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Engineering Materials and Processes

Series Editor

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Vitaly Yu. Topolov • Christopher R. Bowen

Electromechanical Properties in Composites Based on Ferroelectrics

123

Professor Vitaly Yu. Topolov Department of Physics Southern Federal University 5 Zorge street 344090 Rostov-on-Don Russia

Dr Christopher R. Bowen Department of Mechanical Engineering Faculty of Engineering and Design University of Bath Bath BA2 7AY United Kingdom

ISBN 978-1-84800-999-8 e-ISBN 978-1-84882-000-5

DOI 10.1007/978-1-84882-000-5

Engineering Materials and Processes ISSN 1619-0181

A catalogue record for this book is available from the British Library

Library of Congress Control Number: 2008934905

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PrefaceComposite material, also called Composite, a solid material that

results when two or more different substances, each with its own characteristics, are combined to create a new substance whose properties are superior to those of the original components in a specific application.

Encyclopædia Britannica 2006 Ultimate Reference Suite

... functional composites make use of a number of underlying ideas including connectivity patterns leading to field and force concentration; the use of periodicity and scale in resonant structures; the symmetry of composite structures and its influence on physical properties; polychromatic percolation and coupled conduction paths; varistor action and other interfacial effects; sum, combination, and product properties; coupled phase transformation phenomena; and the important role that porosity and inner composites play in composite materials. These ideas provide a basic understanding of functional composites and have been discussed previously.

R.E. Newnham

After the discoveries of piezoelectricity (1880) and ferroelectricity (1921), many attempts have been made to obtain new high-effective materials with predictable physical properties and to develop available technologies. Engineered composites based on ferroelectrics (i.e., composites with ferro-, piezo- and pyroelectric properties) have been manufactured and studied since the late 1970s. The 1980s and 1990s have been concerned with an active development of a previously untapped piezo-composite landscape in order to study interconnections between microstructure, composition and properties in novel piezo-active materials, especially those based on ferroelectrics that belong to so-called “smart materials”.

The modern piezo-composite landscape is a specific area of research and innovations, and research developments in this area depend on multi-disciplinary efforts of scientists and engineers, such as solid state physics, physics of ferroelectrics, solid-state chemistry, materials science, mechanics of heterogeneous media, mechanics of electro-elastic media, mechanical engineering, etc. On studying the area of piezo-composites, it becomes obvious that knowledge of these materials and prediction of their properties cannot be attained without the good physico-mathematical basis and understanding of principles of modern materials science and mechanical engineering.

To the best of our knowledge, there are few books concerned with the piezo-composites and their effective properties, and these problems were mainly considered in separate chapters or sections only. Earlier, two books devoted to methods for prediction of the effective electromechanical properties for some

viii Preface

connectivity patterns of the two-component piezo-composites were written in Russian and published in the USSR (Khoroshun LP, Maslov BP, Leshchenko PV, (1989) Prediction of Effective Properties of Piezo-active Composite Materials. Naukova Dumka, Kiev) and Russia (Sokolkin YuV, Pan’kov AA, (2003) Electroelasticity of Piezo-composites with Irregular Structures. Fizmatlit, Moscow). In such a situation the present book aims to fill a gap in piezoelectric materials science and be an international edition devoted to different groups of piezo-composites and their effective properties.

Our book is intended to discuss recent original theoretical and experimental results on effective electromechanical (piezoelectric, dielectric and elastic) properties in the piezo-composites based on ferroelectrics. For the last decades, single-crystal, bulk ceramic and thin-film ferroelectrics have found a number of applications as a result of their remarkable piezoelectric properties. Piezoelectricity as a physical phenomenon is concerned with an electromechanical interaction in acentric single crystals including ferroelectrics. Recent work performed in the rapidly growing field of smart materials demonstrates that both ferroelectricity and piezoelectricity represent an important link between solid-state science and engineering.

The effective electromechanical properties associated with a complicated distribution of both the electric and elastic fields in piezo-composite samples depend on a number of factors, such as microstructure, connectivity, chemical composition and volume fraction of components, poling conditions for ferroelectric components, etc. Of particular interest are the non-monotonic dependences of the effective electromechanical properties and related parameters on a series of factors, such as the shape, spatial distribution and volume fraction of inclusions, porosity of a matrix, and poling degree of ferroelectric components. Knowledge of the extreme points of the effective parameters is important for manufacturing the high-performance piezo-composites for their particular piezotechnical applications. The characterisation and evaluation of smart materials in general requires a solid basis for the description of interconnections in the well-known dependency triangle of “composition – structure – properties”. For the piezo-composites based on ferroelectrics, this triangle becomes intricate as a result of electromechanical coupling, complex interrelations between the internal mechanical (tensor) and electric (vector) fields and a dependence of the properties in ferroelectric components on domain structure, microstructure, heterophase states, and external fields. Moreover, even in ferroelectric single crystals pertaining to one structural type, the piezoelectric and dielectric properties measured in weak electric fields vary significantly.

The present book summarises and generalises a series of the authors’ works on the problem of prediction and non-monotonicity of the effective electromechanical properties in different two- and three-component composites based on the traditional ferroelectric ceramics and the newly available relaxor-ferroelectric single crystals. Therein we pay due attention to the analysis of interrelations between electromechanical constants of the components and to the description of different analytical schemes of averaging the properties of these materials having different connectivity and microgeometrical characteristics. Undoubtedly, this book is concerned with the important topic related to smart materials and

Preface ix

optimisation of their effective properties. The main aim of the book is to show not only the advantages of different methods for predicting the electromechanical properties and choosing the optimum components, but to demonstrate the non-trivial behaviour of specific composite architectures and their parameters that are valuable for transducer, sensor, actuator, hydroacoustic, and other applications.

This book has been written on the basis of the authors’ research results obtained at the Rostov State University (Russia, until December 2006), Southern Federal University (Russia, since December 2006), University of Bath (UK), and Karlsruhe Research Centre (Germany). The academic style of presentation of the results and the discussion about these results indicate that the book would be useful to engineers, postgraduate students, researchers, and lecturers working in the field of ferro-, piezoelectric and related materials, dealing with methods of mechanics of heterogeneous materials and with their different applications. This book will be of benefit to all specialists looking to understand the modelling and detailed behaviour of the electromechanical response of the piezo-composites and related smart materials. Some chapters and sections of the book could serve as a basis for a university course devoted to piezo-active materials and their properties. In this connection one can mention the well-known sentence “Knowledge itself is power” (F. Bacon). Based on our knowledge and experience, we hope that the 21st century, being called The Century of New Materials and Technologies, will favour the further fruitful development of the piezo-composite landscape and new scientific directions therein and in adjacent areas.

Rostov-on-Don, Russia Prof. Dr. Vitaly Yu. Topolov Bath, United Kingdom Dr. Christopher R. Bowen July 2008

Acknowledgements

The authors are grateful to Prof. Dr. A. V. Turik, Prof. Dr. A. E. Panich, Prof. Dr. V. G. Gavrilyachenko, Prof. Dr. A. A. Grekov, Dr. V. V. Eremkin, and Dr. V. G. Smotrakov (Southern Federal University, Russia), Prof. Dr. R. Stevens and Prof. Dr. A. Mileham (University of Bath, UK), Dr. S. A. Wilson (Cranfield University, UK), Prof. Dr. O. Kraft and Dr. M. Kamlah (Karlsruhe Research Centre, Germany), Dr. W. S. Kreher (Technical University of Dresden, Germany), Dr. H. Berger (University of Magdeburg, Germany), Prof. Dr. M. Lethiecq and Dr. F. Levassort (University of Tours, France), Prof. Dr. P. Bisegna (University of Rome “Tor Vergata”, Italy), Prof. Dr. H. L. W. Chan (The Hong Kong Polytechnic University, P.R. China), Prof. Dr. J. H. Huang (Feng Chia University, Taiwan, Republic of China), Prof. Dr. W. Cao (The Pennsylvania State University, USA), Prof. Dr. N. Kikuchi (The University of Michigan, USA), Prof. Dr. A. Safari and Dr. E. K. Akdogan (Rutgers – The State University of New Jersey, USA), Prof. Dr. E. C. N. Silva (University of São Paulo, Brazil), and Prof. Dr. J. S. Ono Fonseca (Federal University of Rio Grande do Sul, Brazil) for their interest in the research problems and for their interesting papers that have been cited in the book. Furthermore, the authors emphasise the vast geographic area wherein the piezo-composites are studied or manufactured for various applications. Dr. C. R. Bowen would also like to thank past supervisors including Prof. Dr. B. Derby (University of Manchester, UK), Prof. Dr. N. Claussen (Technical University of Hamburg-Harburg, Germany) and Prof. Dr. R. Stevens (University of Bath, UK).

Special thanks are extended to Prof. Dr. R. E. Newnham and his co-workers (The Pennsylvania State University, USA) for the pioneering work that stimulated research activity in the field of piezo-composites and other smart materials in the last decades. The authors express much thanks to Dr. A. Doyle and Mr. S. Rees (Springer London Ltd, UK) for their effective and timely co-operation in the field of editing and producing this book. The authors sincerely thank Mrs. P. Carruthers and Mr. D. Barker (University of Bath, UK) for the technical help and Mrs. D. Stern (Karlsruhe Research Centre, Germany) for the bibliographic help. Copyright permissions obtained from Prof. Dr. P. Bisegna (University of Rome “Tor Vergata”, Italy), Springer (www.springer.com), Elsevier (www.elsevier.com), IOP Publishing (www.iop.org), AIP (www.aip.org), Taylor & Francis

xii Acknowledgements

(www.informaworld.com), and Maney Publishing (www.maney.co.uk) are acknowledged with due attention and gratitude.

Finally, financial support that promoted the fruitful research collaboration and writing this book is acknowledged with many thanks. Hereupon gratefully and proudly the authors mention the timely and effective support from the Royal Society (London, UK), Karlsruhe Research Centre and Helmholtz Society (Eggenstein-Leopoldshafen, Germany), EPSRC (Swindon, UK), National Physical Laboratory, QinetiQ (UK), Great Western Research (GWR, UK), University of Rome “Tor Vergata” (Rome, Italy), Rostov State University, and Southern Federal University (Rostov-on-Don, Russia).

Contents

1 From Smart Materials to Piezo-composites.................................................... 1 1.1 Piezo-composites as an Important Group of Smart Materials.................... 1 1.1.1 Smart Materials .............................................................................. 1 1.1.2 Composites ..................................................................................... 1 1.1.3 Piezo-active Composites ................................................................ 2 1.2 Classification of Composite Materials ....................................................... 4 1.2.1 Connectivity ................................................................................... 4 1.2.2 Sizes and Shape .............................................................................. 4 1.2.3 Arrangement ................................................................................... 4 1.2.4 Classification, Connectivity Patterns and Specific Examples ........ 5 References........................................................................................................... 9

2 Effective Electromechanical Properties in Piezo-composites ...................... 11 2.1 Piezoelectric Medium and Its Properties ................................................. 11 2.2 Sum, Combination and Product Properties .............................................. 22 2.2.1 Sum Properties.............................................................................. 22 2.2.2 Combination Properties ................................................................ 22 2.2.3 Product Properties ........................................................................ 24 2.3 Methods for Evaluation of Effective Parameters ..................................... 25 2.4 Evolution of – Connectivity Patterns .................................................. 30 2.5 Modelling of Effective Properties in Piezo-composites with Planar Interfaces ............................................................................. 32 2.6 Connectivity – Links – Properties............................................................ 35 References......................................................................................................... 35

3 Non-monotonic Volume-fraction Dependences of Effective Properties in – Ceramic / Polymer Piezo-composites..................................................... 43

3.1 Composites with 2–2 Connectivity, Manufacturing and Applications.... 43 3.1.1 Effective Electromechanical Constants of 2–2 Composites......... 46 3.1.2 Examples of Volume-fraction Dependences Predicted for 2–2 Composites....................................................................... 48 3.2 Composites with 1–3 Connectivity, Manufacturing and Applications .... 52

xiv Contents

3.2.1 Examples of Volume-fraction Dependences Predicted for 1–3 Composites........................................................................ 54 3.2.2 Diagrams of Changes in Piezoelectric Properties Predicted for 1–3 Composites........................................................................ 57 3.2.3 Maxima of Squared Figures of Merit of 1–3 Composites............. 61 3.3 Composites with 0–3 Connectivity, Manufacturing and Applications.... 62 3.3.1 Modelling of the Effective Properties in 0–3 Composites with Spheroidal Inclusions............................................................ 63 3.3.2 Piezoelectric Properties in 0–3 Composites Based on PbTiO3-type Ceramics................................................... 65 3.3.3 0–3 Composites with a Hierarchy of Inclusions........................... 75 3.3.4 0–3 Composites with Planar Microgeometry................................ 82 3.4 Composites with 3–3 Connectivity, Increasing the Piezoelectric Sensitivity and Applications.................................................................... 85 3.5 Connectivity – Non-monotonic Behaviour – Manufacturing................... 92 References......................................................................................................... 93

4 Piezoelectric Response of Porous Ceramic and Composite Materials Based on (Pb, Zr)TiO3 .................................................................................. 101

4.1 Porous Materials, General Characteristic and Manufacturing ............... 101 4.2 Volume-fraction Dependences of Parameters of Porous Piezo-active Materials ........................................................................... 103 4.3 Model of the Modified Layered Composite: Application to Porous Materials ............................................................ 110 4.4 Comparison of Calculated and Experimental Results............................ 111 4.5 From 3–3 Connectivity to Porous Materials.......................................... 116 References .......................................................................................................118

5 Effective Properties in Novel Piezo-composites Based on Relaxor-ferroelectric Single Crystals .......................................................... 123 5.1 Relaxor-ferroelectric Solid Solutions and Engineering ......................... 123 5.2 0–3 Single Crystal / Ceramic Composites.............................................. 125

5.3 0–1–3 Single Crystal / Ceramic / Polymer Composites..........................132 5.4 1–3 Single Crystal / Ceramic Composites.............................................. 142 5.5 1–0–3 Single Crystal / Polymer Composites ..........................................150 5.6 High Performance in Wide Ranges........................................................ 154 References .......................................................................................................155

6 Comparison of Results on Two-component Piezo-composites .................. 159 6.1 The Pros and Cons of Different Methods .............................................. 159 6.2 0–3 Versus 2–2 or 1–3............................................................................ 160

6.3 Data on 1–3 Composites.........................................................................165 6.3.1 Composites with Cylindrical Ceramic Rods................................ 165 6.3.2 Composites with Parallelepiped-shaped Ceramic Rods...............168 6.3.3 Variational Bounds for Effective Properties in 1–3 Composites with Cylindrical Ceramic Rods.................... 171

Contents xv

6.3.4 Variational Bounds for Effective Properties in 1–3 Composites with Parallelepiped-shaped

Ceramic Rods................................................................................173 6.4 Data on 0–3 Composites .........................................................................175 References ....................................................................................................... 182

7 Conclusions.................................................................................................... 185 7.1 From Components to Effective Electromechanical Properties .............. 185 References ....................................................................................................... 186

Appendix Formulae for Effective Electromechanical Constants of 2–2 and 1–3 Piezo-composites ....................................................................... 187References .............................................................................................................189

List of Abbreviations.......................................................................................... 191

About the Authors .............................................................................................. 193

Index......................................................................................................................195