency of the dispersive process, and it is associated to a polarization mechanism responsible for the dissipation. The obtained value for the characteristic frequency is in agreement with those reported for other ferroelectric materials commonly used for microwave applications [24, 37]. 1.5

0.6

3

ε' ( 10 )

PLT-15

0.0

1.2 3

300K 390K 420K 440K 445K

ε'' ( 10 )

1.2

0.9 0.6 0.3

8

10

9

10

0.0

Frequency (Hz) Figure 8. Frequency dependence of the real (ε’) and imaginary (ε’’) component of the dielectric permittivity for the PLT–15 ceramics, as a function of the temperature.

The origin of this behavior has been attributed to the ferroelectric domain walls vibrations in the ferroelectric material [38]. In this way, the domain wall motion is well known to contribute to the polarization of ferroelectric systems. The frequency of the domain walls vibration (obtained at the Gigahertz region) may be observed by applying an alternate electric field of very high frequency. For frequencies appreciably lesser than fR, the ferroelectric domains contribute their full share to the polarization so that the real component of the dielectric permittivity becomes equal to the static dielectric permittivity (εs) and, therefore, the losses (associated to the imaginary component of the dielectric permittivity) vanish. With the increase of the frequency, the domain vibrations increase and consequently the imaginary component of the dielectric permittivity starts to increase up to its maximum value. On the other hand, for a frequency higher than fR, the domain wall vibrations are no longer able to follow the field variations and the real component of dielectric permittivity approaches its clamping values (ε∞). In this frequency range, therefore, ε’’ passes through its maximum value and continuously decreases for the highest frequency values.

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On the other hand, a closer inspection in the data of Figure 8 seems to support the picture of a distributed dipolar relaxation mechanism of the dielectric response. Indeed, the obtained value for the characteristic width (λD) at a half-height for the imaginary dielectric permittivity peak (known as full-width half maximum, FWHM), specifically at room temperature, was found to be around 1.91 decades. This value of the FWHM is higher than the FWHM of a Debye-type peak (λD=1.14 decades) [34]. Therefore, the obtained result reveals that the observed dielectric behavior cannot be associated to a Debye-type relaxation process. Results for the dispersive process obtained in the studied PLT–15 samples (in “virgin” state) clearly show a mechanism with a relaxation times distribution function. The data were fitted taking into account the most useful distribution functions for the investigation of the relaxation processes, as reported in the literature [39], and results revealed that the obtained dielectric response was found to be close to a Davidson-Cole (DC) distribution function [40]. The obtained values for the characteristic parameters, such as, the mean relaxation time (τ) and the relaxation time distribution parameter (β), which represents degrees of divergence from the ‘ideal’ Debye model, were 1.45×10-9 s and 0.75, respectively. Compared to singleexponential Debye behavior corresponding to β=1, values of 0 < β < 1 result in broadened imaginary dielectric permittivity peaks. Smaller the values of β the greater the deviation with respect to Debye-type relaxation. Such deviations from Debye behavior are commonly ascribed to a distribution of relaxation times arising from disorder [40]. The obtained mean relaxation time is in good agreement with those obtained for similar ferroelectric systems, as reported in previous works [15]. As can be seen in Figure 8, the dielectric dispersion occurs not only in the ferroelectric region (TTC) close to TC. This behavior, as pointed out in a recent work [26], suggests the existence of polar regions at temperatures higher than the transition temperature, which could be one more evidence of the contribution for an “order-disorder” type paraelectric-ferroelectric phase transition in ABO3 perovskite structures, as reported in the literature [41, 42]. The existence of an order-disorder component in the paraelectric-ferroelectric phase transition of PbTiO3 explains the persistence, although weak, of the dielectric dispersions above TC [26]. It is important to point out that, for higher temperatures, the data also revealed highest values for the FWHM, showing a distributed dipolar relaxation mechanism for all the investigated temperature range. At the same time, a decrease in the distribution parameter (β), as the temperature increases, confirms that the dielectric spectrum becomes extremely diffuse. Correspondingly, the distribution of relaxation times becomes extremely wide. As can be observed, similarly to the results reported by other authors for BaTiO3 [22, 35], PbTiO3 derived materials [8] or some tetragonal tungsten bronze (TTB) structure systems [43], the obtained dielectric response curves suggest a dispersive mechanism of the complex dielectric permittivity, without any evidence of a resonant response. Figure 9 depicts representative curves of the frequency dependence of ε’ and ε’’ for the PLT–27 (relaxor composition) measured at different temperatures below and above the respective temperature of the maximum of the dielectric permittivity, Tm. The data also reveal strong temperature dependent dielectric dispersions for this relaxor ferroelectric composition, not only for temperatures below the temperature of the maximum dielectric permittivity, but also for temperature above Tm.

J. D. S. Guerra

2.0 0.0

3.0 2.4 1.8 1.2

PLT-27

3

226K 259K 290K 325K 350K

3

ε' ( 10 )

4.0

ε'' ( 10 )

180

0.6 0.0 8

10

9

10

Frequency (Hz) Figure 9. Frequency dependence of the real (ε’) and imaginary (ε’’) component of the dielectric permittivity for the PLT–27 ceramics, as a function of the temperature.

The high frequency dielectric dispersion can be related to a microscopic polarization mechanism and, therefore, a possible explanation for the observed behavior could be found taking into account atomic level considerations. Indeed, the mechanism for this dielectric behavior is associated with a shift of Ti4+ (the B-site ion in the perovskite structure) inside the oxygen octahedron. The ion shifts from one potential to the other in a double well potential model (relaxation motion), as shown in the Figure 10a, being ΔU the high of the potential barrier [44]. In fact, such mechanism can be represented as real chains (or volumes) of correlation (named as correlation chains) including a large number of Ti4+ ion cooperative jumps, which must be considered in the relaxation mechanisms. These chains are isolated from each other by several types of defects (vacancies, impurities, point defects, etc.) (Figure 10b).

Figure 10. Double potential model (a) and correlation chains scheme (b) for the high frequency dielectric response.

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In order to obtain additional information of the dielectric spectrum, the obtained results were fitted by using the Eqs. (3) and (4), which consider a damped harmonic oscillator model [45], where the frequency dependence of the complex dielectric permittivity is governed by the Eqs. (3) and (4).

ε ' = A+

ε '' =

BωR2 (ωR2 − ω 2 )

(ω

2 R

−ω

)

2 2

+γ ω 2

(3)

2

BωR2 γω

(4)

(ωR2 − ω 2 ) + γ 2ω 2 2

A and B are constant parameters, which are directly related with the dielectric dispersion parameters. For instance, B=εs–ε∞, defined as dielectric strength (Δε), is the contribution to the dielectric dispersion of the static dielectric permittivity, εs; A=ε∞ is the contribution to the dielectric permittivity of the higher frequency electronic processes; ω=2πf is the angular frequency and

1

τ

fR =

ωR , is the characteristic frequency of the process (defined as, 2π

= 2π f R , where τ is the mean relaxation time). The dispersion characteristic parameters,

such as, Δε, fR and γ (the damping coefficient of the dielectric response), can be obtained directly from the fitting of the obtained dielectric response (frequency dependence of ε’ and ε’’) with the Eqs. (3) and (4), which undoubtedly might be an essential feature in order to identify the mechanism involved in the dielectric anomaly. Figure 11 shows the temperature dependence of the characteristic frequency (fR) and the dielectric strength (Δε) for both PLT–15 and PLT–27 compositions. The results reveal that Δε and fR reach simultaneously a maximum and a minimum, respectively, in a temperature that coincides with its respective maximum real dielectric permittivity, TC and Tm for the PLT–15 and PLT–27 compositions, respectively. 2.8 fR: PLT-15

1.0

Δε: PLT-15

0.8 0.6 0.4 0.2

2.4 2.0 1.6

PLT-27 fR: PLT-27 Δε: PLT-27

1.2

3

PLT-15

Δε ( 10 )

fR ( GHz )

1.2

0.8 0.4

240 270 300 330 360 390 420

Temperature (K) Figure 11. Temperature dependence of the characteristic frequency (fR) and dielectric strength (Δε) for the PLT–15 and PLT–27 compositions.

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Referring to the observed results, the essential features can be summarized as follows. athe microwave dielectric dispersion process persists at temperatures higher than the temperature of the maximum dielectric permittivity for both compositions, vanishing in the temperature interval where 1/ε’ vs. T obeys the Curie law (around TB, the Burns temperature, characterized by the temperature of nucleation and slowing down of the ferroelectric domains); b- above Tm, it is noticed that fR is much more temperature dependent for the PLT– 15 than for the PLT–27 composition, vanishing earlier for the former composition; c- the magnitude of the characteristic frequencies (fR) for both compositions are comparable, although their polar structures and correlation length differ significantly [22, 46, 47]. Similar results were found for incipient ferroelectrics and antiferroelectrics [16, 17]. These experimental results allow us to interpret the microwave dielectric process according to the scenario described as follows. First, the fact that the microwave dielectric dispersions became evident even for temperatures far above Tm clearly demonstrates that the simple presence of polar regions, independently of their size, volume fraction and correlation length, is the sufficient condition for the existence of such dielectric dispersion process in perovskite ferroelectric systems. Nevertheless, the only plausible common mechanism inherent in so different ferroelectric domain structures is the boundaries of ferroelectric domains and nanodomains. Therefore, it has been proposed that the field-induced vibration of polar region boundaries of domains (domain walls) and nanodomains (interphase boundaries between the polar region and the non-polar matrix) is the common mechanism responsible for the dielectric dispersion process in the microwave range. The second intriguing question is why such dispersion occurs around the same frequency interval (fR) for all the ferroelectric systems, although their apparent distinct nature. In this context, in analogy with the oscillating membrane theory [38, 48] and in accordance with the side-way motion of the boundaries of the polar regions discussed above, it is suggested that fR is governed by the ratio between the effective force constant (κeff) and the effective mass (Meff.) of the polar regions boundaries, fR ≈

κ eff / M eff . The effective mass is the mass of

domain walls and interphase boundaries for normal ferroelectrics and relaxors, respectively, while the force constant (κeff) is dictate by elastic properties of the respective polar region boundaries [19, 38, 49]. Thus, it is believed that this ratio would have almost the same value for all perovskite ferroelectric systems, justifying the similar values found for fR. For instance, for normal ferroelectrics the higher force constant would be balanced by the higher effective mass of domain walls. On the other hand, for relaxors and incipient ferroelectrics, the relative smaller κeff is balanced by the relative low massive interphase boundaries, thus keeping the ratio reasonably constant. Finally, such proposed relation for fR is also able to explain satisfactory the behavior of fR (slope) from the paraelectric to ferroelectric phase transition. For temperatures higher than TC, the high thermal energy reduces the dipolar interactions contributing for a low κeff, and consequently, a relatively low value for fR. With the decrease of the temperature, the thermal energy decreases in favor of the formation of the polar regions, promoting the increase of Meff, and consequently fR slightly decreases. For temperatures near TC, a sudden increase in the interaction energy, and consequently in the κeff, takes place, resulting in an increase of fR. Indeed, in the case of PLT–15 the paraelectric-ferroelectric phase transition is predominantly

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183

a displacive-type transition. Therefore, it is expected an abrupt crossover between the two structural phases (paraelectric-ferroelectric), which means an accelerated disappearance of the polar regions (domains and domain walls). This fact results in a sudden change in both order parameter and elastic properties, thus reflecting in the force constant. Moreover, the existence of an order-disorder component in the paraelectric-ferroelectric phase transition explains satisfactorily the existence of the dielectric dispersion above Tm. On the other hand, it is well known that relaxor ferroelectrics do not necessarily present a macroscopic structural phase transition through or bellow the temperature of maximum permittivity (Tm). Therefore, for the relaxor composition, it is proposed that the low slope of fR above Tm reflects the gradual condensation and the slowing down of polar nanoregions below TB. Furthermore, the fact the microwave dielectric dispersion is characterized at temperatures much higher than Tm, for the PLT–27 composition, confirm the existence of nanodomains at temperatures much higher than Tm. 20.0

3

ε' ( 10 )

15.0

(a)

TC = 393 K

(b)

300 K 340 K 360 K 390 K 430 K

10.0 5.0 0.0

30.0

3

ε'' ( 10 )

25.0 20.0 15.0 10.0 5.0 0.0

8

10

9

10

Frequency (Hz) Figure 12. Frequency dependence of the complex dielectric permittivity for the PLT–15 samples under a uniaxial stress, at different temperatures.

3.4. Mechanical and Electrical Driving Field Effects 3.4.1. Stress effect analysis Because the dielectric response in ferroelectric materials is strongly susceptible to the influence of electric and/or mechanical fields, the microwave dielectric properties in the PLT–15 ceramics have been now investigated under the influence of a mechanical uniaxial

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stress, applied parallel to the measurement direction. The dielectric properties were obtained over the same frequency and temperature range to that obtained for the ‘stress free’ samples described in the previous section. The results presented in the Figure 12, clearly show that at room temperature (solid line), ε’ remains essentially flat up to 700 MHz, increases traversing a maximum, and then decreases to its clamped value (see Figure 12a). As can be seen, this anomalous behavior obtained for the stressed samples and indistinguishable from a resonant response, is observed in the whole analyzed temperature range. On the other hand, the stressed samples also exhibited the highest values of the imaginary component of the dielectric permittivity, with its ε’’ peak apparently shifted to a higher frequency (Figure 12b), when compared to that obtained for the ‘stress free’ samples. This dielectric response obtained for the stressed ceramics corresponds to a true resonance rather than a dispersion process, with a characteristic frequency around 900 MHz (at room temperature) higher than the obtained for the ‘stress free’ samples (700 MHz), at the same temperature. It is interesting to point out, from the Figure 12b, that the high values of the maximum imaginary dielectric permittivity for the stressed samples, when compared to the maximum decrease of the real component (εs–ε∞), suggest that is not possible to describe the spectrum as a classical Debye’s dielectric dispersion. At the characteristic frequency (900 MHz), the value of ε’’ at room temperature, is about 2 times higher than that predicted by the Debye’s classical model, [(εs–ε∞)/2], for the stressed samples. This result has an important physical implication; indeed, it clearly confirms that the high frequency anomalies do not correspond to a real dispersion process as predicted by the Debye’s model (relaxation-like behavior). As reported in previous works [21, 22], the assumption that the observed dielectric anomaly could be, in this case, related to a piezoelectric resonance of the grains or individual domains suggests that the main influence of the uniaxial stress would be to decrease the losses related to this process, contrary with the results obtained for the PLT–15 samples. Therefore, the true mechanism responsible for the obtained anomalies remains still not clear. The dispersion characteristic parameters, were now also obtained from the fitting of the obtained dielectric response by using the Eqs. (3) and (4). In order to compare the temperature evolution of the characteristic parameters results for the stressed and ‘stress free’ samples for the PLT–15 ferroelectric ceramics are presented in the Figure 13. As can be observed, the temperature dependence of fR and ∆ε is quite similar for the stressed and the ‘stress free’ samples. So that, with the application of the uniaxial mechanic stress, although the dielectric response evidences resonance characteristics, this behavior remains modulated by the paraelectric-ferroelectric phase transition. As a result, the thermal evolution indicates that, in both cases, the characteristic frequency goes through a minimum while the dielectric strength pass through a maximum around 393 K, which coincides with the paraelectricferroelectric phase transition temperature (TC), as observed in the low frequency dielectric measurements [26]. This result shows that the maximum dielectric dispersion appears near the transition temperature, independently of the applied external mechanical driving field. On the other hand, it is important to point out that the damping coefficient values (γ), obtained from the fitting of the experimental data by using the Eqs. (3) and (4), at room temperature, were lower for the stressed samples (0.45⋅109 s-1), than those obtained for the ‘stress free’ samples (8.80⋅109 s-1). This result suggests that the high frequency dielectric anomalies, dispersion or resonance, can be described as either an over-damped or a damped resonant response, respectively, where the main contribution to the dielectric response can be

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185

associated to the ferroelastic and/or ferroelectric components of the ferroelectric materials, which directly modifies the damping of the system. Referring to the obtained results, the essential aspect to be discussed can be summarized to the feature that with the application of an external mechanic driving field the dielectric response of the system clearly pass from a dispersive to a resonant dielectric behavior. In this way, considering an “over-damped” resonant response, the variations in the strength of the damping coefficient of the system originate mainly due to the contributions of either ferroelastic or ferroelectric dipolar components. For lower damping systems, as the case of the obtained resonant behavior for the stressed samples, the main contribution to the dielectric response is governed by the ferroelectric dipolar component. On the contrary, for higher damping coefficient systems, the major contribution of the dispersive behavior (as observed in the “stress free” samples) is due to the ferroelastic dipolar component, which prevails over the ferroelectric component. On the other hand, it is well known that ordinary ferroelectric materials are classic hybrids ferroics, that is to say, they present a strong coupling between the ferroelectricferroelastic dipolar components [50, 51]. When applying a uniaxial mechanic stress a reorientation of the electric and elastic dipoles takes place. In the same way, a mechanic strain in the material can be observed if applying an electric driving field. Then, as in the case of the stressed samples, applying a uniaxial stress parallel to the measurement direction promotes the dipolar reorientation in the perpendicular direction of the applied uniaxial stress, that is to say, an induced polarization may appears in the perpendicular direction to the applied uniaxial stress direction. Therefore, applying a uniaxial stress parallel to the measurement direction is equivalent to apply a poling electric field in the perpendicular direction of the measurement direction. Thus, in order to obtain a better understanding of the current analysis, the observed anomalies around 1 GHz for the studied PLT–15 ceramics, will be now investigated taking into account the influence of the relative orientation of the macroscopic polarization on the dielectric dispersion in the poled samples. 1.2

6.0 fR ; Δε - stressed fR ; Δε - stress free

4.5 3.0

0.3

1.5

0.0

300

330

360

390

420

3

0.6

Δε ( 10 )

fR (GHz)

0.9

0.0 450

Temperature (K) Figure 13. Temperature dependence of the characteristic parameters (characteristic frequency, fR and dielectric strength, Δε) for the stressed and ‘stress free’ PLT–15 samples.

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J. D. S. Guerra

3

ε' ( 10 )

3.0

'stress free' samples

(a)

1.5

0.0

Unpoled Poled ( I I ) Poled ( )

(b)

(fR = 700 MHz) (fR = 700 MHz)

3

ε'' ( 10 )

2.0 (fR = 1.03 GHz)

1.0

0.0 8

10

9

10 Frequency (Hz)

Figure 14. Frequency dependence of the complex dielectric permittivity, at room temperature, for the PLT–15 unpoled ‘stress free’ samples, and the poled samples measured in the parallel (//) and perpendicularly (⊥) direction to the poling direction; (a)- real and (b)- imaginary component.

3.4.2. Poling field effect analysis The dielectric response was now performed in poled samples (Ep = 2 kV⋅mm-1) at room temperature, in both parallel and perpendicular directions to the poling field direction and in the same frequency interval, following the same experimental procedure previously described. Thus, the temperature dependence of dielectric permittivity (real and imaginary component) was obtained parallel (ε’//) and perpendicularly (ε’⊥) to the polarization direction. The results are shown in Figure 14. The results reveal that the dielectric response, observed in the sample measured parallel to the poling direction, presents an ‘apparent’ dielectric dispersion process, which in turn is similar to that observed for the unpoled sample (see Figure 8). However, it is observed that the maximum of the imaginary component of the dielectric permittivity (ε’’//), for the sample measured parallel to the poling direction, is around 4 times higher than (εs//–ε∞//)/2. Furthermore, a detailed inspection for the FWHM of the imaginary dielectric permittivity peak for the sample measured parallel to the poling direction revealed that the observed dielectric dispersion has not a relaxation-like character, since the FWHM of the peak was found to be around 0.85 decades. This value is lower than the characteristic width of a Debyelike process (λD=1.14 decades, the low limit value for FWHM). Indeed, it implies that it is not

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187

possible to describe the observed dielectric spectrum as a classic Debye’s dielectric relaxation, as previously discussed in the section 3.4.1. Therefore, it is possible to affirm that the observed dielectric anomaly really correspond to a resonant-like dispersion rather than a simple relaxation-like dielectric behavior. Figure 14 also displays the dielectric response in the sample measured perpendicularly to the poling direction. The results show that ε’⊥ slightly increases up to 500 MHz. However, after that, it abruptly increases and subsequently decreases for higher frequencies to its clamped values. The maximum of the imaginary component of dielectric permittivity (ε”⊥) also presents a remarkable high value, now observed around 1.03 GHz. The imaginary component of the dielectric permittivity for the sample characterized perpendicular to the poling direction is about 7 times higher than the values predicted by the theoretical Debye’s model. These results show that the dielectric response obtained for the samples measured perpendicularly to the poling field is characterized by a resonant mechanism, which may be associated to a damped resonance process rather than to a simple Debye’s dielectric relaxation. The above described experimental results clearly show that in the same sample, depending on the relative orientation between the measuring direction and the macroscopic polarization direction, the dielectric dispersion in the GHz region seems to behave as either a dispersive (relaxation-like) or a resonant mechanism. This change in the dielectric response can be well described considering a general resonant behavior, which can be associated with an “over-damped” resonance process. Therefore, it can be affirmed that the microwave dielectric spectra observed in ferroelectric materials may be described in terms of an “overdamped” resonance involving either dispersive or resonant behavior, rather than a simple dispersion process (relaxation-like), which are intimately related to the variation in the damping strength of the system. At the same time, the damping strength is affected by the coupling between the ferroelectric and ferroelastic dipolar components. The values of γ were now obtained for the poled samples, by the fitting of the experimental data, and showed in the Table I, together with those obtained for the ‘stress free’ and stressed samples. As observed, the damping coefficient also shows a decrease when the dielectric behavior pass from a dispersive (relaxation like) behavior to a pure resonant response. As can be seen, the γ value for the poled samples measured in the parallel direction to the poling direction was around 8.97⋅109 s-1, similar to that obtained for the ‘stress free’ samples and, at the same time, higher than those obtained for the poled samples measured in the perpendicular direction to the poling direction. Table 1. Dispersion characteristic parameters obtained for the PLT–15 samples, at room temperature. Sample Stress free Stressed Poled // Poled ⊥

ε∞ 113 266 145 149

Δε 453 691 300 541

fR (GHz) 0.70 1.44 0.70 1.04

γ (109 s-1) 8.80 0.45 8.97 1.15

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Thus, from the obtained results, it is possible to affirm that the dispersive behavior observed for the ‘stress free’ samples may be a consequence of an increase of the damping strength, giving rise an over-damped resonance (reflected by the dispersive behavior). On the other hand, the resonant behavior observed for the poled samples measured in the perpendicular direction to the poling direction, as well as in the stressed samples, may be a consequence of a decrease of the damping strength, giving rise a damped resonance (reflected by the resonant behavior). It is important to point out that although the dielectric behavior observed for the samples measured in the parallel direction to the poling direction has a true resonant-like character, from the previously described analyses, an “apparent” dispersion behavior (relaxation-like) was observed because of the high component of the damping coefficient. Therefore, the gigahertz dielectric anomalies observed in normal ferroelectrics must be interpreted as a resonance instead of a dispersion mechanism. The question as to whether these high frequency anomalies behave as a dispersive (relaxation-like) or a resonant process, described, in general, by an “over-damped” mechanism, may be a consequence of the coupling between the ferroelectric and the ferroelastic dipolar components, whose contribution determines the character of the high frequency dielectric dispersion. This aspect will be discussed in details in the next section.

3.4.3. Discussion The ferroelectric phenomenon, in most of cases, may be follows by a ferroelastic behavior, that is to say, a ‘non-intentional’ stress can be present when an electric field E is applied. As in ferroelectric materials, a ferroelastic crystal contains two or several stable orientation states when there is no mechanical stress. It is possible to change reversibly from one state to another by applying a stress σ in defined directions. Thus, there exists a strainstress elastic hysteresis with spontaneous strain ss and a coercive stress. In this way, a transition from a ferroelastic phase to a higher temperature phase, termed paraelastic, occurs by an increase in symmetry and a change in the crystalline system [52]. The additional ‘nonintentional’ stress originated when applying an electric field may be sufficient for ferroelastic switching to occur [53]. The basic assumption of the polarization switching model is that a single ferroelectric crystallite in a polycrystalline ceramic, which is subjected to an electric field [54] or to a mechanical stress [55, 56] or both, undergoes a polarization change and a corresponding strain change. Nevertheless, either partial or complete coupling may exist between the ferroelectric and ferroelastic properties. When such coupling occurs, ss may be modified by applying an electric field and Ps may be modified by applying a mechanical stress. This leads to a set of four hysteresis cycles: polarization–electric field; strain–stress; strain–electric field; and polarization–stress, as shown in Figure 15 [44]. Crystal growth is usually accompanied by the formation of ferroelastic and/or ferroelectric domains. The crystal can be made monodomain by applying a mechanical stress (ferroelasticity), an electric field (ferroelectricity), or through one of the external actions if coupling occurs between the two properties. Depending upon the crystal structure and the order parameter, the ferroelectricity and ferroelasticity in a crystal could be fully or partially coupled.

Features on the High Frequency Dielectric Response in Ferroelectric Materials

189

Figure 15. Schematic representation of the hysteresis loops for ferroelectric-ferroelastic phases [44].

Concerning to the obtained results for the PLT–15 ceramics, it can be noted that two polarization mechanisms are always present under certain conditions. For all the samples where an external driving field was applied (a uniaxial stress and/or a poling field applied in the perpendicular and parallel direction to the measurement direction) a resonant-like dispersion has been observed. In particular, either uniaxial stress or poling field applied in the perpendicular direction to the measurement direction promotes redistribution in the orientation of the dipolar configuration over the perpendicular direction to the measurement direction. Therefore, the observed resonant behavior, for these conditions, could be associated to a slightly partial coupling between the ferroelastic and ferroelectric dipolar components, being the ferroelectric dipolar component the main responsible for the resonance dielectric response. On the other hand, for the unpoled and ‘stress free’ samples the observed behavior may be caused by the coupling between the ferroelectric and the ferroelastic dipolar components. In these conditions, the dipoles are unable to be reoriented ‘freely’ with the measurements ac electric fields. Therefore, the dielectric response is mainly governed by the contribution of the ferroelastic dipolar components, originating the dispersive dielectric behavior. In order to describe these results, the ferroelastic contributions to the piezoelectric response should be taken into account [57]. In this case, it will be considered the theoretical approach in order to investigate the influence of the external poling electric field on the dielectric response. Thus, the analyses of the data are considered when an oscillating external electric field is applied parallel or perpendicular to the poling direction. The piezoelectric effect can be represented by the Eq. (5), where c and e are the converse of the piezoelectric compliance (or elastic stiffness) and the piezoelectric tensor, respectively, defined as

190

J. D. S. Guerra

[e] = [d ][c E ] [53]. The symbols ν, μ and m correspond to the condensed index of the tensor notation (ν,μ = 1, 2,…, 6 and m = 1, 2, 3). E σ ν = cνμ sμ + emν Em

(5)

In view of the symmetry for a poled ceramic material (∞mm) and considering the respective symmetry operations, the Eq. (5) can be expanded by considering the probing electric fields applied parallel and perpendicular to the poling direction (E1 and E3, respectively) and represented by the following equations:

σ1 = c11s1 + c12 s2 + c13 s3 + e31E3

(6)

σ 2 = c12 s1 + c11s2 + c13 s3 + e31E3

(7)

σ 3 = c13 s1 + c13 s2 + c33 s3 + e33 E3

(8)

σ 5 = c55 s5 + e15 E1

(9)

Some important aspects of the piezoelectric equations (Eqs. (6) – (9)) must be highlighted when applying a probing electric field in two mutually perpendicular directions. First, when the probing electric field (E3) is applied parallel to the poling direction (P3), it generates only compressional/extensional stress (σ1, σ2, or σ3). In contrast, when an electric field (E1) is applied perpendicular to poling direction, only shear stress (σ5) is generated. The fundamental difference between both cases is that stress generated by the electric field E3 produces volumetric changes in the ceramic, while fields applied perpendicularly does not (E1⊥P3) [58]. In other words, ferroelastic dipoles are modified only by the application of an electric probing field E3, which is parallel to the macroscopic polarization. It is important to point out that the elastic stiffness c55, in the Eq. (9), is identical to the coefficient c44, after considering the respective symmetry operations. In terms of the elasticity theory, the dispersion or resonant behavior might be associated to the influence of the electric field on the elastic dipole. In this way, in order to clarify this issue it is necessary to use some basic elasticity concepts. The behavior of an elastic dipole in the presence of stress can be characterized by the relation

σν = cνμ λμ , being λ the strain tensor, which determines the interaction of

the elastic dipole with the stress field [58]. Formally, σ is defined as the negative stresses needed to maintain constant the strain per unit concentration of elastic dipoles. Since the λ tensor represents a strain tensor, it must be symmetric and, therefore, can be characterized by a strain ellipsoid with three mutually perpendicular principal axes. When expressed in the coordinate system of the principal axes, the λ tensor becomes diagonal with the three components λ1, λ2 and λ3 as the principal values. By expanding the relation of the elastic

Features on the High Frequency Dielectric Response in Ferroelectric Materials

191

dipole definition, it is not difficult to notice that results do not depend of the shear components of stress field. It suggests that the resonant behavior obtained for the perpendicular direction is governed by the electrical component of the Eq. (5), where only the shears components of the piezoelectric coefficients play the principal role, without any contribution of the components along the principal axes (σ1, σ2 and σ3). Considering that elastic dipoles in displacive ferroelectrics lie parallel to the electric ones, and that they interact only with the compressional or extensional stress [58], they are excited only by the application of the poling electric field parallel to the measurements direction. This suggests that the resonant response obtained for the perpendicular direction is governed only by ferroelectric components, because only the shear stress components are generated by piezoelectric contribution, without any ferroelastic contribution. Otherwise, the dielectric behavior (associated to an over-damped resonance) observed in the parallel direction results from a coupling between the ferroelastic and ferroelectric contributions. In this case, the ferroelastic contribution becomes the main responsible for the increase of the damping coefficient, contributing to the decrease of the characteristic frequency. It is important to point out that applying a uniaxial stress, parallel to the measurements direction, the resonant response observed can be explained considering that the ferroelectric and ferroelastic domains tend to be oriented perpendicularly to the mechanical stress and, consequently, perpendicular to the measuring electric field direction. As observed, this condition is analogous to the case of applying a poling electric field perpendicular to the measurements direction. Thus, either dispersion or resonance mechanism, are always presented without the presence of an intermediate case. This result confirm that the ferroelectric and ferroelastic contributions, to the high frequency dielectric anomalies, are always coupled each other.

4. CONCLUSIONS In summary, the dielectric microwave properties were investigated in relaxor and normal ferroelectric ceramics. It was concluded that the vibration of the boundaries of polar regions is a common mechanism responsible for the microwave dielectric dispersion process in ferroelectric systems. It was also proposed that the characteristic frequency is controlled by the ratio between the force constant and the effective mass of such boundaries and the behavior of fR above the temperature of the maximum of the permittivity reflects the ferroelectric-type phase transition. On the other hand, the microwave dielectric response of ferroelectric ceramics was investigated considering the influence of external (electric and mechanic) driving fields. Two high frequency dielectric anomalies were found in the same studied material, which were discussed in lights of an over-damped resonant process. It was confirmed that the obtained anomalies are strongly influenced by the contribution of the ferroelectric and/or ferroelastic dipolar components, characteristics of ferroelectric materials. In particular, for all the samples where an external driving field was applied (a uniaxial stress and/or a poling field applied in the perpendicular and parallel direction to the measurement direction) a resonant-like dispersion was observed. On the contrary, a dispersive (relaxationlike) behavior related to an over-damped resonance was obtained for the unpoled (and ‘stress free’) samples. The results can be well explained by considering the influence of the

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ferroelastic-ferroelectric contributions coupling on the high frequency dielectric response, which is a common feature for all ferroelectric systems.

ACKNOWLEDGMENT The author would like to thank to Ferroeletric Ceramics Group (GCFerr), of the Federal University of São Carlos (UFSCar) for experimental support, especially to Sr. F. J. Picon (GCFerr) for the technical assistance, and FAPESP (proc. No. 04/09612-0) Brazilian agency for financial support. The financial support by the ICTP to the Latin-American Network of Ferroelectric Materials (NET-43) is also gratefully acknowledged.

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Hippel, AV. Dielectric Material and Applications; Technology Press books in Science and Technology; John Wiley & Sons: New York, 1954, Vol. 1, pp 3-40. Babbitt, R; Koscica, T; Drach, W; Didomenico, L. Integrated Ferroelectrics, 1995, 8, 65-76. Zimmermang, F; Voigts, M; Weil, C; Jakoby, R; Wang, P; Menesklou, W; Ivers-Tiffée, E. J Eur Ceram Soc., 2001, 21, 2019-2023. Treece, RE; Thompson, JB; Mueller, CH; Rivkin, T; Cromar, MW. IEEE Trans Appl Supercond, 1997, 7 2363-2366. Grigas, J. Microwave Dielectric Spectroscopy of Ferroelectrics and Related Materials; Ferroelectricity and Related Phenomena Series; Gordon and Breach Publisher: Amsterdam, 1996, Vol. 9, pp 9-108. Bassora, LA; Eiras, JA. Ferroelectrics, 1999, 223, 285-292. Haraoubia, B; Meury, JL; LeTraon, A. J Phys E, 1988, 21, 456-460. Mouhsen, A; Achour, ME; Miane, JL; Ravez, J. Eur Phys J Appl Phys, 2001, 15, 97-104. Muller, KA; Burkard, H. Phys Rev B, 1979, 19, 3593-3602. Viana, R; Lunkenheimer, P; Hemberger, J; Böhmer, R; Loidl, A. Phys Rev B, 1994, 50, 601-604. Venturini, EL; Sâmara, GA; Kleemann, W. Phys Rev B, 2003, 67, 214102. Bassora, LA. Caracterização dielétrica de materiais ferroelétricos na região de microondas, Ph. D. Thesis, Federal University of São Carlos, São Paulo, Brazil, 1999, pp 10-90. Böhmer, R; Maglione, M; Lunkenheimer, P; Loidl, A. J Appl Phys, 1989, 65, 901-904. Poplavko, YM; Tsykalov, VG; Molchanov, VI. Sov Phys Solid State, 1969, 10, 2708-2710. Kamba, S; Bovtun, V; Petzelt, J; Rychetsky, I; Mizaras, R; Brilingas, A; Banys, J; Grigas, J; Kosec, M. J Phys Condens Matter, 2000, 12, 497-519. Lente, MH; Guerra, JDS; Eiras, JA; Lanfredi, S. Solid State Commun, 2004, 131, 279282.

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[17] Lente, MH; Guerra, JDS; Eiras, JA; Mazon, T; Andreeta, MBR; Hernandes, AC. J Eur Ceram Soc, 2005, 25, 2563-2566. [18] Cao, WW; Cross, LE. Phys Rev B, 1991, 44, 5-12. [19] Glazounov, AE; Tagantsev, AK. J Phys Condens Matter, 1998, 10, 8863-8880. [20] Arlt, G; Böttger, U; Witte, S. Appl Phys Lett, 1993, 63, 602-xxx. [21] Hippel, AV. Rev Mod Phys, 1950, 22, 221-237. [22] McNeal, MP; Jang, SJ; Newnham, RE. J Appl Phys, 1998, 83, 3288-3297. [23] Zhang, L; Zhong, WL; Wang, CL; Zhang, PL; Wang, YG. Solid State Commun, 1998, 107, 769-773. [24] Maglione, M; Böhmer, R; Loidl, A; Höchli, UT. Phys Rev B, 1989, 40, 11441-11444. [25] Kazaoui, S; Ravez, J; Miane, JL. J Non-Cryst Sol, 1991, 131, 1202-1205. [26] Guerra, JDS; Lente, MH; Eiras, JA. Appl Phys Lett, 2006, 88, 102905. [27] Kersten, O; Rost, A; Schimidt, G. Phys Stat Sol (a), 1983, 75, 495-500. [28] Hippel, AVZ. Physik, 1952, 133, 158-173. [29] Kittel, C. Phys Rev., 1951, 83, 458-458. [30] Turik, AV; Shevchenko, NB. Phys Stat Sol (b), 1979, 95, 585-592. [31] Tappe, S; Böttger, U; Waser, R. Appl Phys Lett, 2004, 85, 624-626. [32] Jiang, GQ; Wong, WH; Raskovich, EY; Clark, WG. Rev Sci Instrum, 1993, 64, 1614-1621. [33] Jiang, GQ; Wong, WH; Raskovich, EY; Clark, WG. Rev Sci Instrum, 1993, 64, 1622-1626. [34] Jonscher, AK. J Phys D Appl Phys, 1999, 32, 57-70. [35] Kazaoui, S; Ravez, J; Elissalde, C; Maglione, M. Ferroelectrics, 1992, 135, 85-99. [36] Petzelt, J; Ostapchuk, T; Gregora, I; Rychetsky, I; Hoffmann-Eifert, S; Pronin, AV; Yuzyuk, Y; Gorshunov, BP; Kamba, S; Bovtun, V; Pokorny, J; Savinov, M; Porokhonskyy, V; Rafaja, D; Vanek, P; Almeida, A; Chaves, MR; Volkov, AA; Dressel, M; Waser, R. Phys Rev B, 2001, 64, 184111. [37] Böttger, U; Arlt, G. Ferroelectrics, 1992, 127, 95-100. [38] Arlt, G; Pertsev, NA. J Appl Phys, 1991, 70, 2283-2289. [39] Garcia, MF; M’Peko, JC; Ruiz, AR; Rodríguez, G; Echevarría, Y; Fernández, F; Delgado, A. J Chem Educ, 2003, 80, 1062-1073. [40] Barsoukov, E; Macdonald, JR. Impedance Spectroscopy: Theory, Experiment, and Applications; John Wiley & Son,s: New Jersey, 2005; Vol. 1, pp 27-42. [41] Baskaran, N; Ghule, A; Bhongale, C; Murugan, R; Chan, H. J Appl Phys, 2002, 91, 10038-10043. [42] Zalar, B; Laguta, VV; Blinc, R. Phys Rev Lett., 2003, 90, 037601. [43] Hornebecq, V; Elissalde, C; Porokhonskyy, V; Bovtun, V; Petzelt, J; Gregora, I; Maglione, M; Ravez, J. J Phys Chem Sol, 2003, 64, 471-476. [44] Ravez, J. Chemistry, 2000, 3, 267-283. [45] Feynman, RP; Leighton, RB; Sands, ML. The Feynman Lectures on Physics; Commemorative Issue; Addison-Wesley Publishing Co: Redwood, 1989, Vol. 2. [46] Tagantsev, AK; Glazounov, AE. Phys Rev B, 1998, 57, 18-21. [47] Bolten, D; Böttger, U; Waser, R. J Eur Ceram., Soc, 2004, 24, 725-732. [48] Fousek, J; Brezina, B. J Phys Soc Jpn, 1964, 19, 830-838. [49] Robels, U; Arlt, G. J Appl Phys, 1993, 73, 3454-3460. [50] Lu, W; Fang, D. N; Li, CQ; Hwang, KC. Acta Mater, 1999, 47, 2913-2926.

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Hwang, SC; Waser, R. Acta Mater, 2000, 48, 3271-3282. Aizu, K. J Phys Soc Jpn, 1969, 27, 387-396. Abplanalp, M; Fousek, J; Günter, P. Phys Rev Lett, 2001, 86, 5799-5802. Hwang, SC; Lynch, CS; McMeeking, RM. Acta Metall Mater, 1995, 43, 2073-2084. Hwang, SC; Huber, JE; McMeeking, RM; Fleck, NA. J Appl Phys, 1998, 84, 1530-1540. [56] Wooster, WA; Wooster, N. Nature, 1946, 157, 405-406. [57] Nye, JF. Physical Properties of Crystals: Their Representation by Tensors and Matrices; Oxford University Press: New York, 1985; Vol. 1, pp 3-168. [58] Nowick, AS; Berry, BS. Anelastic Relaxation in Crystalline Solids; Materials Science Series; Academic Press: New York, 1972; Vol. 1, pp 156-224.

In: Applied Physics in the 21st Century… Editor: Raymond P. Valencia, pp. 195-216

ISBN: 978-1-60876-074-9 © 2010 Nova Science Publishers, Inc.

Chapter 5

THE PRINCIPLE THAT GENERATES CONFIGURATION IN ANIMATE AND INANIMATE SYSTEMS – A UNIFIED VIEW Antonio F. Miguel Geophysics Centre of Evora, Rua Romão Ramalho 59, 7000-671 Evora, Portugal Department of Physics, University of Evora, PO Box 94, 7002-554 Evora, Portugal

ABSTRACT The generation of flow configuration (shape, structure, patterns) is a phenomenon that occurs across the board, in animate and inanimate flow systems. Scientists have struggled to understand the origins of this phenomenon. What determines the geometry of natural flow systems? Is geometry a characteristic of natural flow systems? Are they following the rule of any law? Here we show that the emergence of configuration in animate flow systems is analogous to the emergence of configuration in inanimate flow systems, and that features can be put on a unifying theoretical (physics) basis, which is provided by the constructal law. All scientific endeavors are based on the existence of universality, which manifests itself in diverse ways. Here we also explore the idea that complex flow systems with similar functions have a propensity to exhibit similar behavior. Based on this thought relationships that characterize animate systems are tested in relation to cities and countries, and some conclusions are drawn.

1. NATURE'S SHAPES From the ancient time people have struggled to explain why animals, plants, rivers, etc., are shaped the way we find it. Democritus (460-370 B.C.) attributed natural configuration (shape, structure, patterns) to "chance and necessity." [1]. Aristotle (384-322 B.C.) claims that shape is more truly than matter. He wrote: “Into what then does it grow? Not into that from which it arose but into that to which it tends. The shape then is nature” [2]. In other words, nature is the shape of a fully matured natural object. Therefore, we should understand not

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only matter but especially the shape. He exemplifies “as the teeth, for example, grow by necessity, the front ones sharp, adapted for dividing, and the grinders flat, and serviceable for masticating the food”. In 1860 Ralph Waldo Emerson (1803-1882) published the essay entitled "The Conduct of Life". He wrote [3] "Nature has her own best mode of doing each thing, and She has somewhere told it plainly, if we will keep our eyes and ears open." In Kant's (1724-1804) book entitled "Critique of Judgment " he argues that “the forms of nature are so manifold (…) that there must be laws for these forms (...), if they are to be called laws (as the concept of nature requires), they must be regarded as necessary virtue of a principle of the unity of the manifold” [4]. It has been more than 250 years since Pierre de Maupertuis (1698-1759) wrote "(…) laws of movement and of rest deduced from this principle being precisely the same as those observed in nature, we can admire the application of it to all phenomena. The movement of animals, the vegetative growth of plants ... are only its consequences; and the spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements. (…)" [5]. This “principle” - the “principle of least action” [6] – was properly stated later by scientists like William Hamilton. It came from his idea that the very perfection of the universe demands a certain economy in nature and is opposed to any needless expenditure of energy. In spite of having a wide applicability in mechanics, electricity, magnetism and quantum mechanics, this principle only accounts for point-to-point motion but cannot describe point-to-area and point-to-volume flows [6]. In 1776, Jean Meusnier's study of soap films (very popular among mathematicians of eighteen century) showed an example in geometric optimization [7]. An ordinary twodimensional plane can be twisted infinitely into a helicoid shape (minimal surface) that has the delicate balance of a soap film. Forty years later, Robert Stirling (1790-1878) patented his “Heat Economiser” and Sadi Carnot (1796-1832) wrote about the ideal configuration of a heat engine. Charles Darwin (1809–1882) busied himself with the idea that the configuration of living systems is determined by evolution and natural selection [8]. Josiah Willard Gibbs (1839-1903) in the late 19th century refers that a thermodynamic system to be in an equilibrium state it will configure its components by minimizing the energy. In 1917, D'Arcy Wentworth Thompson (1860-1948) published the book “On Growth and Form”. Thompson introduced the idea that they are principles among quite diverse forms of life. From the observation that the bones of a museum skeleton would lie in a heap on the floor without the clamps and rods pulling them together, he concluded that the tension holds the skeleton together as much as weight does. He wrote that "the form of any particle of matter, whether it be living or dead, and the changes in form which are apparent in its movements and in its growth, may in all cases be described as due to the action of force" [9]. Forces of tension, compression and shear occurred in all living structures and influenced both growth and function. Eighty later, Helbing and Molnar [10] use the concept of “force” to explain the motion of pedestrians (the so-called “social forces model”). In 1975, Benoit Mandelbrot introduced the term fractal and wrote “(…) a fractal is a shape made of parts similar to the whole in some way (…).” [11]. Fractal based description of natural systems has been widely applied. In spite of its incontestable importance, fractals do not account for dynamics hence are descriptive rather than predictive. Natural flow systems are complex and change (evolve) in many ways. Why things in nature are shaped the way they are? Why do tree-shaped designs occur in river basins, deltas,

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lightning and lungs? Is it an optimized behavior? Why stony corals and bacterial colonies present intraspecific variability of patterns? What are the “forces” that shape their growth and form? Adrian Bejan is at the origin of the constructal paradigm, which had its start in 1996 [1214]. He arrived at this idea from a problem of minimizing the thermal resistance between an entire heat generating volume and one point [13]. The occurrence of configuration in nature is a physics phenomenon, and the constructal theory is about the physics principle from which configuration can be deduced. It is based on the following law (constructal law): “For a finitesize system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed (global) currents that flow through it.” [13]. This law states that there is a time arrow “associated with the sequence of flow configurations that constitutes the existence of the system”[14,15] (Figure 1). Besides, the system shape and structure do not develop by chance but result from the permanent struggle for better performance. Better performance means minimization and balance of the resistances (i.e., imperfection) faced by the various internal and external streams under the existing constraints. The morphim structure is the result of optimal distribution of imperfection.

Figure 1. Time arrow in plant growth [18]

Configuration plays a fundamental role in models used for “perceiving” and “understanding” nature. Here, it is shown how the constructal theory provides a unifying picture for the development of flow architectures in natural systems with internal flows. We also show that the complexity is optimized and is a result of the optimization process.

2. THE CONSTRUCTAL LAW A flow system (animate and inanimate) is a nonequilibrium thermodynamic system [1315]. Classical thermodynamics is not concerned with the configurations of its nonequilibrium systems. Basically, the first law of thermodynamics is a statement of the conservation of energy, the second law is a statement about the direction of that conservation (i.e., the

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maximization of entropy generation in an isolated system), and the third law is a statement about reaching absolute zero. The constructal law is a law of thermodynamics distinct of these three [16]. Likewise the second law it contains an arrow of time but of different things. The second law proclaims the entropy of a closed system always increases in time up to an equilibrium state. The constructal law states that the flow architecture morphs in time in the direction of flowing more easily (i.e., the maximization of flow access). The analogy between the formalism of equilibrium thermodynamics and that of constructal theory is presented by [16,17]. Constructal theory begins with the global objective(s) and the global constraint(s) of the flow system [12-17]. There are two global constraints, one external and the other internal: the external constraint is the system size, and the internal global constraint is the "amount" invested in making the flow architecture (e.g., total volume of all the ducts of the flow structure). How do we identify the configuration that brings flow architecture to the best performance? According with constructal law, the architecture of the system must “provides easier access to the imposed (global) currents that flow through it.” [13]. Consider, for example, the case of a fluid that has to be drained from a finite-size area or volume. The volume is a nonhomogeneous porous medium composed of a material of low permeability (high resistance) and various layers of higher permeabilities. The goal is the optimal arrangement of these layers such that the global flow resistance is minimal. The global constraints are the system size (area or volume to be drained) and the total size occupied by the layers. Based on this, the arrangement is optimized in order to reach maximum performance. In this way, the designer “constructs” the optimal flow architecture. A detailed description is provided by [13,14]. The acquisition of shape (architecture) is an evolutionary process not assumed in advance or postulated. Therefore, the flow architecture (shape) of the system is the result of the optimum balance between two competing trends – slow (high resistivity) and fast (low resistivity). If we increase the length of high permeability layer leads to a decrease in the resistance posed to flow in the area (volume) occupied by low permeability layers, but it also increases the resistance along the high permeability layer. Therefore, flow optimization is as a trade-off between competing trends [13-16]. This example is not unique. Behind a broad class of processes in the natural sciences is the dynamics that combines, for example, Brownian motion (diffusion) with some form of deterministic drift (convection). Here we shall consider a convection–diffusion equation of the general form

∂n + ∇.(Un ) = D∇ 2 n ∂t

(1)

where n denotes the density, U is the velocity and D is the diffusion coefficient. The spreading of a tracer or a solute, and the transport of heat or fluid are examples that can be analyzed within the framework of diffusive-convective phenomena. Diffusion is associated with a high resistivity mechanism, whereas convection is low resistivity. Why the flow architecture of systems results of the balance between both mechanisms? By applying scale analysis [13] to Eq. (1), we obtain the time scales for diffusion (tdf) and convection (tcv)

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t df ~

L2 D

(2)

t cv ~

L u

(3)

Diffusion coefficients are usually much smaller than 1 m2 s-1 (for example, the diffusion coefficient for oxygen in air is approximately 2 × 10-5 m2 s-1). For very short distances tdf < tcv and diffusion is the “best” driving mechanism because is “faster”. On the other hand, for larger distances tdf > tcv and convection perform better. The time of transition from diffusion to organized flow is t* ~ D/u2. This simple analysis shows us that the two modes of flowing with imperfection (resistance) should exist in order to enable the best flow architecture. In summary, optimization means finding the best allocation of resistances (i.e., minimum imperfection to the global flow architecture), and therefore the configuration of the system is the one that allows best flow access. To make our point, we illustrate next the application of the constructal law to a variety of animate and inanimate flow systems.

3. CONSTRUCTAL THEORY OF INANIMATE NATURAL FLOW SYSTEMS The phenomenon of generation of flow configuration is everywhere in inanimate flow systems. Agglomerates of aerosol particles often have dendritic shapes instead of spherical shapes [18]. The reason why this occurs was not clear. Reis et al. [19] relied on the constructal law of maximization of flow access in order to construct a theory of aerosol agglomeration. Based on the idea that there are not electrically neutral surfaces in contact with air [18,19], it is assumed that the forces that make aerosol particles stick onto previously deposited particles are of the electrical type. There are two possible “modes” of agglomeration: spherical and conically. The volume of spherical agglomerates is given by

Vsph ~ K 2 t 2

(4)

while the volume of agglomerates of particles with the conical shape is 1/ 2

Vcon

⎛ q el K14 / 3 ⎞ ⎟⎟ ~ ⎜⎜ μ el ⎝ ⎠

t7 / 3

(5)

where μel is the dipole moment, qel is the charge and K is a quantity function of particle size, dipole moment, electric charge, Cunningham correction factor, electric permittivity of the air, surface density of charge and air viscosity [18]. The constructal law is simply about the physics meaning of the time direction of configuration evolution. Therefore, the architecture of the aggregate of particles evolves in time in such a way that the global rate of accumulation of the particles is maximized. In other words, the best configuration is the one that bring the entire flow system (ambient and particles) to equilibrium in the fastest way possible.

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Figure 2. Time evolution of the volume corresponding to conical and spherical agglomerates

The temporal evolution of the accumulation volume is presented in Figure 2. This plot shows that at the critical time, tct, the volume of conical agglomerates overtakes the volume of spherical agglomerates. According to Eqs. (4) and (5) 1/ 3

⎛ μ ⎞ t ct ~ ⎜⎜ 1 / 2 el 1 / 3 ⎟⎟ ⎝ q el el K ⎠

(6)

This means that the agglomerate must first grow as a sphere (t < tct) and then change to a conical shape. Existing flow configuration (spherical) is replaced by a configuration (conical, tree-shaped) that flow more easily. Experimental measurements reported in the literature confirm the main features of this constructal development [18]. The constructal law also predicted configuration generation during liquid droplet impact on a wall [20]. For small and slow enough droplets the splat comes to rest viscously, as a disk. On the other hand, for large and fast enough droplets, it splashes by developing needles that grow radially until they are arrested by viscous effects. Based on constructal theory, Bejan and Gobin [20] gave comprehensive explanation of configuration generation and also present a dimensionless group that governs the selection of geometry. This group is defined by the ratio of two lengths, the final radius of the disc that dies viscously, divided by the radius of the still inviscid ring that just wrinkles. The results of the optimization process match the observed values. A river basin is the portion of land drained by a river and its tributaries. It encompasses the entire land surface dissected and drained by many streams and creeks that flow downhill into one another, and eventually into one river. The final destination is an estuary or an ocean. A river basin is an example of an area-to-point flow. Based on constructal law, Bejan [13] has addressed this problem and optimized the channel network that minimizes the overall resistance (imperfection) to flow. Consider the area allocated to each smallest stream of the river basin. Rain falls uniformly on the elemental area with a mass flow rate. There is an optimal elemental shape defined as the ratio between the length and width such that the total flow rate collected on the elemental area flows with least global flow resistance from the area through one point on its periphery. The optimized area element becomes a building block with which larger rain plains can be covered. The tree-shaped flow architecture of the river

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basin represents the best allocation of resistances (optimal distribution of imperfection), and therefore the configuration of the system that allows best flow access from the area to the outlet [13,18]. The flow architectures of river basins are not the result of change but they constitute the optimal configuration. River basins have geometrical features which can be measured, namely the area (measured on the vertical projection), the elongation ratio (the diameter of a circle with the same area as the drainage basin, divided by the basin maximum length), the relief (the difference of elevation between the highest and the lowest points of the drainage area) and the relief ratio (the basin relief divided by the maximum length of the basin). Based on experimental data of geometric characteristics, authors proposed several allometric scaling laws to describe feature of river basins [18]. The well known Horton, Melton and Hack allometric laws can be anticipated based on constructal law as a result of minimization of the overall resistance to flow. Reis [21] shows that the: (i) ratio of constructal lengths of consecutive streams matches Horton's law for the same ratio, while the same occurs with the number of consecutive streams that match the respective Horton's law; (ii) Hack’s scaling law is also anticipated from the constructal law and the exponent β that relates the length of mainstream, Ls, and the basin area, Ab, (Ls~Abβ, β~0.568) presented in a more accurate way (i.e., β=2τ+1/4τ, where τ is the order of the river basin); and Melton's scaling exponent is 2.45 instead of 2. Reis and Gama [22] relied also on the constructal law of maximization of flow access in order to address beachface adjustment as a response to wave swash forcing. They showed that beachface slope varies with wave height raised to the power 3/4, and sand grain size raised to the power 4/3. The largest flow system on earth (atmosphere circulation) was studied from the point of view of the constructal theory [23,24]. The sun–earth–universe assembly was viewed as a power plant the power output of which is used to force the atmosphere and hydrosphere to flow. The constructal optimization was performed in order to deliver the latitude of the boundary between the Haddley and the Ferrel cells, the boundary between the Ferrel and the Polar cells, the average temperature of the Earth surface, the convective conductance in the horizontal direction, as well as other parameters defining the circulation and the Earth surface temperature. The results of this optimization agree very well with the observed values. These results and many other examples show that the constructal law explains much of shape and structure of inanimate flow systems around us. The cracks patterns evolution during shrinking in soil [13,25], the dendritic crystals formed during rapid solidification [13], the turbulent flow structure [13], Rayleigh-Bénard convection [13], and the electrokinetic transfer through porous media [26] may also be mentioned here among other examples.

4. CONSTRUCTAL VIEW OF ANIMATE FLOW SYSTEMS Animate systems are probably the most complex and diverse system in the universe. The so-called “life” covers more than 27 orders of magnitude in mass from molecules of the genetic code to whales and sequoias [27]. To help understand the underlying configuration (architecture) behind animate systems, three different views (concepts) are employed:

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Antonio F. Miguel (i) An animate system is made up of interacting subsystems that provide a key functional characteristic of the overall system. Subsystems such as the circulatory system, lungs, kidneys, etc. provide a function that is essential to sustain the all system. (ii) Colonies of living organisms (e.g., stony corals and bacterial colonies) refers to several individual organisms of the same species living all time closely together for mutual benefit. (iii) Living organisms that are temporally together as an ongoing group to collectively accomplish a particular purpose (e.g. pedestrians accessing shopping facilities or a stadium).

Systems at these levels of organization demonstrate the complementary nature of structure and function. Therefore, the design of animate systems is not only a matter of molecular biology but also of geometry and physics. To make our point, we review a collection of studies based on constructal theory that explain in a simple manner the configuration that occurs in (i), (ii) and (iii).

4.1. Systems View An animate system is made up of interacting subsystems. Each subsystem provides a key functional characteristic of the overall system. Are they optimized as a whole? Are the subsystems also optimized? The respiratory subsystem was assessed via the constructal principle by Reis et al. [28] and Reis and Miguel [29], with the structure of the respiratory system being the result of this appraisal. The primary function of the respiratory system is the supply of oxygen to the blood and the drainage of carbon dioxide from it, so these in turn delivers oxygen to and remove carbon dioxide from all parts of the body. There are two alternatives for accomplishing this purpose: the lung could be a duct system, or a simple single sac (volume) open to the external air from which the oxygen diffuses to the blood (and carbon dioxide diffuses after being released from the blood). This second possibility is clearly noncompetitive as compared to a duct system: the former has a small access time for duct (convective) flow (Eq. 3) of order tcv ~ 1 s ( u ~ 0.5 m/s) whereas the latter has an access time for a diffusive process (Eq. 2) of order tdf ~ 104 s (L ~ 0.5 m and D ~2 x10-5 m2/s). On the other hand, both solutions have internal imperfections. A duct system has a large friction resistance to airflow whereas the single sac has a large diffusive resistance. Tree-shaped flow architectures are the easiest way to flow between infinity of points (volume, area) and one point or vice-versa [13]. However, a cavity (alveolar sac) at the end of the tree-shaped network should exist, because for very short distances diffusion is the “best” driving mechanism (Section 2) and allows easy oxygenation of the blood from air to the tissues. What are the characteristics of lung configuration to provide the easiest access for blood to oxygen/carbon dioxide? According to the constructal principle, lung configuration must provide the easiest access for blood to oxygen/carbon dioxide under the constraints posed by the space allocated to the respiratory process (chest cavity). Reis et al. [28] and Reis and Miguel [29] show that the configuration that performs these functions at the lowest flow resistance is a tree-shaped flow structure composed of ducts with 23 levels of bifurcation that ends with alveolar sacs from

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which oxygen diffuses into the tissues. In summary, lung configuration results of the trade-off between two competing trends. The configuration that performs best is the one that results of the “harmony” of the best allocation of resistances to allow the best flow access and not from the smash of any of the competing trends. In these studies [28,29], the dimensions of the alveolar sac, the total length of the airways, the total alveolar surface area and the total resistance to oxygen transport in the respiratory tree were also obtained. One of the most remarkable findings was that there is a length defined by the ratio of the square of the first airway diameter to its length which is constant for all individuals of the same species. Kidneys, vascularised tissues and the nervous system are also examples of optimized architectures that have been treated from the point of view of constructal theory [13,16,30]. It’s not only the subsystems that composed the animate systems that are optimized but also the whole system. In the 1940s, Max Kleiber [31] and Samuel Brody [32], based on observation of mammals and birds, established for the first time that the interspecies correlation of metabolic rate scales as 3/4 power of the body mass. Kleiber's and Brody’s works were generalized by subsequent researchers to intracellular levels, unicellular organisms, and plants, and an exponent of 3/4 is found over 27 orders of magnitude [33]. A direct explanation for the 3/4 scaling power between metabolic rate and body mass can be obtained based on constructal theory. The explanation presented by Bejan [34] was obtained by combining the tree architecture optimized for minimum pumping power and the convective heat transfer characteristics of two identical fluid trees superimposed in counterflow. Constructal theory also anticipates other important empirical allometric laws. A direct explanation for the 1/4 scaling power between breathing or heart beating time and body mass was obtained from the minimization of the pumping power required by the thorax for breathing and the heart for blood circulation. This allometric law derived in [35] is based on the following realistic assumption: the flow is intermittent (in and out) and “in” interval is of the same order of magnitude as the “out” interval. Moreover, Bejan [35] also proved that the heartbeat and the breathing time must be of the same order of magnitude, regardless of body size. The allometric laws of the design of the hair coats of animals are also projected by the constructal theory. By minimizing the combined heat loss by conduction and radiation through the hair air coat, the proportionality between the hair strand diameter and the animal body length scale raised to the power of 1/2 , and the hair coats porosity between 0.95 and 0.99 for all animal sizes were obtained [13,36]. Flow configuration (patterns) is generated in space but also in time. The modes of locomotion (flying, running, swimming) are examples that illustrate the generation of patterns in time. Bejan [13] and Bejan and Marden [37,38] showed that the constructal law (a single law) is able to describe the different modes of locomotion. Flying, running and swimming were attributed to the same principle of configuration generation for greater flow access in time (constructal law) [37,38]. Flying, for example, involves two losses. One loss is the lifting of the body weight (vertical loss due to the gravity) and the other is the horizontal loss due to drag. The total loss per distance travelled is the summation of both losses, i.e.,

Mg 3 / 2 h1 / 2 v −1 + C Dρair v 2 L2b , where M is the body mass , v is the velocity, ρair is the air density, CD is the drag coefficient, h is the vertical distance and Lb is the characteristic

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dimension of the body. The optimal flying speed is obtained by minimizing the total loss, which is provided by the constructal law. Therefore, the flying speed scales as 1/6 power of the body mass and flapping frequencies are proportional to the body mass raised to the power −1/6. These results constitute allometric laws for flying and they are in good agreement with the speeds of flying organisms ranging from the insects to the big birds. The minimization of horizontal (friction) and vertical (gravity) losses is also at origin of running and swimming. More details are provided by [37,38]. Recently, Charles and Bejan [39] collected the heights and weights of the fastest swimmers (100 m-freestyle) and sprinters (100 m-dash) for world record winners, since the beginning of the twentieth century. They then plotted the speed data (based on wining times) versus the size of these athletes. The scaling analyze showed that speed records will continue to be dominated by heavier and taller athletes. According to [39], this tendency is attributable to the scaling rules of animal locomotion [37,38], “not to the contemporary increase in the average body size of humans” [39]. The authors also suggest that if athletes of all sizes are to compete in these kinds of events, weight classes might be needed, like in certain sports, such as judo, boxing, weightlifting or wrestling. The constructal theory was applied to the design of animals but also to predict the morphology of plants. Bejan and co-authors [40] showed, among other things, that the tree length is proportional to the wood mass raised to the power 1/3, the tapered shape of the root and longitudinally uniform diameter and density of internal flow tubes, the near-conical shape of tree trunks and branches, and the existence of an optimal ratio of leaf volume divided by total tree volume. In summary, animate systems are optimized flow architectures. Besides, allometric laws can be viewed as a manifestation of the underlying dynamics that is optimized, and can be anticipated by the constructal theory.

4.2. Colonies of Living Organisms A colony refers to several individual organisms of the same species living closely together, usually for mutual benefit (e.g., formation of colonies helps escaping predators or enhance the ability to locate nutrients) despite some detrimental effects such as getting infected more easily by contagious disease [27]. The formation of dissimilar patterns inside similar colonies under different environmental conditions is especially intriguing. It seems that there is an order underlying the apparent variety of shapes. Several authors noticed that for a given set of growth conditions, the colonies experience similar patterns that can be reproduced from the experimental point of view [40-42]. The shape of bacterial colonies depends both on the nutrient level and gel (environment) hardness [41,42]. Bacterial colonies that cope with hostile environmental conditions (i.e., low level of nutrients or hard agar surface) develop branched forms. On the other hand, colonies that cope with high levels of nutrients develop a compact shape. Stony corals also consist of structure of tightly interconnected individuals (called polyps). These corals collected from exposed growth sites, where higher water currents are found, present more spherical and compact shape than corals of the same species growing in sheltered sites, which display a thin-branched patterns [43]. There are 2 questions that need to be answered: how colony

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development displays a precise control of the configuration? why colonies develop characteristic patterns? Increasing complexity is associated with an increased use of modulatory communication signals to organize cooperative behavior. These signals do not elicit specific responses in themselves, but rather operate in a general manner to alter the probability that individuals will respond to other stimuli [41,44-46]. Ants and other social insects, for example, usually have a pheromone produced by the endocrine system for marking trails to food [44]. Therefore, pattern formation requires modulatory communication signals (chemical signals, electrical impulses or other) between interconnected individuals. According to [41], communication is on the basis of configuration (pattern) formation in bacterial colonies. This answers our first question but the following question remains: what is the reason to switch to different patterns? The answer is delivered by the constructal law in Miguel [47] and Miguel and Bejan [48]. Bacterial colonies or stony corals may develop branched (tree shaped) or spherical shapes in a differentiated response to the variability of environmental conditions. Branched and round massive patterns have different abilities to fill the same space, and thus a different ability to harvest the nutrients that are available. According to the constructal theory, the survival of flow systems calls for patterns that promote flow access. The preferred pattern is the one that allows the living system to deplete the nutrients as fast as possible. Consider s to be the characteristic external length scale of the living system, and l the branch (needle) length scale width (l