Springer Series in materials science 90 Springer Series in materials science Editors: R Hull R M Osgood, Jr J Parisi H Warlimont The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design Recognizing the increasing importance of materials science in future device technologies, the book titles in this series ref lect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials 71 Dissipative Phenomena in Condensed Matter Some Applications By S Dattagupta and S Puri 72 Predictive Simulation of Semiconductor Processing Status and Challenges Editors: J Dabrowski and E.R Weber 73 SiC Power Materials Devices and Applications Editor: Z.C Feng 74 Plastic Deformation in Nanocrystalline Materials By M.Yu Gutkin and I.A Ovid’ko 75 Wafer Bonding Applications and Technology Editors: M Alexe and U G¨osele 76 Spirally Anisotropic Composites By G.E Freger, V.N Kestelman, and D.G Freger 77 Impurities Confined in Quantum Structures By P.O Holtz and Q.X Zhao 81 Metallopolymer Nanocomposites By A.D Pomogailo and V.N Kestelman 82 Plastics for Corrosion Inhibition By V.A Goldade, L.S Pinchuk, A.V Makarevich and V.N Kestelman 83 Spectroscopic Properties of Rare Earths in Optical Materials Editors: G Liu and B Jacquier 84 Hartree–Fock–Slater Method for Materials Science The DV–X Alpha Method for Design and Characterization of Materials Editors: H Adachi, T Mukoyama, and J Kawai 85 Lifetime Spectroscopy A Method of Defect Characterization in Silicon for Photovoltaic Applications By S Rein 86 Wide-Gap Chalcopyrites Editors: S Siebentritt and U Rau 87 Micro- and Nanostructured Glasses By D H¨ulsenberg and A Harnisch 78 Macromolecular Nanostructured Materials Editors: N Ueyama and A Harada 88 Introduction to Wave Scattering, Localization and Mesoscopic Phenomena By P Sheng 79 Magnetism and Structure in Functional Materials Editors: A Planes, L Ma˜nosa, and A Saxena 89 Magneto-Science Magnetic Field Effects on Materials: Fundamentals and Applications Editors: M Yamaguchi and Y Tanimoto 80 Micro- and Macro-Properties of Solids Thermal, Mechanical and Dielectric Properties By D.B Sirdeshmukh, L Sirdeshmukh, and K.G Subhadra 90 Internal Friction in Metallic Materials A Handbook By M.S Blanter, I.S Golovin, H Neuh¨auser, and H.-R Sinning M.S Blanter I.S Golovin H Neuh¨auser H.-R Sinning Internal Friction in Metallic Materials A Handbook With 65 Figures and 53 Tables 123 Professor Dr Mikhail S Blanter Professor Dr Igor S Golovin Moscow State University of Instrumental Engineering and Information Science Stromynka 20, 107846, Moscow, Russia E-mail: mike@blanter.msk.ru Physics of Metals and Materials Science Department Tula State University Lenin ave 92, 300600 Tula, Russia E-mail: golovin@relax.tsu.tula.ru Professor Dr Hartmut Neuh¨auser Professor Dr Hans-Rainer Sinning Institut f¨ur Physik der Kondensierten Materie Technische Universit¨at Braunschweig Mendelssohnstr 38106 Braunschweig, Germany E-mail: h.neuhaeuser@tu-bs.de Institut f¨ur Werkstoffe Technische Universit¨at Braunschweig Langer Kamp 38106 Braunschweig, Germany E-mail: hr.sinning@tu-bs.de Series Editors: Professor Robert Hull Professor Jürgen Parisi University of Virginia Dept of Materials Science and Engineering Thornton Hall Charlottesville, VA 22903-2442, USA Universit¨at Oldenburg, Fachbereich Physik Abt Energie- und Halbleiterforschung Carl-von-Ossietzky-Strasse 9–11 26129 Oldenburg, Germany Professor R M Osgood, Jr Professor Hans Warlimont Microelectronics Science Laboratory Department of Electrical Engineering Columbia University Seeley W Mudd Building New York, NY 10027, USA Institut f¨ur Festk¨orperund Werkstofforschung, Helmholtzstrasse 20 01069 Dresden, Germany ISSN 0933-033X ISBN-10 3-540-68757-2 Springer Berlin Heidelberg New York ISBN-13 978-3-540-68757-3 Springer Berlin Heidelberg New York Library of Congress Control Number: 2006938675 All rights reserved No part of this book may be reproduced in any form, by photostat, microfilm, retrieval system, or any other means, without the written permission of Kodansha Ltd (except in the case of brief quotation for criticism or review.) 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prepared by SPi using a Springer LT E Cover: eStudio Calamar Steinen Printed on acid-free paper SPIN: 11014805 57/3100/SPI 543210 To our families Preface Internal friction and anelastic relaxation form the core of the mechanical spectroscopy method, widely used in solid-state physics, physical metallurgy and materials science to study structural defects and their mobility, transport phenomena and phase transformations in solids From the view-point of Mechanical Engineering, internal friction is responsible for the damping properties of materials, including applications of high damping (vibration and noise reduction) as well as of low damping (vibration sensors, high-precision instruments) In many cases, the highly sensitive and selective spectra of internal friction (as a function of temperature, frequency, and amplitude of vibration) contain unique microscopic information that cannot be obtained by other methods On the other hand, owing to the large variety of phenomena, materials, and related microscopic models, a correct interpretation of measured internal friction spectra is often difficult An efficient use of mechanical spectroscopy may then require both: (a) a systematic treatment of the different mechanisms of internal friction and anelastic relaxation, and (b) a comprehensive compilation of experimental data in order to facilitate the assignment of mechanisms to the observed phenomena Whereas the first of these two approaches was developed since more than half a century in several textbooks and monographs (e.g., Zener 1948, Krishtal et al 1964, Nowick and Berry 1972, De Batist 1972, Schaller et al 2001), the second requirement was met only by one Russian reference book (Blanter and Piguzov 1991), with no real equivalent in the international literature The present book, partly based on the Russian example, is intended to fill this gap by providing readers with comprehensive information about published experimental results on internal friction in metallic materials According to this objective, this handbook mainly consists of tables where detailed internal friction data are combined with specifications of relaxation mechanisms The key to understand this very condensed information is provided, besides appropriate lists of symbols and abbreviations, by the introductory Chaps 1–3: after the Introduction to Internal Friction in Chap 1, defining and delimiting the subject and clarifying the terminology, the relevant VIII Preface internal friction mechanisms are briefly reviewed in Chaps (Anelastic Relaxation) and (Other Mechanisms) Although somewhat more space is obviously devoted to the former than to the latter, this part should not be understood as a systematic analysis of the physical sources of anelasticity and damping; in that respect, the reader is referred e.g., to the above-mentioned textbooks The data collection itself, as the main subject of the book, can be found in Chaps and The tables, generally in order of chemical composition, include the main properties of all known relaxation peaks (like frequency, peak height and temperature, activation parameters), the relaxation mechanisms as suggested by the original authors, and additional information about experimental conditions Other (e.g., hysteretic) damping phenomena, however, could not be considered within the limited scope of this book, with very few exceptions Chapter 4, which represents the main body of data on crystalline metals and alloys, is divided into subsections according to the group of the main metallic element in the periodic table, with alphabetic order within each subsection Chapter contains several new types of metallic materials with specific structures, which not fit well into the general scheme of Chap A short summary or specific explanations are included at the beginning of each table Although the authors made all efforts to be consistent in style throughout the book, some difficulties in evaluating individual relaxation spectra led to slight deviations, concerning details of data presentation, between the different chapters and subsections Since some of the data were evaluated from figures, the accuracy should generally be regarded with care; in cases of doubt, the original papers should be consulted Over 2000 references published until mid 2006 were included, among which many earlier ones are still important because certain alloys and effects are not covered by the more recent literature Latest information, if missing in this book, might be found in three conference proceedings published in the second half of 2006 (Mizubayashi et al 2006b, Igata and Takeuchi 2006, Darinskii and Magalas 2006), as well as in forthcoming continuations of these conference series This book is intended for students, researchers and engineers working in solid-state physics, materials science or mechanical engineering From one side, due to the relatively short summary of the basics of internal friction in Chaps 1–3, it may be helpful for nonspecialists and for beginners in the field From the other side, its probably most comprehensive data collection ever published on this topic should also be attractive for top specialists and experienced researchers in mechanical spectroscopy and anelasticity of solids The authors acknowledge gratefully the help of Ms Tatiana Sazonova with the list of references, of Ms Brigitte Brust with figures, and of Ms Svetlana Golovina with tables We are also grateful to the Springer team, in particular Dr Claus Ascheron, Ms Adelheid Duhm and Ms Nandini Loganathan, for good cooperation Moscow, Tula, Braunschweig January 2007 Mikhail S Blanter, Igor S Golovin Hartmut Neuh¨ auser, Hans-Rainer Sinning Contents Introduction to Internal Friction: Terms and Definitions 1.1 General Phenomenon 1.2 Types of Mechanical Behaviour 1.3 Anelastic Relaxation 1.4 Thermal Activation 1.5 Other Types of Internal Friction 1.6 Measurement of Internal Friction 1 Anelastic Relaxation Mechanisms of Internal Friction 2.1 Introduction 2.2 Point Defect Relaxation 2.2.1 The Snoek Relaxation 2.2.2 Relaxation due to Foreign Interstitial Atoms (C, N, O) in fcc and Hexagonal Metals 2.2.3 The Zener Relaxation 2.2.4 Anelastic Relaxation due to Hydrogen 2.2.5 Other Kinds of Point-Defect Relaxation 2.3 Dislocation Relaxation 2.3.1 Intrinsic Dislocation Relaxation Mechanisms: Bordoni and Niblett–Wilks Peaks 2.3.2 Coupling of Dislocations and Point Defects: Hasiguti and Snoek–K¨ oster Peaks and DislocationEnhanced Snoek Effect 2.3.3 Other Kinds of Dislocation Relaxation 2.4 Interface Relaxation 2.4.1 Grain Boundary Relaxation 2.4.2 Twin Boundary Relaxation 2.4.3 Nanocrystalline Metals 2.5 Thermoelastic Relaxation 2.5.1 Theory 11 11 11 12 28 32 36 48 50 51 61 73 77 78 82 83 87 87 X Contents 2.5.2 Properties and Applications of Thermoelastic Damping 90 2.6 Relaxation in Non-Crystalline and Complex Structures 95 2.6.1 Amorphous Alloys 97 2.6.2 Quasicrystals and Approximants 113 Other Mechanisms of Internal Friction 121 3.1 Introduction 121 3.2 Internal Friction at Phase Transformations 121 3.2.1 Martensitic Transformation 121 3.2.2 Polymorphic and Other Phase Transformations 129 3.2.3 Precipitation and Dissolution of a Second Phase 133 3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF) 136 3.4 Magneto-Mechanical Damping 144 3.5 Mechanisms of Damping in High-Damping Materials 148 Internal Friction Data of Crystalline Metals and Alloys (Tables) 157 4.1 Copper and Noble Metals and their Alloys 158 4.2 Alkaline and Alkaline Earth Metals and their Alloys 189 4.3 Metals of the IIA–VIIA Groups and their Alloys 196 4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 223 4.4.1 Rare Earth and Group IIIB Metals 223 4.4.2 Actinides 235 4.5 Metals of the IVB Group 238 4.5.1 Titanium and its Alloys 238 4.5.2 Zirconium and its Alloys 263 4.5.3 Hafnium and its Alloys 275 4.6 Metals of the VB Group 276 4.6.1 Vanadium and its Alloys 276 4.6.2 Niobium and its Alloys 287 4.6.3 Tantalum and its Alloys 321 4.7 Metals of the VIB Group 331 4.7.1 Chromium and its Alloys 331 4.7.2 Molybdenum and its Alloys 338 4.7.3 Tungsten and its Alloys 346 4.8 Metals of the VIIB group: Mn and Re 352 4.9 Iron and Iron-Based Alloys 356 4.9.1 Fe (“pure”) 357 4.9.2 Fe–Interstitial Atoms (C, H, N), Other Elements (As, B, Ce, La, P, S, Y) [...]... microscopic mechanisms Since tan φ is not well defined in these cases, non-linear internal friction should be expressed using more general definitions like the specific damping capacity Ψ in (1.1) A few aspects of amplitude-dependent internal friction (ADIF) are addressed later in Chaps 3.3–3.5 However, in spite of its importance for high-damping materials, ADIF is generally not included in the data collections... relaxation, as the main source of internal friction considered in this book, is seen in Fig 1.2a both as a saturating “creep” strain ε(t) after loading, with “unrelaxed” and “relaxed” values εU and εR , and as a decaying “elastic 4 1 Introduction to Internal Friction: Terms and Definitions after-effect” after unloading, and may also be observed as stress relaxation in case of a constant applied strain It is characterised... damping capacity circular frequency Other, less frequently used or more specific symbols are explained directly in the text If the same symbol is used in different meanings – which sometimes could not be avoided – it is ensured that the correct meaning is clear from the respective context 1 Introduction to Internal Friction: Terms and Definitions In this chapter, the reader is introduced into the terminology... not be confused with its general meaning as a difference sign in combinations like ∆W Sometimes the loss angle φ is defined as internal friction (Nowick and Berry 1972, Fantozzi 2001), implying that internal friction would exist only in linear viscoelastic materials Since there is no physical reason for such a restriction, we prefer the more general use of this term introduced earlier 1.4 Thermal Activation... any peak but goes to in nity in the lowfrequency or high-temperature limit An example of such viscous damping is the so-called “α relaxation” of metallic glasses (see Sect 2.6.1) Non-linear damping, i.e., internal friction beyond linear viscoelasticity, can be described by mechanical models containing specialised non-linear elements (Palmov 1998, Fantozzi 2001) in addition to springs and dashpots; such... and Guicking 1974 Ferry 1970 between models with a continuous chain of springs resulting in a completely recoverable strain (or more precisely, a unique equilibrium relationship between stress and strain, Fig 1.2a), and those with a single dashpot in series showing a permanent deformation after unloading (absence of a stress–strain equilibrium, Fig 1.2b) The terminology of this latter distinction (which... 2.3), and the motion of grain boundaries or other interfaces (Sect 2.4, where a section about nanocrystalline materials is added) The fundamental thermoelastic relaxation, always present in internal friction experiments at least as a background, is treated in Sect 2.5 Specific features of anelastic and viscoelastic relaxation in non-crystalline metallic structures, if not included in the earlier sections,... working in forced vibration far below the resonance frequency of the system The directly measured quantity is the phase lag (loss angle) φ between stress and strain, from which internal friction is determined according to (1.4) Commercial instruments of this type (“dynamic mechanical analyser”), mostly working in bending mode, are widely used for polymers with a generally higher viscoelastic damping... (see Fig 1.1) according to its common use in physics, fluid mechanics and materials science (including glasses and polymers), but which has a second meaning as loss factor (or loss coefficient, Lazan 1968) in structural engineering and part of technical mechanics In this book internal friction is – according to the tradition of materials science, physical metallurgy and solid-state physics from which... variations especially in the reliability of the activation parameters H and τ0 If doubts remain even after consulting the original papers, it is recommended to use the primary experimental data like Tm rather than H and τ0 1.5 Other Types of Internal Friction Although the data collections in this book are focussed on anelastic relaxation, the main characteristics of other types of internal friction should ... Subhadra 90 Internal Friction in Metallic Materials A Handbook By M.S Blanter, I.S Golovin, H Neuh¨auser, and H.-R Sinning M.S Blanter I.S Golovin H Neuh¨auser H.-R Sinning Internal Friction in Metallic. .. experimental results on internal friction in metallic materials According to this objective, this handbook mainly consists of tables where detailed internal friction data are combined with specifications... Mechanical Engineering, internal friction is responsible for the damping properties of materials, including applications of high damping (vibration and noise reduction) as well as of low damping (vibration