Fundamentals and applications of ultrasonic waves by j.david n cheeke 2002

fundamentals and applications (basic) of Ultrasonic waves by j.david n cheeke 2002 Viewed from one perspective, one can say that, like life itself, ultrasonicscame from the sea. On land the five senses of living beings (sight, hearing,touch, smell, and taste) play complementary roles. Two of these, sight andhearing, are essential for longrange interaction, while the other three haveessentially shortrange functionality. But things are different under water;sight loses all meaning as a longrange capability, as does indeed its technologicalcounterpart, radar. So, by default, sound waves carry out this longrangesensing under water. The most highly developed and intelligent formsof underwater life (e.g., whales and dolphins) over a time scale of millionsof years have perfected very sophisticated rangefinding, target identification,and communication systems using ultrasound. On the technology front,ultrasound also really started with the development of underwater transducersduring World War I. Water is a natural medium for the effectivetransmission of acoustic waves over large distances; and it is indeed, for thecase of transmission in opaque media, that ultrasound comes into its own.

Fundamentals and Applications of Ultrasonic Waves © 2002 by CRC Press LLC Fundamentals and Applications of Ultrasonic Waves By J David N Cheeke Physics Department Concordia University Montreal, Qc, Canada © 2002 by CRC Press LLC Cover Design: Polar diagram (log scale) for a circular radiator with radius/ wavelength of 10 (Diagram courtesy of Zhaogeng Xu.) Library of Congress Cataloging-in-Publication Data Cheeke, J David N Fundamentals and applications of ultrasonic waves / David Cheeke p.; cm (CRC series in pure and applied physics) Includes bibliographical references and index ISBN 0-8493-0130-0 (alk paper) Ultrasonic waves Ultrasonic waves–Industrial applications I Title II Series QC244 C47 2002 534.5′5 —dc21 2002018807 This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale Specific permission must be obtained in writing from CRC Press LLC for such copying Direct all inquiries to CRC Press LLC, 2000 N.W Corporate Blvd., Boca Raton, Florida 33431 Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe Visit the CRC Press Web site at www.crcpress.com © 2002 by CRC Press LLC No claim to original U.S Government works International Standard Book Number 0-8493-0130-0 Library of Congress Card Number 2002018807 Printed in the United States of America Printed on acid-free paper © 2002 by CRC Press LLC Preface This book grew out of a semester-long course on the principles and applications of ultrasonics for advanced undergraduate, graduate, and external students at Concordia University over the last 10 years Some of the material has also come from a 4hour short course, “Fundamentals of Ultrasonic Waves,” that the author has given at the annual IEEE International Ultrasonics Symposium for the last years for newcomers to the field In both cases, it was the author’s experience that despite the many excellent existing books on ultrasonics, none was entirely suitable for the context of either of these two courses One reason for this is that, except for a few specialized institutions, acoustics is no longer taught as a core subject at the university level This is in contrast to electricity and magnetism, where, in nearly every university-level institution, there are introductory (college), intermediate (mid- to senior-level undergraduate), and advanced (graduate) courses In acoustics the elementary level is covered by general courses on waves, and there are many excellent books aimed at the senior graduate (doctoral) level, most of which are cited in the references Paradoxically, there are precious few books that are suitable for the nonspecialized beginning graduate student or newcomers to the field For the few acoustics books of this nature, ultrasonics is only of secondary interest This situation provided the specific motivation for writing this book The end result is a book that addresses the advanced intermediate level, going well beyond the simple, general ideas on waves but stopping short of the full, detailed treatment of ultrasonic waves in anisotropic media The decision to limit the present discussion to isotropic media allows us to reduce the mathematical complexity considerably and put the emphasis on the simple physics involved in the relatively wide range of topics treated Another distinctive feature of the approach lies in putting considerable emphasis on applications, to give a concrete setting to newcomers to the field, and to show in simple terms what one can with ultrasonic waves Both of these © 2002 by CRC Press LLC features give the reader a solid foundation for working in the field or going on to higher-level treatises, whichever is appropriate The content of the book is suitable for use as a text for a one-semester course in ultrasonics at the advanced B.Sc or M.Sc level In this context it has been found that material for to weeks can be selected from the fundamental part (Chapters through 10), and material for applications can be selected from the remaining chapters The following sections are recommended for the semester-long fundamental part: 3.1, 3.2, 4.1, 4.2, 4.3, 4.5, 5.1, 5.2, 6.1, 6.3, 7.1, 7.3, 7.4, 8.1, 8.2, 9.1, 10.1, and 10.2 Many of the sections omitted from this list are more specialized and can be left for a second or subsequent reading, such as Sections 4.4, 8.3.1, and 10.5 For each of these chapters, a summary has been given at the end where the principal concepts have been reviewed Students should be urged to read these summaries to ensure that the concepts are well understood; if not, the appropriate section should be reread until comprehension has been achieved A number of questions/problems have also been included to assist in testing comprehension or in developing the ideas further There is more than adequate material in the remaining chapters to use the rest of the semester to study selected applications It has been the author’s practice to assign term papers or open-ended experimental/computational projects during this stage of the course In this connection, Chapters 11 and 12 have been provided as useful swing chapters to enable a transition from the more formal early text to the practical considerations of the applications chapters J David N Cheeke Physics Department Concordia University Montreal, Canada © 2002 by CRC Press LLC Acknowledgments It has been said that a writer never completes a book but instead abandons it This must have some truth in that, if nothing else, the publisher’s deadline puts an end to activities In any case, the completion of what has turned into a major project is in large part due to the presence of an enthusiastic support group, and it is a pleasure to thank them at this stage My graduate students over the last 10 years have been at the origin of much of the work, and I would particularly like to thank Martin Viens, Xing Li, Manas Dan, Steve Beaudin, Julien Banchet, Kevin Shannon, and Yuxing Zhang for many enjoyable working hours together Over the years, my close colleagues Cheng-Kuei Jen and Zuoqing Wang have joined me in many pleasant hours of discussion of acoustic paradoxes and interpretation of experimental results I would like to thank Camille Pacher for her help with the text, equations, and figures Zhaogeng Xu made a significant and muchappreciated contribution with the numerical calculations for many of the figures, including Figures 6.3, 6.4, 6.6 through 6.8, 7.5, 7.6, 8.3, 9.1, 9.3, 9.4, 10.3, 10.5, and 10.6 Joe Shin has made a constant and indispensable contribution, with his deep understanding of the psyche of computers, and I also thank him for bailing me out of trouble so many times Lastly, my wife Guerda has been a constant source of motivation and encouragement I wish to thank John Wiley & Sons for permission to use material from my chapter, “Acoustic Microscopy,” in the Wiley Encyclopedia of Electrical and Electronics Engineering, which makes up a large part of Chapter 14 I also thank the Canadian Journal of Physics for permission to use several paragraphs from my article, “Single-bubble sonoluminescence: bubble, bubble, toil and trouble” (Can J Phys., 75, 77, 1997), and the IEEE for permission to use several paragraphs from Viens, M et al., “Mass sensitivity of thin rod acoustic wave sensors” (IEEE Trans UFFC, 43, 852, 1996) I thank Larry Crum and EDP Sciences, Paris (Crum, L.A., J Phys Colloq., 40, 285, 1979), for their permission to use Larry’s magnificent photo of an imploding bubble in the preface This work was done during a sabbatical leave from the Faculty of Arts and Science of Concordia University, Montreal, and that support is gratefully acknowledged Finally, I would like to thank Nora Konopka, Helena Redshaw, Madeline Leigh, and Christine Andreasen of CRC Press for providing such a pleasant and efficient working environment during the processing of the manuscript © 2002 by CRC Press LLC The Author J David N Cheeke, Ph.D., received his bachelor’s and master’s degrees in engineering physics from the University of British Columbia, Vancouver, Canada, in 1959 and 1961, respectively, and his Ph.D in low temperature physics from Nottingham University, U.K., in 1965 He then joined the Low Temperature Laboratory, CNRS, Grenoble, France, and also served as professor of physics at the University of Grenoble In 1975, Dr Cheeke moved to the Université de Sherbrooke, Canada, where he set up an ultrasonics laboratory, specialized in physical acoustics, acoustic microscopy, and acoustic sensors In 1990, he joined the physics department at Concordia University, Montreal, where he is currently head of an ultrasonics laboratory He was chair of the department from 1992 to 2000 He has published more than 120 papers on various aspects of ultrasonics He is senior member of IEEE, a member of ASA, and an associate editor of IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control © 2002 by CRC Press LLC Contents Ultrasonics: An Overview 1.1 Introduction 1.2 Physical Acoustics 1.3 Low-Frequency Bulk Acoustic Wave (BAW) Applications 1.4 Surface Acoustic Waves (SAW) 1.5 Piezoelectric Materials 1.6 High-Power Ultrasonics 1.7 Medical Ultrasonics 1.8 Acousto-Optics 1.9 Underwater Acoustics and Seismology Introduction to Vibrations and Waves 2.1 Vibrations 2.1.1 Vibrational Energy 2.1.2 Exponential Solutions: Phasors 2.1.3 Damped Oscillations 2.1.4 Forced Oscillations 2.1.5 Phasors and Linear Superposition of Simple Harmonic Motion 2.1.6 Fourier Analysis 2.1.7 Nonperiodic Waves: Fourier Integral 2.2 Wave Motion 2.2.1 Harmonic Waves 2.2.2 Plane Waves in Three Dimensions 2.2.3 Dispersion, Group Velocity, and Wave Packets Summary Questions Bulk Waves in Fluids 3.1 One-Dimensional Theory of Fluids 3.1.1 Sound Velocity 3.1.2 Acoustic Impedance 3.1.3 Energy Density 3.1.4 Acoustic Intensity 3.2 Three-Dimensional Model 3.2.1 Acoustic Poynting Vector 3.2.2 Attenuation Summary Questions © 2002 by CRC Press LLC Introduction to the Theory of Elasticity 4.1 A Short Introduction to Tensors 4.2 Strain Tensor 4.3 Stress Tensor 4.4 Thermodynamics of Deformation 4.5 Hooke’s Law 4.6 Other Elastic Constants Summary Questions Bulk Acoustic Waves in Solids 5.1 One-Dimensional Model of Solids 5.2 Wave Equation in Three Dimensions 5.3 Material Properties Summary Questions Finite Beams, Radiation, Diffraction, and Scattering 6.1 Radiation 6.1.1 Point Source 6.1.2 Radiation from a Circular Piston 6.2 Scattering 6.2.1 The Cylinder 6.2.2 The Sphere 6.3 Focused Acoustic Waves 6.4 Radiation Pressure 6.5 Doppler Effect Summary Questions Refl ection and Transmission of Ultrasonic Waves at Interfaces 7.1 Introduction 7.2 Reflection and Transmission at Normal Incidence 7.2.1 Standing Waves 7.2.2 Reflection from a Layer 7.3 Oblique Incidence: Fluid-Fluid Interface 7.3.1 Symmetry Considerations 7.4 Fluid-Solid Interface 7.5 Solid-Solid Interface 7.5.1 Solid-Solid Interface: SH Modes 7.5.2 Reflection at a Free Solid Boundary Summary Questions © 2002 by CRC Press LLC 428 TABLE B.6 (continued ) Acoustic Properties of Liquids Liquid Carbon disulphide, CS2 at 25°C Carbon disulphide, CS2, 25°C, GHz Carbon tetrachloride, CCl4 , at 25°C Cesium at 28.5°C the melting point Chloro-benzene, C6H5Cl, at 22°C Chloro-benzene, C6H5Cl Chloroform, CHCl3 , at 25°C Cyclohexanol, C6H12O Cyclohexanone, C6H10O Diacetyl, C4H6O2 1, Dichloroisobutane C4H18Cl2 Diethyl ketone Dimethyl phthalate, C8H10O4 Dioxane Ethanol amide, C2H7NO, at 25°C Ethyl ether, C4H10O, at 25°C d-Fenchone Florosilicone oil, Dow FS-1265 Formamide, CH3NO Furfural, C5H4O2 Fluorinert FC-40 Fluorinert FC-70 Fluorinert FC-72 Fluorinert FC-75 Fluorinert FC-77 Fluorinert FC-104 Fluorinert FG-43 Fluoro-benzene, C6H5F, at 22°C © 2002 by CRC Press LLC 1.149 1.31 0.926 0.967 1.304 1.3 0.987 1.45 1.42 1.24 1.22 1.31 1.46 1.38 1.724 0.985 1.32 0.76 1.62 1.45 0.64 0.687 0.512 0.585 0.595 0.575 0.655 1.18 ∆V/∆ ∆T (m/s°°C) −2.7 −3.4 −3.4 −4.87 ρ 3 (10 kg/m ) ZL (MRayl) 1.26 1.221 1.594 1.88 1.106 1.1 1.49 0.962 0.948 0.99 1.14 0.813 1.2 1.033 1.018 0.713 0.94 1.448 1.65 1.48 1.82 1.442 1.432 1.47 1.4 1.391 1.222 1.39 1.07 1.758 1.425 1.755 0.7023 1.241 1.134 1.157 1.19 1.94 1.68 1.76 1.78 1.76 1.85 1.024 1.842 1.67 1.86 1.33 0.86 1.02 V 1.01 1.21 1.205 Loss, α ( Np/cm) 10.1 538 167 317 Fundamentals and Applications of Ultrasonic Waves CRC, M DR CRC, M M LB M CRC,M M M M M M M M CRC, M CRC, M M M M M 3m 3m 3m 3m 3m 3m 3m LB VL (10 m/s) M AS LB M CRC, M M CRC M M M M M Freon, TF Gallium at 30°C mp = 28.8°C (expands 3% when it freezes) Gasoline Glycerin - CH2OHCHOHCH2OH, at 25°C Glycol - 2,3 butylene Glycol - diethylene C4H10O3 Glycol - ethylene 1,2-ethanediol @ 25°C Glycol - ethylene Preston II Glycol - polyethylene 200 Glycol - polyethylene 400 Glycol - polypropylene (Polyglycol P-400) at 38°C Glycol - polypropylene (Polyglycol P-1200) at 38°C Glycol - polypropylene (Polyglycol E-200) at 29°C Glycol - tetraethylene C8H18O6 Glycol, triethylene, C6H14O4 Helium-4, liquid at 0.4 K Helium-4, liquid at K Helium-4, liquid at 4.2 K n-Hexane, C6H14, liquid at 30°C n-Hexanol, C6H14O Honey, Sue Bee Orange Hydrogen, liquid at 20 K Iodo-benzene, C6H5I, at 22°C Isopentane, C5H12 Kerosene Linalool Mercury at 25.0°C Mesityloxide, C6H16O Methylethylketone Methylene iodide Methyl napthalene, C11H10 Monochlorobenzene, C6H5Cl 0.716 2.87 1.25 1.904 1.48 1.58 1.658 1.59 1.62 1.62 1.3 1.3 1.57 1.58 1.61 0.238 0.227 0.183 1.103 1.3 2.03 1.19 1.104 0.992 1.324 1.4 1.45 1.31 1.21 0.98 1.51 1.27 −2.2 −2.1 −3.6 1.57 6.09 0.803 1.26 1.019 1.116 1.113 1.108 1.087 1.06 1.12 17.5 2.34 1.511 1.77 1.845 1.76 1.75 1.71 1.12 1.123 0.147 0.145 0.126 0.659 0.819 1.42 0.07 1.183 0.62 0.81 0.884 13.5 0.85 0.805 1.784 1.81 0.035 0.033 0.023 0.727 1.065 2.89 0.08 2.012 0.615 1.072 1.23 19.58 1.115 0.972 1.09 1.107 1.645 1.411 1.58 120 1.73 70 226 87 5.6 242 5.8 429 (continued) © 2002 by CRC Press LLC Appendix B AS DR M CRC M M CRC JA JA JA M M M M M DR DR DR 430 TABLE B.6 (continued ) Acoustic Properties of Liquids Liquid JA JA JA JA MH MH Morpholine, C4H9NO Neon, liquid at 27 K Nicotin, C10H14N2 , at 20°C Nitrobenzene, C6H6NO2 , at 25°C Nitrogen, N2 , liquid at 77 K Nitromethane CH3NC2 Oil - baby Oil - castor, C11H10O10 @ 25°C Oil - castor, @ 20.2°C @ 4.224 MHz Oil - corn Oil - diesel Oil - gravity fuel AA Oil - jojoba Oil - linseed Oil - linseed Oil - mineral, light Oil - mineral, heavy Oil - olive Oil - paraffin Oil - peanut Oil - SAE 20 Oil - SAE 30 Oil - silicon Dow 200, centistoke Oil - silicon Dow 200, 10 centistoke Oil - silicon Dow 200, 100 centistoke Oil - silicon Dow 200, 1000 centistoke Oil - silicon Dow 704 @ 79°F Oil - silicon Dow 705 @ 79°F © 2002 by CRC Press LLC 1.44 1.2 1.49 1.463 0.86 1.33 1.43 1.477 1.507 1.46 1.25 1.49 1.455 1.46 1.77 1.44 1.46 1.445 1.42 1.436 1.74 1.7 0.96 0.968 0.98 0.99 1.409 1.458 ∆V/∆ ∆T (m/s°°C) −3.6 −3.6 ρ 3 (10 kg/m ) ZL (MRayl) 1.2 1.01 1.2 0.8 1.13 0.821 0.969 0.942 0.922 1.442 0.72 1.505 1.756 0.68 1.504 1.17 1.431 1.42 1.34 0.99 1.17 0.94 0.922 0.825 0.843 0.918 0.835 0.914 0.87 0.88 0.818 0.94 0.968 0.972 1.02 1.15 1.472 1.24 1.37 1.63 1.19 1.23 1.32 1.86 1.31 1.51 1.5 0.74 0.91 0.95 0.96 1.437 1.68 Loss, α ( Np/cm) 23.1 13.8 10100 Fundamentals and Applications of Ultrasonic Waves M DR LB CRC, M DR M JA CRC, M GD JA M M MH JA M JA JA JA M JA M VL (10 m/s) M M M M M AS M M M CRC M M M CRC, DR © 2002 by CRC Press LLC 1.352 1.45 1.43 1.44 1.45 1.391.39 1.38 0.9 1.3 1.027 1.37 1.82 1.41 2.42 1.37 1.62 0.39 1.62 1.05 1.255 1.35 1.4 1.48 1.4967 1.509 1.55 1.47 1.53 1.6 1.531 0.63 0.879 1.32 2.4 2.4 1.11 0.9 0.93 0.88 0.92 0.92 1.6 1.11 1.5 1.3 1.32 1.268 1.34 1.28 1.6 8200 0.626 0.642 100 0.83 0.982 8.81 0.877 1.04 1.51 1.39 21.32 1.202 1.68 11.9 1.05 0.88 0.87 1.104 0.998 1 19.3 1.1 1.104 1.191 1.54 1.483 1.494 1.509 1.55 1.025 2.86 1.37 0.864 1.569 1.8 1.222 1.145 9.9 22 19.1 10.9 22 431 DR M M M CRC DR CRC,M M Oil - silicon Dow 710 @ 20°C Oil - safflower Oil - soybean Oil - sperm Oil - sunflower Oil - transformer Oil - wintergreen (methyl salicylate) Oxygen , O2 , liquid at 90 K Paraffin at 15°C n-Pentane, C5H12, liquid at 15°C Polypropylene oxide (Ambiflo) at 38°C Potassium at 100°C, mp = 63.7°C (see ‘M’ for other temps) Pyridine Sodium, liquid at 300°C (see ‘M’ for other temps) Solvesso #3 Sonotrack couplant Tallow at 16°C Thallium, mp = 303.5°C, used in photocells Trichorethylene Turpentine, at 25°C Univis 800 Water - heavy, D2O Water - liquid at 20°C Water - liquid at 25°C Water - liquid at 30°C Water - liquid at 60°C (temps up to 500°F listed in ‘CRC’) Water - salt 10% Water - salt 15% Water - salt 20% Water - sea, at 25°C Xenon - liquid at 166 K Xylene Hexafloride, C8H4F6, at 25°C m-Xylol, C8H10 Appendix B GD JA JA M JA M JA DR M 432 Fundamentals and Applications of Ultrasonic Waves TABLE B.7 Acoustic Properties of Gases Gas CRC CRC M M M M M M CRC CRC CRC CRC CRC M CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC CRC M CRC M M CRC Acetone vapor (C2H6O) at 97.1°C Air - dry at 0°C Air - at 0°C, 25 atm Air - at 0°C, 50 atm Air - at 0°C, 100 atm Air - at 20°C Air - at 100°C Air - at 500°C Ammonia (NH3) at 0°C Argon - at 0°C Benzene vapor (C6H6) at 97.1°C Cardon monoxide (CO) at 0°C Carbon dioxide (CO2) at 0°C Carbon disulfate Carbon tetrachloride vapor (CCl4) @ 97.1°C Chlorine at 0°C Chloroform - CH(Cl)3 at 97.1°C Deuterium at 0°C Ethane - C2H6 at 0°C Ethylene - C2H4 at 0°C Ethanol vapor - C2H5OH at 97.1°C Ethyl ether - C4H10O at 97.1°C Helium at 0°C Hydrogen at 0°C Hydrogen bromide - HBr at 0°C Hydrogen chloride - HCl at 0°C Hydrogen iodide - HI at 0°C Hydrogen sulfide - H2S at 0°C Methane - CH4 at 0°C Methanol vapor - CH3OH at 97.1°C Neon - at 0°C Nitric oxide - NO at 10°C Nitrogen - N2 at 0°C Nitrous oxide - N2O at 0°C Oxygen - O2 at 0°C Oxygen - O2 at 20°C Sulfur dioxide - SO2 at 0°C Water vapor at 0°C Water vapor at 100°C Water vapor at 134°C © 2002 by CRC Press LLC VL (10 m//s) ∆V/∆ ∆T (m//s°°C) 0.239 0.33145 0.332 0.335 0.351 0.344 0.386 0.553 0.415 0.319 0.202 0.338 0.259 0.189 0.145 0.32 0.59 0.206 0.171 0.89 0.308 0.317 0.269 0.206 0.965 1.284 0.2 0.296 0.157 0.289 0.43 0.335 0.435 0.324 0.334 0.263 0.316 0.328 0.213 0.401 0.405 0.494 0.56 0.3 0.6 0.4 0.24 1.6 0.4 0.3 0.8 2.2 ρ (kg/m ) ZL (kRayl) 1.293 0.4286 0.771 1.783 0.32 0.569 1.25 1.977 0.423 0.512 3.214 0.662 0.19 1.356 1.26 0.1691 0.418 0.4 0.178 0.0899 3.5 1.639 5.66 1.539 0.7168 0.172 0.1154 0.7 0.485 0.889 0.445 0.308 0.9 1.34 1.251 1.977 1.429 1.32 2.927 0.392 0.434 0.418 0.52 0.451 0.433 0.623 0.46 0.6 0.5 0.56 0.47 Appendix B 433 Abbreviations AE = Handbook of Tables for Applied Engineering Sciences AH = Andy Hadjicostis, Nutran Company, 206-348-3222 AJS = A.J Slobodnik, R.T Delmonico, and E.D Conway, Microwave Acoustics Handbook, Vol 3: Bulk Wave Velocities, Internal Report RADC-TR-80-188 (May 1980), Rome Air Development Center, Air Force Systems Command, Griffiths Air Force Base, New York 13441 AS = Alan Selfridge, Ph.D., Ultrasonic Devices, Inc CRC = Handbook of Chemistry and Physics, 45th ed., Chemical Rubber Company, Cleveland, OH, p E-28 DP = Don Pettibone, Ph.D., Diasonics, Sunnyvale, CA FS = Fred Stanke, Ph.D., Schlumberger, Inc., Ridgefield, CT, private communication GD = Genevieve Dumas, IEEE Trans Sonics Ultrason., Mar 1983 JF = John Fraser, Ph.D., ATL, Bothell, WA KF = Kinsler and Frey, Fundamentals of Acoustics, John Wiley and Sons, 1962 LB = Schaaffs, W., Numerical Data and Functional Relationships in Science and Technology, New Series Group II: and Molecular Physics, Vol 5: Molecular Acoustics, K.H Hellwege and A.M Hellwege, Eds., Springer-Verlag, Berlin, 1967 (This reference contains velocity and density information for just about any organic liquid Other volumes in this work contain much information on various anisotropic solids and crystals.) LP = Laust Pederson M = MetroTek Inc., Application Note 23 ME = Materials engineering, Dec 1982 RB = Rick Bauer, Ph.D., Hewlett Packard, Page Mill Road, Palo Alto, CA RLB = Ram lal Bedi, Ph.D., formerly with Specialty Engineering Associates, Milpitas, CA SIM = Simmons, G and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties, 2nd ed., MIT Press, Cambridge, MA, XV, 370, 1971 © Ultrasonic Devices Inc., 1996 Tc = Curie temperature −12 εr = Relative dielectric constant, multiply by 8.84⋅10 for MKS units (F/m) ε33 = Unclamped dielectric constant kt = Coupling coefficient between E3 and thickness mode kp = Planar (radial) moe coupling coefficient tan δ = loss tangent (dimensionless) D V = Velocity corresponding to antiresonance (open circuit) © 2002 by CRC Press LLC 434 Fundamentals and Applications of Ultrasonic Waves V = Velocity corresponding to resonance VS = Shear velocity −6 ZS = Shear impedance times 10 kg ⋅ m /s D Z = Longitudinal wave impedance corresponding to antiresonance times −6 10 kg ⋅ m /s ∆V = Change in acoustic velocity per change in temperature in m/s °C E ∆T Loss, or attenuation, is given in several different formats in these tables The most specific way is with the @ symbol The number before the @ is the loss in dB/cm, the number after the @ symbol is the frequency at which the attenuation was measured in MHz For liquids the attenuation is given in Np/cm To get loss in dB/cm multiply α by 8.686 ∗ f where f is the frequency of interest in Hz This representation obviously assumes that loss increases in proportion to frequency squared, and is most commonly used for low-loss materials such as glass and liquids Transducer modeling programs will commonly assume loss increases only in proportion to the first power If this is the case, then it is appropriate to use the material quality factor, or acoustic Q To convert between dB/cm and Q, the following equations can be useful: ∗ π ∗ ( Stored energy ) Q = Energy dissipated per cycle Stored energy Q = W -Average power loss 86.9 ∗ π ∗ f Q = ( ( dB/cm ) ∗ velocity ) References Selfridge, A.R., Design and Fabrication of Ultrasonic Transducer Arrays, Ph.D thesis, Stanford University, Stanford, CA, 1982 Available from University Microfilms, Ann Arbor, MI Krimholtz, R., Leedom, D.A., and Matthei, G.I., New equivalent circuits for elementary piezoelectric transducers, Electron Lett., 6, 398, 1970 Mason, W.P., Electromechanical Transducers and Wave Filters, Van Nostrand, Princeton, NJ, 1948 Fraser, J.D., The Design of Efficient Broadband Ultrasonic Transducers, Ph.D thesis, Stanford University, Stanford, CA, 1979 Measured by Alan Selfridge using a vector impedance meter and curve fitting techniques Vernitron Piezoelectric Division, Piezoelectric Technol Data Designers, 216-2328600 © 2002 by CRC Press LLC Appendix B 10 435 Private correspondence with Murata As in [5] though later date ITT, Reference Data for Engineers, 6th ed., H.W Sams & Co Kino, G.S., Acoustic Waves: Devices, Imaging and Analogue Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1987 11 Same as in [5] except impedance data were measured using a Tektronix 2430 digitizing oscilloscope 12 Auld, B.A., Acoustic Fields and Waves in Solids, Wiley-Interscience, New York, 1973 13 Ristic, V.M., Principles of Acoustic Devices, John Wiley & Sons, New York, 1983 © 2002 by CRC Press LLC Appendix C Complementary Laboratory Experiments A system of group projects was developed during the evolution of the subject matter of this book when used for teaching purposes One format involved the use of weekly problem sets for the fundamental part of the material (Chapters through 10), similar in type and level to the questions found at the end of these chapters During the second part of the course, two alternative schemes were used One involved the assignment of term papers on a special topic, examples of which are given at the end of this section The other, and more elaborate approach, consisted of experimental projects These projects were open-ended as opposed to set-piece laboratory experiments What was actually done depended on the students’ backgrounds, availability of equipment, and qualified instructors Hence it is stressed that the notes given below should be seen as guidelines or suggestions as to how a suitable laboratory component could be set up and not as formal, readyto-use laboratory methodology descriptions For this second part of the course, students were divided into teams of two or three A term project was carried out by each team, enabling the students to go more in depth in a given area than they could have done otherwise Students were asked to divide up tasks in theory/computer calculation on the one hand and experimental testing on the other Typical subject areas are given below The approach was very flexible, a particular aspect being worked out in consultation with the teacher, and the actual work carried out under the guidance of a graduate student The projects were for approximately month, after which the group compiled a single report synthesising the work of all of the participants The work was then presented in a series of short oral presentations; instruction was given to assist in preparing the report and making the presentation, which was of a length and style similar to that of conference presentations The advantage of this approach was that students were generally very motivated to learn the theoretical part and to carry out a successful project Learning to work in a team and acquiring communication skills were other advantages of this approach The required material was largely accessible from research laboratories Computing requirements were modest and in all cases could be met with © 2002 by CRC Press LLC 438 Fundamentals and Applications of Ultrasonic Waves the departmental PCs The laboratory equipment available included: HP Model 4195A Network/Spectrum Analyzer One of the following: a MATEC RF tone burst ultrasonic generator and receiver (10 to 90 MHz) b RITEC RAM 10000 tone burst ultrasonic generator and receiver (1 to 100 MHz) c UTEX UT 320/340 Pulser/receiver or equivalent, such as those produced by Panametrics or Metrotek (tone burst systems are ideal for this type of experiment as they allow easy control and variation of the frequency and quantitative verification of frequency-dependent effects) Standard RF attenuators, cables, etc Laboratory oscilloscope, ideally digital scope with FFT capability, such as the 300 MHz LeCroy digital oscilloscope A list of typical projects is given below, with notes on particular aspects that can be easily investigated and compared with theory This list is by no means exhaustive, and it is easy to extend it by the procurement of modest additional resources, such as focusing transducers, additional buffer rods, means of temperature variation and control, magnetic field etc Transducer characterization It is useful to obtain a collection of piezoelectric transducers from various sources Commercially packaged resonators can easily be obtained in the range to 20 MHz, as can unmounted transducers, longitudinal or transverse, with either fundamental or overtone polish from suppliers such as Valpey Fisher Inc In the latter case, LiNbO3 transducers with a fundamental in the range of to 15 MHz and with overtone polish are the most convenient choice, typically or mm in diameter Transducer characterization is best made with respect to a welldefined equivalent circuit This could be a series resonant circuit in parallel with the static capacitance (Butterworth–Van Dyke equivalent circuit for resonators) or the full Mason Model for a loaded transducer Suggested experiments include: a Characterization of the resonance of an unloaded transducer (resonator) using the network analyzer; determination of transducer parameters by measurement of amplitude and phase response, as well as series and parallel resonant frequencies; identification of harmonic frequencies; effects of liquid loading on the resonance for both longitudinal and transverse polarization © 2002 by CRC Press LLC Appendix C 439 b Frequency response of a transducer glued to a buffer rod, with air loading on the opposite face Points to verify include: (i) Frequency response of the odd harmonics (ii) Use of inductors/RF transformers to increase the transducer response (iii) Observation of echoes in the buffer rod (iv) Comparison of shape of the first echo with that of the exciting RF pulse; effect of bond quality on the echo shape Bulk acoustic wave (BAW) propagation Experiments in this section are based around the use of a transducer mounted on the end of a buffer rod Ideally, buffer rods made of materials such as fused quartz, sapphire, etc can be obtained with end faces optically polished and parallel from suppliers such as Valpey–Fisher Otherwise, for studies in the low MHz range, it is possible to machine and polish the end faces of materials such as perspex, duraluminium, brass, stainless steel, etc., using standard workshop practices to obtain usable echo trains Duraluminium is particularly useful due to its low attenuation and its machinability The buffer rod should have dimensions of the order of cm in length and cm in diameter; these dimensions are not critical and should be chosen so that the rod diameter is significantly greater than that of the transducer, with the buffer long enough so that clearly separated, nonoverlapping echoes are observed on the oscilloscope Longitudinal transducers with overtone polish and a fundamental frequency of or 10 MHz are recommended for the experiments of this section Such experiments include: a Mount the transducer on the end of the buffer rod with a suitable ultrasonic couplant; vacuum grease or silicon oil are convenient, as they give a good bond at room temperature which is stable for a few hours and is easily changed The transducer bond can be improved by wringing it onto the buffer surface using a soft rubber eraser, for example b Tuning the generator to the transducer fundamental frequency; observing echoes Existence or not of an exponential decay of the echo amplitudes should be registered Transducer bond can be optimized to give maximum echo amplitude c Estimation of VL and comparison with the handbook value; estimation of absolute and relative error d Using the same transducer bond as above, steps (b) and (c) should be repeated at odd harmonic frequencies up to the maximum attainable values with the ultrasonic generator used Variation of the overall modulation of the echo train and the number of © 2002 by CRC Press LLC 440 Fundamentals and Applications of Ultrasonic Waves echoes is particularly significant How can these be explained for the particular buffer rod used? e For a machined buffer rod, remachine one end face so that there are now nonparallel end faces to within a degree or so Repeat step (d) and explain any observed variation in the modulation of the echo train BAW reflection and transmission These experiments are most conveniently carried out with a buffer rod with the end opposite the transducer partially immersed in a liquid In this configuration it is possible to measure reflection at normal incidence and transmission and reflection from a plate immersed in the liquid The appropriate theoretical values can be calculated using the theory of Chapter Recommended experiments are: a Use a 5- or 10-MHz longitudinal wave transducer bonded to one end of the buffer rod as in experiment #2; prepare buffer rods of plexiglass, duraluminum, and stainless steel, which form a convenient trio of buffer rods that have low, medium, and high acoustic mismatch to liquids such as water; design and construct sample holders to enable the far end to be immersed in a fluid bath b Pulse echo experiments at low frequency in bare buffer rod; adjustment for obtaining maximum number of echoes c Exposure of the end of the buffer rod to the fluid in question; recording of the echo pattern and comparison with that for the unexposed rod; calculation of the reflection coefficient for each echo; draw conclusions on the accuracy of the method vs echo number d Systematic study of the three buffer rods against three different liquids with significantly different acoustic impedances; compare with theory e For a given liquid-solid combination at a given frequency, calculate the material and thickness of the layer needed to minimize the reflected signal; attempt to verify this result experimentally f Repeat (c) for the case where there is a reflecting plate immersed in the liquid; trace possible ray paths for various returning echoes in the buffer; compare with experiment to identify all observed echoes; estimate the reflection coefficient at the fluidplate interface SAW device fabrication, measurement, and sensor applications IDTs operating at about 50 MHz can be made very easily in a standard darkroom using photolithography techniques using the following materials; Y-Z LiNbO3 SAW plates, about 15 mm long, 10 mm wide, and 0.5 mm thick; mask for standard transmitter–receiver transducer © 2002 by CRC Press LLC Appendix C 441 design, required to have an impedance of 50 Ω when used with the chosen substrate; 10 finger pairs for two transducers about 10 mm apart, aperture approximately mm for Y-Z lithium niobate The steps for transducer fabrication are as follows: a Clean the substrate with acetone and soak in methanol b Deposit approximately 200 nm film of aluminum by flash evaporation c Deposit a photo-resist film by pipette on the substrate in yellow light conditions Incline the substrate to drain off excess photoresist d Bake the photo-resist film at 120°C for at least 15 to harden the film e Clamp the mask on top of the photo-resist film and expose to ultraviolet light for the recommended time f Remove the mask in darkness and dip the substrate for a few moments in NaOH to remove the exposed portions of the photoresist The remaining photo-resist protects the aluminum during etching g Etch the plate in a solution of HNO3 , HCl, and H2O, removing it rapidly at the required moment to avoid overetching h Thoroughly rinse the plate and then remove excess photo-resist with a small amount of NaOH If sufficient time and facilities are not available for in-house fabrication, then finished SAW plates with IDTs can be bought from the manufacturer A number of instructive experiments can be carried out using the SAW device These include: a Testing the frequency response with the network analyzer: a power splitter can be used to provide a reference signal, enabling tracing of the insertion loss as a function of frequency The result should be compared with the expected theoretical response b Transducer matching: if the impedance is 50 Ω, then it remains to tune out the static capacitance, here about 0.3 pF This is most conveniently done with a variable inductance in series with the transducer c Timing flight measurement: the transmitting transducer is excited by a low-amplitude tone burst To prevent burnout of the IDTs it is advisable to use a fixed attenuator (PAD) of 10 or 20 dB in series with the input if high power sources such as the Matec are used The source and receiver are tuned to the IDT central frequency Absolute and relative Rayleigh wave velocity of the substrate can be measured in this way Compare the measured value with that given in the tables © 2002 by CRC Press LLC 442 Fundamentals and Applications of Ultrasonic Waves d Liquid loading by leaky waves can be demonstrated very effectively by putting a drop of water on the substrate between the electrodes; the propagated acoustic signal immediately disappears It is instructive to repeat the experiment with liquids of lower acoustic impedance and increased volatility, such as acetone e Transforming the SAW device into an oscillator is easily accomplished by placing an RF amplifier into a feedback loop connected between the two IDTs, in series with an RF attenuator The attenuator setting must be low enough so that the loop gain exceeds the losses Interesting conclusions can be drawn from the behavior of the signal across the device observed on an oscilloscope at high and low values of attenuation The oscillation frequency should be measured with a frequency counter f Using the SAW device as a temperature sensor is possible due to the temperature dependence of the sound velocity in LiNbO3, which gives rise to a predicted temperature variation of the propagation time as 94 ppm/°C In light of the discussion in Chapter 13, this can easily be measured as the frequency shift of the oscillator in the preceding section, which is directly proportional to the delay time, hence the velocity variation The SAW substrate can be placed on a cold plate and then a hot plate to cover a temperature range of about 100°C, around room temperature A calibrated thermometer should be attached to the SAW substrate, which should then be cycled slowly in temperature Readings of the frequency shift at various fixed temperatures should be made; the frequency shift vs temperature should give a linear variation of a value close to that predicted Advanced experiments There are a number of more advanced experiments of potential interest, but they rely on the availability of specialized equipment These possibilities will be mentioned only briefly here; they have been found to be relatively easy to set up and to be instructive, even if carried out at an elementary level a Acoustic radiation measurement by hydrophone and water tank If an ultrasonic immersion test bath with x-y-z micropositioners is available, then this provides a suitable means for measuring the acoustic radiation patterns of immersion transducers Immersion transducers can be purchased from vendors such as Panametrics Detection is carried out by a needle hydrophone which contains a small pointlike piezoelectric detector such that it does not perturb the acoustic field Measurement of the radiation pattern of a transducer and comparison with theory for both near field and far field is feasible © 2002 by CRC Press LLC Appendix C 443 b Acoustic microscopy: if a low-frequency acoustic microscope is available, there are a number of simple experiments that can be performed with few complications The most direct of these is experimental verification of the resolution of an acoustic lens The lens is focused on the edge of a plate and scanned in a direction perpendicular to the plate edge at constant height It is important that the lens axis be vertical and the plate accurately adjusted to be horizontal Over the plate the reflected amplitude is constant, and it then decreases continuously to zero as the focal point is scanned away from the plate edge into the bulk liquid The width of the resulting curve gives the resolution This can then be compared with theory for the lens opening and frequency used A second instructive experiment, done in the same configuration as above, is the measurement of a V(z) curve The lens axis is centered on the middle of the plate, roughly in the focal position In this case the x,y coordinates of the lens are held fixed, and the plate is scanned along the z axis toward the plate A series of maxima and minima are observed as described in Chapter 14 The result can be used to deduce the Rayleigh wave velocity in the plate, which can then be compared to the tabulated value c Schlieren imaging: if a Schlieren imaging system is available, then it is the tool of choice to image the propagation paths of ultrasonic waves Typical operation is at 10 MHz in a water bath Phenomena such as direct reflection and Schoch displacement are easily observable, as is the imaging of a focused acoustic beam Topics for term papers If suitable ultrasonic equipment is not available for experimental projects, then term papers involving literature searches and summaries on specific topics are useful Possible topics include: Ultrasonic tomography Fresnel acoustic lens SAW biosensors SAW gas sensors SAW temperature senors Acoustic spectrum analyser Laser generation of ultrasound Equivalent circuit model of IDTs Acoustoelectric effect © 2002 by CRC Press LLC .. .Fundamentals and Applications of Ultrasonic Waves © 2002 by CRC Press LLC Fundamentals and Applications of Ultrasonic Waves By J David N Cheeke Physics Department Concordia University Montreal,... Esche, Noltink, Neppiras, Flynn, and others Ultrasonic machining and drilling Ultrasonic cleaning; GE produced a commercial unit in 1950 Ultrasonic soldering and welding, advances made mainly in Germany... Summary Questions Refl ection and Transmission of Ultrasonic Waves at Interfaces 7.1 Introduction 7.2 Reflection and Transmission at Normal Incidence 7.2.1 Standing Waves 7.2.2 Reflection from a Layer