Internal Friction in Metallic Materials: A Handbook

Springer Series in materials science 90 M.S. Blanter I.S. Golovin H. Neuh¨auser H.-R. Sinning Internal Friction in ...

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Springer Series in

materials science

90

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: [email protected]

Physics of Metals and Materials Science Department Tula State University Lenin ave. 92, 300600 Tula, Russia E-mail: [email protected]

Professor Dr. Hartmut Neuh¨auser

Professor Dr. Hans-Rainer Sinning

Institut f¨ur Physik der Kondensierten Materie Technische Universit¨at Braunschweig Mendelssohnstr. 3 38106 Braunschweig, Germany E-mail: [email protected]

Institut f¨ur Werkstoffe Technische Universit¨at Braunschweig Langer Kamp 8 38106 Braunschweig, Germany E-mail: [email protected]

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.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media. springeronline.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. A X macro package Typesetting: Data prepared by SPi using a Springer LT E Cover: eStudio Calamar Steinen

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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. 2 (Anelastic Relaxation) and 3 (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. 4 and 5. 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 5 contains several new types of metallic materials with speciﬁc structures, which do not ﬁt well into the general scheme of Chap. 4. 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

1

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 1 2 3 5 7 8

2

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 3

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

4

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) <1%, and Low Carbon Steels . . . . . . 360 4.9.3 Fe–(<3%)Me–(C, N) and Low Alloyed Steels (Me = Metal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 4.9.4 Fe–Al Alloys and Steels (Mainly bcc and bcc-Based) . . . 372

Contents

XI

4.9.5 Fe–Al-Based Ternary and Multi-Component Alloys (e.g., Fe–Al–Cr, Fe–Al–Ge, Fe–Al–Si, etc.) . . . . . . . . . . . . 380 4.9.6 Fe–Co, –Ge, –Si, –Mo, –V, –W Alloys . . . . . . . . . . . . . . . . 385 4.9.7 Fe–Cr-Based Steels and Alloys . . . . . . . . . . . . . . . . . . . . . . 389 4.9.8 Fe–Mn-Based Steels and Alloys . . . . . . . . . . . . . . . . . . . . . 397 4.9.9 Fe–Ni-Based Steels and Alloys . . . . . . . . . . . . . . . . . . . . . . 402 4.9.10 Other Fe-Based Multi-Component Alloys . . . . . . . . . . . . . 408 4.10 Co, Ni and their Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 5

Internal Friction Data of Special Types of Metallic Materials (Tables) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 5.1 Hydrogen-Absorbing Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 5.2 Metallic Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 5.3 Quasicrystals and Other Complex Alloys . . . . . . . . . . . . . . . . . . . 449

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

List of Abbreviations

General Abbreviations IF ADIF TDIF MS LT bgr. HT bgr.

internal friction amplitude-dependent internal friction temperature-dependent internal friction mechanical spectroscopy low-temperature background high-temperature background

HT Quen. Annl. Temp. Recr. Prec.tr. Msp. Sint.

heat treatment quenched annealed tempered recrystallised precipitation treated melt-spun sintered

CW Hot roll. Fatig. Irr(n) Irr(e) Irr(p) Irr(d) Irr(γ)

cold worked hot rolled fatigued irradiated by irradiated by irradiated by irradiated by irradiated by

SC PC GB

single crystal polycrystal grain boundary

neutrons electrons protons deuterons γ-rays

XIV

List of Abbreviations

Ufgr. nc. am. SQC QC d-QC n-QC Sput.th.f. Evap.th.f. Gas depos. FM AFM PM SR DSR SRO AES RRR

ultraﬁne-grained nanocrystalline amorphous single quasicrystal (icosahedral phase) (poly-) quasicrystalline (icosahedral phase) (poly-) quasicrystalline (decagonal phase) nanoquasicrystal sputtered thin ﬁlm evaporated thin ﬁlm gas deposited thin ﬁlm ferromagnet antiferromagnet paramagnet structural relaxation directional structural relaxation short-range order(ed) activation energy spectrum residual resistivity ratio

Abbreviations of Relaxation Mechanisms and Internal Friction Peaks Point defects S S(O) S(C) S(N) S(H) S(H/O,N) S(D/O,N)

Snoek (and Snoek-type) relaxation due to: oxygen carbon nitrogen hydrogen hydrogen (H near O, N, etc.) deuterium (D near O, N, etc.)

FR FR(C) FR(N)

Finkelstein–Rosin relaxation due to: carbon nitrogen

G G(H) G(D) IG(H)

Gorsky relaxation due to: hydrogen deuterium intercrystalline Gorsky eﬀect of hydrogen

Z Z(Cu) Z(ord/disord) Z(H)

Zener (and Zener-type) relaxation due to: copper order/disordering hydrogen

List of Abbreviations

PD PD(O) PD(N) PD(C) PD(O/vac) PD(N/int) PD(O/sub) PD(O/dis) PD(O/M) PD(N/M/M) AR

XV

relaxation due to point defects: oxygen carbon nitrogen reorientation of complexes a oxygen atom – vacancy nitrogen atom – self-interstitial atom oxygen atom – substitutional atom oxygen atom – dislocation peaks due to diﬀusion under stress of a foreign interstitial atom near one or two metal atoms atomic reorientation Dislocations

DP(B1 ) DP(B2 ) DP(α) DP(β) DP(δ) DP(γ) DP(Pi ) DP DPi ODR

dislocation (deformation) Niblett–Wilks peak (fcc) dislocation (deformation) Bordoni peak (fcc) dislocation (deformation) α-peak (bcc) dislocation (deformation) β peak (bcc) dislocation (deformation) δ peak (bcc) dislocation (deformation) γ-peak (bcc) deformation Hasiguti peaks: i from 1 to 3 dislocation peaks in the range of intermediate and elevated temperatures; i ≥ 1 overdamped dislocation resonance

DP(am.)

relaxation peak due to dislocation-like defects in amorphous structures

SK SK(O) SK(C) SK(N) SK(H) SK(D)

Snoek–K¨ oster peak, due to: oxygen carbon nitrogen hydrogen deuterium

DES DES(O) DES(N) DES(C) DEFR

dislocation-enhanced Snoek peak, due to: oxygen nitrogen carbon dislocation-enhanced Finkelstein–Rosin relaxation

XVI

List of Abbreviations

Grain boundaries GB GBI GB(Me) GB(LT) GB(IT) GB(HT) SB

grain boundary peak impurity grain boundary peak impurity grain boundary peak due to Me GB peak in low temperature range GB peak in intermediate temperature range GB peak in high temperature range peak due to subgrain boundaries Phase transitions

PhT PhT(α) PhT(θ) PhT(hydr) PhT(deut) PhT(α → β) PhT(mag) PhT(FM–PM) PhT(melt) PhT(cr) PhT(ord) PhT(polym) PhT(mart) PhT(super)

peaks due to a phase transition, namely: α precipitation or dissolution θ phases precipitation or dissolution hydrides precipitation or dissolution deuterides precipitation or dissolution peaks due to α → β transition magnetic phase transition ferro- to paramagnetic magnetic phase transition melting crystallization ordering polymorphic transition martensite phase transition transition to superconducting condition

Main symbols (selected) a C D E E /E EU /ER f G H k Q Q−1 Q−1 m Q−1 b

lattice parameter concentration diﬀusion coeﬃcient Young’s modulus storage/loss modulus unrelaxed/relaxed modulus frequency shear modulus (G , G , GU , GR accordingly) activation energy/enthalpy of relaxation Boltzmann’s constant quality factor loss factor, internal friction height of internal friction peak internal friction background

List of Abbreviations

R t T Tm Tmelt α ∆ δ ε ε0 η σ σ0 τ τ0 φ/ tan φ Ψ ω

XVII

universal gas constant time temperature temperature of IF peak melting temperature attenuation coeﬃcient of ultrasonic waves relaxation strength logarithmic decrement strain strain amplitude viscosity stress stress amplitude relaxation time limit relaxation time (pre-exponential factor) loss angle / loss tangent speciﬁc 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 and nomenclature used in this book. The main subjects are deﬁned and classiﬁed from the phenomenological point of view, and the related theoretical background and experimental techniques are reviewed brieﬂy. The microscopic mechanisms, which are also included in the data collections as an important part of information, will then be introduced in Chaps. 2 and 3.

1.1 General Phenomenon The phenomenon of internal friction – most generally deﬁned as the dissipation of mechanical energy inside a gaseous, liquid or solid medium – is basically diﬀerent from “friction” in the tribological sense, i.e., the resistance against the motion of two solid surfaces relative to each other (“external friction”). In a solid material exposed to a time-dependent load within the “elastic” deformation range – only this case is considered in this book – “internal friction” usually means energy dissipation connected with deviations from Hooke’s law, as manifested by some stress–strain hysteresis in the case of cyclic loading. The corresponding energy absorption ∆W during one cycle, divided by the maximum elastic stored energy W during that cycle, deﬁnes the speciﬁc damping capacity Ψ = ∆W/W , or the loss factor ∆W/2πW , as the most general measures of internal friction, for which no further assumptions are required (but for most metallic materials this hysteresis is rather small, i.e., Ψ 1). The reciprocal loss factor is also called the quality factor Q = 2πW/∆W (Lazan 1968), so that “internal friction” or “damping” can generally be written as Q−1 = ∆W/2πW = Ψ/2π.

(1.1)

It should be mentioned, however, that for some of these terms deviating deﬁnitions exist, which will be discussed later in this introductory chapter. Also the nomenclature (usage of names and symbols) is not always clear,

2

1 Introduction to Internal Friction: Terms and Deﬁnitions σ

Applied stress

t

Strain response: elastic

viscous . σ=ηε (Newton)

σ=Eε (Hooke)

plastic (instantaneous plasticity)

ε

ε

t

ε

t

t

Fig. 1.1. Fundamental types of mechanical behaviour: response of strain ε(t) to a constant stress of ﬁnite duration with abrupt loading and unloading

due to diﬀerent traditions that have developed in the related scientiﬁc and technical disciplines. One example is the symbol η which is reserved here for the viscosity (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 mechanical spectroscopy has emerged – generally denoted as Q−1 .

1.2 Types of Mechanical Behaviour Before characterising the types and sources of internal friction in more detail, we have to consider the phenomenology of mechanical behaviour; for this purpose, the use of mechanical (or rheological) models is very helpful. Elements of such models are deduced from fundamental types of mechanical behaviour of solids and liquids like those shown in Fig. 1.1; most important as linear elements are the spring and the dashpot which denote, respectively, an ideal (Hookean) elastic solid with stiﬀness or “modulus” E, and an ideal (Newtonian) viscous liquid with viscosity η (for non-linear models used to describe plasticity, see e.g. Palmov 1998, Fantozzi 2001). Combinations of springs and dashpots generally deﬁne viscoelastic behaviour (Palmov 1998), in particular linear viscoelasticity since the related constitutive equations are linear (for convenience we consider uniaxial deformation and scalar quantities, but the generalisation to the tensor form is straightforward). Within this deﬁnition, the simplest case of linear viscoelasticity is represented by a Maxwell model, i.e., a spring and a dashpot in series. On the other hand, the respective parallel combination (Voigt–Kelvin model) is unrealistic because of inﬁnite instantaneous stiﬀness. Whereas in principle any number of springs and dashpots can be combined, we have to distinguish

1.3 Anelastic Relaxation

ε

3

ε

εR εU εR−εU t

t

(a)

(b)

Fig. 1.2. Examples of viscoelastic mechanical models, with the same applied stress as in Fig. 1.1: (a) completely recoverable three-parameter models (“standard anelastic solid”); (b) partially recoverable four-parameter model

Table 1.1. Diﬀerent existing terminologies for the distinction between recoverable and non-recoverable types of (linear) viscoelasticity recoverable – non-recoverable anelastic – viscoelastic viscoelastic – viscoplastic viscoelastic – elastoviscous viscoelastic solid – viscoelastic liquid

reference (example) Nowick and Berry 1972 Fantozzi 2001, R¨ osler et al. 2003 Meyer 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 can also be interpreted as a borderline between solids and liquids) is again not consistent throughout the scientiﬁc literature: a list of a few related deﬁnitions is given in Table 1.1. In the present book, a completely recoverable behaviour is named anelastic (Zener 1948, Krishtal et al. 1964, Lazan 1968, Nowick and Berry 1972, Lakes 1999) because this term appears to be the most clearly deﬁned one. The corresponding approach to internal equilibrium, after an external perturbation, is known as anelastic relaxation. Non-recoverable components like in Fig. 1.2b may then be called “viscous” or “viscoplastic” (but are of minor importance in this book), whereas “viscoelasticity” may include both recoverable and nonrecoverable behaviour (Lazan 1968, Ferry 1970, Palmov 1998, Lakes 1999).

1.3 Anelastic Relaxation Anelastic 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 by a relaxation strength ∆ = (εR − εU )/εU 1 which can be written in diﬀerent ways – e.g. as ∆ = (EU − ER )/ER using a time-dependent modulus E(t) deﬁned for stress relaxation (generalised Hooke’s law) – and by a distribution of relaxation times τ . In the simplest possible case, the so-called standard anelastic solid (Nowick and Berry 1972) or standard linear solid (Zener 1948, Fantozzi 2001) deﬁned by the two equivalent three-parameter models in Fig. 1.2a, the timedependent changes are of the form e−t/τ with a single relaxation time τ (either τσ for constant stress or τε for constant strain, with τσ = τε = τ for ∆ 1). More important in the context of this handbook, than this quasi-static behaviour of an anelastic solid, is that one under a cyclic applied stress or strain. In the linear theory of anelasticity (Nowick and Berry 1972), using the mathematically convenient complex notation (with complex quantities marked by an asterisk) for sinusoidally varying stress and strain, σ ∗ = σ0 eiωt

and ε∗ = ε0 ei(ωt−φ) = (ε − i ε )eiωt ,

(1.2)

several dynamic response functions are deﬁned as a function of the circular frequency ω like, for instance, a complex modulus E ∗ (ω) = σ ∗ /ε∗ = E(ω)eiφ(ω) = E (ω) + iE (ω).

(1.3)

The real quantities E(ω), E (ω) and E (ω) are called absolute dynamic modulus, storage modulus and loss modulus, respectively; the phase lag φ between stress and strain is also known as the loss angle.2 The real parts of (1.2) form the parametric equations of an ellipse as stress–strain hysteresis loop (not only in the anelastic case but generally for linear viscoelasticity), so that the calculation of the dissipated energy ∆W shows that in this case the loss tangent tan φ is identical with the more generally deﬁned loss factor introduced earlier (Fantozzi 2001): Q−1 = ∆W/2πW = tan φ = E /E = ε /ε .

(1.4)

The dynamic response functions of the standard anelastic solid are given by the well-known Debye equations (ﬁrst derived in 1929 by Debye for the case of dielectric relaxation) which can be found in detail in many textbooks and monographs (e.g. Zener 1948, Nowick and Berry 1972, Fantozzi 2001). The Debye equations can be written in diﬀerent ways, e.g. 1

2

This speciﬁc use of the alone-standing symbol ∆ for the relaxation strength, following the common practice in the literature on anelastic relaxation, should 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 EU

(a)

E(ω)

ER −1

Q (ω)

−1

E(T) EU(T)

−1 Q (T)

1.144

−2

(b) ER(T)

∆ /2

5

0 log ωτ

1

2

Tm

T

Fig. 1.3. Dynamic modulus E and internal friction Q−1 of the standard anelastic solid: (a) as a function of frequency on a log ωτ scale; (b) as a function of temperature at constant frequency. In the latter case, the relaxation-induced step in E(T ) is superimposed on the intrinsic temperature dependence of EU (T ) and ER (T )

1 ω 2 τε 2 ∆ E (ω) = ER 1 + ∆ = E 1 − U 1 + ω 2 τε 2 1 + ∆ 1 + ω 2 τε 2 and −1

Q

√ ω τσ τε ∆ (ω) = √ , 1 + ∆ 1 + ω 2 τσ τε

(1.5)

(1.6)

where EU , ER , ∆, τσ and τε have the same meaning as in the quasi-static case considered above. In the case of ∆ 1, these equations simplify to ω2 τ 2 ∆ E(ω) = E (ω) = ER 1 + ∆ = EU 1 − (1.7) 1 + ω2 τ 2 1 + ω2 τ 2 and

Q−1 (ω) = ∆

ωτ . 1 + ω2 τ 2

(1.8)

The resulting Debye peak Q−1 (ω), as shown in Fig. 1.3a, is characterised by a well-deﬁned shape and width (1.144 at half-maximum on a log10 ωτ scale) with a damping maximum Qm −1 = ∆/2 at ωτ = 1. The asymptotic behaviour for ωτ → 0 and ωτ → ∞ implies that at these limits the loss angle φ vanishes and the elliptic stress–strain hysteresis loop degenerates to a straight line (purely elastic behaviour with slopes EU for ωτ 1 and ER for ωτ 1), so that losses are detectable only in a certain range around ωτ = 1 (“dynamic” hysteresis).

1.4 Thermal Activation Most of the known mechanisms of anelastic relaxation, to be described later in Chap. 2, have their origin in the thermally activated motion of various kinds of defects. In this case, a reciprocal Arrhenius equation

6

1 Introduction to Internal Friction: Terms and Deﬁnitions

τ = τ0 exp (H/kT )

(1.9)

can be assumed for the relaxation time which now represents a reciprocal jump frequency of the defects (τ = ν −1 ) to overcome the energy barrier H at the temperature T . Inserting (1.9) into (1.8), the Debye peak is now obtained also as a function of temperature at constant oscillation frequency f = ω/2π (Fig. 1.3b), H 1 1 ∆ sech − Q−1 (T ) = , (1.10) 2 k T Tm where the peak (or maximum) temperature Tm is deﬁned by the condition ωτ = 1, and sech x = (cosh x)−1 = 2/(ex + e−x ). On the reciprocal temperature scale (not shown in Fig. 1.3) the Debye peak is symmetric with a half-width of 2.635 k/H. The thermal activation parameters of the relaxation process, i.e., the (eﬀective) activation enthalpy (“apparent activation energy”) H and the “limit relaxation time” (reciprocal “attempt frequency”)3 τ0 = ν0 −1 , are usually determined from the shift of the peak temperature Tm when changing the vibration frequency f , according to f2 1 1 H ln − = . (1.11) f1 k Tm1 Tm2 This is even possible for loss peaks which are much broader than a Debye peak, which means that the underlying physical process includes a whole spectrum instead of a single value of relaxation times; in that case, average activation parameters are obtained (for more details on the analysis of relaxation spectra and peak deconvolution, see Nowick and Berry 1972, San Juan 2001). In fact, more or less broadened relaxation peaks are the experimental rule rather than the exception, so that most data on H and τ0 given in this book, usually determined empirically from the frequency shift of Tm after (1.11), are in this sense some average values. From this latter, experimental viewpoint, it is necessary to point out that the separation of H and τ0 , important for clarifying the relaxation mechanisms as well as for predicting the peak position at arbitrary frequencies, is inevitably connected with a loss in precision compared to directly measured data like Tm . A reliable evaluation of H and τ0 – and even more of discrete or continuous spectra in these quantities – is highly sensitive to the quality of the experiments, and mainly requires the variation of frequency over a range as broad as possible. Such evaluated activation parameters may therefore be questionable in cases of scatter in the primary data or too small frequency variation, which can only partially be estimated from the information given in the tables of Chaps. 4 and 5. Since it has not been possible in this book to classify the quality of the literature data accordingly, the reader should be 3

Sometimes the symbol τ∞ (indicating the limit T → ∞) is used instead of τ0 . On the other hand, the use of τ0 is consistent with other common quantities like D0 in the related diﬀusion equation D = D0 exp(−H/kT ).

1.5 Other Types of Internal Friction

7

aware that there may be strong 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 also be considered brieﬂy. It is useful to know about these characteristics not only for separating anelastic and other contributions when superimposed on each other, but also from the viewpoint of understanding the anelastic relaxation phenomena and mechanisms themselves. Viscous damping, in the sense of non-recoverable linear viscoelasticity introduced earlier, can appear in quite diﬀerent forms depending on the loading conditions and quantities considered. In contrast to anelasticity, all “relaxed” quantities are now either zero or inﬁnite, and some parameters like ∆ or τσ are meaningless; on the other hand, stress relaxation and the modulus-type response functions are quite analogous in both cases. For the Maxwell model as the simplest case, the dynamic functions E (ω) and E (ω) have the same form as for the standard anelastic solid, e.g. a “Debye peak” in E (ω) with relaxation time τε and peak height EU /2; however, the related loss tangent tan φ = (ωτε )−1 does not show any peak but goes to inﬁnity 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 models are beyond the scope of this introduction, however. Generally, non-linearity always means that the loss factor becomes amplitude-dependent, whereas in linear viscoelasticity the related quantities in (1.4) do not depend on the amplitude of a sinusoidal vibration. The amplitude dependence is usually connected with a “static” hysteresis component, i.e., a virtually frequency-independent contribution to the stress– strain hysteresis loop which does not vanish in the limit ω → 0. In simpliﬁed terms, such idealised type of non-linear, amplitude-dependent and frequencyindependent behaviour is often named “hysteretic”, as opposed to “relaxation” (i.e., linear, amplitude-independent and frequency-dependent); although in certain cases of non-linear relaxation this may be an oversimpliﬁcation. For high-damping applications, “hysteretic” damping is generally preferred over relaxation because of its weak frequency dependence. In contrast to linear viscoelasticity with always elliptically-shaped dynamic hysteresis loops (cf. (1.2)), non-linear damping may be based on many diﬀerent

8

1 Introduction to Internal Friction: Terms and Deﬁnitions

types and shapes of static hysteresis loops (see De Batist 2001 for some examples); the underlying mechanical behaviour may be of microplastic, pseudoelastic or other type depending on the related 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 of this book, with very few exceptions. A main reason – besides the mere quantity of data which would by far exceed the volume of the book – is that the amplitude dependence can be very sensitive to the microstructural state of the sample. This makes it more diﬃcult to collect suﬃciently detailed information to compare diﬀerent ADIF studies to each other, but also to condense this information, if available, in the form of tables.

1.6 Measurement of Internal Friction With ascending frequency, the experimental techniques of mechanical spectroscopy are generally divided into four groups: quasi-static, subresonance, resonance and wave-propagation (pulse-echo) methods. While measuring different quantities and response functions, they all can be used to determine internal friction of metallic materials, preferably under vacuum to avoid unwanted aerodynamic losses. More details about the following techniques, which can be mentioned only very brieﬂy in this introduction, can be found in the books by Nowick and Berry (1972), Lakes (1999), Schaller et al. (2001), and related references. Quasi-static tests can be performed using conventional mechanical testing equipment in two diﬀerent ways: (1) in a quasi-static relaxation experiment (as creep/elastic after-eﬀect ε(t) at constant stress like in Fig. 1.2, or as stress relaxation σ(t) at constant strain), or (2) in a cyclic measurement of the stress– strain hysteresis σ(ε), e.g. at an alternating constant strain rate ±dε/dt. The relaxation experiment (1) is suitable to study linear relaxation processes if the loading or unloading time of the testing machine is small compared to the relaxation time of interest. Measured are quasi-static response functions including quantities like ∆ and τ , from which dynamic properties like internal friction can be calculated (Nowick and Berry 1972; cf. (1.8)). On the contrary, the cyclic test (2) is useful for obtaining the frequency-independent component of ADIF directly from (1.1) using the directly measured area ∆W of the “static” hysteresis loop. Whereas quasi-static hysteresis can in principle be measured with arbitrary time functions of stress and strain, the remaining three dynamic methods ideally work with sinusoidal (harmonic) vibrations or waves with a well-deﬁned frequency ω = 2πf and a wavelength λ for the related elastic waves. They

1.6 Measurement of Internal Friction

9

can be distinguished by means of the relation between λ and the length l of the sample. Subresonant experiments, with λ l and no external inertia attached to the sample, are 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 level. For metals, the low-frequency forced torsion pendulum is generally preferred because of its higher sensitivity. The main advantage of this technique is the possibility to perform isothermal experiments in a very large and continuous frequency range (10−4 to almost 102 Hz), which may be important in case of temperature-dependent structural changes (Rivi`ere 2001b). Resonant experiments form the largest and oldest group of mechanical spectroscopy methods, with the greatest variety of special techniques, and may be divided into subgroups where resonance either refers to the eigenvibrations of the sample (λ ≈ l) or to a larger system (λ l, with an external inertia attached to the sample). The most important resonance techniques – torsion pendulum, vibrating-reed (bending vibration of ﬂat samples), composite oscillator (longitudinal vibration of rods), and resonant ultrasound spectroscopy of rectangular parallelepiped samples (Leisure 2004) – altogether span a frequency range from about 10−1 to more than 106 Hz. Internal friction can be determined from resonant experiments in diﬀerent ways. One possibility is the direct determination of ∆W and W by a careful analysis of the relative magnitudes of the input and output signals of the stationary resonant vibration which, however, needs a high stabilisation and calibration eﬀort. More widely used are two other methods, called “resonant bandwidth” and “free decay”, respectively. In the ﬁrst case, the width of the resonance peak at the resonance frequency ωr is measured using forced vibraon both tions with constant excitation. If ω1 and ω2 denote the frequencies √ sides of the peak where the oscillation amplitude falls to 1/ 2 of its maximum value (“half-power” or “3 dB” points), the internal friction is given by4 Q−1 = (ω2 − ω1 )/ωr . 4

(1.12)

In fact, (1.1) and (1.12) are both found in the literature as deﬁnitions of the quality factor Q. In special cases of electrical circuits from which the concept of the quality factor is adopted, both expressions have been shown to be equivalent; possible diﬀerences at higher damping are less important for electrical networks which are normally designed for low damping. The related mechanical problem was analysed by Graesser and Wong (1992), using a linear “complex spring” model with frequency-independent loss factor. In this case agreement within 1% is found between both deﬁnitions for Q−1 < 0.28, whereas beyond that range the √ deviations grow rapidly up to a limit of Q−1 = 2 at tan φ = 1, above which Q−1 after (1.12) is no longer deﬁned. Hence, if Q−1 is used for high damping values, the chosen deﬁnition should be indicated clearly.

10

1 Introduction to Internal Friction: Terms and Deﬁnitions

The second, perhaps still most widely spread method uses free damped vibrations after turning oﬀ the excitation. The measured quantity is the logarithmic decrement δ deﬁned as (1.13) δ = ln(An /An+1 ), where An and An+1 are the vibration amplitudes in two successive cycles. There are diﬀerent ways of determining δ depending on the damping level of the sample, the quality of the signal, and details of measurement technique and data processing. Internal friction is usually determined by Q−1 = δ/π

(1.14)

as a well-known low-damping approximation. The deviations at high damping depend again on the exact response of the material; related results from the literature are restricted to special cases (sometimes also questionable) and will not be given here. In the perhaps most careful analysis available, Graesser and Wong (1992) give Q−1 < 0.2 as range of validity, within 1% deviation, for (1.14) in case of the “complex spring” model. In wave-propagation experiments, short high-frequency pulses (λ l; frequency about 106 –109 Hz or even more) are sent through the sample. The attenuation coeﬃcient α = −d(ln u(x))/dx = δ/λ,

(1.15)

where u(x) is the envelope of the wave during propagation in x direction, corresponds to the logarithmic decrement δ that would be expected for a related free vibration. Hence, the internal friction is Q−1 = δ/π = αλ/π

(1.16)

with limitations analogous to those mentioned earlier for (1.14). In addition to these experimental standard methods, there are also some highly specialised, combined techniques like acoustic coupling or scanning local acceleration microscopy (Gremaud et al. 2001a,b). Furthermore, advanced microfabrication technology and the development of micro- or nanoelectromechanical systems (MEMS/NEMS) open new applications for classical resonance techniques using miniaturised resonators (Yasumura et al. 2000) or thin ﬁlms on specially designed, complex-shaped oscillators (Liu and Pohl 1998, Harms et al. 1999).

2 Anelastic Relaxation Mechanisms of Internal Friction

2.1 Introduction In this chapter the main mechanisms are considered which produce anelastic damping as deﬁned in Chap. 1. They are associated with the diﬀusive motion under stress of point defects (Sect. 2.2), the motion of dislocations or parts of them (Sect. 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, are ﬁnally considered in Sect. 2.6. Damping phenomena which are mainly due to non-linear hysteretic mechanisms will be treated in Chap. 3 even if they also contain some anelastic component.

2.2 Point Defect Relaxation Point defect relaxation generally means an anelastic relaxation caused by a diﬀusive redistribution of point defects under the action of an applied stress (“diﬀusion under stress”). This necessarily requires an elastic interaction between the applied stress and the distortions of a crystal lattice (or possibly of a non-crystalline matrix) created by the point defects, so that under the action of the external stress the internal equilibrium distribution of the defects is changed and a driving force for a directed diﬀusion is produced. One such possibility, already predicted by Gorsky (1935), is the movement of interstitial atoms from compressed to dilated regions in an inhomogeneous stress ﬁeld, i.e., a long-range diﬀusion driven by the hydrostatic stress component. Since this Gorsky relaxation has been observed in fact only for hydrogen as the most mobile interstitial species, it will be introduced later in connection with H-induced anelasticity (Sect. 2.2.4).

12

2 Anelastic Relaxation Mechanisms of Internal Friction

The other possibility, named reorientation, is related to the anisotropy of both the applied stresses and the defect-induced distortions. Compared to the Gorsky relaxation, reorientation processes have much more practical importance for two reasons: (a) they apply to a much larger variety of point defects and their clusters, and (b) they require only short-range diﬀusion, ideally over atomic distances, so that the relaxation times are much shorter and more likely to cause internal friction of elastic vibrations in practically relevant frequency ranges. However, not all point defects in metals are subject to a reorientation mechanism: some of them may cause damping, while others may not. This ability depends on speciﬁc symmetry relations and on the direction of the oscillating applied stress. The main condition is that the symmetry of the local elastic distortions, caused by the defects in the crystal lattice, is lower than the symmetry of the lattice itself; when speciﬁed in crystallographic terms, this is known as so-called selection rules for anelasticity (Table 2.1). The temperature of anelastic relaxation (i.e., of an internal friction peak) is determined by the activation energy of diﬀusion of the point defect and by the frequency of vibrations. The relaxation strength is determined by the concentration of defects and by the strength of the individual, defect-induced distortions. Such a distortion ﬁeld, also called an elastic dipole because of its anisotropic character (Kr¨ oner 1958, Nowick and Berry 1972), is described by the λ-tensor with the components (p)

λij = ∂εij /∂Cp ,

(2.1)

where εij are the components of the strain tensor and Cp is the partial defect concentration in a speciﬁc orientation p(p = 1 . . . nd ; nd = number of possible, crystallographically equivalent defect orientations). The λ-tensor is symmetric, i.e., λij (p) = λji (p) , and in the coordinate system of the 3 principal axes also diagonal: ⎞ ⎛ λ1 0 0 (2.2) λ = ⎝ 0 λ2 0 ⎠ 0 0 λ3 The principal values λ1 , λ2 , λ3 are the same for all orientations p. The properties of the λ-tensor for various defect symmetries are summarised in Table 2.2. If elastic dipoles present in a crystal have diﬀerent λ-tensors (diﬀerent orientations), then they interact with the applied stress ﬁeld in a diﬀerent way. This leads to the reorientation of defects by local atomic jumps in the external stress ﬁeld and to anelasticity. 2.2.1 The Snoek Relaxation The classical Snoek relaxation, a mechanism described ﬁrst by Snoek (1941) to explain the damping due to C in α-Fe, is an anelastic relaxation caused by

S11 –S12 , S44 , S14

S11 –S12 S44

S11 –S12 S66 S44

S11 –S12 S44

compliance

–

– –

0 0 0

1 0

tetragonal

0

0 0

– – –

0 1

trigonal

–

1 0

1 0 0

2 0 0 1 0

1 1

orthorhombic 100 110

–

[001] 2 0

[001] 1 1 0

defect symmetry

110 0 1 1

100 1 0 1

1

[100] 1 1

1 2

2 1

monoclinic 100 110

2

2 2

1 1 2

2 3

triclinic

A dash means the absence of the defect in the crystal; zero means that the relaxation of the compliance is prohibited and 1, 2 or 3 means the existing of relaxation of diﬀerent types

trigonal

hexagonal

tetragonal

Cubic

crystal symmetry

Table 2.1. Selection rules for various defects and crystal systems (Nowick and Berry 1972)

2.2 Point Defect Relaxation 13

14

2 Anelastic Relaxation Mechanisms of Internal Friction Table 2.2. The λ-tensor (Nowick and Berry 1972)

defect symmetry

principal values

principal axes

cubic

λ1 = λ2 = λ3

arbitrary

1

tetragonal, hexagonal, and trigonal

λ1 = λ2 = λ3 or λ1 = λ2 = λ3

axis 1 along major symmetry axis or axis 3 along major symmetry axis

2

orthorhombic λ1 = λ2 = λ3

number of independent λ components

along the three symmetry axes

3

monoclinic

λ1 = λ2 = λ3

axis 1 or 3 along symmetry axis

4

triclinic

λ1 = λ2 = λ3

unrelated to crystal axes

6

“heavy” foreign interstitial atoms (IA) in the body-centred cubic (bcc) metals. It is observed in O, N, C interstitial solid solutions in metals belonging to the groups VB (V, Nb, Ta) and VIB (Cr, Mo, W), and also in α-Fe. The Snoektype relaxation, i.e., the same mechanism extended to the case of alloys, is observed in many bcc dilute and concentrated substitutional alloys where the additional interaction between interstitial and substitutional atoms inﬂuences the relaxation parameters (see 2.2.1).1 Relaxation Mechanism The O, N and C atoms are located in the octahedral interstices of the bcc metal lattice (Dijkstra 1947; Nowick and Berry 1972; Weller 2001). The two metal atoms nearest to the interstice (distance about a/2) move aside by√∼a/10; the displacement of the other four atoms, located in a distance of a/ 2, is about one order of magnitude smaller (Blanter and Khachaturyan 1978) (Fig. 2.1.). The resulting lattice distortions (elastic dipoles) are oriented mainly along one axis (x, y or z) and have a tetragonal symmetry. According to the selection rules (Table 2.1), a defect with tetragonal symmetry in the cubic lattice causes relaxation of the elastic compliance (S11 –S12 ) and therefore must cause energy losses. The three types of interstices corresponding to the three lattice directions (x, y, z) form three sublattices (numbered p = 1, 2, 3). In the absence of external stresses, the dissolved IA are distributed uniformly among the interstices in all three sublattices: the related occupation probabilities n1 , n2 and n3 are equal to each other. By applying a tensile stress along one cubic crystal axis (e.g., “X” in Fig. 2.1), the arrangement of dissolved atoms in the octahedral interstices of the sublattice with the number p = 1 becomes energetically more favourable than those with p = 2 or 3. Therefore, the dissolved IA will 1

A more general case of Snoek-type relaxation, in a very large variety of alloy structures, is found for hydrogen as the lightest foreign IA (see Sect. 2.2.4).

2.2 Point Defect Relaxation Z

15

Y X

Fig. 2.1. Octahedral interstices in the bcc crystal lattice: large circles are metal atoms; small circles, squares and triangles are interstices of the sublattices p = 1, 2 and 3, respectively

diﬀuse from sublattices “2” and “3” into “1”, and n1 will be higher than n2 and n3 . When the stress sign changes the reverse process sets in, and under the action of alternating periodic stresses this “diﬀusion under stress” of IA causes periodic variations of the occupation numbers n1 to n3 . This change in the distribution of IA among the sublattices of octahedral interstices causes an anelastic deformation of the crystal associated with a change in lattice spacings along the three main crystal axes: ax = a0 [1 + λ1 (n2 + n3 ) + λ2 n1 ] ay = a0 [1 + λ1 (n1 + n3 ) + λ2 n2 ]

(2.3)

az = a0 [1 + λ1 (n1 + n2 ) + λ2 n3 ], where λ1 and λ2 are two components of the λ-tensor not equal to each other (Table 2.2); a0 is the lattice parameter of the pure metal. The diﬀerence |λ2 − λ1 | determines the “elastic dipole strength”. Methods for determining λ1 and λ2 are described later. The relaxation time τ of this Snoek relaxation process is associated with the diﬀusion of IA on the octahedral interstices, D = D0 exp[−H/(RT )], where D0 is the pre-exponential factor and H is the activation energy of diﬀusion of IA (Nowick and Berry 1972): τ = a20 /(36 D),

(2.4)

a20 /(36

(2.5)

τ0 =

D0 ).

Therefore, the activation energy of the Snoek relaxation is equal to the activation energy H of the IA diﬀusion. The Snoek peak temperature Tm then follows from (2.4) for 2πf · τ = 1: Tm = H/{R ln[πa20 f /(18D0 )]}, where f is the imposed frequency of mechanical vibrations.

(2.6)

429 314

300

579–596

498 483–515

514 562

422 626 615 420 443 544

458

670–683

Cr–N α-Fe–C

α-Fe–N

Mo–C

Mo–N Mo–O

Nb–C Nb–N

Nb–O Ta–C Ta–N Ta–O V–C V–N

V–O

W–C

188–197

124.0

111 160.6 160.1 106.2 114.7–117.3 151.0

137.5 151.0

125 130–140

165

78.8

114.4 83.7

H (kJ mol−1 )

Calculated values (Blanter 1989)

435

Cr–C

a

Tm (K) (f = 1 Hz)

system

1.0

0.51

3.6 8.55

2.65

1.22

11

2.38

1.43 1.89

τ0 (10−15 s)

2550a

800

490 1030a 730 740 1070a 800

660a 480

2140a 1340a

2170a

2000

1880 2150

2620a

Qm −1 × 104 (per one at.% of dissolved atoms, polycrystal, at T = Tm )

Table 2.3. Snoek relaxation parameters

Zemskij and Spasskij (1966), Golovin et al. (1997) Weller (2001), Klein (1967) Weller (2001), Blanter and Piguzov (1991) Weller (2001), Blanter and Piguzov (1991) Yamane and Masumoto (1981), Shchelkonogov et al. (1968) Weller (2001) Yamane and Masumoto (1981), Grandini et al. (1996a) Weller (2001) Weller (2001), Blanter (1978), Weller et al. (1981b) Weller (2001), Blanter (1978) Weller (2001) Weller (2001), Blanter (1978) Weller (2001), Blanter (1978) Blanter (1978), Weller et al. (1985) Weller (2001), Blanter (1978), Boratto and Reed-Hill (1977) Weller (2001), Blanter (1978), Boratto and Reed-Hill (1977) Shchelkonogov et al. (1968), Grau and Szkopiak (1971), Schnitzel (1965)

reference

16 2 Anelastic Relaxation Mechanisms of Internal Friction

2.2 Point Defect Relaxation

17

Some peak temperatures Tm , determined experimentally for f = 1 Hz, are listed in Table 2.3. Since the respective diﬀusion characteristics diﬀer signiﬁcantly, the Tm values are also rather diﬀerent. If diﬀerent IA are dissolved in the same metal, their Snoek peaks sometimes overlap, as seen for C and O in V, for O and N in Mo or for C and N in Ta, Cr and Fe, respectively; in other cases, each IA gives its own Snoek peak (Fig. 2.2). For all interstitial solid solutions in which the Snoek relaxation has been recorded, the values of D0 (and thus τ0 ) are rather similar. Therefore, there is a reliable linear dependence of Tm on H (Fig. 2.3), which corresponds to τ0 = 2.08 · 10−15 s (quite similar for all solutions) and Tm (K) = 3.765 H (kJ mol−1 ) (Weller 1985). Orientation Dependence The relaxation strength ∆ and the peak maximum Qm −1 depend on the direction of the stress applied to the crystal lattice according to the selection rules and the Snoek relaxation mechanism described earlier. This direction determines the change in the energy of a dissolved IA in the interstices of diﬀerent sublattices if an external stress is applied. This eﬀect is described by the orientation parameter Γ : Γ = cos α1 · cos α2 + cos α1 · cos α3 + cos α2 · cos α3

(2.7)

where α1 , α2 , α3 are the angles formed by the applied stress and the cube axes [100], [010] and [001], respectively (Nowick and Berry 1972). According to (Swartz et al. 1968; Nowick and Berry 1972; Weller 1985) Qm −1 = ηC0 · V · (λ2 − λ1 )2 · F (Γ ) · M/(RTm )

Fig. 2.2. The Snoek peaks of O and N in Nb (Grandini et al. 2005)

(2.8)

18

2 Anelastic Relaxation Mechanisms of Internal Friction

where C0 is the atomic fraction of interstitial atoms in the solution, V is the volume of one mole of the host metal. In case of torsional vibration, the parameter η = 2/3, and M = G, F (Γ ) = Γ ; for ﬂexural vibration, η = 1/9, M = E, F (Γ ) = 1–3Γ . This results in diﬀerent orientation dependences for diﬀerent kinds of deformation. In case of ﬂexure the extending and compressing stresses both are applied along the [100] direction, cos α1 = 1, cos α2 = cos α3 = 0, Γ = 0, thus the value Qm −1 is maximal (Table 2.4 and Fig. 2.4). The most prominent diﬀerences observed are the ones between the IA energies in the octahedral interstices of sublattices p = 1 and p = 2, 3 with the maximum number of atoms passing from one sublattice to√another. If the stress is applied along 111 , cos α1 = cos α2 = cos α3 = 1/ 3, Γ = 3 and Qm −1 = 0. In this case, octahedral interstices of all three sublattices are deformed similarly and “diﬀusion under √ stress” is absent. In case of the 110 direction, cos α1 = cos α2 = 1/ 2, cos α3 = 0, Γ = 1/3 and Qm −1 has an intermediate value. Similar orientation dependences are observed for the longitudinal vibrations. For torsionial and

Fig. 2.3. Plot of the activation energy H versus peak temperature Tm for Snoek relaxations in several bcc metals (Weller 1985) Table 2.4. Orientation dependence of the carbon Snoek peak height of iron monocrystals (Ino and Inokuti 1972) crystal axis 100 110 111 polycrystal

Qm −1 × 104 torsion ﬂexure 1.54 26.7 58.1 40

65.3 28.3 2.7 34.1

carbon concentration, 10−4 wt% 70 ± 10 65 ± 10 65 ± 10 62 ± 10

2.2 Point Defect Relaxation

19

Fig. 2.4. Orientation dependence of the carbon Snoek maximum for iron single crystals (Ino and Inokuti 1972). Crystal orientations: 1, 6: 100; 2, 5: 111; 3, 4: 110. Type of vibrations: 1, 3, 5: ﬂexure, f = 1.15÷1.18 Hz; 2, 4, 6: torsion, f = 3.25– 3.46 Hz

transversal vibrations, the 111 direction of applied stress gives the maximal eﬀect, the 100 direction the minimal eﬀect, and 110 an intermediate one. For polycrystalline samples, averaging over all grain orientations gives Γ ≈ 0.2 (Nowick and Berry 1972). From (2.8) one can obtain for torsional vibrations (2.9) Qm −1 = (0.4G/3) · [C0 V · (λ2 − λ1 )2 /(RTm )], and for ﬂexural vibrations Qm −1 = (0.4E/9) · [C0 V · (λ2 − λ1 )2 /(RTm )].

(2.10)

For metals, the Poisson ratio µ ≈ 0.3 (Livshiz et al. 1980) and therefore G = 0.5·E/(µ+1) ≈ 0.4·E, and then the height of the Snoek peak almost does not depend on the types of oscillation for texture-less polycrystalline samples (Table 2.4) as it follows from (2.9) and (2.10). The presence of a preferred crystallographic orientation of grains in a polycrystal, a texture, also leads to a dependence of Qm −1 on the type of oscillations and on the direction of applied stress (Fig. 2.5). Concentration Dependence A linear dependence of the Snoek peak height on the dissolved element concentration follows from (2.8). It is more prominent for a larger diﬀerence |λ2 −λ1 |, i.e., for a higher asymmetry of distortions caused by the dissolved IA. Such a linear dependence for Fe–C and Fe–N is shown in Fig. 2.6, for Nb–O in

20

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.5. Snoek carbon peaks for iron samples cut parallel to the rolling direction (0◦ ), at 45◦ and at 90◦ to the rolling direction. f = 1 Hz (Magalas et al. 1996)

Fig. 2.6. Concentration dependence (wt%) of the carbon (1) and nitrogen (2) Snoek peak heights for iron. f = 1 Hz (Lenz and Dahl 1974)

Fig. 2.7. The Fe samples were quenched from temperatures, at which the total C or N concentration in iron was within solubility in the α-solid solution. If a supersaturated solution decomposes, the height of the peak is determined by the concentration of interstitials remaining in solid solution. In the metals of the VB group (V, Nb, Ta) having higher solubility of O and N than α-Fe (up to 0.5–1 at.% at room temperature), the linear dependence is observed up to ∼0.3 at.% (Weller et al. 1981c; Heulin 1985a): in the system Nb–O up to 0.35 at.%, and in the system Nb–N up to 0.25 at.% (Ahmad and Szkopiak 1972). In high-purity metals, this boundary may be higher (Weller 2001).

2.2 Point Defect Relaxation

21

Fig. 2.7. Variation of the Snoek peak height in Nb with oxygen content (Schulze et al. 1981)

A deviation from the linear dependence, with a weaker increase in Qm −1 with rising concentration, occurs at higher concentrations of solute IA as a result of the formation of groups of dissolved atoms, e.g., pairs or triplets, due to IA interaction. The IF peaks caused by reorientation of these groups under stress are characterised by higher activation energies and occur at higher temperatures than the main Snoek peak. The Snoek peak broadens at high temperatures (Powers and Doyle 1956; Gibala and Wert 1966a, 1966c; Ahmad and Szkopiak 1970). If the concentration of dissolved IA increases, a signiﬁcant part does not contribute to the main Snoek peak as isolated atoms, thus Qm −1 increases less strongly with concentration. The existence of pairs and triplets of IA is questioned in some papers (Weller et al. 1981b, 1985), while other publications (Cost and Stanley 1985; Heulin 1985a; Gibala 1985) conﬁrm the formation of such complexes. The inﬂuence of IA concentration on the Snoek peak shape can be explained by IA long-range interaction. It was analysed by simulation of IA short-range order and its inﬂuence on relaxation (Weller et al. (1992); Haneczok et al. 1992, 1993; Blanter and Fradkov 1992; Haneczok 1998; Blanter and Magalas 2003). The slope of Qm −1 as a function of C0 (increase per unit concentration of IA) is determined mainly by the value (λ1 − λ2 ), i.e., by the level of distortions created in the crystal lattice by a dissolved IA. The values λ1 and

22

2 Anelastic Relaxation Mechanisms of Internal Friction

λ2 may be determined by two methods (Nowick and Berry 1972; Blanter and Khachaturyan 1978; Khachaturyan 1983): (a) By the dependence of the lattice parameter on concentration in long-range ordered interstitial solid solution with a known atomic structure according to (2.3), as it is done for C and N in iron using the martensite: λ1 = a−1 0 dax /dn1 , λ2 = a−1 0 daz /dn2 ,

(2.11) (2.12)

where z is the tetragonal axis. (b) The diﬀerence (λ1 − λ2 ) can be determined by the concentration dependence of Qm −1 from (2.8), and the value (2λ1 + λ2 ) by the lattice parameter dependence on concentration in the non-ordered solution. According to such a method, λ1 and λ2 were determined for O and N in V, Nb, Ta (Blanter and Khachaturyan 1978) (Table 2.5). For solutions of C in V, Nb, Ta and for solutions of N and O in Cr, Mo, W, there are no reliable experimental data for λ1 and λ2 because of low solubility. It was shown (Blanter 1985) that the tetragonality factor ξ = λ1 /λ2 ≈ −0.1 for all interstitial solid solutions in octahedral interstices of the bcc lattice. The λ2 value is higher if the diﬀerence between the sizes of the dissolved IA and the octahedral interstice is bigger, λ2 is lower in case of stronger chemical interaction between the dissolved IA and host metal atoms. The calculated values λ1 and λ2 for C in V, Nb, Ta and C, O, N in Cr, Mo, W are given in Table 2.5. The level of distortions produced by dissolved IA in a bcc lattice (λ2 ) increases in the sequence O → N → C, and while moving upwards along every periodic table group in the sequence Ta → Nb → V and W → Mo → Cr for each dissolved element. This is due to the increase in size incompatibility, caused in the ﬁrst case by the increase in the dissolved atom diameter and in the second case by the decrease in metal lattice spacings, and to weakening of the metal–metalloid chemical interaction. In the VIB group metals, distortions are more pronounced than in the VB group metals because of lower lattice parameters and weaker chemical interaction. Inserting values |λ2 − λ1 | from Table 2.5 into (2.8), the values Qm −1 per 1 at.% of dissolved IA were calculated for some solid solutions in the metals of the VB and VIB groups (Blanter 1989); these values are also given in Table 2.3. There are no reliable experimental data on the Snoek peak in most of these metals mainly due to the low solubility of IA. The height of the IF peaks caused by O and N are close to each other, while those for C are signiﬁcantly higher. The Snoek maxima are higher in the VIB group metals and in α-Fe than in the VB group metals at similar concentrations due to higher crystal lattice distortions by dissolved IA.

2.2 Point Defect Relaxation

23

Table 2.5. The λ-tensor components for interstitial atoms in octahedral interstices of the bcc metals metal IA α-Fe

λ1

λ2 λ2 − λ1 method reference

C −0.09 0.86 −0.10 0.89 N −0.07 0.83 −0.06 0.92

V

Nb

C N O C N

−0.08 −0.14 −0.10 −0.07 −0.05

0.78 0.69 0.66 0.68 0.60

O −0.06 0.50 Ta

C −0.07 0.67 N −0.05 0.56 O −0.04 0.47

Cr

Mo

W

C N O C N O C N O

−0.09 −0.07 −0.06 −0.08 −0.07 −0.06 −0.08 −0.06 −0.05

0.85 0.69 0.63 0.76 0.67 0.55 0.76 0.64 0.52

0.95 0.99 0.83 0.90 0.98 1.0 0.86 0.83 0.76 0.75 0.65 0.65 0.56 0.61 0.74 0.61 0.70 0.51 0.67 0.94 0.76 0.69 0.84 0.74 0.61 0.84 0.70 0.57

1 1 2 1 1 2 4 3 3 4 3 2 3 2 4 3 2 3 2 4 4 4 4 4 4 4 4 4

Roberts (1953) Cheng et al. (1990) Weller (2001) Bell and Owen (1967) Cheng et al. (1990) Weller (2001) Blanter (1985) Blanter and Khachaturyan (1978) Blanter and Khachaturyan (1978) Blanter (1985) Blanter and Khachaturyan (1978) Weller (2001) Blanter and Khachaturyan (1978) Weller (2001) Blanter (1985) Blanter and Khachaturyan (1978) Weller (2001) Blanter and Khachaturyan (1978) Weller (2001) Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin Blanter (1985), Blanter and Gladilin

(1985) (1985) (1985) (1985) (1985) (1985) (1985) (1985) (1985)

Methods: The values λ1 and λ2 or their diﬀerence were determined: 1 – by the dependence of the lattice parameters on concentration in the martensite; 2 – by the Qm −1 concentration dependence of high-purity monocrystals; 3 – by the Qm −1 and the lattice parameter concentration dependence and 4 – by calculation

Temperature Dependence The height of the Snoek peak Qm −1 is proportional to 1/Tm (2.8), and therefore an increase in vibration frequency is associated with an increase of Tm and decrease of Qm −1 for the same concentration of IA. In some cases Qm −1 ∝ (Tm − T0 )−1 (Nowick and Berry 1972), where T0 is the ordering temperature of IA in a solid solution. However, T0 Tm for low concentration of IA, and the value T0 can be omitted. The relation Qm −1 ∝ 1/Tm is well documented for Ta – 0.074 at.% O (Fig. 2.8; Weller et al. 1981b).

24

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.8. Temperature dependence of the oxygen Snoek peak height in Ta with 0.074 at.% (Weller et al. 1981b)

Grain Size Dependence With decreasing grain size of a polycrystal, the Snoek peak height decreases. The coeﬃcient k in the formula Qm −1 = kC0 , where C0 is the concentration in wt%, is a function of grain size (Ahmad and Szkopiak 1972): 1/k = 1.85 + 0.28 d−1/2 for Nb–O 1/k = 2.14 + 0.3 d−1/2 for Nb–N,

(2.13)

where d is the mean grain size in mm. The value k increases by a factor of two with an increase of grain size from d ≈ 0.04 mm to d ≈ 1 mm. The values of the coeﬃcient k for C and N in iron are given in Table 2.6 (Ferro-Milone and Mezzetti 1975). There are three reasons for the decrease in Snoek peak height with decreasing grain size: (1) diﬀerent textures in ﬁne- and coarse-grained specimens; (2) adsorption of dissolved IA on the grain boundaries which reduces the solid solution concentration of IA (Nowick and Berry 1972; Ahmad and Szkopiak 1972); (3) peculiarities of the stress distribution in crystals with diﬀerent grain sizes (Ferro-Milone and Mezzetti 1975). The data for Qm −1 in Table 2.3 are obtained mainly for coarse-grained polycrystalline specimens without any well deﬁned texture. However, in some papers on the Snoek relaxation the existence of texture was not checked and the grain size was not given. Inﬂuence of Alloying Elements: The Snoek-Type Relaxation in Ternary Alloys (Me–SA–IA) Substitutional atoms (SA) in a host lattice must inﬂuence the parameters of the original Snoek relaxation via SA–IA interaction, i.e., by a change in the

2.2 Point Defect Relaxation

25

Table 2.6. Inﬂuence of grain size on the Snoek maximum height in α-Fe (FerroMilone and Mezzetti 1975) interstitial C

N

grain size (mm)

concentration Cm (wt%)

k = Qm −1 /Cm , 1/wt%

0.015–0.040 0.015–0.050 0.07–0.20 0.5–2.0 0.015–0.025 0.05 0.07 0.15 0.28 0.40 0.70 0.5–2.0

0.02 0.031 0.02 0.023 0.006–0.045 0.032 0.017 0.032 0.017 0.032 0.017 0.006–0.045

0.5 0.53 0.7 1.14 0.74 0.78 0.83 0.9 0.94 1 1.12 1.05

activation energy of the relaxation, and by a change of the value (λ1 − λ2 ), i.e., the relaxation strength. In spite of more than 50 years of study since the pioneering works of Wert (1950, 1952), Dijkstra and Sladek (1953) on alloyed iron, the experimental situation about the inﬂuence of SA on the Snoek relaxation has remained not clear enough. Some SA may not aﬀect the position and height of the Snoek peak, others may reduce the peak height, lead to the appearance of additional peaks at higher temperature besides the height reduction, or suppress the Snoek peak and produce new peaks at higher temperatures (e.g., Krishtal et al. 1964; Saitoh et al. 2004). One can also ﬁnd contradicting results in the literature. The Snoek-type relaxation in alloys can be explained in many cases on the basis of the SA–IA interaction in the crystal lattice, which leads to a change in the diﬀusion activation energy of dissolved IA located near the relatively immobile SA. The recent status of research shows that in most cases two categories of alloys are distinguished with respect to Snoek relaxation: dilute (or non-concentrated) alloys, where SA can be considered as randomly distributed, non-interacting with each other and sometimes giving an additional contribution to the Snoek peak, and concentrated alloys, where SA always aﬀect the IA jumps in the host lattice: SA may be distributed either randomly or in some order on a superlattice. Finally, the type of SA–IA interaction, which may vary from a short-range type in case of a strong ‘chemical’ interaction to a long-range ‘elastic’ interaction, aﬀects the Snoek relaxation. The critical concentration at which alloys should be considered as concentrated depends on the range of SA–IA interaction in the host lattice and is diﬀerent for diﬀerent alloys.

26

2 Anelastic Relaxation Mechanisms of Internal Friction

The Snoek-Type Relaxation in Dilute Alloys Most experimental studies were done using dilute alloys: in most cases the SA concentration in dilute alloys is assumed to be <1 at.%, but sometimes this range is extended up to 2 or even 5 at.%. It has been shown that Cr in Fe–C leads to a decrease, broadening and slight shift to higher temperatures in the main Snoek peak (Golovin 1978; Saitoh et al. 2004); a similar inﬂuence of Mo, V and W was reported in (Golovin 1978). Cr in Fe–N produces an additional peak at a slightly higher temperature as compared to the main peak (Numakura and Koiwa 1996, Guan et al. 2004). Al in iron leads to broadening of the Snoek peak from the high temperature side (J¨ aniche et al. 1966; Tanaka 1971; Golovin et al. 2003a, 2004b, 2005c; see Fig. 2.9a). A similar but smaller eﬀect is produced by Si (Golovin et al. 2005c, Golovin and Golovina 2006, Ruiz et al. 2006). This broadening can be explained by a second Snoek-type peak, caused by C atom jumps near SA. Little inﬂuence 1.0

(Q−1(T)−Qb−1)/(Q−1(Tmax)−Qb−1)

(a)

0.8

Fe-3Al-C Fe-3Si-C Fe-3Ge-C Fe-3Co-C

3Ge 3Co

f, Hz 530

520

0.6

3Al

500

3Si

0.4

490

0.2

3Si

0.0

(b)

(Q−1(T)−Qb−1)/(Q−1(Tmax)−Qb−1)

350

1.0

Fe-7Al

0.8

Fe-3Al

0.6

400

450

7

Fe 0Al

0.4 0.2

T, K

8

10Al

3Al

Fe-8Al Fe-10Al

0.0 350

400

450

500 T,K

Fig. 2.9. The “normalised” TDIF (a) for Fe–3%Me, Me = Al, Ge, Si and (b) for Fe–Al with = 3, 7, 8, 10 at.%Al Golovin et al. (2005c). Frequency vs. T is plotted on the right scale in (a)

2.2 Point Defect Relaxation

27

occurs by up to 2% Co, Mn, Si, Mn, P (Saitoh et al. 2004) and even 3 at.% Ge, Co (Golovin and Golovina 2006) in Fe–C. In some papers an additional Snoek-type peak was reported at higher or lower temperatures and explained by IA–SA and SA–IA–SA interactions (e.g., Fe–B–C, Fe–Co(≤4.5 wt%)–C, Fe–Si(3 wt%)–C (Golovin 1978)). Additional peaks were observed in Fe–N alloyed by Mn (Ritchie and Rawlings 1967), Cu and Ni (Ogi et al. 2000, 2001), etc. Peaks at higher temperatures were observed in Nb–O and Nb–N alloyed by 1 at.% Cr, Zr or Hf, while addition of Mo to these alloys leads only to a decrease in the peak height (Szkopiak and Smith 1975). The theory of the inﬂuence of SA–IA interaction on the Snoek relaxation has been given by Koiwa (1971a,b,c,d, 1972) and Numakura and Koiwa (1996) and has been proved in many experimental papers mainly for iron-based alloys. The Snoek-Type Relaxation in Concentrated Alloys There is no well-established theory as yet for the case of higher SA concentration in a host lattice: diﬀerent approaches were used to describe the situations in diﬀerent alloys. Roughly, one can distinguish between two methods, considering the total IF spectrum either as a sum of several Debye peaks, or explaining it by distributions in either activation energy or relaxation time, e.g., Golovin (2000). The summing of Debye peaks to interpret a total IF spectrum works better in case of short range IA–SA interaction, i.e., for welldeﬁned positions of IA in a solid solution. Some examples of such an interpretation can be found for Fe–Si–C (Krishtal 1965), Fe–Cr–C (Golovin et al. 1987a, 1992), Fe–Al–C (Golovin and Golovina 2006), Nb–Mo–O and Nb–V–O (Kushnareva and Snezhko 1994) alloys. In case of long-range IA–SA interaction the activation energies cannot be described by only few values, and the assumption of a continuous distribution is more reasonable. This distribution leads to a signiﬁcant broadening of the Snoek peak (e.g., in Fe–Al–C (Tanaka 1971; Golovin et al. 1998a) and Fe–Cr–C (Golovin et al. 1997a)). The Snoektype relaxation has been well studied for the Fe–Al system in a wide range of Al concentrations (Fischbach 1962; Hren 1963; J¨ aniche et al. 1966; Tanaka 1971; Golovin et al. 1998c, 2004b; Strahl 2006; see Fig. 2.9b). The Snoek-type peak in Fe–Al alloys (including the Fe3 Al intermetallic compound) is broadened and shifted to higher temperatures. At an Al concentration of 10–12 at.%, the original Fe–C component of the Snoek-type peak vanishes (i.e., no Al free surroundings of a jumping C atom exist any more). The Snoek-type peak also drastically decreases in presence of the carbide-forming elements Ti, Nb (Golovin et al. 2004c, 2005a) and Zr, Ta (Golovin et al. 2006b), where the C interstitials get ﬁxed in carbides. Ordering in Fe–Al decreases the peak widths (Tanaka 1971; Golovin et al. 1998a,c; Pozdova 2001, Pozdova and Golovin 2003) because only a few well-deﬁned C–Al distances occur. High hydrogen concentration inﬂuences the oxygen diﬀusion and therefore the oxygen Snoek peak in Nb and Nb–Ti: the relaxation strength decreases and the activation energy increases with hydrogen content (Schmidt and Wipf 1993; Golovin et al. 1996a, 1998b), see also Sect. 2.2.4.

28

2 Anelastic Relaxation Mechanisms of Internal Friction

2.2.2 Relaxation due to Foreign Interstitial Atoms (C, N, O) in fcc and Hexagonal Metals fcc Metals Interstitial solute atoms in face-centered cubic (fcc) metals occupy octahedral interstitial sites having the same symmetry as the host lattice. For this reason, an isolated interstitial atom does not contribute to anelastic relaxation if a stress is applied. In case they form complexes, the reorientation of atom pairs may occur under an external stress. This eﬀect was reported for the ﬁrst time by Rosin and Finkelshtein (1953) for carbon in fcc steels with 25 wt% Cr and 20 wt% Ni, and later conﬁrmed for Ni–C and Ni–Al–C alloys (Kˆe and Wang 1955a, 1955b). Up to now, such internal friction peaks have been studied in many austenitic steels (e.g., Kˆe and Tsien 1957, Golovin and Belkin 1965, 1972, Golovin et al. 1966), in Co–C, Co–Ni–C, Ni–Ti–H, Yb–O, Yb–N alloys (Mah and Wert 1964, 1968; Numakura et al. 1995, 1996b, 2000; Yokoyama et al. 1998), see Table 2.7. In spite of the fact that the peaks in austenitic steels, known as Finkelshtein–Rosin peaks, have many common features with the peaks in binary alloys (Ni–C, Co–C), they also have some peculiarities and will be described separately. The peaks in other fcc metals (no steels) are not called Finkelshtein–Rosin peaks. The main features of the Finkelshtein–Rosin relaxation can be described as follows (Rosin and Finkelshtein 1953; Hausch et al. 1983; Ito et al. 1981, Ito and Tsukishima 1985; Kˆe et al. 1987a):

Table 2.7. Examples of relaxation processes due to interstitial atoms in fcc metals alloy (wt%) Fe–C(0.5)– Ni(12)–Mo(3) Fe–Cr(18)– Mn(4)–N(0.4) Ni–C Pd–C Ni–Ti–H∗ Yb–N Yb–O ∗

f (Hz) Tm (K) H (kJ τ0 (s) mol−1 )

atom Ref. pairs

1.2 · 10−14 C-sub Teplov (1978, 1985)

2000

648

125

1

625

142

10−13

1 1 1 1 0.5

520 450 165 393 413

144 127 30.8 105 117

8 · 10−16 2 · 10−11

N-sub Banov et al. (1978a,b) C–C C–C H–Ti N-sub O-sub

Numakara et al. (2000) Yokoyama et al. (1998) Numakura et al. (1995) Mah and Wert (1964) Mah and Wert (1964)

In some fcc metals H atoms occupy octahedral interstices as O, N, C; in such cases H relaxation peaks may be similar to those produced by the “heavy” interstitial atoms.

2.2 Point Defect Relaxation

29

1. The FR peak position Tm (at f = 1 Hz) in steels is within the temperature range 470–570 K and depends (not very strongly) on the chemical composition of the steel. 2. An increase in the interstitial atom content leads to an increase in the FR peak height and a decrease in the peak temperature: for instance, in a manganese steel with 0.6–0.75 wt% C, Tm ≈ 540 K(f = 2 Hz), and in a steel with 0.88–0.97 wt% C, Tm is only 530 K. 3. The activation energy is close to the diﬀusion activation energy of carbon (or nitrogen) in alloyed austenitic steel and decreases slightly with increasing content of interstitial elements. 4. The peak height, Qm −1 ≈ 0.005 per atomic per cent carbon, is much lower than that of the Snoek relaxation, Qm −1 ≈ 0.2 per at.%. This is due to the fact that C and N atoms disturb the bcc lattice of α-Fe much more than the fcc lattice of γ-Fe. 5. The FR peak is broader than a Debye peak with a single relaxation time. Sometimes, it can be decomposed into two peaks located close to each other. 6. The peak height Qm −1 is proportional to C 2 at low C or N concentrations C (<0.1–0.25 wt%), but directly to C for higher concentrations. 7. Deformation increases the peak height (Golovin and Belkin 1965). This eﬀect was named dislocation enhanced FR eﬀect (DEFRE); Golovin and Golovin 1996, see section “Dislocation-Enhanced Snoek Eﬀect”. Sometimes deformation leads to additional peaks near the original FR peak. The enhancement of the FR peak can be explained by a change in the elastic distortions of the host lattice near the IA due to dislocations (Blanter et al. 2000a, 2000b). 8. Relaxation mechanism. After a ﬁrst suggestion by Rosin and Finkelshtein (1953) of a reorientation of C–C pairs, the reorientation of interstitial– substitutional atom (IA–SA) pairs was considered (Kˆe and Tsien 1956, 1957; Tsien 1961); later a reorientation of interstitial–interstitial atom (IA–IA) pairs including the kinetics of the formation of such pairs was proposed. Verner (1965) suggested a long-range IA–IA interaction in three to ﬁve coordination shells along the 110 , 112 and 130 directions. This model predicts, in agreement with the experimental data, a square dependence of the peak height on the C or N concentration if this concentration is low, and a linear dependence for higher C or N content. An important feature of the FR relaxation is that it takes place in the fcc lattice of γ-Fe with a high amount of substitutional atoms interacting with interstitial atoms. The eﬀect of such an interaction has been considered by Blanter et al. (2000a, 2000b). Contrary to studies of the FR relaxation in polycrystalline steels, single crystals were used for the case of Ni and Co (Numakura et al. 1995, 1996b, 2000; Mah and Wert 1968). It was concluded that the symmetry of the defects is tetragonal; the relaxation is caused by the reorientation of C–C pairs in the

30

2 Anelastic Relaxation Mechanisms of Internal Friction

second-neighbour positions. For the Ni–C alloy Qm −1 ∝ C n , where n = 1.68 although n = 2 would be expected from the C–C pair reorientation model. This deviation is the result of a strong elastic interaction of C atoms in Ni, which aﬀects the concentration dependence of C–C pairs (Numakara et al. 2000). In the Pd–C alloy, the elastic interaction of C atoms is weaker because of the larger Pd lattice parameter, thus n = 2 (Yokoyama et al. 1998; Numakara et al. 2000). In the Ni–Ti–H alloy, the peak is attributed to the reorientation of H–Ti pairs (Numakura et al. 1995). The orientation dependence of the peak height suggests that the defect symmetry is 111 trigonal. One of the possible conﬁgurations is the H–Ti pair in which hydrogen occupies the second neighbour octahedral sites around the substitutional atom. Simulations of the short range order for these alloys and internal friction spectra taking into account the long-range interaction of solute atoms (Blanter 1999) conﬁrm that the H–Ti complexes can be responsible for the hydrogen peak in Ni with substitutional Ti atoms. To summarise: the internal friction peaks in fcc interstitial solid solution are caused by IA–IA or IA–SA pairs. Hexagonal Metals Relaxation maxima due to “diﬀusion under stress” of “heavy” interstitial atoms are observed in solid solutions of oxygen in Ti, Sc, Hf, Y, Zr, of nitrogen in Ti, Hf, Y and of carbon in Ti, Y (Table 2.8). Similar peaks from dissolved “light” interstitials (H, D) were recorded in the rare earth metals Lu, Sc and Y, and attributed to a Zener or Zener-type relaxation (e.g., Vajda et al. 1981, 1983, 1990, 1991a; Vajda 1994; Kappesser et al. 1993, 1996a, 1997; Trequattrini et al. 1999, 2000, 2004b). In Ti, Zr and Hf with much lower H or D solubility, related eﬀects are found only in the hydride phase but not in solid solution (see also Sects. 2.2.3 and 2.2.4). Here we discuss only the relaxation caused by the “heavy” interstitial atoms. In the literature, only very limited information can be found for most of the materials included in Table 2.8. The Ti–O and Zr–O solid solutions have been most extensively studied. The existing information permits to summarise the main features of the relaxation process as follows: 1. The peak shape is close to a Debye peak both for polycrystals (Fuller and Miller 1977) and single crystals (Ritchie et al. 1976), i.e., this is a process with a single relaxation time. 2. The peak height increases linearly with increasing interstitial concentration C in technical grade pure Zr (Gacougnolle et al. 1970, 1971) and Ti (Bleasdale and Bacon 1976). In the high purity metals, Qm −1 ∝ C 2 (Bertin et al. 1976; Namas 1978; Gacougnolle et al. 1975; Fuller and Miller 1977). The peak is absent in Zr in the case of oxygen concentration less than 3 at.% (Gacougnolle et al. 1975). In Ti, Qm −1 ∝ C if C < 0.3 at.%

2.2 Point Defect Relaxation

31

Table 2.8. Parameters of relaxation processes due to “heavy” interstitial atoms in hexagonal metals a

alloy (wt%)

Tm or Tm (aver) (K)

H or H (aver) (kJ mol−1 )

Hf–Zr(6)–N Hf–Zr(6)–O Sc–O

753 [a] 753 [a] 430(f = 3.5 kHz) [b] 520(f = 3.5 kHz) [b] 677 [c] 773 [l] (697–754)\722 [c,d,e,f,g,h,i] 500 [k] 430 [k] 388 [k] 440(f = 1.8 kHz) [m] (690–704)\700 [l,n,o,p,r]

209 [a] 243 [a]

Ti–C Ti–N Ti–O Y–C Y–N Y–O Y–O Zr–O

Qm

−1b

Qm −1 = 7 · 10−5 CO [b] 202 [c] 241 [l] (200–242)\218 [c,d,g,h,i,j] 117 [k] 100 [k] 90 [k] 67.3 [m] (192–219)\ 202 [l,n,o,p,r]

Qm −1 ≈ 2.8 · 10−5 CC 2 [c] Qm −1 ≈ 0.7 · 10−5 CO 2 [c]

Qm −1 ≈ 1.6 · 10−4 CO [n]. Qm −1 ≈ (2.6 · CO 2 + 0.6 · CO 3 ) · 10−6 [o], Qm −1 ≈ 0.6 · 10−5 CO 2 [r]

after recalculation to f = 1 Hz, if the frequency is not speciﬁed. concentrations CC , CN , CO are given in at.% Tm (aver) and H (aver) are average values.

a

b

References: a-Bisogni et al. 1964; b-Trequattrini et al. 2004a; c-Miller and Browne 1970; d-Bratina 1962; e-Browne 1972; f-Clauss et al. 1974; g-Bertin et al. 1976; h-Namas 1978; i-Wegielnik and Chomka 1979; j-Pratt et al. 1954; k-Borisov et al. 1971; l-Miller 1962; m-Cannelli et al. 1996, 1997; n-Gacougnolle et al. 1970, 1971; o-Gacougnolle et al. 1975; p-Ritchie et al. 1976, 1977, r-Fuller and Miller 1977.

O and Qm −1 ∝ C 2 if C = 3–8 at.% O (Clauss et al. 1974). Qm −1 is much higher in technical grade pure metals than in high purity ones, and also much higher in Ti–O as compared to Zr–O: the O atoms create higher distortions in the Ti crystal lattice according to the concentration coeﬃcients of lattice expansion in Ti and Zr (Blanter et al. 2002). 3. The activation energy of the relaxation process (H) is close to that of the macroscopic diﬀusion HD : for O in Ti, HD = 191 kJ mol−1 , for O in Zr, HD = 201 kJ mol−1 (Bergner 1986). The data summarised in Table 2.8 do not allow to estimate the diﬀerence between H and HD . The H value for oxygen in technical grade pure titanium (205.5 kJ mol−1 ) is lower than that in high-purity titanium (237.4 kJ mol−1 ) (Wegielnik and Chomka 1979). A similar tendency occurs in Zr–O alloys (Gacougnolle et al. 1970, 1971, 1975).

32

2 Anelastic Relaxation Mechanisms of Internal Friction

4. The relaxation parameters depend on solute atoms in the host lattice. For example, introduction of substitutional atoms (0.1–1 at.%) changes the O and N relaxation parameters in Zr essentially and results in the appearance of additional peaks at higher temperatures (Mishra and Asundi 1972). The activation energy of the additional oxygen peaks in diﬀerent alloys is within the range of 167–340 kJ mol−1 . 5. Relaxation mechanism. Although the single O, N, C interstitial atoms in octahedral sites of the hcp crystal lattice represent tetragonal elastic dipoles, their transition into other octahedral interstices does not change the dipole orientation and cannot cause relaxation. Only in case of SA–IA or IA–IA pairs the defect symmetry decreases, and relaxation becomes possible via reorientation of such a pair (Povolo and Bisogni 1966, Nowick and Berry 1972) or of more complex defects (Blanter et al. 2004). A linear concentration dependence Qm −1 ∝ C would be expected for the IA–SA pairs, and a quadratic one, Qm −1 ∝ C 2 , for the IA–IA pairs. In the technical grade pure alloys and also sometimes in the alloys with low concentration of interstitial atoms, the main contribution belongs to the IA–SA pairs, while in the pure metals the main contribution is related to the IA–IA pairs. At the same concentration of the interstitial atoms, the amount of atomic pairs contributing to the relaxation (IA–SA) is higher in the technical grade pure metals (where the main impurities are the substitutional atoms) than in the high purity metals for which the relaxation is produced by the IA–IA pairs. This explains why Qm −1 in technically pure metals is higher than that in the high purity metals. The pair reorientation or the change in short-range order takes place via diﬀusional jumps of the more mobile atoms. There are two types of such jumps: in the basic plane (with the jump frequency ω1 ) and along the hexagonal axis (ω2 ). In the case of IA–SA relaxation in Zr–O (Ritchie et al. 1976, 1977), the relaxation is controlled by ω1 . Further progress in understanding the relaxation mechanism needs more experimental study of single crystals of well-deﬁned chemical composition, and the analysis of results should be based on modeling the short-range order of interstitial atoms and its changes under stress taking into account the long-range interactions of dissolved atoms. 2.2.3 The Zener Relaxation As shown in Sect. 2.2.1, a distortion of the lattice around a defect with a lower symmetry than that of the crystal lattice is the necessary prerequisite for mechanical relaxation to occur; thus single vacancies or single substitutional atoms in a cubic lattice will not produce any relaxation eﬀect on loading. However, as ﬁrst shown by Zener (1943, 1947) for an α-brass alloy (Cu–Zn), the existence of solute next neighbor pairs or clusters results in a relaxation

2.2 Point Defect Relaxation

33

Fig. 2.10. Zener relaxation peaks in Cu–19at.%Al single crystal measured at two frequencies. (From Rivi`ere and Gadaud 1996)

maximum, called “Zener peak”, cf. Fig. 2.10, in a temperature range where the solute atoms are mobile and enable reorientation of the solute atom pair in the lattice under the action of the applied stress. This applies not only for fcc but also for other crystal types (bcc, hcp), and has been reviewed extensively, e.g., by Nowick and Berry (1972), De Batist (1972) and Wert (see Weller 2001). The characteristic parameters, the relaxation strength ∆Z and the relaxation time τZ , show the following dependencies. As pairs of atoms are involved, for dilute and random solid solutions the relaxation strength, which is proportional to the number of reorienting pairs, should be proportional to the solute concentration squared, C 2 (or rather, but in practice not distinguishable, ∝ C 2 (1 − C)2 ), with a Boltzmann factor including the binding energy EB , ∆Z ∼ C 2 exp(EB /kT ) and

τZ = τoZ exp(HZ /kT ).

(2.14)

Surprisingly, this concentration dependence has been found to be valid even for rather high values (Seraphim and Nowick 1961, Wert (see Weller 2001)) as well for polycrystals as for single crystals, where the expected dependence on orientation has been veriﬁed. The relaxation strength varies approximately proportional to 1/T for ﬁxed concentrations (Li and Nowick 1961). The eﬀect of long-range ordering has ﬁrst been demonstrated with the alloy system Mg–Cd (Lulay and Wert 1956), where the relaxation peak is below the ordering temperature. As expected, the relaxation strength falls to zero in case of full ordering, as nearest neighbor solute pairs do not exist. For diﬀerent solid solutions the peak height varies from ≈ 5 · 10−4 (Qm −1 at C = 0.1, Rb in K) to ≈ 530·10−4 (Cu in Al, C = 0.1) (Blanter and Piguzov 1991). If these values are recalculated per 1 at.%, they turn out to be much lower than for the Snoek relaxation (see Table 2.3) because substitutional atoms distort the crystal lattice much weaker than interstitial atoms do.

34

2 Anelastic Relaxation Mechanisms of Internal Friction

As the atom movements during Zener relaxation (activation energy HZ , pre-exponential τoZ ) resemble those in ordinary diﬀusion, the rate of relaxation or relaxation time τZ , can in principle be used to estimate the diﬀusion activation energies HD at temperatures far below those in ordinary bulk diffusion experiments, because in internal friction the site changes involve near neighbours only. Table 2.9 gives a few examples for comparison, showing that the activation energy for tracer diﬀusion is slightly lower than that for the solvent and that the activation energy of the Zener relaxation is smaller than either. This diﬀerence is explained by the fact that in diﬀusion single atoms are active, while the Zener eﬀect involves atom pairs which interact with each other slightly diﬀerently than with the host lattice atoms. Unfortunately the geometry of atom movement in substitutional alloys is not as well known (cf. Nowick and Berry 1972) as for the Snoek eﬀect. Therefore and as several atomic diﬀusional jumps with unknown consecution may be involved in each place change for reorientation, the pre-exponential jump time in diﬀusion may not coincide in general with the corresponding value τoZ of the Zener relaxation (Wert in Weller (2001)), which is in the order of 10−15 s. Nevertheless, quenching experiments have established that the vacancy concentration is as important in Zener relaxation as it is in diﬀusion supporting the close relation of both mechanisms (Nowick and Berry 1972). In the case of concentrated solid solutions the relaxation is accompanied by a change of the degree of short-range order. According to the theory of Le

Table 2.9. Comparison of activation enthalpies determined from Zener relaxation and from tracer diﬀusion for solute and solvent atoms of some binary alloys (HZener from Nowick and Berry 1972, Wert in Weller 2001; HDiﬀusion from Eggersmann and Mehrer 2000, Salamon and Mehrer 2005) alloy

HZener (kJ mol−1 )

Hsolvent (kJ mol−1 )

Hsolute (kJ mol−1 )

Cu–31at%Zn Ag–30at%Zn Ag–32at%Cd

158 134 147

176 151 152

171 148 147

Ag–44at%Au

185

181

192

Fe–53at%Cr Fe–21.7at%Al

285 238 (A2) 270 (D03 )

313

294

Fe–25.5at%Al Fe–25.8at%Al

231 (A2) 269 (B2) 235 (B2) 286 (D03 )

reference Hino et al. (1957) Seraphim et al. (1964) Turner and Williams (1962) Turner and Williams (1963) Hirscher et al. (2000) Golovin and Rivi`ere (2006b) Salamon and Mehrer (2005) Golovin and Rivi`ere (2006a,b)

2.2 Point Defect Relaxation

35

Claire and Lomer (1954) the Zener peak height is Qm −1 ∝ [V0 f (χ0 , C)C 2 (1 − C)2 /(kT )]

(λ(p) )2

(2.15)

p

where V0 is the atomic volume; the coeﬃcients λ(p) = (∂ε/∂χp )σ,T describe the crystal lattice distortion in the direction p, ε is the deformation, χp is the number of bonds of one type in the direction p (χp is the short-range order parameter), χ0 is the value of χp for zero stress σ. The function f (χ0 , C) varies between 0 for the totally ordered and 1 for the totally disordered alloy. Equation (2.15) can approximately describe the Zener relaxation including the absence of the relaxation for ordered solid solutions. Another approximation for the case of concentrated solid solutions is based on a computer simulation of short-range order and changes of distortions around each solute atom due to short-range order. Owing to such asymmetric distortions each solute atom can be treated as an elastic dipole which provides a contribution to IF (Blanter and Kolesnikov 1996, 1997). Such approximation can describe the main features of the Zener relaxation, but the precision of the calculations is limited by the precision of the interatomic interaction energies used. The inﬂuence of ordering has recently been studied for several Fe–(22– 28)Al alloys (disordered A2, ordered either D03 or B2) by Golovin and Rivi`ere (2006a,b). They applied the isothermal forced pendulum technique with varying frequency in order to establish equilibrium conditions, which is not possible in the more commonly used method with a ﬁxed heating rate, and to measure Zener peaks below and above the order(A2)-disorder(D03 ) transition in Fe–22Al and the order(D03 )-order(B2) transition temperatures in Fe– (26–28)Al in order to quantify the function f (χ0 , C) in (2.15). Examples for the measurements on Fe–25.8 at.%Al are shown in Fig. 2.11 in the plots vs. log of frequency at various ﬁxed temperatures (in K), indicating the variation of the maximum damping with temperature in the range of the D03 to B2 transition (820 K). The activation energies of the Zener relaxation in A2, B2 and D03 phases are in the same sequence as those of diﬀusion (Salamon and Mehrer 2005), i.e., HA2 < HB2 < HD03 . The increasing activation energy of self-diﬀusion with increasing order parameter (η) is in agreement with Girifalco’s theory (Girifalco 1964): H(η) = H(0) · (1 + αη 2 ), where α is a parameter. A somewhat modiﬁed Zener eﬀect was described also for interstitial solid solutions with very high hydrogen concentration and for hydrides and deuterides: Lu–D and Lu–H (Vajda et al. 1981, 1983), Sc–D and Sc–H (Vajda et al. 1989, 1990, 1991a), Y–D (Vajda et al. 1991b, Vajda 1994), Y–H (Vajda et al. 1991a,b, Vajda 1994; Kappesser et al. 1997), TiDx (Wipf et al. 2000), TiHx (Kappesser and Wipf 1996; Wipf et al. 2000), and ZrHx (Mazzolai et al. 1976b; Pan and Puls 1996; Wipf et al. 2000); see also Sect. 2.2.4. In particular for TiHx (1.8 < x < 6) Kappesser and Wipf (1996) proposed stress-induced

36

2 Anelastic Relaxation Mechanisms of Internal Friction 100

T=738 K

40

882

-1

Modulus arb. units

4

Q (10 )

1.165

80

856

4

833

2

1.160

20

809 10

0 −3 −2 −1

0

1

738 692 668

783

2

log10(f/Hz)

ln (f/Hz)

Q-1x104

step-by-step: heating cooling

0 1.155

40

Fe-25.8Al

768

753

723

−2 −4

708

−6 20

−8 −3

−2

−1

0

1

2

−10

D03

1.6

log10 (f/Hz)

(a)

1.5

1.4

1.3

B2

1.2

1.1

1000/T (K)

(b)

Fig. 2.11. Zener relaxation in the Fe–25.8at.%Al alloy: (a) overview of Zener peaks measured at diﬀerent temperatures between 668 and 882 K; inset in left-upper corner: isothermal tests at 738 K: IF and relative modulus supplied with exponential background, and IF peak after background subtraction; (b) Arrhenius plot. (From Golovin and Rivi`ere 2006a)

changes in the atomic order of H atoms in their tetrahedral sites to occur, and good agreement with diﬀusion measurements by NMR and neutron spectrometry has been found. For systems which are prone to develop precipitates, or to dissolve them at more elevated temperatures, the Zener relaxation eﬀect may be applied to monitor the not yet precipitated or already dissolved solute content in studies of precipitation kinetics (for examples, see Schaller 2001b, and Sect. 3.2.3). Progressing from binary to ternary (or higher) systems, the Zener relaxation occurs in similar form, being slightly modiﬁed by the interactions of the present solute atoms with each other and with the matrix atoms. This has recently been considered for the system Fe–Al–Me (with Me = Cr, Si) by Golovin (2006b), Golovin et al. (2006b), Pavlova et al. (2006). 2.2.4 Anelastic Relaxation due to Hydrogen Compared to the heavier interstitials C, N, O considered in the previous sections, hydrogen in metals possesses a much higher mobility, sometimes by

2.2 Point Defect Relaxation

37

many orders of magnitude. This is especially true in bcc metals where the activation energies of diﬀusion are of the order of 0.1 eV or even lower, with diﬀusion coeﬃcients at room temperature as high as 10−5 cm2 s−1 correspondolkl and Alefeld 1978, Wipf 1997). Such ing to about 1012 jumps per second (V¨ extreme mobility and some other anomalies point to non-classical diﬀusion including quantum eﬀects and tunneling (at least in bcc metals), but many details of the physics of hydrogen diﬀusion in diﬀerent metallic structures are still not very clear. As concerns anelasticity, shorter relaxation times or lower peak temperatures are not the only consequence of this high hydrogen mobility. This became obvious when the genuine Snoek relaxation, originally expected from the magnitude of H-induced lattice expansion, turned out to be absent for hydrogen in pure bcc metals due to a vanishing dipole strength (i.e., cubic instead of tetragonal symmetry of the λ-tensor, Buchholz et al. 1973), possibly caused by a delocalisation of H in tunneling systems over adjacent tetrahedral sites. Tunneling combined with trapping (e.g., by O in Nb), however, can produce speciﬁc low-temperature H relaxation eﬀects, and on the opposite side of the spectrum we ﬁnd processes which are too slow for other interstitials but readily observable with hydrogen. The experimental study of H-induced anelasticity began with the discovery of an internal friction peak near 100 K in hydrogenated niobium (Cannelli and Verdini 1966a) and then extended over 40 years to more and more complex structures, as documented in several reviews (Berry and Pritchet 1984, Mazzolai 1985, Cannelli et al. 1993, Sinning 1995, Sinning et al. 1999, Sinning 2006c). Today eﬀects are known in pure metals, dilute and concentrated solid solutions, amorphous alloys, intermetallic compounds and quasicrystals. Altogether this variety of H relaxation eﬀects is so large and diﬀerent from the behaviour of other point defects that it is justiﬁed to consider hydrogen separately in this section. Classiﬁcation of Mechanisms To be practically useful, a classiﬁcation of the large variety of hydrogen relaxation eﬀects from the viewpoint of microscopic mechanisms has to be applicable also to the more complex structures. The crystallographic concept of point-defect relaxation summarised by Nowick and Berry (1972), with the selection rules introduced in Table 2.1 – although not restricted to classical diﬀusion jumps but also allowing for quantum eﬀects like (incoherent) tunnelling – is not general enough for this purpose because it deﬁnes the elastic dipoles relative to a perfect and periodic crystal lattice (the same is true for the extension of the theory to high point-defect concentrations, Cordero 1993). The larger the unit cell of a crystal, however, the less important is the crystal lattice type and the more important are local atomic arrangements, up to the limiting case of quasicrystals with “inﬁnite” cell size (not to mention amorphous structures). Taking this into account, it seems more useful to consider

38

2 Anelastic Relaxation Mechanisms of Internal Friction Mechanical relaxation by hydrogen in metals

Motion of hydrogen alone

Long-range diffusion

Short-range reorientation

Gorsky relaxation

Snoek-type relaxation

Transverse or intercrystalline

Single H atoms

Zener-type relaxation H-H bonds

Participation of matrix defect motion

Coupled processes

H + matrix defects: H Snoek-Köster Hydride precipit. H + twin boundaries (example: NiTi )

Indirect processes

H-induced defects: Dislocations H-enhanced host diffusion HISR

Fig. 2.12. Simpliﬁed scheme of the mechanisms of anelastic relaxation due to hydrogen in metals, classiﬁed according to the type of defect motion

as relaxing “defects” or elastic dipoles only the relevant mobile species (on the time scale of the relaxation considered), embedded in a real matrix structure which includes all less mobile defects and disorder as intrinsic constituents (this would mean, for example, to consider the Nb–O–H peak as a relaxation of H in Nb–O rather than of O–H pairs in Nb). This alternative concept leads to a simpliﬁed, practical classiﬁcation scheme (Sinning 2006c) for the anelastic relaxation mechanisms of hydrogen in metals, summarised in Fig. 2.12, which provides the common background to the following speciﬁcation of the diﬀerent mechanisms and will be explained step by step later. Gorsky Relaxation When bending a beam made of a material which contains volume-sensitive point defects like interstitial foreign atoms, the dilatational stress gradient across the sample creates a gradient in the chemical potential of the interstitials, i.e., a driving force for a long-range diﬀusion from the compressed to the dilated side as illustrated in Fig. 2.13a. A concentration gradient is then built up causing an additional curvature of the sample (i.e., interstitials are “squeezed” towards the dilated side), until the initial gradient in the chemical potential is compensated. The resulting anelastic relaxation can essentially be described by a Debye peak with relaxation strength ∆G = EU Ω(trλ)2 C0 /9 kT

(2.16)

2.2 Point Defect Relaxation (a)

39

(b)

h

easy tensile axis

H

H

Fig. 2.13. Scheme of the Gorsky relaxation (see text): (a) transverse and (b) intercrystalline Gorsky eﬀect (dark and light shading symbolises compressed and dilated areas, respectively)

and relaxation time τG = h2 /π 2 D

(2.17)

(Berry and Pritchet 1984),2 , where EU is the unrelaxed Young’s modulus, Ω the atomic volume in the matrix and h the thickness of the sample; C0 and D are the concentration (atomic fraction) and diﬀusion coeﬃcient of the interstitials, respectively. The trace tr λ = λ1 + λ2 + λ3 of the λ-tensor represents the isotropic component (size factor) of the elastic distortions caused by the interstitials. It is important to note that for samples of normal macroscopic dimensions, this classical, transverse Gorsky eﬀect is typically about 10–15 orders of magnitude slower than a related reorientation relaxation (ratio of relaxation times of the order h2 /a0 2 after (2.4) and (2.17)), so that highly mobile defects and low-frequency (preferably quasistatic) techniques are both required for its observation. Experimentally, interstitial hydrogen is indeed the only defect for which the Gorsky eﬀect was ever observed, for the ﬁrst time in Nb (Schaumann et al. 1968) 33 years after its theoretical prediction (Gorsky 1935). Later-on the use of the Gorsky eﬀect became a standard technique for measuring the hydrogen diﬀusion coeﬃcient D according to (2.17) (V¨ olkl and Alefeld 1975). New interest in the transverse Gorsky eﬀect has recently arisen in connection

2

According to Berry and Pritchet (1984), (2.16) corrects an earlier expression by Nowick and Berry (1972) (their (11.2-8)) where an additional factor β was mistakenly included. A more rigorous treatment of the Gorsky relaxation, including higher-order concentration waves and relaxation times, was given by Alefeld et al. (1970) and discussed by V¨ olkl (1972). The higher-order terms contribute only about 1% to the relaxation strength which in most practical cases can be neglected.

40

2 Anelastic Relaxation Mechanisms of Internal Friction

with nanomechanical vibration sensors where impurity H in Si is expected to produce unwanted damping at frequencies as high as 104 –105 Hz (Srikar 2005a). More generally, the Gorsky relaxation should of course not only occur in a bent beam but in any case of an alternating gradient of the hydrostatic stress component. One such case (in fact also predicted by Gorsky 1935 but forgotten later) is a polycrystal with elastically anisotropic grains, where an (even homogeneous) applied stress creates local misﬁt stress gradients across the grains (Fig. 2.13b). The relaxation parameters of this intercrystalline Gorsky eﬀect are given by (2.18) ∆IG = RKU Ω(trλ)2 C0 /kT and τIG = d2 /3π 2 D,

(2.19)

where KU is now the unrelaxed bulk modulus, R an elastic anisotropy factor and d the dominating grain size in the polycrystal (Sinning 2000a). The intercrystalline Gorsky eﬀect can easily be observed, in a material with suﬃcient H absorption and elastic anisotropy, as an internal friction peak in the kHz range if the grain size is around 100 nm. It was identiﬁed hitherto in some tetragonal intermetallic phases crystallised from Zr-based metallic glasses, but is absent in elastically isotropic icosahedral quasicrystals and in crystalline compounds with local icosahedral order (Sinning et al. 2001; Sinning 2004). A distribution in grain size of course broadens the peak, but in spite of open theoretical questions concerning the peak shape at uniform grain size, some experiments have shown surprisingly little deviation from a Debye peak (see Fig. 2.16). Snoek-Type Relaxation Snoek-type relaxation means an extension of the mechanism of the original Snoek relaxation to other matrix structures than pure bcc metals: therefore, we speak of a Snoek-type relaxation of hydrogen if the reorienting elastic dipoles are formed by single interstitial H atoms. When we apply this definition to real matrix structures as suggested earlier – as diﬀerent as dilute alloys, intermetallic compounds, metallic glasses or quasicrystals – we include some cases where the selection rules of Table 2.1 cannot be applied, and we also have to ask for the possible inﬂuence of structural disorder on the reorientation process. Of course, an interstitial H atom creates an elastic distortion ﬁeld, described by a λ-tensor and possibly forming an elastic dipole, also in a disordered matrix. Compared to the few well-deﬁned, discrete values of the λ-tensor in a perfectly crystalline matrix ((2.1) and (2.2)), however, quasicontinuous variations of dipole strength and orientation may now occur, and

2.2 Point Defect Relaxation

41

the ideal case of energetically exactly equivalent dipoles with a ﬁxed number nd of possible orientations may not always exist. A Snoek-type reorientation may nevertheless be expected if the relevant elastic dipoles are both orientationally distinguishable (Berry and Pritchet 1984) and “suﬃciently” equivalent, which means that the energy splitting between the equilibrium positions for two diﬀerent dipole orientations (i.e., the asymmetry of the respective two-level system) must be so small that the site occupation probabilities can still change signiﬁcantly under the inﬂuence of an external stress. This latter point has been considered as a problem to explain the relaxation strength especially in amorphous alloys (Yoshinari et al. 1983b) where it is still under discussion (see later). Concerning the relaxation kinetics in case of disorder, energy distributions of the interstitial sites occupied by hydrogen, as well as of the related saddle points in case of thermally activated jumps, must be taken into account. Site-energy distributions may range from quasi-discrete trapping sites in dilute alloys over varying metal atom conﬁgurations in concentrated solid solutions (chemical disorder) or elastic distortions near dislocations (topological disorder) up to broad continuous site-energy distributions in amorphous alloys (chemical and topological disorder). In all these cases the site occupation by hydrogen obeys Fermi–Dirac statistics (Beshers 1958, Kirchheim 1982, 1988), whereas the problem of saddle-point energy cannot be treated in such a universal way but needs more speciﬁc considerations. The result is a distribution in activation energy for the relevant hydrogen jumps, which may cause a broadening of the Snoek-type relaxation peak relative to a Debye peak, and/or a shift with increasing H concentration (CH ) mostly to lower temperatures (activation energies). Experimental observations of Snoek-type relaxations of hydrogen in metals have been reported in many diﬀerent cases: (a) Trapping in “pure” metals containing interstitial or substitutional impurities (i.e., “dilute” alloys). The best-studied example, ﬁrst observed in the pioneering work of Cannelli and Verdini (1966a) mentioned earlier, is the so-called “Nb–O–H peak”, i.e., a reorientation of the highly mobile H around the much less mobile O interstitial (e.g., Baker and Birnbaum 1973, Schiller and Schneiders 1975b); but also substitutional atoms like Ti in Nb (Cannelli et al. 1982a) can act as such trapping centres. As long as their concentration is low, the relaxation peak looks like a “normal” Snoek peak with a CH -independent position (Cannelli et al. 1993), but above some critical density of trapping centres (between 0.1 and 1 at%) the shift to lower temperatures with increasing CH sets in. A statistical trapping model using Fermi–Dirac statistics was developed to describe this “anomalous” behaviour (Cannelli et al. 1985). Similar trapping eﬀects were also found in fcc metals (Yoshinari et al. 1991). In the bcc metals where tunneling states exist for hydrogen, the above relaxation peak (observed typically around 100 K) reﬂects the

42

2 Anelastic Relaxation Mechanisms of Internal Friction

reorientation jumps between diﬀerent tunnel systems. However, the tunneling itself, i.e., the motion of H within a tunnel system, also means reorientation around the trapping centres which is seen as relaxation peaks at liquid helium temperatures. There is some evidence that due to the different symmetries of interstitial (O in Nb) and substitutional (Zr in Nb) trapping centres, two-site tunneling is preferred in the former and foursite tunneling in the latter case, respectively (e.g., Cannelli et al. 1986a, 1994b) (b) In concentrated solid solutions (disordered alloys) a Snoek-type reorientation is generally expected if H interacts with the alloying elements diﬀerently, because then the symmetry of the local coordination shells around H may be lower than that of the crystal lattice, giving rise to elastic dipoles. However, the situation is theoretically diﬃcult and has been studied experimentally only in a few cases. Measured spectra of H-induced internal friction show either single, broadened relaxation peaks as in bcc Nb–V (e.g., Snead and Bethin 1985a) or fcc Pd–Pt (Coluzzi et al. 1992) or more complex phenomena as in Pd–Ag (Lewis et al. 1994). The analysis of all possible site occupation and transition probabilities, performed both for fcc and bcc binary alloys (Biscarini et al. 1994b, 1999c), is very puzzling already in the binary case and impracticable for multi-component alloys (where continuous distribution functions like in the amorphous case should be a better choice). One conclusion from this work is that the Snoek-type reorientation of H in concentrated alloys is probably not a pure one but mixed with other contributions, like “reaction modes” (i.e., jumps between non-equivalent high-symmetry sites without reorientation, Nowick 1970), and reorientation of H–H pairs at least at higher H concentration (Zener-type relaxation, see later). (c) In intermetallic compounds the selection rules of Table 2.1 deﬁne possible Snoek-type relaxations if the occupancy of interstices by hydrogen is known (or at least reasonable assumptions exist); this may, however, be a problem in more complex crystals. After pioneering experiments in Nb3 Sn (Berry et al. 1983) the Snoek-type mechanism was identiﬁed in the C16 phases CoZr2 and NiZr2 (Sinning 1992a,b, 1995) and in C15 Laves phases (TaV2 , Foster et al. 2001b). More recently the “200 K peak” (at 1 Hz) in NiTi-type shape memory alloys, well-known as part of rather complex damping spectra below the martensitic transition, could be attributed to a Snoek- (or possibly Zener-) type hydrogen relaxation as well (Mazzolai et al. 2003, 2004b). Additional relaxation peaks below 50 K due to H tunneling, with (Coluzzi et al. 2004) or without (Atteberry et al. 2004) trapping, were also found in some of these compounds. A further interesting case is Pd3 Mn where the inﬂuence of order–disorder transformations on the H-induced relaxation spectra was studied (Sobha et al. 1991, 1992). (d) Amorphous alloys and icosahedral quasicrystals. Beginning with Berry et al. (1978), around 50 observations in diﬀerent alloys have shown that

2.2 Point Defect Relaxation

43

a pronounced H-induced relaxation peak is a general phenomenon in all H-absorbing metallic glasses, as reviewed in diﬀerent aspects e.g., by Berry and Pritchet (1986), Sinning (1995, 2000b, 2006a) or Yagi et al. (2004). As exempliﬁed in Fig. 2.14, the peak is generally wide and asymmetric and shifts to lower temperatures with increasing H concentration CH or peak height Qm −1 , due to related distributions in activation energy as mentioned earlier. Typical are activation energy spectra with half-widths around 0.1 eV and average values of 0.3–0.5 eV depending on CH , with τ0 ∼ 10−12 –10−13 s (although in some studies higher or lower τ0 values are reported). Diﬀerences in peak shape and kind of shift, like those in Fig. 2.14, obviously reﬂect variations in alloy composition and short-range order, and can in principle be used as a local structural probe on the atomic level. If the CH dependence is plotted in coordinates Tm (Qm −1 ) at constant frequency (Fig. 2.15), many results for amorphous alloys have been found in a “main” data band A, but some speciﬁc Pd- and Zr-based glasses form separate ranges B and C, respectively. While a similar hydrogen eﬀect is to be expected also in icosahedral quasicrystals (QCs), it is nevertheless remarkable that the related peaks are

10−2 Co24Zr76

Damping Q−1

10−3

10−4 10−2 Co45Zr55

10−3

10−4

100

200

300

400

T [K]

Fig. 2.14. H-induced loss peaks, with stepwise CH increase between about 0.3 and 10 at.%, in two amorphous Co–Zr alloys (after Winter et al. 1996)

44

2 Anelastic Relaxation Mechanisms of Internal Friction

Peak Temperature, Tm (300 Hz) [K]

350

C

300

A

glasses without QC formation

250

200

150

Ti-Zr-Ni quasicrystals

100 −4 10

QC forming glasses

B

−3

10

−2

10 −1 Peak Height, Q m

−1

10

Fig. 2.15. Scheme of the temperature variations of the H damping peak in metallic glasses and icosahedral quasicrystals. Circles: Zr69.5 Cu12 Ni11 Al7.5 ; triangles: Zr61.6 Ti8.7 Nb2.7 Cu15 Ni12 ; full/open symbols: amorphous/quasicrystalline states; ranges A, B, C: see text (Sinning 2006a)

indeed almost indistiguishable from each other if the QCs have formed from the amorphous phase at the same composition (Scarfone and Sinning 2000, Sinning et al. 2003, 2004a). Relative to these QC-forming glasses, peak temperatures are found lower for the more stable Ti–Zr–Ni QCs but higher for bulk metallic glasses without QC formation before crystallisation, respectively; this tendency should be taken into account for developing, in range C of Fig. 2.15, glassy alloys with improved high-damping properties at room temperature (Sinning 2006a; cf. Sect. 3.5). The relaxation mechanism of the hydrogen loss peak in amorphous alloys is under continuing discussion since about 25 years. A Snoek-type reorientation should exist in polytetrahedral structures (including both amorphous and icosahedral phases) because of the geometrically necessary distortions of the space-ﬁlling tetrahedra, leading to orientationally distinguishable elastic dipoles in the above sense (Sinning 2006c). Although the Snoek-type mechanism is accepted by most authors, a satisfactory quantitative theory still does not exist in spite of considerable earlier eﬀorts (cf. Sinning 1995). Besides problems of correlated site and saddle-point energies, and of choosing a modiﬁed “Fermi” site occupation function appropriate to the relaxation problem (taking into account local H–H repulsion and site blocking), the most serious objection against the Snoek-type mechanism is certainly the possible suppression of relaxation strength due to asymmetric two-level systems (Yoshinari et al. 1983b, Takeuchi et al. 2004) already mentioned earlier. To overcome this diﬃculty, Berry and Pritchet (1986) already conjectured, in

2.2 Point Defect Relaxation

45

implicit agreement with model calculations by Richards (1983), that suﬃciently symmetric two-level systems may exist even in a disordered amorphous structure. This viewpoint is now conﬁrmed experimentally by the close correspondence between amorphous and quasicrystalline structures with respect to the hydrogen relaxation peak. A brief summary of the present state of this discussion has been given by Sinning (2006a). Zener-Type Relaxation Zener-type relaxation i.e., the reorientation of H–H bonds, can be observed in pure form only if the selection rules of Table 2.1 exclude a Snoek-type reorientation. This is especially true for fcc and hcp metals where related eﬀects were identiﬁed in Pd, Zr, Ti, Lu, Sc and Y, including moderate H concentrations in solid solution as well as very high concentrations in hydride phases (see also Sect. 2.2.2 and 2.2.3 and, for an early review, Mazzolai 1985). The mechanism is analogous, in certain aspects, both to the “original” Zener relaxation in substitutional alloys (Sect. 2.2.3; Nowick and Berry 1972) and to the relaxation of “heavy” (C, N, O) interstitial (i–i) pairs described in Sect. 2.2.2. Although Wipf and Kappesser (1996) developed a lattice-gas model which applies to both the substitutional and interstitial cases – thus justifying the use of the term “Zener relaxation” for either case – this terminology is in practice not free from ambiguity because (a) part of the i–i pair reorientations in Sect. 2.2.2 are usually not called a Zener relaxation and (b) there is still a tendency in the more recent literature to use this term only for the substitutional case (Weller 2001). To avoid this ambiguity, the term Zener-type relaxation is chosen here for the H–H pair reorientation. A Zener-type relaxation of hydrogen was also observed in the intermetallic compound CuZr2 with the tetragonal C11b structure, where also no Snoek-type eﬀect is expected from the selection rules (Sinning et al. 2000). An example of this peak is shown in Fig. 2.16a together with the intercrystalline Gorsky eﬀect mentioned earlier, using a four-component alloy containing a CuZr2 -type phase with an average grain size of only about 30 nm. The apparent activation energy is 0.5 eV for both peaks, whereas the τ0 values (10−13.5 and 10−9.4 s) diﬀer by four orders of magnitude in agreement with the ratio of diﬀusion distances for the two mechanisms (Sinning 2000a). The width of the Zener-type peak and the diﬀerent curvatures in Fig. 2.16b (exponents m of power-law ﬁts; ideally m = 2 in the dilute limit) indicate a strong attractive H–H interaction with possible clustering especially in the binary and ternary alloys (Sinning and Scarfone 2003). More generally, contributions from a Zener-type process may always be expected at high H concentrations, independent of the existence of a Snoek-type mechanism in the respective structure. If both mechanisms are superimposed on each other they depend on the same diﬀusion jumps, so that an experimental separation is not possible. At still higher H concentrations

46

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.16. The intercrystalline Gorsky (IG) and Zener-type (Z) eﬀects of hydrogen in CuZr2 -type polycrystals. (a) Example of a spectrum of Zr65 Cu17.5 Ni10 Al7.5 with both peaks (grain size ∼30 nm; dashed line: Debye peaks at 0.5 eV); (b) plot of the peak heights against each other (solid lines: power law ﬁts with exponents m) (Sinning and Scarfone 2003)

(e.g., in hydride phases) the concept of individual elastic dipoles eventually breaks down and should be replaced, similar to the substitutional Zener relaxation, by a description in terms of a stress-induced directional short-range order of H atoms on the sublattice of the interstitial sites available. Coupled Processes Whereas the above mechanisms are all based on short- or long-range motion of H atoms alone, in a matrix considered immobile on the time scale of the relaxation, there are also H-related relaxation eﬀects for which the motion of matrix defects is essential. Such eﬀects are to be mentioned here, although most of them are beyond pure point-defect relaxation and partly described in the other chapters. We distinguish between “coupled” processes directly based on the interaction of hydrogen with mobile matrix defects like dislocations or interfaces, and “indirect” processes if hydrogen is producing or modifying matrix defects which are then carrying the relaxation alone. Coupled processes, in this sense, mean a stress-induced, coupled motion of at least two mobile species interacting with each other; the most important examples are the hydrogen Snoek–K¨ oster eﬀect, the so-called hydride precipitation peak, and the coupled motion of hydrogen and twin boundaries. The Snoek–K¨ oster eﬀect is a dislocation relaxation in the presence of foreign interstitial atoms (e.g., hydrogen) trapped at the dislocation. It is mainly caused by a diﬀusion-controlled bowing out of dislocation segments, i.e., a coupling of stress-induced dislocation motion and interstitial diﬀusion (with different models for the microscopic details of this coupled motion). The reader is referred to Sect. 2.3.2 for a closer description of the phenomenology and mechanism of this type of anelastic relaxation.

2.2 Point Defect Relaxation

47

The hydride precipitation peak is found in hydride-forming metals when the solvus temperature is crossed during cooling or heating; it was observed e.g., in V, Nb, Ta, Ti, Zr and Pd containing a few at.% of hydrogen (Yoshinari and Koiwa 1982a,b, 1987; Koiwa and Yoshinari 1984, 1985; Numakura and Koiwa 1985; Pan and Puls 2000). The peak consists of two components: a transient eﬀect with a magnitude proportional to T˙ /f , and a rate-independent equilibrium component. The transient eﬀect is dominating at heating or cooling rates above 1 K min−1 , at least if measured with a low-frequency technique around 1 Hz; such non-relaxation phase transformation eﬀects are described further in Sect. 3.2.3. The equilibrium component is strongest in vanadium with the highest H diﬀusivity, where it is thermally activated with an apparent activation energy of 0.17 eV. Both components were attributed to a stressassisted preferential precipitation or dissolution of the hydrides (and/or shape change of precipitates, i.e., a diﬀusion-controlled motion of hydride–matrix interfaces) as the main mechanism, but the physical details of energy losses seem to be not well understood yet. Generation and movement of dislocations also play a role in both components, completed by intrinsic (e.g., Zener-type) processes in the hydride as part of the equilibrium component. Assuming this latter component proportional to the hydride volume fraction, Yoshinari and Koiwa (1982b) have shown for V that an underlying, true relaxation peak (if any) would be at much higher temperature, so that only the low-temperature “tail” can be observed experimentally. Twin boundaries are generally a very eﬃcient source of damping in thermoelastic martensite (see Sects. 2.4.2, 3.2.2 and 3.5), in particular NiTi-type shape-memory alloys which are also able to absorb hydrogen. Diﬀerent types of twin boundaries, varying with details of the martensitic transformation (with B2, B19, B19 or R phases) depending on alloy composition and heat treatment, are considered as sources of the H-free damping spectra; such spectra may involve either an almost constant high damping (Q−1 ∼ 10−2 ) in all the martensitic state, or a well-developed (non-relaxation and nontransient) peak at the B2 ↔ B19 transition. Hydrogen may strongly enhance this “transformation peak” (and at the same time decrease the damping in the low-temperature regime) probably due to a pinning/depinning process; in other cases (B19 martensite) a very high thermally activated relaxation peak, just slightly below the martensitic transition as well, can be produced by relatively small amounts of hydrogen. This latter peak, with an activation energy about 0.6–0.7 eV compared to 0.4 eV for the Snoek-type “200 K peak” mentioned above, has been attributed to a H dragging process similar to the Snoek–K¨ oster relaxation for dislocations (Biscarini et al. 1999a, 2003a,b; Mazzolai et al. 2003). While in the above examples the coupling between hydrogen and matrix defects is “positive”, insofar as hydrogen produces new relaxation eﬀects or enhances existing ones, a “negative” coupling with suppression of existing eﬀects is also possible. This is the case e.g., for the inﬂuence of rapidly diﬀusing hydrogen on the oxygen Snoek peak in Nb and Nb–Ti (Schmidt and Wipf

48

2 Anelastic Relaxation Mechanisms of Internal Friction

1993, Golovin et al. 1996a) where, besides a minor eﬀect on the relaxation rate, the relaxation strength is reduced up to complete suppression at very high H concentration (H/Nb > 0.75). Indirect Processes Indirect processes due to the motion of H-induced matrix defects are not easily separated from coupled ones, because it is diﬃcult in practice to rule out the direct participation of H atoms. For example, the dislocation contribution to the above-mentioned hydride precipitation peak, sometimes observed as a separate satellite peak (Yoshinari and Koiwa 1982a), might represent such an indirect process if that motion of the dislocations, produced by plastic accommodation of the volume change during hydride formation, would occur without any further participation of H diﬀusion; otherwise the process would be a coupled one. This uncertainty is almost unavoidable in most practical cases. A few ideas of such indirect processes have been reported for amorphous alloys. For instance, Khonik and Spivak (1996) considered dislocation-like defects, generated during hydrogenation, as a possible alternative to the Snoek-type mechanism; however, regarding the universality of the H relaxation peak in amorphous and other polytetrahedral structures as described earlier (after quite diﬀerent kinds of hydrogenation), as well as some characteristic diﬀerences between hydrogen and deformation peaks in amorphous alloys (Winter et al. 1996), this indirect mechanism should be considered as an independent process which might exist in addition to (not instead of) the Snoek-type mechanism in some particular cases. In a combined study of the H-induced reorientation and Gorsky relaxations in a Ni40 Zr60 metallic glass at CH = 0.78 H/M, Berry and Pritchet (1988) have found a third, still slower relaxation eﬀect beyond the Gorsky relaxation, which they attribute to an H-enhanced host diﬀusion, linked to the volume expansion at such high H concentration which may provide additional free volume to promote matrix diﬀusion. The same idea is discussed in terms of H-induced structural relaxation (HISR in Fig. 2.12) by Matsumoto et al. (1995), which may reduce the Snoek-type H relaxation strength by structural rearrangements in the matrix (Mizubayashi et al. 2004b). The diﬀerent kinds of relaxation in amorphous alloys are considered further in Sect. 2.6.1. 2.2.5 Other Kinds of Point-Defect Relaxation Besides the relaxation mechanisms described above, caused by diﬀusion under stress of single solute atoms or their complexes, similar eﬀects may also be produced by intrinsic point defects (self-interstitials and their complexes), or by complexes of solute atoms with self-interstitials and vacancies. Internal friction maxima due to self-interstitials, which produce lower-symmetry distortions in the crystal lattice, were observed after neutron, electron, deuteron or proton irradiation in Mo (Hivert et al. 1970; Okuda and Mizubayashi

2.2 Point Defect Relaxation

49

Table 2.10. Parameters of the main maxima due to self-interstitials in irradiated Mo and W (f ≈ 500 Hz) metal Tm (K) H (kJ mol−1 )

τ0 (s)

source of relaxation

reference

−14

Mo

12 39

2.3 8.1

4.3 · 10 single self-interstitials Mizubayashi and 6.2 · 10−15 bi-interstitials Okuda (1981)

W

8 27

1.8 5.5

7 · 10−16 single self-interstitials Mizubayashi and 7 · 10−15 bi-interstitials Okuda (1981)

1973; Tanimoto et al. 1992a,b, 1993, 1994), W (DiCarlo and Townsend 1966; Townsend et al. 1969; DiCarlo et al. 1969; Okuda and Mizubayashi 1976; Mizubayashi and Okuda 1981, 1982; Tanimoto et al. 1996), Fe (Hivert et al. 1970; Moser and Pichon 1973; Moser et al. 1975), Cr (Weller and Moser 1981a), Ti and Zr (Moser et al. 1975), Ni and Cu (Moser and Pichon 1973), Ag (B¨orner and Robrock 1985) and others. In the most completely studied metals Mo and W two main maxima, caused by reorientation of the free splittype self-interstitials and bi-interstitials (Table 2.10), are found together with several minor peaks. The latter are partly attributed to interstitials trapped by impurity atoms, and partly to interstitial clusters. The main features of the two peaks displayed in Table 2.10 are: (a) the peak heights are proportional to the irradiation dose, (b) the peak widths are slightly broader than that for a single relaxation time and (c) the relaxation strength depends on the crystal direction, as both peaks appear about ten times higher for the 100 than for the 111 strain direction. In Nb quenched from sub-melting temperatures and containing an increased vacancy concentration, a relaxation maximum was observed and attributed to diﬀusion under stress of oxygen atoms near vacancies (Blanter and Granovskij 1999). Apparently, related maxima induced by intrinsic defect groups generated during quenching, irradiation or plastic deformation, or by complexes comprising such defects and solute atoms, were observed for many metals. Such complexes were used to explain a number of relaxation eﬀects, but unfortunately, the relaxation mechanism cannot be determined unambiguously in most cases. For this reason, the explanations given by diﬀerent authors often contradict each other and can be considered as hypothetical only. Finally it is noted that many other kinds of point-defects, and hence of point-defect relaxation, occur in more complex intermetallic and non-metallic structures. Examples are known for ordered compounds like Ni3 Al (Numakura et al. 1999, Numakura 2005), quasicrystals and related crystalline approximants (see Sect. 2.6.2), and are also expected for so-called “structurally complex alloy phases” with giant unit cells (Urban and Feuerbacher 2004). The situation is even more complicated in ionic crystals like oxide ceramics (Weller 2001) and high-Tc superconductors (Weller 1993), where the additional condition of charge neutrality has to be fulﬁlled. This, however, is out of the frame of this book.

50

2 Anelastic Relaxation Mechanisms of Internal Friction

2.3 Dislocation Relaxation Dislocations are line defects in crystals that are characterised by their complex distortion or stress ﬁeld (e.g., Hull and Bacon 1984, Hirth and Lothe 1968) and may have an even richer variety of relaxation eﬀects than point defects. These eﬀects show up in plastically deformed metals and alloys with a suﬃciently high density of dislocations. Figure 2.17 gives an overview of various dislocation damping contributions in a wide range of frequencies of the applied vibration. As dislocation motion usually is associated with an elongation of the dislocation line (e.g., bowing out between anchoring points and nucleation of kinks), a restoring force arises from the dislocation line energy (“line tension”) which in principle would infer a resonance phenomenon of the dislocation itself (not to be confused with the macroscopic resonance of the sample considered in Chap. 1). However, as dislocation movement is heavily overdamped by phonon relaxation eﬀects (e.g., Alshits and Indenbom 1986, Granato and L¨ ucke 1956a,b), we may neglect the restoring force and restrict in the following to relaxation eﬀects. The dislocation motion caused by the imposed alternating shear stress in damping experiments very often implies an amplitude dependence of internal friction. The amplitude eﬀects will be treated in Sect. 3.3, while the current chapter will concentrate on relaxation eﬀects produced by the presence of dislocations. The respective relaxation peaks may be subdivided into: (1) Those caused by movement of dislocations themselves due to the nucleation and propagation of thermal or geometrical kinks (Bordoni, Niblett– Wilks and related internal friction maxima, Sect. 2.3.1). (2) Those caused jointly by dislocations and proper lattice point defects (vacancies, self-interstitials: Hasiguti maxima mostly below room temperature, see section “Hasiguti Peaks”).

Fig. 2.17. Schematic damping spectrum (internal friction IF) due to dislocations on the frequency scale (after Gremaud 2001)

2.3 Dislocation Relaxation

51

(3) those caused jointly by dissolved foreign interstitial atoms and dislocations (Snoek–K¨ oster relaxation, dislocation-enhanced Snoek eﬀect) at more elevated temperatures, see sections “The Snoek–K¨oster Relaxation” and “Dislocation-Enhanced Snoek Eﬀect”. (4) Those caused, at still higher temperatures, by dislocation climbing or other diﬀusion-controlled processes, see section “Dislocation Relaxation Peaks at Medium Temperatures”. Moreover, movement of dislocations produces a low-temperature internal friction background attributed to tunneling states (dependent on, or independent of the vibration amplitude, see section “Background Damping at Very Low Temperatures”), as well as an exponentially rising high-temperature background (see section “Damping Background at Elevated Temperatures”). The eﬀects of substitutional solute atoms are also considered in the latter section. Beyond these largely linear relaxation processes, there are non-linear hysteretic eﬀects connected with plastic deformation, i.e., movement across various obstacles and multiplication of dislocations. These strongly amplitudedependent eﬀects will be described brieﬂy in Sect. 3.3. In order to demonstrate the large variety of dislocation-related peaks in the structural classes of fcc, hcp and bcc metals, in Figs. 2.18–2.20 schemes of location and relative height of internal friction peaks in plastically deformed pure metals are presented. The intrinsic peaks of the above type (1) are designated as B (Bordoni peaks), those of type (2) related to the interaction of dislocations with self-point defects (Hasiguti peaks) are signed by the letter P , and those caused by foreign interstitial atoms in the stress-ﬁeld of dislocations (Snoek–K¨ oster relaxation (3) and related ones) by the letters SK, DES. In bcc metals, however, greek letters are used instead of B and P (Chambers 1966): α for damping peaks between 50 and 200 K, β for a second type around 150–300 K, and γ for others in the range 300–500 K. More details will be explained later, where the important features of the various relaxations in diﬀerent lattice structures will be considered. 2.3.1 Intrinsic Dislocation Relaxation Mechanisms: Bordoni and Niblett–Wilks Peaks Dislocation motion occurs basically by nucleation and sideways movement of kinks in the dislocation line (Fig. 2.21). We will ﬁrst consider the damping peaks (usually observed at low temperatures) attributed to these intrinsic lattice properties without interaction with any other defects. For some historical remarks and recent reviews, see Fantozzi et al. (1982), Ritchie and Fantozzi (1992), Benoit (2001a), Seeger (2004a). In fcc metals with a relatively low Peierls potential, at correspondingly low temperature, in fact two maxima are observed and designated, in the order of increasing temperature, as B1 (Niblett and Wilks 1956) and B2 (Bordoni 1949, 1954). (Sometimes the name “Bordoni maxima” is extended to both B1

52

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.18. Generalised internal friction spectra of deformed fcc metals recalculated for f = 1 Hz (Ni: f = 30 kHz). (From Blanter and Piguzov 1991)

and B2 , and also to damping maxima in metals with other crystal lattices, which are caused by the movement of dislocations proper.) Figure 2.18 gives a schematic overview of the location of Bordoni (Bi ) peaks on the temperature scale for various fcc metals at a typical frequency of 1 Hz (for Ni: 30 kHz). Some characteristic parameters of internal friction peaks in deformed fcc metals are displayed in Table 2.11. The Bordoni peaks in bcc metals are commonly called α /α (or α1 /α2 ) and γ with increasing peak temperature (Chambers 1966); some examples are shown in Fig. 2.22. The β peak (Chambers and Schultz 1962; M¨ uhlbach 1982; Suzuki 1989b) between α and γ is mainly attributed to interaction of dislocations with intrinsic point defects (Hasiguti peaks). In hexagonal metals the Bordoni peaks have diﬀerent designations. Some important features of the Bordoni peaks are the following: 1. The underlying relaxation processes are thermally activated (cf. Table 2.11), and inﬂuenced by the conditions of previous plastic

2.3 Dislocation Relaxation

53

Fig. 2.19. Generalised internal friction spectra of deformed hexagonal metals recalculated for f = 1 Hz for most metals. For Zn previous deformation was done (a) in the basal slip system; (b) in the pyramidal one. (From Blanter and Piguzov 1991)

54

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.20. Generalised internal friction spectra of deformed bcc metals recalculated for f = 1 Hz. (From Blanter and Piguzov 1991)

deformation ε which determines the dislocation structure. In very pure metals dislocation-related loss peaks may even be observed without preliminary deformation (Fantozzi et al. 1982). In fcc metals at very small deformation only the Bordoni maximum B1 arises (highly pure aluminium, deformation 2–4%, Alnaser and Niblett 1987). At large deformation also B2 appears and grows with ε, being still small and strongly broadened in stage I of the deformation curve. It increases in height and narrows after deformation into stage II, and slowly decreases again in stage III (Fantozzi et al. 1982). Deformation of gold by 7% at liquid nitrogen temperature gives a maximum B2 about ten times higher than deformation at room temperature (Fantozzi et al. 1982). On the whole, however, the ratio of heights B2 /B1 increases with deformation temperature.

2.3 Dislocation Relaxation

55

Fig. 2.21. Scheme for kinks in dislocations: (a) geometrical kinks on a dislocation extending from A to B not parallel to a close-packed direction; (b) a thermal kink-pair characterised by kink width w and slope tg πm ; a = distance between neighbouring Peierls valleys. (From Ritchie and Fantozzi 1992)

Table 2.11. Thermal activation parameters of the deformation-induced internal friction maxima in some fcc metals (Fantozzi et al. 1982, Burdett and Queen 1970a, Ritchie and Fantozzi 1992). H (kJ mol−1 ) as numerator, τ0 (s) as denominator. Bi Bordoni maxima, Pi Hasiguti peaks (see section “Hasiguti Peaks”) B1

B2

P1

P2

P3

Ag

8.7 10−12

8.7−12.5 10−12 −10−13

21.2 5·10−10

35.7 5·10−13

44.5 5·10−13

Al

14.5−16.4 10−12 −10−13

13.5−24.1 10−10 −10−14

Au

6.5−9.6 10−9 −10−12

15.2−19.3 10−11 −10−13

21.5 5·10−10

32.8 3·10−10

34.7 3·10−10

Cu

4−4.8 10−9 −10−13

9.6−14.5 10−10 −10−13

31 10−12

33.8 1.6·10−12

41.4 1.2·10−10

Ni

13.5 ≈10−13

38.6 2·10−15

metal

Pb

3.2 10−9

Pd

25.1 2·10−13

Pt

19.3 ≈10−13

2. Complex spectra were found in the hcp metals Mg, Ti, Zr and comparatively simple ones in La, Lu, Re, Be, Zn. In one case of magnesium (99.99%; Vincent et al. 1981), only a wide damping maximum at 100– 150 K is observed instead of the numerous peaks shown for the high-purity (6N) metal in Fig. 2.19. In such favourable cases it is possible to distinguish Bordoni (B1 and B2 in Mg and Zn, one maximum in Re) and Hasiguti peaks (see section “Hasiguti Peaks”). 3. The related peaks in bcc metals have been most thoroughly studied in Nb, Ta, Mo, Fe and less thoroughly in V, Cr and W, cf. Figs. 2.20 and

56

2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.22. A diagram of intrinsic dislocation relaxation maxima in pure deformed bcc metals (Schultz 1991)

2.22. Three kinds of Bordoni maxima were revealed, i.e., α1 or α , α2 or α and γ. The γ peak may split into two peaks, γ1 and γ2 , one of them probably being DES(O) (see section “Dislocation-Enhanced Snoek Eﬀect”). In vanadium, a low-temperature maximum δ is connected (according to the opinion of some authors) with non-screw dislocations, and a second one with interactions of dislocations with impurities (Mizubayashi et al. 1979, 1982). In the two bcc alkaline metals Li and K deformation-induced damping maxima exist while in Na they were not found (Hammerschmid et al. 1981a,b). In Ba α- and γ-maxima were observed (Hammerschmid and Schoeck 1985). 4. The presence of impurities in general decreases the height of Bordoni deformation peaks owing to anchoring of dislocations. However, a certain inﬂuence may occur by the variation of the dislocation structure due to changes in the stacking fault energy. Figure 2.23 demonstrates the decrease in height of the peak B2 by an increasing content of Au in Ag and Ag in Au, respectively. The rise of the peak at very low Au concentrations may be associated with a change in the stacking fault energy.

2.3 Dislocation Relaxation

57

Fig. 2.23. Change of the height (Qm −1 ) and temperature (Tm ) of the Bordoni maxima in the Ag–Au system. (From Fantozzi et al. 1982) Table 2.12. Dependence of characteristics of the Bordoni maximum B2 on crystal orientation for Cu (Grandchamp 1971) direction H (kJ mol τ0 (s)

−1

)

[111]

[110]

[100]

14.7 4 · 10−12

11.9 2.6 · 10−10

11.3 1.6 · 10−10

5. Irradiation with neutrons or electrons before plastic deformation may both increase and decrease (Guenin et al. 1971) the height of the Bordoni maxima in fcc metals; the height of B1 decreases to a larger extent. High-dose neutron irradiation after deformation results in pinning of dislocations and disappearance of the maxima B1 and B2 (Fantozzi et al. 1982). Electron irradiation of deformed magnesium changes rather signiﬁcantly the whole damping spectrum. The Bordoni peak heights change and additional maxima at Tm = 6 K, 14 K and 140 K (1 kHz) arise (Fantozzi et al. 1984b; Minier et al. 1982, 1983a). In niobium, proton irradiation suppresses the α1 peak and converts it partly to the α2 peak (Okumura et al. 1989). Irradiation of Ta can create the α peak (Mizubayashi et al. 1991a). 6. Annealing treatments at temperatures below the recrystallisation threshold do not inﬂuence the heights of the Bordoni maxima. 7. The data concerning the inﬂuence of crystal orientation are equivocal. According to some authors, the relaxation parameters of the maximum B2 depend signiﬁcantly on the single crystal orientation, e.g., for aluminium (Kosugi and Kino 1989) or copper (Table 2.12). According to other authors (Zein 1987), such dependence in aluminium is absent.

58

2 Anelastic Relaxation Mechanisms of Internal Friction

Mechanisms of the Bordoni Relaxation The assignment of mechanisms to the various deformation-induced loss maxima (see e.g., the reviews by Fantozzi et al. 1982, Magalas 1984a; Magalas and Gorczyca 1985, Ritchie and Fantozzi 1992, Schultz 1991, Benoit 2001a, Seeger 2004a) suﬀers from contradictions in the identiﬁcation of every particular maximum and in the comparison of maxima observed in diﬀerent metals. However, the main features of relaxation processes in deformed metals have been determined, and can now be used to investigate the processes of plastic deformation of metals themselves. A summary of progress and problems has recently been given by Seeger (2004a). The reason for the two Bordoni maxima B1 and B2 in metals with the fcc lattice and of moderate purity (Fig. 2.18 and Table 2.11) was expressed for the ﬁrst time by Seeger (1955), namely that B1 is caused by the thermally activated formation of double kinks on screw dislocations, and B2 on mixed ones (Lauzier and Minier 1981, Alnaser and Niblett 1987, Magalas and Niblett 1987). In data on highly pure Al (Kosugi and Kino 1989) four relaxation peaks could be resolved which, with the aid of charging by hydrogen (Hauptmann et al. 1992), were assigned to diﬀerent types of dislocations, as indicated in Fig. 2.24. The Bordoni peaks (α- and γ-maxima) in bcc metals (Figs. 2.20 and 2.22) are explained by the movement of geometrical kinks (α , α1 ), and by the thermally activated nucleation of kink pairs on screw (γ) or non-screw dislocations (α, α2 ), respectively (cf. Fig. 2.21). A summary of parameters of these relaxation mechanisms (collected by Magalas (1984a) on the basis of works of Seeger (Seeger and Wurtrich 1976, Seeger 1981) and Fantozzi et al. (1982)) is given in Table 2.13. In bcc metals the height of the Peierls barrier, and correspondingly the peak temperature Tm , increases for the diﬀerent dislocation

Fig. 2.24. Bordoni relaxations in high purity Al single crystal (f = 51 kHz) and assignment of the peaks to diﬀerent dislocation characters. (From Seeger 2004a)

2.3 Dislocation Relaxation

59

Table 2.13. Main parameters of relaxation processes due to thermal kink pair formation or migration of geometric kinks on dislocations (after Magalas 1984a) kink pair formation

kink migration

peak height and relaxation parameters Qm −1 ∝ Λln ; 1 ≤ n ≤ 2 H = 2Hk [1 − (σ/σp )n ]; n ≈ 3/4 τ0 ∝ ln ; 0.5 < n < 2 peak broadening 2 < β < 4 for non-screw dislocation due to H and τ0 distributions β ≈ 0 for screw dislocation activation volume 10b3 < V < 100b3 V m σ = const, m = 4 V depends on stress

Qm −1 ∝ Λl2 H ∝ Hk M τ0 ∝ l2 (τ0 exceeds that for kink pair formation by a factor of about 100) β ≈ 1.5 due to τ0 distribution

V ∝ b3 V does not depend on stress M

Hk : kink formation enthalpy; Hk : kink diﬀusion activation enthalpy; σp : Peierls stress; σ: external stress; for the other symbols, see text

processes in the following sequence (Magalas and Niblett 1987): Migration of geometric kinks on non-screw (71◦ ) dislocations, migration of geometric kinks on screw dislocations, formation of pairs of thermal kinks on non-screw dislocations (α, low Tm ), and the same process on screw dislocations (γ, high Tm ). The ﬁrst two processes are probably superposed onto the third one, giving a complicated structure of α-peaks. In particular, in iron (Gindin et al. 1984) four α-peaks were observed at 11, 16, 22 and 30 K (f ≈ 1 Hz). The complicated structure of the α-maximum may be caused also by non-screw dislocations. The peak temperatures of both processes γ and α increase with the metal melting temperature (Fig. 2.22). Important microscopic dislocation parameters are the dislocation segment length L (or the dislocation density Λ, given by the degree of previous deformation), and the obstacle distance l along the dislocation (length of a free dislocation loop, reﬂecting the purity of the sample). As a function of temperature, the individual peaks of the Bordoni relaxation are generally Debye peaks in the framework of the “standard anelastic solid” as described earlier in Chap. 1, with the relaxation strength and the relaxation time

Λb2 KJu τ = B/K

∆=

(2.20) (2.21)

(cf. Benoit 2001a and for more elaborate formula Seeger 2004a), where ω is the circular frequency of the imposed vibration, B the drag coeﬃcient of the dislocation velocity, K the restoring force due either to internal stresses or

60

2 Anelastic Relaxation Mechanisms of Internal Friction

to the line tension Γ of the dislocation (≈Gb2 /2, with shear modulus G and length of the Burgers vector b), and Ju is the unrelaxed compliance. In case of low Peierls barriers, the dislocation model of a vibrating string (with length L, cf. Granato and L¨ ucke 1956a) is appropriate, and K = 12Γ/L2 Ju = 1/G, so that τ=

BL2 12Γ

and

∆=

ΛL2 . 6

(2.22)

For example, in case of phonon drag on dislocation motion (Alshits and Indenbom 1986), B = aB T with aB ≈ 10−7 N s m−2 K−1 , and a relaxation peak results in the MHz range (Alers and Thompson 1961, Akune et al. 1975). In case of pinning by discrete point defects (e.g., after cold work or irradiation), K = (12Γ/Λ2 )(n0 + nD (t))2 , where n0 + nD (t) denotes the number of point defects present and arriving at the dislocation loop during the time t. This results for ωτ 1 in Q−1 ∝ ∆ · τ ∝ K −2 ∝ L4

and δJ/J = ∆ ∝ K −1 ∝ L2

(2.23)

In case of high Peierls barriers, the kink model is adequate. For the kink chain model of dislocation bow-out and motion (cf. Seeger and Sestak 1971), the following relaxation times are found in the limiting cases of very large and very small kink separation distances χK in comparison with the distance l(= L/n) of obstacles along the dislocation: τ = l(kT )2 exp[(2HK + HKM )/kT ] 2

3/2

τ = l (kT )

exp[(HK +

HKM )/kT ]

for l χK for l χK

(2.24) (2.25)

where HK and HK M are the activation enthalpies for generation of a single kink and for kink diﬀusion along the dislocation, respectively. In the ﬁrst case (small obstacle distance) the enthalpy 2HK for double kink separation enters, while in the latter case (few obstacles) only that of a single kink. The following relationships can be given between the measured relaxation enthalpies of the respective internal friction peaks, Hα , Hα and Hγ , and the corresponding kink parameters (after Benoit 2001a): Hα = HkM (screw)

(2.26)

Hα = 2Hk (edge) + HkM (edge) − 2kT Hγ = 2Hk (screw) + HkM (screw) − 2kT.

(2.27) (2.28)

Dislocation parameters in the kink model, as derived from internal friction experiments on the α , α and γ peaks, are displayed in Table 2.14. The acoustic coupling technique devised by Gremaud (1987, 2001) can be applied to distinguish between mechanisms using the dependence of damping on bias stress (or stress amplitude). The characteristic Bordoni “signature” exhibits a loop shape as shown in the example of Fig. 2.25.

2.3 Dislocation Relaxation

61

Table 2.14. Peak temperatures (f = 1 Hz), activation energies and dislocation parameters in the kink model as derived from internal friction experiments on the α , α and γ peaks in bcc metals (Schultz 1991) metal

Tα (K)

Hα (eV)

HkMscrew (eV)

Tα (K)

Hα (eV)

2Hk,edge (eV)

K Ba Nb Ta Cr Mo

– – ≤40 22 – 35 58 46 90 12

– – 0.070 0.034 – 0.074 0.086 – 0.187 0.001

– – 0.070 0.034 – 0.074 0.086

– 22 ∼40 31 50 93 125 162

– 0.047 0.075 0.057 0.12 0.16 0.25 0.479

– 0.051 0.08 0.062 0.13 0.18 0.27 0.507

26 20 16

0.018 0.011 0.008

0.022 0.014 0.011

W α-Fe

0.187 0.001

Tγ (K)

Hγ (eV)

2Hk,screw (eV)

27 150 280 400 – 400–490

0.046 0.38 0.67 0.85–1.0 – 1.09

0.051 0.41 0.72 0.96–1.1 – 1.09

640

1.9–2.1

1.9–2.1

350

0.8–0.9

0.94

Fig. 2.25. Characteristic “signature” of Bordoni peak behaviour as measured by the ultrasonic coupling technique. α = attenuation of ultrasonic wave, σ = quasistatic bias stress applied to the specimen (Bujard et al. 1987). Full line for loading, dashed line for unloading. Frequency of applied bias stress 0.02 Hz, ultrasound frequency 8.5 MHz. Al single crystal deformed by 0.1% at 10 K, annealed for 2 h at 220 K between the measurements at various indicated temperatures

2.3.2 Coupling of Dislocations and Point Defects: Hasiguti and Snoek–K¨ oster Peaks and Dislocation-Enhanced Snoek Eﬀect The interaction of the strain ﬁeld of a dislocation with the strain (or stress) ﬁeld of point defects produces low-energy positions of the latter which may

62

2 Anelastic Relaxation Mechanisms of Internal Friction

lead to relaxation eﬀects if either the dislocation or the point defects move, or if the dislocation breaks away from the point defects with a characteristic thermally activated relaxation time. Such relaxation eﬀects may be caused either (a) by intrinsic lattice point defects (vacancies, self-interstitials, substitutional foreign atoms), called Hasiguti peaks (Pi , see section “Hasiguti Peaks”) or (b) by interstitial defects of light (hydrogen) or heavier (carbon, nitrogen, oxygen) foreign atoms. The latter, mainly observed in bcc transition metals, are called Snoek–K¨ oster (SK ) peaks if located at a slightly higher temperature than the Snoek peak (see section “The Snoek–K¨ oster Relaxation”), or dislocation-enhanced Snoek eﬀect (DES ) if found at the same position as the Snoek peak, but with a higher peak maximum (section “DislocationEnhanced Snoek Eﬀect”). Hasiguti Peaks An analysis of the internal friction spectra of deformed metals with diﬀerent crystal lattices, as summarised in Figs. 2.18–2.20, is rather complicated and controversial; it is even accepted to designate damping peaks of the same type in diﬀerent metals diﬀerently (Magalas 1984a). Besides the Bordoni peaks (Bi , α, γ) treated in Sect. 2.3.1, and the SK and DES maxima to be described later, the so-called “Hasiguti peaks” (Pi and some other related peaks, essentially found in pure metals) form another family of deformationinduced relaxation eﬀects. In fcc metals there are in general three Hasiguti peaks, denoted as P1 , P2 , P3 with increasing peak temperatures Tm (Hasiguti et al. 1962, Benoit et al. 1970). In bcc metals the peaks of type β (Chambers 1966; see Fig. 2.20), sub-divided into β1 , β2 , β3 (Ritchie et al. 1978), were identiﬁed as the Hasiguti maxima (Hasiguti et al. 1962), but other designations (like βα , βγ ) also exist. In hexagonal metals with quite diﬀerent and partially complex spectra (Fig. 2.19), Mg, Ti and Zr show not only the main Hasiguti peaks Pi (in Ti also called Pα and Pα ; Miyada et al. 1977a,b) but also some additional low-temperature peaks (e.g., π1 , π2 ). Some important features of the Hasiguti peaks are the following: 1. The number of Hasiguti maxima depends on the deformation conditions (Burdett and Queen 1970a). Thus, in pure copper (99.999%) after deformation by torsion or tension at room temperature, only P1 and P2 were observed. Deformation at the temperature of liquid nitrogen gave a large maximum P2 . The height of P1 is approximately two times higher in specimens deformed by torsion in comparison with those after deformation by bending, drawing or tension. 2. The Hasiguti peaks, of thermally activated relaxation nature as well (see Table 2.11), are less broadened by deformation than the Bordoni maxima. Also in non-cubic metals a very strong inﬂuence of the kind of deformation is found. In bismuth (rhombohedral lattice, Fig. 2.26) deformation by slip

2.3 Dislocation Relaxation

63

Fig. 2.26. Generalised internal friction spectra of Bi deformed by slip (1 solid lines) and twinning (2 dashed lines), for f = 70 kHz (From Sato and Sumino 1977)

gives three damping maxima, while by twinning only two other ones arise. In zinc (hcp) after deformation in the basal plane (Fig. 2.19) three maxima are observed, while deformation in the pyramidal system yields only one maximum. 3. The presence of impurities in general decreases the height of the Hasiguti “deformation peaks” (similar to that of the Bordoni peaks) as a result of dislocation pinning. 4. Annealing at temperatures below the recrystallisation threshold inﬂuences the heights of the Bordoni and Hasiguti maxima in diﬀerent ways; while the former remain up to recrystallisation, the latter anneal out in the recovery stage. However, for copper and gold it was shown that after annealing at the recovery temperature, the Hasiguti maximum P2 (due to the interaction of dislocations with self-interstitials, see later) has a maximal Qm −1 value (Okuda 1963a) because of diﬀusion of selfinterstitials to dislocations. Annealing eﬀects were observed also for zinc (Kayano 1969). Mechanisms The microscopic mechanisms of deformation eﬀects like the Hasiguti peaks are still known insuﬃciently (see e.g., the reviews by Fantozzi et al. 1982, Magalas 1984a, Magalas and Gorczyca 1985). Occurring in pure metals, the Hasiguti relaxation appears to be connected with processes of dislocation motion in the presence of self-point defects produced during plastic deformation (Burdett and Queen 1970a). The three Hasiguti peaks in fcc metals (Table 2.11), for instance, were attributed to the interaction of dislocations with vacancies (P1 ), self-interstitials (P2 ), and divacancies (P3 ) (Burdett and Queen 1970a). However, there are also some other explanations, in particular, those based on models of interaction of dislocations with higher complexes of point defects. In bcc metals like α-Fe, the Hasiguti maxima can be associated with the release

64

2 Anelastic Relaxation Mechanisms of Internal Friction

of geometrical kinks on non-screw dislocations from immobile self defects (β1 ), the incorporation of self-point defects into mobile dislocation segments (β2 ), and the movement of non-screw dislocations in an atmosphere of immobile carbon atoms (βα ). In hexagonal metals, interactions of geometric kinks with vacancies (π1 ), of dislocations with self-interstitials (P1 in Mg), or of dislocations with clusters of self point defects (P2 in Mg, P1 in Zn) were suggested. The β relaxation in bcc metals has most recently been proposed by Seeger (2003, 2004b) to be identical with the “reversible” γ relaxation (D’Anna and Benoit 1993b; cf. also M¨ uhlbach 1982), both being caused by the same mechanism, namely the stress-assisted thermally activated generation of kink pairs on {110} slip planes in (a0 /2) 111 screw dislocations with incorporation of interstitial atoms into the dislocation cores (Seeger 2004b). This was concluded from measurements on pure Mo (Seeger and Sestak 1971), yielding a kink formation enthalpy of Hγ = 1.275 eV (with τ0 = 1.04 × 10−14 s−1 ) and Hβ = 0.62 eV (with τ0 = 1.2 × 10−13 s−1 ) (Seeger 2004b). Therefore the β peaks may also be associated with the group of Hasiguti peaks. In metals of the VIB group with a lower degree of purity, deciphering of deformation peaks is even more contradictory. It seems that α and γ peaks are of the Bordoni type, and β peaks are connected with point defects, self and foreign atom ones. All these peaks are broadened and may be divided into several Debye peaks. There are several other deformation-induced loss peaks which have not been reliably understood, though many hypotheses were expressed. Possibly some of these unexplained deformation peaks may rather be attributed to the Snoek–K¨ oster eﬀect (see later). The Acoustic Coupling Technique (Gremaud et al. 1987a), with measuring the acoustic wave attenuation ∆α during a low frequency sweep of an applied bias stress σ in dependence of time and temperature, helps to further clarify the mechanism. The “signature” (plot of ∆α versus σ) shows characteristic loop shapes measured with a 99.999% Al sample after cold working of 0.4% at 4 K, for the case of breakaway from a row of immobile point defects (Fig. 2.27a,

Fig. 2.27. Signatures of damping mechanisms as measured by the Acoustic Coupling Technique (Gremaud et al. 1987a) for various dislocation-point defect (Hasiguti) interactions (cf. text). Ultrasonic frequency 10 MHz, frequencies of sinusoidal bias stress: (a) 0.02 Hz, (b) 0.1 Hz and (c) 10−4 Hz

2.3 Dislocation Relaxation

65

T = 150 K), for pinning-depinning in two clouds of slowly migrating point defects (Fig. 2.27b, T = 250 K), and for dragging a cloud of mobile point defects (Fig. 2.27c, T = 350 K). The Snoek–K¨ oster Relaxation The Snoek–K¨ oster (SK ) relaxation shows up as a large eﬀect in deformed bcc metals containing dissolved foreign interstitial atoms, and involves the stress-induced short-range statistical reorientation of the interstitials residing in octahedral (O, N, C) or tetrahedral (H, D) positions. Similar deformation maxima of internal friction in hexagonal metals such as Ti and Zr (where dislocations may be strongly pinned by the interstitials as well) may also be attributed to the SK relaxation. Table 2.15 gives an overview over related damping peaks observed, including the respective peak temperatures. It is necessary to point out that the SK relaxation is observed in systems where the interstitial solute atoms produce a reorientation relaxation also without a previous plastic deformation, by means of elastic dipoles formed either by single interstitials (C, N, O in bcc metals; classical Snoek relaxation) or by their pairs or complexes (O in hcp metals or H, D in bcc or hcp metals; Snoekor Zener-type relaxation, cf. Sect. 2.2). Some important features of the SK peak are the following: 1. The peak height Qm −1 is determined both by the concentration of interstitals in solid solution and by the degree of deformation. It increases with solute concentration and then saturates (Fig. 2.28), at a value being the higher, the higher is the degree of previous plastic deformation. In all cases, the height of the SK maximum is lower than that of the Snoek peak. A considerable inﬂuence of the interstitial element is observed: the peak is remarkably higher in Fe–N than in Fe–C alloys. However, it is impossible to correlate this inﬂuence with the strength of interaction between interstitials and dislocations: N and C have almost identical energies of interaction with dislocations in α-Fe. In tantalum, hydrogen interacts considerably weaker with dislocations than O, but the heights of both SK maxima are of the same order (Seeger et al. 1982; Funk and Schultz 1985; Rodrian and Schultz 1982), and in vanadium, increased concentrations of N and O, which pin dislocations stronger than H, decrease and annihilate the SK (H) maximum (Chang and Wert 1975). The peak height also depends on annealing. For the formation of a SK (N) peak the annealing treatment during internal friction measurement is sufﬁcient. In the system Fe–C a peak also arises during ﬁrst heating; however, aging for several hours at 240◦ C increases its height by 50% before starting to decline (Nowick and Berry 1972), i.e., the peak forms by combined deformation and aging, and it decreases when carbon is trapped in carbide precipitates. Annealing at higher temperatures leads to a decrease of the SK (C) maximum, until it vanishes soon after annealing at temperatures oster et al. 1954, Shushaniya and Golovin 1961). exceeding 600◦ C (K¨

66

2 Anelastic Relaxation Mechanisms of Internal Friction

Table 2.15. Temperatures Tm of Snoek–K¨ oster maxima (for f = 1 Hz if not speciﬁed diﬀerently) system

Tm (K)

reference

Fe–C

470–590

Fe–H Fe–N Lu–D Lu–H Mo–H Nb–D Nb–H

110; 150a 520 260b 250–260b 320 150c ; 160d 110–150a

Nb–N Nb–O

760–800 540–750a

Sc–H Ta–D Ta–H

190e 130f 140–150

Ta–N

810 530–660

K¨ oster and Lampschulte (1961); Shushaniya and Golovin (1961); Magalas and Ngai (1997); Tkalcec and Mari (2004); Tkalcec et al. (2006) San Juan et al. (1985a) Petarra and Beshers (1967) Vajda et al. (1981, 1983) Vajda et al. (1981, 1983) Suzuki (1989b) Mazzolai (1975); Okuda et al. (1984) Ferron et al. (1978); Igata et al. (1979a); De Lima and Benoit (1981b); Yoshinari and Koiwa (1982a,b) Dahlstrom et al. (1971) Seeger et al. (1982); Molinas et al. (1987, 1990, 1994) Trequattrini et al. (1999, 2000) Cannelli and Cantelli (1975) Yoshinari and Koiwa (1982a); Funk and Schultz (1985); D’Anna and Benoit (1990) Ooijen and Goot (1966) Seeger et al. (1982); Rodrian and Schultz (1981, 1982), Fang et al. (1996) Tinivella and Povolo (1975) Yoshinari et al. (1977, 1978) Chang and Wert (1975); Shibata et al. (1978); Koiwa and Shibata (1980a,b); Yoshinari and Koiwa (1982a) Kappesser et al. (1994) Trequattrini et al. (1999, 2000) Miyada-Naborikawa and De Batist (1983, 1985) Ritchie (1982)

Ta–O Ti–H V–D V–H

620; 720a 221 150 140–200

Zr–H

220 210e 205–220a

Zr–O

800; 870a,g

Y–H

a

Two maxima SK f = 0.6 Hz c f = 850 Hz d f = 2800 Hz e f = 3600 Hz f f = 15 kHz g f = 4 Hz b

2.3 Dislocation Relaxation

67

Fig. 2.28. Inﬂuence of N (1) and of C (2) concentration (determined by the Snoek as abscissa) on the Snoek–K¨ oster maximum height Q−1 peak height Q−1 S SK in Fe. (From K¨ oster and Lampschulte 1961)

The peak width is approximately twice of the value for a single relaxation time process (Nowick and Berry 1972). 2. The peak temperature Tm is determined by the type and concentration of solutes, the degree of deformation and the diﬀusion characteristics of the dissolved element. With rising solute concentration, Tm increases and approaches a constant value. With increasing degree of previous deformation Tm decreases, e.g., in the systems Fe–C and Fe–N (K¨oster et al. 1954). However, an opposite behaviour is also possible: in the system V–H a stronger deformation leads to an increase in Tm (Chang and Wert 1975), and in the system Nb–H Tm decreases slightly with increasing H concentration (Igata et al. 1979a). In some alloys two SK maxima are found. In Nb–O at a frequency of 1.2 Hz, for instance, there is one maximum (SK (O)-1) at 545 K, and another one (SK (O)-2) at 733 K (Seeger et al. 1982, Molinas et al. 1987). Analogously, two maxima were observed in alloys like Fe–H (San Juan et al. 1985a), Ta–H (Yoshinari and Koiwa 1982a, Mizubayashi and Okuda 1982), Ta–O (Fang et al. 1996) and Nb–H (Ferron et al. 1978). The complicated dependence on concentration and deformation conditions does not permit to show unequivocally the SK peak temperatures, and thus, in Table 2.15 either a temperature range or approximate temperatures are given. It is evident from these data that the temperatures of the SK peaks are higher than those of the Snoek maxima in these systems, and also ordered in the same sequence: in the metals of the VB group (V, Nb, Ta,), for instance, Tm increases in the sequence H → O → N.

68

2 Anelastic Relaxation Mechanisms of Internal Friction

3. The activation energy H and the relaxation time τ0 are also structurally sensitive characteristics. Thus, the activation energy characterizing the SK (H) maximum in V increases substantially and τ0 decreases with increasing deformation (Chang and Wert 1975). With increasing carbon solute concentration in α-Fe, H rises from 125 to 159 kJ mol−1 for the SK (C) peak, and τ0 decreases from 10−14 to 10−18 s (Petarra and Beshers 1967). In all investigated systems the H values of the SK relaxation are signiﬁcantly higher than those of the respective Snoek maxima. 4. Introduction of substitutional foreign metal atoms inﬂuences signiﬁcantly the SK peak parameters (Chang and Wert 1975, Gridnev et al. 1976); for instance, some substitutional atoms decrease Tm in Fe (Petarra and Beshers 1967, Surin and Blanter 1970). In particular, 5% Ni in Fe decrease H from 175 to 135 kJ mol−1 , Tm from 490 to 450 K, and Qm −1 from 1.55 · 10−5 to 1.15 · 10−5 (Surin and Blanter 1970), which may be associated with changes in pinning of dislocations. 5. Maxima were observed not only in previously deformed specimens, but also in those quenched to produce martensite in steel, and also in specimens where an increased density of dislocations arose because of precipitation of second phases, e.g., hydrides and deuterides in vanadium, niobium and tantalum (Yoshinari and Koiwa 1982a, 1982b). Mechanisms The exact mechanisms of the Snoek–K¨oster (“cold work”) relaxation (and related eﬀects like DES and “M-peak”, cf. section “Dislocation-Enhanced Snoek Eﬀect”) are a matter of long-standing discussion (Nowick and Berry 1972; De Batist 1972; Hirth 1982; Schoeck 1963, 1982, 1988; Seeger 1982; Ritchie 1982; Weller 1983; Gavrilyuk and Yagodzinskij 1986; Ogurtani and Seeger 1987; Magalas 1996a). The strength of the SK relaxation, if counted per dissolved interstitial atom absorbed at a dislocation, is several times higher than that of the Snoek relaxation (Nowick and Berry 1972): therefore, the simplest possible mechanism for the SK relaxation, the reorientation of the elastic dipoles formed by the dissolved atoms in the stress ﬁeld of the dislocations, as supposed by K¨ oster, cannot describe the experimental data. Schoeck supposes (Schoeck 1963, 1982, 1988; Schoeck and Mondino 1963) that the source of anelastic deformation responsible for relaxation is the movement of dislocation segments bowing out under the action of the applied stress (dislocation string model) with a speed limited by the speed of migration of dissolved atoms pinning the dislocation and being dragged along with the moving dislocations. Then the relaxation time will be 2 αkT L cd (2.29) τSKT = 3 Gb DT

2.3 Dislocation Relaxation

69

with DT = DT0 exp(−H/kT ),

H = HB + HD ,

(2.30)

and the maximum damping value is (cf. (1.5) and (2.22)) Qm −1 = (1/2)βΛL2

(2.31)

where L is the mean length of dislocation segments between immobile and unbreakable ﬁxing points (where a reaction with a forest dislocation has occurred), cd the concentration of solute atoms on dislocations, b the length of the Burgers vector, DT the coeﬃcient of diﬀusion for transverse motion of impurities in the dislocation core, HD the enthalpy of migration of dissolved atoms in the lattice, HB the binding enthalpy of an interstitial atom to the dislocation, and α and β(= α/π) are constants. On the basis of this theory it is possible to understand the general regularities of the SK relaxation. However, there are at least two diﬃculties: ﬁrst, the peak height does not depend on the impurity concentration, and second, for hydrogen HB ≈ 0 although in all four metals (V, Nb, Ta, Fe) the activation enthalpy H of the SK (H) maximum is signiﬁcantly higher than HD . An extended approach takes into account not only the transverse motion (with respect to the dislocation oscillating with the frequency ω) of impurity atoms but also their longitudinal diﬀusion along the dislocation (see Blanter and Piguzov 1991). The related dislocation motion gives broadened relaxation maxima due to the distribution of segment lengths between obstacles. Thus this model may explain the existence of two SK maxima (corresponding to the longitudinal and transverse diﬀusion of impurity atoms on dislocations), and predict the structural sensitivity of the relaxation parameters. Seeger’s model (Seeger 1979, 1981, 1982; Ogurtani and Seeger 1987) connects the SK relaxation with the formation of double kinks on dislocations in the presence of mobile dissolved atoms (kink pair formation model). The SK relaxation, from this point of view, is a particular case of the wide class of relaxation phenomena caused by the movement of kinks on dislocations: the Bordoni relaxation (cf. Sect. 2.3.1), DES (cf. section “Dislocation-Enhanced Snoek Eﬀect”), etc., now including the interaction with solute atoms. The time of relaxation, associated with the formation of kink pairs under stress, is ρeq kT L k L , (2.32) τSKP = 1 + 2 2 2a2 ΓDk (peq k ) where a is the distance between two neighbouring Peierls valleys (Fig. 2.21) (or the lattice period in the respective direction), Γ the dislocation line tension, Dk the diﬀusion coeﬃcient of kinks, and ρeq k

1 = wk

2πHk kT

1/2 exp(−Hk /kT )

(2.33)

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2 Anelastic Relaxation Mechanisms of Internal Friction

is the linear density of kinks of the same sign in thermal equilibrium; wk the kink width, Hk the energy of kink formation. The relaxation strength is given by (2.22), where only the density Λ of those dislocations is considered, on which dissolved impurity atoms are adsorbed. ∆ does not depend on temperature. In case of the Snoek–K¨oster relaxation, the diﬀusive mobility of kinks along the dislocation in the presence of foreign dissolved atoms, which are able to migrate and change the orientation of elastic dipoles axes, is considered. Then the kink diﬀusion coeﬃcient is either DK ∝ exp(−HD /kT )/cd

(2.34)

DK ∝ exp(−(HD + HK M )/kT )/cd

(2.35)

or where the enthalpy of the kink migration Hk M is included or not included depending on details of the model, cd is the concentration of impurity atoms along the moving dislocation line, and cd = cp /{1 + exp(−GB /kT )}

(2.36)

where cp is the concentration of dissolved atoms in solution, GB = HB − T SB is the binding free enthalpy of an impurity atom with a dislocation, and SB is the binding entropy. The eﬀective activation enthalpy of the relaxation, Heﬀ = d ln τp /d(1/kT ), is found to be a structurally sensitive characteristic and depends on the experimental conditions, the presence of an equilibrium or non-equilibrium atmosphere of impurity atoms at the dislocations, the dislocation type (i.e., the value Hk ) and the diﬀusion mobility of impurity atoms. For four extreme cases the Heﬀ values of the SK relaxation are given in Table 2.16. In case of low concentrations of impurity atoms on dislocations when cp exp[GB /(kT )] 1, Heﬀ includes energetic parameters of kinks, impurity atoms and the binding energy HB of an impurity atom at the dislocation. In the opposite case of a saturated atmosphere on a dislocation, Heﬀ does not include the energy HB . As Table 2.16 indicates, it is possible to explain theoretically the existence of several SK maxima at diﬀerent temperatures (diﬀerent values of ρk eq L), or the appearance of peaks caused by dislocations of diﬀerent types. For example, Table 2.16. Components of the eﬀective activation energy of the Snoek–K¨ oster relaxation. (From Seeger 1982) ρeq k L

cp exp[GB /(kT )] 1

cp exp[GB /(kT )] 1

1 1

2Hk + Hk + HD + HB − 2kT Hk + Hk M + HD + HB − (3/2)kT

2Hk + Hk M + HD − 2kT Hk + Hk M + HD − (3/2)kT

M

2.3 Dislocation Relaxation

71

in α-Fe, Nb, Ta and V, SK (H) is connected with non-screw dislocations (Hk is low), while SK (O) or SK (N) is due to screw dislocations (Hk is high). However, the Seeger theory, just as other theories of the SK relaxation, cannot explain the complicated concentration dependence of Qm −1 . One can explain the existence of two maxima in iron with hydrogen also by the interaction of single hydrogen atoms (the ﬁrst maximum) and of H atom pair complexes (the second one) with geometric kinks on non-screw dislocations (San Juan et al. 1987a,b). However, there exists also the other viewpoint (Ritchie 1987) that all low-temperature SK (H) maxima in V, Nb, Ta and Fe are associated with non-screw dislocations. A third model (“coupling model”) which is able to explain the very low measured activation enthalpies HSK for C relaxation in high purity Fe (Iwasaki 1984, Magalas 1984a, 1996a) as well as the skew shape of the SK peak, has been proposed by Magalas and Ngai (Magalas 1996a; Magalas and Ngai 1997). It includes not only the dragging of Cottrell atmospheres by the dislocations (as in Schoeck’s model), but takes into account the cooperative migration of foreign interstitial atoms caused by two kinds of interactions: (a) between the foreign interstitials themselves, and (b) between interstitials and the time dependent strain ﬁeld of dislocations. This results in slowing down the migration rate of the interstitials and is described by a relaxation function containing a stretched exponential, ψ(t) = exp{−(t/τ )βs } with βS < 1, instead of oster relaxation the Debye behaviour (βS = 1). The resulting average Snoek–K¨ time is then HS } (2.37) τav SK = τoav SK exp{ (1 − n)kT with τoav SK =

2 1/(1−n) παR2 kT cd lm tc −n τ0 S , 2 5 10Gaj b

(2.38)

where aj is the characteristic jump distance of foreign interstitial atoms, n(= 1 − βS ) is the coupling parameter, and tc denotes the crossover time separating the regime of Debye behaviour at very short times (t < tc which is less than detectable times in common experiments) from that of the stretched exponential behaviour (t > tc ). Taking an interaction parameter n = 0.084, the measured Heﬀ = HSK value of 90.7 kJ mol−1 (Iwasaki and Hashiguchi 1982) is explained with the Snoek activation energy of HS = 84.7 kJ mol−1 (Magalas and Fantozzi 1996b). Dislocation-Enhanced Snoek Eﬀect (DES) The Snoek relaxation in bcc iron is ampliﬁed after cold plastic deformation (e.g., Stephenson and Conard 1968). This phenomenon was ﬁrst observed by Magalas (1984a) for C in pure Fe (Fig. 2.29), and called “dislocation-enhanced Snoek eﬀect”. The DES relaxation maximum arises at the same temperature as the Snoek peak but is higher and signiﬁcantly wider, and accompanied by a

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2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.29. Initial (0) Snoek maximum in Fe + 0.004%C alloy, enhanced by dislocations after deformation at room temperature by 6% (1) and by 13% (2). (From Magalas 1984a)

neighbouring “M peak” at a slightly higher temperature. The H and τ0 values are very similar to those of the Snoek relaxation: for instance, in iron with 0.1% C we ﬁnd 81.1 kJ mol−1 /6.3 · 10−14 s for the DES, and 80.6 kJ mol−1 /5.5 · 10−15 s for the original Snoek eﬀect, respectively. The width of the DES peak is associated with a normal distribution of ln τ0 (Rubianes et al. 1987). The eﬀect is inﬂuenced (Magalas 1984a, Rubianes et al. 1987) by: (a) Temperature and degree of the plastic deformation. Qm −1 is higher after deformation at room temperature than at low temperatures where screw dislocations prevail owing to their low mobility. Therefore the main contribution to DES after room temperature deformation is given by non-screw dislocations; (b) Annealing at a temperature lower than the recrystallisation temperature. Although this treatment does not inﬂuence the Snoek peak height, it removes the additional DES internal friction. A peak is observed when dislocations, which arise by plastic deformation, are not completely ﬁxed by dissolved atoms; (c) Interstitial atom concentration. The eﬀect is stronger at lower than at higher concentration (e.g., in iron: 0.025% compared to 0.1% C). At very low concentrations when the Snoek maximum is absent, there is still a DES after deformation; (d) Heating rate during the measurement. At higher heating rates the maximum is higher, probably because the aging processes is less complete.

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73

Analogous eﬀects were observed in the systems Ta–O and Nb–O (Seeger et al. 1982; Rodrian and Schultz 1981, 1982; Molinas et al. 1987; MelikShakhnazarov et al. 1975, 1981a,b), both in polycrystals and single crystals. In case of Ta alloys, DES (O) peaks have also been called γ2 deformation peaks (Magalas 1984a, cf. Fig. 2.20). A similar peak was also observed in Zr–H (Miyada-Naborikawa and De Batist 1983, 1985). The mechanisms of DES and M relaxations are not yet fully clear, but the following variants are possible (Magalas 1984a, Rubianes et al. 1987, Magalas and Gorczyca 1985, Magalas 1996a): (a) Movement of non-screw dislocations in the atmosphere of dissolved atoms, connected with reorientation of elastic dipoles and obstructed by the dissolved atoms; (b) The mechanism of the SK relaxation according to Seeger, in the case when a non-screw dislocation is moving at temperatures which are not suﬃcient for diﬀusion of dissolved impurity atoms over large distances; (c) Migration of kinks along the dislocation in an atmosphere of point defects retarding them; (d) Ordering of the interstitial atoms in the dislocation strain ﬁeld, as proposed by Melik-Shakhnazarov et al. (1981a) to explain the DES of O in Nb. It should be noted that similar to the SK relaxation, also the DES mechanism is in principle not restricted to bcc systems showing a classical Snoek relaxation, but may be extended to other cases of point-defect reorientation enhanced by dislocations. An important example, besides the hexagonal Zr–H system already mentioned, is the “dislocation-enhanced Finkelshtein–Rosin eﬀect” (DEFRE, see Sect. 2.2.2) due to interstitial impurity pairs or complexes in fcc austenitic steels. As a general rule deformation raises the height and width of the FR peak and also the IF background, whereas the peak temperature is rather stable or slightly decreases (Golovin and Belkin 1965; Golovin et al. 1966, 1997c). Computer simulations (Blanter et al. 2000a,b) showed that the elastic ﬁeld around a dislocation enhances the asymmetry of metal atom displacements around interstitial atoms, thus intensifying the FR peak. On the other hand, the relatively weak carbon-dislocation interaction in the fcc lattice does not lead to signiﬁcant changes in the site energies of interstitial carbon, so that the corresponding activation energy for “diﬀusion under stress” of carbon remains nearly the same as in the undeformed alloy. For the same reason and in contrast to ferrite, there is no additional “Snoek–K¨ oster” peak in austenite. 2.3.3 Other Kinds of Dislocation Relaxation In this section we brieﬂy summarise several other dislocation-related relaxation processes beyond Bordoni, Hasiguti, Snoek–K¨ oster and dislocationenhanced peaks. Besides further relaxation peaks at more elevated but still

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2 Anelastic Relaxation Mechanisms of Internal Friction

“medium” temperatures (see section “Dislocation Relaxation Peaks at Medium Temperatures”), two diﬀerent kinds of continuous background damping occur at very low (see section “Background Damping at Very Low Temperatures”) and at high temperatures (see section “Damping Background at Elevated Temperatures”), respectively. More dislocation-related damping processes are connected with microplasticity (i.e., dislocation movement after depinning and even multiplication) and give rise to a hysteretic (i.e., non-linear) type of anelastic behaviour, which with a transition to fully amplitude-dependent internal friction will be considered in Sect. 3.3, together with some remarks on fatigue. Background Damping at Very Low Temperatures At very low temperatures (<10 K), when phonon damping is “frozen out” and electron damping is removed in case of superconductivity, a temperatureindependent damping level of Qm −1 ≈ 10−5 . . . 10−3 has recently been discovered by Xiao et al. (1999) in aluminium, Al alloys and other metals in thin ﬁlm and bulk form. This behaviour is quite similar to that observed at comparable temperatures in amorphous materials (see Sect. 2.6.1), and is believed to arise from relaxation of a broad spectrum of tunneling states at dislocations, possibly associated with kinks. It is interesting to note that the commercial Al alloy Al-6061 (with 1 at.% Mg, 0.6 at.% Si, 0.3 at.% Cu, 0.25 at.% Cr) behaves quite similar to pure Al, while Al-5056 (with 5.3 at.% Mg, 0.1 at.% Mn, 0.1 at.% Cr) exhibits a damping level one order of magnitude lower, indicating a strong obstruction of kink movement by precipitates, consistent with the exceptionally high yield stress of the latter alloy. Dislocation Relaxation Peaks at Medium Temperatures Several broad relaxation peaks, in general superimposed on a background increasing with temperature (see section “Damping Background at Elevated Temperatures”), have been observed in the intermediate temperature range (0.3 < T /Tmelt < 0.7) depending on sample condition (single or polycrystal), purity, deformation and heat treatment (see reviews by N´ o (2001) and Benoit (2004)). The correlation with the microstructure, as studied by transmission electron microscopy and X-ray diﬀraction, indicates that these peaks may originate from speciﬁc dislocation mobility mechanisms, like cross-slip from one compact plane to another or between planes of diﬀerent nature (including glide on non-compact planes), or dislocation motion controlled by climb of jogs in the dislocation lines. This interpretation is also supported by the activation parameters determined from internal friction, as compared to those from creep measurements. In all cases diﬀusion (mainly pipe diﬀusion, sometimes bulk diﬀusion) is involved, and the splitting of dislocations into partials explains the considerable diﬀerences between metals with high and low stacking-fault energies.

2.3 Dislocation Relaxation

75

Fig. 2.30. Internal friction spectra of Cu polycrystals and single crystals in the medium temperature range, showing peaks superimposed on a strongly increasing damping background. (From Woirgard et al. 1975; or Rivi`ere 2000)

However, the explanation of these “medium-temperature” relaxation peaks by a dislocation mechanism is not generally accepted in all cases but has been a matter of controversy. The dislocation mechanisms are quite well established for copper (Tm = 670 . . . 910 K, see Fig. 2.30) where careful experiments have also been performed on single crystals, including the forced vibration pendulum technique in a wide range of frequencies at various temperatures (Woirgard et al. 1974, 1975, 1981; Rivi`ere 2000). On the other hand, the origin of related peaks in aluminium (with Tm ≈ 520 . . . 560 K at f = 1 Hz, depending on grain size and on the purity of the material) is not as clear: they have been attributed either to grain boundary relaxation (Kˆe 1947a,b, 1990a, 1998), or to relaxation by climb processes in the dislocation network (N´ o and San Juan 1983; N´ o et al. 1988a, 1989). A grain boundary relaxation mechanism was conﬁrmed by Cao et al. (1994) for a peak observed at 1,100 K in Ni–Cr (not clearly distinguishable, however, from the continuous high-temperature background, see section “Damping Background at Elevated Temperatures” and 2.4.1), which was suppressed if the grain boundaries were pinned by precipitates. A series of peaks observed in Al–Mg alloys has been discussed in terms of diﬀerent mechanisms: an interaction of dislocations with Mg-vacancy and Mg-divacancy pairs (peaks PL1 and PL2: Fang and Kˆe 1990), a diﬀusion of the

76

2 Anelastic Relaxation Mechanisms of Internal Friction

substitutional Mg atoms along with or perpendicular to the sidewise motion of dislocation kinks (P0, P1 , P1 : Kˆe et al. 1987a, Tan and Kˆe 1987, 1990, Kˆe and Fang 1990, Fang and Kˆe 1996, Fang 1997), a reorientation of Mg pairs in the stress ﬁeld of moving dislocations (P2: Kˆe 1985a, Kˆe and Tan 1991), and an interaction of Mg Cottrell atmospheres around dislocation kinks involving long-range diﬀusion (P3: Tan and Kˆe 1991). Similar behaviour has been found for Al–Cu alloys (Kˆe and Zhu 1992) Damping Background at Elevated Temperatures Starting a few hundred degrees above room temperature (relative to the melting temperature, at T > (0.6–0.7)Tmelt ) a continuous damping contribution, increasing nearly exponentially with temperature (Fig. 2.30) and corresponding to viscous plastic deformation, is observed in all materials. This damping “background” is highly structure-sensitive, decreases with increasing grain size, is enhanced in deformed, partly recovered and polygonised samples, and reduced by annealing at higher temperatures. It may partly overlap with the peaks described in the preceding section, and also the discussion of the underlying mechanisms is similarly controversial (see reviews by Rivi`ere (2000, 2006) and Benoit (2004)). The mechanisms proposed, mainly diﬀusion-controlled dislocation movement in or near grain boundaries and grain-boundary sliding (see Sect. 2.4.1), are diﬃcult to separate by experiment. One of the problems is that the background depends on the heating rate (Kiss et al. 1985) because the microstructure responsible for the background may change and evolve during the measurement. Assuming diﬀerent mechanisms for the relaxation peaks and for the viscous background, respectively, which is not always the case (!), the superposition of these relaxation eﬀects on the viscous damping background is commonly accounted for by ﬁtting to the measured damping the formula Q−1 = b0 +

b2 exp(−b3 /T ) + Q−1 max sech[b1 (T −1 − Tm −1 )] T

with Q−1 max = f2 (0, β)

∆ , 1 + ∆/2

(2.39)

(2.40)

where the ﬁrst term (b0 ) in (2.39) describes the trivial background produced by the measuring set-up itself and is assumed to be temperature-independent; the second term (with b2 , b3 ) describes the exponential (viscous) background (see later), and the third term (with Q−1 max , Tm , b1 ) represents a log-normal distribution f2 (0, β) of relaxation times of the high temperature peak around Tm , where β characterises the width of Debye peaks (Nowick and Berry 1972). This concept has been successfully applied, for instance, to analyse the high temperature damping in a commercial Al–Mg–Si alloy (Carreno-Morelli et al. 1996a), where the dragging of Mg–Si pairs in the strain ﬁeld of dislocations

2.4 Interface Relaxation

77

(Pichler and Arzt 1994, according to Schoeck’s model (1963, 1982, 1988)) has been concluded to be the relevant relaxation mechanism producing the peak. In order to explain the exponential high-temperature background, Schoeck considers a broad spectrum of diﬀusion-controlled relaxation processes (with an average activation energy U0 ) resulting in the background damping Qbg −1 = (A/ω n ) exp(−nU0 /kT )

(2.41)

with the constant A and the characteristic exponent n. Povolo and Hermida (1996a) has recently analysed the diﬀerent empirical approaches to the hightemperature background damping and concluded that none of them describes properly the observed behaviour, however, (2.41) provides a reasonable approximation (Rivi`ere 2001a). In conclusion of this Sect. 2.3.3 it is noted that in addition to the above considerations, the damping processes due to dislocations in general imply a deﬁnite and strong dependence on the imposed vibration amplitude and can be regarded as anelastic relaxation only for very low amplitudes. The processes at more elevated amplitudes will be brieﬂy considered in Chap. 3.3 on amplitude-dependent internal friction (ADIF). In the materials tables in Chaps. 4 and 5 of this volume the large body of ADIF experiments could not be included for reasons of space, as they concentrate on the basic relaxation processes themselves.

2.4 Interface Relaxation Some indications about relaxation in polycrystalline aggregates arising from the mobility of grain boundaries (GB) have already been given in sections “Dislocation Relaxation Peaks at Medium Temperatures” and “Damping Background at Elevated Temperatures”, as far as the movement of dislocations was involved. A recent detailed account of the various structures of GB with diﬀerent misorientations, applying the notions of incommensurate systems, and of the related internal friction (considered as due to a thermal excitation of the GB), has been provided by Darinskii et al. (2003). In the following we just give a brief more general overview of interface-related relaxations. In principle, GB relaxations, which occur in pure metals as well as under the inﬂuence of solute interactions in alloys, may originate from (a) GB sliding and disordering or reordering of atom groups in the GB (Kˆe 1990b) (Sect. 2.4.1) and (b) GB movement in normal direction, i.e., growth of a favourably oriented grain at the expense of an adjacent one. The latter is usually too small to be observed, except for special cases such as twinning (Sect. 2.4.2), martensitic phase transformations (Sect. 3.2.2), movement of order domains around the ordering temperature (Sect. 3.5), and at very high temperatures, where GBs may move with the aid of vacancy diﬀusion

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2 Anelastic Relaxation Mechanisms of Internal Friction

(Nabarro or Coble creep, see, e.g., Sutton and Balluﬃ 1996). Another special case is the movement of low-angle boundaries which is induced by motion of dislocations (combined glide and climb, sometimes with dragging of impurities). These processes have already been considered in section “Dislocation Relaxation Peaks at Medium Temperatures” and “Damping Background at Elevated Temperatures”. A special section will be devoted later to nanostructured materials (Sect. 2.4.3) where GB relaxations play a prominent role. 2.4.1 Grain Boundary Relaxation GB relaxation was one of the earliest examples considered by C. Zener (1941) as the source of damping in polycrystals at suﬃciently elevated temperatures (Barnes and Zener 1940). He discussed the anelastic strain due to grain boundary sliding resulting from a shear stress and slip along the boundary of two adjacent crystals. The restoring force arises from the back stress built up at the triple junctions where the boundary ends. Zener found for polycrystals (grain size d < sample diameter) with random grain boundaries (width δ) a relaxation time τσ σd ηd = (2.42) τσ = GU δ GU ν(0) where η is an appropriate viscosity for grain boundary sliding (correlated with atomic self diﬀusion: η = kT /Da, D = 1/2νj a2 is the diﬀusion constant, νj is the atomic jump frequency, a is the atomic distance), GU is the unrelaxed shear modulus, σ the acting stress, ν(0) = σb/η is the initial shear velocity. A more recent grain boundary sliding model was proposed by Roberts and Leak (1975). For the relaxation time in a polycrystal with random grains, a slightly more reﬁned derivation by Benoit (2001b, 2004) results in τpolycr =

η 2 JU kT = d∆ = τ0 GB exp(E GB /kT ) γδkP γβ νj a3

(2.43)

with the relaxation strength ∆ = β/dkP JU , where JU = 1/GU is the unrelaxed compliance, kP = σ/u (u: displacement across the GB), νj = νD exp(−E GB /kT ) (νD : Debye frequency, E GB : activation energy for grain boundary sliding given approximately by that for self diﬀusion, E GB ≈ E SD ), and γ, β are two geometrical parameters of the order of unity. Thus the relaxation time τ is expected to increase with grain size d, while the relaxation strength should be independent of d for random polycrystals with grain sizes less than the sample diameter, because kP = σ/u and u ∝ d. However, for crystals with a bamboo grain boundary structure, the grain boundary sliding mechanism would result in a relaxation strength proportional to the number of boundaries, while the relaxation time should be independent of d. According to Ashby and Raj (1970), Raj and Ashby (1971) and Benoit (2001b, 2004), assuming a sinusoidal boundary shape with wavelength λ and amplitude A (able to build up a back stress in the absence of triple junctions), the relaxation time for a bamboo structure is

2.4 Interface Relaxation

79

Fig. 2.31. Grain boundary “Kˆe peak” in polycrystalline Al (Kˆe 1947a), compared to the internal friction of an Al single crystal which does not show this peak

τbamboo =

η γδkB

with

kB =

π 3 EA2 (1 − χ)2 λ3

(2.44)

with χ = Poisson ratio and E = Young’s modulus, while the relaxation strength is similarly as before ∆ = β/dkB JU , where d is now the distance of the grain boundaries along the specimen axis. These expressions have been conﬁrmed by experiments on Al polycrystals and bamboo structure crystals by Kˆe (1947a, 1990a, 1998; cf. Fig. 2.31). However, more experiments on Al of diﬀerent purity and after various deformation and heat treatments, as well as on other metals, have shown that the situation is more complex as already indicated in sections “Dislocation Relaxation Peaks at Medium Temperatures” and “Damping Background at Elevated Temperatures”. For instance, in Cu a peak of the Kˆe-type has been observed by Woirgard et al. (1975) and Rivi`ere (2000) even in single crystals (cf. Fig. 2.30), and therefore must be associated with dislocations rather than with grain boundary sliding. On the other hand, careful checks for the system Ni–20at%Cr (Cao et al. 1994; Benoit 2001c, 2004) on polycrystals and single crystals have shown that besides a dislocation-related peak (P1) there exists in fact another peak (Fig. 2.32) which has to be attributed to grain boundary sliding (P2), because this latter peak can be eﬀectively suppressed by appropriate heat treatment which produces Cr7 C3 carbide precipitates on the grain boundaries blocking their mobility. This has been proved by TEM evidence.

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2 Anelastic Relaxation Mechanisms of Internal Friction

Fig. 2.32. Grain boundary peak (P2) developing in Ni–20at%Cr polycrystals after ﬁrst heating (dissolution of precipitates) in addition to the peak P1 present also in single crystals. 1: ﬁrst heating run, 2: subsequent cooling. (From Cao et al. 1994)

A grain boundary sliding model with presence of particles at the boundaries has been proposed by Mosher and Raj (1974). They assume the rate of sliding to be controlled by diﬀusive accommodation across the particles involving either bulk (DV ) or boundary diﬀusion (DB ), and ﬁnd τ=

kT (1 − χ2 ) p4 d 1 ΩE λ2 δ DB

(2.45)

(with p = particle diameter, Ω = atomic volume), if the diﬀusion along the grain boundary (diﬀusion coeﬃcient DB ) is dominant. The corresponding damping peak is expected to occur at higher temperature than in the pure metal without precipitates which retard the accommodation; however, the relaxation should have the same activation energy. This has been veriﬁed by Mosher and Raj (1974) in measurements with polycrystalline Cu containing SiO2 or GeO2 inclusions. Finally, the models involving grain boundary dislocations should be mentioned (Woirgard and De Fouquet 1974, Shvedov 1979, Benoit 2001b), which also yield an Arrhenius-type expression for the relaxation time including the sum of the activation energies for jog formation and for self-diﬀusion. Ashmarin et al. (1977) arrived at a similar expression. The variety of possible grain boundary microstructures, including faceting and the dependence of GB energies on GB orientation, implies a wide distribution of the relaxation times. The same self-diﬀusion mechanism, which controls the GB mobility in all conceivable models, is also involved in the rapidly increasing high-temperature background (see section “Damping Background at Elevated Temperatures”) as well as in various dislocation mechanisms (such as jog nucleation and motion, climb and point defect dragging, cf. section “Dislocation Relaxation Peaks at Medium Temperatures”). This superposition

2.4 Interface Relaxation

81

prevents an easy interpretation of the GB peak (cf. N´ o et al. 1988a,b, Molinas and Povolo 1993, Iwasaki 1993). Moreover, unreasonable activation parameters (e.g., pre-exponential times τ0 much less than 10−10 . . . 10−11 s) can often be found in the literature. These may arise from microstructural changes of the GBs occurring during measurement, in particular when the peak is measured as a function of temperature with a prescribed heating rate (see Benoit 2001c). Such low τ0 values then in turn imply that the determined activation enthalpies are meaningless. Rather, as all mechanisms are controlled essentially by self diﬀusion, the activation enthalpy of the GB peak is expected to be in the order of that for self diﬀusion in the high-diﬀusion-rate path of GBs (i.e., (0.5 . . . 0.6)E SD bulk , cf. Sutton and Balluﬃ 1996), at least in pure metals. Nevertheless, the appearance and variation of the GB peak with heat treatments can well be used to study the processes of recovery and recrystallisation (grain nucleation and growth) (Schaller and Rivi`ere 2001). The GB-type peak in several Fe3 (Al,Si) intermetallic compounds has been observed in the same range as the order-disorder transformation, and the activation parameters were found by Golovin et al. (2005b, 2006b) to depend on this transformation. This is explained by diﬀerent mobilities of GB dislocations in ordered and disordered phases. The IF peak in Fe-38Al in a similar temperature range is explained in terms of intrinsic dislocation movement by San Juan et al. (2006). In a recent study by Shi et al. (2005), the speciﬁc relaxations of grain boundaries with diﬀerent misorientations (5.8◦ to 44◦ ) have been investigated on bicrystals of pure Al with a large grain boundary area (parallel to the specimen axis in a torsion pendulum). Activation enthalpies from 134 to 159 kJ mol−1 (τ0 = 5.1 × 10−12 to 3.7 × 10−16 s, respectively) were found which change abruptly around 14◦ at the transition from low- to high-angle boundaries. The authors suggest dislocation climb to be the rate-controlling mechanism in low angle boundaries, while local rearrangements in the disordered atom groups found in high-angle boundaries (Kˆe 1990b, 1999) are thought to cause the relaxation in this latter case. Although there are no generally accepted atomistic models so far for GB sliding, a plausible two-step model has been proposed by Machlin and Weinig (as sketched by Nowick and Berry 1972), deduced from the variation of the activation energy of GB relaxation in substitutional alloys with solute concentration. This model considers the ledges which are in general present in the GBs and block the sliding process. Therefore a ﬁrst step consists in the local smoothing of ledges (migration, activation energy Em ), and a second one (in series) in the shear (slip) along part of the GB (activation energy ES ). As the slower process is the rate-controlling one, it follows that at very low solute concentrations where Em is known to be small, the sliding between ledges (with ES > Em ) is governing the eﬀective relaxation rate, while at high solute concentrations it is the migration at ledges (with Em now approaching E SD > ES ) which explains the observed rate of the GB relaxation.

82

2 Anelastic Relaxation Mechanisms of Internal Friction

Table 2.17. Parameters of grain-boundary maxima in some pure metals (f = 1 Hz) (after Ashmarin 1991) Me

peak

Tm (K)

Tm /Tmelt

H (kJ mol−1 )

Al

A C A B C A B C

480–610 795 473–638 703–820 925–1025 670–783 843–893 953–1075

0.5–0.65 0.85 0.35–0.47 0.52–0.60 0.68–0.76 0.39–0.45 0.49–0.52 0.55–0.62

117–160 294 113–168 189–210 202–263 185–294 217–246 260–328

Cu

Ni

A: low temperature peak; B: medium temperature peak; C: high temperature peak.

In pure metals three GB-induced damping maxima can exist (Ashmarin 1991): (a) a low-temperature peak with Tm ≈ (0.35–0.65)Tmelt (sometimes called “Kˆe peak”), (b) a medium-temperature peak with Tm ≈ (0.5–0.6)Tmelt associated with special grain boundaries but not observed in all metals, and (c) a high-temperature peak with Tm ≈ (0.55–0.85)Tmelt observed in coarsegrained samples. Examples of these peaks are displayed in Table 2.17. In low-concentrated substitutional solid solutions we may distinguish the lowtemperature peak (at the same temperature as in a pure metal) from an additional peak at higher temperature (so-called impurity grain-boundary peak), which might be connected with the aforementioned change in the ratecontrolling mechanism. The role of grain-boundary relaxation may become dominant in materials with extremely ﬁne grains, where the GB regions constitute a substantial part of the total sample volume. These nanocrystalline materials (produced e.g., by extreme plastic deformation), with GB structures mostly far from equilibrium and particular mechanical properties, may require special model descriptions of deformation and anelastic relaxation beyond those mentioned earlier, and will be considered separately in Sect. 2.4.3. 2.4.2 Twin Boundary Relaxation A twin boundary is a very special type of grain boundary, separating two “twin” crystallites that are, with respect to their lattice, mirror images of each other (which is possible only at a well-deﬁned misorientation angle). If the twin boundary is identical with the mirror plane, usually a low-indexed, close-packed crystallographic plane, it is called a coherent twin boundary. Since the twin crystals can be transformed into each other by a shear transformation parallel to the mirror plane, the formation of twins (“twinning”), which may occur under suﬃciently high stress or during recrystallisation (in metals and alloys of low stacking-fault energy), represents an additional deformation mechanism. Also the perpendicular shift of a twin boundary (growth of one twin at the expense of the other) means a shear deformation.

2.4 Interface Relaxation

83

For anelastic relaxation and internal friction peaks to occur by stressinduced movement of twin boundaries, these boundaries must be suﬃciently mobile. As crystallographic coherency exists across the twin interfaces, the relaxation mechanism cannot involve interfacial sliding (Nowick and Berry 1972). However, certain types of twin boundaries can be shifted as the result of movement of partial dislocations (Hirth and Lothe 1968); then, the corresponding dislocation mechanisms will be involved in twin boundary relaxation. Examples for the few existing experiments are those by Siefert and Worrell (1951) on Mn–12at%Cu, De Morton (1969) and Postnikov et al. (1968b, 1969, 1970) on In–Tl alloys. Twinning is most frequently accompanying diﬀusionless phase transformations (e.g., from cubic to tetragonal structure), which themselves involve a shear that can be accommodated by twinning in order to retain the external shape and to avoid high residual stresses in the sample. The high density of twin boundaries often produced in this case may give rise to large eﬀects of anelastic relaxation and internal friction. The relation to martensitic transformations will be treated in Sect. 3.2.1. 2.4.3 Nanocrystalline Metals Subject of this section are polycrystals with ultra-ﬁne grain sizes in the nanometer range. Such nanocrystalline materials form a special group of nanostructured materials (or “nanomaterials”) which also include other types of “nanosized” structures in one, two or three dimensions. Owing to the extremely rapid development of the ﬁeld, a generally accepted terminology of nanomaterials has not yet been fully established. From the viewpoint of materials science, nanostructured materials may be classiﬁed into diﬀerent groups according to the shape (dimensionality) and chemical composition of their constituent structural elements (Gleiter 1995, 2000); however, a less precise, synonymous use of terms like “nanocrystalline”, “nanostructured,” or “nanophase” is also found in the literature. There is also no commonly agreed grain size limit to deﬁne nanocrystalline materials. In the physical concept of highly disordered solids, it is the fraction of atoms situated in the cores of defects (grain boundaries, interfaces) which should be as high as possible. Under this viewpoint the grain size should be below 10 nm (Gleiter 1989, 2000), but also limiting values of 15, 20 or 30 nm have been mentioned. Engineers developing new materials, on the other hand, are sometimes using the preﬁx “nano” for length scales almost up to 1 µm, which generally lacks a physical justiﬁcation. An application-oriented delimitation of “nanocrystalline” grain sizes should rather be linked to speciﬁc properties, which are expected to be diﬀerent from those of conventional materials if dominated by the high density of grain boundaries. In some recent reviews, an upper limit of about 100 nm is introduced (Tjong and Chen 2004, Suryanarayana 2005), which seems to be a reasonable compromise.

84

2 Anelastic Relaxation Mechanisms of Internal Friction

Many diﬀerent methods and techniques have been employed to produce nanocrystalline metallic materials (n-Me), like inert gas condensation, mechanical alloying, severe plastic deformation, devitriﬁcation of amorphous precursors and many others. They all have their speciﬁc advantages or drawbacks concerning the compositions, properties or shapes (e.g., porous or fully dense, bulk or thin ﬁlm) of materials produced; for example, the amorphous route is well established to produce nanocrystalline soft magnetic alloys since the successful development of FINEMET (Yoshizawa et al. 1988). With respect to improved mechanical properties, severe plastic deformation (SPD) is one of the most important and widely used routes, as bulk and fully dense materials with ultra-ﬁne grain (UFG) structure can be obtained in this way (Valiev et al. 2000, Mulyukov and Pshenichnyuk 2003). The surprisingly high temperature stability of such UFG structures has been attributed to a high GB diﬀusivity and low driving force of recrystallisation (Valiev 2002). In many cases it is not clear, however, whether there is a signiﬁcant diﬀerence in GB diﬀusivity between the nanocrystalline and annealed states (Kolobov et al. 2001) or not (W¨ urschum et al. 2002). The small grain sizes of genuine n-Me lead to distinct changes in the mechanical properties including increased yield strength and hardness. A particular feature is the breakdown of the Hall–Petch relation at grain sizes around 20 nm or below. In this range, a decreasing grain size leads to anomalous softening, referred to as inverse Hall–Petch behaviour, which is associated with the operation of diﬀusion-controlled mechanisms combined with GB sliding (e.g., Schiøtz et al. 1998, 1999, Yamakov et al. 2002a,b, Van Swygenhoven 2002, Van Swygenhoven et al. 2003). The cross-over from normal to inverse Hall–Petch behaviour has been treated in a ‘two-phase’ model (Kim et al. 2000, Kim and Estrin 2005), in which the grain boundaries deform by a diﬀusion mechanism, and the grain interiors by a combination of dislocation glide and diﬀusion-controlled mechanisms. Anelastic grain-boundary relaxation (Kˆe 1999) is considered, in a recent theory of non-equilibrium GBs (Chuvildeev 2004), to be hardly detectable in UFG metals below a certain temperature (∼0.35Tmelt ), unless the dislocation density at the GBs is decreased. Alternatively, disclination concepts have also been discussed in connection with relaxation processes in n-Me (Romanov 2002, 2003). The conditions for GB relaxation are even less clear in multicomponent n-Me produced by the amorphous route, where the same factors which favour glass formation may also lead to stabilised and more densely packed GB structures, being less susceptible to relaxation. This latter type of n-Me (for which, to our knowledge, no systematic studies of GB relaxation exist) is not included in the following considerations, but will be mentioned further below in connection with the respective amorphous alloys (Sect. 2.6.1). Experimental studies of anelastic properties of n-Me were undertaken by several research groups using diﬀerent mechanical spectroscopy techniques. The main results of some systematic and therefore reliable studies, including the materials studied and the main eﬀects observed, are summarised brieﬂy in

2.4 Interface Relaxation

85

Table 2.18. In most of these cases, the total temperature-dependent internal friction Q−1 (T ) can be written as −1 Q−1 (T ) = Q−1 b (T ) + ΣQr (T ),

Q−1 b (T )

(2.46)

ΣQ−1 r (T )

where the terms and represent a “background” of internal friction and a superposition of diﬀerent anelastic relaxation peaks, respectively. The ﬁrst term, closely related to composition and microstructure of the respective alloy phases as well as to the dislocation structure, can depend on the annealing time, as well on the amplitude and frequency of the imposed oscillatory strain. This contribution was reported to be substantial enough to consider nanostructured Cu (Mulyukov and Pshenichnyuk 2003) and Mg (reinforced by diﬀerent microparticles, Trojanova et al. 2004) as high-damping materials (see Sect. 3.5) even for low vibration amplitudes. The second term, which may contain contributions not only from GB relaxation but also from almost all relaxation mechanisms related to dislocations or point defects, is time-independent but frequency-dependent and can often be described by the Debye equation. Because of the lack of a combined study of nanostructured metals by diﬀerent mechanical spectroscopy techniques, varying as many experimental parameters (frequency, temperature, amplitude, annealing conditions) as possible, it is not easy to distinguish between “pure” anelastic relaxation mechanisms (most important: GB relaxation) and irreversible mechanisms of structural relaxation, which are in most cases due to changes in the density and distribution of dislocations. Summarising the pertinent results published in the literature (partly presented in Table 2.18), one can draw the following conclusions: – Almost all UFG and nanostructured metals (except those produced from the amorphous state, see above) exhibit an IF peak (very roughly with an activation energy of about 1 eV), which is not often found in well annealed (coarse-grained) metals. – The nature of this peak is still not entirely clear: some authors report a thermally activated, reversible anelastic GB relaxation consistent with the Kˆe approach (Kˆe 1999), while others attribute the eﬀect to irreversible structural changes like recovery and recrystallisation, connected with short-range GB diﬀusion in non-equilibrium GB. – Internal friction can generally be correlated with superplastic properties and thus can be used for determining the optimum temperature for superplastic deformation. – Structural changes in severely deformed metals occur already around ambient temperature, as indicated by a group of low-temperature IF peaks observed after high-pressure torsion in Ti, Mg and several Fe-based alloys, which is extremely sensitive to heating. – In some SPD-processed metals like Cu, a high damping capacity was reported in a broad range of strain amplitude and temperature, however, has not been reproduced all published works (see Sect. 3.5).

86

2 Anelastic Relaxation Mechanisms of Internal Friction Table 2.18. Mechanical spectroscopy studies of UFG metallic materials

materials

∗

mechanical spectroscopy – short summary

references

Pd

1

Weller et al. (1991)

Cu: 99.997% 99.98%

2

Au 99.99%

3

Al, Ni

4

Cu (99.98%) Ni (99.98%)

2

Cu, Fe18Cr9Ni

5

TDIF, 1–5 Hz. Several IF peaks. IF peak H = 62.7 kJ mol−1 (reordering phenomena) TDIF at ∼10 Hz and ∼100 kHz; TD- and ADIF ∼5 MHz. IF peak ∼420 K: reversible dynamic GB rearrangement TDIF, 300–500 Hz: Bordoni peak ∼120 K, dislocation peak ∼460 K, GB peak ∼750 K. TDIF, 1–30 Hz , 0.01–200 Hz, 0.1–10 kHz. Relaxation IF peak 159 kJ mol−1 (Al: 475 K 1 Hz, GB relaxation) TDIF, 1–7 Hz and ∼1 kHz (time-dependent IF). Irreversible changes in the structure TDIF, ∼2.5 Hz, ADIF, ∼35 Hz. High damping; IF peaks at 54 and 475 K

Mg

6

Mg alloys: Mg–6Zn Mg–9Al Fe–25Ni

2

7

Fe–0.8C

5

Fe–25Al

5

Ti grad2

5

∗

TDIF, 0.5, 5, 50 Hz. Relaxation peaks at ∼70 K (116 kJ mol−1 due to dislocations) and at ∼620 K due to GB TDIF, ∼10 Hz. Irreversible IF peak 530–570 K, ∼87 kJ mol−1 enhanced GB diﬀusion TDIF, 0.5–5 Hz. IF peaks due to martensitic transformation TDIF, 1–2 kHz. Irreversible IF peak ∼550 K: recovery TDIF, 0.5–2 kHz. IF peaks (150–300 K) due to dislocations and self-interstitial atoms; unstable with respect to heating. TDIF, ∼2 kHz. IF (Hasiguti) peak ∼210 K: dislocations and self-interstitial atoms; possibly hydrogen-related eﬀect at ∼410 K.

Akhmadeev et al. (1993)

Okuda et al. (1994) Bonetti and Pasquini (1999) Gryaznov et al. (1999) Mulyukov and Pshenichnyuk (2003) Trojanova et al. (2004)

Chuvildeev et al. (2004a) Wang et al. (2004a) Ivanisenko et al. 2004 Golovin et al. (2006a,c)

Golovin et al. (2006a)

Fabrication methods: (1) evaporation, condensation, compaction; (2) equal channel angular pressing (ECAP); (3) gas deposition; (4) mall milling; (5) high-pressure torsion; (6) ball milling, compaction, hot extrusion; (7) consolidation.

2.5 Thermoelastic Relaxation

87

2.5 Thermoelastic Relaxation 2.5.1 Theory Physical Principle In every solid, there exists a fundamental thermoelastic coupling between the thermal and mechanical states (e.g., between stress and temperature ﬁelds), with the thermal expansion coeﬃcient α as the coupling constant. The best known phenomenon of thermoelastic coupling is thermal expansion, as the response of the mechanical state to an applied change in temperature. Conversely, fast adiabatic (i.e., isentropic) changes of the dilatational stress component result in (small) temperature changes, known as the thermoelastic eﬀect. If such stress variations are spatially inhomogeneous – either externally according to the mode of loading (e.g., bending) or internally in a material with heterogeneous mechanical properties – temperature gradients are produced which can then relax by irreversible heat ﬂow (thermoelastic relaxation), causing entropy production and dissipation of mechanical energy. The resulting thermoelastic damping 1 – not to be confused with damping due to “thermoelastic” martensite2 (Sect. 3.2.1) – represents the most fundamental among all mechanical damping mechanisms, since it does not require any defects but exists in all solids with non-zero thermal expansion, even in the most perfect crystals. Assuming that the mean free path of the phonons is small compared to the length scale of the stress inhomogeneities, which is generally the case except for very low temperatures and high frequencies, the heat ﬂow during thermoelastic relaxation can be described as a classical diﬀusion process. Biot (1956) pointed out that it is the entropy which satisﬁes the diﬀusion equation. Zener’s Theory Thermoelastic damping is known since the late 1930s, when Zener was the ﬁrst to give both a detailed theory (Zener 1937, 1938b) and a collection of related experimental results (Zener et al. 1938, Randall et al. 1939). The theory was developed in scalar (one-dimensional) form mainly for the transversal vibration of homogeneous reeds and wires, but some other cases like spherical cavities or polycrystals with randomly oriented crystallites were also considered 1

2

As a fundamental thermodynamic phenomenon, thermoelastic damping is sometimes also referred to as “thermodynamic damping” (e.g., Panteliou and Dimarogonas 1997, 2000). Other authors have called it “elastothermodynamic” (Bishop and Kinra 1995, 1997; Kinra and Bishop 1996) because the cause is “elastic” and the eﬀect is both “thermal” and “dynamic” (i.e., time-dependent). A martensitic transformation is called “thermoelastic” if its thermal hysteresis and transformation energy is relatively small, comparable in magnitude with usual elastic strain energies. This alternative use of the term “thermoelastic” has nothing to do with thermoelastic coupling considered here.

88

2 Anelastic Relaxation Mechanisms of Internal Friction

by Zener. The simplest and best described case is certainly that of alternating transverse thermal currents (Nowick and Berry 1972) between the compressed and dilated sides of a homogeneous and isotropic, rectangular beam, vibrating in ﬂexure with the frequency f . The thermoelastic damping of such a beam is in good approximation given by Q−1 (f, T ) = ∆T

f · f0 f 2 + f02

(2.47)

with the relaxation strength ∆T = α2 EU T /ρCp

(2.48)

f0 = πλ/2h2 ρCp ,

(2.49)

and the peak frequency where α is the linear thermal expansion coeﬃcient, EU the unrelaxed Young’s modulus, ρ the density, Cp the speciﬁc heat capacity at constant pressure (or stress)3 , λ the thermal conductivity and h the thickness of the beam (i.e., the distance over which heat ﬂow occurs). Equation (2.47) has the same functional form as (1.8) and represents a Debye peak as a function of frequency, with a single relaxation time τT = 1/2πf0 = h2 /π 2 Dth

(2.50)

where Dth = λ/ρCp is also called the thermal diﬀusivity. The analogy between (2.50) for the thermoelastic and (2.17) for the Gorsky relaxation, respectively, reﬂects the more general analogy between “thermal” and “atomic” diﬀusion already pointed out by Zener (1948). In the same way, the intercrystalline Gorsky eﬀect introduced in (2.18) and (2.19) is analogous to the case of intercrystalline thermal currents (Zener 1948, Nowick and Berry 1972) with ∆IT = R(3α)2 KU T /ρCp τIT = d2 /3π 2 Dth ,

(2.51) (2.52)

where R is an elastic anisotropy factor (see Zener 1938b for an estimate for cubic metals with randomly oriented crystallites), 3α denotes the volumetric expansion coeﬃcient, KU the unrelaxed bulk modulus and d the dominating grain size in the polycrystal. Despite this analogy between atomic and thermal diﬀusion, it should be noted that the Arrhenius relation of thermal activation, (1.9), only holds for 3

Here we understand Cp per unit mass as found in most data collections; if considered per unit volume as in Zener’s original equations, the density ρ does not appear in these equations. Instead of Cp , the symbol Cσ (for constant stress) has also been used in the literature. If, on the other hand, Cp or Cσ is replaced by Cν or Cε (at constant volume or strain), a small error in ∆T (of the order of ∆T 2 ) is introduced (Lifshitz and Roukes 2000).

2.5 Thermoelastic Relaxation

89

the former but not for the latter having a comparatively weak temperature dependence. Thus, unlike the Gorsky relaxation, the thermoelastic Debye peak is found only as a function of frequency but not of temperature. Instead, both ∆T /T in (2.48) and f0 in (2.49) are only weakly temperature-dependent (at least above the Debye temperature), so that thermoelastic damping is nearly proportional to the temperature. Another possibility of thermoelastic damping is related to longitudinal thermal currents between the “hills” and “valleys” of longitudinal elastic waves. In this case, treated in some detail by L¨ ucke (1956), the relaxation time is itself frequency-dependent as ω −2 because the thermal diﬀusion distance is given by half the wavelength, which means that in contrast to the normal case adiabatic conditions are expected here in the low-frequency (!) limit. With expected peak frequencies in the GHz range or even higher, longitudinal thermoelastic damping is usually negligibly small (Nowick and Berry 1972). Advanced Theories More extended and fundamental, three-dimensional and mathematically more rigorous treatments can be found in many later theoretical papers (e.g., Biot 1956, Alblas 1961, 1981, Chadwick 1962a,b, Lord and Shulman 1967b, Kinra and Milligan 1994, Lifshitz and Roukes 2000, Norris and Photiadis 2005). However, although the general thermoelastic equations and also some speciﬁc solutions (most often for the transversely vibrating Euler–Bernoulli beam) are now well known, it is up to the present date still diﬃcult to calculate the thermoelastic damping explicitly for more complex cases beyond those already treated by Zener. An exact solution for the thin Euler–Bernoulli beam was given by Lifshitz and Roukes (2000), who also showed that Zener’s approximation is valid within 2% in most of the relevant frequency range, except for the highfrequency side of the peak far above f0 where the deviations grow up to a 20% underestimation in the limit f → ∞. Therefore, the still widely spread use of Zener’s (2.47)–(2.49) is suﬃciently accurate for many practical purposes, at least in the classical case of transverse thermal currents during ﬂexural vibration of homogeneous samples. The analysis of Kinra and Milligan (1994) formed the basis for further model calculations of thermoelastic damping also in heterogeneous structures like ﬁbre- or particle-reinforced composites (Milligan and Kinra 1995, Bishop and Kinra 1995), hollow spherical inclusions (Kinra and Bishop 1997), laminated composite beams (Bishop and Kinra 1993, 1997; Srikar 2005b) or some speciﬁc cases of pores and cracks (Kinra and Bishop 1996, Panteliou and Dimarogonas 1997, 2000; Panteliou et al. 2001). In the special case of ﬂexural resonators made of polycrystals (e.g., of silicon) with particularly low thermal conductivity across the grain boundaries compared to that in the crystals,

90

2 Anelastic Relaxation Mechanisms of Internal Friction

a preliminary fast equilibration of the transverse thermal currents is possible inside the grains, which has been called intracrystalline thermoelastic damping (Srikar and Senturia 2002). Another branch of theories is devoted to resonators with more complex external shape, usually in form of planar structures made of thin, ﬂat plates vibrating predominantly either in ﬂexure or in torsion. Although the thermoelastic loss should be zero in case of pure shear, it is important to note that even the nominally torsional vibration modes almost always contain some ﬂexural component which can produce signiﬁcant thermoelastic damping. To solve this problem, a ﬂexural “modal participation factor” (MPF) has been deﬁned as the fraction of potential elastic energy stored in ﬂexure (Photiadis et al. 2002, Houston et al. 2002, 2004). Assuming classical transverse thermal currents for this ﬂexural component, the thermoelastic damping of any particular vibration mode is then obtained by multiplying the MPF with the classical result for the ﬂexural beam e.g., from Zener’s theory. The MPF itself can be calculated by integrating the curvature tensor of the vibration mode over the volume of the sample, provided the displacement ﬁeld of the mode is known (Norris and Photiadis 2005). The problem then mainly consists of determining the mode shape, e.g., with the help of ﬁnite element modelling and/or advanced experimental techniques like laser-Doppler vibrometry (Liu et al. 2001). 2.5.2 Properties and Applications of Thermoelastic Damping To judge the practical importance of thermoelastic damping in a given material, we have to consider primarily the magnitude of the transverse relaxation strength ∆T and the related peak frequency f0 according to (2.48) and (2.49). A detailed compilation of room-temperature relaxation strengths, including results of four data collections from the literature as well as re-calculated data using (2.48), is given in Table 2.19 for many pure metals and also a limited number of non-metallic materials. It is typical that in Table 2.19 the ∆T values taken from diﬀerent sources never match exactly. This scatter may come from unspeciﬁed microstructural inﬂuences (defects, textures) causing some variation mainly in the possibly anisotropic quantities α and E, among which deviations in α have a particularly strong eﬀect due to the quadratic dependence in (2.48). For our own re-calculations of ∆T , the underlying basic data were checked for reliability by comparing diﬀerent sources wherever possible. Ideally, the data in Table 2.19 refer to random polycrystals at least in case of metals. Exceptions are Si and Ge where single crystal values are given, according to the [100]-oriented wafers from which most of the respective resonators are fabricated. The second practically important quantity is the peak frequency f0 or, vice versa, the sample thickness h(f0 ) which belongs to a pre-selected peak frequency according to (2.49). With thermal diﬀusivities Dth usually in the

70

23.1

Al

78

287 32 50 209 130 211 100 (Srikar 2005b) 11 528 45 329

14.2

11.3 13.4 30.8 13.0 16.5

11.8

6.0 32.1 6.4 25 (Weast 1973)

4.8

Au

Be Bi Cd Co Cu

Fe

Ge In Ir Mg

Mo

Al2 O3

83

E (GPa)

18.9

α (10−6 K−1 )

Ag

material

251

10280

449

7874 321 233 131 1025

1820 122 231 421 384

1850 9780 8650 8900 8920

5323 7310 22650 1738

129

19300

904

2700

0.88

0.63 2.0 2.2 4.7

2.5

3.3 1.44 7.1 2.8 3.1

1.9

4.7

0.86

0.45 3.1 2.35 4.8–5.4

2.2–2.6

4.6 1.4 10 3.4 3.0–3.7

1.7–2.2

2.7–3.7

4.6–5.1

2.4–3.5

235

10490 3.6

∆T Lit × 103

∆T calc Cp ρ −3 −1 −1 (kg m ) (J kg K ) × 103

Zener (1948), Riehemann (1996), Srikar (2005b) Zener (1948), Kinra and Milligan (1994), Riehemann (1996), Srikar (2005b) Kinra and Milligan (1994), Srikar (2005b) Zener (1948), Kinra and Milligan (1994), Riehemann (1996), Srikar (2005b) Zener (1948) Zener (1948) Zener (1948) Riehemann (1996) Zener (1948), Riehemann (1996), Srikar 2005b Zener (1948), Riehemann (1996), Srikar 2005b Srikar 2005b Riehemann (1996) Riehemann (1996) Zener (1948), Kinra and Milligan (1994), Riehemann (1996) Riehemann (1996)

reference for ∆T Lit

Table 2.19. Thermoelastic relaxation strengths ∆T of pure metals and some other selected materials at 300 K: ∆T calc calculated from the intrinsic properties α, E, ρ and Cp , and ∆T Lit taken directly from the literature

2.5 Thermoelastic Relaxation 91

388 278

7140 6510

108 68

5.7

Zr

0.37

10.7

0.98

4.4 0.95 1.1

2.8 1.72 1.39 1.8 1.44 0.2

0.74 2.7

0.68

5.8–18(!)

1.4 0.8–1.3

0.22 0.003 4.0–4.8 0.3 0.8–1.2

2.5–2.8 2.0–2.5 1.5 0.7 1.5–1.8 0.19 0.35–0.6

0.71 2.6–2.9

∆T Lit × 103

Riehemann (1996) Zener (1948), Riehemann (1996), Srikar (2005b) Zener (1948), Riehemann (1996) Zener (1948), Riehemann (1996) Zener (1948) Zener (1948) Zener (1948), Riehemann (1996) Srikar (2005b) Kinra and Milligan (1994), Srikar (2005b) Srikar (2005b) Srikar (2005b) Zener (1948), Riehemann (1996) Zener (1948) Kinra and Milligan (1994), Riehemann (1996),Srikar (2005b) Kinra and Milligan (1994) Zener (1948), Riehemann (1996), Srikar (2005b) Zener (1948), Riehemann (1996), Srikar (2005b) Riehemann (1996)

reference for ∆T Lit

References: unless noted otherwise, the intrinsic properties α, E, ρ and Cp were taken from WebElements [http://www. webelements.com/].

132

30.2

19 250

Zn

411

227 140 522

127 244 133 243 207 712

4.5

7310 16 650 4507

11 340 12 023 21 090 12 450 6697 2330

265 445

TiC W

50 186 116

16 121 168 275 55 160 (Srikar 2005b)

8570 8908

105 200

∆T calc Cp −1 −1 (J kg K ) × 103

22.0 6.3 8.6

28.9 11.8 8.8 8.2 11.0 2.6

Pb Pd Pt Rh Sb Si SiC

ρ (kg m−3 )

E (GPa)

Si3 N4 SiO2 Sn Ta Ti

7.3 13.4

α (10−6 K−1 )

Nb Ni

material

Table 2.19. Continued

92 2 Anelastic Relaxation Mechanisms of Internal Friction

2.5 Thermoelastic Relaxation

93

range of 10−6 to 10−4 m2 s−1 , samples have to be prepared mostly with thicknesses between 0.05 and 0.5 mm in order to have maximum thermoelastic damping at 1 kHz. Metallic Materials In Table 2.19 the strongest eﬀect is predicted for Zn with a relaxation strength as high as 0.01 (according to ∆T calc ) and a maximum thermoelastic damping Qm −1 = ∆T /2 ≈ 0.005, followed by Cd, Al, Mg, Sn; but also for Ag, Be, Co, Fe, Ni and Pb the thermoelastic loss factor at room temperature can exceed 10−3 . Although such values are easily observable and practically signiﬁcant, the interest in thermoelastic damping of metals has as yet been rather limited from both the fundamental and applied sides, and systematic experimental studies are very scarce. On the fundamental side, mechanical spectroscopy is usually concerned with thermally activated relaxation peaks, measured as a function of temperature to study defects and transformations in solids. Thermoelastic damping is then noticed mainly as a linear background to be subtracted, but very rarely studied for its own sake. This has also experimental reasons: to trace out the full peak after (2.47), ﬂexural frequency and sample thickness have to be mutually adjusted and varied accordingly, e.g., over at least two orders of magnitude in frequency, which requires more eﬀort than just varying the temperature on a single sample. In addition, to observe the pure thermoelastic losses, other kinds of damping have to be suppressed eﬀectively e.g., by suitable alloying. Only in the early days – before many other mechanisms were known – thermoelastic damping in metals was a subject of intense study as a main source of energy dissipation. The probably still most careful measurements of the thermoelastic relaxation peak come from that time, like the study of Bennewitz and R¨otger (1938) on German silver, and in particular that of Berry (1955) on α-brass which gave an impressively exact conﬁrmation of Zener’s theory of transverse thermal currents without any adjustable parameters (see also Nowick and Berry 1972). Based on this fundamental work, the height and position of the thermoelastic peak were occasionally used later to determine coeﬃcients of thermal expansion and conductivity, respectively, e.g., for some metallic glasses (Berry 1978, Sinning et al. 1988) or commercial Al and Mg alloys (G¨ oken and Riehemann 2002). As an example, Fig. 2.33 shows the annealing-induced shift of the thermoelastic Debye peak, according to an increase in thermal conductivity from 7 over 11 to 17 W mK−1 , due to structural relaxation and subsequent crystallisation of an amorphous Ni alloy (Sinning et al. 1988). In this case, the measurement temperature had been lowered to 170 K to reduce the amount of other damping contributions, partly still visible in Fig. 2.33 on the low-frequency side of the peak for the as-quenched state; therefore, the thermoelastic peaks in Fig. 2.33 are almost a factor of two smaller than they would be at room temperature.

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Fig. 2.33. Frequency-dependent internal friction of a rapidly quenched, meltspun Ni78 Si8 B14 ribbon (thickness h = 0.05 mm) at T = 170 K after diﬀerent annealing treatments (the solid lines are ﬁts to (2.47)): (a) as-quenched amorphous state, f0 = 1200 Hz; (b) after 2 h at 618 K (structurally relaxed amorphous state), f0 = 1730 Hz; (c) crystallised, f0 = 2750 Hz (Sinning et al. 1988)

Also worth mentioning in this context is the early work of Randall et al. (1939) on α-brass with systematically varied grain sizes, which seems still to represent the only known example of a reliable observation of intercrystalline thermal currents. On the side of application, the main problem is that damping due to transverse thermal currents is available only in a relatively narrow frequency range around f0 , depending on the geometry of the respective structural component. On the other hand, it might be possible in certain cases to adjust the geometrical dimensions or the thermal conductivity (by alloying) according to the technical requirements of damping properties. Much more interesting from the applied viewpoint are those thermoelastic damping contributions that occur in heterogeneous metallic materials like composites or porous metals. Three types of eﬀects may be expected from such heterogeneities: 1. The introduction of new internal length scales, in addition to the sample dimensions, will distribute the dissipation processes over a much wider frequency range. This eﬀect has been discussed qualitatively for metallic foams (Golovin and Sinning 2003b, 2004). 2. Thermoelastic damping will no longer be conﬁned to ﬂexural vibrations but will occur also in other deformation modes. 3. Additional heterogeneities cause additional temperature gradients and thus additional dissipation processes, i.e., more damping will be produced. This is the most promising but also least understood aspect: in fact, model calculations for speciﬁc arrays of pores (Panteliou and Dimarogonas 1997, 2000) have predicted a strong increase of thermoelastic damping with porosity, up to much higher values than in the case of classical transverse thermal currents; but the consequences for real materials are not yet clear. There is a strong need for theoretical as well as experimental

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research in this ﬁeld, which then might open new perspectives towards the development of heterogeneous metallic materials with tailored properties of thermoelastic damping. Applications in Microsystems The recently renewed interest in thermoelastic damping is, in its main part, not related to the aforementioned perspectives of metallic materials but has a completely diﬀerent reason: the rapid development of micro- and nanoelectromechanical systems (MEMS and NEMS) which include silicon-based micromechanical resonators as central elements. Irrespective of the speciﬁc application (e.g., force sensors, accelerometers, bolometers, magnetometers, high-frequency mechanical ﬁlters or ultrafast actuators), the performance of the micromechanical system (e.g., sensor sensitivity) critically depends on the quality factor Q of the resonator which should be as high (i.e., the damping Q−1 as low) as possible. That is, contrary to the metallic case discussed earlier, the aim is here not to produce damping but to avoid it. If in the most perfect silicon resonators all defect-induced sources of dissipation are removed, the thermoelastic damping remains and can be inﬂuenced only by a proper geometrical design and fabrication of the resonator. Especially with more complex-shaped resonators like single- or double-paddle oscillators (Kleiman et al. 1985, Liu et al. 2001, Houston et al. 2004) attempting quality factors as high as 108 , or in case of layered structures including metallic or ceramic coatings (Srikar 2005b), this is not a trivial task. Since most of the recent theoretical progress on thermoelastic damping since about 2000 (see above) was without doubt strongly motivated by the needs of MEMS and NEMS, we have brieﬂy sketched these important new developments here – although their basic material, silicon, is as a semiconductor not included in the main data collections of this book. Finally, it should be mentioned as well that thermoelastic damping is also an important factor limiting the ultimate sensitivity of interferometric gravitational wave detectors (Black et al. 2004).

2.6 Relaxation in Non-Crystalline and Complex Structures With the important exception of the universal thermoelastic damping treated in the preceding section, most mechanisms of anelastic relaxation comprise the motion of defects interacting with an applied stress. According to the classical understanding of defects as structural imperfections in (periodic) crystals, such relaxation mechanisms are traditionally deﬁned for crystalline solids (Nowick and Berry 1972). This classical line was also followed in the Sects. 2.2–2.4 on point defects, dislocations and interfaces, where the respective microscopic processes of relaxation were introduced for the crystalline

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case. An extension of such defect-related mechanisms to non-crystalline structures is not obvious, except for some special cases like interstitial diﬀusion jumps of hydrogen atoms (if not coupled with the motion of matrix defects, see Sect. 2.2.4). In this context, the term “non-crystalline” is traditionally understood as opposed to periodic crystals, which then includes both amorphous solids and quasicrystals. To some extent this is still common practice (and practically useful), although it deviates from crystallographically correct terminology. In proper crystallographic terms, quasicrystals are in fact crystals in the wider sense of quasiperiodic crystals, which include both periodic and aperiodic, long-range ordered structures (Lifshitz 2003). From the viewpoint of anelastic relaxation of metals, on the other hand, quasicrystals and amorphous structures have many things in common, at least in case of icosahedral short-range order (cf. Sect. 2.2.4). There is a borderline, however, between common periodic crystals (in most practical cases with relatively simple crystal structures) on the one side, and other metallic structure types – amorphous alloys, quasicrystals and to some extent even structurally complex periodic crystals with giant unit cells (Urban and Feuerbacher 2004) – on the other side: in the former case, most defect-related mechanisms are quantitatively well understood and classiﬁed within the systematic and wellfounded concepts of “anelastic relaxation in crystalline solids” (Nowick and Berry 1972; at that time “crystals” were always understood as periodic crystals), whereas in the latter case many details of the theoretical concepts have still to be developed. In principle we may distinguish roughly, in relation to the classical relaxation processes in crystalline solids, between three types of relaxation mechanisms in “non-crystalline” structures (in the above “traditional” meaning including quasicrystals): (a) Mechanisms which are independent of the structure type and exist in the same way in crystalline as well as in non-crystalline structures, with only numerical diﬀerences. Examples are thermoelastic damping and the Gorsky eﬀect (at least in the basic form of transverse thermal or atomic diﬀusion currents), where relaxation strength and time may vary according to the values of the respective parameters, but all essential characteristics of the relaxation remain unchanged. (b) Mechanisms which are modiﬁed by the structure type, i.e., which are based on the same principle but with some conceptual diﬀerences calling for a modiﬁed or extended theoretical treatment. Examples are the Snoek-type relaxation in the generalised form as introduced for hydrogen in Sect. 2.2.4, or a hypothetical dislocation relaxation in an amorphous structure which can only be treated using a more general dislocation concept (independent of a crystal lattice). (c) Mechanisms which are speciﬁcally found in “non-crystalline” but not in (simple) crystalline structures. Examples are cooperative processes of

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directional structural relaxation or viscous ﬂow (e.g., near the glass transition) in metallic glasses, or some types of relaxation related to phasons in quasicrystals. While there is no reason to mention again type (a), we will focus in the following on mechanisms of types (b) and in particular (c) which can not always be diﬀerentiated clearly from each other. The aim is to give an introduction into those aspects of anelastic/viscoelastic relaxation in amorphous (Sect. 2.6.1) and quasicrystalline (Sect. 2.6.2) structures that have not yet been considered in the previous parts of this chapter. 2.6.1 Amorphous Alloys The most important aspect to be considered in amorphous alloys, also called metallic glasses, is the relation between structural and mechanical relaxation which are closely connected. To discuss this relation, it is ﬁrst necessary to know the a-priori diﬀerent deﬁnitions and characteristics of both kinds of relaxation. Since mechanical (anelastic or viscoelastic) relaxation has already been introduced in Chap. 1, a brief introduction into structural relaxation will be given here. Structural Relaxation In the literal sense, any time-dependent equilibration of the atomic structure of condensed matter, after any kind of external perturbation, may be called “structural relaxation” (SR). This may in principle include production, annihilation and rearrangement of defects in crystals (like equilibration of thermal vacancies after changes in temperature, or recovery and recrystallisation after plastic deformation or irradiation), and even certain cases of phase transformations. However, it is more common to use the name “structural relaxation” more speciﬁcally for continuous changes of amorphous structures – in particular in glass-forming systems – which are not so easily expressed in terms of defect concentrations but rather appear as integral modiﬁcations of the whole structure. For instance, temperature changes generally give rise to SR due to the temperature dependence of amorphous structures in (stable or metastable) equilibrium. The Glass Physics Approach Understanding SR in glass-forming systems is the key to understand “glass” per se, i.e., the formation and nature of glasses and the glass transition below which SR is largely frozen. According to many renowned experts, this is still the most challenging unsolved problem in condensed matter physics. The difﬁcult task of summarising the state of knowledge in this complex ﬁeld was

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tackled by Angell et al. (2000), by posing detailed key questions and reviewing “the best answers available” as given by experts and specialists in about 500 references. The subject was divided into four parts, i.e., three temperature domains A–C with respect to the glass transition temperature Tg , and a fourth part D dealing with “short time dynamics” which can be skipped here. The main emphasis in the review by Angell et al. (2000) is put on the hightemperature domain A of the (supercooled) viscous liquid at T > Tg where the system is ergodic (i.e., its properties have no history dependence). Important items to be understood are the temperature dependences of transport properties and relaxation times, e.g., in form of the Vogel–Fulcher–Tammann (VFT) equation and deviations from it, as well as non-exponential relaxation functions of the form exp[−(t/τ )β ] with 0 < β < 1 (Kohlrausch–Williams– Watts (KWW) or stretched exponential function, which was given a physical meaning e.g., by Ngai’s coupling model of cooperative many-body molecular dynamics (Ngai et al. 1991, Ngai 2000)). The VFT equation, e.g., for the viscosity η, can be written as η = η0 exp[D∗ T0 /(T − T0 )],

(2.53)

with the so-called fragility parameter D∗ and VFT temperature T0 , which are coupled with respect to the glass transition according to Tg /T0 = 1 + D∗ / ln(ηg /η0 ) ≈ 1 + D∗ /39,

(2.54)

where ηg and η0 represent the viscosities at T = Tg and T → ∞, respectively (Angell 1995). The fragility parameter D∗ is used to distinguish between “strong” liquids or glasses with large D∗ and almost Arrhenius-like behaviour (which would be exact for D∗ = ∞ implying T0 = 0), and “fragile” ones with small D∗ , a pronounced curvature in a Tg -scaled Arrhenius plot, and a very rapid breakdown of shear resistance on heating directly above Tg . A similar temperature dependence is also found for the relaxation time τ , which in this range A is so short that the structure can generally be considered to be in a “relaxed” state of internal equilibrium. The low-temperature domain C of the “truly glassy” state (T Tg ), on the opposite side, can be deﬁned as the range where the cooperative SR of the viscous liquid (also called “main”, “primary” or “α” relaxation) is completely frozen. Here the properties change essentially reversibly with temperature (as they do in range A) but now depend strongly on history, i.e., on the initial time-temperature path on which the system was frozen. Relaxation in this glassy range is possible only by decoupled, localised motion of easily mobile species (also called “secondary” relaxations4 ). 4

These secondary relaxations are sometimes classiﬁed further as β, γ, δ, . . . relaxations, which is more appropriate for polymers where the stepwise freezing of various local degrees of freedom may be associated with speciﬁc molecular groups, than for anorganic or metallic systems.

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In the intermediate temperature domain B near and not too far below the glass transition (T Tg ), primary SR must be considered explicitly as it occurs continuously on all experimental time scales, but without reaching equilibrium except for long annealing times. This is the most diﬃcult range in which structure and properties depend on both history and actual time during the measurement. A ﬁrst approach relies on the “principle of thermorheological and structural simplicity” (Angell et al. 2000) which relates the molecular or atomic mobility to the structural departure from equilibrium, as described by a single parameter like the so-called ﬁctive temperature Tf . As depicted in Fig. 2.34, the ﬁctive temperature can be found by projecting the actual value of a certain property p (like volume, enthalpy, entropy, etc.) on the equilibrium curve for the liquid extrapolated from range A, using the slope ∂p/∂T from the frozen range C. Structural relaxation in range B can then be described as a relaxation of Tf , in the simplest case according to T˙f = (T − Tf )/τ

(2.55)

with limiting conditions Tf = T in range A and Tf = const. in range C, respectively. The relaxation time τ now depends on both T and Tf , as expressed ﬁrst by Tool (1946) τ (T, Tf ) = τ0 exp[xA/kT + (1 − x)A/kTf )],

(2.56)

where x is a dimensionless “non-linearity parameter” (0 < x < 1, typically x ≈ 0.5), and A is an activation energy (J¨ackle 1986, Angell et al. 2000).

Fig. 2.34. Deﬁnition of the ﬁctive temperature Tf in diﬀerent relaxing or frozen glassy states: (1) during and (2) after rapid cooling, (3) during slow cooling, (4) during heating after slow cooling. Indicated are also the temperature ranges A–C (Angell et al. 2000; see text). For frozen states like in case (2), Tf may be considered identical with Tg for a given heating or cooling rate

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2 Anelastic Relaxation Mechanisms of Internal Friction

In this simple form the ﬁctive temperature concept has been useful for modelling relaxation in the diﬃcult temperature range B; however, some ambiguity remains as regards which property p is chosen, and also the non-exponentiality (KWW function), found here as well, is not accounted for. The latter point is addressed by more advanced concepts like that of “hierarchically constrained dynamics”, considering elementary atomic relaxation events to occur not in parallel but in series (Palmer et al. 1984). The link in relaxation dynamics between ranges A and B is also underlined by correlations between the parameters β, D∗ , A and x (Angell et al. 2000). Up to this point, the synopsis of SR under the viewpoint of glass physics applies to all kinds of glasses (polymers, metals, oxides), necessarily neglecting more speciﬁc aspects in these diﬀerent classes of materials. In particular, for certain characteristics of SR in metallic glasses, some diﬀerent viewpoints exist independently in the traditions of solid-state physics and materials science rather than of glass physics. SR in Metallic Glasses An obvious diﬀerence, as compared to non-metallic glasses, is that in metallic glasses SR has long been noticed mainly as a strong irreversible (irrecoverable) eﬀect deep in the solid range (T Tg ) existing even at room temperature, rather than as a phenomenon originating in the reversible properties of the undercooled melt above Tg as introduced earlier. This is a consequence of the high cooling rates used during production, especially in case of rapidly quenched “conventional” metallic glasses being in a highly unstable state far from equilibrium (high Tf ). The undercooled melt, on the other side, is more diﬃcult to study and has been totally inaccessible before the development of “bulk” metallic glasses which, although ﬁrst prepared by Chen (1974), became popular not before the 1990s (see Wang et al. 2004b for a review). On this historical background, some conceptually restricted usage of the term “structural relaxation” has partly developed for metallic glasses, regarding SR as being absent in the state of metastable equilibrium above Tg (e.g., Fursova and Khonik 2000) as observed macroscopically. This would however unnecessarily exclude from the term those fast dynamic processes in the viscous liquid which are needed to maintain equilibrium (e.g., during temperature changes), and which in glass physics just form the core of SR, being only slowed down below Tg . To avoid this obvious inconsistency, in this chapter we use “structural relaxation” in its general physical meaning and only speak of diﬀerent “types” or “components” of SR if necessary. It was shown long ago that the irreversible type of SR in metallic glasses, e.g., during annealing of a rapidly quenched Pd–Si glass, can increase viscosity by ﬁve orders of magnitude (Taub and Spaepen 1979, 1980), indicating enhanced atomic mobility in the initial unrelaxed state. In other words: this irreversible SR, aﬀecting virtually all physical and mechanical properties p

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(Cahn 1983), cannot be a “secondary” relaxation in the frozen temperature range C but should be considered as a primary one in range B, kinetically extended to lower temperatures. At this point it seems surprising that at temperatures so far below Tg , there is also a reversible (recoverable) component of SR being even faster than the irreversible one, as observed e.g., for Young’s modulus (Kurˇsumovi´c et al. 1980, Scott and Kurˇsumovi´c 1982) or enthalpy (Scott 1981, Sommer et al. 1985, G¨ orlitz and Ruppersberg 1985), but hardly for density or volume (Cahn et al. 1984, Sinning et al. 1985). This (selective) low-temperature reversible SR component, to be distinguished from reversible behaviour at the glass transition, is diﬃcult to understand in terms of ﬁctive temperature or primary/secondary relaxations, but at least roughly consistent with an earlier hypothesis by Egami (1978) relating reversible and irreversible SR, respectively, to changes in chemical and topological (or geometrical, Egami 1983) short-range order. The (also non-exponential) kinetics of such “solid-state” SR phenomena in metallic glasses, extensively studied in both “conventional” and “bulk” metallic glasses during the past three decades, have been widely analysed in terms of an activation energy spectrum (AES) model, introduced by Gibbs et al. (1983) on the basis of earlier work by Primak (1955), and subjected to some later extensions and modiﬁcations. This model is based on a wide non-equilibrium distribution of Debye-type relaxation events, which during annealing is gradually cut down from the low-energy side. While mathematically equivalent to the use of a KWW function, the physics behind this model seems to be more consistent with the idea of independent “relaxation centres” (see later), instead of the picture of true cooperative motion associated with a KWW function. For a microscopic understanding of SR in metallic glasses, the oldest and maybe still most widely spread concept is that of free volume, which was introduced by Cohen and Turnbull (1959) and worked out later by van den Beukel and coworkers, incorporating also Egami’s distinction between topological and chemical short-range order (e.g., van den Beukel 1993 and references therein). Alternative concepts were added more recently, for example based on interstitialcy theory (describing an amorphous solid as a crystal containing a few per cent of self-interstitials; e.g., Granato 1992, 1994, 2002; Granato and Khonik 2004), or on the theory of local topological ﬂuctuations (of atomic bonds and atomic-level stresses; Egami 2006). As SR is closely related to diﬀusion, much can be learned from the recent progress in understanding diﬀusion mechanisms in metallic glasses (Faupel et al. 2003), which generally revealed highly collective atomic processes (contrary to crystalline metals): according to molecular dynamics simulation supported by critical experiments, atomic migration mainly occurs in thermally activated displacement chains or rings. Being rather local at low temperature, these chains grow in size and concentration with increasing temperature until they ﬁnally merge into ﬂow.

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Relation Between Structural and Mechanical Relaxation Any structural relaxation – whatever the exact microscopic mechanism is – must involve atomic movements directed to lower the Gibbs free energy under the acting external perturbation, generally including anisotropic atomiclevel distortions oriented in diﬀerent directions (like the above displacement chains). If the external perturbation is isotropic, e.g., in case of a purely thermal deviation from equilibrium, such local anisotropies may be averaged out so that only a macroscopically isotropic volume change is observed. In the presence of a mechanical stress, however, the distribution of the local events may become asymmetric producing a net distortion in the direction of energetically favoured orientations, i.e., a mechanical relaxation due to a directional structural relaxation (DSR). In this generality, and using the widest meaning of SR which in principle applies to crystalline structures as well (see above), every mechanical relaxation mechanism based on the motion of defects, including all cases considered in Sect. 2.2–2.4, might be called a DSR: under this viewpoint, DSR forms a very general principle of mechanical relaxation which of course also applies to amorphous structures. Thus, the connection between structural and mechanical relaxation is generally a rather close and direct one. More speciﬁcally, the diﬀerent types and temperature ranges of SR in glassforming systems must be considered. In the range of the primary α relaxation around the glass transition, the same cooperative atomic motions cause both viscous ﬂow and SR (i.e., “SR occurs by viscous ﬂow”), so that relaxation time and viscosity can directly be converted into each other (for which, in spite of non-exponential relaxation, often a simple Maxwell model with τε = η/EU is used, cf. Chap. 1). Therefore, in the range where a mechanical (e.g., internal friction) measurement is dominated by viscous ﬂow, the result directly reﬂects the structural α relaxation. There is a superabundant number of (mechanical and other) studies of the α relaxation over wide frequency and temperature ranges in more stable non-metallic glass formers, whereas in metallic systems the α relaxation is accessible only under favourable conditions using the best bulk metallic glass formers and low frequencies (see later). The situation is less clear in metallic glasses at temperatures further below Tg down to about 400 K where the above-mentioned, speciﬁc types of irreversible and reversible SR are found, mechanical relaxation is at least partly anelastic (recoverable) in nature (Berry 1978), but plastic deformation still occurs mainly by homogeneous ﬂow. By assuming spatially separated structural “relaxation centres” represented by two-well systems, Kosilov, Khonik and coworkers developed a speciﬁc DSR model which applies in this range not only to mechanical relaxation but to mechanical properties in general (e.g., Kosilov and Khonik 1993; Khonik 2000, 2003 and references therein). The relaxation centres (two-well systems) were divided into irreversible (highly asymmetric) and reversible (rather symmetric) ones, the former being responsible for mainly viscoplastic low-frequency internal

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friction, plastic ﬂow and even for reversible strain recovery (Csach et al. 2001), whereas the latter cause anelastic processes seen at higher frequencies (Khonik 1996, Eggers et al. 2006). At still lower temperatures where plastic deformation of metallic glasses is known to change to a highly localised shear band mode, the primary SR is eventually frozen (range C in Fig. 2.34, in many cases below about 400 K). If speaking of “DSR” in this range at all, this can only mean “secondary” relaxations of special, easily mobile species, like those of interstitially dissolved hydrogen which have already been treated in Sect. 2.2.4. However, since such anelastic processes in metallic glasses – classiﬁed as “type (b)” in the introduction to non-crystalline structures at the beginning of this section – have more in common with crystalline structures than primary DSR, a true solidstate picture with a clear distinction of the relaxing defect might be more appropriate in this low-temperature range than the more general viewpoint of DSR. Internal Friction Phenomena in Metallic Glasses General Aspects Amorphous alloys have to be produced with the help of some non-equilibrium procedure (like rapid cooling from the melt, mechanical alloying, various kinds of deposition, etc.), during which the formation of the thermodynamically stable crystalline state is kinetically hindered. Therefore, all amorphous alloys crystallise when heated into a temperature range with suﬃcient atomic mobility, which is always connected with a maximum of internal friction at a temperature close to the onset of crystallisation (Fig. 2.35). In fact this “crystallisation peak”, with a position usually depending on heating rate but not on frequency (e.g., Zhang et al. 2002), is not a true relaxation peak but a transitory eﬀect. It basically reﬂects the irreversible transition from the high and monotonically increasing IF in the glassy amorphous phase to a much lower damping level in the crystalline state, but can be a quite complex-shaped superposition of many diﬀerent eﬀects in the frequent case of a multiple-step crystallisation process. Once passed during heating, the crystallisation peak completely disappears during subsequent cooling or during a second heating run. It has been used in some cases to study details of the crystallisation process including kinetics and activation energies (Sinning and Haessner 1985, Klosek et al. 1989, Nicolaus et al. 1992). In contrast to the high damping level at the onset of crystallisation, the internal friction in metallic glasses is generally low at room temperature and below, and at acoustic (vibrating-reed) frequencies often reduced to the thermoelastic background (see Sect. 2.5) if no special low-temperature eﬀects are there (see later). The temperature dependence of IF is rather weak up to about 400–500 K, where a stronger, often exponential increase sets in which

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Fig. 2.35. Comparison of the low- and high-frequency IF behaviour, at a heating rate of 0.3 K min−1 , for two Ni-based glasses with (Ni60 Pd20 P20 ) and without (Ni78 Si8 B14 ) a glass transition before crystallisation. (1) Ni60 Pd20 P20 , 0.08 Hz; (2) Ni60 Pd20 P20 , 450 Hz; (3) Ni78 Si8 B14 , 0.095 Hz; (4) Ni78 Si8 B14 , 400 Hz. The maxima of all curves (at ∼600 K for Ni60 Pd20 P20 and ∼700 K for Ni78 Si8 B14 ) correspond to the onset of partial (primary) crystallisation followed by further transformations (Sinning and Haessner 1988a)

continues up to crystallisation. At all temperatures damping is higher at 0.1 Hz than at acoustic frequencies, indicating a broad spectrum of additional low-frequency processes. In this context, two main groups of metallic glasses have to be distinguished: those which crystallise from the solid state before reaching the glass transition, and those which ﬁrst show a glass transition and then crystallise from the undercooled melt (which largely corresponds to the distinction between “conventional” and “bulk” metallic glasses, except for a few intermediate cases like CuTi showing a Tg in a torsion pendulum at 0.3–0.5 Hz without being a bulk glass former (Moorthy et al. 1994)). Glass Transition and α Relaxation As shown in Fig. 2.35 for a still moderate example, the occurrence of a glass transition has a dramatic eﬀect on the height of the crystallisation peak at low frequencies which easily exceeds tan φ = 1, while the high-frequency IF peak remains unaﬀected and shows about the same height (tan φ < 0.1) as without a glass transition. The reason for this dramatic low-frequency IF increase, seen in Fig. 2.35 as the strong upward bend of curve 1 at Tg which is missing for the “conventional” metallic glass (curve 3), is the onset of dominating viscous damping Qv −1 due to the α relaxation (described as Qv −1 (T ) = EU /ωη(T ) using a Maxwell model). It has been shown that this viscous onset,

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shifting to higher temperature with increasing frequency, is located just at the dynamic glass transition (assuming ηg = 1012 N s m−2 ) if the frequency is around 0.1 Hz; under certain conditions, it could be used for determining Tg at heating rates much lower than possible with the common DSC technique (Sinning and Haessner 1986, 1987, 1988b; Sinning 1991a, 1993a). It is important to note, however, that such maxima in the loss factor tan φ (or Q−1 ) remain always transitory “crystallisation peaks” as mentioned earlier, even in presence of a glass transition: there is no “glass transition peak” or “ α relaxation peak” in tan φ in metallic (or more generally in low molecular weight) glasses, contrary to occasional misinterpretations in the literature. The glass transition alone, without the intervention of crystallisation, produces an α relaxation peak only in the loss modulus E (or G in case of shear) but not in tan φ = E /E which would in this case grow inﬁnitely as E goes to zero in the supercooled liquid. The typical situation, producing a “peak” in tan φ, is depicted in Fig. 2.36 for Zr65 Al7.5 Cu27.5 (a moderate bulk glass former not very diﬀerent from Ni60 Pd20 P20 in Fig. 2.35): whereas the loss modulus E shows two separate peaks, being identiﬁed with the α relaxation and with losses during crystallisation, respectively (Rambousky et al. 1995), the single maximum in tan φ does not reﬂect these two peaks. It is rather dominated by the behaviour of the storage modulus E in the denominator, which falls down in the supercooled liquid above Tg by more than one order of magnitude, to a sharp minimum that is solely determined by the onset of crystallisation (note the diﬀerent, logarithmic and linear scales for the moduli and tan φ, respectively). Therefore, only the rising part of the damping “peak” may be associated with the α relaxation.

Fig. 2.36. Storage modulus E , loss modulus E and damping tan φ of as-quenched amorphous Zr65 Al7.5 Cu27.5 , measured at 1 Hz during heating with 10 K min−1 using a dynamic mechanical analyser (Rambousky et al. 1995). Tg denotes the onset of the calorimetric glass transition

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For studying the α relaxation by mechanical spectroscopy, it is therefore more appropriate to look at E and E (or G and G ) separately, rather than just considering internal friction. To trace out the full α relaxation peak in the loss modulus as a function of either temperature or frequency, it is important to have a wide supercooled liquid range, i.e., to use the best bulk metallic glasses available. Meanwhile such studies have been performed on several more advanced Zr- and Pd-based bulk glasses (e.g., Schr¨ oter et al. 1998, Pelletier and Van de Moort`ele 2002a, Pelletier et al. 2002b, Lee et al. 2003a, Wen et al. 2004); an example is shown in Fig. 2.37. The results follow the time-temperature superposition principle, well known from non-metallic glass formers: all curves fall on a master curve when shifted by a temperaturedependent relaxation time which usually obeys the VFT equation. Occasional low-temperature shoulders of the α peak in E are sometimes interpreted as a β relaxation (Pelletier and Van de Moort`ele 2002a). Contrary to the loss modulus, the loss compliance J does not show an α relaxation peak either, but monotonically falls (like tan φ) with increasing frequency or decreasing temperature. An analysis of its frequency dependence, with an exponent typically changing from −1 at low to −1/3 at high frequencies, may be used to separate Newtonian viscous ﬂow from “relaxation” components and to discuss related models (Schr¨ oter et al. 1998). In addition, the interest in more speciﬁc questions of glassy dynamics in this range (which are beyond the scope of this chapter), calling for advanced or extended experimental conditions, has triggered some remarkable new experimental developments in mechanical spectroscopy: for instance, a non-resonant

Fig. 2.37. The α relaxation of the Zr46.75 Ti8.25 Cu7.5 Ni10 Be27.5 bulk metallic glass studied by dynamic mechanical analysis. (a) Temperature dependence during heating with 1 K min−1 at diﬀerent frequencies; (b) isothermal frequency dependence and ﬁt to the KWW equation with an exponent β = 0.5 (solid lines) at diﬀerent temperatures (Wen et al. 2004)

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vibrating-reed technique with an extremely wide frequency range (Lippok 2000), or a special “double-paddle oscillator” for studying thin ﬁlms (Liu and Pohl 1998) applied to glassy alloys at high temperatures and high frequencies (R¨osner et al. 2003, 2004). The results of such fundamental studies on bulk metallic glasses generally conﬁrm the main characteristics of the α relaxation in the high-temperature domain A as brieﬂy outlined above, known from non-metallic glass formers: in this respect, the underlying physics appears to be the same for quite diﬀerent classes of glass-forming systems. Intermediate Temperature Range This is the classical range of materials science in which the study of internal friction in metallic glasses began (Chen et al. 1971), and where most of our knowledge is still based on results obtained on rapidly quenched samples (although in this range there seems to be no big diﬀerence to bulk alloys; Berlev et al. 2003, Eggers et al. 2006). The main feature is here the exponential increase of IF with temperature mentioned earlier, e.g., in form of the (on the logarithmic scale) linear rise of curves 2–4 in Fig. 2.35 towards the maximum. The following main characteristics have been reported for this rising part of the IF spectrum: 1. It is reduced in its lower part (or shifted to higher temperature) by irreversible structural relaxation. For instance, if an as-quenched sample is heated with a constant rate to successively increasing temperatures (Fig. 2.38), in each heating run the IF is reduced compared to the previous one, in close correlation to an irreversible increase of Young’s modulus or resonance frequency (seen more clearly in isothermal experiments; Morito and Egami 1984a, Neuh¨ auser et al. 1990). Such an annealing behaviour is often analysed in terms of the AES model mentioned earlier, resulting in a broad spectrum for irreversible structural (not mechanical) relaxation ranging from about 100 to 200 kJ mol−1 in case of Fig. 2.38. 2. Using appropriate isothermal anneals, Morito and Egami 1984b and Bothe (1985) have been able to cycle the IF spectrum reversibly (Fig. 2.39), proving an eﬀect of reversible SR as well. 3. At frequencies about 1 Hz and below, the IF of as-quenched samples depends on the heating rate (Bobrov et al. 1996, Yoshinari et al. 1996b). 4. After a stabilising anneal and subtraction of the thermoelastic background Q−1 B , the IF at constant frequency often shows a straight line in an Arrhenius plot (Fig. 2.40), i.e., it is of the empirical form −A/kT . Q−1 − Q−1 B ∝e

(2.57)

The slope parameter A increases with annealing (Berry 1978). 5. The IF increase shifts to higher temperatures at higher frequencies, i.e., it is a thermally activated relaxation eﬀect (Fig. 2.40). The apparent activation enthalpies H, taken from cuts at constant damping according to

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Fig. 2.38. Variation of (a) frequency and (b) damping of a vibrating amorphous Ni78 Si8 B14 reed during heating-cooling cycles with 1 K min−1 . The vertical arrows indicate the onsets of structural relaxation and crystallisation, respectively, (Neuh¨ auser et al. 1990)

ln(f2 /f1 ) = (H/k)(T1−1 − T2−1 ),

(2.58)

vary between 115 and 250 kJ mol−1 for diﬀerent Pd- and Fe-based glasses and annealing treatments (with sometimes unphysically high attempt frequencies τ0−1 ), and are in most cases much higher than the related slope parameters A (22–125 kJ mol−1 ) (Soshiroda et al. 1976, Berry 1978, Neuh¨ auser et al. 1990). The problem of this discrepancy could be solved by Kr¨ uger et al. (1993) by showing theoretically that the ratio A/H is identical with the KWW exponent β obtained under quasi-static conditions, which also reduces the attempt frequency to reasonable values of the order of the Debye frequency. Including such A/H ratios, experimental KWW exponents of metallic glasses may span a very wide range between e.g., 0.23 for Fe75 P15 C10 (Berry 1978) and 0.67 for Zr65 Al7.5 Cu27.5 (Weiss et al. 1996). 6. At a ﬁxed temperature, the thermally activated damping Q−1 − Q−1 B should exhibit a frequency dependence proportional to 1/f β in case of a KWW law (Kr¨ uger et al. 1993), or to ln (1/f ) from the empirical equations (2.57) and (2.58) corresponding to Fig. 2.40, as based mainly on results at acoustic and lower frequencies down to about 1 Hz. However, when extending frequency into the infralow range down to 3 mHz,

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Fig. 2.39. Damping of amorphous Fe32 Ni36 Cr14 P12 B6 at 0.4 Hz and 2.5 K min−1 . (a) as quenched; (b) annealed at 300◦ C for 72 h; (c) annealed further at 375◦ C for 3 min; (d) additionally annealed at 270◦ C for 50 h (Morito and Egami 1984b)

Fig. 2.40. Thermally activated IF of amorphous Fe80 B20 (expressed as logarithmic decrement δ = πQ−1 ), measured under a saturating magnetic ﬁeld to suppress magnetoelastic damping (Berry 1978)

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Fig. 2.41. Internal friction of amorphous Co70 Fe5 Si15 B10 at f = 0.003–300 Hz and T = 500–700 K as a function of the vibration period. The inset shows the “highfrequency” range (f > 0.1 Hz) on an enlarged scale (Fursova and Khonik 2000)

Fursova and Khonik (2000) have found in an as-quenched Co-based glass that below about 0.1 Hz the damping varies linearly with the period of vibration (Fig. 2.41, obtained from isothermal cuts of linear heating curves at 3.3 K min−1 and diﬀerent frequencies), i.e., that in this low-frequency range IF is dominated by a component proportional to 1/f rather than to ln (1/f ) or 1/f β . According to these results and some additional isothermal experiments (e.g., Morito 1983, Bothe and Neuh¨ auser 1983, Bobrov et al. 1996, Fursova and Khonik 2002a), at least four or ﬁve components of IF in metallic glasses may be distinguished in this intermediate temperature range: (a) the thermoelastic background, (b) thermally activated IF in the “structurally relaxed” state with KWW kinetics, (c) a relatively small component which follows reversible SR and (d) a larger component (mainly in as-quenched glasses) which is gradually eliminated by irreversible SR, and which probably splits up into a high- and a low-frequency part, the latter having transient character (Yoshinari et al. 1996b). A coarse scheme of “primary” and “secondary,” or “α” and “β” relaxations seems rather inadequate for such subtle distinctions. As an additional unexplained anomaly, an isothermal re-increase of low-frequency IF at 0.1 Hz, after the decay of component (d), was observed in as-quenched Pd40 Ni40 P20 but not in other cases like Pd77.5 Ag6 Si16.5 at temperatures approaching the glass transition (Sinning 1991a, 1993a).

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To understand this IF behaviour in relation to structural relaxation, the question whether the atomic rearrangements which contribute to anelasticity and those which change it are identical or not, has already been posed by Morito and Egami (1984b). Exactly this identity (but not restricted to anelasticity) is assumed in the DSR model mentioned earlier, where IF is considered to be proportional to the rate rather than to the degree of SR (Khonik 1996, Fursova and Khonik 2000) – like in the case of the α relaxation above Tg where, however, the “degree” of SR is without meaning because the system is in metastable equilibrium. A similar interpretation was given by Yoshinari et al. (1996b) for the “transient” heating-rate dependent IF component in Fe33 Zr67 . According to the DSR model, damping should be viscoplastic in nature as described by a Maxwell body, and under linear heating conditions proportional to T˙ /f (Khonik 2000). This is conﬁrmed by the low-frequency behaviour in Fig. 2.41, and by the observed heating-rate dependence. Therefore, the DSR model seems to describe some extension of the viscous α relaxation to highly irreversible non-equilibrium conditions at lower temperatures, and is apparently consistent with low-frequency IF of as-quenched metallic glasses. As regards the underlying microscopic mechanisms of internal friction, the above-mentioned progress with respect to diﬀusion mechanisms (Faupel et al. 2003) seems to show where to go for a better understanding of mechanical relaxation as well. The main problem will be to bring together this kind of knowledge about possible atomic rearrangements with the respective microscopic aspects (e.g., coupling/cooperativity versus separated relaxation centres) of the diﬀerent relaxation models. Low-Temperature Eﬀects True low-temperature anelastic relaxation peaks5 – i.e., true “secondary relaxations” in the sense of decoupled, localised processes in the language of glass physics – have been found in metallic glasses mainly in two cases: after absorption of hydrogen and after cold plastic deformation 6 . Since the former case has already been treated in Sect. 2.2.4, we will now focus on the latter one. IF peaks due to plastic deformation are usually located below room temperature, in form of quite diﬀerent spectra ranging from well-deﬁned single 5

6

“Low temperature” means here the range from room temperature down to about 50–100 K. Eﬀects at liquid helium temperature and below, like tunneling and low-energy excitations, are not considered. There are some reports of similar IF peaks in metallic glasses without a speciﬁc treatment, especially in the earlier literature, where either no hypothesis about their origin or some speculations about other relaxation mechanisms were given (e.g., K¨ unzi et al. 1979, Sinning et al. 1988). Most of them have been identiﬁed later, or may be suspected, to originate either from hydrogen (as an impurity, in alloys containing metals like Zr or Y with a high aﬃnity to hydrogen), or from unintentional deformation (due to gripping or clamping in the sample holders).

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relaxation peaks over more irregular ones up to broad, multiple-peak spectra; a frequent case is a main peak at about 200–300 K and a smaller side peak around 100 K. The dependence on the degree of deformation can be very diﬀerent and is as yet hardly predictable: whereas Pd77.5 Cu6 Si16.5 showed a monotonically increasing damping from 23% to 79% deformation (Zolotukhin et al. 1985), in most other cases (Ni60 Nb40 , Cu50 Ti50 , Ni78 Si8 B14 ) quite the opposite trend was found: a relatively sharp, though scattered maximum of the eﬀect at only about 2–3% plastic strain followed by a strong decrease towards stronger deformation (Zolotukhin et al. 1989; Khonik 1994, 1996; Khonik and Spivak 1996). Intermediate rolling degrees around 20% were successful to produce damping peaks in Co33 Zr67 (Winter et al. 1996) but ineﬀective in both Zr52.5 Cu17.9 Ni14.6 Al10 Ti5 and Pd40 Cu30 Ni10 P20 (Eggers et al. 2007). In addition, the eﬀect usually shows a pronounced amplitude dependence, and is suppressed by annealing or irradiation. An example is given in Fig. 2.42, indicating a mixture of hysteretic and relaxation components (Khonik 1996). It is obvious that the origin of this deformation-induced IF must lie in the local structural changes (i.e., “defects”) produced in the shear bands which carry the highly localised plastic deformation of metallic glasses at low temperatures. A microscopic understanding of the relaxation processes must therefore be based on an understanding of the shear-band deformation itself. Some main ideas have been based on free volume (Spaepen 1977, Argon 1979, Steif et al. 1982, Wright et al. 2003, Kanungo et al. 2004), polycluster (Bakai 1994, Bakai et al. 1997) or dislocation concepts (Gilman 1973, 1975; Li 1978); however, as this is an own extensive topic since about 30–40 years, it cannot be discussed here. Since several characteristic features of the deformation-induced IF peaks

Fig. 2.42. Low-temperature IF peaks in amorphous Ni78 Si8 B14 after cold rolling (f ≈ 290 Hz): (a) temperature dependence at constant strain amplitude (7 · 10−6 ) and diﬀerent rolling degrees; (b) amplitude dependence at constant rolling degree (3.6%) and diﬀerent temperatures; the almost amplitude-independent behaviour of the “as cast” undeformed sample is shown for comparison (Khonik 1996)

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in metallic glasses (not to be listed here in detail) have been found analogous to those of dislocations in crystals, most authors of the above damping studies favour a dislocation concept, i.e., they assume that in metallic glasses deformation occurs by non-crystalline types of dislocations or dislocation-like defects (Bobrov and Khonik 1995, Khonik 2003 and further references). An idea by Khonik and Spivak (1996) that even the IF peak produced by hydrogen in metallic glasses (Sect. 2.2.4) – observed in almost the same temperature range as the deformation peak – could be an indirect, hydrogenationinduced deformation eﬀect, rather than a Snoek-type relaxation, gave rise to a longer controversy and further critical experiments (Khonik 1996, Winter et al. 1996, Takeuchi et al. 2004, Sinning 2006a, Eggers et al. 2007). However, apart from the more fundamental considerations on the Snoek-type mechanism in a wider structural context given in Sect. 2.2.4, it turns out that the properties of both types of IF peaks in metallic glasses (only to mention annealing behaviour and amplitude dependence) are plainly too diﬀerent to be explained by the same mechanism. There remain some earlier, less detailed observations of smaller IF peaks around or above room temperature, preceding the exponential IF increase towards the glass transition (e.g., Yoon and Eisenberg 1978, Hettwer and Haessner 1982, Deng and Argon 1986), which appear neither to be related to hydrogen nor to plastic deformation, so that the question for their origin must remain open. Beyond anelastic relaxation, in ferromagnetic metallic glasses also magnetomechanical damping (and a “giant” ∆E eﬀect) is observed, which is generally analogous to the respective phenomenon in crystalline materials (cf. Sect. 3.4), but modiﬁed by the absence of magnetocrystalline anisotropy in the amorphous structure (Berry 1978, Kobelev et al. 1987, Lu et al. 1990). 2.6.2 Quasicrystals and Approximants Quasiperiodic Order and the Role of Phasons Similarly as structural relaxation played the key role in the earlier discussion of anelasticity and viscoelasticity in amorphous alloys, so do the phasons in case of quasicrystals. Phasons are speciﬁc perturbations of the quasiperiodic long-range order that deﬁnes this novel class of solid-state structures, which was discovered by Shechtman et al. (1984). Quasiperiodic order is characterised by sharp Bragg diﬀraction spots in spite of the absence of translational periodicity. There are diﬀerent types of quasicrystals with quasiperiodic order in one, two or three dimensions (and periodic order in the remaining directions); the most important are the decagonal (2D) and the icosahedral (3D) ones. Mathematically, quasiperiodic order can be constructed as a cut through a periodic hyper-structure in a higher-dimensional space, like a 3D cut through a 6D periodic hyperlattice in case of icosahedral quasicrystals (Duneau and

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Fig. 2.43. Simpliﬁed scheme of phason defects in quasicrystals: (a) hyperlattice construction of a 1D quasicrystal with a phason ﬂip produced by an orthogonal shift of the cut; (b) a 2D phason ﬂip; (c) 2D simulation of shear deformation with a phason wall in the glide plane behind the dislocation (after Mikulla et al. 1995)

Katz 1985, Elser 1985). The construction is symbolised in Fig. 2.43a for a simple, 1D example: the “quasilattice points” in the “real” 1D space are determined by the cuts through “atomic hypersurfaces” in the orthogonal space around each point of the 2D hyperlattice. In this hyperspace, additional degrees of freedom exist orthogonal to physical space, which give rise to deviations from perfect order (from the “ideal” cut) in form of dynamic excitations (“phasons” as opposed to phonons in physical space) as well as static “phason defects”. The latter are violating certain “matching rules” in real space (instead of perturbing translational symmetry as defects in crystals do), and are connected with correlated rearrangements of certain local atomic conﬁgurations. Since these rearrangements also change the elastic energy (“phason strain”; G¨ ahler et al. 2003), it should in principle be possible to study their dynamics by mechanical spectroscopy. In the most elementary case (so-called “phason ﬂips”; Fig. 2.43b), the situation may be similar to that of point defects in regular crystals forming “elastic dipoles” (Weller and Damson 2003). However, as most “conventional” defects known from regular crystals also exist in quasicrystals, contributions to mechanical relaxation may be expected from these conventional defects as well as from the presence and motion of phasons. As concerns plastic deformation, quasicrystals are usually brittle at room temperature, while shear deformation by dislocation glide is possible at high temperatures. An important diﬀerence from crystals is that dislocation glide does not restore perfect order, but a “phason wall” (a special type of stacking fault) is left behind each gliding dislocation (Fig. 2.43c). Such coupling between conventional defects (dislocations) and phasons might also give rise to relaxation eﬀects.

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115

Survey of Mechanical Spectroscopy Studies Although mechanical spectroscopy was used from the very beginning to characterise the quasicrystalline state, the number of related studies in this young ﬁeld is still limited. As seen in the semi-chronological, comprehensive list in Table 2.20, the ﬁrst papers appeared in the ﬁeld of low-temperature physics. The next steps were inﬂuenced by the development of sample preparation, from ultraﬁne-grained melt-spun ribbons over coarse-grained polyquasicrystals up to large-size single quasicrystals grown by advanced techniques (Feuerbacher et al. 2003): with this increase in available crystal size, fundamental studies on single quasicrystals became possible ﬁrst for elastic constants and later for anelastic relaxation which generally needs longer samples. On the other hand the Ti- and Zr-based quasicrystals, related to more applied aspects like hydrogen storage (Stroud et al. 1996) or precipitation strengthening (Xing et al. 1999, Inoue et al. 2000), oﬀer access to the other extreme case of nano-quasicrystalline structures close to the amorphous limit (Nicula et al. 2000, Jianu et al. 2004). With a few exceptions mentioned later, most mechanical spectroscopy studies were performed on the icosahedral (3D) type of quasicrystalline structures. Table 2.20. Topics introduced into the study of quasicrystals by mechanical spectroscopy (left column: year of ﬁrst publication) year

subject

reference

1987

low-temperature (0.01–100 K) acoustics and relaxation elastic constants of Al-based single quasicrystals (ultrasonic techniques) anelastic relaxation in Al-based poly-quasicrystals anelastic relaxation in Al-based single quasicrystals

Birge et al. (1987), VanCleve et al. (1990) Reynolds et al. (1990); Sathish et al. (1991); Amazit et al. (1992); Spoor et al. (1995) Okumura et al. (1994), Damson et al. (2000a) Feuerbacher et al. (1996), Weller et al. (1996), Damson et al. (2000a,b), Weller and Damson (2003) Foster et al. (1999b)

1990

1994 1996

1999 2000

2002 2004

elastic moduli of Ti-based (poly-) quasicrystals relaxation in Ti/Zr-based quasicrystals, including hydrogen-induced damping peaks quasicrystalline coatings and composites with quasicrystals nano-quasicrystalline states and amorphous-quasicrystalline transitions

Foster et al. (2000), Scarfone and Sinning (2000); Sinning and Scarfone (2002); Sinning et al. (2003, 2004a) Fikar et al. (2002, 2004b) Sinning et al. (2004b,c)

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With increasing temperature (in total covering a range from about 0.01 to 1000 K), the following relaxation and IF phenomena can roughly be distinguished: – A low-temperature damping plateau at T < 1 K, – A linear damping increase with temperature (typical range 5–100 K), – A hydrogen-induced relaxation peak in H-absorbing Zr/Ti-based quasicrystals (see Sect. 2.2.4), – An intrinsic relaxation peak in Al-based quasicrystals around 400 K, – A high-temperature relaxation peak in Al–Pd–Mn single quasicrystals at about 900 K, – A strongly (e.g., exponentially) increasing high-temperature background. The low-temperature eﬀects, not to be considered here in detail, were mainly explained by atomic tunneling systems resulting from structural disorder, assumed to be of phasonic type and hence correlated with phason strain; the following linear increase may be of mainly thermoelastic origin. Since the hydrogen peak has been treated separately in Sect. 2.2.4, the following considerations will focus on the remaining three points (i.e., intrinsic relaxation peaks and high-temperature background), before brieﬂy coming back to a speciﬁc aspect of the hydrogen peak. Internal Friction Phenomena in Quasicrystals Intrinsic Eﬀects The as yet most careful studies of the intrinsic dynamic losses in quasicrystals have undoubtedly been performed by Weller and coworkers, including also high-quality icosahedral Al70.3 Pd21.5 Mn8.2 single quasicrystals (see references in Table 2.20). Two well-deﬁned, thermally activated relaxation peaks (denoted “A” and “B” by the authors, see curves 1 and 2 in Fig. 2.44) were observed near 400 and 900 K. Thanks to a frequency variation by seven orders of magnitude (10−3 –104 Hz, using forced and resonant torsion pendula as well as a resonant bar apparatus), the apparent activation energies and pre-exponential frequency factors could be determined rather accurately as 95 kJ mol−1 /2·1015 s−1 for peak A and 386 kJ mol−1 /3·1024 s−1 for peak B, respectively. These values were considered as indicating a point-defect mechanism for peak A, but a collective motion of a large number of atoms for the high-temperature peak B (Damson et al. 2000a, 2000b; Weller and Damson 2003). Phasons are considered to contribute to both types of mechanisms, in form of (A) isolated phason ﬂips and (B) extended phason formation and migration connected with the movement of dislocations. However, a clear distinction between e.g., phason ﬂips and ordinary vacancy jumps, in case of the point-defect mechanism of peak A, is not possible at the present stage. Obviously, this point-defect mechanism is not conﬁned to single quasicrystals,

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Fig. 2.44. Examples of high-temperature IF spectra of icosahedral quasicrystals. Curves 1, 2: Al70.3 Pd21.5 Mn8.2 single quasicrystals with peaks “A” and “B” (curve 1: frequency 3 Hz, curve 2: 2 kHz; Weller and Damson 2003); curves 3, 4: microcrystalline Ti41 Zr42 Ni17 (curve 3: 360 Hz, curve 4: 3.6 kHz; Sinning et al. 2003)

since a similar peak had previously been observed in icosahedral Al75 Cu15 V10 polycrystals (Okumura et al. 1994). A related peak, with somewhat higher activation energies (135–210 kJ mol−1 ) but otherwise similar characteristics, was also found in Al–Ni–Co alloys with decagonal quasicrystals (Damson et al. 2000a, Weller and Damson 2003). On the other hand, as exempliﬁed by curve 3 in Fig. 2.44, intrinsic relaxation peaks like peak A are absent in all Ti- and Zr-based icosahedral quasicrystals studied as yet (Sinning et al. 2003, 2004a, 2004b). As concerns peak B which was seen only in the icosahedral Al–Pd–Mn single quasicrystals, one should not exclude that it exists in icosahedral polycrystals as well, but such measurements at suﬃciently high temperatures (sometimes prevented, like in the Ti–Zr–Ni system, by the formation of crystalline phases) are not found in the literature. Therefore, results like curves 3 and 4 in Fig. 2.44 are often treated as a monotonic high-temperature background; the frequency shift between these two curves, taken very roughly at a damping level of Q−1 = 0.01, corresponds to activation parameters of 320 kJ mol−1 /1025 s−1 comparable to those of peak B. A high-temperature background also exists in decagonal Al–Ni–Co up to 1000 K or even 1200 K; in that case, however, there is no such huge diﬀerence in activation parameters (especially as concerns the pre-exponential factors) like that between peaks A and B in Al–Pd–Mn. Consequently, the mechanisms of the “hightemperature damping background” may well be diﬀerent between icosahedral and decagonal quasicrystals, and in the latter case mainly associated with volume diﬀusion (Weller and Damson 2003). Another interesting observation has been made in two bulk metallic glasses, which form quasicrystals as the ﬁrst devitriﬁcation product from the undercooled melt above Tg : diﬀerent from all previous observations in comparable cases, the damping level above room temperature was in this case found

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Fig. 2.45. High-temperature damping increase in two bulk metallic glasses forming icosahedral quasicrystals from the undercooled melt (2 K min−1 , 330–350 Hz). Solid lines Zr69.5 Cu12 Ni11 Al7.5 , dashed lines Zr61.6 Ti8.7 Nb2.7 Cu15 Ni12 ; thin lines structurally relaxed amorphous, and thick ones quasicrystalline states (Sinning 2006b)

higher in the ﬁne-grained quasicrystalline than in the initial amorphous state (Fig. 2.45). This seems to indicate that for building up long-range quasiperiodic order (though only over grain diameters of some tens of nanometres), defects or free volume must be produced in the relatively densely packed, structurally relaxed bulk metallic glass, which then become part of the ﬁne polyquasicrystalline structure and give rise to enhanced anelastic or viscoelastic relaxation (Sinning 2006b). Hydrogen as a Probe It was already mentioned brieﬂy earlier in Sect. 2.2.4 that H-induced IF peaks can be used as a local structural probe, e.g., in case of Fig. 2.14 to detect diﬀerences in short-range order between amorphous alloys. We should add here that of course the same is true for H-absorbing quasicrystals, i.e., that the position (like in Fig. 2.15) and shape of a Snoek-type hydrogen peak contain information about the local atomic structures in which the interstitial H atoms are moving. Prominent examples of such local atomic structures are in icosahedral quasicrystals the so-called “Bergman” and “Mackay” clusters (e.g., Kim et al. 1998), which seem to be distinguishable by the width of the hydrogen relaxation peak: Sinning (2006b) found evidence for a wider, composed peak (i.e., a stronger splitting of interstitial site or saddle point energies) for the Mackay clusters (in Ti65 Zr10 Fe25 ) compared to that one observed for the Bergman clusters (e.g., in Ti41 Zr42 Ni17 ). If, in the latter case, the sharpness of the mechanical loss peak can be related to the degree of icosahedral order in the local clusters, then this local order seems to be practically the same in amorphous and nano-quasicrystalline structures up to grains sizes of about 20 nm (in spite of a strong Young’s

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modulus increase up to 50% between these two states), but distinctly improved at grain sizes beyond about 100 nm (Sinning 2006b). Approximants and Complex Alloy Phases Approximants are periodic crystals that “approximate” quasicrystals in the sense that, despite diﬀerent long-range order, their structures are locally the same, i.e., they contain the same atomic clusters or structural building units as their quasiperiodic counterparts. In the higher-dimensional description mentioned earlier (Fig. 2.43a), they are called “rational approximants” as represented by rational coordinates of the cut through the hyperlattice, contrary to irrational ones for quasiperiodic structures. Due to the possibility of classical crystallographic structure determination, approximants are the main key for analysing the structure of quasicrystals. Unfortunately we are not aware of systematic mechanical spectroscopy work on approximants, except for one ultrasonic study of the hydrogen peak in the Ti–Zr–Ni W phase (a large-unit-cell “1/1 bcc approximant” containing Bergman clusters, Kim et al. 1998) by Foster et al. (2000) which, however, allows only for a limited comparison with the respective eﬀect in the quasicrystal because of diﬀerent H concentrations. Apart from their value as approximants to study quasicrystals, the so-called “structurally complex alloy phases” – deﬁned as intermetallic phases with giant unit cells (Urban and Feuerbacher 2004) – are very fascinating to be studied in their own right, because they contain novel types of defects neither found in quasicrystals nor in simpler metallic structures, which may also produce interesting new physical properties. The most prominent of such defects are the so-called “metadislocations” (Klein et al. 1999) carrying plastic deformation, which would be a very promising new class of defects to be studied by mechanical spectroscopy.

3 Other Mechanisms of Internal Friction

3.1 Introduction In this chapter those internal friction phenomena are described which are not only associated with an anelastic mechanism, but which are mainly due to some hysteretic deformation occurring during stress cycling. Such hysteresis may originate from several kinds of phase transformations, like polymorphic or martensitic transformations or precipitation/dissolution of second phases (Sect. 3.2), from dislocation motion (Sect. 3.3), or from magnetostriction in ferromagnets (Sect. 3.4). Some of these mechanisms may lead to exceptionally high damping values deﬁning so-called “Hidamets” (high-damping materials), which are considered in Sect. 3.5.

3.2 Internal Friction at Phase Transformations If a phase transformation is connected with a volume change or a shear deformation, it may oscillate under the inﬂuence of an alternating stress so that a transformation-induced, alternating strain is produced in addition to the elastic strain. There is usually a phase lag between stress and strain in such cases, causing a hysteresis and an energy loss measured as internal friction. The most important types of such stress-active phase transformations are considered brieﬂy in this section, together with some typical damping eﬀects (see Benoit 2001d for a review). 3.2.1 Martensitic Transformation A martensitic transformation (MT) is a special type of phase transformation, characterised by the following features (Cohen et al. 1979): – It is a diﬀusionless transformation between a high-temperature “austenite” and a low-temperature “martensite” phase; even if diﬀusion occurs it is not essential for the transformation

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3 Other Mechanisms of Internal Friction

– It involves a lattice distortion, which consists mainly of a deviatoric but not a dilatational component – The kinetics and morphology are dominated by the strain energy There are three types of MT: athermal, isothermal and thermoelastic.1 Another distinction refers to ferrous and non-ferrous martensite. Athermal in this sense refers to the way how the martensite phase is growing upon cooling, e.g., by a sudden, jump-like (“athermal”) formation of martensite plates of a certain size which cannot grow further due to immobile interfaces, so that a further transformation forth or back requires new nucleation events. This athermal MT, characterised by large values of all relevant energy and strain parameters and high hardness in the martensitic state, is mainly found in interstitial Fe-based alloys including steels (ferrous martensite). Because of its large transformation hysteresis, it is of little interest from the viewpoint of internal friction and will not be considered further. The isothermal, i.e., time-dependent MT, discovered by Kurdyumov and Maksimova (1948, 1950), is a relatively rare type of MT; its eﬀect on internal friction will shortly be discussed at the end of this chapter. Finally, it is the thermoelastic MT (Kurdyumov and Khandros 1949) in (mostly) non-ferrous materials which is of high importance for internal friction. With e.g., small transformation strains, energies, hysteresis and easily mobile interfaces, it is in many respects opposite to the athermal MT. The amount of research papers on the thermoelastic MT is huge, also because many of these alloys exhibit a shape-memory eﬀect, and it is diﬃcult to provide the reader even with a list of corresponding review papers. Under the aspect of IF and damping capacity, recent reviews by Van Humbeeck (2001, 2003), San Juan and P´erez-S´aez (2001) and San Juan and N´ o (2003), are recommended for deeper reading and have been used here. In the following short overview, we can only give an outline of the main damping mechanisms related to the thermoelastic MT, and mention the main groups of alloys in which these mechanisms occur. Damping Mechanisms Usually the total internal friction Q−1 tot associated with a phase transition consists of three components (Bidaux et al. 1989): −1 −1 −1 Q−1 tot = QT r + QP T + Qint .

(3.1)

The ﬁrst two components belong directly to the phase transition in form of ˙ a transient part Q−1 T r depending on a ﬁnite heating or cooling rate T = 0, 1

Here the term “thermoelastic” refers to the comparability between thermal transformation and elastic strain energies, which has nothing to do with the fundamental thermoelastic coupling considered in Sect. 2.5.

3.2 Internal Friction at Phase Transformations

123

Fig. 3.1. Scheme of the three contributions to IF during a martensitic phase transformation: the transitory term IFTr , the phase transition (or isothermal) term IFPT and the intrinsic term IFInt (From San Juan and P´erez-S´ aez 2001)

and a rate-independent, non-transient part Q−1 P T found even under isothermal conditions. The third, intrinsic part −1 −1 Q−1 int (T ) = V Qmart (T ) + (1 − V )Qβ (T )

(3.2)

represents the intrinsic IF in both co-existing phases (the high-temperature (β) and martensite phases in case of the MT), taking into account the temperature-dependent volume fraction V of martensite. As sketched schematically in Fig. 3.1, the three contributions sum up to form an IF peak, with often very high damping capacity in case of a thermoelastic MT (see Sect. 3.5); this peak is usually accompanied by a minimum in the temperature-dependent elastic modulus. The experimental methods to separate these components have been discussed in detail by San Juan and N´ o (2003). For the non-transient phase-transformation damping Q−1 P T , diﬀerent mechanisms (related e.g., to interface or dislocation movements) are discussed in the literature with respect to diﬀerent materials (Dejonghe et al. 1976, Mercier and Melton 1976, Clapp 1979, Koshimizu 1981, Kustov et al. 1995). Two basic approaches can be distinguished (Van Humbeeck 2001): (1) Q−1 P T is a result of coexistence of macroscopic amounts of martensite and austenite phases, or (2) Q−1 P T results from a “pre-transformation” state with sub-microscopical nuclei of the martensite phase. These approaches assume diﬀerent dependencies of Q−1 P T on frequency and amplitude of vibrations, as studied by Kustov et al. (1995). The transient damping Q−1 T r , being the dominating part if the frequency is in the Hz range, is basically attributed to the transformation rate ∂n/∂t, where n is the amount of transformed material (Scheil and M¨ uller 1956). The related

124

3 Other Mechanisms of Internal Friction

anelastic strain dεan = k(∂n/∂t)dt, which determines Q−1 T r , comes from the lattice deformation when the material is transformed. Several approaches have been developed on this background: 1. Belko et al. (1969a) introduced a model of thermally activated formation and growth of nuclei of the martensitic phase. 2. Delorme and Gobin (1973a,b) suggested a “transformation plasticity” approach with the transformation deformation dεp = kσdn to be linearly dependent on the transformed volume fraction and on the applied stress σ, leading to k dn T˙ . (3.3) Q−1 Tr = J dT ω 3. Dejonghe et al. (1976) added a stress-dependent term to the transformation rate, and the possibility of retransformation during one cycle, to obtain

3 σC 2 ∂n k ∂n T˙ −1 QT r = + σ0 1− , (3.4) J ∂T ω 3π ∂σ σ0 where σC is the critical stress necessary to re-orientate already existing martensite variants or to nucleate new ones. 4. Similarly, the inﬂuence of the stress amplitude σ0 on the transformation rate was taken into account by Gremaud et al. (1987b) by ∂n ∂n = · (T˙ + ασ), ˙ ∂t ∂T where α is the Clausius–Clapeyron factor (α = υεt /∆S with the molar volume υ, the transformation strain εt and the transformation entropy ∆S), which also agrees better with experiments showing that Q−1 T r does not linearly depend on T˙ /ω. 5. Stoiber introduced a “fragmentation” parameter x(n) which represents additional anelastic deformations due to the migration of intervariant boundaries (Stoiber 1993, Stoiber et al. 1994): ˙ T ∂n ·f . (3.5) Q−1 T r = k · x(n) · ∂t ω · σ0 More models have been discussed by San Juan and P´erez-S´aez (2001). Important Factors ˙ Q−1 tot increases with heating or cooling rate T via the corresponding changes −1 ˙ in QT r , known as the so-called “T eﬀect”. At T˙ = 0, Q−1 T r = 0; in that case, some frequency dependence was measured in the low-frequency range (Pelosin and Rivi´ere 1997). If T˙ = 0, Q−1 T r is inversely proportional to the frequency;

3.2 Internal Friction at Phase Transformations

125

Fig. 3.2. Dependence of IF on oscillation amplitude (ε0 ) measured in Cu–Zn–Al martensite according to Koshimizu et al. (1979). Domain C: ε0 < 10−6 ; domain B: ε0 < 10−5 ; domain A: ε0 > 10−5

on the other hand, in the martensitic phase the (intrinsic) IF is frequencyindependent apart from some relaxation peaks. Three amplitude domains can be distinguished in martensite, as suggested by experimental data on Cu–Zn–Al (Koshimizu et al. 1979, see Fig. 3.2) and ucke Au–Cd (Zhu et al. 1983). At low amplitudes (10−7 −10−6 ), the Granato–L¨ mechanism can be accepted (Granato and L¨ ucke 1956a, 1956b; see Sect. 3.3). No clear amplitude dependence is observed between 10−6 and about 10−5 , whereas above that range the amplitude dependence is clearly seen again. For many diﬀerent alloys, the critical onset values of the second amplitudedependent range are found between 5×10−6 and 2×10−5 . Several models were applied to this latter range, i.e., by Granato and L¨ ucke (1956a,b), Takahashi (1956) and Peguin et al. (1967). At constant amplitude, an additional time dependence of damping (either decreasing with time or going through a maximum, following structural changes in the material) was observed in NiTi and CuAlZn e.g., by Mercier et al. (1979), Morin et al. (1985, 1987b), Van Humbeeck and Delaey (1982, 1984) and Van Humbeeck et al. (1985). In several Mn–Cu based alloys, a magnetic ﬁeld increases the damping in the premartensitic range, above the IF peak temperature at the MT, during cooling but not during heating (Markova 2004, Markova et al. 2004). This contribution is characterised by the area SQ between the TDIF curves measured with and without magnetic ﬁeld, which is proportional to the magnetic ﬁeld applied (Fig. 3.3). The eﬀect is explained by weak ferromagnetism in antiferromagnets due to spinodal decomposition and an inhomogeneous distribution of Mn atoms. Some Selected Materials (see also Van Humbeeck 2001) Ni–Ti-Based Alloys Ni50 Ti50 -based alloys with an approximate content of Ni between 48 and 52 at% are known as shape-memory alloys (Saburi 1989, 1998; Wayman

3 Other Mechanisms of Internal Friction 1200

80

Mn-Cu-Ni

60 Q-1, 10-4

SQ arb.un.

126

Ms

5

40

4

800 400 0

3

20

Mn-Cu-Cr-Ni Mn-Cu-Ni Mn-Cu-Cr Mn-Cu

1

2 H[104A/m]

2 1

0 80

110

140

170

200

230

T,⬚C

Fig. 3.3. Inﬂuence of a magnetic ﬁeld on TDIF at 1 Hz for Mn–Cu–Ni, with (1) H = 0; (2) H = 0.6 · 104 A m−1 ; (3) H = 1.3 · 104 A m−1 ; (4) H = 1.9 · 104 A m−1 ; (5) H = 2.5 · 104 A m−1 . Inset: Inﬂuence of magnetic ﬁeld on the damping in the premartensitic range (area SQ , see text) in the Mn–Cu based alloys Mn80 Cu20 , Mn80 Cu17 Ni3 , Mn80 Cu17 Cr3 and Mn80 Cu14 Ni3 Cr3 (from Markova et al. 2004)

1989; Markova et al. 1996; Golovin et al. 1997b; Ilyin et al. 1998; Ilchuck and Moravic 1998; Coluzzi et al. 2000; Golyandin et al. 2000; Biscarini et al. 2003a; Igata et al. 2003a; Yoshida and Yoshida 2003; Straube et al. 2004; Mazzolai et al. 2004). During cooling in the temperature range between 150 and −40◦ C (depending on the Ni content), the high-temperature B2 phase is transformed into the B19 monoclinic martensite. In some cases the martensitic transformation is preceded by formation of the rhombohedral R-phase, followed by the R-to-B19 transformation (an example is given in Fig. 3.4.). At heating only the reverse MT takes place. Adding a third element, i.e., replacing some Ni or Ti atoms, helps to adapt Ni–Ti alloys to diﬀerent applications by inﬂuencing the strength, ductility and parameters of the MT (Eckelmeyer 1976, Honma et al. 1979, HuismanKleinherenbrink 1991, Kachin 1989, Kachin et al. 1995): Cu decreases and Nb increases the transformation hysteresis; Fe, Cr, Co, Al lower and Hf, Zr, Pd, Pt, Au rise the transformation temperatures; Mo, W, O, C strengthens the matrix, H increases the total damping around room temperature. The eﬀect of hydrogen on internal friction in Ni–Ti alloys (Coluzzi et al. 2006a,b) is discussed in Sects. 2.2.4 and 3.5. Cu-Based Alloys These are Cu–Zn-, Cu–Al- and Cu–Sn-based alloys with the structure of the Hume–Rothery β phase and fcc Cu–Mn-based alloys, which all show the martensitic transformation.

3.2 Internal Friction at Phase Transformations Q−1,10−4 B19’

← R ← B2

450

127

0.9

f cooling

f,

heating

Hz

Q−1 300

cooling

0.8

heating 150

1 K / min 0

0.7 200

250

300

350

T, K

Fig. 3.4. Temperature dependencies of IF (Q−1 ) and resonance frequency (f) at cooling and heating for a Ti–50.6at%Ni alloy after annealing at 575◦ C (Golovin et al. 1997b)

Most of the former alloys have disordered bcc structures at high temperatures which order to the B2, D03 or L21 structures at lower temperatures. They are often used as Hidamets (Sect. 3.5) because of their very high damping, and are also shape-memory alloys (Favstov et al. 1980, Favstov 1984, Kustov et al. 1996a,b, Shen et al. 1996, Coluzzi et al. 1996, Deborde et al. 1996, Kustov et al. 2000, Mazzolai et al. 2000a, Covarel et al. 2000, Van Humbeeck 2001, Kustov et al. 2006). Damping in fcc Cu–Mn alloys is very sensitive to heat treatment and carbon content (Birchon et al. 1968, Sugimoto et al. 1973, Men’shikov et al. 1975, Vintaykin et al. 1978, Sugimoto 1981, Kˆe et al. 1987a, Udovenko et al. 1990, Laddha and Van Aken 1997, Markova 1998, 2002, 2004, Kostrubiec et al. 2003, Pelosin and Rivi´ere 2004, Recarte et al. 2004). These alloys can lose about 50% of their damping capacity during natural ageing even at room temperature. This eﬀect can be prevented by additional alloying. Fe-Based Alloys The thermoelastic (“non-ferrous”) type of MT is also found in some Fe-based alloys. Depending on composition, the austenite phase (γ) can be transferred into three kinds of martensite (α (bcc), ε(hcp) and fct martensite), accompanied by the shape-memory eﬀect (Delaey 1995, Gu et al. 1994, Maki 1998). Most attention has been paid to alloys with the γ → ε transformation like Fe–Mn, Fe–Mn–Cr, Fe–Mn–Si, Fe–Mn–Al or Fe–Cr–Ni (Sato et al. 1982a,b; Volinova et al. 1987; Volinova and Medov 1998; Sato 1989; Robinson and McCormick 1990; Lee et al. 2003a, 2004; Okada et al. 2003; Igata et al. 2003a, 2004; Wan et al. 2006; Sawaguchi et al. 2006; Dong et al. 2006). The amount

128

3 Other Mechanisms of Internal Friction

of ε martensite plays the most important role if high damping is required (see Sect. 3.5), the speciﬁc damping capacity is about 20–25% (see also two symposium proceedings on High Damping Materials: J. All. Comp. 355 (2003) and Key Eng. Mater. 319 (2006)). Isothermal Martensitic Transformation Martensitic transformations of the ferrous type occur as athermal barrierless transformations when a certain driving force is achieved, or with the help of a thermally activated process at lower driving force. Type and kinetics of the MT in a certain Fe-based alloy depend on the structure and on the state of the high-temperature austenite phase, and may be either athermal or isothermal (Kurdyumov 1949a, Kurdyumov and Maksimova 1948, 1950, 1951; Maksimova 1999). In the latter case special attention is paid to the interrelated development of two subsystems in the crystals: the formation and growth of interphase boundaries, and the migration of lattice imperfections (Roitburd 1978; Roytburd 1995, Wang and Khachaturyan 1997). The redistribution of defects in the lattice may aﬀect the mode of MT substantially (Olson and Cohen 1976, Clapp 1995, Golovin et al. 1999). The IF method was ﬁrst applied by Rodrigues and Prioul (1985, 1986) to study the isothermal MT in Fe–Ni–Mo alloys which, exhibiting diﬀerent kinetics and types of the γ → α transformation, give a prominent example as regards the eﬀects of composition and initial morphology on the transformation. By measuring IF during cooling in the ranges of athermal and isothermal MT, both by low- and high-frequency techniques, the inﬂuence of the dislocation-impurity interaction on the MT was studied in several Fe–Ni, Fe–Ni–Mo and Fe–Ni–Cr steels, and estimations of the activation energy for the isothermal MT were given (Golovin et al. 1994, 1995, 2000; Golovin and Golovin 1996). It was thus shown that IF is sensitive to the isothermal MT and permits to follow its kinetics. Several IF peaks occur in connection with the isothermal MT: the FR relaxation peak in austenite, a transformation peak including transient and intrinsic components, and a peak in martensite; these peaks give information on the behaviour of interstitials and dislocations before, during and after the diﬀusionless transformation. From this viewpoint, two states of Fe–Ni–Mo austenite may be distinguished with respect to their eﬀect on the MT (see Fig. 3.5): (a) A state with saturated atmospheres of interstitial atoms around dislocations (weak amplitude dependence of IF and existence of an FR peak, see Sect. 2.2.2, indicating pinned dislocations and supersaturation of the fcc solid solution with C, respectively), resulting in an athermal MT during cooling. (b) A state with non-saturated dislocation atmospheres (stronger amplitude dependence and absence of an FR peak), connected with an isothermal MT component.

3.2 Internal Friction at Phase Transformations (a)

0.50

(b)

0.45 0.40

2 0.35 0.30

0 0.02

0.04

0.06

0.08

0.10

C, %

0

MSiso

−50

MSath

MS

4

QFR−1

QFR−1 (104)

tgαADIF

tgαADIF

0.00

129

−100 −150 0.00

0.02

0.04

0.06

0.08

0.10

C, %

Fig. 3.5. Eﬀect of the carbon content in Fe–24Ni–5Mo on (a) the amplitude dependence of IF (slope tgαADIF of IF taken in the linear part) and the height Q−1 FR of the FR peak and (b) the start temperatures (in ◦ C) for the athermal and isothermal martensitic transformations

The correlation between dislocation pinning (suppression of ADIF), stress relaxation in austenite and the martensite points (MS.iso , MS.ath ), i.e., the type of MT kinetics, shows the importance of dislocation–interstitial interaction. Dislocation pinning by interstitials in austenite therefore leads to an athermal MT and to a suppression of the isothermal MT component. The activation energies of the isothermal MT, 15–35 kJ mol−1 in Fe–Cr– Ni–Mo and 3–12 kJ mol−1 in Fe–Ni–Mo compared to 135–145 kJ mol−1 for the C diﬀusion in austenite, cannot be explained by diﬀusion processes but seem to be consistent with a dislocation-assisted nucleation of isothermal martensite (Golovin et al. 1996b, 2000). The binding energy between dislocations and interstitials in Fe–Ni–Mo alloys is found to be ≈10 kJ mol−1 . 3.2.2 Polymorphic and Other Phase Transformations Polymorphic Transformations In the vicinity of polymorphic phase transition temperatures, high maxima or jumps of IF may occur (Figs. 3.6–3.7). For example, maxima were observed in Zr (Garber et al. 1976, Boyarskij 1986), Co (Selle and Focke 1969a; Boyarskij et al. 1986; Bidaux et al. 1985, 1987), Ti (Wegielnik and Chomka 1975, Semashko et al. 1988), La (Dashkovskij and Savitskij 1961, Pan et al. 1985), Ce (Sharshakov et al. 1977, Postnikov et al. 1975a, Korshunov et al. 1981), Nd (Maltseva et al. 1980), Tl (Mordyuk 1963, Maltseva and Ivlev 1974), Fe (Dashkovskij et al. 1960a), Np (Selle and Rechtien 1969b), whereas jumps were found in U and Pu (Selle and Focke 1969a). According to Selle and Focke (1969a), the mechanisms of allotropic transformations can be classiﬁed by comparing the IF of both phases directly above and below the transformation temperature: considerably diﬀerent values indicate a diﬀusive transformation, and approximately equal ones a shear

130

3 Other Mechanisms of Internal Friction

Fig. 3.6. Changes in internal friction at f = 1 Hz of (a) uranium and (b) plutonium during polymorphic transformations. Solid lines: heating; dashed lines: cooling (Selle and Focke 1969a)

transformation. For instance, in U all transformations are diﬀusive (Fig. 3.6a); in Pu α → β, δ → δ and δ → ε are shear transformations, while β → γ and γ → δ are diﬀusive ones (Fig. 3.6b). IF maxima at polymorphic transformations have the following features: 1. They have a non-Debye shape and are often narrow. 2. They do not shift in temperature with changes in the measurement frequency, that is, they are not thermally activated. 3. They display a temperature hysteresis: on heating, they occur at higher temperatures than on cooling, and also the respective peak heights may diﬀer signiﬁcantly (Fig. 3.7). Magnetic Transformations Maxima of mechanical losses, as well as steps due to diﬀerent IF in the diﬀerent phases, may appear at magnetic phase transitions as well. For example, Fig. 3.8a shows the maxima of ultrasonic attenuation found in dysprosium, where transitions exist both from paramagnetic to antiferromagnetic (N´eel temperature, 174 K) and from antiferromagnetic to ferromagnetic states (Curie temperature, 84 K). These non-relaxation maxima are located at somewhat lower temperatures than the phase transitions themselves, as predicted by Landau and Khalatnikov (1954), due to the eﬀect of stresses on the magnetic ordering processes in the spin system and related ﬂuctuation processes. This kind of internal friction is essential only at high frequencies in a narrow temperature interval close to the respective phase transition. Another kind of IF behaviour is shown in Fig. 3.8b for terbium single crystals (Shubin et al. 1985), where transitions occur from FM to AFM at 214–221 K (θ1 ), and from AFM to PM at 225–230 K (θ2 ). At θ1 and θ2 , respectively, a bending and a sharp drop in Q−1 can be seen with increasing

3.2 Internal Friction at Phase Transformations

131

Fig. 3.7. Changes in internal friction of neptunium during the β → γ and γ → β polymorphic transformations (f ≈ 1.5 Hz; Selle and Rechtien 1969b)

Fig. 3.8. Temperature-dependent eﬀects in rare-earth metals: (a) longitudinal (α1 ) and transversal (αt ) ultrasonic attenuation in a Dy polycrystal (f = 10 MHz; Rosen 1968c); (b) IF and elastic modulus of a Tb single crystal (f = 1 kHz; Shubin et al. 1985)

132

3 Other Mechanisms of Internal Friction

temperature. The diﬀerence between these two examples is due to the fact that Dy was studied at a frequency of 10 MHz, but Tb at about 1 kHz. At 1.3 Hz the maximum at the PM → AFM transition in Dy is absent, too, and a stepwise increase in IF is observed (Sharshakov et al. 1978a). In chromium, a non-relaxation IF peak at the N´eel temperature (TN = 310-312 K) was ﬁrst reported by Fine et al. (1951) and then conﬁrmed by many authors (see Table 4.7.1). Another magnetic IF eﬀect due to a spinﬂip transition at Tsf was found by De Morton (1963) and Street (1963), and again conﬁrmed by many authors (Table 4.7.1). Between the N´eel and spinﬂip temperatures the spin-density waves are transversely polarised, i.e., the polarisation vector P is perpendicular to the wave vector Q (TSDW); below TSF the polarisation is longitudinal (LSDW) and P is parallel to Q (Dubiel 2003); a related measurement is shown in Fig. 3.9. The IF peak at the N´eel temperature can be asymmetric or even double-shaped, which may be explained by the inﬂuence of internal stresses of diﬀerent origin (Pal-Val et al. 1989, Golovina and Golovin 2004). In steels an IF peak due to a magnetic transformation in Fe3 C was detected by Sudnik et al. (1974), and conﬁrmed by Rokhmanov and Sirenko (1993). Melting In the vicinity of the melting point at T ≈ (0.94–0.99)Tmelt, , internal friction maxima are observed due to grain boundary melting (Postnikov et al. 1963,

Fig. 3.9. Temperature dependence of Q−1 (bigger grey filled circles) and f (smaller black points) for chromium near the N´eel point (≈ 311 K) and spin-ﬂip transition (≈ 120 K) (Golovina and Golovin 2004). The dotted lines show the inﬂuence of quenching from 1100◦ C on the peak near the N´eel point. The intervals of magnetic transformations are shown in the bottom (after Dubiel 2003)

3.2 Internal Friction at Phase Transformations

133

Table 3.1. Internal friction peaks due to grain boundary melting metal f (Hz) Tm (K) Tm /Tmelt Qm −1

Bi

Cd

Pb

Sn

548 538 0.99 0.07

636 573 0.97 0.02

524 563 0.94 0.01

707 493 0.98 0.05

Drapkin et al. 1980, Drapkin and Kononenko 1981; see Table 3.1), which are in fact pseudo-maxima on the high-temperature background due to a decrease in internal friction. There have been some attempts to use this eﬀect for highdamping applications (see Sect. 3.5). Superconducting Transition The transition to the superconducting state is accompanied by the evolution of hysteresis maxima, e.g., in Nb (Postnikov et al. 1975b; Pal-Val et al. 1993) or Ta (Miloshenko and Shukhalov 1976), or by a drop in the internal friction curve (e.g., Nb–H; Wang et al. 1984). In perfect single crystals, it is necessary to introduce defects by preliminary plastic deformation for the maxima to appear. 3.2.3 Precipitation and Dissolution of a Second Phase A special group of ﬁrst-order phase transitions produces, by means of nucleation and growth, a two-phase mixture consisting of precipitates in a host matrix, in general with diﬀerent compositions and structures (Hardy and Teal 1954, Kelly and Nicholson 1963). If an external stress induces some change in shape and distribution of these precipitates (by aﬀecting volume, elastic constants, transformation temperatures, and/or diﬀerent defect mobilities), this will result in internal friction. The high sensitivity of IF for any structural change can be used to monitor changes in the precipitated state; however, owing to the wide variety of possible reasons for the IF signal, the identiﬁcation of the relevant mechanisms is usually a diﬃcult task and requires support by other methods (e.g., DSC, TEM, X-ray diﬀraction, thermoelectric power), which detect the microstructural changes in a more direct way. For the simple case of an isotropic material, Krivoglaz (1960, 1962) proposed a theory for anelastic relaxation of the bulk modulus in such a phase mixture, controlled by the time for the phase transformation to occur. In case of two components, this time is governed by the diﬀerence in composition between precipitate and matrix as well as by diﬀusion, resulting in a relaxation time τσ (aﬀected by the external stress σ) τσ =

r03 , 2Dx2

(3.6)

134

3 Other Mechanisms of Internal Friction

where r0 is the radius of the particles (assumed to be spheres), and x2 is the volume fraction of the second (particle) phase. The ﬁrst-order transition (nucleation and growth) implies the occurrence of a temperature hysteresis in sequential heating and cooling experiments, connected with dissolution and re-precipitation of the particles. As a characteristic feature of (3.6), important for identifying the nature of the resulting damping peak, the peak position on the temperature scale is independent of the vibration frequency, which only aﬀects the peak height. Many examples can be found in the literature, as reviewed by Nowick and Berry (1972) and more recently by Schaller (2001b); a typical one is shown in Fig. 3.10. In this case (and also in systems like Al–Cu or Cu–Ag), precipitation from the homogeneous solid solution – produced by quenching from a suﬃciently high temperature – starts with the formation of coherent solute clusters or Guinier–Preston (GP) zones, which grow while the surrounding matrix is depleted from the solute. In order to reduce strain and surface energy, the system may transform via metastable conﬁgurations into incoherent precipitates which ﬁnally attain their equilibrium structure and shape. Such transformations can be followed by mechanical spectroscopy in different ways: besides the IF signals found at the transformation itself like in Fig. 3.10, one can also monitor the height of the Zener peak (cf. Sect. 2.2.4), which decreases during precipitation as the number of reorientable, free solute pairs is diminished. Another possibility is to follow the decrease of the dislocation hysteresis peak due to the blocking of dislocation motion by the evolving precipitates (Schaller 2001b). The signals associated directly with the precipitation reactions, as in Fig. 3.10, may consist of one or several new relaxation peaks corresponding to

Fig. 3.10. Damping spectrum (Q−1 ) and elastic modulus (∝ f 2 , f = frequency) of Al–20wt%Ag, (1) after quenching, and (2) after 10 min annealing at 520 K. Peak P1 corresponds to the formation of GP zones from solid solution, and P2 to the transformation of the GP zones into metastable γ precipitates. These transform during the annealing treatment into stable γ precipitates which produce peak P3 . (From Schaller 2001b)

3.2 Internal Friction at Phase Transformations

135

the various conﬁgurations of precipitates, superimposed on the increasing high-temperature IF background (cf. section “Damping Background at Elevated Temperatures” in Sect. 2.3.3). These peaks may arise from the anelastic strain due to stress-induced shape changes of the precipitates themselves (Damask and Nowick 1955). As such shape changes occur by dissolution on one side and precipitation on the other side of the particle, it will be governed by solute diﬀusion in the interface region, thus the activation energy of the process is expected to be somewhat less than that for solute diﬀusion in the bulk. In more detail, according to Schoeck and Bisogni (1969) and Schoeck (1969), the movement of partial dislocations around the precipitates may be involved, in agreement with electron microscopic observations, with dragging of solutes by the moving dislocations (cf. Sect. 2.3). Miner et al. (1969) propose ledge motion along the edges of the precipitate particles, and Entwistle et al. (1978) consider the relaxation of atomic groups within individual clusters involving vacancies, thus a point-defect process (Sect. 2.2). Even more spectacular IF eﬀects are observed in case of discontinuous precipitation which starts at favourable places in the sample, such as grain boundaries or dislocations, subsequently spreading out into the interior, e.g., in Al–Zn (Nowick 1951). As the same mechanism may produce both the hightemperature background and some characteristic relaxation peak, these are diﬃcult to separate (cf. Sect. 2.3.3). The reason for internal friction again lies in processes within the interface between precipitate particles and matrix, e.g., of the types considered in Sect. 2.4.1. Some features of the IF mechanisms due to precipitates have been compiled in the review by Schaller (2001b), and can be divided into (a) Interface relaxation, considered by Schoeck (1969) who distinguished between volume changes of coherent precipitates, and modulus changes due to both coherent and incoherent particles. While the ﬁrst two involve elastic strain energy due to the imposed stress, the last one comprises shear along the interface if the local stress exceeds some critical stress value. This implies that only incoherent and semi-coherent precipitates should give a hysteresis relaxation peak, while the coherent ones only contribute to the background damping. This has been veriﬁed with the systems Al–Cu (Hanauer et al. 1972), Cu–Co (Mondino and Schoeck 1971) and Cu–Si (Mondino and Gugelmeier 1980). However, the situation may be more complex, because in Cu–Fe the coherent precipitates do produce a peak which disappears when they loose their coherency (Pelletier et al. 1975). In another approach by Kohen et al. (1975), an anisotropic interface mobility of the precipitates is suggested to cause relaxation, in particular if this interface mobility is high. (b) Relaxation within the precipitates, e.g., in Al–Ag alloys with semicoherent, hcp γ (Ag2 Al) precipitates, which can be distinguished from interface relaxation by its stability against overageing (Ostwald ripening, with strongly varying volume-to-surface ratio; Merlin et al. 1978,

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3 Other Mechanisms of Internal Friction

Schaller 1980). This was corroborated by a test with a sample consisting of the pure γ phase (Al–85at%Ag, Schaller and Benoit 1980). In this case the relaxation is explained by a reorientation of elastic dipoles within the γ precipitate, i.e., a Zener eﬀect. (c) Internal friction, of only partly anelastic relaxation character, by diﬀusion-controlled movement of interfaces at suﬃciently elevated temperatures beyond the Zener eﬀect. Corresponding “precipitate peaks” near the solvus have been observed by Kiss et al. (1986) in Al–Ag. The common experiments performed with gradually increasing temperature (e.g., with T˙ = dT /dt = const) may exhibit peaks near the transition temperature which do not reﬂect the true precipitation kinetics because of ongoing transformation during the temperature rise. This problem can be avoided in isothermal experiments with variation of frequency where the microstructure has been stabilised by previous annealing. For example, this method permitted to detect a new (not thermally activated) relaxation peak due to θ precipitates in the 2024 Al alloy (Rivi`ere and Pelosin 2000), and was also applied by Ogi et al. (2000) to study the Snoek relaxation in a Cuprecipitated alloy steel. Internal friction due to phase precipitation and dissolution has been investigated best for the cases of hydrides and deuterides in metals of the groups IV and V, as well as in Pd (“hydride precipitation peak”, see also Sect. 2.2.4): V–D (Cannelli and Mazzolai 1971, 1973; Yoshinari et al. 1977, 1978), V–H (Cannelli and Mazzolai 1970; Koiwa and Shibata 1980a,b; Yoshinari and Koiwa 1982a; Cannelli et al. 1983, 1984b), Nb–D (Buck et al. 1971), Nb–H (Wert et al. 1970; Yoshinari and Koiwa 1982a,b; Yoshinari et al. 1985), Ta–D (Cannelli and Cantelli 1974, 1975), Ta–H (Cannelli and Mazzolai 1969, Yoshinari et al. 1980; Yoshinari and Koiwa 1982a; Li et al. 1985), Ti–D (Numakura and Koiwa 1985; Kato et al. 1988), Ti–H (K¨ oster et al. 1956a; Tung and Sommer 1974; Ritchie and Sprungmann 1982; Gong et al. 1990), Zr–D (Provenzano et al. 1974; Numakura et al. 1988), Zr–H (Provenzano et al. 1974; Ritchie and Sprungmann 1983; Numakura et al. 1988; Pan and Puls 2000), Pd–H (Yoshinari and Koiwa 1987). During cooling, internal friction begins to increase abruptly at the precipitation temperature, before a non-relaxation IF peak appears below this temperature. This peak has a λ form with two com ˙ /f . ∝ T ponents, i.e., an equilibrium value and a transient damping Q−1 Tr

3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF) In Sect. 2.3, those dislocation-related relaxation mechanisms were considered which can be regarded as purely anelastic, i.e., as linear and amplitudeindependent, and which prevail at very low vibration amplitudes. However, with increasing amplitude of applied stress or strain, the dislocations may

3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF)

137

break away from their pinning points, move over considerable distances, and even start to multiply (Hull and Bacon 1984, Hirth and Lothe 1968), resulting in an increasing amplitude dependence of internal friction caused by non-linear relaxation and/or hysteretic phenomena (Gremaud 1987). Although the data part of this book (Chaps. 4 and 5) generally does not include ADIF data, a few aspects of ADIF will be treated here because their knowledge is important for separating the diﬀerent damping components and for identifying the relevant relaxation mechanisms. ADIF studies are extensively applied to investigate the microstructure and its evolution with deformation and heat treatments in various materials. As an example, Fig. 3.11 shows typical ADIF curves of an Al–Mg alloy (Schwarz 1985). Starting from a plateau value at low amplitudes (note the logarithmic scale!), the damping rises exponentially if a certain amplitude is exceeded, indicating some critical stress necessary to overcome obstacles for dislocation motion (see also, e.g., Nishino et al. 2004, Trojanova et al. 2004, G¨ oken et al. 2005). An extended and thorough review of important results, measuring techniques and theoretical treatments of dislocation mechanisms can be found in the paper by Gremaud (2001), who considers ﬁve categories of dislocation mechanisms leading to diﬀerent kinds and amounts of ADIF: (a) Relaxation models which include drag mechanisms acting continuously along the line of the moving dislocation, such as phonon and electron

Fig. 3.11. Amplitude dependence of the decrement δ(= π · Q−1 ) for Al–0.1at%Mg at 128 K before (a) and after (b) plastic deformation (bending with surface strain of ≈ 0.02). (From Schwarz 1985)

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3 Other Mechanisms of Internal Friction

drag; these are relevant at very high frequencies and show at most a slight amplitude dependence, if any. (b) Drag resulting from the diﬀusion of point obstacles distributed on the dislocation segments (i.e., point defects moving together with the bowing dislocation segment at suﬃciently high temperature, as in the cases of Hasiguti or Snoek–K¨ oster peaks), where in addition to what has been said in Sect. 2.3, also a slight amplitude dependence may occur. (c) Dissipation due to breakaway of the dislocation from immobile point obstacles segregated at the dislocation line, yielding a pronounced ADIF from the resulting hysteresis of the stress–strain curve (Fig. 3.12a). As the dislocation will be repinned by the same point obstacles during its reverse motion, the damping is of quasi-static hysteresis type. In the kHz range, the breakaway time is negligible and the shaded area in Fig. 3.12a corresponds to the dissipated power per stress cycle, as ﬁrst treated by Granato and L¨ ucke (1956a). The related anelastic strain is taken as

Fig. 3.12. Dislocation models (dislocation loops and obstacles) and stress-strain hysteresis loops for (a) dislocation breakaway from obstacles along the dislocation line (case (c)) and (b) dislocation motion across a random array of point obstacles in the slip plane (case (c)). The shaded area indicates the energy loss during a full vibration cycle; the diﬀerent symbols are explained in the text. In (a) the situation with a stress less than the Frank–Read stress for dislocation multiplication is shown. (From Gremaud 2001)

3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF)

εd = Λ b y m

139

(3.7)

with the dislocation density Λ and the mean eﬀective shift ym of the dislocation averaged over its length. Taking the distribution of segment lengths l between pinning points in a loop of length L as f(l) = 2 ) exp(−l/lm ) with an average segment length lm (Koehler 1952, (Λ/lm Granato and L¨ ucke 1956a, Gremaud 2001), a damping contribution of Kt Λ K 2 Ec exp − Q−1 = (3.8) ε0 lm ε0 is found, with Kt = 4Ω(1–G)L3 /(π4 lm ) (depending on the crystal orientation Ω) and K2 = ∆G/G, where Ec is the dislocation–obstacle interaction energy and ε0 the applied strain amplitude. Although this theory has been devised for T = 0 (athermal behaviour), it compares well with experiments at T > 0, where the breakaway from pinning points occurs with a thermally activated waiting time (relaxation time) τ = τ0 exp(Ec /kT ) (Teutonico et al. 1964, Granato and L¨ ucke 1981, L¨ ucke and Granato 1981). This leads to a similar expression as (3.8) with a slight additional frequency dependence of Q−1 , corresponding to an intermediate mode between relaxation and hysteresis. According to (3.8), ADIF may be used to extract information on dislocation density as well as on obstacle strength and concentration by means of the so-called Granato–L¨ ucke plot of log(ε0 Q−1 ) vs. 1/ε0 , which ideally gives a straight line with slope and intercept determined by the mean segment length lm and by the dislocation density Λ, respectively. Equation (3.8) may also be written as ∆ σ0cr σ0cr −1 · exp − Q ≈ (3.9) π σ0 σ0 with the critical yield stress σ0cr = f0cr /b¯l = nf0cr /bL, where σ0 , f0cr , L and l are the applied stress amplitude, the critical force on the obstacle at breakaway, the dislocation loop length between anchoring points, and the segment length between n point obstacles along the dislocation, respectively. The relaxation strength ∆ is found to be 2

Λb2 L ∆= 12Γ J

(3.10)

with the dislocation line tension Γ and the unrelaxed compliance J. The dependence of Q−1 on temperature and frequency enters through σ0cr which is mainly controlled by thermally activated processes depending on temperature and deformation rate. (d) Damping losses resulting from thermally activated motion of dislocations through a random array of point obstacles, providing a hysteresis diﬀerent from that in case (c) (cf. Fig. 3.12).

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3 Other Mechanisms of Internal Friction

Neglecting ﬁrst thermal activation, the dependence of damping on the stress amplitude σ0 becomes (Gremaud 2001) 4∆ σ0cr σ0cr −1 · Q = (3.11) 1− if σ0 > σ0cr π σ0 σ0 and Q−1 = 0 if σ0 < σ0cr . Thus damping again depends indirectly on temperature and frequency and shows a maximum at σ0 = 2σ0cr . Taking now thermal activation into account, diﬀerent dependencies are found in the various ranges of temperature and obstacle strength (see Gremaud 2001). With a transition stress σtr = 4∆Gm /h2 b depending on the maximum interaction energy ∆Gm between dislocation and point defect and on the average area h2 = 2d¯l of the glide plane per point defect (with distances d and ¯l between neighbouring point defects normal and along the average dislocation line, respectively), the cases σ0cr (T ) > σtr (Friedel’s (1964) statistics, in the low-temperature range) and σ0cr (T ) < σtr (Mott’s statistics (see Labusch 1970, Schwarz and Labusch 1978), in the higher temperature range may be distinguished. The corresponding Granato–L¨ ucke (G–L) plot of ln(σ0 Q−1 ) vs. 1/σ0 will now be positively curved (instead of the straight line for case (c)), as shown in the elucidating experiments by Schwarz (1981), Schwarz and Funk (1983), Fig. 3.13.

Fig. 3.13. Granato–L¨ ucke plots of ADIF in Al–0.1at%Mg at 300 K: (A) measured directly following a 10 min high-amplitude straining, (B) after several static anneals of 1, 5 and 10 min. (From Schwarz and Funk 1983)

3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF)

141

The stress amplitude necessary to keep a constant ADIF value is found to provide a direct measure of the critical yield stress σ0cr , which thus can be studied by mechanical spectroscopy with the advantage that microstructural changes are largely avoided (Lebedev 1992, Lebedev and Ivanov 1993, Lebedev and Pilecki 1995), contrary to usual deformation experiments. An analysis of applicability of the G–L model to study the structure of diﬀerent materials has shown the necessity to specify better in which interval of amplitudes the dislocation hysteresis plays the dominating role, i.e., in which amplitude intervals the G–L model can describe experimental data reliably (Krishtal et al. 1964). For that reason, critical amplitudes of deformation restricting this interval were introduced, by writing the ADIF (here as a function of strain amplitude, Q−1 (ε0 )) as (Golovin 1968): m−2 C2 ϕ2 (ε0 ) (ε0 − εcr1 ) −1 exp , Q (ε0 ) = ϕ1 (ε0 ) + + ϕ3 (ε0 ) m ε0 − εcr1 ε0 − εcr1 εcr1 (3.12) where εcr1 and εcr2 are the ﬁrst and second critical amplitudes. The resulting IF is amplitude-independent below εcr1 , is reversible and nearly linearly increasing with amplitude (dislocation hysteresis) between εcr1 and εcr2 , and becomes irreversible above εcr2 where the hysteretic loop is not closed, but new dislocations can be generated and microdeformation takes place. ϕ1 , ϕ2 , ϕ3 , C2 and m are numerical parameters. The study of damping mechanisms in diﬀerent amplitude and frequency domains was carried out for materials with diﬀerent types of structures (Beresnev and Sarrak 1966, Golovin et al. 1979, Levin et al. 1980, Lebedev and Kustov 1987, Dudarev 1988), which helped to understand microdeformation mechanisms and to determine their inﬂuence on possible fatigue damage at ε0 > εcr2 (Golovin and Puˇsk´ar 1980). With increasing temperature the point obstacles, which up to now have been considered as immobile, may attain some diﬀusional mobility which then leads to a transition from depinning to dragging. While pure dragging was considered in case (b), the transition region provides special diﬃculties (cf. Gremaud 2001). An anomalous behaviour of relaxation peaks (a maximum in the amplitude dependence of the peak height) was discovered by Kˆe (1950) in Al–Cu and Al–Mg alloys and discussed in terms of diﬀusion of solute atoms in the dislocation core (Kˆe 1985a, Fang and Kˆe 1985, 1996, Kˆe et al. 1987a, Fang 1997; Fang and Wang 2000a). (e) Finally, the hysteretic damping resulting from an athermal long-range interaction with point obstacles distributed in the bulk has recently been discussed and treated by Gremaud and Kustov (1999), and Kustov et al. (1999, 2006), who investigated this type of ADIF by detailed

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3 Other Mechanisms of Internal Friction

Fig. 3.14. Strain amplitude dependence of the decrement measured for a Cu– 7.6at%Ni single crystal at various temperatures (f = 100 kHz). The domains (I) (II) and (III) are explained in the text. (From Gremaud and Kustov 1999)

measurements in a wide temperature range in solid solutions of Cu–Ni alloys (example in Fig. 3.14). Their model includes short-range (localised) obstacles (i.e., solute atoms in planes adjacent to the dislocation glide plane), long-range (diﬀuse) obstacles (i.e., weak obstacles in some distance from the glide plane), and unbreakable pinners (i.e., nodes in the dislocation network). Two critical stresses σ0cr1 and σ0cr2 exist for the diﬀuse (athermal) and localised (thermally activated) forces, respectively, of which only the latter depend on temperature and frequency. This model predicts, in agreement with the measurements in Fig. 3.14, three domains: In domain (I) at low temperatures, neither σ0cr1 nor σ0cr2 are exceeded by the external stress, so that low-amplitude ADIF due to the dislocation motion over diﬀuse forces remains purely athermal. In domain II at more elevated temperatures and moderate amplitudes, σ0cr2 is exceeded but not σ0cr1 , resulting in a gradual increase of ADIF. In domain III at still higher amplitudes both critical stresses are exceeded, resulting in a steep increase of internal friction (Gremaud and Kustov 1999). These mechanisms also explain the so-called peaking eﬀect during irradiation (Caro and Mondino 1981a, 1982), i.e., the development of an IF maximum as a function of irradiation time. Damping Eﬀects in Fatigue Internal friction connected with fatigue is not only an extreme case of hysteretic damping, but has also been applied extensively as a method to study fatigue. Without discussing this in detail, readers should at least be provided with some important references. The high sensitivity of IF to monitor the accumulation of cyclic microdeformation has been pointed out by many authors (e.g., Lazan 1961, Koca´ nda 1972, Puˇsk´ar and Golovin 1985, Klesnil and Lukas 1992, Blanter et al. 1994,

3.3 Dislocation-Related Amplitude-Dependent Internal Friction (ADIF)

143

(a)

(b) Fig. 3.15. Internal friction (torsion pendulum 0.3 Hz, surface strain < 10−5 ) of polycrystalline Cu wire after ultrasonic fatigue with 20 kHz: (a) after N = 4 · 105 cycles at diﬀerent amplitudes ε0 , compared to an annealed sample (650◦ C/2 h); (b) after diﬀerent cycle numbers N at constant ε0 = 3.5 · 10−4 . (From Bajons and Weiss 1971)

Puˇsk´ar 2001, Terentev 2002). For example, some fatigue-induced changes of temperature-dependent, low-frequency IF spectra are shown in Fig. 3.15. As concerns amplitude dependence, the relation between “critical” amplitudes (with respect to IF and related modulus changes) and the fatigue characteristics (W¨ohler curves, microstructures) has been discussed by Puˇsk´ar and Golovin (1985), Klesnil and Lukas (1992) and Vincent and Foug`eres (2001). It was shown that a clear correlation exists between fatigue lifetime and certain intervals in the ADIF curve, so that the fatigue behaviour at diﬀerent amplitudes can be predicted from ADIF measurements. However, for further analysis (Puˇsk´ar 2001), a serious diﬃculty is the inhomogeneity of the dislocation structure.

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3 Other Mechanisms of Internal Friction

Such application of mechanical spectroscopy to fatigue problems is possible in diﬀerent ways and with diﬀerent objectives: (a) By applying deformation- or energy-based empirical criteria of fatigue life. The resistance to fatigue is known to depend on the area of the hysteresis loop (Feltner–Morrow criterion, see Morrow 1960, Feltner and Morrow 1961), and on the value of anelastic deformation which can also be evaluated from the hysteresis loop shape (Coﬃn–Manson criterion, see Coﬃn 1954 and Manson 1953). Some modiﬁcations of these criteria, including their applicability to diﬀerent types of metallic materials in cases of low and high cycle fatigue, have been the subject of diﬀerent studies (Langer 1962, Troschenko 1980, Troschenko et al. 1985, Puˇsk´ar and Golovin 1985, Puˇsk´ar 2001, Vincent and Foug`eres 2001). (b) By studying the mechanisms of deformation and damage accumulation in materials subjected to cyclic loading. Several models of interpreting dislocation-related IF during fatigue damage accumulation have been proposed (Peguin et al. 1967, Burdett 1971, Jon et al. 1976, Golovin et al. 1979), and analysed with respect to their applicability to diﬀerent materials (Jon et al. 1976, Puˇsk´ar and Golovin 1985, Puˇsk´ar 2001). The similarity between parameters of micromechanical tests and of ADIF was pointed out by Golovin (1968), Browne (1972), Koca´ nda (1972), Golovin and Puˇsk´ar (1992). Ultrasonic tests after (Bajons and Weiss 1971) or during fatigue cycling (Hirao et al. 2000) were used to study the kinetics of the process, to ﬁnd out a dislocation model for fatigue development (Vincent and Foug`eres 2001), and to control the material state under cycling (Schenk et al. 1960, Golovin et al. 1975). Additional aspects of IF originating from microcracks and other types of damage were considered e.g., by Golovin et al. (1975), Carre˜ no-Morelli (2001), Robby (2001), Schaller (2001a), G¨ oken et al. (2004), Golovin et al. (2004a) and Arkhipov et al. (2005, 2006).

3.4 Magneto-Mechanical Damping Applying a stress to a ferromagnetic material causes a variation of magnetisation due to the magneto-elastic coupling (magnetostriction), which results in the so-called “∆E eﬀect” (i.e., an apparent reduction of Young’s modulus below the purely elastic value found in the magnetically saturated state), and also in a related dissipation of mechanical energy during loading/unloading or in case of vibration. The latter eﬀect can give rise to a strong magneto-mechanical damping with stress-dependent and stress-independent components, used for application in high-damping materials (Chap. 3.5). Whereas the basics of magnetisation phenomena are treated in many standard textbooks (e.g., Bozorth 1951, Chikazumi 1966, Jiles 1998), more speciﬁc information on the corresponding internal friction eﬀects can be

3.4 Magneto-Mechanical Damping

145

found in reviews by e.g., Smith and Birchak (1968, 1970), Berry and Pritchet (1975), Degauque and Astie (1980), Astie et al. (1981), Augustyniak (1994), Kekalo and Potemkin (1969), Kekalo et al. (1970), Kekalo (1973, 1986), Kekalo and Samarin (1989), Stolyarov (1991), Riehemann (1996), Blythe et al. (2000). The following short summary is partly based on an introduction into magneto-mechanical damping given recently by Degauque (2001). Considering ﬁve main contributions to the total energy of a ferromagnet without an external ﬁeld (exchange energy Wex , magnetocrystalline anisotropy energy WK , magneto-elastic or magnetostrictive energy Wλ , magnetostatic energy Wm , energy of magnetic domain walls WW ), four main mechanisms of magneto-mechanical damping may be deﬁned: – – – –

Magnetoelastic hysteresis damping (Qh −1 ) Macroeddy-current damping (Qa −1 ) Microeddy-current damping (Qµ −1 ) Damping at magnetic transformations (QPhT −1 ) (e.g., at Curie and N´eel temperatures, spin-ﬂip transitions etc.; see Sect. 3.2.2).

Therefore, the total magnetomechanical damping QM −1 in ferromagnets can be considered as a sum of these components: QM −1 (ε, f, T ) = Qh −1 (ε, f, T ) + Qa −1 (f, T ) + Qµ −1 (f, T ) + QPh.T −1 where, contrary to Qa −1 and Qµ −1 , the hysteretic contribution Qh −1 depends on the strain amplitude ε. Macroeddy-Current Macroeddy-current amplitude independent damping (Qa −1 ) is a result of the eddy currents induced temporarily in an electrically conductive sample as a response to a stress-induced change dB/dσ in the total magnetic induction B. For the case of a partially magnetised rod of radius R vibrating with a periodic stress σ of frequency f, Qa −1 has been given by Bozorth (1951) in the low(Lf)- and high(Hf)-frequency limits, respectively, as Q−1 a(Lf ) =

π 4

dB dσ

2

R2 Ef ρ

and Q−1 a(Hf ) =

1 3/2

8π 2 µr

dB dσ

2

R2 f ρ

−1/2 , (3.13)

where ρ is the electrical resistivity and µr the reversible magnetic permeability. Zener (1938a) also considered the damping due to macroeddy currents by summation of single Debye peaks. Some experimental examples given by Berry and Pritchet (1975, 1976, 1978a) have been discussed by Degauque (2001). Microeddy-Current Microeddy-current amplitude independent damping (Qµ −1 ) is due to the microscopic eddy currents caused by local changes of the magnetisation arising during the stress-induced displacement of magnetic domain walls. Unlike Qa −1

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3 Other Mechanisms of Internal Friction

which requires substantial magnetisation to be eﬀective, Q−1 µ has its largest value near the demagnetised state (M/MS < 0.3, Cangana et al. 1971). Depending on the frequency range and on the type of motion assumed for the domain walls, diﬀerent equations have been suggested for Q−1 µ , like Q−1 µ =A

El2 MS2 · f, µρσi2

(3.14)

for reversible motion of rigid domain walls at relatively “low” frequency, where µ is the magnetic permeability, MS the saturating magnetisation, and A a parameter depending on the level of internal stresses σi with wavelength l (Bozorth 1951, Williams et al. 1950) or Q−1 µ =

GN a2 ¯l 2 mω/β · 2, 12Ww 1 + (mω/β )

(3.15)

for reversible motion of ﬂexible domain walls considered as elastic membranes pinned by dislocations (Latiﬀ and Fiorre 1974). Here G is the shear modulus, N a2 the area per unit volume of domain walls with eﬀective mass m, ¯l the average distance between pinning dislocations, and β a viscous damping parameter. A similar expression was introduced by Mason (1951, 1958) in form of a Debye-type law Q−1 µ =

9µi λs E f /fr · , 20πMS 1 + (f /fr )2

with

fr =

πρ , 2 24µi Dw

(3.16)

where µi is the initial magnetic permeability, λS the saturation magnetostriction, and DW the domain size. Values for Armco iron (DW ≈ 3×10−3 cm, ρ ≈ 10−5 Ωcm, µi ≈ 800) give rise to a peak at fr ≈ 180 kHz; for the same material, taking the frequency value f in Hz, Coronel and Beshers (1998) proposed the relation f 3 . (3.17) Q−1 µ = 3 · 10 · 3.2 · 1010 + f 2 Magnetoelastic Hysteresis Damping Magnetoelastic hysteresis damping (Q−1 h ) is the most important and powerful type of damping in ferromagnets, so that the terms “magnetomechanical” or “magneto-elastic” are sometimes narrowed down to denote only this hysteretic, amplitude-dependent damping component. It is due to the stress-induced motion of non-180◦ domain walls (while the 180◦ walls are stress-insensitive), including irreversible Barkhausen jumps beyond a critical stress τcr . At low applied shear stresses τ or shear strains γ (i.e., in the “Rayleigh region” of the magnetisation curve), the hysteretic energy dissipated is (Kornetski 1938, Bozorth 1951, Degauque 2001): ∆Wh =

4 dG−1 3 ∆Wh τ , so that Q−1 . h = 3 dτ 2πW

(3.18)

3.4 Magneto-Mechanical Damping

147

As the vibration energy W varies with τ 2 , this implies a linear amplitude dependence of internal friction. For higher stresses, however, the hysteretic losses ∆Wh no longer increase with τ 3 but with a stress-dependent exponent 0 < n < 3 (Sumner and Entwistle 1959), and ﬁnally reach a saturation level; consequently, Q−1 h shows a maximum as a function of stress or strain amplitude. Relating the saturation value of ∆Wh to the magnitude of the “eﬀective” internal stresses opposed to the movement of the domain walls, Degauque (2001) pointed out that the position and height of the amplitudedependent damping maximum of Q−1 h can be used to determine the level of these internal stresses, and found a value of 7 MPa for the case of high-purity iron if carefully recrystallised. Magneto-elastic ADIF curves measured with rising and falling shear amplitudes γ, respectively, do not necessarily coincide but can be diﬀerent according to the details of magnetisation and demagnetisation. This behaviour may also be inﬂuenced by microplastic deformation processes, depending on the relative magnitudes of the peak position γh. max , the highest amplitude γ0 used in the tests, and the amplitude γcr2 of the onset of microplastic deformation (Golovin 1993, Degauque 2001; cf. Sect. 3.3). Moreover, these eﬀects depend on temperature, time and static stress applied. The temperature dependence of Q−1 h , although always approaching zero at the Curie point, may vary from material to material (sometimes even with rather diﬀerent literature data for similar materials), as discussed e.g., by Kekalo (1973) and Degauque (2001). Finally, a frequency dependence of Q−1 h is not expected as long as the time for an irreversible domain jump, related to the relaxation time of the microeddy currents, can be neglected: thus, Q−1 h should decline at frequencies where the microeddy current peak appears (Nowick and Berry 1972). To summarise, the diﬀerent dependencies of magneto-elastic hysteresis damping on temperature, amplitude, frequency and magnetic ﬁeld are given schematically, in simpliﬁed form, in Fig. 3.16. The total damping Qtot −1 of ferromagnetic high-damping materials (Sect. 3.5) can often be described approximately as the sum of magnetomechanical damping (QM −1 , mainly represented by the hysteretic component

Fig. 3.16. Schematic representation of the dependence of magneto-mechanical damping on temperature, strain amplitude, frequency and magnetic ﬁeld (adapted from De Batist 1983)

148

3 Other Mechanisms of Internal Friction

Qh −1 ), and dislocation damping (Qd −1 ) as an eﬃcient nonmagnetic damping source: Qtot −1 (ε, f, T ) ≈ QM −1 (ε, f, T ) + Qd −1 (ε, f, T ). Kekalo (1973) summarised the six most typical ADIF curves for diﬀerent materials of this type, depending on the amplitude values for the maximum of Qh −1 (εh. max ) and for the beginning of irreversible motion of dislocations (εcr2 ), respectively (see Sect. 3.3). For separating the magnetic and nonmagnetic contributions, one may apply a saturating magnetic ﬁeld to suppress the magnetic losses. Some examples of the competing ADIF contributions QM −1 and Qd −1 in Fe– Cr and Fe–Al alloys, measured at diﬀerent temperatures, have been reported by Golovin (1994), Golovin et al. (2004b). A particular situation is met in some Fe-based metallic glasses (cf. Sect. 2.6) with also rather high magnetostriction values but small anisotropy energies (due to the absence of a crystal lattice), so that domain wall motion is supplemented and partially replaced by reversible and irreversible rotation processes of magnetisation. Besides some related modiﬁcations of the “normal” magneto-elastic damping and ∆E eﬀects, a special “giant” ∆E eﬀect has been found for a particular domain structure, achieved by a speciﬁc annealing treatment in a magnetic ﬁeld (Kobelev et al. 1987; cf. Degauque 2001). Finally, the aforementioned damping QPhT −1 at magnetic transformations should also be noticed, in addition to the three kinds of magneto-mechanical damping (Qa −1 , Qµ −1 , Qh −1 ) described earlier. Found e.g., at kHz frequencies in a narrow interval around Curie (TC ) or N´eel (TN ) points, QPhT −1 may result from the inﬂuence of an external stress on the processes of magnetic ordering (Stolyarov 1991). Such eﬀects have already been discussed in more detail in Chap. 3.2.2.

3.5 Mechanisms of Damping in High-Damping Materials High-damping metallic materials, often abbreviated as “Hidamets” or HDM (Birchon 1964, James 1969), are used in various practical applications like, for instance, reducing noise and vibration, preventing fatigue problems or increasing the quality of cutting tools. Contrary to this wide application, there is some confusion as concerns the physical mechanisms which can eﬀectively produce high damping, including the deﬁnition of “Hidamets” themselves. Here we will brieﬂy consider “engineering” and “physical” viewpoints on metallic materials with high intrinsic (“passive”) damping. Questions of active vibration control and resonance damping due to the shape or mass of a construction, as well as damping in non-metallic materials, are not subject of this chapter. One speciﬁc engineering viewpoint was summarised in a panel discussion at the International HDM Symposium, Tokyo 2002 (Igata et al. 2003b): “. . . the deﬁnition of Hidamets . . . is only possible when a particular application is speciﬁed”. This concept is directed to the practical needs for damping under speciﬁc operating conditions, but asks neither for the physical origin

3.5 Mechanisms of Damping in High-Damping Materials

149

of “high” damping nor for a more general deﬁnition of “Hidamets” as engineering materials. Consequently, under this viewpoint a material may already be called a HDM if, for one particular application, the special operating conditions (frequency, temperature) match the damping maximum of a narrow relaxation peak, while under deviating conditions the damping of the same material can be much lower. It is clear that this viewpoint, although reasonable for the speciﬁc engineering application considered, does not lead to an unambiguous classiﬁcation of Hidamets. Therefore, for such a classiﬁcation it has been suggested to specify the physical mechanisms which may reliably cause “true” high-damping properties; or in the words of Schaller (2003): “HDM . . . should exhibit high damping over a wide frequency and temperature range. In metals, only a limited number of dissipative mechanisms . . . can be used to achieve such performance. Point defect relaxations are not useful in this application because, generally, they give rise to relaxation peaks located in narrow frequency and temperature domains. A damping mechanism is active over a wide frequency range only if it is not thermally activated”. This latter, “physical” viewpoint seems more appropriate to clarify the physical (or structural) background for high damping, i.e., to deﬁne which materials should be called Hidamets (Golovin 2006a). Important steps into this direction were done in many earlier publications, to mention only a few of them: James (1969), Sugimoto (1974), De Batist (1983, 1994), Schaller and Benoit (1985), Golovin et al. (1987), Ritchie and Pan (1991b), Graesser and Wong (1992), Schaller (2001a). It is obvious that HDM must possess not only a stable and powerful source of damping but also a certain level of strength. From the viewpoints of physics as well as of engineering, therefore, the damping capacity for diﬀerent materials should be estimated under homologous conditions, like THD = n · Tmelt , σHD = m · σ0.2 (with n, m < 1, e.g., m = 0.1 (James 1969) in case of anelasticity), relating the operating conditions (temperature THD and stress amplitude σHD ) for high damping to the melting temperature Tmelt and yield stress σ0.2 , respectively. On the other hand, for many engineering applications it is desirable to consider damping at room temperature, which leads to a somewhat diﬀerent engineering classiﬁcation of Hidamets (James 1969, Sugimoto 1974) than comparing diﬀerent materials under strictly homologous temperature conditions e.g., with n = 0.3 (Golovin and Arkhangelskij 1966). Before turning to the mechanisms of high damping, a short historical survey of the problem might be useful to explain the importance of the “engineering” approach. As often found in history, the ﬁrst HDM were used by people without deep knowledge about structure and physical mechanisms. This is especially true for cast iron which has been used for centuries in countless applications, e.g., in tools and processes like forging, pressing, stamping or extruding, in order to protect people and machinery (for the eﬀect of vibration frequencies on the human body see Frolov and Furman 1990): although

150

3 Other Mechanisms of Internal Friction

being a cheap material, grey cast iron eﬀectively reduces vibration and noise at plants, fabrics, and workshops (Golovin et al. 1980, Millet et al. 1985). In the next, more recent stage, a speciﬁc damping index (SDI) was deﬁned in order to achieve a better comparability of diﬀerent materials. The SDI is the speciﬁc damping capacity Ψ measured by means of a torsion pendulum at 1 Hz, under a surface shear-stress amplitude of one tenth of the 0.2% tensile yield stress, thus denoted as Ψ0.1σY S or more shortly as Ψ0.1 . By comparing many diﬀerent materials, deﬁnitions of low-, medium- and high-damping materials were given by Ψ0.1 < 1%, 1% < Ψ0.1 < 10%, and Ψ0.1 > 10%, respectively (James 1969). Mg-based, Cu–Zn–Al, Mn–Cu and Ni–Ti alloys take the ﬁrst places in such a classiﬁcation. Already at this stage, the problem of standardisation and uniﬁcation of tests of damping capacity became very important, not to say crucial, and has not been solved up to our days. As already mentioned in the Introduction (Chap. 1), measures of damping cannot be properly transformed into each other if the damping is very high, because the relative deviations increase almost exponentially with increasing damping values (Rivi`ere 2003). Moreover, diﬀerent measuring techniques (free decay, resonance and sub-resonance methods, torsion, bending etc.) have diﬀerent limitations and accuracies in case of high damping. Several helpful conclusions and recommendations on the interrelation of damping measures for materials with high damping capacity, and on the methods of measuring high damping, can be found in the articles by Golovin et al. (1987), and Graesser and Wong (1992). A problem of comparability of damping values arises in the experimental measurements on equivalent samples performed by several laboratories both in Western Europe (organised by Rivi`ere) and in Soviet Union (organised by Blanter, Golovin and Sarrak), where a lack of agreement was reported. Considering the SDI alone is not suﬃcient for selecting materials for applications requiring high damping at a certain strength level. Consequently, the next stage was to consider the damping capacity in connection with other mechanical properties. Plotting the SDI Ψ0.1 against the ultimate tensile strength σUTS (Sugimoto 1974, 1975; Fig. 3.17), high-damping materials were characterised by a parameter α = Ψ0.1 × σUTS > 100, or even > 1000, where Ψ0.1 and σUTS are given in % and kg mm−2 , respectively (or by α > 1000 or even 10000 if SI units are used). Other authors suggested to use the logarithmic decrement δ0.1 instead of Ψ0.1 ≈ 2δ0.1 (in case of freely decaying vibrations), and the yield stress σYS instead of the ultimate tensile strength, or its ratio to the density ρ in applications where weight is important: (δ0.1 × σYS )/ρ (Skvortsov et al. 1987, Golovin and Golovin 1989, Golovin and Sinning 2003a). As another combination of properties, the loss coeﬃcient Q−1 vs. Young’s modulus E was proposed by Waterman and Ashby (1991). Most HDM are, with respect to their strength, exceptions from the common rule of thumb that damping of metals is inversely proportional to the yield stress. Such decoupling of damping and strength implies that the

3.5 Mechanisms of Damping in High-Damping Materials

151

Fig. 3.17. Sugimoto plot: speciﬁc damping index vs. tensile strength for diﬀerent metallic materials

mechanism responsible for damping should not be identical to that one controlling mechanical properties like the yield stress. One can ﬁnd in the literature of the last century a large number of diﬀerent mechanisms proposed for high damping, and many diﬀerent solutions for particular practical applications. Some high-damping alloys are well known in industry, e.g., Sonoston and Incramute (Mn–Cu based), Proteus (Cu–Zn–Al), Nitinol (Ni–Ti), Maximum (Mg–Zr based), Nivco (Ni–Co based), Silentalloy (Fe–Cr–Al based), Gentalloy (Fe–Mo–W), Trancalloy, Vacosil, etc. However, most of these Hidamets remain rather expensive materials. As an important step forward to bring more physical clarity into the problem of Hidamets (polymers and ceramics as non-metallic materials are not discussed in this book), a useful as well as simple structure-based approach was introduced by Kondratev et al. (1986), and discussed in detail by Golovin and Golovin (1989, 1990)). By considering the main “structural units” responsible for high damping (instead of the detailed physical mechanisms), all Hidamets were consistently divided into four sub-groups: 1. 2. 3. 4.

Hidamets Hidamets Hidamets Hidamets

with with with with

highly heterogeneous structure thermoelastic martensite magnetic domains easily moveable dislocations

152

3 Other Mechanisms of Internal Friction

Within these subgroups damping can be rather high, and stable with respect to varying test conditions (T , f, σ). It can be optimised with respect to other properties (strength, stiﬀness, etc.) by choosing a proper heat treatment or chemical composition, and shows as a rule of thumb a monotonically increasing amplitude dependence. On the basis of new developments, however, the addition of a ﬁfth group was recently suggested by Golovin (in the aforementioned panel discussion, Igata et al. 2003b): 5. Hidamets with extremely high hydrogen concentration. This additional group mainly consists of some amorphous or crystalline, Zr- or Ti-based alloys capable of absorbing a high amount of hydrogen. The related relaxation peaks are really high, situated not far away from room temperature, and much broader that a Debye peak (see also Sect. 2.2.4), which at least partly compensates the disadvantages of a thermally activated mechanism for damping applications. These alloys are attractive from the practical viewpoint and may be collected in one group from the physical background, i.e., easily activated hydrogen atom jumps in metallic materials. An additional advantage of this mechanism is that the high damping is amplitude-independent and occurs already at very low vibration amplitudes. In the following, these ﬁve groups of Hidamets are characterised brieﬂy with respect to their main damping mechanisms and limitations. A certain instability of the high damping values against heat treatment is a limiting factor in almost all cases. 1. Hidamets with highly heterogeneous structure. In these natural or artiﬁcial composites (see e.g., Schaller 2003, Skvortsov 2004a), the main damping mechanism is local plastic deformation of soft phases and at interphase boundaries. Examples for “natural” composites are cast iron (where the main contribution arises from dislocations in graphite), lead bronze or pseudo-alloys (e.g., Fe–Cu, Fe–Pb, Al–Zn, Al–Sn, Ti–Pb, Ti–Sn). An unlimited variety of additional opportunities and advantages is provided in case of artiﬁcial composites (including cellular metals, see later) to combine damping and other properties of metallic materials, and also to vary the properties in diﬀerent directions. 2. Hidamets with thermoelastic martensite (e.g., Van Humbeeck 1996, 2003, San Juan and N´ o 2003, Lee et al. 2003a, Igata et al. 2003a, Wuttig 2003). Here the damping is mainly due to the hysteretic movement of interphase (e.g., martensite–austenite) or twin boundaries, stacking faults or dislocations in martensite (see also Sect. 3.2.2). These materials exhibit the second highest values of Ψ0.1 after pure Mg, and in some alloys (e.g., Cu– Zn–Al) damping can be as high as in Mg if tested in a proper temperature interval. Common examples are Ni–Ti, Cu–Mn, Cu–Zn–Al, Cu–Al–Ni, In–Tl and (α + β) Ti-based alloys, but also Fe–Mn-based alloys with ε martensite are included in this group. The main limitation is the martensitic transformation temperature, as the damping in the parent austenitic

3.5 Mechanisms of Damping in High-Damping Materials

153

phase is low. Important factors are also heat treatment and the frequency of vibration, with generally lower damping at high frequencies. 3. Hidamets with magnetic domains (e.g., Kekalo 1986, Coronel and Beshers 1998, Skvortsov 2004b, Udovenko and Chudakov 2006). The main mechanism is magneto-mechanical hysteresis, causing a pronounced peak of ADIF at ε ∼ 10−4 (see also Sect. 3.4). Materials are Fe, Ni, Co and their alloys, like Fe–Cr, Fe–Al, Fe–Cr–Al, Fe–Co, Ni–Co or Co–Zr. The main limitation is the external magnetic ﬁeld, and heat treatment may also have a strong inﬂuence. While the absolute values of Ψ0.1 are lower than those of Mg, Cu–Mn or Ni–Ti, the advantage is that some Fe-based Hidamets of this type are relatively cheap and have good mechanical characteristics. 4. Hidamets with easily moveable dislocations (e.g., Sugimoto et al. 1977, Favstov 1984, Nishiyama et al. 2003, Schaller 2003, Trojanova et al. 2003, Mielczarek et al. 2006, Trojanova et al. 2006). The main mechanism is dislocation movement; see also Sects. 2.3 and 3.3. Materials are Mg-based alloys (with Zr, Ni, Si etc.) which probably exhibit the highest values of Ψ0.1 , and some austenitic steels. Heat treatment is an important factor, and low weight an additional advantage. The main limitation is the low yield stress in pure Mg, as both damping and strength are controlled by the same mechanism, i.e., dislocation mobility. The problem can be solved at least partially by creating structures of natural composites as suggested by diﬀerent authors (Table 3.2).

Table 3.2. Damping in some Mg alloys (group 4) (a) James (1969), Driz and Rokhlin (1983), Favstov (1984) alloys (group 4)

σ0.2 (MPa)

Ψ0.1 (%)

21 61 45 52 120 130 190 280

60 48 60 52 4 0.27 6.5 0.2

Mg 99.9% Mg 99.9% Mg–0.6Zr Mg–0.7Si Mg–9.8Al–0.2Mn Mg–9Al–2Zr–0.2Mn Mg–3Al–1Zn–0.4Mn Mg–3Th–1.2Mn

state as cast CW as cast as cast as cast as cast CW CW

(b) Schaller (2003) alloys (group 4) Mg–5Ni Mg–10Ni Mg–15Ni Mg–22.6Ni (eutectic) Mg–6Al–3Zn (AZ63)

σ0.2 (MPa)

Ψ (%) (ε = 10−5 )

Q−1 × 103 (ε = 10−5 )

68 117 163 170 113

4.7 4.6 3.8 1.5 0.1

7.5 7.4 6.1 2.4 0.2

154

3 Other Mechanisms of Internal Friction

5. Hidamets with extremely high hydrogen concentration. Depending on the alloy structure (amorphous, quasicrystalline or crystalline), the main damping mechanism may be either a strongly broadened, pure Snoek- or Zener-type hydrogen reorientation or a coupled process involving both H diﬀusion and motion of matrix defects, like twin boundaries in the presence of a martensitic transformation (cf. Sect. 2.2.4). Materials include bulk metallic glasses (mostly Zr-based; see e.g., Mizubayashi et al. 2003, 2004b, Hasegawa et al. 2003, Yagi et al. 2004, Sinning 2006a) as well as NiTi(Cu) shape-memory alloys (Biscarini et al. 1999a, 2003a,b; Mazzolai et al. 2003, Coluzzi et al. 2006). Here the temperature range of eﬀective damping may be limited either by the vibration frequency in case of relaxation peaks (often situated slightly below room temperature at 1 kHz), or (as in group 2 earlier) by the martensitic transformation temperature in case of H-enhanced “transformation” peaks. Another limiting factor is the necessity to introduce hydrogen into the alloys and to keep it inside. Although this structure-based distinction of ﬁve groups has clearly improved the classiﬁcation of Hidamets, it may be subject to further modiﬁcation during the continuing development of novel materials. As an example we may think of nanostructured metals: it has been reported that nanostructured Cu (Mulyukov and Pshenichnyuk 2003) and Al (Koizumi et al. 2003), produced by severe plastic deformation (SPD), can exhibit relatively high damping due to a contribution of grain boundary dislocations (in combination with a signiﬁcant increase in yield strength), as compared to the undeformed state. At present these results remain questionable in view of other publications where an increase in damping due to SPD was not observed. In addition, several IF peaks at diﬀerent temperatures are enhanced by SPD (cf. Sect. 2.4.3 and Table 2.18). Highly porous cellular metallic materials (CMM) form another type of relatively new, rapidly developing engineering materials, attractive from the viewpoint of low weight. In the above classiﬁcation CMM may belong to the ﬁrst group (“highly heterogeneous structure”), although the variety of possible damping mechanisms in CMM is reduced as compared to “true” composites: in CMM like metallic foams, sponges or porous (sintered) metals, most damping contributions come from the same basic mechanisms as in dense metals. It is the combination of the existing damping mechanisms with the mechanical properties and the extremely low density which makes these materials interesting: the capability of damping mechanical vibrations, when estimated by complex parameters which also consider strength, stiﬀness and weight, demonstrates some advantages of CMM compared to the dense materials they are made from (Golovin and Sinning 2003a, 2004). Studied in a wide range of vibration amplitudes (Han et al. 1997, Liu et al. 1998a,b, 2000, Golovin and Sinning 2002, 2003a, 2004), three amplitude ranges of IF in CMM can be distinguished in a similar way as

3.5 Mechanisms of Damping in High-Damping Materials

155

considered earlier for dislocation-related ADIF (Sect. 3.3): an amplitudeindependent range with linear relaxation (including thermoelastic damping), a ﬁrst amplitude-dependent range with reversible hysteresis eﬀects, and a second one with irreversible phenomena connected with fatigue problems. The critical point in CMM is the quantitative modiﬁcation of the diﬀerent, known damping mechanisms determining the extension of and the transitions between these ranges, which has as yet been treated only in relatively simple models (Golovin et al. 2004a, Arkhipov et al. 2005, 2006) and remains still an open problem for real cellular structures. Whereas from this viewpoint the direct applicability of CMM as Hidamets is unclear, Al foams have already found related, dissipative applications for sound and energy absorption (when crashed) in cases where weight minimisation is demanded (Gibson and Ashby 1997, Banhart et al. 2001). Absorption coeﬃcients for airborne sound as high as 90% have been found even for some closed-cell foams (Gibson and Ashby 1997, Ashby et al. 2000), although other authors report lower values (Han et al. 1998, Kovacik and Simancik 2002). Open-cell sponges with interconnecting pores are in principle more appropriate for this kind of aerodynamic losses in the surrounding atmosphere which are, however, beyond “internal” friction and hence outside the topic of this book. To sum up, there are two main viewpoints on high-damping materials. The ﬁrst, “engineering” approach regards the damping of vibrations or noise under the speciﬁc conditions of a particular application; any material which is able to give the desirable damping at the chosen conditions – whatever the mechanism of damping is – is a high-damping material under this viewpoint. Within the second, “physical” approach, high-damping metals are deﬁned, instead of varying application conditions, on the background of the most powerful damping mechanisms acting in the material, as resulting from its structure and physical properties.

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

In the following tables we attempt to collect the experimental material about internal friction produced by anelastic relaxation in crystalline metals and alloys, as published until mid 2006. If not speciﬁed otherwise, the data refer to temperature-dependent mechanical loss peaks, including (a) the measured primary quantities vibration frequency (f), temperature (Tm ) and height (Qm −1 ) of the damping maximum, (b) the related activation enthalpies (H) and preexponential times (τ0 ) if available, and (c) the specimen conditions and probable relaxation mechanisms. Comments and further parameters, if necessary, are added directly on the spot. Each table starts with a brief summary of important features of internal friction in the considered group of metals and alloys, and of the observed relaxation mechanisms. The data collection is strictly conﬁned to metallic materials, i.e., data on ceramics, semiconductors or polymers are not included even in cases where the same mechanisms occur as in metals. Experimental results refer exclusively to dynamic measurements (sub-resonance and resonance vibrations as well as ultrasonic waves), whereas quasi-static creep, stress relaxation or elastic after-eﬀect data are not considered. That means, slow phenomena like viscous ﬂow or Gorsky eﬀects are included only if studied, with dynamic methods, in form of damping of vibrations. The selection of data is further restricted to those studies in which the information on relaxation has really been evaluated. So, for instance, a big volume of work is intentionally omitted that concentrates on amplitudedependent internal friction phenomena (see some indications on data in this ﬁeld in Sect. 3.3). Another limiting area is that of low-temperature physics (at liquid helium temperatures and below): such data are mentioned only occasionally as part of a broader characterisation of a material, whereas exclusive low-temperature studies e.g., on tunneling systems or spin glasses are generally omitted as well. In some cases, earlier data collections have been used and are referred to, rather than citing the original papers. Of course, the present collection cannot

158

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

be fully complete and exhaustive, and the authors apologise for not having detected all the relevant publications. It should be noted that the data and mechanisms given in the tables are those provided by the authors of the cited papers; no judgment as to the accuracy of values or plausibility of mechanisms has been attempted from the view of present knowledge, except for some rare cases in which later papers question the proposed mechanism. The task to judge each value would be formidable and even impossible to fulﬁll with the available information. For the same reason we have to renounce indications of error limits to the values given in the tables; in cases of doubt, primary data like Tm are generally more reliable than evaluated parameters like H or τ0 . For more information the reader has to consult the original papers referred to. The order, in which the data for the diﬀerent metals and alloys are presented, largely follows the groups of metals in the Periodic Table of the Elements, with alphabetical order within each individual table (cf. the headings given in the table of contents). In each case the values are presented ﬁrst for the pure metal, and then for binary, ternary and more complex alloys in succession. The compositions are given either in weight or in atomic percent as speciﬁed at the beginning of each table, owing to the fact that in the literature diﬀerent styles are prevailing for diﬀerent metals (depending on their diﬀerent use in research and application). If subscripts are used for the composition (as often in multi-component alloys and intermetallic compounds), they always mean atomic concentrations or stoichiometries. Entries in the tables belonging to diﬀerent alloys, diﬀerent qualities (e.g. purities) of elemental metals, or in some cases groups of alloys with certain concentration ranges, are separated by thin horizontal lines. In general, the entries in each column, within such a block between the horizontal lines, apply also to the following lines if these are empty. On the contrary, a hyphen in a cell means that the preceding entry does not apply to this cell. For some special groups of multi-component alloys with particular structures or properties (hydrogen-absorbing alloys, metallic glasses, quasicrystals), which do not ﬁt well into the above ordering scheme, the data are compiled in the Tables of Chap. 5 (see also the introduction to this table).

4.1 Copper and Noble Metals and their Alloys Copper with its alloys is one of the most thoroughly investigated metals. Thus, nearly all kinds of known relaxation eﬀects have been found in the group of Cu and noble metals. The following internal friction eﬀects have been observed: In pure metals: – Point defect related peaks (PD), in particular after irradiation, in Ag, Cu;

4.1 Copper and Noble Metals and their Alloys

159

– Intrinsic dislocation related relaxations (DP), namely Bordoni (B1 ) and Niblett–Wilks (B2 ) peaks in Ag, Au, Cu, Pd, Pt; Hasiguti peaks (P1 , . . . , P4 ) and other not speciﬁed DP, in Ag, Au, Cu; – Low temperature background (probably dislocation related) in Ag, Au, . . . ; – High temperature background (related to dislocations, diﬀusion, recovery or recrystallization), in Au, Cu – Grain boundary related relaxations (GB), sometimes involving impurities or particles, often associated with grain boundary sliding, sometimes with special boundaries like twin boundaries, sub-boundaries, in Ag, Au, Cu, Ir – Zener-type relaxations with divacancies in Au – Overdamped dislocation resonance (MHz range) in Cu, etc. In solid solutions: – – – –

Point defect related relaxations (PD), in Ag-based solid solutions; Snoek–K¨ oster relaxations (SK) (involving dislocations) in Pd–H Zener peaks (Z), in Ag-, Au-, Cu-, Pd-based solid solutions Peaks due to phase transformations of various kinds, including ordering, martensitic transformation – Grain boundary (GB) and interface relaxations, associated with diﬀusional stress relaxation at interfaces between matrix and precipitates. In pure Ag and Cu, as well as in Cu–Zn and Cu–Ni–Zn alloys, thermoelastic damping by transverse and intercrystalline thermal currents has been observed.

f(Hz)

240

1.5

8 · 103 –8 · 105

1000

0.7 1.5

1

20

600

0.2

composition

Ag Ag

Ag(99.999)

Ag(99.8)

Ag(99.99)

Ag(99.999) Ag(99.99)

Ag(99.999)

Ag(99.9)

Ag(99.999)

Ag(99.999)

45–85 55 850

173 200 245 61 523 630 436 629 280

410 580 80

293

mechanism state of specimen

8–108 6 40

60 185 60 38 39 30

55 190 25

147

172 235

21 35.5 44 9.6

99 167 12

1 · 10−9

3.8 · 10−22

5 · 10−10 5 · 10−13 5 · 10−13 1.6 · 10−12

2.5 · 10−13

GB, jogs

DP(B1 )

DP(P1 ) DP(P2 ) DP(P3 ) DP(B2 ) GB GB GB GBI DP/interstitials

GB GBI DP(B2 )

PC, CW at 77 K SC, CW PC bamboo structure

annl.

CW annl.

CW

CW

annl.

30 incl. bgr. ﬁrst report of IF peaks as transverse wire, diam. a function of frequency thermal currents 1.01 mm

Tm (K) Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.1. Copper and Noble Metals and their Alloys (at.% if not speciﬁed diﬀerently)

Okuda (1963a,b,c) Postnikov et al. (1963) Cordea and Spretnak (1966) Pstroko´ nski and Chomka (1982) Mecs and Nowick (1969) Roberts and Barrand (1969b)

Bennewitz and R¨ otger (1936), after Zener et al. (1938) Pearson and Rotherham (1956) Bordoni (1960), Bordoni et al. (1960a,b) Hasiguti et al. (1962)

reference

160 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

45–70 456 666

∼1 ∼1 1 (ﬂ = ﬂexural, to = torsional vibration)

Ag(99.9999)

Ag(99.999)

Ag (collected data from literature) Ag(99.995)

60

∼103

40

740 937

521

∼103 ∼103 ∼103

Ag(99.95) Ag(99.998) Ag(99.995) +Cu(50) ppm Ag(99.995) +Cu(150) ppm Ag(99.999)

1

18 88 23 40 (ﬂ) (to) (ﬂ) (to)

15–60

10–6

3.5

93.6 – 99.7 – 149 116 8.7 8.7–12.5

–

164 –

495 533 500

1

Ag(99.999) 13.5 30 9.5

435 305–785 85 526 67–170 109 588 188–595 166 741 256–961 193 Qm −1 dependent on grain size 456 35 96

0.3

Ag(99.999)

3 · 10−12 – 10−9 – 10−11 3 · 10−8 2 · 10−12 10−12 − 10−13

10−12

2.3 · 10−11 4.9 · 10−12 2.1 · 10−15 1.5 · 10−14

DP DP DP(B1 ) DP(B2 ) PD(int)

DP

DP

DB(B)

DP(B)

DP

GB

irr(e)

CW, annl., recr. CW, annl., recr. SC, PC

CW, annl., recr.

annl.

CW, annl., recr.

Fantozzi et al. (1982) orner and B¨ Robrock (1985)

Stadelmann and Benoit (1977) Stadelmann and Benoit (1977) Rivi`ere et al. (1981)

Isor´e et al. (1976)

Povolo (1975)

Woirgard et al. (1974)

4.1 Copper and Noble Metals and their Alloys 161

1

5 · 103

0.8–1

Ag(99.999)

Ag(99.999)

Ag(99.999)

(10

40–85

1 1

Ag–Cd(29) Ag–Cd(39) 503

591–541

1

Ag–Cd(21–35.3)

∼100

2.7–20

Qm

1 2 400 130 50 10–100 500 13 230 280–390 40 390

430–400

40 60 0.4–150

Tm (K)

solutions 40 40 0.36 733 0.36 613 0.36 623 1 637–771 0.36 733 1.5 510 708 Ag–Cd(3.5–15.8) 1.5 725–703 Ag–Cd(32.4) 1.5 533 640 Ag–Cd(32) 0.6 493

Ag binary solid Ag–Al(0.1) Ag–Au(0.1) Ag–Au(42.1) Ag–Au(58.5) Ag–Au(68) Ag–Au(25–80) Ag–Au(42) Ag–Cd(0.88)

f(Hz)

composition

−1

−4

152.3 123

152–140

– 183 – 176 165.3 – 170 184–189 – 159 147

85

12.5

(9–0.7)·10−15

GB

10−11

Z Z

Z

PD(int) PD(int) GB GB GB Z GB GB GBI GBI GB GBI Z

DP(B1 ) DP(B2 ) LT bgr.

annl. 600◦ C

irr(e) irr(e) PC various grain size

nc Gas depos.

sput.th.f.

mechanism state of specimen

7 · 10−13

) H(kJ mol−1 ) τ0 (s)

Table 4.1. Continued

Turner and Williams (1962) Shtrakhman and Piguzov (1964) Mills (1971)

Turner and Williams (1963) Pearson and Rotherham (1956)

B¨ orner and Robrock (1985) Turner and Williams Jr. (1960)

o and San Juan N´ (1993) Xiao Liu et al. (1999) Y. Wang et al. (2001)

reference

162 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

500

10−3 –10−1

1.6

1.5

0.4–1.8

0.7–30

Ag–In(10.8–18.1)

Ag–In(16)

Ag–In(1–16)

Ag–La(50)

Ag–Mg(12–25)

483–543 723–628 123–450 640

543 6–15 320–350 20 100

145

100

– 172–188 – 70 176–151

147–140

10−16.7 – 10−14.3

Z Z

GB GBI

Z

Z

Z Z

159–133 153–130.5

PhT(ξ ↔ ξ )

3–30 580–536

1 1

Ag–In(7.5–15.6) Ag–In(9.6–17.9)

10−12.5

PD

388

Ag–Ge(0.1)

135

PhT(β ↔ ξ) PhT(ξ ↔ β) PhT(Θ) PD(int) PD(int) PD

PhT(β → β )

0.7

1

Ag3 Ga 44

2500

533–638

613

Ag–Cu(0.1)

Ag–Cu(0.1)

75–80 1 10 0.2–1.7

450–530 730 590–570 25 40 35–75

0.4–2.5

700

Ag–Cd(50)

193

1

Ag–Cd(45)

annl. 600◦ C

annl. 600◦ C

irr(n)

irr(n)

irr(e)

quen.

quen.

orner and B¨ Robrock (1985) Kobiyama and Takamura (1985) Artemenko et al. (1975) Kobiyama and Takamura (1985) Mills (1971) Finkelshtein and Shtrakhman (1964) Williams and Turner (1968) Childs and LeClaire (1954) Pearson and Rotherham (1956) Artemenko et al. (1975) Banerjee and Millis (1976)

Sharshakov et al. (1978b) Artemenko et al. (1975)

4.1 Copper and Noble Metals and their Alloys 163

274

440

1.5

10−3 –10−1

Ag–Si(0.2)

Ag–Sn(0.05)

Ag–Sn(0.93)

Ag–Sn(8.1) 40 38–74

Ag–Zn(0.05)

470 610 550

72

Ag–Zn(0.1)

255

510

10−3 –10−1

Ag–Sb(6.3) 34–92

38–44

393

Ag–Pb(0.1)

423 523 48–74

365

0.4–1.8

Ag–Mg(50)

Ag–Sb(0.1)

20

Ag–Mg(25.3)

270 255 255

40

20

Ag–Mg(23.2)

0.2

1

6 350 25

0.2

0.5

25

0.3

1

10 20 40 5 5 60 0.1

Tm (K) Qm

Ag–Pt(0.1)

f(Hz)

composition

−1

(10

−4

– 172 131.8

136

– 77

mechanism state of specimen

PD(Zn/int)

PD(int)

GB GBI Z

PD(Sn/int)

PD(Si/int)

Z

PD(Sb/int)

PD(int)

irr(n)

irr(e)

annl. 600◦ C

irr(n)

irr(n)

irr(n)

irr(e)

No peaks DP/interstitials, ordered in unde- impurities disord. formed ordered state disord. annl. 600◦ C PhT(ξ → β ) Z PD(Pb/int) irr(n)

) H(kJ mol−1 ) τ0 (s)

Table 4.1. Continued

Artemenko et al. (1975) Kobiyama and Takamura (1985) B¨ orner and Robrock (1985) Kobiyama and Takamura (1985) Williams and Turner (1968) Kobiyama and Takamura (1985) Kobiyama and Takamura (1985) Pearson and Rotherham (1956) Williams and Turner (1968) B¨ orner and Robrock (1985) Kobiyama and Takamura (1985)

nski and Pstroko´ Chomka (1982)

reference

164 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

100

398 513 573–600 713

1

115

0.7 1.6 · 104

0.5

Au(99.99)

Au(99.88)

Au(99.999) 43 65 77

511 677 603

1

Au(99.9998)

Au Au (collected data from literature)

90–130

570–533

1

25 – 30

20

220 160

50

60–70

533–505

0.7

10–490

300

Ag–Zn(15–30) Ag ternary alloys Ag–Al(14.3–25)– Mn(14.3–25) Ag5 MnAl

510

120

763–633

0.6

Ag–Zn(17)

533

Ag–Zn(3.7–30.25)

0.7

Ag–Zn(15)

9.6 18.4 18.3

15.2

6.5 15.2 −19.3 144.3 242.7 141.4

150–139

142–136

140

PC, CW

CW

2.3 · 10−11 DP(B2 )

DP(B1 ) DP(B2 )

5 · 10−13 1 · 10−13

CW, annl.

quen. 780◦ C

annl. 780◦ C

CW, annl.

PhT(β) PhT(γ2 ) Z PhT(α ↔ β)

Z

Z

Z

Z

DP(B1 ) 3 · 10−10 1.5 · 10−13 DP(B2 ) 1.4 · 10−11 GB GB GB

10−14.6 – 10−14.4

10−14.6

Z

Marsh and Hall (1953) oster et al. K¨ (1956b) Bordoni (1960), Bordoni et al. (1960a,b) Okuda (1963a,b,c)

Fantozzi et al. (1982)

Sharshakov et al. (1981)

Putilin (1985b)

Pirson and Wert (1962) Kobiyama and Takamura (1985) Seraphim and Nowick (1961) Nowick (1952) 4.1 Copper and Noble Metals and their Alloys 165

1

1

0.5

1.3 · 104

Au(99.999)

Au(99.99995)

Au(99.999)

Au(99.999)

45 77 200–210

Au(99.9999)

1

113

10

15 · 103

120 200. . . 190 63 113 93–118 – 36 – 68 273

130 190 220 160 230 290 210 673

Tm (K)

Au(99.99)

Au(99.9999)

4

Au(99.999)

104–5 7 · 104

f(Hz)

composition

20 30 50

3 2. . . 45 1.3 1.4 – – 0.05 – 0.05

10 100 30 10 10 20 2 500

6.5 19.3 11.6 – 14.5 – 11.6 62.7

57.7 435

21.4 32.9 34.7

2.5 · 10−10 1.3 · 10−13 1.6 · 10−10 – 4 · 10−12 – 2.5 · 10−10

5 · 10−10 – 3 · 10−10

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.1. Continued

DP(B1 ) DP(B2 ) DP(P1 )

DP(B)

DP(P1 ) DP(P2 ) DP(B1 ) DP(B2 ) DP(B2 ) DP(B1 ) DP(B2 ) DP(B1 ) DP(B2 ) Z(divac)

Z(divac) GB sliding

DP(P1 ) DP(P2 ) DP(P3 ) DP DP

mechanism

De Morton and Leak (1967) Benoit et al. (1970)

Neumann (1966)

Okuda and Hasiguti (1963)

reference

CW

quen. 1000◦ C

SC 111 Franklin and Birnbaum (1971) Stadelmann and Benoit (1977) Bonjour and Benoit (1979)

CW annl. PC, CW, irr(n) Grandchamp (1971) SC 100 SC 110

quen. 800◦ C quen. 1100◦ C annl. 900◦ C

quen. 700◦ C

CW

state of specimen

166 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

0.3–3 · 103

1 270–470

5 · 103 340 145

Au(99.9999)+ Pt(10–1000) ppm Au(99.9999)

Au

Au(99.99)

Au(99.999)

Au(99.9999)

Au

4 · 103

Au(99.9999)+ 4 · 103 Cu(10–1000) ppm Au(99.9999)+ 1 Pt(10–500) ppm

Au(99.9999)+ Cu(10–500) ppm

60, 90

110 30, 50

60

30 50 400–550 0.8–3

70 370 –

20–10 30–13 24–12

45–50 78–83 105–115 60 100 180 40 80 120–130 210 430–450 0.5–100

23–2

19–4 28–6 40–17/8

47–530 80–90 200– 175/215 105–115

∼19

18.3

7 · 10−13

double peak

GB

GB

DP(B1 ) DP(B2 ) DP(B) DP(P1 ) recovery LT bgr.

DP

CW (10 K)

DP(B1 ) DP(B2 ) DP(B)

Okuda et al. (1994)

o and San Juan N´ (1993)

Baur and Benoit (1986)

Bonjour and Benoit (1979)

Bonjour and Benoit (1979)

Xiao Liu et al. (1999) nc. Gas depos. Tanimoto et al. Ribbon (2004a) nc. Gas depos. Tanimoto et al. Ribbon, irr(e), (2004b) irr(p)

Sput.th.f.

Gas depos. thin ﬁlm

Study of IF background

CW (300 K)

CW (300 K)

CW (10 K)

DP(B)

DP(B1 ) DP(B2 ) DP(Pi )

4.1 Copper and Noble Metals and their Alloys 167

f(Hz)

1 1 1 ∼0.5 0.7 0.2–1

0.7

Au–Fe(5–7)

Au–Fe(10–27) Au–Ni(7.7–90.8) Au–Ni(30) Au–Zn(15)

Au–Zn(50)

Au ternary alloys Au–Ag(42)–Zn(15) 0.5

1

Au3 Cu (Au–Cu(25))

Au–Cu(21–42)− Zn(15–17)

0.75

Au3 Cu

Au binary solid solutions ∼1; 5 · 104 ; Au–Cd(46.1–52.5) 5 · 106 Au–Cu(10–90) 1

composition

200 300 400 12–85 75–60 175–75

490 625 760 638–653 808–837 663 670–925 ∼653 523

550 2500–700

573–653

50

533

533–563

250–100 >20 700–3800 5–20

448–523 600–665 825–1102 170–230

320

40–160

146

140

– 190 240 159 177.8 151 182–251 88.3 218

– 115–165 202–342

PhT(ord)

Z

PhT(ord) + vac

PhT(ord) Z GB Z PhT(Fe) Z Z Z(vac) Z

GB Z GBI anom. peak

PhT(mart)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism

300–360

Tm (K)

Table 4.1. Continued

annl.

quen.

quen., CW, annl. quen. only quen., annl.

state of specimen

Pirson and Wert (1962) Pirson and Wert (1962)

Ang et al. (1955) Cost (1965b) Pirson and Wert (1962) Mukherjee (1966)

Mynard and Leak (1970)

Iwasaki (1986c)

Y. Wang et al. (1981) Maltseva et al. (1963); De Morton and Leak (1967) Iwasaki (1981a)

reference

168 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

(0.5–10)106

1.09 · 104

1

1.5 1 1 5 600

1.2

Cu(99.999)

Cu(99.999)

Cu(99.999)

Cu(99.999)

Cu(99.999)

Cu(99.987)

Cu(99.999)

2 · 104 –6 · 106

Cu (techn. purity, (99.7))

488 573 30 70 190 483

149 166 240 22

80. . .100 60 135 38 79

40

293

Cu Cu

900

613

Au–Cu(63)–Zn(17) 0.5 Z Pirson and Wert (1962)

23 incl. IF peak as a function of transverse cold roll. 0.45 mm Zener et al. (1938) bgr. frequency thermal currents ≈5 4 DP(B1 ) Bordoni (1960), 1 · 10−9 PC, CW, annl. Bordoni et al. DP(B2 ) ≈30 11.8 (1959, 1960a) 1.2 · 10−11 4.8 DP(B1 ) SC Alers and 5 · 1013 DP(B2 ) 10.9 1 · 10−12 Thompson (1961) 4.2 V¨ olkl et al. (1965), DP(B1 ) SC, CW Niblett and Wilks 11.7 DP(B2 ) (1956), Sack (1962), Okuda (1963a,b) DP(P1 ) CW Koiwa and Hasiguti 26 31 10−12 DP(P2 ) – (1963) 34 1.7 · 10−12 DP(P3 ) – 41.5 1.2 · 10−10 DP(B1 ) CW Okuda (1963b,c) 0.3 4.3 2.5 · 10−11 11.6 DP(B2 ) 157 GB Peters et al. (1964) 156.9 GB annl. DP(B1 ) quen., CW Mecs and Nowick DP(B2 ) (1965) DP(P) GB CW, annl. 165 132 Cordea and 2 · 10−15 Spretnak (1966)

130

4.1 Copper and Noble Metals and their Alloys 169

∼1

Cu(99.9999)

0.6

0.3

6 · 106 1 · 104 1

4 4 4 4 0.6 0.6

Cu(99.999)

Cu (electrolytic purity)

Cu(99.999)

Cu(99.999)

Cu(99.999)

1.6

Cu(99.999)

Cu (spectro1 scopical purity

f(Hz)

composition 689 1008 570 820 970 150 173 225 1110 660 730 140 225 240 165 105 – 550 690 590 715 835 950 540 670 – 30 50 200 30 60 30 10 10 70

145 70 200 24 38 11 650 60 10

– 16.4

435 169.5 154 290 445 30 63 100 201 – – 10−11.2 – –

10−13.3 10−12 –10−21 10−21.4

Tm (K) Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

GB twin boundaries GB DP(P1 ) DP(P2 ) DP(P3 ) GB(HT), jogs DP(P2 ) DP(P3 ) DP(divac) disl.(vac) disl.(int) disl.(int) DP(B1 ) – DP(P1 )? DP(P2 ) DP(P1 ) DP(P2 ) DP(P3 ) DP(P4 ) DP(P1 ) DP(P2 )

GB sliding

mechanism

Table 4.1. Continued

Woirgard (1974)

Besson et al. (1971)

Bajons and Weiss (1971)

Roberts and Barrand (1969b)

Iwasaki (1981b)

De Morton and Leak (1966, 1967) Williams and Leak (1967b)

reference

SC, CW, annl. 900◦ C

SC, CW, annl. Woirgard et al. (1975) 600◦ C

PC

SC, CW

fatig.

bamboo structure

CW

annl. 400◦ C

state of specimen

170 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

293

293

(1–5) · 107 (1–9) · 109 107 –8 · 107 107 –2 · 108 2

103 –2 · 104 200–400

Cu + Au(50) ppm

Cu(RRR=1100) +Fe(100) ppm (RRR=15) Cu(RRR=1100)

Cu(RRR=2200)

Cu(99.999)

Cu(99.999)

Cu(99.9999) 32 65

170 220 270

273–50

13

Cu

Cu(99.999)

12

Cu(99.999) Cu(99.999)

740 910 550 30 50 170 25 60 343 353 135–165

0.6 0.6 1 1.5

10.6 –9.6

3.8 13.5

92.6

2 4

30 5 5

γ dose-dependent

50 60 – 50 70 20 17 17 9.4 · 10−13 16 · 10−13

1 · 10−9 1 · 10−12

10−10

DP(P2 ) DP(P3 ) DP(P4 ) peaking eﬀect DP(B1 ) DP(B2 )

ODR

DP(P3 ) DO(P4 ) DP DP(B1 ) DP(B2 ) DP(P2 ) DP(B1 ) DP(B2 ) DP(B) DP(B) DP(B)

SC, PC, irr(γ, e)

SC 111 compr., irr(γ) SC, CW, annl., irr(γ) intern. oxidised

internally oxidised

SC 110 SC 100

SC, CW

CW

Caro and Mondino (1981a,b) Lauzier et al. (1981)

Marx et al. (1981)

Lenz et al. (1981)

Schmidt et al. (1981b)

Soifer and Shteinberg (1978) Farman and Niblett (1980) Schulz and Lenz (1981) Schmidt et al. (1981a)

Povolo (1975) Lauzier et al. (1975)

4.1 Copper and Noble Metals and their Alloys 171

1 (1–5) · 107 15 15 5 · 106 5 · 107

Cu

Cu(RRR=1500)

Cu(99.997)–nc Cu(99.98)–nc Cu(99.98)–nc Cu(RRR=1500)

Cu(99.95)

Cu(99.99) 1

1

Cu(99.999)

Cu (collected data from literature)

f(Hz)

composition

383 453 433 170 155

140 155 220 516 708 926 30 56 128–173

556 732 868

Tm (K) Qm

−1

(10

−4

132 181 237 – 13.5

8.3 17.4

91.7 168 250 3.8–4.8

mechanism

5 · 10−13 − DP(B1 ) 10−9 DP(B2 ) 10−15 − 2 · 10−10 DP(P1 ) DP(P2 ) DP(P3 ) GB(LT) GB(IT) GB(HT) DP(B1 ) DP(B2 ) 7 · 10−13

τ0 (s) )H (kJ mol−1 )

Table 4.1. Continued

Moreno-Gobbi and Eiras (1994)

SC, CW 3% SC, CW 10%

ufgr, nc

Moreno-Gobbi and Eiras (1993) Soifer (1994)

o and San Juan N´ (1993)

Ashmarin et al. (1990)

Quenet and Gremaud (1989)

Fantozzi et al. (1982)

Rivi`ere et al. (1981)

reference

SC, CW

CW, annl. CW CW, annl.

CW

SC, PC

state of specimen

172 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.6

0.7

3

160

Cu(99.99) N-implanted

Cu(99.99)

Cu(99.95)–nc

Cu(99.99) Cu(99.99999) Cu (zone reﬁned)

20–60 100–200

1000 570–600 750

DP GB + disl. + irr.defects 30 560 DP 70–120 680 GB + disl. + irr.defects No IF peak in nc material (contrary to recrystallised sample with grain size 32 µm: peak at 123 K) 75–100 recrystalSmall peak depending on heating rate and impurities lisation

<100

DP(B1 ) DP(B2 ) GB

DP(B2 ) kink pairs at jogs DP(B)

GB + disloc. dragging and depinning

0.2

Cu(99.99)

40 65 500 750 700–950 11.6 –

5

Cu(99.999) 10 30 50–180

Depending on purity and annealing 5–300 7.14

(1–5) · 107

5–100

∼65

200

Cu(99.99) Cu(99.99999) Cu (zone reﬁned) Cu(99.999)

grain size 30–60 nm PC, CW, annl.

PC, CW, irr(n)

PC, annl. 1107 K 1 h 4h SC 111 irr(n)

SC

PC

PC, CW, annl.

Lee and Okuda (1997)

Weins et al. (1997)

Lambri et al. (1996a)

Lambri et al. (1996d) Lambri et al. (1996c)

Moreno-Gobbi et al. (1996) Ghilarducci et al. (1996)

Okuda and Lee (1995), Okuda (1996)

4.1 Copper and Noble Metals and their Alloys 173

1

Cu(RRR=1500)

Cu(99.95) OFHC

5 · 103 9 · 10−4

Cu–Ag(0.1)

Cu–Al(0.5)

Cu binary solid solutions Cu–Ag(0.03) 540 223 283 150 240 350

68

110–145

1 4 80

0.1

0.5–22

5–20

200 – 73–54

34.3 50.5 60.5

27

5 · 10−10 1.5 · 10−9 10−10

4.6 · 10−13

300

(1–2) · 107

Cu(RRR=1500)

Cu(99.98; 99.99) 0.3–3 without and with H

65–60 150–170 130–170

10–20 (1–3) · 107 (1–5) · 107

Cu(RRR=1500)

120–300

Peak after 20–40% of total fatigue life

(2–5) · 106

Cu(99.99) 13.5 6.8 7.5

0.4–200

5.5 · 103

Cu(>99.9) 6–9

Tm (K)

f(Hz)

composition

τ0 (s) Qm −1 (10−4 ) H (kJ mol−1 )

Table 4.1. Continued

DP(Ag) PD

PD

DP(disl. in cell walls) DP(P) by oxidation, vacancies relax. due to H

DP(B) DP(B) DP(B)

LT bgr.

mechanism

SC, CW

CW

irr(n)

SC 111 CW electrochemical oxidation CW, recov. El.chem. H loading

SC, CW

SC, CW

PC, fatig.

sput.th.f.

state of specimen

Kobiyama and Takamura (1985) Iwasaki et al. (1980) Tonn et al. (1983)

Aaltonen et al. (2004)

Jagodzinski et al. (2000a)

Xiao Liu et al. (1999) Hirao et al. (2000) Moreno-Gobbi et al. (2000) Moreno-Gobbi and Eiras (2000) Eiras (2000)

reference

174 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

145

1.5 · 107 1

1

1.1 1 ∼2 0.66 0.1 0.1 0.1 0.1 1–16

Cu–Al(2–10)

Cu–Al(3.1–7.3)

Cu–Al(9.3–11.4)

Cu–Al(10)

Cu–Al(10.1) (wt%)

Cu–Al(15) (wt%) Cu–Al(16.8)

Cu–Al(3.1) Cu–Al(7.3) Cu–Al(11.4) Cu–Al(14) Cu–Al(3–19)

1–20 3 peaks

689 618 – – 640–700

553 545 213 633 4 7 18 27 ∼120

35

903–1068 1213– 1325 1195–992 1328– 1124 700–850 (heating)

823 250 200–143

1 1.6 1.6

Cu–Ag(0.71) Cu–Ag(2–15) Cu–Al(0.01–1)

166 170 180 192 166–183

174.9

192–220 154–192

192–145 160–125

24

193

1.6 · 10−14 1.7 · 10−14 1.5 · 10−15 1.2 · 10−16 1.6 · 10−14 − 2 · 10−16

10−10 –10−11 10−7 –10−8

10−11 –10−9 10−6

6 · 10−52

Z Z Z Z Z

Z

PD(vac) ordering.

PhTβ → β

DP(B)

GB DP(solute)

SC

quen., annl. slow cooling CW

quen. 950◦ C

SC, CW

SC, CW

CW, annl. CW, annl. ADIF CW

Rivi`ere and Gadaud (1996)

Sharshakov et al. (1978c) Lebienvenu et al. (1981b) Iseki et al. (1977) Li and Nowick (1956) Belanui et al. (1993)

Belhes et al. (1985)

Kayano et al. (1967) Belhes et al. (1985)

Peters et al. (1964) Kong et al. (1981a) Ishii (1994)

4.1 Copper and Noble Metals and their Alloys 175

675–752 704–741 662

680 800 560 730

1

1

837

∼1 1 1 1 0.35

2.5–52 6–114 8 · 104

1.6

1

Cu–Au(0–100)

Cu3 Au

Cu–Au(0.02)

Cu–Au(1.5) Cu–Au(12–25) Cu–Au(18) Cu–Au(25) Cu–Au(5)

Cu–Au(18) Cu3 Au Cu3 Au (Cu–Au(25))

Cu3 Au

Cu–B(0.38)

223 670–690 780 770

290–400 400 – – 653 873–930 12–87

0.1

Cu–CuAlO

Tm (K)

f(Hz)

composition

173 188

4 · 10−15 3.2 · 10−16

– 6.9 · 10−10 5 · 10−24 –3 · 10−14

τ0 (s)

DP(Au) Z Z Z HT bgr.

– Z GB PD

Rel.around particles

mechanism

≈200 Z ≈300 +PhT(ord) (jump in Q−1 from 2 to 4 · 10−4 on heating when passing the order/disorder (Kurnakov) ordering temperature) Z 90 241 700 GB GB 370 GB(?) 80

10–80 80 250

0.4

Qm −1 (10−4 ) H (kJ mol−1 ) 2–10 – 70–80 86.8 436–168

Table 4.1. Continued

annl. 730◦ C

quen., annl.

SC

Ashmarin et al. (1985b)

Povolo and Hermida (1996b) Povolo and Hermida (1996a) Miura and Maruyama (1985) Iwasaki (1986b) PC

CW PC SC

Kobiyama and Takamura (1985) Iwasaki (1978) Povolo and Armas (1983)

Ngantcha and Rivi`ere (2000) De Morton and Leak (1967)

reference

irr(n)

PC, int.oxid.

state of specimen

176 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

503 630–670 780–810 593–623 753–823 1073–1123 603 961 280

∼1 2 ∼1 ∼1 1

∼1 0.2

0.2 1299 1–4

Cu–Co Cu–Fe(0.07–0.1)

Cu–Fe(0.5–10)

Cu–Fe(<1.5)

Cu–Ga(16) Cu–Ge(0.2) (wt%)

Cu–Ge(8)

Cu–Li(1.07–2.01)

Cu–Li(18)

Cu–Mg(3)

Cu–Mn(13–22)

2.5–6

100

500

200–110 120–160

0.3

126

184.9 – 205 159 209 125

520–560 725–740

71–130 240–200 –

1 135 174

650 50 550 20 625 30 720 25 Peak at 625 K: melting of Cu–18at% Li crystals (?) 160 650

34–217

646

Cu–Be(1)

10−14 10−14

2 · 10−14

irr(n)

Electr. depos.

SC, PC, CW irr(e) Electrodeposition

Diﬀerent grain sizes quen. 850◦ C

quen. 800◦ C

ageing

irr(n)

quen. 850◦ C PD(vac) PhT(→ layers)

PD

Z + GB

Z GB + particles twinning (pseudoel.) Z GB(LT) PT GB(IT)

GB GB GBI GB GB(Fe)

PD

Lambri et al. (1996b) Kobiyama and Takamura (1985) Kutelija et al. (1985)

Kobiyama and Takamura (1985) Peters et al. (1964) Piguzov and Pinus (1982) Karmazin and Startsev (1970) Postnikov et al. (1966) Attia (1967) Roberts and Leak (1975) Numakura et al. (1993) Lambri et al. (1996b,d)

4.1 Copper and Noble Metals and their Alloys 177

863–1000 34 150 ∼870 ∼1070 160 170 240 510 950 30–150

∼1 ∼1 ∼1 2

1 2.2 3 · 106 0.3–1.3

Cu–Ni(5.6–94.9) Cu–Ni(25–75)

Cu–Ni(45)

Cu–O(0.0004–0.007)

Cu–O (traces)

Cu–P(0.025)

Cu–Pd(0.01–0.3)

Cu–Si(0.006) (wt%) ⇒ Cu–SiO2 (0.005), vol.% 465 702

425–490

2000

Cu–Ni(10–30)

10 32

400

100 250 20 20–25 8 345

650–550

125 164

197

208 25 35 39 131

368–264 79.9 111.3

70–82

3 · 10−13

8–277

105

Cu–Ni(1.3–7.6) 0.06–0.35

10

∼850

∼1

Cu–Ni(3) 151

τ0 (s) Qm −1 (10−4 ) H (kJ mol−1 )

Tm (K)

f(Hz)

composition

Table 4.1. Continued

GB + particles

ODR

GBI

GB PhT PhT recr. DP PD(O/disl) DP(P2 ) DP(P3 ) GB

DP(solute)

Z

mechanism

intern. oxid.

SC 111

quen. 800◦ C

intern. oxid.

CW

CW

quen. 720◦ C

quen. 1105◦ C

ADIF

annl. 1,110◦ C

state of specimen

Ashmarin et al. (1985b) Piguzov and Pinus (1982) Ikushima and Kaneda (1968) Mori et al. (1983)

Wolny et al. (1985)

Postnikov et al. (1968a)

Roberts and Barrand (1969a) Gremaud and Kustov (2000) Kashevskaya et al. (1981) Roberts (1970) Dey (1968)

reference

178 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

473 473

69–96

Cu–Si(5.09) (wt%) 3

504

1.8 1–4

1000

1.6 0.7

1.3

0.5

Cu–Sn(0.02)

Cu–Sn(3–9) Cu–Sn(3.8–10.1)

Cu–Ti(4)

Cu–Zn(2.5–30) Cu–Zn(10–30)

Cu–Zn(17.7–29.4)

Cu–Zn(30)

0.3

118 117

155 PhT(prec.) Relax. at prec. interfaces in stacking faults PD

GB + particles

698

657–614 600

17–36 172

182–161

GB

Z

GB 763–773 700–760 151–205 PD(vac) 215–250 – 118–128 10−14 375–350 – 157–153 10−14 450–440 PhT(prec.) – 178–173 10−14 210–230 50–100 118–128 10−14 PD(vac) 360–340 75–200 157–153 10−14 410 PhT(prec.) 250–350 178–173 10−14 DP 293–593 5 40–43 (dislocations formed by α → β transformation) DP(solute) 6 · 10−52 200 2–8 193 159–178 Z 563–623

901

Cu–Si(0.1)

CW, annl.

irr(n)

quen. 700◦ C

irr(n)

prec.tr.

Kong et al. (1981a) Finkelshtein and Shtrakhman (1964) Shtrakhman (1967a,b) Kˆe (1948a)

Golub et al. (1984)

Kobiyama and Takamura (1985) Marsh (1954) Kutelija et al. (1989)

Roberts and Leak (1975) Mondino and Gugelmeier (1980)

4.1 Copper and Noble Metals and their Alloys 179

293 293 17.2 17.2

0.9 0.9

0.9

−4

(10

22 incl. bgr.

Qm

Cu–Zn(45) (β) 0.9 343 – Cu–Zn(45) (β) 0.9 450 7 Cu–Zn(43) (α − β) 0.9 558 40 Cu–Zn(50) (β − γ) 0.9 463 – Cu–Zn(19.9) (wt%) 1 210 8–15 Cu–Zn(36.1) (wt%) 280 – Cu ternary and multi-component alloys Cu–Al(14).– 0.01 361 0.2 Be(0.45) (wt%) 10 0.02 Cu–Al(9)–Fe(1.4)– 1 150–300 5–50 Zn(23.4)

21 135

293 293

11200 30000

Cu–Zn(37.5) (α)

293

6000

Cu–Zn(31) (α)

293

40

Cu–Zn (“brass”)

Tm (K)

f(Hz)

composition

−1

τ0 (s) transverse thermal currents

mechanism Wire, diam. 1.25 mm

state of specimen

IF peaks as a fct. of grain size

dislocat. vacancies

PhT oxidised in tap water

intercrystalline 750◦ C/0.15 mm thermal 700◦ C/0.11 mm currents 620◦ C/0.065 mm (annl./grain size) IF peaks as a fct. of transverse strip 1.6 mm frequency thermal strip 0.635 mm currents (annl. 550◦ C) 69.5 diﬀ. Zn, vac quen. 400◦ C 130 Z(Cu) stress relaxation at β − α interfaces 159 stress relaxation at β − γ interfaces 130 dislocat. oxidation vacancies

ﬁrst report of IF peaks as a fct. of frequency

) H (kJ mol−1 )

Table 4.1. Continued

Song et al. (2001) Jagodzinski et al. (2000a)

Aaltonen et al. (1998a)

Clareborough (1957)

Berry (1955)

Bennewitz and R¨ otger (1936), after Zener et al. (1938) Randall et al. (1939)

reference

180 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Cu–Al(13)– Ni(7.9) (wt%) Cu–Al(27.96)– Ni(3.62) Cu–Al(13.2)– Ni(4) (wt%) Cu–Al(13.75)– Ni(4.95) (wt%) Cu–Al(12)– Ni(3) (wt%)

Cu–Al(11.9)– Mn(2.5) (wt%) Cu–Al(14 Al)–Ni(16)

Cu–Al(16.6–20)– In(16.7–20) Cu–Al(10–20)– In(10–20) Cu–Al(13)–Ni(4) (wt%) Cu–Al(8.9–12.7)− Mn(4.7–9.3) (wt%) Cu–Al(10)– Mn(4–14)

260–290 230–270 904

1 0.3

7–300

105

520–680

10

1

1.1

1

low T anomaly, associated with dislocation rather than interface mechanism 3300 PhT(mart) 1800 β1 → γ1 → β1 183 8.6 · 10−4

Z

PhT 448(T ↑) 420(T ↓) 283(T ↑) 210 PhT(mart) 253(T ↓) 180 273–113 350–2000 (transformation into martensite) 403–173 300–2000 (transform. from martensite) 370(T ↑) 1. cycle (reverse martensitic transforma325–340 2–20 tion., eﬀect of vacancies) 300 30 (transform. into martensite) 330 5 (back transf. from martensite) 370 25 (back transf. from martensite) 323 twin boundary relaxation of γ martensite PhT(Θb )

10−14.4

0.6

167–157

650–120

635–602

1

(melting of In inclusions)

20–180

430

1.3

on heating on cooling

Perez (2004) martensite transf. ADIF

Kustov et al. (1996a, 1998, 2000) Recarte et al. (1993) Pelosin and Rivi´ere (2004)

Mitani et al. (1980)

Vasilenko and Kosilov (1982)

Wang et al. (2005)

annl., quen.

PC

Sharshakov and Putilin (1983) Kostrubiec et al. (2003) Mielczarek et al. (2006) Sharshakov et al. (1978c)

Putilin (1985a)

4.1 Copper and Noble Metals and their Alloys 181

465 430 ∼470

10−4 –40 10−3 1

500

32

Cu–Al(8)–Zn(14)

579(T ↑) 329(T ↓) 300–310 317 329 480–510 215 315 400

350–360

220–300

2.2 · 105

5 · 104 − 2 · 105 700

350

1

10−3

Cu–Al(28.76)–Ni(2.3)– Zn(4.76) Cu–Al(8.5)– Zn(14.5) (wt%) Cu–Al(8.5)–Zn(14.5)

Cu–Al(13.2)–Ni(3) (wt%) Cu–Al(11.9)–Ni(4.8)– Ti(1.0)

Cu–Al(13.1)–Ni(3.2) (wt%) Cu–Al(28)–Ni(3.6)

210–280 223–300 160/130 240/240 435

1

Cu–Al(13.2–14.3)– Ni(3.3–4.2) Cu–Al(13.2)– Ni(4) (wt%) Cu–Al(13.2)–Ni(3) 5 · 106

Tm (K)

f(Hz)

composition

(10

)H (kJ mol−1 )

<1600 8 90 –

motion of interfaces PhT

PhT(mart) β → γ PhT(mart)

PhT(mart)

PhT(mart)

PhT(mart)?

PhT(mart)

mechanism

37

2 · 10−12 PhT(mart)

(transformation into martensite) (back transform. from martens.) (back transform. from martens.)

change of damping and elast. constants 15–90 during heating during cooling – dependent on heat treatment

τ0 (s)

Table 4.1. Continued −4

630–3400 on heating 580–2200 on cooling 30/60 60/20 80

Qm

−1

resonant US spectroscopy SC, PC, CW 4.5% hot rolling, water quen., ageing

before/after impact load SC

state of specimen

Van Humbeeck and Delaey (1983)

Kostrubiec et al. (2003) Bojarksi et al. (1983)

Shen et al. (1996)

Cesari et al. (1996)

Rivi`ere et al. (2006)

Emelyanov et al. (2000) Covarel et al. (2000) P´erez-Sa´ez et al. (2000) Perez-Landazabal et al. (2004)

Ibarra et al. (2004)

reference

182 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

20

500

Cu–Al(4.1)–Zn(27.3) 800/650

20–160 – 700/550

330–333 290–295 325/305

4.3–5.8

Cu–Al(4)–Zn(26) (wt%) Cu–Al(18)–Zn(12.7) Cu–Al(17.2)–Zn(12.4) Cu–Al(8.5)–Zn(14.5)

160/193

900–480

292

1

1

Cu–Al(6)–Zn(4.7)

14–42 8–34 40 8 25

621–658 632–662 628 662 649

1

1

Z(Zn)

28–52

641–625

∼1

Cu–Al(−3.9)– Zn(19.1)

Z

623–672

1

172–179 174–182 174 182 179

178–172

PhT(mart) (reversible)

PhT(mart) (reversible)

PhT(mart)

PhT(mart)

Z(Zn) Z(Al) Z(Zn) Z(Al) Z(Al)

Z

175–160

593–615

0.4–0.6

Cu–Al(3.5–4.1)– Zn(27.8–25.6) Cu–Al(2.4–9)– Zn(29.5–17) Cu–Al(2–8)– Zn(5–20) Cu–Al(2.1–4.2)– Zn(15–20.9) Cu–Al(3.9–7.8)– Zn(9.4–19.7) 151–163

300 (back transform. from martensite 100 (back transform. from martensite) up to 150

250 320 450

0.1

Cu–Al(4)– Zn(25.5)

quen. heating/ cooling

quen., annl.

ADIF

Ilczuk et al. (1993)

Ilczuk et al. (1993)

Shtrakhman et al. (1976) Sugimoto et al. (1981) Ilczuk et al. (1994)

Shtrakhman et al. (1976)

Harangozo et al. (1987) Shtrakhman (1967a) Shtrakhman et al. (1971) Shtrakhman et al. (1976) Shtrakhman et al. (1976)

Morin et al. (1987a)

4.1 Copper and Noble Metals and their Alloys 183

Ir Ir(99.96) Pd Pd(99.91)

Cu–Sn(0.1)–Zn(15)

Cu–Sn(0.1)–Zn(10)

339 1.3 2 3

1720 <71 107 180

24 900

26

18.8

16.9

Table 4.1. Continued

25.1

197

8 · 10−13

– 270–280 IF peaks as a fct. of frequency

τ0 (s) (10−4 ) H (kJ mol−1 )

90–30 60–120 17.4

Qm

2

1

1

340–365 375–505 360 500 360 475

1

Cu–Sn(0.1)–Zn(0.2–5)

76

6.9

Cu–Ni(28.3)–Zn(22.6)

654

72 1

293

10

Cu–Ni(10)–Zn(20)

293

5.6

2

Cu–Fe(0.029– 0.059)–P(0.027) Cu–Ni–Zn (German silver)

Tm (K) 740–690 960–1000 293

f(Hz)

composition

−1

DP(B1 ) DP(B2 )

GB

GB GBI(Sn) GB GB(Sn, Zn) GB GB(Zn)

Z

Z

GB GBI transverse thermal currents

mechanism

CW

PC, annl.

SC

wire 0.1992 mm wire 0.1151 mm wire 0.0505 mm

quen. 800◦ C

state of specimen

Bordoni (1960), Bordoni et al. (1960a,b)

Murray (1968)

Coleman and Wert (1966) De Rooy et al. (1980) Piguzov et al. (1989) Piguzov et al. (1989) Piguzov et al. (1989)

Piguzov and Pinus (1982) Bennewitz and R¨ otger (1938)

reference

184 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Pd77 Ag23 H0.05–0.44 Pd60 Ag40 H0.006–0.27

Pd90 Ag10 H0.1–0.3

Pd60 Ag40 D0.004–0.223

Pd–Ag(7–30)

Pd < 10 ppm H

Pd(H)

Pd

Pd

Pd(99.8)

DP(B1 ) Mazzolai et al. CW 95 1 18.3 5 · 10−15 164 6 (1980a,b) 32.8 1.2 · 10−15 DP(B2 ) Rivi`ere et al. 610 CW, annl. 1 200 67.5 10−12 730 200 96.5 10−15 700–1, 000◦ C (1985) Rivi`ere and 895 – 122.5 10−16 Woirgard (1983) 1080 – 135 10−14 (maxima due to dislocation motions in dislocation structure developed during recrystallisation) 213–685 Kappesser et al. Z 100 40 165 90 (1996a) SK DP(B1 ) Hauptmann et al. 6.3 70 17 15.4 10−12 DP(B2 ) 130 34 (1993b) 26 10−12 SK 10−10 6.3 110 34 19.3 ∼103 –104 623–773

∼25

151–163

Z

quen. 1, 100◦ C Andreeva et al. (1976) (Qm −1 Zener maximum at 15at% Ag is proportional to concentration squared, and decreases with development of long-range order) ∼129–138 15.4 2500 2.5–125 · Z(D) Mazzolai and Lewis In β phase 10−11 (1985b); Lewis In β phase ∼220 – et al. (1982) 31.8–19.3 5 · 10−13 – Z(D) 10−11 (possible also interaction of D with dislocations (Mazzolai et al. 1981)) 17.4 Z(H) Mazzolai and Lewis 5 · 10−12 in β phase (1985a) Mazzolai and Lewis ∼1400 120–150 In β phase up to 100 15.4 1.7 · 10−11 Z(H) ∼2800 145–119 2–38 18.3 1.7 · 10−11 Z(H) (1985a) In β phase 215–154 1.4–36 29–24 8 · 10−13 − H2 2 · 10−12 (relaxation of H in partially ordered domains enriched with Ag

2500

4.1 Copper and Noble Metals and their Alloys 185

15500 180 30 (interaction of H with dislocations) 3000 130–160 5–62

78–86

3 peaks in 10–300 K

3224

3000 3000 107 2.7

1–10, 450–2100 2.7

Pg35 Ag65 H0.003

Pd90 Ag10 H0.2

Pd73 Ag27 + H

Pd68 Ag32 + H Pd60 Ag40 + H Pd D0.67

Pd–D(40–73)

Pd–(Gd; Ce)x x = 1–9

Pd–H(40–75) 70–80

130–210 130–220 173

∼3300

Pd45 Ag55 H0.005–0.56

10–350

8–60 2–60

1.4–11 4–30 1.2 7–27 1.3

145–116 222–182 98 225–200 235

∼3000

Pd53 Ag47 H0.002–0.137

1.2 · 10−14

2 · 10−9 19.6 3 · 10−12 17.4 17.4–25 4 · 10−10 12.3–16.2

15.9–20.7

21.1

(dependent on H concentration)

τ0 (s) (10−4 ) H (kJ mol−1 )

Tm (K)

f(Hz)

composition

Qm

Table 4.1. Continued −1

PD

With β phase in β phase

state of specimen

Z(D pairs in β annl., electrolyt. phase) loaded Z(H in β) SK H-RE Z(H pairs in β annl., phase) electrolyt. loaded

Z

Z(H) H2 (as before) Z(H) H2 (as before) H2 (as before)

mechanism

Arons et al. (1967a)

Ege et al. (1996)

Leisure et al. (1986) Arons et al. (1967a)

Mazzolai and Lewis (1985a) Mazzolai and Lewis (1985a) Mazzolai and Lewis (1985a) Mazzolai and Lewis (1985b) Lewis et al. (1994)

reference

186 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

n = 0.005–0.69

Pd1−x Ptx Hn x = 0.05–0.27

Pd–MgO(1.9)

Pd H0.7

Pd H0.54–0.7

Pd H0.64–0.67

Pd–H(0.22–0.75)

Pd–H(<0.12)

Pd–H(β phase)

120 Arons et al. S(H) DP(impur.) ∼150 (1967b) 2500 Mazzolai et al. 105–115 <25 13.5 1.2 · 10−11 Z 185 24.1 6.3 · 10−13 (1980b) (interaction of H atoms with dislocations in α-hydride; peak temperature decreases with change of H concentration in interval H/Pd = 0.048–0.47 from 167 to 148, Qm −1 increases from (3 to 11) · 10−4 (Mazzolai et al. 1981). According to other data this maximum has been observed in alloys with H/Pd = 0.7 at 110 K (f = 1.6 Hz, H = 18.6 kJ mol−1 ), and the observed maximum has been separated into contributions at 113, 116,5 and 122.5 K (Jacobs et al. 1976) FR 1.4 cooling 160–220 <20 Yoshinari and (hydrides) 230–280 <12 heating Koiwa (1987) 106 –107 190 22.3 Leisure et al. 1.6 · 10−14 Z (1983), Barmin et al. (1983a) 0.6–15 FR(pol.) 50 Jacobs et al. 250 20 (1976) 320 FR(pol.) 30 Zimmermann (1976) Kappesser et al. oxidation ∼100 Z Qm −1 suppressed Z Qm −1 reduced ∼165 (1996a,b) of PdMg2 in O2 320 145 new H-induced peak peak width 190 · 10−4 4750 Z(H) 125–135 <32 Mazzolai et al. (variation of degree of short-range order in hydride, Qm −1 (1987) maximal for n = 0.5) 150–190 (no interaction of H with dislocations for x > 0.17)

∼103

4.1 Copper and Noble Metals and their Alloys 187

1–10 660–1900

6

6

9600

0.8 0.38

10−2 –1 5 · 103 –6.5 · 104

Pd98 Y2 –H

Pd95 Y5 –H

Pt Pt

Pt(99.999) Pt(99.99)

Pt (“pure”) Pt (“pure”)

f(Hz)

Pd100–x Yx , x = 1–8

Pd–W (20)–H

composition

940–1090 70

73 101 173 125 337

120–190 260–300 80–100 120 160 110 94 80

Tm (K)

3 5 9 40 53

<15 <2 – 0.8–2 – – – –

Qm

−1

(10

275 11.6

– – 18.5 28

– 17.4 – – 18.3 11.6 20.6 18.3 11.6 – – 1.6 · 10−10 2 · 10−13

– 3 · 10−12 – – 2.5 · 10−12 1.2 · 10−9 4 · 10−12 4.6 · 10−12 1. · 10−9

τ0 (s) )H (kJ mol−1 )

Table 4.1. Continued −4

recr. SB

Hauptmann et al. (1993a)

Hauptmann et al. (1993a)

Ege et al. (1994)

He and Shui (1985)

reference

Bordoni (1960), Bordoni et al. (1960a,b) Okuda (1963a,b,c) Turner and De Batist (1964) Shestopal (1968b) CW, annl. Coremberg and Mazzolai (1967)

CW higher H content

CW

state of specimen

CW DP(B1 ) DP(B2 ) DP(B2 ) CW PD(int), disloc. CW(6%)

Z reorient SK SK Z(H–Y) Z SK Z(H–Y) Z

DP(H)

mechanism

188 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.2 Alkaline and Alkaline Earth Metals and their Alloys

189

4.2 Alkaline and Alkaline Earth Metals and their Alloys In alkaline and alkaline earth metals, the following internal friction eﬀects have been observed: Very few measurements exist for the alkaline metals: – Dislocation peaks and Zener peaks were found for K, Zener peaks for Li–Mg. – No peaks were found for Na, Rb, Cs. For the alkaline earth metals, no measurements exist for Ca. For other metals: – Point defect peaks were found for Be (with Fe, C) – Dislocation peaks (Bordoni) for Ba (α, γ), for Be, and for Mg on both basal and non-basal systems – Dislocation peaks (Hasiguti) for Mg (π1 , Pα , P1 , P2 ) – Zener peaks for Mg alloys, Be (with Fe) – Grain boundary peaks for Be, Mg, Mg alloys – Peaks due to phase transformations for Be, Mg alloys, Sr

14

Ba Ba(99.9)

1

0.46

1

5000

104

Be(98.56)

Be

Be(98.6)

K K (nominal purity)

K (high purity)

Be Be–0.4 Fe 1.2 (+ O impurities) Be–BeO(0.3–7) 20 Be(99.95) 1

f(Hz)

composition

80–5 140 120

773–1143 573–673 900 430 743 433 733 753–843 843 213 408 101.7 199.2 102.3 196.9 121.6 218.1 50.2 100

174.6–259.5 163.2

63.9

4.5 36.7

H(kJ mol−1 )

4 · 10−12 1.6 · 10−16

τ0 (s)

125 <10 160 (stress-induced volume changes of coherent oxide precipitates) 3 · 10−10 4.4 <40 50 (formation of double kinks in dislocations)

3 5

30

2 3

Qm −1 (10−4 )

270

37 223

Tm (K)

DP

Z (Fe) PD(Fe/C)? Z(Fe) GB GBI DP(B) PD(Fe/C) ?

GB GB PhT(?)

PD(Fe/C)?

DP(α) DP(γ)

mechanism

SC, CW

annl.

CW, annl.

sintered quen. 1000◦ C

CW

state of specimen

Hammerschmid et al. (1981b)

Gulden and Shyne (1968)

Ang and Chamber (1983)

Elias and Rowling (1965) Ivanov et al. (1966a) Tikhinskij et al. (1977) Tkatchenko et al. (1977b) Bussiere et al. (1982)

Hammerschmid and Schoeck (1985)

reference

Table 4.2. Alkaline and Alkaline Earth Metals and their Alloys (at.% if not speciﬁed diﬀerently)

190 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Mg(99.98)

Mg(99.996)

Mg(99.99)

Mg(99.99)

0.5 4 · 104

Mg Mg(99.97) Mg(99.992)

5.5 9.5 41.4–40.4 40.4

490 20 100 180 225 ≈20 37

450

MT below 77 K, no relaxation peak above 77 K 400 90

183.5 179.5

Z

Z

GB DP(B)? DP(B) 28.9 DP 103 42.3 DP – electrons 15–75 · 106 0.9 dislocation motion in basal plane 106.5 8.7 in non-basal plane 155.5 40.7 ? 4 ∼10 20 – GB(?) 20–240 disl. motion in (0001) slip system 458 1000 1 GB 133 according to Shwedow et al. (1982) there are 2 GB peaks owing to anisotropy

1380

104

3700 13 000

Li Li (<1 ppm impurities) Li–Mg(57)

K–Rb(20–50)

hot forged

PC CW CW CW

SC

Smith and Leak (1975)

Tsui and Sack (1967)

Koda et al. (1963)

Kˆe (1947a) Caswell (1958) Sack (1962) Hasiguti et al. (1962)

Hammerschmid et al. (1981a) Seraphim and Nowick (1961)

Gulden and Shyne (1968)

4.2 Alkaline and Alkaline Earth Metals and their Alloys 191

1.4

1

Mg(99.9999)

Mg(99.9999) 318 300–0 640–1270

340 430

60–200 250–650 650

260

62.5 122 430

disappears after annealing increasing by thermal cycling

– 14.5 96.5

2

Mg(99.99)

Mg(99.9995)

15 100 (interaction of geometrical kinks with vacancies) 40 up to 70 7.2 10−9 80 up to 70 14.5 3 · 10−11 105 – 30 – (interaction of dislocations with interstitial atoms) 220 17 (interaction of dislocations with clusters of vacancies or interstitials) 420 500 96.5 (motion of dislocations controlled by climb and diﬀusion of vacancies along dislocations) 100–150 300

1

Mg(99.9999) (see Fig. 2.21)

) H(kJ mol−1 ) τ0 (s)

Tm (K) (10

Table 4.2. Continued

f(Hz)

Qm

−4

composition

−1

P1

DP(B1 ) DP(B2 ) DP(P1 ) jog climbing P0 dragging H by dislocations PD

DP

DP(Pα )

DP(P2 )

DP(B1 ) DP(B2 ) DP(P1 )

DP(π1 )

mechanism

PC

irr(e)

CW

CW

N´ o et al. (1993a)

Vincent et al. (1981) Haneczok et al. (1983) o (1990) N´

Fantozzi et al. (1982, 1984a,b) Fantozzi and Esnouf (1983), Esnouf and Fantozzi (1981)

state of reference specimen

192 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Complex spectrum DP(disl)

393 583 553 313 348 303 51

<0.2

1 1 15 · 106

Mg–In(20–62)

Mg–In(55)

Mg–In(60–70)

Mg–Li(1.88) 99.5

473–413

1

10−14.3 10−20 10−14.1 − 10−14.9

10−14.3 − 10−16.7

PhT (β , β ) order Z PhT β → β Z

Z

GB

Z

1.74 DP (dislocation motion in basal slip plane) 9.6 DP

80.8 129.7 78.3–85.8

105–133

–

473

1 –

117.2–115.1 10−15

423

1

irradiation by electrons after CW changes the height of DP(B1 ) and DP(B2 ), suppresses DP(π1 ) and causes the appearance of DP(π10 ) (6 K), DP(π0 ) (14 K), and DP at 140 K

0–300

Mg–In(28–50)

Mg–In(5–15)

800

Mg + small 1.5 · 10−2 amounts of Al, Zn, Cd, Tl, In Mg (<0.53 ppm 1000 impurities) CW, irr(e)

Brozel and Leak (1976) Brozel and Leak (1976) Koda et al. (1963)

Smith and Leak (1975), Lauzier and Hillairet (1985), Minier et al. (1983a,b, 1982) Brozel and Leak (1976), Berrisford and Leak (1981) Brozel and Leak (1976) Berrisford and Leak (1981)

Roberts (1968)

4.2 Alkaline and Alkaline Earth Metals and their Alloys 193

15 · 106

490 15 · 106

Mg–Li(4.45)

Mg–Li(43)

Mg–0.0048 N

Mg–Si(2) (wt%) 0.08 with short Al2 O3 ﬁbres

Mg–Si(1.34) (wt%) 1 eutectic, with Mg2 Si ﬁbres

Mg–O

154.5 50

mechanism

Seraphim and Nowick (1961) Koda et al. (1963)

Koda et al. (1963)

reference

Mayencourt and Schaller (1997, 1998)

Ivanov et al. (1966b) uni-directional Mayencourt and solidiﬁcation Schaller (1997, 1998)

SC

state of specimen

150 180 relaxation 180 130 of thermal stresses by strong dependence on amplitude, heating local plasticity rate, solidiﬁcation rate, matrix orientation: Qm−1 up to 470 inﬁltration (T ↑)300 0.1–1 (T ↓)200 depending on (disloc. relacooling rate xations)

GB

DP

DP

(dislocation motion in non-basal slip planes) 126 1.45 DP 0.5 (dislocation motion in basal slip plane) 6.75 DP 1 (dislocation motion in non-basal slip planes) 34.7 4.9 90 Z 90

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

46 1 (dislocation motion in basal slip plane) 116 22 (dislocation motion in non-basal slip plane) 157 35 673 159

157 383

98

Tm (K)

f(Hz)

composition

Table 4.2. Continued

194 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Sr Sr

98 for prec.

weak T dependence

5–50

a maximum was observed at 373–398 K, further a strong increase of IF at 510 K caused by polymorphous transformation fcc → hcp, decrease at 700 and decrease at 893 because of polymorphous transformation hcp → bcc

DP not found

300–800

500–600 530

293

20–30

quen. (823 K)

severe CW (ECAP)

powder metallurgy severe CW (ECAP)

inﬁltration

microstructural nc and changes microcryst.

GB sliding PhT(prec.)

thermoelasticity

GB, diﬀus.

no peak on cooling (T ↓) 573 on 1900 78 heating

1–10

3100 GB, diﬀus.

533(T ↑)

transient damping due to thermal stress relaxation by hysteretic dislocation motion same 75

1–10

0.05–1

10–13 Mg–Ag(2)–Nd(2)– 1 Zr (wt%) (QE22) Mg + 3 vol.% 130–140 powders of Al2 O3 , ZrO2 , C Na Na

Mg–Al(9)–Zn(1)– Mn(0.2) (wt%) (AZ 91) Mg–Al(3)–Zn(1) (wt%) (AZ 31)

Mg + 25 vol.% saﬃl short ﬁbres Mg–1 vol.% C nanotubes Mg–Zn(6)–Zr(0.5) (wt%) (ZK 60)

Dashkovskij (1963)

Hammerschmid et al. (1981b)

Lambri and Riehemann (2005) Trojanova et al. (2004)

Watanabe et al. (2004)

Chuvildeev et al. (2004a,b)

Chuvildeev et al. (2004a,b)

Yang and Schaller (2004)

4.2 Alkaline and Alkaline Earth Metals and their Alloys 195

196

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.3 Metals of the IIA–VIIA Groups and their Alloys Aluminium and its alloys is one of the most thoroughly investigated metals, accordingly all possible relaxation peaks have been detected in Al and its alloys. The following internal friction peaks have been found in metals of the IIA–VIIA groups: – Point defect peaks (PD). Intrinsic and impurity peaks in Al – Dislocation peaks (DP). In Al (Bordoni peaks B, Hasiguti peaks P), in Bi, in Pb (Bordoni peaks), in Zn (Bordoni peaks for basal, prismatic and pyramidal systems; Hasiguti peaks) – Zener peaks (Z). In Al, Cd and In alloys – Grain boundary peaks (GB). In Al, Bi, Cd, In, Pb, Sn and Zn – Phase transformation peaks (PhT). In Al, Bi, Cd, In, Sn, Tl; connected with melting in Bi, Cd, Pb and Sn.

548 24 21–31 80 127 213 235 83 119 130 153 196 70 100 115 155 613 ∼573

83

0.69 1.2 · 104

2·104 –106 104 600

103

107 –5·107

3

2.32

∼1

Al Al

Al(99.991) Al(99.99)

Al (low purity) Al(99.9) Al(99.999)

Al(99.99)

Al(99.994)

Al(99.999)

Al(99.6)

Al(99.999)

293

f(Hz)

composition

Tm (K)

τ0 (s)

2.3

48.2

10−9 10−10

3 · 10−8 3 · 10−13 3 · 10−13

9 · 10−9

ﬁrst report of IF peaks as a function of frequency 134 2.3

H(kJ mol−1 )

8.7 38.5 42.5 16.3 28.9 4.1 6.0 19.5 11.6 18.3 depending on annealing depending on annealing 144.3

42 35 14 16

26 incl. bgr.

Qm −1 (10−4 )

DP

DP(B1 ) DP(B2 ) DP–PD DP–PD GB

DP(P1 ) DP(P2 ) DP(P3 ) DP(B1 ) DP(B2 )

DP(B)

transverse thermal currents GB DP(B)

mechanism

CW

CW

SC [111] SC [100] SC [110] CW, annl.

CW PC CW

CW

wire, diam. 1.5 mm

state of specimen

Cordea and Spretnak (1966) Perez and Gobin (1967)

olkl et al. (1965) V¨

Baxter and Wilks (1963) Mongy et al. (1963)

Bennewitz and R¨ otger (1936), after Zener et al. (1938) Kˆe (1947a) Lax and Filson (1959); Bruner (1960) Lax and Filson (1959) Bordoni (1960) Hasiguti et al. (1962)

reference

Table 4.3. Metals of the IIA–VIIA Groups and their Alloys (at.% if not speciﬁed diﬀerently)

4.3 Metals of the IIA–VIIA Groups and their Alloys 197

0.5

4000

4000

1

∼1

Al(99.6)

Al (zone reﬁned) Al(99.996)

Al(99.999)

Al(99.999)

9

2.5

Al(99.999)

Al(99.9999)

Al(99.9) + 500–5000 Cu, Ti, Fe, Zr (0.005 (wt%) each) Al(99.999) 0.2–2

f(Hz)

composition

≈46

– 41.5 –

87–94 233 290 495 625 675 65 95 75 10–80 10–40 – 30 80 70 30 65 40

40 100 5 7

mechanism

– 10−9 –

DP(B2 ) DP(PF ) DP(PC ) GB(P1 ) GB(P2 ) GB(P3 ) DP(B1 ) DP(B2 ) DP(PA )

shear def. and recryst. GB DP(B1 ) DP(B2 ) DP(B1 ) DP(B2 ) DP DP(P1 ) DP(P2 ) DP(B) + impurities impurity diﬀusion along dislocations

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

10–30

673 92 134 92 118 115 90 160 130

543

Tm (K)

Table 4.3. Continued

CW at 10 K, annl.

bicrystal

CW, fatigue

CW CW, annl. at 133K

SC, CW

SC, CW

CW

state of specimen

Esnouf and Fantozzi (1979)

Woirgard et al. (1975)

Tirbonod and Vittoz (1975)

Chevalier et al. (1972) Krishtal et al. (1974)

Burdett and Queen (1970a) Burdett and Queen (1970a) Benoit et al. (1970)

Galkin et al. (1969)

reference

198 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

∼1

1.7

1

1

0.03–0.6 1

1.4

1 0.65 1.4

107 1 0.48–1.7

Al(99.999)

Al(99.999)

Al(99.9999)

Al(99.9999) Al(99.999) Al (collected data from literature) Al(99.99993)

Al(99.999) Al(99.6) Al(99.91)

Al(99.999 ) Al(99.999) Al(99.999)

1

Al(99.999) Al(99.9999) Al(99.9)

493 510 533 510 563–577 638 185–190 510 570

400 606 681 65 110 90 250 110 270 450 550

110 150

600 300 670 210 700 100 50–85 300 80

80 200 30 110 80 50 60–120

75 15 3 25–95

2.5 · 10−12

3 · 10−13 5 · 10−10 10−10

∼10−11

130 – 154 126 135–142 209 14.5–16 10−15

11.6–16.4 10−11 –10−13 10.6–48.2 2.5 · 10−11 –10−16

101

7.7 13.5 91.7 98.4 94.55

GB GB GB GB GB GB DP(B2 ) GB GB(Kˆe)

DP(B1 ) DP(B2 ) DP(B2 ) DP(PF ) DP(B2 ) DP(PF ) DP(P1 ) GB(P2 ) DP(B1 ) DP(B2 )

DP(PA ) DP(PB ) DP(B1 ) DP(B2 )

Kˆe et al. (1984c)

Chicois et al. (1981) Bandraz et al. (1981) Bandraz et al. (1981) Esnouf and Fantozzi (1981) Fantozzi et al. (1982)

Esnouf and Fantozzi (1980) Rivi`ere et al. (1981)

Iwasaki (1984) Kˆe et al. (1984b) Kˆe et al. (1984a,b), annl. 450◦ C bamboo structure Su and Kˆe (1986) Zein (1985) CW Kiss et al. (1985) Kˆe (1985a) PC

annl. 320◦ C annl. 620◦ C CW + annl.

CW, annl. CW

cycl. def. annl.

Tors. creep, ext. stress cycl. def. annl.

PC, SC

PC, CW, annl.

4.3 Metals of the IIA–VIIA Groups and their Alloys 199

Al(99.9999) Al(99.999)

Al(99.999)

Al(99.999)

Al(99.9999)

Al(99.999) Al(99.999)

Al(99.9999)

Al(99.999)

composition

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

– DP(P1 ) 325 30 450 DP(P2 ) 350 106 DP(P1 ) is due to motion of screw dislocations, DP(P2 ) is due to motion of mixed dislocations controlled by jog climb and vacancy diﬀusion disl. jog mobility CW, creep 1 10−11 470 200 97.5 1 1.2 · 10−12 disl. sub-bound. CW, creep 537 350 122.6

1

peak disappears after annealing at T > 430◦ C SC no GB SC, annl. 638 176 1.4 · 10−16 jog climb 543 GB sliding PC, CW, annl. ≈200 polygonization 2 · 10−4 CW −1 annl. 402◦ C 1 145 802 77.2 DP(P1 ) microcreep 1 378 jog climb+pipe diﬀus. 446 116 DP(P2 ) jog climb+self-diﬀus. GB 154 1 10−15 541 7 168 14.5 CW 10 2.7 · 10−12 DP(B1 ) 226 21.2 1.6 · 10−12 DP(B2 ) (τ0 and H were determined from the analysis of many works) CW 1.7 DP(B1 ) 65 170 100 DP(B2 ) 230 CW 0.1 DP(Pc ) 250–280 15

f(Hz)

Table 4.3. Continued

Esnouf et al. (1987) Esnouf et al. (1987)

N´ o et al. (1987a,b)

Gremaud et al. (1987a) Gremaud et al. (1987a)

Iwasaki (1986a) Alnaser and Niblett (1987)

N´ o (1985, 1990) o (2001)) (cit. in N´

Yan and Kˆe (1987)

reference

200 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1.5

3.5 3.5

3.5

1

5 · 104

Al(99.999)

Al(99.999) Al(99.999)

Al(99.999)

Al(99.999)

Al (zone reﬁned)

1.7

1.25 0.01–10

Al(99.999) Al(99.9999) +10 ppm Ag +10 ppm Cu Al(99.999)

Al(99.9999)

1

Al(99.999) GB DP DP

GB

180

120

30

70 90 200 680 590 550 670 580 570 65 95 11

DP(PA ) DP(PB ) DP(PC ) kink pair short-circuit mechanism and pipe diﬀusion enhancement DP(B1 ) 50 DP(B2 ) 230 DP(P2 ) 200 200 DP(P2 ) 700 DP(P2 ) 180 160 DP(P3 ) DP(P2 ) 700 DP(P2 ) 500 DP(B1 ) 20.3 DP(B2 ) −10 DP(B) 5 1.16 10 11230◦ assumed 7 DP(B) 11290◦ DP(B) 40–60 11060◦ DP(B) 1100◦ 30

6 · 10−13 10−14

8 · 10−10 – 3 · 10−13

60–120 120–200 200–300 14

139 123 150

102–136

400 500 500

280–400

460 526 562

490–510

Cheng and Kˆe (1987, 1988) Esnouf et al. (1987)

Iwasaki (1987)

SC, def.

SC, def.

SC, def.

SC, ann.

as-rolled after creep

PC PC

(1990) (cit. in (2001)) (1990) (cit. in (2001))

o and San Juan N´ (1993) Kosugi and Kino (1989, 1993)

o N´ N´ o o N´ N´ o

CW at 4 K Gremaud and (acoust. coupl. Quenet (1989) techn.) CW at 10 K Gremaud and Quenet (1989) annl.

CW + annl. 300–600◦ C bamboo GB CW, creep CW, creep

4.3 Metals of the IIA–VIIA Groups and their Alloys 201

489–660 70–600 90–150 220–300 313–373 12–65

1.5 · 107 1 1

0.06–16

0.08–25

1.5 · 107

Al(99.999) Al(99.999) Al(99.9999)

Al(99.9)

Al(99.9)

Al + 70 ppm impurities Al(99.999)

98 394

310 320 353

300 580–600 320 460 440 489–660

103

Al (zone ref.)

Al(99.999)

130

1

Al(99.999)

270

11 30 120 155 190 458

5 · 104

40 to 48

30–480 570–700 130 350 65 70–580

90

5 ≈5 ≈5 ≈5 ≈5 400

−4

(10

Al + 50 ppm Zn

Qm

Tm (K)

f(Hz)

composition

−1

53

60

145–193

177

85

10−15 –10−17

bending GB(Kˆe) torsion constrained GB diﬀusion

DP(B,vac) disloc. breakaway GB sliding 2 · 10−12–13

no DP, GB?

10−10

DP(B,vac)

DP (B) DP(B) DP(B) DP(B) DP(B) GB

mechanism

DP DP(imp) DP(P1 ) DP(P1 ) DP(P1 ) no DP, GB?

7 · 10−9

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

Guan and Kˆe (1993) Lauzier et al. (1993) Zhu and Fei (1993) N´ o et al. (1993b)

Kosugi and Kino (1989, 1993)

reference

Rivi`ere and Woirgard (1993) CW, annl. Rivi`ere and Woirgard (1994) Charvieux et al. (1993) sput.th.f. on Si Prieler et al. (1993) Su and Bohn thin foil (100 µm) (1993) sput.th.f. on Si

fatigue creep def tangled disl. tangled disl. polygon. disl. CW, annl.

CW, Irr.

SC, def. SC, def. SC, def. SC, def. bicrystal

state of specimen

202 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

0.5–1.8 3

Al(99.999)

Al(99.999) Al

1

Al(99.9999) +10 ppm Cu

2.2 1.5 1.4 1.6

290 425 570 540 680 520

107

Al(99.999) Al(99.9999) Al(99.997)

Al(99.999) Al(99.999)

17

5.5 · 10 9 · 105

680 530 510 620 0.4–200 0.07–1.1

400 550 650 465 460

550

560 637–620 450

Al(99.9)

18 4

1

Al(99.999)

3800

1.2 4–6 3

Al(99.999) Al(99.99) Al nc

60 60 1100 1100 650 1800

1–40 0.15–1 1.2–2.8 64

100 1000 100 40–60

100

100

800

– 77 144 – – 130

1.4

96 128 96 135

77

10−12

10−12 10−17 10−12 10−14

10−12

DP(PC ) DP(P2 ) DP(P2 ) DP(P2 ) DP(P3 ) DP(P2 )

DP(B)??

LT bgr. LT bgr.

GB

Koizumi et al. (2000) CW Bremnes et al. (2000) PC, CW, annl. Gallego et al. PC, creep at (2000) 543 K PC, CW, annl.

CW, annl.

sput.th.f. on Si Xiao Liu et al. bulk, CW (1999)

annl. 850 K nc.

disl. generation SC creep Cai et al. (1999) Bonetti et al. nc., annl., no GB (1996a) grain growth GB annl. 770 K nc.

Zhu and Kˆe (1993) PC irr(He) Zaritzky (1993) Powd.comp,nc Al Sadi et al. (1994) N´ o et al. (1996) disl. jog mobil- CW ity disl./impur jog CW, recryst. o et al. (1996) N´ mobil.

GB GB GB sliding

4.3 Metals of the IIA–VIIA Groups and their Alloys 203

0.025 6.3 120 135 1

0.3–3.1

0.26

Al(99.9999)

Al(99.85)

Al(99.999) grain size 1.8 mm Al(99.993) grain size 1.3 mm Al(99.9) grain size 0.07 mm Al(99.9)

Al(99.999)

Al(99.9)

420 500 690–577

1.1 1.0 0.1

Al(99.9999) +10 ppm Cu Al(99.9)

553–579 613 464 500 500 500

0.001 0.032 0.1 1700 1300 950

430 580 350 96.5 – –

– 187 152

260 140

135

57.7 96 106

693–733 455 520

250 130 2 1.5

– –

mechanism

10−19

Evap.th.f. on Si

PC, creep at 543 K

state of specimen

plasma evaporation, Al/Al2 O3 GB compaction nc. Kˆe-GB annl. 893 K 7h, CW GB bamboo annl. 893 K 6 h, CW Kˆe-GB annl. 673K 2 h, CW HT bgr + DP CW, Quen, annl.

DP(P1 ) DP(P2 ) PhT (Θ , Θ ) interfaces no Debye peak GB (sliding) GB (diﬀus.) DP(P1 ) 2 · 10−14 jog climb+pipe diﬀus. DP(P2 ) 5 · 10−15 jog climb+self-diﬀus. Al diﬀusion 10−17

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

135

0.26

0.26

(10

430 320 20–600

Qm

−4

438–458

522

321 392 360 600–630 430

Tm (K)

f(Hz)

composition

−1

Rivi`ere (2004)

Xiaohui and Changzhi (2004)

Cai et al. (2001)

Gallego (2001) (cit. o (2001)) in N´

Harms et al. (2000)

Rivi`ere and Pelosin (2000) Rivi`ere (2001a)

reference

204 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Al binary solid solutions 40 Al–Ag(0.032) GB(Ag) 174 10−16 1 592 Al–Ag(0.5–5) PhT(prec.) 1 20 428 27 4 · 10−4 (wt%) Al–Ag(2.5–30) 1 413–443 2.5–40 155 (wt%) diﬀusion controlled relaxation of partial dislocations at precipitates ≈50 ≈425 PhT(γ ) Al–Ag(1.6) 0.7 PhT(ord) depending on ageing 120 Al–Ag(5–20) PhT(γ), 0.45 433 Al–Ag(10) 120 483 clusters Al–Ag(5–85) 0.8 410–450 320– Z and (wt%) peaks 400 PhT(αss → GP → γ +γ) Al–Ag(2) (wt%) 0.8 570, 630 – Al–Ag(5) (wt%) 0.8 645/605 150 Al–Ag(10) (wt%) – PhT 0.8 680 prec. shape change 0.6 Al–Ag(20) (wt%) 105–113 0.25 413 change of parts of precipitates Al(99, 99) + Al2 O3 ≈150 relax. of 0.1–7 280(T ↑) Saﬃl ﬁbres 15–30 500 180(T ↓) thermal vol.% stresses non-anelastic Al–Cr(0.4–0.7) 1 maxima by recrystallisation (wt%) Al–Cu(0.001) DP1 150.5 10−12 1 562 Kiss et al. (1983a) Esnouf et al. (1987)

Damask and Nowick (1955) Carreno-Morelli et al. (1996a)

quen. and aged squeeze casting

Kiss et al. (1986)

Iwasaki (1984) Schoeck and Bisogni (1969) Schoeck and Bisogni (1969) Merlin et al. (1978) Miner et al. (1969) Schaller and Benoit (1981)

heating/cooling

quen., 200◦ C

quen., aged

annl.

CW, annl. CW, annl.

4.3 Metals of the IIA–VIIA Groups and their Alloys 205

1.2

2

Al–Cu(0.5) (wt%)

1.16

1.14

0.56

0.56 0.56

2

Al–Cu(0.5) (wt%)

Al–Cu(0.19) (wt%) Al–Cu(0.29) (wt%)

Al–Cu(0.015) (wt%) Al–Cu(0.1) (wt%) Al–Cu(0.29) (wt%) Al–Cu(0.5) (wt%)

164 134

10−15 GB(Cu) P1 (GB)

state of specimen reference

– 207 – 204 1.4 135 231 1 – 1 – 212 231 1.5 – 800 556 50 336 549 600 446 200 340 800 310 1000 512 850 407 850 328 900 299 1000 206 150 135 Cu–Al complexes and vacancies near DP/sol–vac. pairs DP/sol–vac. pairs R DP/single sol. (P) DP/sol–vac. pairs R DP/single sol. (P) GB sol.sol DP(P1 ) GB sol.sol. DP(P2) DP(P1 ) DP(P1 ) DP(P3) DP(P2) DP(P1 ) DP(P1 ) 4 · 10−34 dislocations

– 2 · 10−14 – – –

CW, annl. 150◦ C

bamboo crystal

PC

PC

CW

CW, annl.

Zhang et al. (1982)

Zhu and Kˆe (1993)

Zhu and Kˆe (1993)

Zhu and Kˆe (1993)

Kˆe and Zhu (1992)

Yan and Kˆe (1987)

Cui and Kˆe (1987)

90 900–400

mechanism

P2 663 200 563 100 P3 P2 and P3 from relaxation by dissolution of Θ phase at boundaries of precipitates 0.3 polygonization 872 0.22 CW, annl.

571 550–500

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Iwasaki (1984) Cui and Kˆe (1987)

1 2

Al–Cu(0.068) Al–Cu(0.015– 0.29) (wt%) Al–Cu(0.8) (wt%)

Tm (K) CW, annl.

f(Hz)

composition

Table 4.3. Continued

206 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

553 583

Al–Fe(0.25)

20

550

0.9 105

Al–Al2 Cu

117 167

140

GB

Z 450 1.3–10 130 10−15–5 33.5 340–420 15–40 PD (Cu/vac) 490–570 60–120 96.5 relaxation connected with Θ phase and dislocations PhT(Θ) 590–570 75–80 135 10−12.5 458 3 Z, reorient. of second 458 neighbour 90 pairs GB 548–610 80–100 134 690–715 250 PhT(Θ) 280 393 12 92 modiﬁcation of the precipitates by stresses 450 10 Z 117–128 170/130 (heating/cooling)

Al–Fe(0.06) (wt%) 1

0.5

1–1.3

2.8

1.64

Al–Cu(2–2.95) (wt%) Al–Cu(4) (wt%)

Al–Cu(1.8)

Al–Cu(0.09–3.08) 1 (wt%) Al–Cu(1–4) (wt%) 0.7 Al–Cu(1–4) (wt%) 69–114

Al–Cu(0.5) (wt%) 2

annl.

lamellar eutectic

SC, torsional vibration SC, ﬂexurial vibration quen. 540◦ C

quen. 550◦ C

224 200 – – formation of clusters at dislocations 217–225 12–20 CW, annl. maximum consists of two parts: one connected with relaxation by dislocation movement, the other non-relaxation PhT(Θ) CW, annl. DP 210 70 10−17.3 500 CW, annl. 100–500

Berry and Nowick (1958), Fitzpatrick (1965) Lebedev and Nikanorov (1996) Pines and Karmazin (1970) Attia et al. (1967)

Li et al. (1985)

Berry (1961)

Kiss et al. (1977) Mahmoud et al. (1981, 1982)

Ting-Chuan Lei (1981)

Kˆe et al. (1983)

4.3 Metals of the IIA–VIIA Groups and their Alloys 207

1

Al–Fe(0.16–0.5) (wt%)

1

0.38

Al–Ge(2) (wt%)

Al–Mg(0.02) (wt%) Al–Mg(0.02) (wt%)

1.2

1.5

Al–Mg(0.05) (wt%)

Al–Mg(0.12) (wt%)

1.08

60

Al–Ge(0.3–1.4) (wt%)

Al–Fe(0.07–0.47) 1 (wt%) Al–Ga(0.5) (wt%) 0.8

f(Hz)

composition

−4

82

140 200

4 · 10−24

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

disl. kink dragging DP(B2 ) PD(Ge/dis) PD(Ge/dis) PD(Ge/int)

GB Fe precipit. on GB

mechanism

130 250 290 230 – 420 70 450 103 20 198 DP(PL2) 100 77 204 116 DP(PL1) 70 340 DP(P1) 1400 – DP(P2) 400 800 67.5 10−8 P2: reordering split interst. or Mg pairs in disl.kinks 490 DP(P3) 900 DP(PL1) 125 210 10−34 40 DP(P1 ) 230 120 106 10−34 .15 DP(P1 ) 250 67.5 80 10 203 DP(PL2) 180 223 DP(PL1) 170 disloc./Mg-vacancy (PL1), Mg pair – vacancy (PL2) 258 DP(P1 ) 140

10

189

(10

300–100

Qm

210–225

580–630 713–753

Tm (K)

−1

Fang and Wang (2000a,b)

Kˆe and Tan (1991)

Kanazawa et al. (1983) Fang and Kˆe (1990)

Chountas et al. (1978)

Kong et al. (1981b)

Ting-Chuan Lei (1981)

Pines and Karmazin (1970)

reference

PC, CW, quen. Fang and Kˆe (1990)

CW

SC, CW, annl. SC, CW (twisting), annl.

CW CW CW irr(n) ageing

CW, annl.

CW, annl.

state of specimen

208 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Al–Mg(1.1) (wt%)

Al–Mg(1.1) (wt%)

Al–Mg(1) (wt%)

Al–Mg(0.55) (wt%)

Al–Mg(0.55) (wt%)

Al–Mg(0.5) (wt%)

Al–Mg(0.12) (wt%) DP(P2) 433 annl. 0.5 h 270 443 310 DP(P2) annl. 1.5 h PC GB 1.19 546 450 462 400 DP(P3) 400 400 DP(P2) DP(P1 ) 357 350 DP(P1 ) 313 500 note similarity to Al–Cu alloys PC twisted, DP(P1 ) 1.67 303 600 DP(P1 ) 363 300 annl. 393 200 DP(P2) DP(P3) 528 900 PC, CW, annl. DP(P1 ) 1.38 303 570 DP(P1 ) 333 400 403 300 DP(P2) ageing 1 240 4 260 5 DP(P1 ) CW, annl. 10−9 1.35 357 300 46 −9 DP(P1 ) 1.39 400 200 54 10 longitud. (P1 ) and transvers. (P1 ) Mg diﬀusion in kinks in dislocation core Bamboo DP(P1 ) – 1.1 293 800 – crystal, DP(P1 ) 323 800 – – 403 700 DP(P2) – – twisted, annl. DP(P3) 533 600 125 10−13 P3: Cottrell atmosphere around moving dislocation kinks 1.34

Tan and Kˆe (1991)

Othmezorni-Decerf (1983) Tan and Kˆe (1990)

Kˆe and Tan (1991)

Tan and Kˆe (1991)

Zhu and Kˆe (1993)

Kˆe and Tan (1991)

4.3 Metals of the IIA–VIIA Groups and their Alloys 209

1.54

2.5 · 104 4–6 1 1.3 ∼2

Al–Mg(1.1) (wt%)

Al–Mg(2)

Al–Mg(2) (wt%) Al–Mg(4.7) (wt%)

Al–Mg(6) (wt%)

Al–Mg(7.5) (wt%)

Al–Mg(0.9–12) (wt%) 0.4–98 Al–Mg(5.45) (wt%) 1.5 Al–Mg(5.5) 45

f(Hz)

composition

373–473 438 358 423 508

453 523 313 353 393 500 496

490–522 250

343 393 433 483 273

Tm (K)

0.5–10 3.5 60 160 120

300 380

8

900 1000 800 600

Qm −1 (10−4 )

135 116.3

66.9 – 102.5 125.5 125.5

H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued state of specimen

Z Z

DP(P2) DP(P3) Relax. solute clusters Z Z

GB

quen., aged CW, annl.

annl., slowly cooled

PC, twisting, annl. annl., quen.

irr(He) CW

PC, twisting, DP(P1 ) DP(P1 ) annl. DP(P2) DP(P3) thermoelasticity

mechanism

Belson et al. (1970) Nilson (1961) Ali et al. (1981)

Dey and Quader (1965)

Randall and Zener (1940) Zaritzky (1993) Othmezorni-Decerf (1983) Kˆe and Tan (1991)

Kˆe and Tan (1991)

reference

210 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

493 533 125 167 GB (solute) GB (solute)

493 493 110–170 460

Al–Si(0.14) (wt%) 0.9

Al–Si(0.86) (wt%) 0.8

Al–Si(0.86) (wt%) 1–2

3

1.3–8.5

Al–Si(0.7)

Al–Si(1) (wt%) 429

210 21 112 483 461

0.032 2.4

80

100–150

40–60

120–160

80–160

300–250

50 2.5

88.8

96

108

157 2 12

10−13

1.3 · 10−12

1.6 · 10−40 1.6 · 10−13 9 · 10−15

CW, annl.

CW irr(e)

PC, quen., aged PC, quen., aged SC, quen., aged drag of Si by SC, PC disloc., PhT disl., diﬀus. SC, PC, around precip. quenc., annl.

Si clusters interchanging with free vacancies

GB(Si)

disl./impur.

DP/HTbgr. 796 CW, annl. 2100 quen. 170 5 205 12 ﬁrst stage of the formation of Guinier–Preston zones 0.2–2 recryst. 560–580 500 CW recryst. 810 400 maxima are found which arise from primary and secondary recrystallisations

0.3–2.6

Al–Mn(0.03–1.1) (wt%) Al–Mn(1.12) (wt%) Al–Si(0.05) (wt%) 1 Al–Si(0.07) (wt%) 107 3 · 107 Al–Si(0.27–1.17) 1 (wt%) Al–Si(0.39) 1.1

Al–Mg(5) (wt%) + Mn, Cr impurities Al–Mg(5) (wt%) Al–Mg(13) (wt%)

Pichler et al. (1993b) Okabe et al. (1981)

Guan et al. (1996) Johnson and Granato (1985) Ting-Chuan Lei (1981) Molinas and Povolo (1993) Entwistle et al. (1978)

Kiss et al. (1983a)

Rivi`ere (2004) Othmezorni-Decerf (1983)

Baik and Raj (1982)

4.3 Metals of the IIA–VIIA Groups and their Alloys 211

1

0.1

Al–Si(11.8)

Al(99,97) + SiC(60), vol.%

Al–Zn(21) >373 1.9 Al–Zn(25–30) 1 100–150 50–200 Al(99.999) wires 373 – 0.05–3 + Cu, Zn 550 140 covering Al ternary and industrial alloys Al–Cu(0.3) 35000 245 (wt%) +H

Al–Sn(0.011) 1 Al–Zn(3.7) (wt%) 0.26

−4

(10

6–60 95–180

0.6 0.8 0.85 0.76 0.75

Qm

250/200 heating/ cooling 559 60 294 5

240 485

333 323 463 378 440 470

334 405 207 507 347 0.55

Al–Si(1) + Au impurities Al–Si(1) + Cu, Pt,W impurities

Al–Si(3.8–11.5)

Tm (K)

f(Hz)

composition

−1

5.8

96

174 53

58 48 96 82 96 154

3 · 10−7

10−17

5.3 · 10−4

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

PD(H/Cu)

PhT(prec.) PhT(prec.) Zn GB

GB(Sn) PD(Zn/vac)

disl. from PhT GB sliding

GB(Si)

GB sliding

GB sliding

mechanism

electrolytic deposition

PC, CW, annl.

def., annl. quen.

rapidly solidiﬁed eutect. Si particles

Sput.th.f. on Si

state of specimen

Leger and Piercy (1981)

Iwasaki (1984) Haefner and Schneider (1971) Nowick (1951) Merlin et al. (1974) Kiss et al. (1994)

Carreno-Morelli and Schaller (2002)

Tan and Liou (1989) Zhou et al. (1993)

Bohn and Su (1993), Su and Bohn (1993)

reference

212 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Al–Li(8)–Zr(0.03) (wt%) Al–Mg(0.16) (wt%) + H Al–Mg(2)–Sc(0.2) (wt%) Al–Mg(0.6)– Si(0.64) (wt%) Al–Mg(1.17)– Si(0.64) (wt%)

Al–Cu(0.86)– Si(0.34)– Mg(0.155–0.47) Al–Fe(0.007)– Zn(0.1) (wt%) Al–Fe(0.168)– C(2) (“AlC2”)

Al–Cu(4.5)– Mg(1.5)– Mn(0.6) (wt%) Al–Cu(4.5)– Mg(1.5)– Mn(0.6) (wt%) (2024) Al–Cu–Mg–Si

520–530 488 450

4–6

2.25

1.1

35000

1

0.02–10

(1–3) · 107

1530

180

275 126

GB

GB

293 56.5 stress-induced ordering of complex atom groups 293 Z (anisotropy 0.44–4 of relax. depending on orientation strength) PD(Zn/int) PD(Fe/int) 20 0.7 DP(P1 ) 250 50 – – 450 250 – – 630 250 212 8.6 · 10−21 dislocat. dragging 460 30 116 4.5 · 10−14 Z 530 110 – – – PD(H/Mg) 245 6.7 2 · 10−7

PhT(prec.) θ prec

2 · 103

400

757

0.16

58–77

517

24

CW, annl. 450◦ C

quen., aged.

quen.

dispersoids

irr(e)

SC, quen., aged

sol.tr, quen, aged 300 K

quen.

Szenes and Zs´ ambok (1974)

Williams (1967a)

Perez-Landazabal et al. (1996) Leger and Piercy (1981) Zaritzky (1993)

Wallace et al. (1985) Pichler et al. (1993a)

Entwistle (1953–1954) Elliott and Entwistle (1964)

Rivi`ere and Pelosin (2000)

Malachevsky and De Salva (1987)

4.3 Metals of the IIA–VIIA Groups and their Alloys 213

Al–Mg–Mn–Cr (5056) Al–Mn(1)– Fe(0.5) (wt%) Al–Mn(0.8)– Fe(0.03) (wt%)

Al–Mg–Si (6062) Al–Mg–Si (6063) Al–Mg–Si(6063/T6)

Al–Mg(1)–Si(2) (wt%)

1

Al–Mg(0.64)– Si(0.56) (wt%) Al–Mg(0.45)– Si(0.46) (wt%) Al–Mg(0.57)– Si(0.5) (wt%)

Qm (10

−4

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

GB

mechanism

0.4–50 550–600 590–680

low low

483 0.1–0.15

120 154

PhT

PhT

LT bgr.

1.3 · 10−18 HT bgr.

360 up to 22 79 10−12 reorientation of complexes which contain Si near dislocations 360 84 DP(P0 ) 440 113 DP(P1 ) 440 130 PhT(prec.) 490 128 GB(P3 ) 560 146 SB(P4 ) 640 243 disl. climb GB + 530–550 <28 118 4 · 10−15 precipitates Si in GB 450–470 <28 145 2 · 10−17 430 100 149 1.9 · 10−18 dislocation breakaway and dragging GB + particles 480 180

moving of Si atoms near grain boundaries 450 14

Tm (K)

5500

1

1

1 ≈1

44

1–30

1–30

f(Hz)

composition

−1

Xie et al. (1996)

Urreta de Pereyra et al. (1988)

Urreta de Pereya et al. (1987) Ghilarducci de Salva et al. (1985) Ghilarducci de Salva et al. (1985)

reference

Carreno-Morelli et al. (1993) extruded, aged Carreno-Morelli et al. (1996b) (T6) sput.th.f. Xiao Liu et al. (1999) Diallo and Mondino (1980)

macrocryst. quen., aged

PC, quen.

PC, quen.

PC, quen.

CW, annl. 500◦ C quen., CW

state of specimen

214 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Al–Si–Cu– Mg(6,061) Al–Si(0.0014)– Mg(0.001)– Zn(0.0019) (wt%) + Saﬃl ﬁbres Al–Cu(4) (wt%) +Al2 O3 (10–30), vol.% Al(7075) + SiC (15), vol.% Al–Si(7)–Cu(4), wt% + Al2 O3 (10–30), vol.% Al–Cu(4) + Al2 O3 (10–30), vol.% Al–Cu(4)–Mg(1)– Ag(0.5), wt% + SiC (60), vol.% Al–Zn(6) + SiC (60), vol.%

Al–Si(1)–Cu(0.5) (wt%) Al–Si(0.66)– Fe(0.22) Al–Si(1)–Ti(0.2)

400–700

430–450

140 200

130 150–200 cooling 180

2

2

0.3 1

1 0.016

0.016

no peak

∼350 0.4–3.5

130–230

105

5500

210–270

475

no peak on heating

60

50–200

≈10

1–40

0.05

interface microcracking

disloc. generation at particles

disloc. generation

P1 , P 2

modiﬁed GB struct. LT bgr.

GB

squeeze casting

squeeze casting

squeeze casting

quen., annl. (T7561) squeeze casting

squeeze casting

dep. on annealing

Sput.th.f.

amplitude dependence sput.th.f. on Si

sput.th.f.

Carreno-Morelli and Schaller (2002)

Parrini and Schaller (1996) Carreno-Morelli and Schaller (2002)

Carreno-Morelli et al. (1996a)

Vincent et al. (1996)

Parrini and Schaller (1994)

Urreta and Schaller (1993)

Xiao Liu et al. (1999)

Bohn and Su (1993)

Mizubayashi et al. (2004a) Lebedev (1992)

4.3 Metals of the IIA–VIIA Groups and their Alloys 215

5 20 90 40 53 413 538

358 190

7 · 104

592 548 1

1.64

2 · 104

714 423 636 573 (8–9) · 103 210–260

1 − 104

1

Bi(99.999)

Bi

Bi–Ag(2.5)

Cd Cd(99.90)

Cd

Cd

Cd(99.999)

Cd(99.9995)

Cd–Ge(1.9)

300

413

0.5

Bi Bi(99.9)

Tm (K)

f(Hz)

composition

(10

−4

DP DP DP

GB

mechanism

SC, CW (slipping)

state of specimen

86.6 – 11.6

91.2

GB PhT(melt) recovery

(motion of interstitials)

GB CW (bamboo)

SC, CW DP (twinning) 2.2 9 · 10−8 motion of twinning dislocations GB 82–92.1 PhT(melt) – diﬀusion at the boundaries of inclusions 78

108.8

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued

Qm −1 ∼ f −n with n = 0.09 for f = 0.8–103 Hz; n = 1 for f = 103 –104 Hz (diﬀusion at the boundary of inclusions) 57

500 200

80

1000 700

0.05 0.05 2.5 0.1 0.4

Qm

−1

Postnikov et al. (1963) Gindin et al. (1973) Drapkin et al. (1980) Youssef and Bordoni (1994) Cook and Lakes (1995a) Artemenko et al. (1970)

Drapkin et al. (1980) Artemenko et al. (1970)

Postnikov et al. (1963) Sato and Sumino (1977)

reference

216 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

18 no peak within 296–390 392–383 1450

1

1

0.2

0.01

4.5 · 103

5 · 104

Cd–Mg(8–85)

In In(99.99)

In(99.9)

In(99.99)

In(99.999)

In

0.5

3.5 · 104

In–Bi(62) (wt%)

In–Sb compound

In (comm. purity) 3(10−3 10−2 )

300

1

Cd–Mg(30) Cd–Mg(33)

80

79.5 Z

Z

231

608 1148 222

333 383 300

233–293 300

1620 1680

4.5

0.5–0.6

300 1000

GB

Enrietto and Wert (1958) Lulay and Wert (1956) Cost (1965a) Cook and Lakes (1995b) White et al. (1967)

Hermann (1968)

Zhu et al. (2004)

Rivi`ere (2004)

Postnikov et al. (1963) Cook and Lakes (1995a) creep recovery Ledbetter et al. (1996b) sput.th.f. Xiao Liu et al. (1999) Hermida et al. (2000)

–

creep def. PC

peak close to melting point, superposed on expon. high T backgrd. structural changes in the melt liquid state 32.8 disl. on surface [111] surface damaged [211] surface 41.5 same damaged

broad spectrum of tunneling states associated with dislocations

superposed low frequency background (diﬀusion controlled)

74

2.5 · 10−14 Z 1200 Z + high T backgrd. Z 283–433 H = 0.577 Tm − 146.5 (Qm −1 minimal for compositions MgCd3 , MgCd, Mg3 Cd)

293

0.75

up to 1450

Cd–Mg(29.3)

293

1

Cd–Mg(5–30)

4.3 Metals of the IIA–VIIA Groups and their Alloys 217

Pb Pb

In–Tl(18–24) In–Tl(24)

In–Tl(24)

In–Tl(10)

In–Sn eutectic In–Tl(10)

803 1038 297 Qm −1 ∼ f −n with n = 0.2

5800 5600

100 300 150

400 10−4 –10−5 273 270 2 5–100 67.4 368–390 40–500 111.7 (reorientation of Tl atom pairs with ∼1 273 67 390 29 21 293 300 60.8 (pre-martensitic ﬂuctuations) 330–180 up to 270 1 104–121 100 312 100 77 (pre-martensite, higher temperature

10−1 –105 In–Sn(83.4) (γ) In–Sn(48) eutectic

In–Sn(77.6) (wt%) 4

38

140

5 · 104

In–Sn eutectic

340

20.4

mechanism

thermoelastic eﬀect

PhT(mart) 3 · 10−15 than necessary for MT)

creep Z 10−14 5.6 · 10−17 respect to grain boundaries) Z motion of twin boundaries

super-posed on high temperature backgrd structural changes in the liquid state PD

) H(kJ mol−1 ) τ0 (s)

5 · 104

(10

In–Sn (γ)

Qm

Table 4.3. Continued

f(Hz)

Tm (K)

−4

composition

−1

twinning

PC

melt

state of specimen

Kamel (1949)

Hwang et al. (1987)

Postnikov et al. (1969, 1970) Wuttig et al. (1985) De Morton (1969)

Lakes and Quackenbush (1996) Brodt et al. (1995) De Morton (1968)

Hermida et al. (2000) Hermida et al. (2000) Zhu et al. (2004)

reference

218 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Pb(99.999)

4.5 · 103

250 1.8 · 107 1.8 · 107 35 low T plateau

40–60 150 21 20 3.5

100–30

235 100–300

Pb(99.999)

120 160

35 300

235

Pb

87.9

4.1 4.1 0.48

3.9

–

70 3.2 20 – 900 88–96 – 20 70

Pb up to 70 (99.999) Pb(99.9999) Pb(99.9999)

566 524 10

Pb

up to up to up to 100 up to up to 30 250 200 30–110

800

Pb(99.999)

1

338

0.78

0.3

Pb(99.999)

35

104

0.15

40 130 423 563 15 30 40 30 110 250 35

35

104

Pb (purity commercial) Pb (purity chemical) Pb(99.9)

3.3 · 10−9 3.3 · 10−9 –

1.5 · 10−9

3.3 · 10−9

1.5 · 10−8 –

DP(B). DP(B) DP(B) + vacancies DP (dislocat. kinks)

DP(B) GB?

GB PhT(melt) DP DP(B2 ) DP DP(B1 ) DP(B2 ) DP(P1 ) DP(B)

DP(B2 )

GB

sput.th.f.

CW, annl.

annl.

acoustic coupling technique CW, annl.

CW

PC

Xiao Liu et al. (1999)

Cook and Lakes (1995a) Progin et al. (1996a,b)

Progin et al. (1994)

Postnikov et al. (1963) Wagner and Stangler (1977b) Drapkin et al. (1980) Soifer and Shteinberg (1982) Quenet et al. (1993)

Bordoni (1960)

4.3 Metals of the IIA–VIIA Groups and their Alloys 219

3.2

8

4 · 103

Pb(99.9999)

Pb(99.9999)

Pb–In(30)–Sn(14), ppm Sn Sn(99.99)

296–390

5 · 104

Sn(99.99)

Sn

Sn(99.99)

Sn(99.9985)

1.36 114 780 707 1

350

260

120–130 215 120 250 230 280

Tm (K)

318 438 373 493 313 363 393–403 1 and 200 300

Sn(99.92)

3.2

Pb(99.9999)

300

f(Hz)

composition

100 600 500 600 200 100

200

500

10 400 20 400 190 20

Qm

−1

(10

−4

mechanism

54.8

cooling heating

77–88

81.6

72–87

4 · 10−4

9.6 binding to disl.

HT bgr.

PhT(polym) GB

GB PhT(melt.) GB PhT(melt)

GB

(ADIF)

DP(P1 ) 2 · 10−15 62.5 – DP(P1 ) – Climb of jogs, pipe diﬀusion

) H(kJ mol−1 ) τ0 (s)

Table 4.3. Continued reference

annl.

SC

CW

recrystallised

Cook and Lakes (1995a) Hermida et al. (2000)

Rotherham et al. (1951) Postnikov et al. (1963) Drapkin and Fokin (1980) Kopylov et al. (1983)

Guti´errez-Urrutia et al. (2004) Hinton and Rider (1966)

Gallego (2001)

CW (as rolled) Gallego (2001)

state of specimen

220 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

HT bgr. Qm −1 ∼ f −n with n = 0.17 (no Debye peaks) GB 423 192.5 up to 10−25 1000 (relaxation along interphase boundaries in eutectic) Qm −1 ∼ f −n with 300 HT bgr. n = 0.12 (no Debye peaks) 300 Eutectic

CW

∼100

1

∼2 · 107

1.1

Zn(99.99)

Zn(99.999)

Zn(99.999)

<100 5.8

21.8 GB

GB

DP (basal. plane) ∼170 15.4 DP (prism. plane) ∼230 19.2 DP (pyram. plane) GB 383 930 95.4 10−13.8 according to Shwedow et al. (1982), the GB peak consists of

413

180

Zn Zn(99.5)

annl. two peaks

CW compression at RT

PC

maxima observed for hcp → bcc with Qm −1 ≤ 0.02. According to data of Maltseva and Ivlev (1974) a shrinkage of PhT occurs at polymorphous transformation: Qm −1 = 0.02 for hcp at 507 K and 0.016 for bcc at 513 K

10−6 − 104

Sn–Sb(5) (wt%)

Tl Tl(99.99)

0.57

Sn–Pb(38)

Sn–Cd(32.25), wt% 10−6 − 104

Roberts et al. (1969)

Barnes and Zener (1940) Postnikov et al. (1963) Kayano (1969)

Mordyuk (1963) Maltseva and Ivlev (1974)

Quackenbush et al. (1996)

Quackenbush et al. (1996) Homer and Baudelet (1977) 4.3 Metals of the IIA–VIIA Groups and their Alloys 221

0.1–0.3

Zn–Al(27.26) (wt%)

Zn–Al(22) (wt%) 1 Zn–Al(22)– 1 Sc(0.55)–Zr(0.26) (wt%)

1

Zn–Al(7.2–55.2)

10−6 –105 ∼2000

10

Zn(99.997)

Zn(99.99) Zn(99.999) + 5 ppm Cd + 1 ppm Fe

f(Hz)

composition

(10 3.4 15.4

) H(kJ mol−1 ) τ0 (s)

570–670 (1. run) 558 (3. run) 491 468

GB GB PhT(precipitates)

DP(δe )

0.21 3500 3200

DP(δt )

0.15–0.17

–

2.9 · 10−8

7.1 · 10−8

DP(B1 )? DP(B2 ) basal syst. DP(Ph ) Hasiguti DP(Bp ) pyramid. DP(P1 ) basal and pyramidal GB(?)

basal disl. pyram. disl.

mechanism

0.22–0.25

80–130

–

>10

240–260 460–475

16.4

0.5

200

14,5

20

little variation with frequency 2 13 13.5 2.1 · 10−8

Qm

Table 4.3. Continued −4

200

300 140–160 170

140–295

Tm (K)

−1

Soifer and Shteinberg (1982) Wang et al. (2004) Yokoyama (1985)

reference

quen., CW, annl.

Luo et al. (2004)

quen. 350 ◦ C Barinov et al. (1961) superplastic Kawabe and deformation Kuwahara (1981)

SC, CW (impact)

SC

state of specimen

222 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides

223

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 4.4.1 Rare Earth and Group IIIB Metals In rare earth metals and their alloys, the following internal friction eﬀects are observed: – Dislocation peaks. Intrinsic peaks (La, Lu, Y) and impurity peaks SK(H), SK(D) (Lu, Y, Sc) – Eﬀects due to magnetic phase transitions (Ce, Dy, Er, Eu, Gd, Ho, Tb) – Grain boundary peaks (Nd, Pr) – Eﬀects due to polymorphic transformations (Ce, La, Nd) – Relaxation due to C, N, O (Sc, Y, Yb) – Relaxations due to H and D diﬀusion including H and D tunneling and additional peaks due to interaction of H, D with O atoms (Sc, Y) – The Zener relaxation due to H and D (Lu, Sc, Y)

1

Ce

Ce–Nd(2.5–12) (wt%)

Ce–Dy(2–16) (wt%) Ce–La(2.5–12.5) (wt%)

1

1

245 400 185

1

Ce(99.84)

Ce

12.5 45 190 400

4.5

Ce Ce(98.5)

640–480 –

–

210 170–90 400

80–20 –

up to 600

(cooling) (heating) (electron transition) (electron transition)

≈100 – up to 600

τ0 (s)

(AFM ↔ PM) 2 · 10−12 9.6 – – – –

H(kJ mol−1 )

10–80 160 640 300

100

Qm −1 (10−4 )

12.5–9 130

185–140

650

f(Hz)

composition

Tm (K)

PhT(α → γ) PhT(β → γ)

PhT(β → γ)

PhT(mag) PhT(α → γ)

PhT(α ↔ γ)

PhT(polym) β↔γ PhT(α ↔ γ)

PhT(mag) DP(B2 ) PhT(polym) PhT(mart)

GB(?)

mechanism

Korshunov et al. (1981)

state of specimen

Table 4.4.1. Rare Earth and Group IIIB Metals (at.% if not speciﬁed diﬀerently)

Polner et al. (1975); Postnikov et al. (1975a); Polner and Sharshakov (1976) Sharshakov et al. (1977)

Goncharova et al. (1976) Korshunov et al. (1981)

Dashkovskij and Savitskij (1961) Postnikov et al. (1975a); Polner and Sharshakov (1976); Sharshakov et al. (1977)

reference

224 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

107 1.5 · 107 5 · 107 1 (1–2) · 103 (1–2) · 103

1980

2030 305 2 · 107

Dy

Dy Dy

Dy(99.9)

Dy

Dy(99.9)

Dy (high purity)

Dy(99.9 and 99.99)

Dy–Gd(50) (wt%)

Dy(99.8)

Dy

231.5

231

(Curie temperature = 232 K)

PhT(mag)

PhT(mag)

SC

Goncharov et al. (1974)

sharp increase of IF just below the Curie temperLevitin and Nikitin ature (85 K) (1961) ≈175 (AFM-PM) PhT(mag) the peaks were observed just below the Curie (85 K) and N´eel Rosen (1968c) (178 K) temperatures a sharp peak in the vicinity of the N´eel temperature SC, c-axis Tachiki et al. (1968) 177.3 the N´eel temperature PhT(mag) uthi SC Pollina and L¨ (1969) ≈90 ≈80 (FM-AFM) Sharshakov et al. PhT(mag) PhT(mag) ≈178.5 (inﬂection) (AFM-PM) (1978a) 85 (FM-AFM) PhT(mag) SC Kataev and Sattarov PhT(mag) 162 (1989a) 178 (AFM-PM) PhT(mag) ≈100 sharp increase of IF below this temperature Kataev and ≈190 sharp increase of IF above this temperature Sattarov (1989b) ≈30 ≈260 ≈6.7 ≈170 SC, c-axis Tishin and Shipilov 1.6 · 10−14 37 85 (inﬂection) (FM-AFM) PhT(mag) (1992) ≈5 ≈178 (AFM-PM) PhT(mag) ≈5 ≈250 – DP magnetic damping in the FM phase Burkhanov et al. 37 215 (1993) 270 – 36.5 2.9 · 10−11 DP

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 225

(FM-AFM) (AFM-PM)

SC

state of specimen

1 · 107 300

1 1

Eu

Gd Gd

Gd

190 240 (bend) 15

broad peak

PhT(mag)

microeddy currents

(below the N´eel temperature) PhT(mag) (change of the electron structure in PM) PhT(mag) very sharp drop at the AFM → PM transition

230–240 up to 50

86 150 87

PhT(FM-AFM) 20 (anomalous behaviour) 60 (change in the antiferromagnetic structure) 220 (formation of short-range order in the PM phase) 1.78 36–37 SC, c-axis 240 (very sharp peak) PhT(mag) 110–120 (in a paramagnetic phase) ≈70 1.9 · 10−12 DP 350 52 points of anomalous behaviour due to magnetic transitions were observed at 18.5, 27.3, 29.8, 33.8, 36.8, 41.3, 53 and 82 K 36.8 (spin-slip transition) ≈200 PhT(mag) SC, c-axis ≈70 – 350 –

1 · 107

Eu(99.9)

Eu

Er–Sn(0.3)

Er

Er

Er

– – ≈15

≈100 ≈186 ≈260

(1–2) · 10

Dy–Tb(12.5) PhT(mag) PhT(mag)

PhT(mag)

(AFM-PM)

≈2

≈175

≈103

Dy–Tb(12.5) 3

mechanism

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Tm (K)

f(Hz)

composition

Table 4.4.1. Continued

Burdett (1968)

Burdett and Layng (1967)

Bodryakov and Nikitin (1998a)

Rosen (1968b)

Nikitin et al. (1993, 1994)

Bodryakov and Nikitin (1994)

Rosen (1968c)

Kataev and Sattarov (1989b)

Shubin et al. (1985)

reference

226 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

≈230 ≈290 221 294 140

≈103

800–1200

Gd

Gd

10

210–234 291

(3–6) · 107

Gd

Gd–Tb(40)

290.2

5 · 106

Gd

270 320

221

220–240 ≈290

3 · 103 1.6 · 103

Gd(99.8)

3

up to 8 up to 1.5 Curie temperature

≈230 ≈285

(5–7) · 103

Gd(99.8)

10 15

FM → PM –

PhT(mag) –

PhT(mag)

PhT(mag) PhT(mag) PhT(mag)

PhT(mag) PhT(mag)

≈1 change of the easy axis ≈4 Curie temperature (FM-AFM) (AFM-PM) (possible change in the magnetic structure) (FM-AFM)

PhT(mag) PhT(mag)

PhT(mag)

PhT(mag)

PhT(mag)

PhT(mag) PhT(mag)

PhT(mag) PhT(mag) PhT(mag)

spin reorientation Curie temperature

(Curie temperature, sharp λ-shaped peak)

up to 8 macro-eddy current loss Curie temperature

(change of the easy axis) (FM-PM)

220 290

5 · 107

Gd

(drop) – (Curie temperature)

15 115 224 292.5

1 · 107

Gd

SC

SC, b-axis

SC, c-axis

P, SC

magnetic ﬁeld

magnetic ﬁeld

SC, c-axis

Kataev and Shubin (1979)

Spichkin et al. (1999)

Bodryakov et al. (1991, 1992)

Anikeev et al. (1983)

Long and Stern (1971)

Maeda and Somura (1971b)

Maeda (1971a)

Moran and L¨ uthi (1970)

Rosen (1968c) 4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 227

≈240 245–280

≈103

8.9 · 104

Gd–Tb(40)

Gd–Y(5.5–12)

105 123 20 39 50 104

3.1 · 103

3 · 103

4.5

Ho

Ho–Er(50)

La La(98) 615 600

20 24

1.5 · 107

Ho

200 –

(heating) (cooling)

(inﬂection) (rapid rise at the Curie point) (inﬂection) (inﬂection at the N´eel point)

(broad smooth maximum) (anomalous abrupt increase)

(Curie point) (change of the magnetic structure)

PhT(α → β) PhT(β → α)

PhT(mag) PhT(mag) PhT(mag) PhT(mag)

PhT

PhT(mag) PhT(mag)

PhT(mag)

132.1

5 · 107

Ho N´eel temperature

sharp peak at the N´eel temperature

4.5 · 107

Ho

SC

SC, b-axis

SC

SC

SC, c-axis

the following peaks were observed: at 20 K (PhT(FM-AFM)); 72 K (changes in AFM); 133 K (PhT(AFM-PM)); 160 K (short-range order in the PM phase)

SC

state of specimen

107

PhT(mag)

≈7

mechanism PhT(mag)

τ0 (s)

≈1

Qm −1 (10−4 ) H(kJ mol−1 )

Ho

Ho

Tm (K)

f(Hz)

composition

Table 4.4.1. Continued

Dashkovskij and Savitskij (1961)

Spichkin et al. (1996b)

Bodryakov and Nikitin (1998a)

Tachiki et al. (1974)

uthi Pollina and L¨ (1969)

Tachiki et al. (1968)

Rosen (1968c)

Beznosov et al. (1999, 2001)

Kataev et al. (1985)

reference

228 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.6 160 215 350 up to 15 up to 13 up to 30

on screw dislocations

kinks on edge dislocations

DP DP DP(B)

CW

Vajda et al. (1981, 1983)

peaks at 130 and 160 K were detected

(La0.77 Gd0.33 )Al2 1

Lu Lu

Trivisonno et al. (1981) Garber et al. (1965)

very broad maximum PhT(bcc → hcp) or strong increase of damping

(La0.77 Gd0.33 )Al2 107

CW

Hammerschmid et al. (1981a,b)

in the range 75–250 K no DP has been detected

(La0.77 Gd0.33 )Al2 104

Lenz and Ewert (1980)

same as with LaAl2

Ewert et al. (1981)

Bodryakov (1993)

Pan et al. (1985)

(La0.77 Gd0.33 )Al2 107

three damping anomalies were observed in the super-conducting state, connected with non-paired electrons or with hydrogen

107

1.4 · 10−5 7.3 · 10−9 2 · 10−8

LaAl2

1.73 20.4 27.7

96–120 252–266 382–404

≈1 ≈10 ≈50

≈100 2 200 33.8 70 DP the maximum was observed after CW or the polymorphic transformation and is accounted to interaction of interstitial atoms with dislocations ≈270 2 ≈380 5 (heating) 520 PhT(α → β) 10 620 PhT(β → γ) up to 500 (heating) 580–590 up to 300 PhT(γ → β) (cooling) 450–470 up to 300 PhT(β → α) (cooling)

1.2–2.3

≈4

2

La(99.8)

La(99.8)

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 229

0.6

0.6 0.6

Lu–D(0.05–0.2D/Lu)

Lu–H(0.2H/Lu)

Lu–H(0.1H/Lu)

Sc–D(up to 0.3D/Sc)

Sc

Pr

Pr

Nd

1

1–2

1–2

0.6

Lu–D(0.2D/Lu)

Nd

f(Hz)

composition

Qm

up to 20 –

210

730 840 990

850 920 1015 1135

up to 15

10 15 10

10 20 30 150

≈215 250–260 up to 25 342–354 up to 25

55.8

137 264 509

196 323 587 –

53.8 214 Qm −1 ≈ 7.5 · 10−3 · (H/Lu)

≈225 ≈260 350

1 · 10−11

1 · 10−13

Z(D)

GB – –

PhT(polym)

GB –

Z(H) SK(H) DP(B)

Z(H)

Z(D) SK(D) DP(B)

CW

CW

Vajda et al. (1989, 1990, 1991a)

Maltseva et al. (1980)

Maltseva et al. (1980)

Vajda et al. (1981, 1983)

Vajda et al. (1981, 1983)

Vajda et al. (1981, 1983)

Vajda et al. (1981, 1983)

mechanism state of reference specimen

3.7 · 10−15 Z(D)

(10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.4.1 Continued

61.5 220 Qm −1 ≈ 7.5 · 10−3 · (D/Lu)

Tm (K)

−1

230 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

8 20

3.5 · 103

1

Sc–D(0.3–10)

Sc–H(up to 0.3H/Sc)

Curie temperature shoulder N´eel temperature

PhT(mag) PhT(mag)

SC

223 227.6

5 · 107

Tb

PhT(mag)

PhT(mag) (near the N´eel point) (formation of short-range order in the paramagnetic state)

≈229 260

(FM-AFM)

≈17

223

1 · 107

Tb

Tb

Tb

PD(O) PD(O/O)

Qm −1 = 7 · 10−5 CO (at.%) up to 0.2

430 520

3.5 · 103

Sc–O(0.024–0.91)

PD(H/O) PD(H/O) Z(H)

up to 0.02 (tunneling) up to 0.08 up to 0.1

20 130 280

SC

3.5 · 103

PD(H)

Sc–H(0–3)

(tunneling)

the following peaks were observed: at 10 K(PD(H/O/O, tunneling); at 30 K (PD(H/O), tunneling); at 80 K (PD(H/O/O)), 130 K (PD(H/O)), and 190 K (SK(H)); at 270 K (PD(H/H))

up to 6

51.9–58.7 7.5·10−16 − Z(H) 3.6 · 10−14

PD(D) PD(D)

SC

SC

3.6 · 103

25

up to 30

(tunneling) up to 1.5 (tunneling)

PD(D) PhT(ord)

≈0.5 – (tunneling) –

PD(D)

up to 9

Sc–H(0.085)

Sc–H(H/Sc=0.25) 9.7 · 105

50 170

1.01 · 106

Sc–D(D/Sc=0.1)

200

≈50

(0.73–3.23) · 106

ScD0.18

Pollina and L¨ uthi (1969)

Rosen (1968c)

Belov et al. (1961)

Trequattrini et al. (2004a)

Trequattrini et al. (2004b)

Trequattrini et al. (1999, 2000)

Leisure et al. (1993b,c)

Vajda et al. (1989, 1990, 1991a)

Trequattrini et al. (2004b)

Leisure et al. (1993a)

Leisure et al. (1993c) 4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 231

≈228 ≈231 ≈220 220 229 224

(3–6) · 107

≈103

(1–2) · 103

1.5 · 10

2 · 10

1000

Tb

Tb

Tb

Tb(99.9)

Tb–Dy(50)

Tb–Er(25)

3

214–219

1.5 · 107

Tb

(10

) H(kJ mol−1 ) τ0 (s)

Table 4.4.1. Continued

≈15 ≈80 –

≈30

(FM-AFM) (AFM-PM) –

(FM-AFM) (AFM-PM) (FM-AFM)

(FM-AFM) (AFM-PM) –

(FM-AFM)

(FM-AFM) (AFM-PM)

PM-AFM

spin-spiral structure-FM PM-spin spiral structure (shoulder)

Qm

−4

PhT(mag) PhT(mag) PhT(mag)

PhT(mag) PhT(mag) PhT(mag)

PhT(mag) PhT(mag) PhT(mag)

PhT(mag)

PhT(mag) PhT(mag)

PhT(mag)

PhT(mag) PhT(mag)

mechanism

anomalous IF was observed at 20, 135 and 200 K (PhT(mag))

154 204 ≈270

220 229 ≈210

219.7 225

1.5 · 107

Tb

3

Tm (K)

f(Hz)

composition

−1

SC

SC, b-axis

SC, c-axis

SC, B=0.08 Tl

SC

SC, c-axis

SC, c-axis

SC

SC, c-axis

state of specimen

Kataev and Shubin (1979)

Kataev and Sattarov (1989a)

Spichkin et al. (1996a)

Kataev et al. (1989)

Shubin et al. (1985)

Anikeev et al. (1982, 1983)

Jiles et al. (1981)

Maekada et al. (1976)

reference

232 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

279 87 160

1 500 8.1 · 105 1

500 109–126

628 1710

Y–D(D/Y=0.2)

Y–D(D/Y up to 0.17)

Y–D(D/Y=0.1)

Y–H(0.05–0.2H/Y)

Y–H(H/Y up to 0.17)

Y–H(H/Y=0.1)

Y–H(up to H/Y=0.1)

–

≈9 up to 5 up to 25

257–259 ≈280 ≈280

57.7

≈58

57.7

50–59.6

≈16

Qm −1 ∼ H/Y

up to 11

0.058 –

57.7

52.9

PD(D) tunnel PhT(ord)

PD(D)

Z(D)

DP

PhT(mag)

Z(H)

DP(B) or SK(H)

PD(H)

2 · 10−12 − Z(H) 6 · 10−15

5 · 10−11 –

5 · 10−13

(basal plane)

(AFM-PM)

≈130 ≈210 257–259

272

219

0.6 –

Qm −1 ∼ D/Y

up to 11

up to 60

≈400

≈1 · 103

Y 223

(inﬂection) ≈5

170 290

≈178

1 · 103

MHz range

Y(99.5)

Y

Tb–Ho(49) (wt%)

Bodryakov (1992)

Isci and Palmer (1977)

SC, b -axis SC, c-axis

CW

SC

Kappesser et al. (1996a, 1997)

Kappesser et al. (1994)

Kappesser et al. (1993)

Vajda et al. (1991a,b); Vajda (1994)

Leisure et al. (1993a,c)

Kappesser et al. (1993)

Vajda et al. (1991b); Vajda (1994)

Tishin et al. (1995) SC and textured PC

SC

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 233

1 0.5

Yb–N

Yb–O

Yb

Y–C(0.29)–N(0.031)– 1.3 O(0.328)

413

393

383–393 403–413 423 433 493–523

up to 130

up to 160

up to 20 – – 2 –

to 14

to 1.5 to 1.5 to 2

117

105

90 – – 98.8–108 113–121

(tunneling) 14.4 24 57.7 52.9 67.3 3 · 10−13 5.8 · 10−13 – 1 · 10−13 10−12 –10−14

up up up – – up

≈20 ≈90 ≈150 ≈220 ≈280 ≈440

1.8 · 103

Y–H(up to 2.5)– O(up to 0.5)

PD(O/sub)

PD(N/sub)

PD(O) PD(N/O/disl.) PD(C/O/disl.) PD(N) PD(C)

PD(H/O) PD(H/O) PD(H/O) DP(disl./H) PD(H/H) PD(O)

PC

Mah and Wert (1964)

Mah and Wert (1964)

Borisov et al. (1971)

Cannelli et al. (1996, 1997)

Cannelli et al. (1991)

Cannelli et al. (1991)

PD(H/O) PD(H/O) PD(H/O) –

SC

(tunneling) 13.5 21.2 –

≈0.15 ≈0.08 ≈0.07 –

≈20 ≈100 ≈170 ≈220

8.6 · 103

Y–H(1.6)–O(0.27)

PD(H/H)

57.7

3.2

308

8.6 · 103

state of reference specimen

Y–H(0.1)–O(0.054)

mechanism

Trequattrini et al. (1999, 2000)

) H(kJ mol−1 ) τ0 (s)

(2–3.6) · 103 the following peaks were observed: at 10–20 K (PD(H/O/O), tunneling); 30–40 K (PD(H/O), tunneling); 90 K (PD(H/O/O); 150 K (PD(H/O)); 210 K (SK(H)) (dragging of H by dislocations); 280 K (PD(H/H))

(10

Y–H(0.088)

Qm

f(Hz)

Tm (K)

Table 4.4.1. Continued −4

composition

−1

234 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides

235

4.4.2 Actinides In actinides and their alloys, the following internal friction eﬀects are observed: – – – –

Eﬀects due to polymorphic transformations (Np, Pu, U) Dislocation peaks (U) Relaxation due to substitutional impurities (Th) Eﬀects due to the cooperative electron transition (Pu).

β↔γ

65

1 · 107

Pu–Ce(5)

1.44 1.3

0.30

0.25

Th Th–Co(0.004– 0.24)

Th–Co(0.2)

Th–Fe(0.0008– 0.18)

≈193 ≈293

≈213 ≈303

367 238 318

65

1 · 107

Pu–Al(5)

Th

changes of IF due to polymorphic transformations were observed (Fig. 3.7)

≈20 ≈35

6 8 9–13

52.7 81.2

58.6 73.6

78.0

quen. 1300◦ C quen. 1300◦ C

2.9 · 10−15 – 1.8 · 10−15 PD(Fe)

quen.

state of specimen

5.2 · 10−16 2.5 · 10−14 PD(Co)

1.77 · 10−14 PD(Co)

co-operative electron transition

co-operative electron transition

66

PhT(polym)

PhT(polym) PhT

mechanism

≈1

co-operative electron transition

α↔β up to 300 precipitations in the β phase up to 2000

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Pu

852–856

543–556 ≈750

Tm (K)

1 · 107

1.2–1.9

f(Hz)

Pu

Pu

Np

Np

composition

Table 4.4.2. Actinides (at.% if not speciﬁed diﬀerently)

Weins and Carlson (1982)

Weins and Carlson (1982)

Axtell and Carlson (1989)

Rosen et al. (1969)

Rosen et al. (1969)

Selle and Focke (1969a)

Rosen et al. (1968)

Selle and Rechtien (1969b)

reference

236 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

up to 15 up to 3

≈393 ≈425–445 36 250

changes of IF due to polymorphic transformations (IF decreases at ≈938 K due to α → β transformation and increases at ≈1104 K due to β → γ transformation) (Fig. 3.6)

≈700

≈700

1 · 107

≈1

U

U–Mo(1.2– 4.5) (wt%)

U

U

–

PhT(hydr.)?

ﬁrst-order structural change –

–

88

10−14

≈3

520

100

DP DP

U(99.9)

23.1 42.3

155 202

1 · 103

recrystal. PhT(α → β) PhT(β → γ)

PD(Ni)

U

1.1 · 10−11 1.7 · 10−14

3.3 · 10−13 1.8 · 10−15

up to 950 bend ≈400 sharp increase of IF to 1300 · 10−4 phase transitions α → β and γ → β decrease IF

48.5 83.7

≈375 ≈725–775 900–920 1040

≈203 ≈393

2

0.30

U(99.9)

U

Th–Ni(0.2)

–

β-quenching

CW

quen. 1300◦ C

Selle and Focke (1969a)

Rosen (1968b,d)

Hasiguti et al. (1965)

Hasiguti et al. (1965)

Ivanov and Shapoval (1963)

Hasiguti et al. (1962)

Dashkovskij et al. (1960a,b); Dashkovskij (1961)

Weins and Carlson (1982)

4.4 Metals of the IIIB Group, Rare Earth Metals and Actinides 237

238

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.5 Metals of the IVB Group 4.5.1 Titanium and its Alloys In Ti and its alloys, the following internal friction eﬀects are observed: – Dislocation peaks (intrinsic peaks and the impurity peak SK(H)) – Grain boundary peaks – Relaxations due to C, N, O and additional peaks due to interaction between the substitutional and interstitial atoms – Relaxations due to H and D diﬀusion and additional peaks due to interaction of H, D with substitutional atoms – Eﬀects of hydrides and deuterides precipitation and dissolution – Peaks due to phase transitions in hydrides – The Zener relaxation due to H and D in hydrides and deuterides – Peaks due to the polymorphic transformation – Eﬀects in the intermetallic compound TiAl – Eﬀects in the intermetallic compound TiNi – Eﬀects in the carbide TiC and in the cemented carbides based on TiC – Eﬀects of phase transitions in several titanium alloys

115 162 225 1100 1150 26.5 50.5

1

400

5–30

2.9 · 104

1–20 000 140–300 the peak was separated into two components – A and B 38.5 5 · 10−13 − 16.5 · 103 ≈265 10−11

Ti

Ti

Ti

Ti

Ti

0.03–0.14 0.03–0.08

500 –

2–3

5 10

up to 80

2.1 6.8

46.3

33.7 42.3 51

5 · 10−10 5 · 10−13

10−4

1.65 · 104 ≈223 ≈298

1.1 · 10−11 1 · 10−10 1.4 · 10−11

Ti(99.97 and 99.999)

2 – –

220 305 336

1000

Ti(99.7)

200.3

1048

1 110

τ0 (s)

Ti(99.6)

192

Qm −1 (10−4 ) H(kJ mol−1 )

≈893

Tm (K)

0.5

f(Hz)

Ti

Ti

composition

A

DP

DP(π1 ) DP(π2 )

GB PhT(polym)

DP

PD –

DP DP

DP(Pα ) DP(Pα ) DP(Pβ )

GB

GB

mechanism

CW

CW

CW

irr(n)

CW

CW

state of specimen

Table 4.5.1. Titanium and its Alloys (at.% if not speciﬁed diﬀerently)

Petit and Quintard (1976)

Petit et al. (1976)

Wegielnik and Chomka (1975)

Petit et al. (1975a)

Moser et al. (1975)

Petit et al. (1971)

Hasiguti et al. (1962)

Winter and Weinig (1959)

Pratt et al. (1954)

reference

4.5 Metals of the IVB Group 239

Tm (K)

Qm (10

−4

) H(kJ mol−1 ) τ0 (s)

Table 4.5.1. Continued mechanism state of specimen

6

1

Ti

Ti

993

200–225 the peak 165–175 190–220 ≈240

153

390–540 240–247

up to 15 was separated into peaks A, B and C 4.2–4.8 4.3–10 –

≈30

25

GB

C B A

DP

DP

853 GB 200 219 948 GB 200 244 two peaks are accounted to the anisotropy of the hcp crystal lattice

≈2 · 10

Ti (commercially pure)

4

1

≈200

degazation +CW

CW

B 10−11 − 2 · 10−10 the peak A is attributed to the dragging of hydrogen atoms in the vicinity of dislocations, and the peak B to the thermally activated depinning of dislocations CW, irr(n) 0.7–1 DP(Pd ) 133 173 DP(Pd ) 198 DP(Pα ) 223 DP(Pα ) the Pd and Pd peaks correspond to Bordoni-type, and the P α and Pα peaks to Hasiguti-type relaxation peaks in fcc metals. As a result of neutron irradiation after deformation, the Hasiguti peaks are intensiﬁed signiﬁcantly at the expense of the Bordoni peaks

f(Hz)

Ti(5N)

Ti(99.97)

composition

−1

Shwedow et al. (1982)

Gridnev and Kushnareva (1982)

Besse et al. (1979)

Besse et al. (1978)

Miyada et al. (1977a,b)

reference

240 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

GB(?) PhT(polym)

470 873–973 873–973

≈1000

≈1000

TiC0.83

TiC0.9

166.5

120.5 151

5 · 10−14

5 · 10−14 6 · 10−14

PD(C)

peaks may correspond to dislocation motion

673 1 202.4 Qm −1 ≈ 2.8 · 10−5 C2C (at.%)

95–115 225–280

0.8

915

increasing of voids concentration up to 0.26 increases Q−1 from (7–10) · 10−4 to (27–37) · 10−4

Ti–C(up to 2)

Ti–C, N, O Ti–C

Ti

Ti

150 1–6 CW DP SC, CW 1 DP(π2 ) 30 DP 150 1–12 a broad peak at 150 K consisting of three or more component peaks was attributed 20 dislocations to 13 11¯

1.3 1

Ti (commercially pure)

sharp non-relaxation peak. After annealing the peak disappears

sintered

CW

≈390 1147– 1170

5 · 105

GB

Ti(99.96)

10−14

212

970–990

1–4

CW

Ti

DP 10−11 2.5 · 10−15 DP

25.1 48.2

175 215

1600

Ti

Bukatov et al. (1975a)

Bukatov et al. (1975a)

Miller and Browne (1970)

Duﬀy (2000)

Ledbetter et al. (1996a)

Numakura et al. (1991)

Semashko et al. (1988)

Okrostsvaridze et al. (1985)

Tanaka (1985)

4.5 Metals of the IVB Group 241

Tm (K)

Qm (10

) H(kJ mol−1 ) τ0 (s)

Table 4.5.1. Continued mechanism

712

743–753 800

1

1

0.4

1–1.74

9

1

Ti–O

Ti–O(0.08–9.13)

Ti–O(0.5–1.7)

Ti–O(0.9–2.3)

Ti–O

Ti–O(2)–Al(0.1) 723

690

700–725

242 693 Qm −1 ≈ 0.7 · 10−5 C2O (at.%)

0.8

Ti–O(0.93–1.71)

0.24

up to 20

5–25

up to 2.5

up to 50

237.4

207.6

220.5

200

≈25

713–723

0.5

200 313

up to 60 –

Ti–O

240.6

≈710 ≈1000

773

0.5

1

10

−14

2 · 10−17

PD(O/?)

PD(O/O)

PD(O/O)

PD(O/O)

PD(O/O)

PD(O/O)

PD(O)

PD(O)

PD(O) GB

PD(N)

1 356 1210 10−17 30 the peak is related to the movement of dislocations in the TiWCN by a Peierls mechanism GB 1 1520 130 471 10−17 1790 900 548 10−18

f(Hz)

−4

Ti–O(0.8–4.5)

Ti–O

Ti–N(3–4)

Ti–N

Ti WCN–Co(10 vol.%)

composition

−1

TiC+TiWCN +Co

state of specimen

Gupta and Weining (1962)

Wegielnik and Chomka (1979)

Namas (1978)

Bertin et al. (1976)

Clauss et al. (1974)

Browne (1972)

Miller and Browne (1970)

Bratina (1962)

Pratt et al. (1954)

Miller (1962)

Buss and Mari (2004)

reference

242 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1 1 0.8

Ti–O(0.4)–Nb(32)

Ti–O(2)–Zr(0.06– 0.5)

Ti–O(0.09–0.2)– Zr(1–10)

0.2–0.8

713–730 PD(O/Zr)

S(O)

PD(O/?)

705–673 0.7–15 PD(O/Zr) 200.3 the peak height is much greater than for Ti–O alloys

50

12.5

468

723–750

1

1 3.4

Ti–N–O–Mo(9–27)

Ti–N–O–Mo(39)

Ti–N(≥0.04)– O(0.68)–Mo(33) (wt%) 441 486 516 548 587 635 683 738

182–203 218–228

183–203 218–228 500 683

18–63 14–60 7–12 9–10 6–43 4 4 40

up to 8 up to 8 up to 90 –

148 160 172 186

51.4 62.8

51.4 62.8 160.3 180 PD(O/vac) PD(N/vac)

10−14 10−14

PD PD PD PD PD PD PD PD

PD(O/vac) PD(N/vac) S(O) SK

10−14 10−14 10−15 –

468–495 Ti–O(0.4)–H(up to 1 S(O) 0.6 H/Me)–Nb(32) hydrogen increases the peak temperature and decreases the peak height Ti–N–O

1

Ti–O(2)–Fe(0.1)

bcc structure

bcc structure

bcc structure

bcc structure

bcc structure

Gridnev et al. (1983); Kushnareva and Pecherskij (1986a)

Mishra and Asundi (1977)

Mishra and Asundi (1977)

Golovin et al. (1996a, 1998b)

Miller and Browne (1970)

Gupta and Weining (1962)

Gupta and Weining (1962) Golovin et al. (1996a, 1998b)

4.5 Metals of the IVB Group 243

f(Hz)

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

peaks at Tm ≤ 548 K are accounted to oxygen and O–Mo clusters. The other peaks are accounted to nitrogen and N–Mo clusters Ti–N–O–Nb(34) 26 S(O) or S(N) bcc structure 223 1–2 78.7 thermome520 – 80 PhT chanical 820–870 – – PhT treatment Ti–N(up to 3.4 bcc structure 459 PD 4–16 1.3)–O(up to 495 PD 10–63 0.0.044)–Nb(37) 528 PD 20–80 (wt%) 570 S(N) 20 615 PD 24 666 PD 13 the three ﬁrst maxima are accounted to oxygen and O–Nb clusters. The other peaks (H = 143–168 kJ mol−1 ) are accounted to nitrogen and N–Nb clusters Ti–D, H Ti–D Ti–D(0.9–4.1) 1 PhT(deut) 430–450 up to 40 Ti–D(4.1) 2 · 10−13 PD(D) (in deuteride) 49 1.6 219 3 Ti–D(0.18–0.75 2 16.4 bcc structure 95 4.8 · 10−11 S(D) 250 – (D/Me=0.75) D/Me)–V PhT(deut) (25 at%) 160–1300 240–340 TiDx (1.5 ≤ × 57.7 δ(fcc) or ε(fct) Z(D) ≤ 2) phases

composition

Table 4.5.1. Continued

Wipf et al. (2000)

Numakura and Koiwa (1985) Kato et al. (1988)

Gridnev et al. (1983) Kushnareva and Pecherskij (1986a)

Shapoval et al. (1980)

reference

244 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ti–H(0.0065) (wt%)

Ti–H

Ti(5N)–H

Ti–H(3.9–26)

Ti–H(up to 0.36) (wt%) Ti–H(up to 5)

Ti–H(up to 0.15) (wt%) Ti–H(up to 30)

Ti–H

Chomka and Wegielnik (1976); Wegielnik and Chomka (1979) Besse et al. (1979)

K¨ oster et al. (1956a) Someno and Saito (1970a) Tung and Sommer (1974) Tinivella and Povolo (1975)

≈1

≈4 · 10−11 CW ≈110 23.1 DP DP ≈3 · 10−11 29.8 ≈145 DP ≈2 · 10−11 38.5 ≈190 two kinds of mechanism are considered: thermally activated depinning of dislocations pinned by hydrogen atoms and, in the higher temperature range, dragging by the dislocations of hydrogen atoms situated in their vicinity hydrogeni200–225 DP Besse et al. ≈2 · 104 up to 7 zation + CW (1979) 4 PhT(hydr) Ritchie and 384 (a narrow peak) Sprungmann (1982)

258 61 PD(H) – 430–540 PhT(hydr) PD(H) in 200 up to 30 46 254 hydride up to 5 66.8 CW 390 DP 1 · 107 26.9 2.5 · 10−11 430–550 – PhT(hydr) – SK(H) 3.2 · 10−9 0.8 221 0–10 36.5 250 PD(H) – – – the lowest temperature peak is interpreted in terms of an interaction between dislocations and hydrogen atoms and the other one as due to a stress-induced redistribution of hydrogen in the hydride DP 10−9 3–30 170–250 20–30 29 400–600 PhT(hydr) 2–150 – –

0.23 1 1

4.5 Metals of the IVB Group 245

TiH1.64 Ti–H–Mn(3.25–5.95) (wt%) Ti–H–Nb(34) Ti–H(up to 30 at%)– Al(3.06 wt%)

TiHx (1.6 ≤ x ≤ 1.8)

Ti–H(0.12–1.12) (wt%) TiHx (0 ≤ x ≤ 1.5)

203–213

Tm (K) up to 10

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) PD(H) or DP PhT(hydr)

mechanism state of specimen

up to 70 up to 30 up to 5

115 200 254

2000 1

≈130

260–280 83–113

222–1325 70

1

66.4

46

47.1 21

S(H) PD(H) in hydride

Z(H) S(H)

Tanaka (1985)

Gorpinchenko et al. (1987) Gong et al. (1990)

Galis et al. (1983)

reference

Kappesser and Wipf (1996) δ-phase(fcc) Wipf et al. (2000) bcc structure Someno and Saito (1970b) bcc structure Du (1981, 1982) Someno and Saito (1970a)

420–680 – ≈2 annl. ≈225 ≈16 CW ≈180 0.5–0.8 513–598 PhT(hydr) 40–70 (heating) 433–498 20–80 (cooling) 1.7/1600 (A) 1 · 10−11 125/175 up to 10 25 175/215 up to 10 48.1 2.5 · 10−15 (B) (C) 210/270 up to 80 55.8 1 · 10−14 (D) 257/325 up to 50 69.2 5 · 10−15 the peaks A and B are accounted to dislocations moving in the hcp α-phase, C to hydrogen diﬀusion in a hydride and D to hydrogen reorientation in a tetragonal hydride 169–1290 δ-phase(fcc) 240–270 Z(H) 100 47.1

1

Ti–H(up to 13)

Ti–H(up to 3.5)

f(Hz)

composition

Table 4.5.1. Continued

246 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ti–H(0.014)– Al(3.97)–Fe(2.50)– Mo(2.84)–V(5.04) (wt%)

Ti–H–Al(6.18)– V(4.67) (wt%) Ti–H(0.0007)– Al(4.68)–Fe (2.01)–Mo(1.93)– V(3.0) (wt%)

298 1

–

15.4–16.4

15.4

(0.8–8.5) · 10−11 –

3 · 10−11

PD

PhT(hydr)

S(H)

S(H)

S(H)

S(H)

annl. CW bcc structure

bcc structure

β-phase(bcc)

β-phase(bcc)

1800

2.5 · 10−15 PD(H) (bcc phase) 116 6 23.4 289 2 46.4 4.3 · 10−13 PD(H) (hcp phase) α + β phases S(H) ≈1 120 up to 50 25.1 3 · 10−12 200 – ≈10 – – the ﬁrst peak is attributed to stress-induced redistribution of hydrogen atoms in the β-phase (bcc). The second peak is due either to defects in martensite or to interfaces between the martensite and β-phase β (bcc) phase S(H) ≈1 120 up to 300 29.9 2 · 10−14 the peak is attributed to stress-induced redistribution of hydrogen atoms in the β-phase (bcc)

2000

Ti–H–Al(5)– Sn(2.5) (wt%)

≈200 1

250–275 ≈333

≈1

Ti–H(0.1)–Y(0.26)

≈200 ≈190 84

1 2

≈2 ≈12 80–450

123

1.4 · 103

up to 250

93–113

70

up to 250

93–113

70

Ti–H(0.1–1 H/Me)– V(25 at%)

Ti–H(up to 7 at%)– Fe(2.72 wt%) Ti–H(up to 7 at%)– Mn(3.25–5.95 wt%) Ti–H(0.2–1 H/Me)– V(25 at%) Ti–H(up to 4)–V(2)

Guan et al. (1999)

Guan et al. (1999)

Du (1981, 1982)

Hairong et al. (1993) Du (1981, 1982)

Someno and Saito (1970a) Someno and Saito (1970a) Kato and Tanaka (1986) Gorpinchenko et al. (1987) Kato et al. (1988)

4.5 Metals of the IVB Group 247

f(Hz)

Tm (K)

Qm

(10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.5.1. Continued

Brossmann et al. (1999) Brossmann et al. (1999) Weller et al. (2000, 2001, 2004b)

Perez-Bravo et al. (2004)

α2 /γ structure

α2 /γ structure

Brossmann et al. (1999); Hirscher et al. (1999)

reference

duplex α2 /γ structure duplex α2 /γ structure

γ-TiAl extruded

mechanism state of specimen

10 1060–1100 40–60 285.6 2.5 · 10−16 PD the maximum can be attributed to the reorientation of structural defects ≈1300 10 up to 400 (cooling) this relaxation maximum is tentatively ascribed to the motion of grain boundaries or dislocations which are pinned by precipitates in γ-TiAl Ti–Al(47.5)–Cr(1.95) 10 ≈1100 PD the maximum observed at 1300 K in TiAl is absent Ti–Al(47.8)– ≈1100 PD 10 the maximum observed at 1,300 K in TiAl is absent. No relaxation Cr(2.2)–C(0.22) is observed at temperatures below 900 K Ti–Al(46.5)–(B, 0.01–10 in samples with primary annealed structure peaks in Cr, Nb, Ta)(4) the temperature range 300–1270 K are absent 900–1050 up to 120 288 1.4 · 10−15 the peak is only observed in samples with fully lamellar microstructure and is assigned to movement of dislocations segments which are pinned at α2 /γ and γ/γ interfaces as well as within γ lamellae Ti–Al(46.5)–(B, Cr, 0.03–5 in the temperature range 300–1200 K no relaxation peak is observed, only the high temperature damping Nb, Ta)(4) background

Ti–Al Ti–Al(54.1)

composition

−1

248 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1043

≈115 365

≈1000 278.8 5 · 10−15 0.01–10 the peak is only observed in samples with fully lamellar microstructure. This is assigned to movement of dislocations segments which are pinned at α2 /γ and γ/γ interfaces as well as within γ lamellae

0.5

Perez-Bravo et al. (2004) α2 /γ structure Weller et al. (2004a)

Ti–Ni The following abbreviations are used in the TiNi: A – austenite; B2 – austenite with the CsCl structure; M – martensite; B19 – orthorombic martensite; B19 – monoclinic martensite; R – rhombohedral premartensitic structure; I – incommensurate phase 1.5 · 107 TiNi 335 PhT Pace and Saunders (1971) Ti–Ni(49.9) Mercier et al. (1979) PhT(A→R) 0.4–0.8 330 up to 320 (cooling) 310 up to 370 PhT(R→M) 360 up to 500 (heating) PhT(M→A) Ti–Ni(55.07 285 1.2 800 PhT(A→M) (cooling) Liu et al. (1983) annl. 7th PhT(M→A) 315 300 (heating) (wt%)) therm. after 30 thermal cycles the additional PhT(A→R) peak is observed (cooling) cycles ≈400 Ti–Ni(55.3 (wt%)) 0.2–0.3 Huang et al. ≈305 annl. (cooling) PhT(A→R) ≈290 – PhT(R→M) (1985b,c) ≈700 PhT(M) ≈275 ≈400 PhT(M→A) ≈315 (heating) the PhT(R → M) and PhT(M → A) peak heights are inﬂuenced by the external stress ≈100 Ti–Ni(48.92) Sugimoto et al. 320 PhT(B2 → M) 1000 (1985)

Ti–Al(45)–Nb (5–10) Ti–Al(46)–Nb(9)

4.5 Metals of the IVB Group 249

0.5

≈1 · 107

0.2–0.5

Ti–Ni(49.86)

TiNi

Ti–Ni(49.86 and 54.92)

the movement

200 200 340

≈250 ≈200 ≈200 ≈300 325 308 200 200 340 320 310 290 200 300 325 253 ≈200 315 300–308

≈1

Ti–Ni(51)

110 100 100 60 – 65 60 70 60 65

≈400 ≈200 ≈200 ≈300

(cooling)

(heating)

(cooling)

(heating)

(cooling)

(heating)

(cooling)

mechanism

PhT(A → R) relaxation peak relaxation peak PhT(R → A) PhT(A → R) PhT(R → M) relaxation peak relaxation peak PhT(M → A) PhT PhT PhT relaxation peak PhT PhT(M → A) PhT(A → R) – PhT(A → R) PhT(R → M)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

ageing

quen.

annl. at 673 K

state of specimen

(cooling) up to 100 70 relaxation peak (heating) 70 relaxation peak up to PhT(M → A) 50 of dislocation pinning point defects is the probable origin of the relaxation peak

Tm (K)

f(Hz)

composition

Table 4.5.1. Continued

Matsumoto and Ishiguro (1988) Zhu et al. (1988, 1989, 1990)

Zhu and Gotthardt (1988)

Iwasaki and Hasiguti (1987)

reference

250 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ti–Ni(55.1 wt%)

Ti–Ni(55.1 wt%)

Ti–Ni(48)

TiNi

Ti–Ni(55.1 wt%)

Ti–Ni(49.3)

Ti–Ni(51)

178 (cooling) PhT(B2 → B19 ) 181 (heating) PhT(B19 → B2) 303 ≈100 PhT(B2 → R) (cooling) 171 ≈300 PhT(R → B19 ) ≈100 PhT(B19 → R) 279 (heating) 307 ≈200 PhT(R → B2) all peak temperatures increase with increasing ageing time (cooling) PhT(I → R) 0.1 283–313 PhT(R → M) 263–283 PhT 218–263 up to 1500 (cooling) PhT(B2 → R) 20 331–286 PhT(R → M) 263–223 1.5 PhT(A → M) 316 410 (cooling) 347 200 PhT(M → A) (heating) ≈250 PhT(A → M) ≈350 (cooling) ≈0.5 ≈100 PhT(M → A) ≈385 (heating) ≈100 1 PhT(B2 → R) (cooling) 320 292 ≈200 PhT(R → M) ≈150 PhT(B2 → M) 283 (cooling) ≈310 (cooling) 1 PhT(B2 → R) PhT(R → M) ≈290 ≈260 – ≈325 (heating) PhT(M → R) PhT(R → B2) ≈350 Irradiation (60 Co) decreases the PhT(R → M) and PhT(M → R) peak temperatures and increases the peak heights

≈1

Mo et al. (1991b)

ageing quen. annl.

Lin et al. (1991)

Mo et al. (1990)

Lin et al. (1990)

Wu et al. (1989, 1990); Wu and Lin (2003); Lin et al. (1993)

Goubaa et al. (1991, 1992) Mo et al. (1991a)

cooling rate=0.5– 4 K min−1

solution treatment ageing

4.5 Metals of the IVB Group 251

) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

Ti–Ni(49.86)

Ti–Ni(54.92 wt%)

Ti–Ni(51)

Ti–Ni(50.2–51)

0.25

PhT(B2 → R) annl. + 8 318 thermal 308 PhT cycles 290 PhT ≈150 ≈300 PhT(A → M) quen. 1000 (cooling) ≈310 (cooling) 900 PhT(B2 → R) ageing 258 PhT(R → M) 1060 ≈500 ≈305 PhT(A → M) quen. (cooling) 1 ≈300 relaxation peak ≈200 ≈200 (heating) ≈350 relaxation peak ≈400 ≈335 PhT(M → A) the relaxation peaks are related to dislocation damping ≈320 (cooling) 0.5 quen. PhT(A → R) 308 PhT(R → M) ≈120 ≈90 relaxation peak ≈200 ≈90 ≈200 (heating) relaxation peak ≈60 ≈340 PhT(M → A) the relaxation peak is associated with the movement of dislocations in the martensite ≈320 (cooling) 0.28 quen. PhT(A → R) ≈90 ≈300 PhT(R → M) relaxation peak ≈200 ≈80 ≈80 ≈200 (heating) relaxation peak ≈50 ≈340 PhT(M → A) ≈330 (cooling) 0.6 quen. + ageing – PhT(A → R) ≈310 ≈50 PhT(R → M)

(10

Ti–Ni(55.1 wt%)

Qm

Table 4.5.1. Continued

f(Hz)

Tm (K)

−4

composition

−1

Li et al. (1994)

Zhu et al. (1994)

Lin et al. (1993)

Lin et al. (1993)

Mo et al. (1992)

reference

252 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ti–Ni(50.6)

Ti–Ni(50.6–51)

Ti–Ni(49.6)

TiNi

Ti–Ni(49.6)

TiNi

≈70 310 peaks are absent 520 up to 15 870 up to 200

(cooling) PhT(A → M) (heating) austenite Z 1 130 2.5 · 10−14 – 308 (1.5–2.7) · 10−19 the peak at 870 K is associated with a relaxation due to dislocation segment motion After (CW + Annl.) during cooling PhT peaks are observed at 255, 15 220 and 190 K; after ageing and thermal cycling – at 285, 265 and 245 K; after quenching-at 225 K ≈285 ≈0.8 475–900 (cooling) annl.575◦ C PhT(B2 → R) ≈265 470–900 PhT(R → B19 ) ≈305 400–700 (heating) PhT(B19 → B2) ≈250 200–300 (disl) ≈700 ≈600 PhT(Ti2 Ni3 )

≈150

≈50 PhT ≈290 ≈80 relaxation peak ≈200 the peak at 290 K is associated with the M-transition near the Ti-rich precipitates ≈300 ≈320 (cooling) 1 1st cycle PhT(A → M) 315 shoulder 21st cycle – ≈400 PhT(A → M) 305 ≈150 1st cycle PhT(M → A) 350 (heating) ≈200 343 21st cycle PhT(M → A) −4 10 –10 an increase of IF is observed at low frequencies in the martensite and isotherm. austenite states. The IF is thermally activated (H = 67–82 kJ mol−1 ) measure.

Golovin et al. (1997b)

Morawiec et al. (1997)

Pelosin et al. (1996)

Deborde et al. (1995); Pelosin and Rivi´ere (1997, 2002) Lin et al. (1995)

Jordan et al. (1994a,b, 1995)

4.5 Metals of the IVB Group 253

state of specimen

Ti–Ni(50.8)

Ti–Ni(50.8)

Ti–Ni(49.6)

≈305 (cooling) quen. PhT ≈150 ≈265 PhT(A → M) ≈70 ≈355 PhT(M → A) (heating) ≈65 270 PhT(A → M) 29 thermal (cooling) 331 ≈30 ≈355 PhT(M → A) cycles (heating) 325–300 (cooling) CW + ageing – PhT(A → R) 1.4 · 103 ≈250 PTWR – ≈110 PTWM – ≈110 (heating) – PTWM ≈260 PhT(M → R) – ≈140 ≈320 PhT(R → A) PTWM and PTWR are due to stress-induced hysteretic motions of twin-boundaries within the martensite and the R-phase, respectively ≈120 ≈220 PhT(A → M) solubilisation (cooling) 1.4 · 103 ≈160 ≈260 PhT(M → A) + quen. (heating) 96 – ≈10−10 10.6 – 6.8 · 103 the peak at 96 K is attributed to stress-induced motion of dislocations within the B19 structure of the martensite ≈90 1145 PhT(A → M) quen. (cooling) 237 ≈140 ≈250 PhT(M → A) (heating) ≈110 dislocation relaxation – with increasing number (up to 1.8 · 104 ) of thermal cycles the peak (A → M, M → A) decreases to disappear almost completely; Tm also decreases.

mechanism

TiNi

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

f(Hz)

composition

Tm (K)

Table 4.5.1. Continued

Biscarini et al. (1999b); Coluzzi et al. (2000)

Liu and Van Humbeeck (1997) Liu et al. (1997b) Pelosin and Rivi´ere (1998) Coluzzi et al. (1999) Biscarini et al. (1999a)

reference

254 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1 · 105

≈1.3

≈1.3

2 · 106

0.5

0.6

TiNi

Ti–Ni(49.89)

Ti–Ni(50.85)

Ti–Ni(55) (wt%)

Ti–Ni(50.2)

Ti–Ni(51)

TiNi 325 double PhT 220 layer ﬁlms PhT ≈400 ≈295 (cooling) PhT(A → R) quen. at heating peaks are not observed ≈300 ≈325 (cooling) PhT(A → M) ≈180 – – ≈180 – – (heating) ≈330 PhT(M → A) ≈350 ≈250 ≈250 (cooling) PhT(A → R) ≈600 PhT(R → M) ≈210 ≈250 (heating) PhT(M → A) ≈700 There are three peaks at 290, 264, and 233 K in the cooling run, and one peak at 234 K and a drop from 297 K in the heating run ≈600 298 (cooling) PhT(B2 → M) quen. ≈300 relaxation peak 200 ≈300 200 (heating) relaxation peak PhT(M → B2) 335 ≈140 178 (cooling) PhT(A → M) annl. ≈140 181 (heating) PhT(M → A) ≈150 309 (cooling) PhT(A → R) ageing ≈300 221 relax. peak 400◦ C, ≈400 PhT(R → M) 10 h 183 ≈300 relax. peak 212 (heating) ≈100 PhT(M → R) 285 ≈150 311 PhT(R → A)

Lin et al. (2003)

Fukuhara et al. (2002) Wu and Lin (2003)

Yoshida et al. (2000)

Craciunescu and Wuttig (2000) Golyandin et al. (2000) Yoshida et al. (2000)

4.5 Metals of the IVB Group 255

Ti–Ni(47)–Co(3)

Ti–Ni(48.21)– Al(2) Ti–Ni(47)–Co(3)

Ti–Ni(44.1–46.3)

Ti–Ni(46.1–54.4)

composition

Tm (K)

Qm −1 (10−4 )

H(kJ mol−1 ) τ0 (s) mechanism state of specimen

the 200 K relaxation peak (H = 37.5 kJ mol−1 , τ0 = 1.6 · 10−10 s) is associated with the interaction of twin-related dislocations with the pinning agents by quenched-in vacancies or Ti11 Ni14 precipitate-vacated lattice sites ≈240 up to 80 B19 phase 150 the relaxation peak is attributed to the dislocation motion thin ﬁlms PhT(A → R) 325 up to 1.7 2 · 103 (cooling) 280 (heating) PhT(M → R) – on Si PhT(R → A) 320 up to 1.5 substrates PhT(B2 → R) 270 1 · 103 PhT(R → M) 195 ≈1 PhT(A → R) 290 up to 180 (cooling) PhT(R → M) 248–275 up to 450 Tm of the PhT(R → M) peak decreases as a function of thermal cycling 278 (heating) PhT PhT 300 up to 150 (cooling) PhT(R-trans) 1 1st cycle 290 shoulder 276 ≈450 PhT(A → M) ≈120 PhT(A → R) 288 21st cycle ≈200 PhT(R → M) 228 ≈300 1st cycle PhT(M → A) 306 (heating) 21st cycle PhT(M → R) 291 – PhT(R → A) 298 –

f(Hz)

Table 4.5.1. Continued

Jordan et al. (1994a,b, 1995)

Sugimoto et al. (1985) Jordan et al. (1993)

Igata et al. (2004) Khelfaoui et al. (2004)

reference

256 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ti50 Ni40 Cu10

Ti50 Ni50−x Cux (x = 8–20)

Ti50 Ni30 Cu20

Ti50 Ni40 Cu10

Ti50 Ni25 Cu25

Ti50 Ni40 Cu10

Ti–Ni(46.2)– Cu(4.2)

≈283 (cooling) PhT(A → R) ≈300 PhT(R → M) ≈273 ≈255 (heating) – – PhT(M → R) ≈295 – ≈300 PhT(R → A) ≈250 the peak at 255 K (heating) is attributed to martensitic variants reorientations ≈700 quen. PhT(B2 → ≈315 (cooling) 1 B19) ≈1200 PhT(B19 → ≈270 B19 ) ≈1200 PhT(B19 → ≈285 (heating) B19) ≈700 PhT(B19 → ≈325 B2) 0.46 PhT(M → A) ageing 328 1600 (heating) (5–15) · 104 331–338 30 1.2 · 103 peaks are absent in the temperature range of ageing phase transitions 1.5 · 103 peaks are absent in the temperature range of quen. phase transitions ≈325 0.5–3 small peak or PhT(B2-B19) solution shoulder treatment – ≈250 up to 2000 the large broad peak at 250 K is considered to be due to the overlapping of the relaxation type peak and the transient peak due to B19–B19 transformation MHz range Attenuation peaks (at 322, 320, and 314 K during SC, annl. cooling and at 327 K during heating) are observed in the temperature range of phase transitions

≈0.5

Mazzolai et al. (2004a)

Rotini et al. (2001); Mazzolai et al. (2003) Biscarini et al. (2003a,b) Yoshida et al. (2003, 2004)

Liang et al. (1999)

Lo et al. (1993b)

Goubaa et al. (1991, 1992)

4.5 Metals of the IVB Group 257

reference

Ti40 Ni47 Cu3 Hf 10 –H 517 solut. treatm. ≈40 3 · 10−5 40 1 S(H) or Z(H) ≈200 2 · 10−16 240 58 (H/Me = 0.01) the 40 K relaxation is due to quantum–mechanical transitions of H bound to Hf atoms Ti–Ni(44)–Fe(1) 1 263 PhT(B2 → I) annl. up to 600 (cooling) 230 up to 1000 (wt%) PhT(I → R) 215 PhT(R → M) bend 275 PhT(M → B2) up to 200 (heating) Ti–Ni(46.6)– 196 (cooling) PhT(R-phase) 9 · 109 196 PhT(R-phase) ageing Fe(3.4) 230 PhT(I-phase)

Ti50 Ni30 Cu20 –H (0.01 H/Me) Ti40 Ni47 Cu3 Hf 10

a tall broad peak at 175–325 K which is composed of ageing two partially superimposed hydrogen relaxation peaks PH 10−13 ≈270 48 10−12 ≈300 PTWH 48 The PH peak is likely due to stress-assisted reordering of H elastic dipoles within a hydride phase, PTWH to H dragging processes by twin boundaries S(H) or Z(H) quen. 480 260 5 · 10−13 (bump) 42 290 – 750 PhT(A ↔ M) – 1330 ≈50 solut. treatm. 150 motions of twin-boundaries

Rao and Jiang (1990)

Chui and Huang (1987)

Biscarini et al. (2003a,b) Coluzzi et al. (2004) Coluzzi et al. (2004)

Rotini et al. (2001); Mazzolai et al. (2003)

state of specimen

1.2 · 103

mechanism

Igata et al. (2003b, 2004)

) H(kJ mol−1 ) τ0 (s)

≈240 up to 200 the peak is observed in the alloys Ni(40.1)–Cu(10.1) and Ni(47.7)–Cu(2)

(10

Ti(49.8–52.1)– Ni(23.9–47.7)– Cu(2–24) Ti50 Ni40 Cu10 –H (0.004–0.018 H/Me)

Qm

Table 4.5.1. Continued

f(Hz)

Tm (K)

−4

composition

−1

258 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

≈150

(cooling) PhT(B2 → R) ≈310 ≈295 PhT(R → B19 ) peaks are absent (heating) Ti–Ni(50.8)– ≈235 1140 up to 800 (cooling) PhT(A → M) H (H/Me up to ≈225–235 ≈250 (heating) PhT(M → R → A) 0.045) ≈260 up to 800 48 1 · 10−12 (a) the relaxation peak is most likely associated with stress-induced motion of H in solid solution within the R-phase or within a hydride. (b) at low H content (≤0.008 H/Me) the peaks (A → M) and (R → M) dramatically increase with increasing H content Ti–Ni(49)–H 315 ageing 500 8.6 · 103 57.7 3 · 10−14 (H/Me=0.004) the peak is attributed to motions of twin boundaries interacting with mobile H atoms ≈400 S(H) or Z(H) Ti–Ni(50.8)–H ≈275 52 600 quen. (H/Me=0.01) the so-called 200 K relaxation and the PH peak are interpreted as a S(H) or Z(H) ≈200 PhT(B2 → R) ≈270 (cooling) 1.3(x = 1) quen. Ti50 Ni50−x Pdx ≈800 PhT(R → B19 ) ≈250 x = 1–15 ≈400 PhT(B19 → B2) ≈290 (heating) ≈400 (cooling) 1.3(x = 11) ≈285 PhT(B2 → B19) ≈400 PhT(B19 → B2) ≈300 (heating) Ti50 Ni47 Pd3 0.5 PhT(B2 → R) 252 240 deformation (cooling) 226 relaxation peak 540 amplitude PhT(R → B19 ) 217 940 ε = 4.75 · 10−5 226 540 (heating) relaxation peak 252 690 PhT(B19 → B2) ε = 2.05 · 10−4 244 400 PhT(B2 → R) (cooling)

Ti–Ni(49.5)– Fe(0.5)

Lo and Wu (1993a)

Biscarini et al. (1999a) Mazzolai et al. (2004b) Lo and Wu (1992)

Biscarini et al. (1999a,b)

Lin et al. (1995)

4.5 Metals of the IVB Group 259

200–217

948–1048 25–110 988

1 1 1

1.2 · 105 2 · 103

Ti–Au(0.10)

Ti–B(16) (wt%)

Ti–B(15.6)

Ti–Cr(10)

Ti–Cr(14) (wt%)

259

113 630 20 up to 20

(β1 + ω precipitation)

non-relaxation maxima at 470–570 K, relaxation maxima at 890 and 980 K 152 553–603 653–713 (non-relaxation peak) ≈773 – – 152 175

95

(cooling) (heating)

(heating)

Ti–Ni(48.6 at.%)– 1.2–1.4 TiC(up to 20 wt%) other titanium alloys Ti–Al(up to 0.12) 1

(10

700 1200 700 930 800

f(Hz) 223 217 223 239 246 335 385

composition

Qm

) H(kJ mol−1 ) mechanism state of specimen

10−12 – –

DP(B) PhT

PhT – PD(vac)

690–890 K and

GB

GB

quen. from 950◦ C quen. β + α phases

quen. from melt quen. from melt

relaxation peak PhT(R → B19 ) relaxation peak PhT(B19 → R) PhT(R → B2) metal PhT(A → M) matrix PhT(M → A) composite

τ0 (s)

Table 4.5.1. Continued −4

Tm (K)

−1

Doherty and Gibbons (1971b) Simson and or¨ ok (1981) T¨

Winter and Weinig (1959) Winter and Weinig (1959) Okrostsvaridze et al. (1985) Tavadze et al. (1986)

Mari et al. (1995)

reference

260 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

three peaks in shear friction are observed at 1020, 1120 and 1300 K, but their causes are not speciﬁed

Ti–Al(6)–V(4) (wt%) 2.25 · 106

9.6

180

PD(vac)

GB

PD(vac)

Ti–Al(6)–V(4) (wt%) 1 · 107

20

1.7 · 10−11

≈30 PhT(β ↔ ω) ≈120–140 up to 50 O (0.08–0.42 at.%) suppresses the PhT peak and H (0.03–5 at.%) raises it 973–1048 16–110 1 GB 200–501

Ti–V(20–50) (wt%)

Ti–Zr(up to 0.12)

140–161

1.2 · 105

Ti–V(20–50) 2 · 104

923–1048 40–60

1

Ti–V(up to 0.12)

21 200–334

152

1.2 · 105

PD(vac)

Ti–Ni(10)

65

177

1.2 · 105

GB

Ti–Nb(25)

200–263

898–1048 50–110

1

Ti–Nb(up to 0.10)

Ti–Mo(43) (wt%)

Ti–Mo(17) (wt%)

740 – (β2 + α precipitation) PhT PhT 930 170 (β0 precipitation) 180 20.9 2.2 · 10−14 1.2 · 105 interaction of dislocations with oxygen atoms and vacancies 573–683 167.4 1 PhT(β → ω1 ) – 113 20.9 10−9 1

quen. from 950–1100◦ C

quen. from 950◦ C quen. from 950◦ C

Winter and Weinig (1959) Mason and Wehr (1970) Fukuhara and Sanpei (1993)

Mishra and Asundi (1977) Winter and Weinig (1959) Doherty and Gibbons (1971b) Doherty and Gibbons (1971b) Winter and Weinig (1959) Doherty and Gibbons (1971b) Buck et al. (1975)

Mishra and Asundi (1977)

4.5 Metals of the IVB Group 261

160 245 345 410

8 14 2 35 → 20

120 1

20.9 180 2.2 · 10−14 183–203 up to 8 54.4 10−14 218–228 up to 8 62.8 10−14 500 S(O) (in β) up to 90 160.3 10−15 683 180 – – SK(?) (in β) the peaks at 180–230 K are accounted to interaction of dislocations with vacancies and oxygen atoms in the metastable β-phase (bcc) Ti–Al(2.5–4.5)– 820 268 14 S(O) Cr(1–2.5)–Fe(1.5)–Mo 1150 ≈3000 PhT(α ↔ β) (1–2.8) (wt%)

Ti–Al(0.3)–C(0.07)– Fe(0.25)–N(0.04)– O(0.2)–Si(0.1) (wt%) Ti–Mo(11.5)– Sn(4.5)–Zr(6) (wt%)

1515 1500 1430 1800 → 1400

DP(P1 ) 36.5 2 · 10−13 DP(P2 ) – – DP(P3 ) sharp decrease in f and Q−1 at increasing temperature due to PhT(H) DP(P1 ) is more stable against annealing as compared with the DP(P2 ) 1880 DP(P1 ) 175 23 1840 DP(P2 ) 245 34 DP(P1 ) is more stable against annealing as compared with the DP(P2 )

mechanism

Ti–C(0.1)–Fe(0.3)– N(0.05)–O(0.25) (wt%)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

f(Hz)

composition

Tm (K)

Table 4.5.1. Continued reference

Wegielnik and Chomka (1975, 1979)

Mishra and Asundi (1977)

severely CW Golovin et al. nanograined (2006a,b)

severely CW Golovin et al. nanograined (2006a,b)

state of specimen

262 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.5 Metals of the IVB Group

263

4.5.2 Zirconium and its Alloys In Zr and its alloys, the following internal friction eﬀects are observed: – Dislocation peaks (intrinsic peaks and the impurity peaks SK(H), SK(O), DES(H)) – Grain boundary peaks – Relaxations due to N,O and additional peaks due to interaction between the substitutional and interstitial atoms – Relaxations due to H diﬀusion – Eﬀects of hydrides and deuterides precipitation and dissolution – Peaks due to order–disorder and other phase transitions in hydrides – The Zener relaxation due to H and D in hydrides and deuterides – Peaks due to the polymorphic transformation – Peaks due to phase transitions in several zirconium alloys

Zr(99.9) Zr(99.99) Zr(99.99 and 99.999)

1

2 · 104 228 248 130–150 210–230 up to 60 up to 20 up to 13 –

up to 20 up to 40 ≈150 48 – 12.5 –

10−5 –

2 · 10−14 2 · 10−12

DP DP DP DP

DP DP GB

CW

CW

CW, α + ω phases

1.3 · 104

Zr 12.5 27.9 288

1300–1600

Zr

80 250 843

1000

Zr(99.9)

1 · 105 Zr(99.9 and 99.999) Zr (iodide reﬁned) 1

823 bend GB 1138 PhT(polym) CW 17.3 205 3.3 · 10−8 DP DP 242 48.1 5 · 10−14 1.1 · 10−13 DP 258 49 CW 200–210 up to 5 12.5 U(0.5wt%) decreases and Nb and Th(1(wt%)) completely suppress the peak CW 223 DP up to 4 33.7

3.6

GB

Zr

20–200

793–823

state of specimen

≈1

mechanism

Zr Zr

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

f(Hz)

composition

Tm (K)

Table 4.5.2. Zirconium and its Alloys (at.% if not speciﬁed diﬀerently)

Savino and Bisogni (1971)

De Fouquet et al. (1970) Doherty and Gibbons (1971c) Gacougnolle et al. (1971) Petit et al. (1971)

Grusin and Semenichin (1963)

Bungardt and Preisendanz (1960) Barinov et al. (1961) Hasiguti et al. (1962)

reference

264 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

1280

Zr(99.99 and 99.999)

Zr

up to 25 up to 8 – up to 23

220–250 203

(plateau)

80–90 ≈150

903

–

10.6 8.6–12.5

DP 2 · 10−7 2.6 · 10−6 – DP 4 · 10−4 – DP DP

GB

1

1

Zr

Zr

823 241

10−16

GB

75 PD(int) 115 126 400 Zr DP 2 14.5 10−9 DP 200 2 36.7 10−14 225 1 – – DP Zr(99.7 and 99.99) 336–360 10−13 123–125 up to 26 26 the peak is accounted to pinning of dislocations by complexes of O with self ≈100 1125 1 Zr PhT(polym) ≈100 1128 (recrystallisation of the β-phase) 2.83 · 104 Zr(4N) 28 DP up to 1.2 1.6 5 · 10−9 DP 55 0.2 6.7 2 · 10−12 Zr(99.999) 98 1 DP(B) ≈180 DP ≈100 1000 (superplasticity) 1 Zr

1.3

Zr (iodide pure)

CW

Petit et al. (1976) Bolcich and Savino (1980) Garber et al. (1980, 1982) Ritchie and Sprungmann (1981)

CW CW

Garber et al. (1976)

Petit et al. (1975b)

Petit et al. (1975a)

irr(n)

CW interstitial

Provenzano et al. (1974) Moser et al. (1975)

CW

CW

Mishra and Asundi (1977) Savino and Bisogni (1974)

4.5 Metals of the IVB Group 265

Zr(99.4)

Zr(99.95)

Zr(99.99)

Zr(99.99)

Zr(99.99)

composition

Tm (K)

Qm (10

−4

)

H(kJ mol−1 ) τ0 (s)

Table 4.5.2. Continued mechanism state of specimen

0.5

CW 1.9 · 10−11 DP(Pd ) 140 up to 85 28.8 188 39.4 – 3.2 · 10−12 DP 205 56.7 – 6.2 · 10−15 DP 219 60.6 – 1.9 · 10−14 DP CW 80 DP(Pd ) 145 up to 90 173 up to 120 28.8 3.3 · 10−11 DP(Pd ) DES(H) 212 up to 25 42.3 5 · 10−13 233 up to 40 65.4 3.3 · 10−17 SK(H) SK(H) 255 up to 20 60.6 2 · 10−15 280 (twin boundary migration) – the DP(Pd ) and DP(Pd ) peaks are caused by dislocation relaxation through kinkpair generation in 11¯ 20 screw dislocations moving in the prismatic and pyramidal planes, respectively CW at 8 K 80 DP(Pd ) 140 (kink-pair generation) 170 DP(Pd ) (kink-pair generation) 210 DP(P1 ) (DES(H)) 232 DP(P2 ) (H-dislocation interaction) 280 DP (twin boundary movement) 750 GB 10 105 1100 PhT(polym) 30 255 29.8 37 8.7 · 104 CW 1.3 · 10−12 DP(B)

f(Hz)

−1

Boyarskij et al. (1986) Pal-Val et al. (1991a,b, 1992); Trojanova et al. (1996)

MiyadaNaborikawa et al. (1985)

MiyadaNaborikawa and De Batist (1983, 1985)

MiyadaNaborikawa and De Batist (1983)

reference

266 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Zr–O–Ag(0.24)

Zr–O

Zr–O(2.1–6.3)

Zr (ultra purity)–O(4.8– 8.8) Zr–O(0.065) (wt%) Zr–O(up to 2.85) Zr (commercial purity)–O(2.85–4)

Zr–N, O Zr–O Zr–O(up to 5) 683–698 200–202 Qm −1 ≈ 1.6 · 10−4 CO (at.%) 803 up to 150 670 1.5–6.3 219–207 GB PD(O/O)

PD(O/sub)

Qm −1 = 0.026 · 10−4 C2O + 0.6 · 10−6 C3O (at.%) 123.5 360 9 CW the peak is accounted to pinning of dislocations by complexes of O with-self interstitial ≈13.7 738 192 SC 9.1 · 10−16 PD(O/sub) 4.5 PD(O/sub) 2.438 723 SChk0 6.5 200 2 · 10−16 1.213 708 SC001 11.5 the hk0 sample (2.85 at.% O) was tested in ﬂexure and the 001 sample (4 at.%O) was tested in torsion 0.44 PD(O/O) 683 0.2–2.5 201 Qm −1 ≈ 0.6 · 10−5 C2O (at.%) ≈740 ≈4 160 CW + annl. DP (thermally assisted unpinning) ≈800 130 SK (O) (longitudinal core diﬀusion) ≈870 SK(O) 190 (transverse core diﬀusion) 738 227 PD(O/Ag) 1.3 (1.0 at.% O) 813 50 PD(Ag/3–O) (0.22 at.% O) 250

0.28

1

Mishra and Asundi (1972)

Fuller and Miller (1977) Ritchie (1982)

Ritchie et al. (1976) Ritchie et al. (1977)

Petit et al. (1975b)

Gacougnolle et al. (1975)

Gacougnolle et al. (1970, 1971)

4.5 Metals of the IVB Group 267

1.3

1.3

1.3

1.5 1.3

Zr–O–Si(0.075)

Zr–O–Sn(0.5)

Zr–O(4)–Ti(10)

Zr–O–Ti(1) 703 795

743 803 653 733 900 918 703

1.3

Zr–O–Nb(0.25– 1.3 0.515) Zr–O(0.5)– 4.5 Pr(0.15) (wt%) Zr–O–Ru(0.125) 1.3

293 841 918 – 30 747–756 232–238 823 – 10 an oxygen peak is absent

0.75

Zr–O(up to 4.5)–Hf(1) Zr–O(1)–Hf(2.4) (wt%) Zr–O–Hf(0.3)

7.5

65 ≈15

5

22

207 261

230 263 177 – 351 – 206.6

219

9 · 10−17 –

PD(O/Ti) PD(Ti/3–O)

PD(O/Ru) PD(Ru/3–O) PD(O/Si) PD(Si/3–O) PD(O/Sn) PD(Sn/3–O) PD(O/Ti)

PD(O/Hf) PD(Hf/3-O) PD(O/Nb) PD(Nb/3–O)

PD(O)

1

Zr–O–Fe(0.8)

≈12

715

1.3

Zr–O–Ge(0.126)

PD(O/Gd) PD(Gd/3–O) PD(O/Ge) PD(Ge/3–O) PD(O/Fe) PD(Fe/3–O) PD(O/Hf)

mechanism

248 5 · 10−18 259 2 · 10−27 218 263 25 167 4 · 10−16 – – 15 Hf increases the peak height

779 813 723 793 623 698 695

) H(kJ mol−1 ) τ0 (s)

1.3 0.7 1.3

(10

Zr–O–Gd(0.25)

Qm

Table 4.5.2. Continued

f(Hz)

Tm (K)

−4

composition

−1

(4.0 at.% O) (0.22 at.% O)

(1.0 at.% O) (0.22 at.% O) (1.5 at.% O) (0.22 at.% O) (1.0 at.% O) (0.22 at.% O)

bamboo-type structure (2 at.% O) (0.22 at.% O) (1.0 at.% O) (0.22 at.% O)

(1.2 at.% O) (0.22 at.% O) (1 at.% O) (0.24 at.% O) (3 at.% O) (0.3 at.% O)

state of specimen

Mishra and (1972) Mishra and (1972) Rosinger et (1976) Mishra and (1972) Mishra and (1972) Mishra and (1972) Mishra and (1971) Mishra and (1972)

Asundi

Asundi

Asundi

Asundi

Asundi

al.

Asundi

Asundi

Mishra and Asundi (1972) Mishra and Asundi (1972) Mishra and Asundi (1972) Gacougnolle et al. (1971) Browne (1971a,b)

reference

268 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1.3

Zr–O–Y(0.25)

≈1

413

1.96 · 104

ZrH1.92

ZrH1.15

160– 1300

ZrDx (x = 1.6–2)

Zr–H Zr–H(up to 1.26) (wt%)

≈1

Zr–D(up to 5)

Zr–N–O Zr–N(0.0067)– 22–27 O(0.057)–Al(1)– Nb(8) (wt%) Zr–D, H Zr–D Zr–D(2.7) 1560

1.3

Zr–O–W (0.235)

230 268 493– 523 ≈90 in the 403

280 ≈600 ≈300

203 383 ≈150 230

600 633 673

733 790 843 863 270 170 –

222 – 296 –

S(O) GB(?)

PD(O/W) PD(W/3–O) PD(O/Y) PD(Y/3–O) bcc structure

(1.0 at.% O) (0.22 at.% O) (1 at.% O) (0.22 at.% O)

up to 180 ≈83 ZrH1.6 peaks are absent up to 100

up to 40 up to 130 5–40

up to 10 (0.5 at% D) 49.0

PhT(deut) Z(D)

δ + γ phases

δ (fccc) or ε (fct) phases

≈2 (deformation due to deuteride) DP up to 15 PhT(deut) (dislocations generated by deuteride precipitation) these peaks are interpreted as being related to diﬀerent deuteride phases, γ and δ, which can coexist in the α phase

100

10

Brown et al. (1967)

Chang (1960)

Bungardt and Preisendanz (1960)

Wipf et al. (2000)

Provenzano et al. (1974) Numakura et al. (1988)

Peretti and Ghilarducci de Salva (1987)

Mishra and Asundi (1972) Mishra and Asundi (1972)

4.5 Metals of the IVB Group 269

Zr–H(up to 60)

ZrHx (x = 1.71–1.98) ZrH1.71

ZrH1.65

Zr–H(up to 6.7)

Zr–H(up to 56)

composition

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

1

(dislocations and H atoms) 144 up to 5 19.2 2 · 10−8 PD(H) (in γ-hydride) 230 6 · 10−13 up to 25 50 (twins in γ-hydride) 291 up to 130 62.3 5 · 10−14 1560 DP 203 up to 5 30.5 deformation due to hydride precipitation PhT 293 (shoulder peak) 59.3 383 up to 30 70.9 8.3 · 10−11 PhT(hydr) 1500 150 10 δ-hydride (fcc) 205 10 300 60 1500 ε-hydride (fct) PhT(ord) 190 0.1 (order-order) 340 110 (disorder–order) PhT(ord) 285 31 ε-hydride (fct) 220 48.2 4 · 10−12 313 160 49.2 4 · 10−11 383 125.4 80 10−13 possible mechanisms: 285 K – change of the axis of tetragonality under stress; 313 K – diﬀusion under stress of hydrogen atoms between octahedral and tetrahedral intersticies; 383 K – moving of domain boundaries 7–34 6 · 10−12 260 0.2–5 28.8 the peak is accounted to pinning of dislocations by hydride Z(H) in γ-hydride 300 up to 24 64.4 5 · 10−16 Z(H) in δ-hydride 425 up to 140 6 · 10−15 74

f(Hz)

Table 4.5.2. Continued

Mazzolai et al. (1976b)

Naskidashvili et al. (1974) Fedorovskij et al. (1974)

Naskidashvili et al. (1974)

Provenzano et al. (1974)

Povolo and Bisogni (1969)

reference

270 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

ZrH1.95

Zr–H(0.5–55)

ZrHx (x = 1.62–1.97)

ZrHx (x = 1.66–1.99)

280 ≈550 4.5 · 104 373 423–573 343–393 up to 160 40.4 4.5 · 104 423–493 – 54 353 up to 8 4 · 104 53.8 2 · 10−13 −1 Qm ∼ CH (the total hydrogen concentration) ≈155 280–1033 50 the relaxation peak may be correlated with low-temperature hydrogen ordering 300–320 400–150 47.1

(dislocations generated by hydride precipitation) these peaks are interpreted as being related to diﬀerent hydride phases, γ and δ, which can coexist in the α phase – up to 6 (0.5 at.% H) PhT(hydr) δ and ε-phase

≈150 230

≈1

Z(H)

Wipf et al. (2000)

Pan and Puls (1996)

Z(H) in δhydride (fcc) ε-phase (fct)

δ and ε-phases Markin et al. (1990)

Syasin et al. (1988)

Numakura et al. (1988)

Ritchie and Sprungmann (1983)

Mazzolai and Ryll-Nardzewski (1976a)

Z(H) in δhydride (fcc)

SC

(a sharp peak or spike)

PC

260–270

PhT(hydr)

7.1

PD(H)

Gorski eﬀect 160–200

48

2.2

≈50

Zr–H(0.0009) (wt%) Zr–H(0.0034) (wt%) Zr–H(up to 5)

690

5.7

Zr–H(2.8)

4.5 Metals of the IVB Group 271

f(Hz)

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

Zr–H(1.8)– Nb(2.5)

4.1 · 104

α + β phases DP 225 8 the peak is attributed to an intrinsic dislocation relaxation process on misﬁt dislocations 340 7 PhT(γ-hydr) 450 2 PhT(δ-hydr) the peaks are due to stress-induced growth and shrinkage of γ- and δ-hydrides quen. from 4 · 104 DP Zr–H(1.4–1.6)– 228 0.3–0.7 353 53.8 – 2 · 10−13 Z(H) in δ400◦ C Nb(2.5) −4 hydride (fcc) 453 71.2 – 6 · 10 the peak at 453 K may be due to the stress-induced growth and shrinkage of hydrides caused by the migration of hydrogen atoms through their interfaces ≈8 Zr–H(0.0141)– PhT(hydr) ≈340 (cooling) 2.2 ≈380 (heating) ≈7 Nb(2.5) (wt%) α + β phases PhT(hydr) Zr–H(0.004– 353 up to 5 4.06 · 104 the peak is attributed to the stress-induced growth and shrinkage of the metastable 0.014)– Mo(1)–Nb(1)– γ-hydride Sn(3.5) (wt%) Z(H) in γ-hydride (fct) Zr–H(1.2 at%)– 4 · 104 321 Z(H) in δ-hydride (fcc) 353 Mo(1)–Nb(1)– 4 PhT(hydr) 423 – Sn(3.5) (wt%)

composition

Table 4.5.2. Continued

Pan and Puls (1996)

Pan and Puls (2000) Pan et al. (1994)

Pan and Puls (1996)

Ritchie and Pan (1991a)

reference

272 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

12 ≈40 ≈160 163–207

(8–10) · 104 8 · 104

1.2 · 105

1.3

Zr–Nb(5–25)

Zr–Nb(12–50)

Zr–Nb(0.25) 879

213

1.2 · 105

Zr–Mo(6)

Zr–Hf(0.3)

80

up to 6 up to 8 up to 30 5–59

136

80

1313 873

≈300 ≈600 (bend)

1.3

3.6

Zr–Hf(50) (wt%)

Zr–Hf(2.4) (wt%) 1 0.84 Zr–Hf(30) (wt%) 3.6 (bend)

1.3 · 104 1.3

(plateau)

≈1.9 4.8 28.8

(plateau)

242 –

(5 at.%) (17 at.%)

GB

PD(vac)

PhT(β ↔ ω)

PD(vac)

PhT(polym) GB

PhT(polym)

GB PhT(polym)

Peaks were observed at 533, 643, 673–693, 743, and 803 K 220 up to 12 33.6 DP(B) 913 80 GB (plateau) ≈843 1133 1173 1413 1233

Zr–Cu(1.6–2.5) Zr–Gd(0.25)

other zirconium alloys Zr84 B16 1

Darsavelidze et al. (1987) Boch et al. (1968) Mishra and Asundi (1972) Bratina and Winegard (1956) Barinov et al. (1961) Barinov et al. (1961)

β(β + ω)-phase Doherty and quen. Gibbons (1971b) Mishra and Asundi (1972)

Mishra and Asundi (1972) β-phase quen. Doherty and Gibbons (1971b) 950◦ C Nelson et al. (1966) PC and SC quen. CW

quen. from melt CW

4.5 Metals of the IVB Group 273

f(Hz)

913 843 193

2

1.3

1.3

1.2 · 105

1.3

Zr–Sc(0.06–0.3)

Zr–Sn(0.5)

Zr–Ti(1)

Zr–V(10)

Zr–W(0.23) 858

≈830

233

303 773–813 318 400–440 813 255

Tm (K)

Zr2 Pd

Zr–Nb(2.5) (wt%) 0.2

composition

65

1.5

65

90

3 210 2 – 320 40

(plateau)

(plateau)

(plateau)

73.7 222.6 83.7 – 222.6

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.5.2. Continued

GB

PD(vac)

GB

GB

GB

PD GB PD DP GB

mechanism

Gindin et al. (1984)

reference

Hazelton and Johnson (1984) Velikodnaya et al. (1989) Mishra and Asundi (1972) Mishra and Asundi (1972) (β + ω)-phases Doherty and quen. 1100◦ C Gibbons (1971b) Mishra and Asundi (1972)

CW

state of specimen

274 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

τ0 (s) mechanism

state of specimen

3.6

3.6

0.9

0.9

Hf–Zr(20)

Hf–Zr(50)

Hf–N–Zr(6)

Hf–O–Zr(6)

Hf–Zr(5)

730 1800

753

1073–1273 1473 1233 1413 753 209 243

(bend) (fall) up to 3 up to 10

(bend)

PD(O/Zr)

GB PhT(polym) GB PhT(polym) PD(N/Zr)

foil 222 GB 1073–1123 60 ﬁlm 57.6 25 – 373 72.4 60 – 543 142.8 30 – 633 peaks are due to the transition of the dislocation structure in the foil into an equilibrium structure. Similar peaks were also observed in deformed hafnium GB 3.6 923–1073 (bend)

H (kJ mol−1 )

Hf(99.7)

Qm −1 (10−4 )

f(Hz)

composition (wt%)

Tm (K)

Table 4.5.3. Hafnium and its Alloys (at.% if not speciﬁed diﬀerently)

Barinov et al. (1961) Barinov et al. (1961) Barinov et al. (1961) Bisogni et al. (1964) Bisogni et al. (1964)

Zolotukhin et al. (1976)

reference

Only very limited data exist for Hf and Hf–Zr alloys, with eﬀects due to grain boundaries, dislocations, phase transformations, and interstitial atoms as indicated below.

4.5.3 Hafnium and its Alloys

4.5 Metals of the IVB Group 275

276

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.6 Metals of the VB Group 4.6.1 Vanadium and its Alloys In V and its alloys, the following internal friction eﬀects are observed: – Dislocation peaks (intrinsic peaks δ, α , β and impurity peaks SK(H), SK(D)) – The Snoek relaxation due to C, N, O and additional peaks due to interaction between the substitutional and interstitial atoms – The Snoek-type H and D relaxation and additional peaks due to interaction of H, D with substitutional atoms – Eﬀects of hydrides and deuterides precipitation and dissolution – Peaks due to H and D in the intermetallic compound V2 Ta – Peaks due to phase transitions in the intermetallic compounds V2 Zr, V2 Hf

f(Hz)

Tm (K)

Qm −1 (10−4 )

H(kJ mol−1 ) τ0 (s) mechanism state of reference specimen

in deformed V, the following DP are observed (Fig. 2.20): (a) intrinsic δ peaks in the range 14–19 K (f = 1–3.9 · 104 Hz) and the α peak at 50 K (f ≈ 1 kHz) which can be explained by the kink motion or kink pair formation in dislocations. The δ-peak is removed by hydrogen impurities (<0.05 at%). (b) SK(H) and SK(D) peaks at 125–230 K which in some papers are denoted as DP(α). (c) β1 and β2 peaks at 250 and 285 K (f = 39 kHz) ≈5 V(99.99) 18.5 DP(δ) 3.9 · 104 2 · 10−8 1.16 CW Cannelli and DP(β1 ) 250 – – – Mazzolai (1970) DP(β2 ) 285 – – – the δ-peak is removed by the hydrogen impurities (<0.05 at.%) and the α-peak is introduced ≈7 203 3.3 · 10−18 DP(α) = 50 SK(H) V 1.5 Chang and Wert 140–180 up to 120 14.5–29 10−8 −10−6 DP(α) = CW SK(H) (1975), Shibata the peak is removed by dehydrogenisation et al. (1978) V (dehydrogenised) 300–900 DP(δ) SC, CW Mizubayashi et al. 14–15 0.1–0.6 the peak is identical to DP(α) in Nb and Ta and (1979), Mizubayashi accounted to the non-screw dislocation moving and Okuda (1982) 57–60 DP 0.1–1 the peak is accounted to interaction of impurity atoms with screw dislocations V the α-peak is absent after dehydrogenisation DP(α) CW Koiwa et al. (1980)

V V

composition

Table 4.6.1. Vanadium and its Alloys (at.% if not speciﬁed diﬀerently)

4.6 Metals of the VB Group 277

1

864

0.55

V (iodide)

V(99.75)

V–C, O, N V–C V–C

V–C V–C

VC0.79–0.84

VC0.76

V–C

820

1

V

≈0.01 ≈0.01 ≈1

50

≈470 65 870–970 152 1 117.3 443 the coeﬃcient K ≈ 0.107 in the equation Qm −1 = K · CC (CC in at.%) (theoretical estimation)

136

113.9

113.9

106 125 139 159 168 178

38

S(C)

DP(δ) DP(α ) DP(α)

GB(?)

mechanism

10−13 –10−11DP(?) DP(?) ≈10−13 S(C) 2 · 10−15 S(C)

6 · 10−14

5.7 · 10−15 S(C)

10−13 8 · 10−14 6 · 10−14 5 · 10−14 2 · 10−14 10−14

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

(internal friction + elastic after– eﬀect) 870–970

435

413–423 463 513–523 613–633 703–733 823 18 50 126

Tm (K)

f(Hz)

composition

Table 4.6.1. Continued

as-machined

quench from the liquid state rapid quenching from the liquid state

state of specimen

Powers and Doyle (1958) Powers and Doyle (1959) Bukatov et al. (1975a) Bukatov et al. (1975a) Weller (1985) Blanter (1989)

Duﬀy and Umstattd (1994)

Okrostsvaridze et al. (1983) Darsavelidze et al. (1989)

reference

278 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

V–O(up to 1.6)

V–O

V–N V–O V–O V–O

V–N

V–N

V–N(up to 10)

V–N(up to 1.1)

V–N

V–N V–N V–N 538 535 142.3 S(N) S(N)

544 151

5.1 · 10−16 S(N)

454 447 119.3 122.3

S(O) S(O)

bamboo structure

(internal friction) S(O) 123.5 1 · 10−15 (internal friction and elastic 121 2 · 10−15 after-eﬀect) 459 0.73 S(O) the coeﬃcient K = 0.0805 in the equation Qm −1 = K · CO (CO in at.%). The peak asymmetry is observed above 0.8 at.% O

0.7 0.55

in the average for polycrystal samples Qm −1 = 0.0800 · CN (CN in at.%)

1

(internal friction) 144.4 1.6 · 10−15 S(N) (internal friction + elastic after142.1 2.8 · 10−15 eﬀect) 540 0.73 S(N) the coeﬃcient K = 0.0805 in the equation Qm −1 = K · CN (CN in at.%) 538 1 S(N) the linear dependence of the peak height is observed only up to 0.8 at.% 533 153.1 0.5 S(N) 5 · 10−16

0.7 0.55

H¨ orz (1968)

Powers (1954) Powers and Doyle (1958) Powers and Doyle (1959)

Monroe and Cost (1969) Boratto and Reed-Hill (1977) Weller (1985, 1996, 2001) Blanter (1978)

H¨ orz (1968)

Powers (1954) Powers and Doyle (1958) Powers and Doyle (1959)

4.6 Metals of the VB Group 279

0.5

V–O

(10

) H(kJ mol−1 ) τ0 (s) irr(n)

mechanism state of specimen

458 124.0

1 · 10−15 S(O)

S(O) 1.44 459 217–240 111.5 2.7 · 10−14 hydrogen addition does not inﬂuence on the parameters of the oxygen Snoek relaxation

V–O(0.2)–H(0.11– 0.45)

the S(O) peak is supressed

chromium addition (0.3 wt%) does not inﬂuence on the S(O) peak

iron addition (9 wt%) does not inﬂuence on the S(O) peak

in the average for polycrystal samples Qm −1 = 0.0800 · CO (CO in at.%) copper addition (0.4 wt%) does not inﬂuence on the S(O) peak

1

V–O V–O(0.03–0.14) (wt%)–Cu V–O(0.03–0.14) (wt%)–Cr V–O(0.08)– Be(0.18) (wt%) V–O(0.2) (wt%)–Fe

V–O

V–O(0.2)

Qm

the S(O) was decreased by irradiation and post-irradiation annealing below 200 or 250◦ C, while it began to recover by annealing above this temperature S(O) 445 115.6 10−15

Tm (K)

Table 4.6.1. Continued −4

117.31 (4–6) · 10−15 S(O) 1 457–462 the peak is shifted to higher temperatures with increasing oxygen content accompanied by a continuous and also symmetric broadening. This broadening is accounted for a continuous distribution in relaxations times S(O) 1.41 459 219 111.5 2.1 · 10−14

1.3

V–O

V–O(0.18–0.85)

f(Hz)

composition

−1

Indrawirawan et al. (1987b) Weller (1985, 1996, 2001) Blanter (1978) Shikama et al. (1977a) Shikama et al. (1977a) Shikama et al. (1977a) Shikama et al. (1977a) Indrawirawan et al. (1987b)

Boratto and Reed-Hill (1977) Diehl et al. (1987)

Eto et al. (1974)

reference

280 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

405 up to 290 116

2.1 · 10−15 S(O)

1.72

≈460 ≈600 up to 100 up to 80 S(O) PD(O/Ti)

503 up to 220 138 2.6 · 10−15 PD(O/Nb) nickel addition (0.3 wt%) does not inﬂuence on the S(O) peak

0.3

Mo addition broadens the oxygen Snoek peak at higher temperature side

manganese addition (0.3 wt%) does not inﬂuence on the S(O) peak

0.7

443 S(O) 533 S(N) 663 twin boundaries V–N(0.02)– 479.7 1 17.36 S(O) 115.48 O(0.02) S(N) 568.5 16.09 156.44 458 V–N–O(up to ≈1.4 up to 60 S(O) 473–493 (2.5 at.% Al) 0.4)–Al(up to 10) – ≈6 538 S(N) – ≈590 (5–10 at.% Al) aluminum addition by 0.9–1.4 at.% broadens the S(O) peak. As the Al concentration increases the S(O) peak is suppressed and some new damping appears V–N–O–Ti(45) 113 20.9 10−9 1 S (C) 533 146.5 5 · 10−16 583 178 S(O) – 633 178 S(N) –

V–O(0.03– 0.14) wt%–Ni V–O(up to 1.145)–Ti(1.3) V–N–O V–N–O

V–O(0.06–0.35)– Nb(0.50)

V–O(0.03– 0.14) wt%–Mn V–O–Mo

Mishra and Asundi (1977)

Haneczok and Weller (1990) Shikama et al. (1977a,b)

Mondino et al. (1969)

Shikama et al. (1977a) Hasson and Arsenault (1970)

Shikama et al. (1977a) Shikama et al. (1977b) Carlson et al. (1987)

4.6 Metals of the VB Group 281

≈1.4

V–N–O(up to 2)– Ti(up to 10)

Tm (K)

190–260

104 1.4

V–D(0.6–6)

V–D(0.017– 0.113), D/V

V–H(0.27–6.5)

2–24

up to 0.4 16.4

2 · 10−12 PhT(deut)

S(D/N, O)

S(O) PD(O/Ti) S(N) PD(N/Ti) –

mechanism

93–77 2–30

≈14.4

PD(D/Ti)

≈210 up to 340 270 (cooling) three peaks at ≈200, 250 and 320 K were observed during heating PhT(hydr) (1–2) · 104 190–350

0.8

SK(D) 150 5 230–320 50–400 PhT(deut) the SK(D) peak is due to deformation around hydride precipitations 1.4 PhT(deut) 230–260 up to 120

80–100

104

V–D, H V–D V–D(up to 0.18)

V–D(0.017– 0.112 D/V)– O(0.7–1 at.%) V–D(0.21–0.82)– Ti(3.9) V–H V–H(1.2–14.5)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

458 121.2 513 125 538 133.7 608 137.5 648 – titanium addition suppresses the S(O) and S(N) peaks

f(Hz)

composition

Table 4.6.1. Continued state of specimen

Butera and Kofstad (1963) Cannelli and Mazzolai (1970)

Tanaka and Koiwa (1981a)

Yoshinari et al. (1978)

Cannelli and Mazzolai (1973) Cannelli and Mazzolai (1973) Yoshinari et al. (1977, 1978)

Shikama et al. (1977a,b)

reference

282 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

156

1.4

1.4

V–H(50–350) (at. ppm) V–H(0.326) ≈80

110

V–H(0.8)

1.3

≈253 up to 60 153 – ≈253 – after dehydrogenisation the DP(α)=SK(H) is absent V–H(0.0045–0.04) 300–900 60 10–30 120–170 3–5 150 1 V–H(2) 250 90 V–H(0.92–1.24) 230–250 up to 60 1.2

200

32.7–33.7 1.5 · 10−14 – 4.7 · 10−13

145

2000

VH0.73

9 SK(H)

170

368

V–H(0.06)

Koiwa and Shibata, 1980a,b

Mizubayashi et al. (1982) Yoshinari and Koiwa (1982a) Koiwa and Yoshinari (1983)

SC, CW DP PhT(hydr) SK(H) PhT(hydr) PhT(hydr)

Koiwa et al. (1980) CW

CW

CW

CW

Owen and Scott (1972) Chang and Wert (1973) Chang and Wert (1975) Chang and Wert (1975) Mizubayashi et al. (1979) MelikShakhnazarov et al. (1980) Koiwa et al. (1980)

Ph(hydr) DP(α) PhT(hydr)

DP(α)

DP(α)

PhT(ord)

SK(H) PhT(hydr)

8 · 10−11

SK(H)

PhT(hydr)

180–230 up to 22 oxygen decreases the peak V–H(0.045) 150–200 8–10 1.5 36.7 H and τ0 depend on degree of deformation V–H(up to 0.084) 1.5 170–240 2–24

up to 120

1.55

170–200

V–H(0.1–2)

V–H(up to 0.0145) 0.32

4.6 Metals of the VB Group 283

0.8

0.8

0.8

0.8

0.33 0.33

V–H(1.5)–Cu(1)

V–H(1.5)–Fe(1)

V–H(1.5)–Mo(1)

V–H(1.5)–Nb(1)

V–H(3)–Nb(10) V–H(3.5–4.7)– Nb(25–50) V–H(0.11– 4.44)–Ti(0.4– 3.9)

V–H(0.01–0.05)– Ti(1) (wt%) V–H(1.5)–Zr(1)

0.8

V–H(1.5)–Cr(1)

state of specimen

0.8 90 115 3 1

PD(H/Zr)

0.8 62–80 up to 70 12.5 3.7 · 10−12 PD(H/Ti) the peak increases its height and shifts towards lower temperatures with the increase in hydrogen content 0.8 150–300 PhT(hydr) up to 90 the PhT(hydr) peak is observed at 1 (wt%) Ti but the peak is absent at (5–10) wt% Ti

PhT(hydr) 180 15 in the temperature range 80–300 K peaks are absent

in the temperature range 10–140 K peaks are absent

in the temperature range 10–140 K peaks are absent

in the temperature range 10–140 K peaks are absent

in the temperature range 10–140 K peaks are absent

95 S(H/N,O) 0.07 15.4 2 · 10−13 160 PhT(hydr) – 0.01 – in the temperature range 10–140 K peaks are absent

3.9 · 104

mechanism

V–H(0.03–0.8)

) H(kJ mol−1 ) τ0 (s)

Tm (K) (10

Table 4.6.1. Continued

f(Hz)

Qm

−4

composition

−1

Owen and Buck (1983) Tanaka and Koiwa (1981a,b)

Tanaka and Koiwa (1981a,b)

Cannelli et al. (1983, 1984b) Tanaka and Koiwa (1981a,b) Tanaka and Koiwa (1981a,b) Tanaka and Koiwa (1981a,b) Tanaka and Koiwa (1981a,b) Tanaka and Koiwa (1981a) Owen et al. (1985) Owen et al. (1985)

reference

284 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

kHz range

1.2 · 105

480

V–Si(25,25)

V2 Zr

V2 Zr

≈20 123 85 50

460–540 570–620 50 725–820 50 several maxima were not clear 498–523 573 ≈60 ≈30

PhT PhT

S(O) S(N)

135 S(N) or S(O) PD(B) 150 10−11 184 – GB observed but their mechanism is

Laves phase

Laves phase

quench from liquid state quench from liquid state

≈10 ≈30 C15 structure PhT ≈260 100 PhT ≈50 75 PhT V2 Hf 0.75 Zr0.25 ≈150 ≈110 PhT V2 Hf 0.5 Zr0.5 ≈50 ≈10 PhT V2 Hf 0.25 Zr0.75 ≈70 PhT ≈72 ≈96 ≈400 PhT V2 Zr all peaks are no relaxation peaks. The possible origin of the PhT peaks is the pinning and depinning of boundaries of the transformed phase V–Ta–D V2 TaD0.47 2.472 · 106 20 2 Laves phase 270–290 ≈40 24.0 3.4 · 10−12 S(D) (0.94–2.46) · C15 106

kHz range

3–5

V–Ga(2–7)

V–Hf–Zr V2 Hf

1

V–B(1–18)

other vanadium alloys V–B(13) 1

Foster et al. (2001a)

Finlayson et al. (1975, 1978)

Darsavelidze et al. (1989) Dedurin et al. (1997) Finlayson et al. (1975) Doherty and Gibbons (1971a) Snead and Welch (1985b)

Okrostsvaridze et al. (1983)

4.6 Metals of the VB Group 285

f(Hz)

Tm (K)

Qm (10

−4

) H(kJ mol−1 ) τ0 (s)

Table 4.6.1. Continued mechanism state of specimen

V2 TaD0.17

1.3 · 106

TD(D) ≈20 2–3 Laves phase C15 PhT(ord) 80 – S(D) ≈275 27.9 80 6 · 10−13 TD(D) ≈30 – 2.5 – V2 TaD0.50 PhT(ord) – ≈125 – 2 260 140 25.0 2.2 · 10−12 S(D) the peaks at 20 and 30 K were interpreted as D motion within a hexagon of g-sites. The peak at 260–275 K have been attributed to D hopping between the hexagons V–Ta–H 1 · 106 V2 Ta peaks are absent over the temperature range 15–345K Laves phase 245–250 26–88 26–27 (5.2–9.6) · S(H) V2 TaH0.06–0.18 C15 10−13 – 7.7–11.5 – (5–11) · 10−9 V2 TaH0.34–0.53 242 108–129 21.2–22.1 (5.7–3.9) · 10−12 the peaks were associated with H hopping between g-site hexagons. Two Arrhenius processes at the lower H concentration were interpreted as phonon-assisted tunneling between ground state and excited states TD(D) V2 TaH0.18 1 · 106 1 Laves phase PhT(ord) ≈70 0.3 C15 the peak at 1 K was interpreted as H motion within a hexagon of g-sites

composition

−1

Atteberry et al. (2004)

Foster et al. (1999a, 2001a,b)

Foster et al. (2001a); Atteberry et al. (2004)

reference

286 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.6 Metals of the VB Group

287

4.6.2 Niobium and its Alloys In Nb and its alloys, the following internal friction eﬀects are observed: – Dislocation peaks (intrinsic peaks α, β, γ and impurity peaks SK(H), SK(D), SK(N), SK(O) and DES(O)) – Eﬀects at transition from the normal to superconducting state – Grain boundary peaks – The Snoek relaxation due to C,N,O and additional peaks due to interaction between the substitutional and interstitial atoms – The Snoek-type H and D relaxation (including H and D tunneling) and additional peaks due to interaction of H, D with substitutional atoms – Eﬀects of hydrides and deuterides precipitation and dissolution – Peaks due to ordering and other phase transitions in hydrides – Peaks due to self-interstitials

Nb

Nb

Nb

Nb

Nb Nb

Nb Nb

composition

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

reference

in deformed Nb, the following DP are observed (f ≈ 1 Hz, Fig. 2.20): (a) δ, α, α , α1 , α2 peaks in the range 20– 150 K which are explained by the kinks moving in screw dislocations and the kink pair formation in non-screw dislocations. Hydrogen degassing eliminates the peaks in the range 100–150 K (SK(H)) and allows to observe the intrinsic peaks at 20–60 K; (b) SK(H) and SK(D) peaks at 110–160 K or two SK(H) peaks (at 110 and 130–137 K); (c) one, two or three β peaks in the range 190–250 K accounted for dislocation interaction with intrinsic point defects (Hasiguti peaks); (d) γ peaks in the range 270–400 K accounted for the kink pair formation in screw dislocations. They split into two peaks-DP(γ1 ) and DP(γ2 ) with the ﬁrst one – DP(γ1 ) – probably DES(O); (e) DES(O) at 334–450 K; (f) SK(O) peaks at 605–740 K which split into two SK(O) peaks (at 545 and 733 K); (g) SK(N) at 760–800 K CW DP 18 · 103 173 Bruner (1960) 21 ≈0.1 CW DP 18 · 103 10 Chambers and DP 165 up to 13 Schultz (1960) 29 CW (18.6–174.4) · 173–197.6 ≈40 25.5 Bordoni et al. 1.6 · 10−13 DP (1961) 103 ≈13 DP(α) 15 · 103 170 CW Chambers and DP 310 – Schultz (1961) ≈130 7.8 DP(α) ≈4 CW 22–25.5 Chambers and (1–8) · Schultz (1962) 10−12 DP(γ) ≈240 ≈6 45.2 10−11 CW DP 2.2 · 103 148 De Batist (1962) 10 DP 178 10 43.5 · 103 DP 208.5 0.5 – DP 222.5 – 232 – DP

f(Hz)

Table 4.6.2. Niobium and its Alloys (at.% if not speciﬁed diﬀerently)

288 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Nb

Nb

Nb

Nb

9.2

8 · 104

Nb

DP(α) DP(β)

3.6 · 10−13 DP(α) 1.8 · 10−12 DP

220

105

DP(α)

DP(α) DP(α) DP(β)

105 220–240

up to 200 24

2 · 10−12 − DP(α) 5 · 10−11 increasing α-peak height and temperature with higher purity 115 2 – – – DP(α) DP(β) ≈10−11 ≈210 ≈43 – 13 · 103 40 27 DP 170 – – DP(α) 310 – – DP(β)

– – – up to 4 +smaller subsidiary peaks at about 190 and 220 K up to 80

≈190 ≈115 ≈200

1

4 · 10−11

0.002 0.154

an abrupt decrease marks the normal to superconducting transition 0.001 0.183 2.6 · 10−10 0.01 – –

up to 0.7 up to 3

≈10

27 26

2.08

3.24 3.24

105–115 190–250

≈1

Nb

253

5 · 10 6

Nb Nb

De Batist (1963) Polotskiy et al. (1966) Stanley and Szcopiak (1966, 1967a) Kramer and Bauer (1967)

CW during manufacturing

SC, CW

SC, CW

Wert et al. (1970)

Amateau et al. (1969) Gibala et al. (1970)

Amateau et al. (1968)

SC, supercond. SC, supercond., CW SC, normal (magnetic ﬁeld) SC, CW Stanley and CW Szkopiak (1967b)

SC

CW, irr(n)

SC, CW

4.6 Metals of the VB Group 289

Nb

Nb(99.9)

Nb

Nb Nb

Nb

Nb

composition

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism

CW annl. in ultrahigh vacuum CW

by the

CW

CW

state of specimen

300–2000

≈10 ≈50 DP(α ) ≈160 DP(α) up to 30 DP(β1 ) ≈200 38.5 – 8 · 10−13 ≈240 43.3 – 1.3 · 10−12 DP(β2 ) electron irradiation and impurities (N + O) decrease the α peak. The maxima of the β1 and β2 peak heights were observed versus electron irradiation dose and interstitial impurity contents ≈360 ≈2.5 irr(n) 250 DP(β) CW ≈1050 ≈9 45 DP(α ) 150 DP(α) up to 30 150 DP(α) up to 10 CW + Irr(n) 200 DP(β1 ) – 235 DP(β2 ) – CW 118 DP(α) 1 DP 10−10 228 38

1000

DP(α ) 4.5 60 5 · 10−9 1 – 145 – SK(H) (?) 4 12 · 103 178 DP(α) up to 40 26 313 48 DP(β1 ) – 378 67 DP(β2 ) – α-peak explained by the formation of kinks on edge dislocations and β-peaks formation of kinks on screw dislocations 422–1115 ≈5 378 DP(β) 2.9 · 104 ≈130 19.2 2 · 10−13

f(Hz)

Table 4.6.2. Continued

Ferron et al. (1975)

Igata et al. (1975b)

Igata et al. (1975a)

Lupinc (1972) Mazzolai (1975)

Burdett and Queen (1970a) Rieu and De Fouquet (1971)

reference

290 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Nb

Nb

Nb

113–133 DP(α) 365–385 up to 60 DP(β) DP(γ) 510–520 – DP(γ1 ) 300–340 57.7 10−11 the peak may be caused by the extrinsic double kink formation aﬀected by impurity atoms DP(γ2 ) 350–360 76.9 10−11 the peak may be caused by the intrinsic double kink formation on screw dislocations 500 – – – the peak may be caused by the catastrophic thermal unpinning of screw dislocations from oxygen atoms CW bamboo structure CW

0.5

≈30 DP(α2 ) 120 20.2 SC, CW 5 · 10−10 ≈50 147 29.8 1.6 · 10−11 DP(α1 ) the α1 and α2 peaks are due to the formation of kink pairs on non-screw dislocations and the diﬀusion of geometrical kinks on screw dislocations, respectively. Proton irradiation suppressed the α1 peak and converted it partly to the α2 peak ≈40 123 CW 1.5 DP(α) by annealing with Zr foils, the hydrogen and oxygen content was reduced considerably. For such specimens, no α peak was observed 300–330 58 1 DP(γ1 ) 10−11 CW DP(γ2 ) 350–360 77 10−11 520 2 – – – ≈2.5 9.37 · 104 31.5 DP(δ) 2.7 10−12 CW SK(H) ≈4 182.5 26.9 3 · 10−14 ≈0.03 without CW 113 – – S(H) ≈8 · 104 hydrogen saturation increases the SK(H) height up to 25 · 10−4

1.5–1.7

Nb

Nb(RRR=2500)

1

Nb (high-purity)

Verdini and Bacci (1980)

Igata et al. (1980)

Shibata and Koiwa (1980)

Klam et al. (1977, 1979)

Igata et al. (1977)

Ferron et al. (1977)

4.6 Metals of the VB Group 291

1

1

300 650

Nb

Nb

Nb (high-purity)

Nb(<0.0001 H)

120 DP(α2 ) 150 DP(α1 ) DP(γ) 270 58.7 10−12 the α1 and α2 peaks are due to the interaction of hydrogen with dislocation ≈25 1500 DP 70

1.3

120 147 40 275 10–35 58.9 1.3 · 10−12 1370 100 360 grain boundary relaxation 1520– 100–300 414 1570 special boundaries after high temperature annealing 44 8 160 45

DP(α, α ) SK(H)

GB

DP SK(H) DP(γ) GB

DP(α) DP DP(δ)

Nb interstitial concentration ≈0.01

140 200–300 23

0.5

mechanism

Nb

) H(kJ mol−1 ) τ0 (s)

0.5

(10

Nb (high purity)

Qm

f(Hz)

Tm (K)

Table 4.6.2. Continued −4

composition

−1

SC, CW

CW

SC, CW

CW

CW

SC, CW

state of specimen

Funk et al. (1983)

Gridnev et al. (1982), Yakovenko (1986)

Maul and Schultz (1981) De Lima and Benoit (1981b)

Kuramochi et al. (1980) De Lima and Benoit (1981a)

Klam et al. (1980)

reference

292 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

9.7 64.7

DP(α) 5 · 10−14 1.5 · 10−13 DP(γ) SC, CW

Nb(RRR=1600)

Nb(H-free, RRR=4500)

Nb

360

≈9 ≈35 CW DP(α) ≈4 ≈130 SK(H) 734–2500 5.15–4.6 ≈2 supercond. DP with increasing frequency the peak temperature decreases. CW increases the peak height ≈30 44 400 DP(α) CW CW+irr(prot) ≈22 – 44 irradiation suppressed the α1 peak and converted it partly to the α2 peak DP(γ) CW 10−4 –10 230–280 25 56.7 7 · 10−12 reversible peak frequency CW + anneal dependence 65.4 1.2 · 10−12 – irreversible peak

≈15 DP(α) 60 1100 SC110, CW the peak was explained by the thermally activated kink-pair formation in non-screw dislocations ≈0.5 PD(self-int) SC, CW, ≈6–11 1110–1140 irr(e)

10 up to 80

Nb(RRR=4000) O, N, C ≤ 3, H ≤ 1 at. ppm Nb(RRR=4000) O, N, C ≤ 3, H ≤ 1 at. ppm Nb(RRR=2000)

39.5 279

1.2

Nb

Nb

Nb

after hydrogen degassing the SK(H) peak can be removed completely and the intrinsic dislocation relaxation peaks α, α can be observed. Hydrogen introduction suppresses the α, α peaks and gives rise to the SK(H) peak DP(α1 ) 600–3700 CW 25–40 20 6.8 10−12 DP(α2 ) 60 15 7.2 3 · 10−11 35 7.7 DP(α1 ) 600 CW 10−14 55 – – DP(α2 )

D’Anna and Benoit (1993a)

Okumura et al. (1989)

Miloshenko (1987)

Arai et al. (1987)

Lauzier et al. (1986, 1987b)

Kuramochi et al. (1984, 1987) Kuramochi and Okuda (1985), Okuda et al. (1985) Funk and Schultz (1985), Schultz et al. (1985) Lauzier et al. (1986, 1987a)

4.6 Metals of the VB Group 293

in the range 0.065–2 K maxima are absent

9 · 104

9 · 104

7.9 · 104 7.3 · 104

Nb(RRR=60)

Nb

Nb(RRR=5500)

Nb(RRR=290) Nb(RRR=2100) Nb(RRR=10 000) Nb–C, N, O Nb–C Nb–C

198–251 255 265

1.2 82 145 189 202 38

894 885 876 7.8 · 104

1–0.7 150 15

0.001 ≈0.1 ≈0.1 6.4 16.6 10

Natsik et al. (1999)

Pal-Val et al. (1993) Natsik and Pal-Val (1993, 1997), Pal-Val et al. (1993, 1995, 1996) Duﬀy and Umstattd (1994)

reference

internal friction + elastic after-eﬀect

Wert (1950)

ach and Wasserb¨ Thompson (2001) SC, CW ach and Wasserb¨ Thompson (2001); Wasserb¨ ach et al. (2002) without CW Natsik et al. (2001, SC 100, CW 2004) without CW

112.7

DP(α)

without CW CW PC, CW

as-machined

DP(α) 3 · 10−10 2.8 · 10−10 1.6 · 10−11

1 · 10−10

S(H/O, N) DP(α) DP(α)

supercond. normal

state of specimen

14.4 – –

14.4

PhT(super)

mechanism

2.1 · 10−10 DP (kink 1.1 · 10−10 migration)

Nb(99.8)

0.183 0.26

3.1 2.05

9 · 104

Nb up to 0.6 up to 1

9.3

9 · 104

Nb(RRR=10 000)

) H(kJ mol−1 ) τ0 (s)

Tm (K) (10

Table 4.6.2. Continued

f(Hz)

Qm

−4

composition

−1

294 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

1 1

Nb–C

Nb–C Nb–C(0.05–0.7)– Zr(2)

Nb–N(up to 0.35)

Nb–N

558

514 ± 2 428 463 493 528 573 613 5 11 25 9 19 5

internal friction internal friction + elastic after-eﬀect 512

531

541

145.2

0.55

549

bamboo structure

bamboo structure

Bamboo S(N) SK(N) structure to deformation produced by

S(N)

S(N)

S(C) S(O) S(N)(?) PD(C/Zr)

2.1 · 10−15 S(C)

135.6

137.5

7.5 · 10−15

137.8

S(C)

6 · 10−15

S(C)

138.5

139

internal 145.2 3.7 · 10−15 friction internal friction + 145.7 3.5 · 10−15 elastic after-eﬀect 573 1 760–800 up to 100 the SK(N) was observed after CW and without CW due Nb2 N precipitations

1

0.55

Nb–C

Nb–N Nb–N

1

Nb–C

Dahlstrom et al. (1971)

Powers and Doyle (1957a) Powers and Doyle (1959)

Schulze et al. (1981), Weller (1985) Weller (1996, 2001) Heulin (1985b)

Powers and Doyle (1957a) Powers and Doyle (1959)

4.6 Metals of the VB Group 295

implantation of N-ions caused the appearance of DP(α) and DP(β) peaks

quen. 673 S(N) 170 40 the peak was resolved into three Debye peaks with H = 141, 152 and 161 kJ mol−1 562 151.4 ± 2 1 (1.2 ± 0.1) · S(N) 10−15 in the average for polycrystal samples K = 0.3190 in the equation Qm −1 = K · CN (CN in wt%) the dependence of the coeﬃcient K on the grain size d (mm):1/K = 2.14 + 0.3d−0.5 0.3–1.3 S(N) 540–562 100–145 145.2 7 · 10−15 the activation parameters of the Snoek nitrogen peak are not aﬀected by hydrogen quen. 635 S(N) 50 23–18 768 PD(N/Hf) 30–36

Nb–N

Nb–N(0.3)

Nb–N(0.38)– H(0–1) Nb–N(0.40)– Hf(1–2)

Nb–N

Nb–N

153 –

quen.

quen.

685

S(N)

2.7 · 10−15 S(N)

S(N)

143

147.6

133.5

645

33.4

≈65

30–40

state of specimen

Nb–N(0.25–0.4)

mechanism

566

τ0 (s)

Nb–N(0.005), wt% 1.3

H(kJ mol−1 )

635

)

50

(10

Nb–N(0.45)

Qm

f(Hz)

Tm (K)

Table 4.6.2. Continued −4

composition

−1

Ahmad and Szkopiak (1972) Brasche et al. (1988) Yelutin et al. (1972)

Yelutin et al. (1972) Weller et al. (1981b) Novikov et al. (1982a); Bakhrushin et al. (1985) Bulmer and Miodownik (1985) Bakhrushin et al. (1989) Weller (1985, 1995, 1996, 2001) Blanter (1978)

reference

296 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

30

645 143 peaks at 685, 695, 725, 780 and 815 K Nb–N(0.4)–Hf(2) 40 ≈748 90 the peak was resolved into six Debye peaks Nb–N–Mo(0–50) 3–8.6 310–324 12–23 368–390 1–7 435–448 2–13 501–512 3–20 582–587 11 660–670 5 ≈25 Nb–N(0.25)– 635 133.5 50 ≈25 693 146.1 Ti(1–2) Nb–N–V(0–50) 588–593 152 3–8 688–693 179 743–748 192 798–803 206 848–853 220 645 40 Nb–N(0.03)– 50 143 685 170 153 W(23.7) wt% 745 40 167 ≈673 40 Nb–N(0.21)– 170 the peak was resolved into three Debye peaks W(12) Nb–N–Zr(0.3–0.8) 0.56 548 ≈635 (0.8 at.% Zr)

Nb–N(0.4)–Hf(2)

S(N) PD(N/Zr)

S(N) PD(N/Mo) PD(N/Mo/Mo) PD(N/3 Mo) PD(N/4 Mo) PD(N/5 Mo) S(N) PD(N/Ti) S(N) PD(N/V) PD(N/V/V) PD(N/3V) PD(N/4V) S(N) S(N)(?) PD(N/W) S(N)

S(N) PD(N/Hf) S(N)

Yelutin et al. (1974) Kushnareva and Snezhko (1993)

Novikov et al. (1982b) Bakhrushin et al. (1989) Powers and Doyle (1959)

quen.

quen. from 1880◦ C quen.

quen.

Novikov et al. (1982a) Bakhrushin et al. (1989) Kushnareva et al. (1992b)

quen.

4.6 Metals of the VB Group 297

f(Hz)

2.8

1

Nb–N(0.37)– Zr(4.3) (wt%)

Nb–N(0.03)– Mo(10)–Ti(3)– Zr(1) (wt%)

0.55

0.6

Nb–N(0.16–2)– Zr(2–3.8)

Nb–O Nb–O

50

Nb–N(0.45)–Zr(1–2)

Nb–N(0.04) 1.97 Zr(0.04–0.56) (wt%)

composition

412

488 567 656 760 635 738 523 573 626 708–713 580 618 673 768 510 550 610 650

Tm (K)

−4

(10

internal friction

100 30 1 8 3 15

32–26 34–43

Qm

−1

111

151 157

172 197

156.5

165.7 190.3

PD(O/Zr) S(N) PD(N/Zr) PD(N/Zr/Zr) S(N) PD(N/Zr) PD(O/Zr) – PD(N/Zr) PD(N/Zr/Zr) S(N) PD(N/N) PD(N/Zr) PD(N/Zr/Zr) PD(N/Mo) S(N) PD(N/Ti) PD(N/Zr)

mechanism

2.1 · 10−15 S(O)

4.7 · 10−15 5.6 · 10−15

) H(kJ mol−1 ) τ0 (s)

Table 4.6.2. Continued

quen. from 1200◦ C

quen.

state of specimen

Powers and Doyle (1959)

Vasiljeva and Voronova (1981)

Gridnev et al. (1978)

Heulin et al. (1972)

Yelutin et al. (1972)

Mosher et al. (1970)

reference

298 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

334

1300 1.1

Nb–O(0.0005) (wt%) Nb–O(0.035) (wt%) Nb–O(0.016) (wt%) Nb–O(0.11–0.71)

Nb–O(0.0965)

Nb–O

Nb–O(0.09)

520

0.6

Nb–O(up to 2)

1.7 · 10−15 1.2 · 10−15 7.3 · 10−15 3.3 · 10−15

1.4 · 10−15

600

47 113

197

5 · 10−22

SK(O)

DP

CW

SC, CW

of the peak and a shift to

S(O) S(O)

CW

CW S(O) 424 bamboo DES(O) 420 80 SK(O) structure 605 90 147.1 5.8 · 10−14 the oxygen Snoek peak was enhanced by the plastic deformation and increased further during annealing

1.28 0.53

1.26 2.4

DES(O)

DES(O) CW

bamboo S(O) PD(O/O) structure PD(O/O/O) PD(O/O/O/O)

Qm −1 = 0.041 · CO (CO ≤ 1.1 at.%) S(O)

111.8 119.3 122.3 124.4

112.3

7.6 · 10−15 425 102 107.1 92.5–334 423.2– 427.3 with increasing oxygen content a symmetrical broadening slightly higher temperature were observed 1000 30

425

0.9

Nb–O(0.015–0.25)

internal friction + elastic after-eﬀect 418 136–400 439 16–300 476 5–80 515 5–15

Maul and Schultz (1981) Varchon et al. (1982) Seeger et al. (1982)

Vercaemer and Clauss (1969) Melik-Shakhnazarov et al. (1975) Melik-Shakhnazarov et al. (1981b) Weller et al. (1981b) Weller et al. (1981d)

Gibala and Wert (1966b,c)

4.6 Metals of the VB Group 299

1

Nb–O(up to 4) >0.3 at.% >0.9 at.%

10 1 up to 60 – up to 200 62.5 – 193 162

4 · 10−13 – 4.2 · 10−20 3.4 · 10−13

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) DP(α) DP(γ) DES(O) SK(O)–1 SK(O)–2 S(O) PD(O/O) PD(O/O/O)

mechanism SC, CW torsion axis 110

state of specimen

1.33

3.5

Nb–O(up to 2) 446.5 452.5 452.2

424 290 730 1120

161 101 86 87

109.6

S(O)

6.3 · 10−14 S(O) 2.8 · 10−12 1.1 · 10−12

4 · 10−15

quen.

110.4 2.9 · 10−15 S(O) 1 421–427 1000 427–428 β increases from 0.4 to 1 with oxygen content. This broadening is account for by a continuous distribution in relaxation times and it is shown to originate from a distribution in activation energies

1

Nb–O(0.2)

Nb–O(0.12–0.85)

135 300 420 545 733 429 443 493

Tm (K)

110.6 2.8 · 10−15 S(O) 421.2– 425.1 1000 538.9– 543.7 the maxima are rather symmetrically broadened and shifted to higher temperatures with increasing oxygen content. The broadening may only accounted by a continuous distribution of relaxation times

1.2

Nb–O(0.01)

Nb–O(0.12–0.85)

f(Hz)

composition

Table 4.6.2. Continued

Gridnev and Kushnareva (1987), Kushnareva and Pecherskij (1986b)

Indrawirawan et al. (1987a)

Diehl et al. (1987)

Weller et al. (1985, 1992)

Heulin (1985a)

Seeger et al. (1982) Weller (1983) Molinas et al. (1987)

reference

300 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Nb–O

Nb–O

Nb–O

Nb–O

Nb–O(0.050– 0.077) Nb–O(0.01–0.02)

Nb–O(0.007) Nb–O(0.6 at%) Nb–O

Nb–O(0.03) Nb–O(0.01–0.12)

the dependence of the coeﬃcient K on the grain size d (mm):(1/K) = 1.85 + 0.28d−0.5

the broadening parameter β increases from 0.45 to 1.45 with oxygen content. Broadening is asymmetrical (on the high temperature side) and explained by creation of oxygen atom pairs and triplets 697 150 2.5 SK(O) 187.5 PC, CW 720–780 80–190 3 SK(O) 151–182.7 SC, CW the peak height and the high-temperature halfwidth of the maximum increase and the peak temperature and the low-temperature halfwidth decrease with the amplitude of oscillation 427.25 17.36 1 S(O) 112.0 427.0 322 91.5 420 1.5 surfaceS(O) oxidised specimens after surface oxidisation the Snoeck oxygen peak broadens 420 3 S(O) 26 106.7 1 · 10−14 the relaxation process is not controlled by a single relaxation time 350 101 PD(O/vac) 0.5 quen. from 393 – S(O) melting point 422 111.0 ± 1 (2.7 ± 0.6) · S(O) 1 10−15 In the average for polycrystal samples the coeﬃcient K = 0.2850 in the equation Qm −1 = K·CO (CO in (wt%)) K = 0.2400 up to CO = 0.25 wt%

Shirashi et al. (1979) Ahmad and Szkopiak (1972)

Povolo and Lambri (1993, 1994) Blanter and Granovskij (1999) Weller (1985, 1995, 1996, 2001) Blanter (1978)

Haneczok and Weller (1990) Yoshinari et al. (1993)

Molinas et al. (1990, 1994)

4.6 Metals of the VB Group 301

state of specimen

Nb–O(0.315)– Mo(20) Nb–O(1.25)– Ta(20)

Nb–O(0.09–0.67)– Mo(0.8–50)

S(O)

481 PD(O/Mo) 515 PD(O/Mo) 4.5 451 114 S(O) 493 127 PD(O/Mo) 543 140 PD(O/Mo/Mo) 597 154 PD(O/3 Mo) the 543 K peak appears at 8 at.% Mo and higher. The 597 K peak appears at 25 and 50 at.% Mo. The 451 K peak is absent at 50 at.% Mo 6.26 625 PD(O/Mo) 400 SC, [122] axis the broad peak can be separated into, at least, six peaks 7.82 SC, [122] axis 560 S(O) 400 116.45 the peak shape is asymmetric

3.0–4.5 446

SC, [122] axis S(O) 6.62 560 1200 S(O) 1.3 423 228–254 107.7 7 · 10−15 the Snoek oxygen parameters are independent of the hydrogen concentration 99–115 495–505 109.6–119.2 S(O) the relaxation strength decreases and the activation energy increases with hydrogen content 1 425–437 S(O) the hydrogenisation increases the Snoek oxygen peak temperature and decreases height 0.6 440 S(O)

mechanism

Nb–O(2.3) Nb–O(0.25)– H(0.19–0.65) Nb–O(O/Nb ≈0.0012)– H(H/Nb=0–0.83) Nb–O(0.3 at.%)– H(0–0.5 H/Nb) Nb–O(up to 2)– Mo(5.3) Nb–O(0.09–0.5)– Mo(0–9.8)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

f(Hz)

composition

Tm (K)

Table 4.6.2. Continued

Miura et al. (2003)

Miura et al. (2003)

Kushnareva et al. (1992a) Kushnareva and Snezhko (1994)

Golovin et al. (1996a, 1998b) Vercaemer and Clauss (1969) Barabash et al. (1989)

Miura et al. (2003) Indrawirawan et al. (1987b) Schmidt and Wipf (1993)

reference

302 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4

0.9

0.5

Nb–O–Ti(0.3–46) (wt%)

Nb–O(0.87)–Ti(3.1)

Nb–O(0.10–0.90)– V(0.24–0.5) Nb–O(0.01–0.91)– V(1.5–10) 4

4

Nb–O(0.05–0.50)– V(0.5–50)

Nb–O (0.1–0.6)–V (0.5–50)

0.6

1.3

Nb–O(0.041– 0.076)–Ti(0.3)

512–522 up to 175 135–146 (1.5–2V) PD(O/V) 630–650 up to 120 173–184 (2.5–5V) PD(O/V/V) 672 40 192 (10V) PD(O/V/V/V) 451 114 PD(O/V) 558 142 – 598 153 – 643 164 – 693 179 PD(V/O/V) PD(O/V) 558 70–350 142 PD(O/O/V) 693 50–200 179 the additional peaks at 325 K (H = 153 kJ mol−1 ) and 370 K (H = 164 kJ mol−1 ) were separated

S(O) 430 12–20 110.6 PD(O/O) 445 2–6 113.5 476 3–7 PD(O/Ti) 119.3 H = 86.5 kJ mol−1 for 0% Ti, 72 for S(O) 0.3 and 1.6 (wt%), 69 for 16 (wt%) and 67 for 46 (wt%) ≈170 ≈420 the peak was resolved into three Debye peaks 397 110.6 S(O) 418 118.3 PD(O/Ti) 528 151 S(N) 444 up to 400 119 3.2 · 10−15 S(O)

Kushnareva et al. (1995)

Kushnareva and Snezhko (1994)

Carlson et al. (1987) Indrawirawan et al. (1987a)

Almeida et al. (2004)

Grandini et al. (2005)

Grandini et al. (1996a)

4.6 Metals of the VB Group 303

3.7 · 104

Nb–N–O

Nb–N(0.003– 0.05)–O(0.11– 0.18)

0.9

Nb–N(0.002)– 0.6 O(0.002) (wt%)

2.133

Nb–N–O Nb–N–O 441 583 650 856 ≈420 ≈480 ≈540 420 440 485 559 ≈10 –

≈100 ≈150

109.3 121.9 118.1 146.9

115.2 161.1 109.7 146.5

1.8 · 10−15 0.5 · 10−15 2.6 · 10−14 3.5 · 10−15

S(O) S(N) S(O) S(N) S(O) SK(O) S(N) S(O) PD(O/O) PD(O/N) S(N)

S(O) 430 up to 400 ≈500 up to 50 PD(O/Zr) the experimental relaxation spectra were resolved into four constituent peaks: 430 91–219 99–109 (5.5–85) · S(O) 10−14 443 22–218 105–115 (2.8–42) · PD(O/O) 10−14 474 7–66 128.5 (6.6–7.8) · PD(O/O/O) 10−15 503 7–47 145.6 (6.7–8.3) · PD(O/Zr) 10−16

mechanism

3.5

) H(kJ mol−1 ) τ0 (s)

Nb–O–Zr(0.08– 0.14) (wt%)

(10

Tm (K)

f(Hz)

Qm

Table 4.6.2. Continued −4

composition

−1

axis texture

CW

SC, oxidation

state of specimen

Gibala and Wert (1966a)

De Lamote and Wert (1964)

Marx et al. (1953)

Ang (1953)

Botta et al. (1990)

reference

304 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

8 · 104

≈650 ≈11 SC [100] S(O) S(N) ≈860 ≈25 the peak height is maximum for the [100] orientation and actually zero for the [111] orientation Nb–N(up to 0.9)–O 0.73 S(O) 413 141 543 S(N) −4 Nb–N–O(up to 1.2) 0.73 per 1 at.% O Q−1 S(O) max ≈ 800 · 10 −4 per 1 at.% N S(N) Q−1 540 max ≈ 800 · 10 429 Nb–N–O 1 in the equation Qm −1 = K · S(O) CO (CO in at.%) the coeﬃ560 S(N) cient K = 0.0650 for O and K = 0.0460 for N Nb–N–O(up to 1.2) 1 110.8 430 2.8 · 10−14 S(O) 116.4 443 1.7 · 10−14 PD(O/O) 121.5 473 3.1 · 10−14 PD(O/O/O) 129.6 496 2.2 · 10−14 PD(O/N) 145.8 562 2.2 · 10−14 S(N) 151.7 578 1.8 · 10−14 PD(N/N) 157.9 613 2.7 · 10−14 PD(N/N/N) 433 Nb–N–O 1 irr(n) S(O) 573 S(N) annealing in the range 0–500◦ C decreases the S(O) and S(N) peak heights of nonirradiated samples and increases once of irradiated samples Nb–N(0.125)– 430 1 ≈120 S(O) ≈35 O(0.20) 560 S(N)

Nb–N–O

Szkopiak and Smith (1975)

Igata et al. (1971)

Ahmad and Szkopiak (1970)

Szkopiak (1969)

Gebhardt et al. (1966) H¨ orz (1968)

Hoﬀman and Wert (1966)

4.6 Metals of the VB Group 305

1

3.4

Nb–N–O

Nb–N(0.03)– O(0.05) wt% Nb–N–O–Al(0.29) (wt%)

1

1

Nb–N(0.102)– O(0.232)–Cu(1)

Nb–N(0.086)– O(0.239)–Cr(1)

Nb–N–O– 1 Cr(0.53–3.1) wt%

1

Nb–N(0.112)– O(0.159)–Al(1)

1

f(Hz)

composition

Qm mechanism

PD(O/Cr) PD(N/Cr) PD(O/Cr) PD(N/Cr)

nitrogen Snoek peaks are lower than those for the unalloyed

DP(α) DP(β1 ) DP(β2 ) DP(γ) S(O) – S(N) 102.2 S(O) 165.3 S(N) S(O) S(N) SK(O) nitrogen Snoek peaks are lower than those for the unalloyed

(10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.6.2. Continued

≈120 ≈230 ≈285 ≈400 423 510 555 430 55 560 15 425 up to 510 556 – 683 up to 17 both the oxygen and and slightly broader niobium both the oxygen and and slightly broader niobium <3 ≈425 ≈90 546 ≈25 675 540 650

Tm (K)

−1

CW

state of specimen

Arakelov et al. (1981)

Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

Florencio et al. (1996) Davenport and Mah (1970)

Ferron et al. (1977)

reference

306 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

both the oxygen and nitrogen Snoek peaks are lower and slightly broader than those for the unalloyed niobium ≈4 Nb–N(0.069)– ≈550 1 ≈6 ≈620 O(0.293)–Hf(1) both the oxygen and nitrogen Snoek peaks are lower 1 Nb–N(0.089)– and slightly broader than those for the unalloyed O(0.319)–Mo(1) niobium 475 S(O) Nb–N–O–Mo(3.8– 500 up to 120 110.6 650 S(N) up to 50 144 5.2) (wt%) irradiation decreases the peak and shifts it to higher temperatures Nb–N(0.069)– both the oxygen and nitrogen Snoek peaks are lower 1 O(0.186)–Ni(1) and slightly broader than those for the unalloyed niobium Nb–N(0.109)– both the oxygen and nitrogen Snoek peaks are lower 1 O(0.422)–Re(1) and slightly broader than those for the unalloyed niobium both the oxygen and nitrogen Snoek peaks are lower 1 Nb–N(0.069)– and slightly broader than those for the unalloyed O(0.259)–Ta(1) niobium Nb–N(0.06–0.15)– 1 411 PD(O/Ta/Ta) 29 106.8 O(0.05–0.15)– 430 S(O) 41 110.6 Ta(25) (wt%) 453 PD(O/Ta) 57 117.3 475 PD(O/O/Ta) 25 123.1 562 S(N) 29 145.6 595 PD(N/Ta) 37 152.3

Nb–N(0.086)– O(0.275)–Fe(1)

irr(e)

Szkopiak (1976)

Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

Zaijkin et al. (1988)

Szkopiak and Smith (1975) Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

4.6 Metals of the VB Group 307

Nb–N(0.65-2.6)– O–Ti(4.6)

Nb–N(0.086– 0.416)–O(0.081– 0.2)–Ti(1)

Nb–N(0.125)– O(0.203)–Ti(1)

0.6

Nb–N–O(up to 2.4)–Ti(4.6)

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism

393 PD(O/Ti/Ti) 422 S(O) 463 PD(O/Ti) 503 PD(O/Ti) 541 S(N) 588 PD(N/Ti) ≈385 1 ≈5 466 PD(O/Ti) ≈70 ≈30 608 PD(N/Ti) 1 387 PD(N/Ti/Ti) 5–18 100.2 463 PD(O/Ti) 25–63 119.8 Q−1 max = oxygen concentration (in at.%)/30.06 602 PD(N/Ti) 19–87 156.1 Q−1 max = nitrogen concentration (in at.%)/43.1 the internal friction curves were separated into additional constituent peaks at 497 K (H = 128.9 kJ mol−1 ), 532 K (138.1 kJ mol−1 ) and 641 K (165.7 kJ mol−1 ) 1 393 PD(O/Ti/Ti) 463 PD(O/Ti) 543–553 S(N) 618–623 PD(N/Ti) 658 PD(N/N/Ti) 683 PD(N/Ti/Ti)

f(Hz)

composition

Table 4.6.2. Continued state of specimen

Clauss and Heulin (1980); Heulin and Clauss (1981)

Cantelli and Szkopiak (1976)

Szkopiak and Smith (1975)

Vercaemer and Heulin (1971)

reference

308 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

1

Nb–N(0.092)– O(0.258)–V(1)

Nb–N(0.050)– O(0.157)–W(1)

Nb–N(0.01– 1.33 0.015)–O(0.005– 0.35)–Zr(0.9) (wt%)

3.5

Nb–N–O–Ti(48) (wt%)

– – 25 before treatment (the sample A) 42 after treatment in a nitrogen atmosphere (the sample B) the spectrum A was separated into four peaks: S(O) 430 4.14 110.7 467 9.75 PD(O/Ti) 119.1 495 12.46 PD(O/O/Ti) 124.8 541 7.54 S(N) 146.5 the spectrum B was separated into six peaks: S(O) 430 11.23 110.6 PD(O/O) 443 10.17 116.6 467 29.33 PD(O/Ti) 118.6 495 13.97 PD(O/O/Ti) 124.6 523 10.33 PD(O/O/O/Ti) 136.5 S(N) 541 8.68 146.5 ≈7 ≈365 ≈70 PD(O/V) 523 ≈25 PD(N/V) 646 both the oxygen and nitrogen Snoek peaks are lower and slightly broader than those for the unalloyed niobium ≈425 112.2 (0.031 O) S(O) 119.3 (0.123 O) 483 120.2 PD(O/Zr) – 585 – S(N) – 622 – PD(N/Zr) –

758 833 ≈470 ≈450

Bunn et al. (1962)

Szkopiak and Smith (1975)

Szkopiak and Smith (1975)

Florencio et al. (1994)

4.6 Metals of the VB Group 309

≈200 107

240 160 ≈153

1.3 · 104 820

5 · 107 2.8 · 103 1.5

Nb–D(0.26) Nb–D(up to 2)

Nb–D(0.46)

Nb–D Nb–D(0.001 and 0.65) 0.9 up to 80

0.2

≈2 up to 2.2

Cantelli et al. (1970) Buck et al. (1971) Schiller and Schneiders (1975b), Schiller (1976) Mattas and Birnbaum (1975) Mazzolai (1975) Shibata and Koiwa (1980) 7.0

19.3

17.3

4 · 10−13

SC

DP(α) = SK(D) CW CW DP(α)

S(D/O)

the Gorsky eﬀect of D PhT(deut) 6.6 · 10−12 S(D/O)

Szkopiak and Smith (1975)

Miner et al. (1970, 1973)

245

SC

Florencio et al. (1996)

S(O) PD(O/Zr) PD(O/Zr/Zr) S(N) PD(N/Zr)

peaks are absent

Nb–N(0.03)– 1.9–2.4 O(0.06)–Zr(1–1.2) (wt%) Nb–D, H Nb–D Nb–D(0.088) (wt%) 8

3 · 10−15 5.4 · 10−14 5.4 · 10−14 3.6 · 10−15 5 · 10−14

1

110.6 111 123.1 146 147

Nb–N(0.102)– O(0.261)–Zr(1)

reference

642 749 830 855 986 ≈10 ≈480 ≈7 ≈560 ≈15 ≈640 In the range 300–700 K

state of specimen

5 · 104

mechanism

Nb–N–O(up to 0.53)–Zr(1)

) H(kJ mol−1 ) τ0 (s)

Tm (K) (10

Table 4.6.2. Continued f(Hz)

Qm

−4

composition

−1

310 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.7 0.7 ≈5 0.5 0.2 0.05–0.75 5.4(0.07D) 0.03–0.15 11.5 0.1–1.5 33.7–22.1 up to 0.7

105 150 10.5 1.5 4 45–62 99–100 177–148 2

852

107

2 · 104

Nb–D(0.015– 0.14)–Zr(0.13– 0.45)

4 · 104

Nb–D(0.016– 4.2 · 104 0.079)–Zr(0.45)

Nb–D(0.07-1.76)– 2 · 104 Ti(5)

PD(D) (tunneling) S(D/O)

the peak is due to deuterium tunneling within (Zr–D) pairs 100 – – 150 up to 0.6 PD(D/Zr) 2 D tunnel 6–7 diﬀusion PD(D/Zr) 100 130–150 –

PD(D/Ti/Ti) PD(D/?) PD(D/Ti) PD(D/Zr)

Mazzolai and Birnbaum (1987b)

SC

SC

SC

Cannelli et al. (2001), Cordero et al. (2003)

Cordero et al. (1999)

Huang et al. (1985a) Cannelli et al. (1986a, 1987b, 1989) Cannelli et al. (1984a)

SC, supercond. Morr et al. state (1989a,b) Okuda et al. (1984)

(ﬂuctuations caused by stresses in β- or µ- (ν-) phases)

SK(D) 5.5 · 10−12 PD(D/D/O)

5 · 10−16

(3–7) · 10−14

anelastic relaxation due to the tunneling of D trapped by oxygen

0.44

35.7

250 5.5

1.1 · 108

Nb–D(0.24)– N(0.15) Nb–D(0.12)– O(0.26)

Nb–D(0.2)– O(0.01–0.02) Nb–D(0.14)– O(0.13)

17.4

156

106

NbDx (x = 0.83–0.86)

4.6 Metals of the VB Group 311

Tm (K)

27 ≈200 460

4.15 · 104

Nb–H

Nb–H(8) Nb–H(0.006) (wt%) Nb–H(0.01–9.1)

Nb–H(0.06–0.25)

) H(kJ mol−1 ) τ0 (s) mechanism

≈2 ≈1 up to 600

0.4

≈24 10.5

17.4

4 · 10−15 S(H/N or O)

DP(δ) SK(H) 16 the Gorsky eﬀect due to H and O 40 DP(δ) 1.3 · 104 100 S(H) 170 27 DP(α) 220–230 up to 4 PhT(hydr) – 230 (a very sharp spike) – 310 DP(β) – 360 eutectoid phase transformation 1.3 · 104 PhT 9.6 200 5.67 the Gorsky eﬀect of H 210–250 26 PhT(hydr) 1.3 · 104 the height of the maximum is proportional to the hydrogen concentration and to higher temperatures with increasing of hydrogen concentration

97

1.7 · 104

Nb–H

Qm −1 (10

Table 4.6.2. Continued state of specimen

SC it shifts

SC 100

SC and PC

CW

the peaks at 7 and 100 K are associated with nearly undistorted Zr–D pairs. The peaks at 2 and 150 K must be associated with Zr–D pairs whose symmetry is lowered by the elastic interactions with the other complexes

f(Hz)

Nb–H Nb–H

composition

−4

Wert et al. (1970) Cantelli et al. (1970) Buck et al. (1971)

Cannelli and Verdini (1966a) Mazzolai and Nuovo (1969) Cantelli et al. (1969) Wert et al. (1970)

reference

312 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

up to 3

123 203 242–238 361–383 438–408 ≈240 380–384 156 235 385 408 110 130–137 133–138

800–2300

5 · 107

1 1

107

1

1

230

Nb–H(up to 1.5)

Nb–H(0.54)

Nb–H NbHx (x = 0.43–0.75)

NbH0.78

NbH0.84

Nb–H

Nb–H(0.15–0.55)

10−35 – – –

10−27 –10−30 – –

4 · 10−12

≈26

PhT(ord) PhT(β − α ) S(O) SK(H) I SK(H) II SK(H)

CW

CW

SC

CW

S(H/O)

7.7 · 10−13

15.1 DP(α) PhT(ord) – PhT(β − α ) S(O) Z(H)(?) PhT(β − α )

S(H/O) CW SK(H) S(H/H) S(H/O) S(H/(O or N))

4.2 · 10−15 3 · 10−10 1.4 · 10−12 1.5 · 10−11

35.9 5.3 16.4 12.5

126–146 – 111.3 46 (very sharp peak) 104.6 – – 111.3 9.7–15 12–19 0.5–2

0.5

200

2.1 · 107

Nb–H(0.7)

≈1 ≈50 1 1.5 0.7–3

65 160 170 260 80

760

Nb–H(0.1)

Igata et al. (1979a)

Ferron et al. (1978)

Amano and Birnbaum (1977) Amano and Sasaki (1977)

Baker and Birnbaum (1972) Baker and Birnbaum (1973) Schiller and Schneiders (1975b), Schiller and Nijman (1975a), Schiller (1976) Mattas and Birnbaum (1975) Ferron et al. (1976) Amano and Sasaki (1977)

4.6 Metals of the VB Group 313

2.62 98 98

2 · 104 2.05 · 104 1 107 1.1

1.2

Nb–H(0.2)

Nb–H(0.28)

Nb–H(0.68–4.1)

NbH0.78

Nb–H(1.2–1.8)

Nb–H(2)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism

113 200–280 230–240 383 240–280 ≈120 240–280 ≈410 ≈530 ≈130 ≈270

0.172 –

SK(H) PhT(hydr) PhT(ord) PhT(ord) PhT(hydr) DP(α) PhT(hydr) DP DP DP PhT(hydr)

2.5 · 10−9 – S(H/(O or N)) S(H/(O or N))

4 · 10−14 29 ≈40 up to 20 – ≈15 ≈30 CW due to hydride precipitation

10–70

≈0.3 ≈0.9 0.7

(deformation due to DP hydride precipitation) ≈25 PhT(hydr) 230 (cooling) Nb–H(0.001 and 4) 1.5 ≈50 DP(α) 143 oxygen seems to suppress the peak SK(H) Nb–H(7–200), at. 158–165 ≈120 1.3 · 103 oxygen suppressed and shifted the peak to lower temperatures ppm PhT(ord) NbH0.83 (1–6) · 103 100 250 PhT(ord) 190 100

≈120

1.1

Nb–H(1)

Tm (K)

f(Hz)

composition

Table 4.6.2. Continued

CW

SC, CW

CW

state of specimen

Yoshinari et al. (1985)

Shibata and Koiwa (1980) Maul and Schultz (1981) MelikShakhnazarov et al. (1981a) Cannelli and Cantelli (1982b) Cannelli et al. (1982a) Yoshinari and Koiwa (1982a,b) Amano and Mazzolai (1983) Koiwa and Yoshinari (1983)

Yoshinari et al. (1980)

reference

314 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

2.3 the peak is absent in normal state 7 superconducting state after rapid 5 normal state cooling the peaks are explained by quantum tunneling of hydrogen trapped by oxygen 0.5–3 350–370 160 the peak is caused by the α /β interphase boundary sliding 3–165 deviation of the dependence ln(τ) on 1/T from a lin{110}110 ear function was detected at low temperatures for the texture S(H/N) relaxation due to hydrogen tunneling S(H/N) 0.76 SC 60 19.3 3.3 · 10−13 the peak height increases with the crystal orientation from 111 to 110 and 110. 3 4.5 · 107 PD(H/N) (tunneling of trapped hydrogen) supercond. 9.2 PhT(super) (drop) 3.5 PD(H), SC, 9 · 107 tunnel supercond. the peak is absent in the normal conducting state state (in the magnetic ﬁeld) 32 73 S(H/O)

1 · 107 3 · 107

Nb–H(0.1–1)– O(0.1) Nb–H(0.19–0.38)– (5–13) · 107 200–220 S(H/O) SC the relaxation parameters are a function of a ultrasonic direction: at O(0.5) 100H = 17.4 and τ0 = 5.3 · 10−13 ; at 110H = 26 and τ0 = 4 · 10−15 ; at 111H = 11.6 kJ mol−1 and τ0 = 1.6 · 10−11 s 7 Nb–H(0.07)– 2.3 H tunneling 0.17 10 2.6 · 10−11 5.5 0.39 – O(0.01)

Nb–H(0.25)– N(0.15) Nb–H(0.3)– N(0.15)

Nb–H(0.33)– N(0.56)

Nb–H(0.4)– N(0.39–0.57)

Nb–H(10–50)

Nb–H(0.01–0.07) (wt%)

Poker et al. (1984); Drescher-Krasicka and Granato (1985)

Chen and Birnbaum (1976) Zapp and Birnbaum (1980a)

Morr et al. (1989a,b)

Wang et al. (1984)

Hanada et al. (1981)

Katz and Spivak (1993) Zapp and Birnbaum (1980a)

Drescher-Krasicka and Granato (1985)

4.6 Metals of the VB Group 315

f(Hz)

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

Nb–H–N–O Nb–H(0.07)– O(0.002–0.02) Nb–H(0.04)– (N + O)(0.13)

19.2 SC 3.3 · 10−13 S(H/N) (4.5–10.5) · 107 250–275 7 ≈0.06 PD(H/O) 2.4 10 SC 6.3 up to 1.5 0.53 3.3 · 10−12 PD(H/H/O) 4 S(H/O, N) 100 1.36 · 10 0.15 PhT(hydr) 160 (step) the remarkable increase of dissipation below 4 K is likely the tail of a relaxation ascribable to H tunneling Nb–H–Cr(2) ≈130 CW due to hydride precipitation 1.2 DP PhT(hydr) 220–240 the PD(H/Cr) peak is absent Nb–H–Mo(2) 220–240 1.2 PhT(hydr) the PD(H/Mo) peak is absent 130 312 5 Nb–H–Sn 260 30 (Nb3 Sn–H) PD(H/Ti) Nb–H(0.36–3.54)– 2.05 · 104 130–100 up to 2.5 the peak initially shifts towards lower temperature with increasing H Ti(2) concentration and above a certain value (0.7 at.%) the peak temperature remains constant ≈0.03 H tunnel Nb–H(0.08-1)– 4 (0.08 at.% H) 2 · 104 diﬀusion Ti(5) 18 –

composition

Table 4.6.2. Continued

Cannelli and Cantelli (1981) Cannelli et al. (1986b)

Cannelli and Cantelli (1977)

Berry et al. (1983)

Yoshinari et al. (1985)

Yoshinari et al. (1985)

Cannelli et al. (1990)

Shi and Li, 1985 Huang et al. (1985a)

reference

316 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Nb–H(up to 1.3)–Ti(2) Nb–H(0.02–0.1 H/Me)– Ti(50 at.%) Nb–H(0.5–1)– Ti(2)

Nb–H(0.15–4.2)– Ti(5)

Nb–H(0.36–3.5)– Ti(2)

Nb–H(0.08–4.2)– (N + O)(0.11– 0.15)–Ti(2–5)

≈0.2 164 (0.48 at.% H) PD(H/Ti) ≈0.1 H tunnel 4 diﬀusion 18 – 90 ≈0.25 PD(H/Ti/Ti) ≈0.9 141 PD(H/Ti) H tunnel 4 0.2–0.7 2 · 104 diﬀusion 18 0.1–0.3 60–90 0.1–7.5 PD(H/Ti/Ti) 110–160 0.6–2 PD(H/Ti) 2.07 · 104 125 0.5 11.9 (0.36 H) PD(H/Ti) 60 0.1 – (0.57 H) PD(H/Ti/Ti) PD(H/Ti) 110 0.8 8.17 60 0.05 – (0.70 H) PD(H/Ti/Ti) 100 0.8 PD(H/Ti) 7.2 100 1.5 – (3.5 H) PD(H/Ti) 2.09 · 104 160 0.2 15.6 (0.15 H) PD(H/Ti) 85 0.02 – (0.72 H) PD(H/Ti/Ti) PD(H/Ti) 130 0.6 11.1 90 7.5 4.4 (4.2 H) PD(H/Ti) 55–64 12.5 1.2 PD(H/Ti) 5 · 10−13 80–83 – PD(H/Ti) – 60 ≈2 up to 120 7.7 1.6 · 10−8 S(H) 90 up to 180 16.3 4.4 · 10−14 1.1 · 103 the peak has diﬀerent activation parameters at T > 75 K and T < 75 K 58.2 2.78 5.3 PD(H) (0.93 H) 60.9 2.32 3.6 (0.99 H) Yoshinari et al. (1985) Sato et al. (1989)

Yoshinari et al. (1996a)

bcc alloy

SC 111 SC 100

Cannelli et al. (1982a)

Cannelli and Cantelli (1981, 1982a); Cannelli et al. (1981, 1982a,b, 1989) Cannelli et al. (1982a)

4.6 Metals of the VB Group 317

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

Nb–H(0.28–36)– Zr(0.75)

Nb–H(0.55–0.93)– V(10) Nb–H(0.5–0.97)–O (0.03–0.7)–V(10)

Nb–H–V

18.4 S(H) 120 300 Q−1 max ∼ CH up to 28 at.% H in the Nb–V alloys hydrogen creates tetragonal distortions with (λ1 –λ2 ) ≈ 0.11 and the S(H) relaxation is associated with the “diﬀusion under stress” of isolated hydrogen atoms 92.5–85.0 25–38 0.2 S(H) 0.26

95.5–85

18–34

13.8–12.2

(1.1–1.8) · S(H) 10−8 a small decrease in the hydrogen peak height and small increase of the broadening due to oxygen were observed, but there was no change in the activation parameters 1160 SK(H) 160–175 0.3–0.5 CW

582–1000

Nb–H(28)–V(50)

S(H) 90–100 20–58 17.3–20.2 2 · 10−12 in the alloys (1.5H + 10V) and (3.5H + 50V) in the temperature range 80–300 K peaks are absent but the alloys show the indication of a peak below 80 K S(H) 9.6–30 5 · 10−13 119–130 160–480

582–4240

0.33

two conﬁgurations of a Ti–H pair exist simultaneously and the peak is considered to be due to successive jumps of the H atoms between the two tunnel systems 0.15–0.72 in the range 78–300 K peaks are absent

f(Hz)

Nb–H(8)–V(50)

Nb–H(0.034–6)– V(50) Nb–H(0.29–3.5)– V(10–50)

composition

Table 4.6.2. Continued

Igata et al. (1979a)

Buck et al. (1989)

Buck et al. (1989)

Cost et al. (1985), Snead and Bethin (1985a) Snead and Bethin (1985a) Mazzolai (1987a)

Owen et al. (1985)

Owen et al. (1981)

reference

318 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1.2

40 3.85 5 · 10−6 50–42 – – PD(H/Zr) 63–75 14.4 2 · 10−12 ≈220 – – PhT(hydr) PD(H/Zr) Nb–H(0.13–0.2)– (2.8–5.2) · 104 ≈125 broad peak at 0.13 at.% H the peak was separated into three peaks: Zr(0.45) 100 0.1 6.6 1.5 · 10−9 2.8 · 104 130 0.7 – – 160 0.05 16.6 1.5 · 10−11 ≈0.1 SC Nb–H(0.065– (2.8–5.2) · 104 2 6–10 – 0.27)–Zr(0.45) 30 ≈0.01 the relaxation processes observed at 2 and 10 K are attributed to the redistribution of H within the levels of tunnel systems formed near the Zr impurities PD(H/Zr) Nb–H(0.002)– ≈100 4 · 104 SC ≈150 Zr(0.45) the peak at 150 K is present in the E-type ([s11 –s12 ]/2) but not in the T-type (s44 ) mode Nb–H(0.7–4.2)– 202–235 S(H/O) (1–3) · 107 8–80 15.2–17.9 (0.4–2) · O(0.04)–Zr(1) 10−12 other niobium alloys NbC0.77 (7–12) · 104 363–523 75 873–973 134 1063–1123 163

Nb–H(up to 1.6)–Zr(2)

Korostin et al. (1975)

Grandini et al. (1994)

Cordero et al. (2003)

Cannelli et al. (1994b,c)

Cannelli et al. (1994a)

Yoshinari et al. (1985)

4.6 Metals of the VB Group 319

873–973 1063–1123 1793–1853 1470

(7–12) · 104

1

NbC0.913

Nb–Cr(1.5–3.1) (wt%)

Nb–Mo(3.7–8) (wt%) Nb–Mo(1.2) (wt%) Nb3 Sn

138 184 377 385

(10−4 ) H(kJ mol−1 ) τ0 (s)

GB

mechanism

1630 427

GB

SC, CW

state of specimen

sharp increase of internal friction T < 49 K due to the martensite transformation

1

Nb–Cu(35) (wt%) 3

Nb–Mo(1.3–16) (wt%)

Qm

Table 4.6.2. Continued

≈440 ≈150 ≈665 DP(α) ≈200 105 up to 10 the peak height is an order of magnitude lower than that for unalloyed niobium 105 2 (1.3–2)wt% Mo DP(α) DP(β) 220–260 1610 1 418 GB

Tm (K)

f(Hz)

composition

−1

Finlayson et al. (1975), Bussiere et al. (1982), Snead and Welch (1985b)

Yakovenko (1986)

Igata et al. (1982a)

Gridnev et al. (1982), Yakovenko (1986) Arzhavitin et al. (1997) Amateau et al. (1969)

Korostin et al. (1975)

reference

320 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.6 Metals of the VB Group

321

4.6.3 Tantalum and its Alloys In Ta and its alloys, the following internal friction eﬀects are observed: – Dislocation peaks (intrinsic peaks α , α1 , α2 , γ and impurity peaks SK(H), SK(D), SK(N), SK(O) and DES(O)) – Eﬀects at transition from the normal to superconducting state – Grain boundary peaks – The Snoek relaxation due to C, N, O and additional peaks due to interaction between the substitutional and interstitial atoms – The Snoek-type H and D relaxation (including H and D tunneling) and additional peaks due to interaction of H, D with substitutional atoms – Eﬀects of hydrides and deuterides precipitation and dissolution – Peaks due to ordering in hydrides

f(Hz)

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

reference

in deformed Ta, the following DP are observed (Fig. 2.20): (a) α, α , α1 , α2 peaks in the range 20–45 K (f = 1 Hz–1 kHz) which are explained by the kinks moving in screw dislocations and kink pair formation in non-screw dislocations; (b) α peaks in the range 130–270 K (f = 7 Hz–18 kHz) which are likely to be SK(H); (c) SK(H) peaks in the range 66–200 K (f = 1 Hz–20 kHz); (d) SK(D) peaks in the range 130–180 K (f = 1 Hz–15 kHz); (e) γ peaks in the range 350–445 K (f ≈ 1 Hz) accounted for by kink pair formation in screw dislocations. They split into two peaks, DP(γ1 ) and DP(γ2 ), with one of which probably DES(O); (f) DES(O) at 420–430 K (f ≈ 1 Hz); (g) SK(O) peaks in the range 530–740 K (f ≈ 1 Hz) which split into two SK(O) peaks (at 640 and 740 K); (h) SK(N) at 810 K (f = 1 Hz). 0.65 Ta 1370 GB Schnitzel (1959) 350 418 ≈17 1.5 · 104 Ta 180 DP(α) Chambers and CW 310 DP Schultz (1961) – −11 1 · 10 24.0 ≈4 ≈130 7 Ta DP(α) Chambers and CW DP(β) 1 · 10−11 41.3 ≈5 ≈200 Schultz (1962) 0.3 Ta De Batist (1962) 203.5 CW DP 215.5 DP 224.5 DP 1500 1 500 8 · 10−17 Ta GB Murray (1968) 406 2.26 · 104 Ta 25 DP(B2 ) 1.2 · 10−13 3.65 Verdini and CW 3 Vienneau (1968) 3.5 · 104 Ta 172 high vacuum Mazzolai (1975) 2 · 10−13 25.0 annealing Ta(RRR= 150 DP(α ) 5.5 · 10−8 8.6 1.8 · 104 SC, CW Knoblauch et al. 220–270 up to 160 (1–5) · 10−10 DP(α) 25.0 6000–8000) 1.7 · 104 (1975); Knoblauch (1976)

Ta Ta

composition

Table 4.6.3. Tantalum and its Alloys (at.% if not speciﬁed diﬀerently)

322 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ta(RRR=11 000)

Ta(7 at. ppm O)

66 172 424–440 444

12 20 30 96.2

SK (H) SK(H) DP(γ) DP(γ2 )

8

D’Anna and Benoit (1990)

Baur et al. (1989)

Baur et al. (1989)

Lauzier et al. (1987a)

SC 110 CW

SC, CW

Arai et al. (1987)

Funk and Schultz (1985) Schultz et al. (1985)

Postnikov et al. (1975b) Miloshenko and Shukhalov (1976) Mizubayashi and Okuda (1982) Funk et al. (1983)

CW

SC, CW

SC, CW

SC, CW degassing.

CW

SC, CW

thin ﬁlm

SC, CW (2.4–15.9) · 10−13 it was suggested that γ2 is a modiﬁed γ relaxation, related to screw-dislocation segments, stabilised by oxygen-decorated kinks ≈45 140 SK(H) 1 CW ≈30 DP(γ) 400

Ta(RRR=8000, 1140 O, N, C < 3 at. ppm) 5.6 Ta(RRR=17 700) (1 at. ppm O)

Ta(RRR=2000)

Ta (H-free)

Ta (H-free)

Ta (high-purity)

PhT(super)

DP(α1 ) 18 DP(α2 ) 30 ≈20 DP(α, α ) 48 1.2 · 103 the intrinsic dislocation relaxation peaks α(α ) are observed after hydrogen H introduction suppresses the α(α )-peaks and creates the SK(H)-peak 30 5 1.2 DP(α) DP(γ) 350 40 DP(α2 ) 21.9 3.3 4 · 10−9 1.2 DP(α1 ) 31.5 5.5 8 · 10−11 358 50 82–89 10−13 –10−14 DP(γ) ≈15 ≈45 DP(α) 300 proton irradiation decreases the peak 1140 DP(α1 or α2 ) 4.2–8

1000

0.3–0.8

Ta

4.5–4.7

2.9

1000

2

Ta

70

1000

Ta

4.6 Metals of the VB Group 323

TaC

Ta–C

Ta–C Ta–C(0.013–0.062) (wt%) Ta–C Ta–C(up to 0.013) (wt%)

Ta–C, N, O

Ta(RRR=11 000)

Ta(RRR=6000, H-free) Ta(RRR=11 000)

composition

Tm (K)

Qm

(10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.6.3. Continued mechanism state of specimen

423 113 165.3

104 2 · 10−15

S(C) S(C)

1.6 · 10−14 S(C)

Qm −1 ≈ 0.1200 · CC (CC in at.%) up to CC = 0.075 at.% (internal friction) 164.8 2.1 · 10−15 S(C) (IF + elastic after-eﬀect) 160.7 5 · 10−15 570 8.4 · 104 87.7 1 5 · 10−14 1070 184.1 2 1.6 · 10−15 1870 GB 355.7 2 5 · 10−16

(IF + elastic after-eﬀect) 0.27–1.33 598–628

1

400 25 1 DP(γ) CW measure of the internal friction as a function of the frequency deﬁnes two γ-peaks 280–370 40 CW 10−4 –10 68.3 6.1 · 10−10 DP(γ) CW + anneal 76.0 2.6 · 10−11 DP(γ) frequency dependence. The ﬁrst peak (after CW) is reversible and the second one is irreversible

the SK(H) peak consists of the SK(H)1 peak at about 140 K and SK(H)2 peak at about 150 K. The SK(H)1 peak is caused by kink diﬀusion on screw dislocations, and the SK(H)2 peak is caused by kink pair formation on 71◦ edge dislocations DP(α) 40 1 · 103 irr(p)

f(Hz)

−1

Powers and Doyle (1959) Bukatov et al. (1975b)

Wert (1950) Powers and Doyle (1957b)

Kˆe (1948b)

Mizubayashi et al. (1991a) D’Anna and Benoit (1993a) D’Anna and Benoit (1993b)

reference

324 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

626 ± 2

Ta–O Ta–O Ta–O

611 657 700

634 615

443 1 (internal friction) (IF + elastic after-eﬀect)

2.6 1

64.4

121 107.2 106.2

155.8 166.3 177.9 1 · 10−15 5 · 10−15 7 · 10−15

∼1

Ta–N Ta–N(0.06)– Re(1.3–3.9)

Ta–N(0.008) (wt%) Ta–N

SK(N)

S(N)

S(N) S(N)

S(C)

SC, CW

CW

S(O) S(O)

S(N) or SC PD(O/Re) S(N) PD(N/Re) PD(N/Re/Re)

(CN in at.%) S(N) PD(N/Re) PD(N/Re/Re)

S(N) S(N)

1.25 · 10−9 DP(α ) 1.6 · 10−11 DP(α)

7 · 10−15 5 · 10−15

Ta–N–Re(1.3-6)

up to 30

10.6 24.0

156.5 157.9

184

160.6

Ta–N(0.06)–Re(3.8)

(1.4–1.8) · 104 120–150 190–200

623 1 370 602 0.55 Qm −1 ≈ 0.058 · CN (CN in at.%) (internal friction) (IF + elastic after-eﬀect) 810 1

1

154.4 1.2 · 10−14 (3.6 ± 2.5) · 160.1 10−15 ± 1.9 −1 in the average for polycrystal samples Qm = 0.0730 · CN ≈30 613 0.8 ≈20 653 167.8 8 · 10−15 698 177.4 ≈10 8 · 10−15 the PD(N/Re/Re) peak is absent at 1.3–2.1 at.% Re ≈625 1.6

Ta–N(0.024)

Ta–N

Ta–C Ta–N Ta–N Ta–N(up to 0.012) (wt%) Ta–N

Kˆe (1948b) Powers and Doyle (1959)

Sagues and Gibala (1975) Sagues and Gibala (1974)

Kˆe 1948 Powers and Doyle (1957b) Powers and Doyle (1959) Ooijen and Goot (1966) Knoblauch et al. (1975), Knoblauch (1976) Weller et al. (1981b) Weller (1995, 1996, 2001) Blanter (1978) Sagues and Gibala (1971)

Weller (1996, 2001)

4.6 Metals of the VB Group 325

1.3

Ta–O(0.074)

Ta–O(0.125)

Ta–O

Ta(99.99)–O

Ta–O(0.07)

65.5

Qm (10 106.2

mechanism

1.1 · 10−14 S(O)

) H(kJ mol−1 ) τ0 (s)

Table 4.6.3. Continued

60–180 390 420 440 530–660 10–55 0–50 10–50 – 0–15 119.7 108.1 112.9 214

10−16 5 · 10−14 1.6 · 10−14 2 · 10−19 – 10−21

state of specimen

irr(e)

CW

SC, CW SK(H) DP(γ1 ) DP(γ2 ) = DES(O) DP SK(O)

S(O) 426 65 DES(O) 420–430 100 600–640 35 139.4 3.5 · 10−13 SK(O) S(O) 100 500 up to 180 105.8 irradiation decreases the peak and shifts it to higher temperatures S(O) ≈420 1.5 after surface oxidisation the S(O) peak broadens S(O) 1250 585 6

1.94 1–5

Ta–O(up to 0.017) 1

Ta–O

423

Tm (K)

−4

46–450 S(O) 105.8–91.5 419.5– 423.7 the peak is highly symmetrical and somewhat broadened. With increasing of O contents it shifts to slightly higher temperature. The broadening can be described by a continuous distribution of relaxation times CW 186 1.2 · 10−8 SK(O)

Ta–O(0.034–0.59) 1

f(Hz)

composition

−1

Yoshinari et al. (1993) Biscarini et al. (1993)

Zaijkin et al. (1988)

Seeger et al. (1982)

Varchon et al. (1982) Rodrian and Schultz (1981, 1982)

Weller et al. (1981b) Weller et al. (1981c,d)

reference

326 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Ta–O Ta–O(up to 0.11)–Nb(9.2) Ta–O(0.04)– Re(3.8) Ta–O(up to 0.285)–W(2) Ta–N–O Ta–N–O

Ta–O

Ta–O(0.01–0.02)

Ta–O(0.034– 0.113) Ta–O(0.022– 0.113)

Ta–O(0.01–0.6)

≈650 408–418

428 633

5 · 104

1.15

1.433

260

114 166

60.1–66.4

S(O) S(N)

S(O) or PD(O/Re) S(O)

SC

≈1 and 105.8 S(O) ≈1000 the maxima are broadened and shifted to higher temperature with increasing O content 430 2.5 SC, CW S(O) the Snoek peak changes very little by deformation 428 CW 2.5 20 105.8 7.3 · 10−14 S(O) 641 20 134.6 7.2 · 10−12 SK1(O) 738 50 201.9 3.3 · 10−14 SK2(O) it was suggested that SK1(O) corresponds to the migration of geometrical kinks on screw dislocations and SK2(O) corresponds to the formation and migration of kink pairs on screw dislocations 340–360 96–108 PD(O/vac) 1 quen. from Tmelt 420 106.2 ± 1 (8.55±18)· S(O) 1 10−15 −1 in the average for polycrystal samples Qm = 0.0740 · CO (CO in at.%) 438 2.3 up to 80 46.3–48 S(O)

Ang (1953)

Blanter and Granovskij (1999) Weller (1995, 1996, 2001) Blanter (1978) Hasson and Arsenault (1970) Sagues and Gibala (1975) Hasson and Arsenault (1970)

Fang et al. (1996)

Fang (1996)

Haneczok et al. (1994)

4.6 Metals of the VB Group 327

126 133 220–250 130 225

2 · 103

≈1.6 · 104

1.5 · 104

Ta–D Ta–D

Ta–D(0.2–8)

Ta–D(7.5)

up to 2.5 0.1 1 37.4

3 · 10−13

8 · 10−10

1.111 1.085

Ta–N–O

11.6

0.6

Ta–N–O

0.3

0.6

Ta–N–O

Ta–D, H

170 203 255 355 114 ≈30 ≈10 662 162 four peaks were observed in the range 330–440 K 104.3 410 435 – 448 – 607 – 635 – 423 13 623 7 423 35 570 45 426.6 50.6 102.1 618 9.21 147

3.7 · 104

Ta–N–O

) H(kJ mol−1 ) τ0 (s)

Tm (K) (10

Table 4.6.3. Continued

f(Hz)

Qm

−4

composition

−1

S(H/N, O) PhT(deut) SK(D) PhT(deut)

S(D/O, N)

S(O) PD(O/O) PD(N/O) S(N) PD(N/N) S(O) S(N) DES(O) SK(O)(?) S(O) S(N)

PD(H) – – S(O) S(N)

mechanism

CW

CW

foil

state of specimen

Cannelli and Verdini (1966b) Cannelli and Cantelli (1974) Cannelli and Cantelli (1975)

Boratto and Reed-Hill (1978)

De Lamote and Wert (1964)

Powers (1955), Powers and Doyle (1956)

Marx et al. (1953)

reference

328 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

up to 60 up to 50 0.3

203 190 274 309 327 483 92

175

Ta–H(0.022– 0.033)

Ta–H(0.12–0.25) Ta–H Ta–H(5)

Ta–H

Ta–H

0.5

1.65

3 · 104

9.1

1.2 · 10−8

D tunneling S(D/N)

11.6

10−12 –10−11

2.05 · 104

27 DP(δ) up to 2.5 16.3 10−8 190–200 – ≈24 DP(α)=SK(H) – 14.4 H Gorsky eﬀect 2.8–23 290–588 S(H/N, O) 97 34.94 · 103 PhT(hydr) 230 (cooling) 1.6 ≈25 265 (heating) S(H/O, N) 80 180 SK(H) 180 60 the SK(H)–peak can be separated into two peaks

2 · 104

100

PhT(ord) in Ta2 H Short- and long-range order in Ta2 H S(H/O, N)

a sharp peak due to the tunneling of trapped D atoms S(H/O, N) 130 0.06 1270 PD(D/O) 65–95 up to 3 deuterium loading decreases the temperature of the peak

up to 3

65

≈1

Ta–D(up to 0.95)– N(1) Ta–D(0.25)– N(0.016)– O(0.053) Ta–D(up to 2.3)– Nb(25)–O(0.91) Ta–H Ta–H(up to 42.4)

0.5

1.7

7.5 · 103

Ta–D(0.25)

CW

CW

Cannelli and Verdini (1966a,b) Mazzolai and Nuovo (1969) Cantelli et al. (1971) Mazzolai (1975) Yoshinari et al. (1980) Mizubayashi and Okuda (1982)

Kofstad and Butera (1963)

Colluzzi et al. (1995)

Cannelli et al. (1987a)

Cannelli et al. (1987b) Ebata et al. (1991)

4.6 Metals of the VB Group 329

mechanism state of specimen

Ta–H(up to 0.9)– N(1) Ta–H(0.15-2.9)– Nb(25)–O(0.15) Ta–H(up to 2.3)– Nb(25)–O(0.86)

Ta–H(0.05)

Ta–H

Ta–H

Ta–H

50 up to 8 9.4

6.25

S(H/N) S(H/O)

3 · 10−8 3 · 10−11

9.6–11.5

PD(H/O) (5–500) · 10−11 SK(H) – 150–170 – – hydrogen loading decreases the temperature of the PD(H/O) peak and increases the temperature of the SK(H) peak

(1.26–6.92) · 74.0–83.3 0.3–1.4 103 1270 100–120 up to 7

0.6–1

1

100 S(H/O, N) 150 SK(H) 220–260 20–120 PhT(hydr) the SK(H) peak is caused by deformation due to hydride precipitation and can be separated into two peaks 180 1.4 · 103 SK(H) 70 CW after hydrogen degassing the SK(H) peak can be removed completely 2.5 100 SK(H) 30 CW+ H ≈200 ≈65 – PhT(hydr) charging hydrogen charging of the deformed specimen decreases the SK(H) peak, but results in a precipitation peak 1.2 150 SK(H) 30 SC, CW 350 DP(γ) 40 H tunneling (1–5.5) ·107 1.7

(10−4 ) H(kJ mol−1 ) τ0 (s)

Ta–H(0.76-17.8), H/Ta

Qm

f(Hz)

Tm (K)

Table 4.6.3. Continued

composition

−1

Biscarini et al. (1994a) Colluzzi et al. (1995)

Funk and Schultz (1985) Maschhoﬀ and Granato (1985) Ebata et al. (1991)

Li et al. (1985)

Funk et al. (1983)

Yoshinari and Koiwa (1982a)

reference

330 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.7 Metals of the VIB Group

331

4.7 Metals of the VIB Group 4.7.1 Chromium and its Alloys In Cr and its alloys, the following internal friction eﬀects are observed: – One dislocation peak α – Grain boundary peaks – The Snoek relaxation due to C and N and additional peaks due to interaction between the substitutional and interstitial atoms – Eﬀects due to magnetic phase transitions – Peaks due to self-interstitials – The Zener relaxation in Cr–Fe alloys

1

Cr Cr Cr(99.98)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

825 5 5 1

990 50 120 310

2.8 107

7.2

1 4.5

Cr Cr(99.9)

Cr

Cr Cr 274 12 – –

(sharp peak ≈3 − 4) 5 5

126 35 50

0.5–3

10−13

PhT(spin-ﬂip) irr(e) PD(self-int) PD (pairs of self-interstitials) GB SC, CW DP(α) PhT(spin-ﬂip) SC PhT(mag)

PhT(mag) 310 7 PhT(spin-ﬂip) 123 20 SC 10 PhT(mag) ≈313 <1 PhT(spin-ﬂip) 120 CW 310 3 PhT(mag) PhT(spin-ﬂip) 120 20 CW + annl. PhT(mag) 310 10 PhT(mag) 310 3 the peak is suppressed by the precipitation of supersaturated nitrogen GB 1190 PhT(PM-AFM) 47 (very sharp peak)

Tm (K)

Cr

Cr(0.0008wt% N) 35

f(Hz)

composition

Table 4.7.1. Chromium and its Alloys (at.% if not speciﬁed diﬀerently)

Vysotskij (1983) Yoshinari et al. (1983a)

Belous et al. (1966) Zaporozhets and Tikhonov (1979, 1980) Weller and Moser (1981a)

Klein (1964)

Street (1963)

Fine et al. (1951) De Morton (1963)

reference

332 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Cr–N(0.0025) (wt%) Cr–N (0.0004–0.017) (wt%) 4.2–1.7

5–20

149–172 313 419–426

0.427–2.018

0.8

up to 50

480 223–263

20–2000

Cr–C(0.044)– Fe(28.7) Cr–C–Fe(49.2) Cr–H 18

9

433

1 468

17

413–435

0.7–1.35

86.1

101.4

118 58–77

111

107

9 · 104

Cr

Cr–C, N, H Cr–C (0.006) (wt%) Cr–C (0.013)

124.8 0–10 the peak height increases with deformation amplitude 311 13 <13 309.7

90 kHz

Cr

(very sharp peak)

≈37.7

107

Cr

PhT(mag) S(N)

S(N)

S(C) S(H)?

S(C)

S(C)

quen. from 850◦ C quen. from 1150◦ C

quen. from 1250◦ C quen.

SC 831 CW

PhT(mag) PhT(mag)

S(C)

SC 831

SC 110

PhT(spin-ﬂip)

PhT(mag)

Klein and Clauer (1965)

Grankin et al. (1977) De Morton (1962)

Zemskij and Spasskij (1966) Golovin et al. (1997a)

Pal-Val et al. (1989), Pal-Val and Pal-Val (1990)

Zaporozhets et al. (1986) Pal-Val et al. (1986)

4.7 Metals of the VIB Group 333

1

≈0.2 (2 − 4) · 103 ≈310 ≈580–600 ≈0.3 2–3 423–473

Cr–N

Cr–N(0.04) (wt%)

Cr–N(0.125– 0.145)–Ce(1.08– 2.67) (wt%)

Cr–N Cr–N Cr–N

Cr–N

3480

Cr–N(0.04) (wt%)

433 429 122 310 435 428–435

1 1 660–1500

1–2 1.8–2.5

445

10–25

5 10

10

mechanism

1.4 · 10−15

quen. from 1000◦ C quen.

quen. from 1150◦ C

state of specimen

Mitsek and Golub (1988)

Polotskij et al. (1981) Hirano et al. (1985)

Klein (1967)

reference

S(N) S(N)

quen. as-cast or Yakovenko (1990) as-cast+CW or quen.

as-cast or Yakovenko (1990) as-cast+CW or quen. S(N) Golovin (1996) S(N) Weller (1996, 2001) quen.from Golovina and PhT(spin-ﬂip) 900–1200◦ C Golovin (2004) PhT(mag) +ageing

PhT(mag) S(N) S(N)

S(N)

4.1 · 10−15 S(N)

1.4 · 10−15 S(N)

the peak is splitted (∆T ≈ 1 K) – 106.4– 108.5

107.4 114.4

105.8 104.3– 115.2

413 115 Qm −1 = 0.7CN (wt%) 603 44 112

0.4

Cr–N

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s)

f(Hz)

composition

Tm (K)

Table 4.7.1. Continued

334 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

89.4 126 101.7

17 0.2

200 200 60 820 65 30 75

≈403 ≈463 413 588

250.5 242 193 1093 920 920 930 288 283.6 281.7 270.2

108.4

108.4

1.4

0.2

587

2960

108.5– 133.5

425–538

2–2.5

Cr–N(0.05)– 0.8 Y(0.12) (wt%) Cr–N(0.04)– 3030 La(1.3)–Nb(0.2) (wt%) other chromium alloys Cr–Fe(2.6) Cr–Fe(3.8) Cr–Fe(6.65) Cr–Fe(0.2) (wt%) 0.43 Cr–Fe(47) 4.7 10 11

Cr–N(0.105– 0.156)–Ce(1.47– 3.53)–V(0.677– 3.06) (wt%) Cr–N(0.04)– La(1.3) (wt%) Cr–N(up to 0.018)–Re(35)

1.6 · 10−18 1.7 · 10−18 7.7 · 10−18

5.4 · 10−15

SC 110 SC 100 SC 111

or¨ ok Hausch and T¨ (1977a) Vysotskij (1983) Hirscher et al. (2000)

GB Z(Cr, Fe)

Polotskij et al. (1981)

S(N)

PhT(mag)

Klein (1966)

Polotskij et al. (1981) Klein (1965)

as-cast or Yakovenko (1990) as-cast+CW or quen.

S(N)

S(N)

S(N)

4.7 Metals of the VIB Group 335

f(Hz)

Tm (K)

Qm

(10−4 ) H(kJ mol−1 ) τ0 (s)

Table 4.7.1. Continued

0.5

Cr–Ni(0.2) (wt%)

Cr–V(1) (wt%) Cr–Y(1) (wt%) Cr–Y(0.8–1) (wt%)

Cr–V(0.37) (wt%)

2–2.6

Cr–La(0.25–0.36) (wt%) 423–431

1235 803 883 1273 990 311 460 ≈35

>1600

107.7– 109.3

188 230 – 277

970 1200 251 1170 975 307 990 500 1 276 1170 380 301 1170 760 1 in the temperature range 293–1273 K peaks are absent 803 188 1 883 230 1273

1 (2 − 4) · 103

Cr–La(0.5) (wt%) Cr–La(0.5)

Cr–Ga(1) (wt%) 1 Cr–La(0.8–1) (wt%) 1

Cr–Fe(40.2–66.2) 298 2–80 2 · 10−19 850–1050 the relaxation strength shows a maximum near the equatomic composition Cr–Fe(40) 12 940 50 292

composition

−1

GB GBI GB

GB GBI(?) GB GBI GBI

S(N)

recryst. struct.

cell structure

as-cast or as-cast+CW or quen.

recryst struct

cell structure

SC 111

Z(Cr, Fe) GB GB GBI GB GB PhT(mag)

SC 111

state of specimen

Z(Cr, Fe)

mechanism

Vysotskij (1983) Belous et al. (1966) Tkachenko and Alifanov (1977a)

Vysotskij (1983)

Vysotskij (1983)

Vysotskij (1983) Mitsek and Golub (1988) Yakovenko (1990)

Hirscher and Ege (2002) Hirscher and Ege (2002) Belous et al. (1966) Tkachenko and Alifanov (1977a)

reference

336 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Cr–La(0.5)–Re(0.4)– Ta(0.2) (wt%) Cr–La(0.5)–Re(0.4)– Ta(0.2)–Zr(0.5) (wt%)

Cr–La(0.5)–Re(0.4) (wt%) Cr–La(0.5)–Ta(0.2) (wt%) Cr–La(1)–V(1) (wt%)

Cr–La(0.5)– Ni(0.2), wt%

Cr–Fe(0.2)–La(0.5) (wt%) Cr75 (Fe0.64 Mn0.36 )25 1053 800 278

GB

500

1173

1

1

375 180 500

970 1170 1173

0.45

450

1273

1

301

301

325

GB

GB GBI GB

GB

0.05–3 280 up to 50 a sharp peak whose position does not change with frequency; not coincident with the Neel temperature (=210 K) 0.4 GB 970 830 254 1190 810 GBI(?) 315 1.5 GB 1153 400 294

0.35

Vysotskij (1982)

Vysotskij (1982)

Vysotskij (1983)

Vysotskij (1982)

Vysotskij (1982)

Vysotskij (1983)

Wu et al. (1999)

Vysotskij (1983)

4.7 Metals of the VIB Group 337

338

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.7.2 Molybdenum and its Alloys In Mo and its alloys, the following internal friction eﬀects are observed: – – – – –

Dislocation peaks (intrinsic peaks α, β, γ) Grain boundary peaks The Snoek relaxation due to C, N, O The Snoek-type H relaxation Peaks due to self-interstitials

Mo Mo

Mo

Mo

Mo

Mo

Mo

Mo Mo

composition

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

reference

in deformed Mo, the following DP are observed (Fig. 2.20): (a) α, α , α1 , α2 , α3 , α4 peaks in the range 30–150 K (f = 0.5−25 Hz) or in the range 100–200 K (f = 1−25 kHz) which are explained by kink motion in screw dislocations and kink pair formation in non-screw dislocations; (b) β peaks in the range 260–650 K (f = 0.5 − 60 kHz) accounted for by dislocation interaction with diﬀerent types of intrinsic point defects. They split into several peaks (up to 7); (c) γ peaks in the range 440–500 K accounted for by kink pair formation in screw dislocations ≈12 1.5 · 104 115 DP(α) Chambers and CW ≈6 400 Schultz (1961) DP(β) at successively increasing annealing temperatures the β peak begins to break up into at least three subpeaks located at about 260, 320 and 400 K ≈80 17,3 5 1.2 · 10−12 DP(α) Chambers and CW ≈240 44.2 3.8 · 10−11 DP(β1 ) Schultz (1962) – ≈290 – DP(β2 ) 2.65 · 103 80 DeBatist (1962) 10 CW DP 90 20 DP 4 · 104 DP 216 0.5 40 ≈200 SC, CW 5 · 106 173 DP 18.3 Polotskiy et al. 10−12 ≈20 – ≈270 – DP (1966) 1270–1420 GB Belyakov et al. 371 ≈1 1570–1870 (1967) secondary recrystallisation 0.25–1 PD(int) 41 10–12 irr(e), irr(n) Hivert et al. (1970) 1 · 105 140–160 up to 250 SC, CW DP(α) Gibala et al. (1970)

f(Hz)

Table 4.7.2. Molybdenum and its Alloys (at.% if not speciﬁed diﬀerently)

4.7 Metals of the VIB Group 339

Mo

Mo(99.992)

Mo(RRR=2000)

Mo

Mo(99.995)

Mo

Mo

1.9 · 104

Mo

Tm (K)

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism state of specimen

Rieu and De Fouquet (1971)

De Fouquet et al. (1970) Rieu et al. (1970)

reference

Borisov and Vedenyapin (1972) SC 100, CW Mongy (1972) 190 11.5 7.6 · 10−11 DP 1 · 107 SC 110, CW 195 23.3 1.3 · 10−13 DP SC 111, CW 195 28.8 2.1 · 10−15 DP PC, CW 17.3 1.2 · 10−10 DP 31 0.5 PD(int) irr(n) Moser and Pichon 41 (1973) DP(α) 120 SC, CW 1 · 108 Sklad et al. (1973) the occurrence of the peak was found to depend on the presence of an optimum dislocation conﬁguration, internal stresses, and applied strain amplitude PD(int-vac) 11 up to 1.2 2.88 SC, irr(n) 500 Okuda and 10−15 PD(int) 39 up to 1.1 8.46 Mizubayashi (1973) 10−15 1323 1.3 330 Gridnev and 389 1.2 · 10−6 GB Kushnareva (1973)

DP(α) 143 CW DP(β) 350 DP(β) 430 650 DP(β) 1.9 · 104 128 19.2 DP(α) CW 353–363 48.1 DP(β1 ) 398 57.7 DP(β2 ) 548–573 72.1 DP(β3 ) DP(α) peak is explained by the formation of kinks on edge dislocations and DP(β) peaks by the formation of kinks on screw dislocations ≈1470 1 2000 GB

f(Hz)

composition

Table 4.7.2. Continued

340 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

920 172 relaxation on cell boundaries 980 259 impurity segregation on cell boundaries SC 001, CW Mo(RRR=10 000) ≈6 · 104 ≈140 DP up to 80 10.6 10−10 DP ≈300 – 28.8 10−13 ≈400 up to 60 – – DP Mo(RRR=10 000) 5.5 · 104 100 DP(α ) 10.6 SC, CW 5 · 10−11 ≈80 160 27.9 1.4 · 10−14 DP(α) 350 – – – DP(β1 ) 6 · 104 470 – – – DP(β2 ) the DP(α ) peak is explained by the motion of kinks on non-screw dislocations, the DP(α) peak – by the kink pairs formation on non-screw dislocations, the DP(β1 ) and DP(β2 ) – by the interaction of intrinsic point defects with screw dislocations 130 1000 Mo DP(α) 8 CW 17.4 10−12 12 2.3 500 Mo 4.3 · 10−14 PD(int) single irr(e) self-int 39 8.1 6.2 · 10−15 PD(int) bi-self-int Mo(RRR=40 000) 25 7.2 SC, CW 1.3 · 10−15 DP(α4 ) 8.4 1.5 · 10−10 DP(α3 ) ≈60 14.4 3.3 · 10−12 DP(α2 ) 115 21.7 3.6 · 10−13 DP(α1 ) ≈500 – – DP(γ) 2.5 · 104 Mo 130 200 SC, CW 14.5 6.2 · 10−11 DP(α) 2.5 · 104 Mo 100 14.5 SC, CW 1.2 · 10−12 DP(α1 ) 140–200 17.4 3.3 · 10−10 DP(α2 )

Mo

uhlbach (1982) M¨ uhlbach (1982) M¨

Grau and Schultz (1981)

Igata et al. (1981a) Mizubayashi and Okuda (1981)

Rieu (1978)

Tkachenko and Alifanov (1977a) Rieu (1975a)

4.7 Metals of the VIB Group 341

f(Hz)

Tm (K)

Qm (10−4 )

H(kJ mol−1 ) τ0 (s) mechanism

Table 4.7.2. Continued state of specimen

Mo(RRR=32 000)

0.5

DP(α4 , α3 , α2 , α1 ) SC 111 CW ≈30–100 DP(γ) ≈440 up to 70 the amplitude dependence of the γ peak shows anomalous behavior for low amplitudes, and partly irreversible eﬀects at larger amplitudes Mo(RRR=8000) ≈30 DP(α) SC, CW ≈150 550 300–400 ≈3 DP(β) the β-peak was separated into seven peaks: 240 K(β1 ), 280 K(β2 ), 315 K(β3 ), 320 K(β3 ), 350 K(β4 ), 365 K(β5 ) and 410 K(β6 ) which were explained by interaction of diﬀerent types of point defects with dislocations Mo(RRR=8000– 500 the transient damping in the temperature range of the SC, small CW 9000) β-peak was separated into several β-peaks at 450, 470, 490, 500, 510, 520 K or 90, 120, 160, 220, 300 K Mo 1 1733 SC 111 1223 SC 100 1223, 1573, SC 110 2103 Mo (RRR=10 100, 3.7 DP(α) + DP(β) SC, CW 300–450 (very wide peak) 1 at. ppm C) Mo(RRR=20 700) 3.9 DP(α) 120 490 DP(γ) Mo(RRR=3000– 500 ≈150 up to 50 DP(α) + DP(β) + CW, irr(e) 8500) dislocation background Mo(RRR=3000– 400–600 125–160 up to 20 DP(α) as-machined, 8000) irr(e), SC

composition

−1

Garcia et al. (1990)

Garcia et al. (1989)

Suzuki (1989a)

Markin et al. (1987)

Garcia et al. (1986a,b)

Abdelgadir et al. (1986)

Grau and Schultz (1983)

reference

342 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

500

Mo(RRR>400)

41

41

0.68 25 103 ≥300 13 0.0188 (H tunneling) DP(α ) – DP(α) – DP(β) – PD(int) single (at dose self-int 13 · 1015 p cm−2 ) PD(int) up to 0.7 (at dose bi-self-int 18 · 1015 p cm−2 ) 0.15 PD(int)

0.00033 0.067 0.16 2.7 up to 1.5

SC, irr(e)

(2–3) · 103

0.8–3

Mo(RRR=8000) 440 620–640

≈560 ≈660 ≈20 –

≈10 – DP(γ) DP

148–167 DP(α1 ) 17.3 1 · 10−13 167–189 21.2 5.5 · 10−14 DP(α2 ) DP(α3 ) 206–240 19.2 2 · 10−13 7 156 DP(α1 ) 1 · 10 DP(α2 ) 184 DP(α3 ) 230 γ irradiation decreases temperature and height of the α-peaks 41 500 PD(int)

(5–28) · 106

Mo(99.995)

Mo(RRR=4100)

Mo(99.995)

Mo(99.995)

SC, impulse ultrasonic treatment SC, CW

SC, irr(p)

CW

PC + SC, CW

Lambri et al. (2004a)

Tanimoto et al. (1994) Golub et al. (2001)

Alnaser and Zein (1991), Zein and Alnaser (1993) Alnaser et al. (1993)

Tanimoto et al. (1992a) Suzuki and Seeger (1992)

H annealing at Duﬀy (1991, 1992) 1700◦ C, CW due to machining SC, irr(p) Tanimoto et al. (1992b, 1993)

Mo(RRR=25 000) 3.8 150 30 SC, CW DP(α) DP(γ) 450 3.7 45 115.4 8 · 10−14 the DP(γ)-peak is explained by the kink-pair formation on a0 111/2 screw dislocations

500

1090

1100

Mo(RRR= 4000–7100)

Mo(99.95)

4.7 Metals of the VIB Group 343

3.14

1000

2.87 · 104 3

Mo–H

Qm −1 (10−4 ) H(kJ mol−1 ) τ0 (s) mechanism

Mo–H Mo–H

up to 13 ≈3

60

210

152

164

134 – 166

153

S(N) S(C) PD(?)

S(C)

S(C)(?) – S(C)

DP

after carburisation the Snoek peaks were not observed DP(α) 135 17.4 10−12 DP(β) 380–400 6–8 44.4 10−10 372 DP(β) 4 · 10−13 0.4 56 120 24 DP(α) 350 20 36.5 1.7 · 10−8 SK(H) 460 – 12 DP(γ) –

528 620 440

6.5

6.4

603

473–500 550–573 573

820

1.5

Mo–C–Re(47) (wt%)

Mo–C(0.031) (wt%) Mo–C

Tm (K) state of specimen

reference

CW SC, CW

CW

uhlbach (1982) M¨ Suzuki (1989b)

Igata et al. (1981a)

SC, quen. from Schnitzel (1964) 2300◦ C Shchelkonogov et al. (1968) Yamane and quen. from Masumoto (1981) 1860◦ C Kushnareva and quen. from Snezhko (1989) 2000◦ C Kushnareva and quen. from Snezhko (1989) 2250◦ C

SC, 110, CW +annl. 0.77 SC, 149, DP 996 45 249 CW + annl. possible mechanism of the peaks at 820 and 996 K is an interaction of dislocations with vacancy type point defects

f(Hz)

Mo–C, H, N, O 1–1.5 Mo–C(0.247) (wt%) 0.7 Mo–C

composition

Table 4.7.2. Continued

344 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

S(N)

1.1 · 10−14

S(N) – S(N) S(O)

16 S(N) 119.2 7 S(O) 129.8 the broad peak was separated into three peaks ≈108 S(N) ≈134 S(O) ≈163 S(C) ≈7

125 – 125 139.3

DP(β) 79.8 3 · 10−12 125 1.1 · 10−14 S(N) (wt%)+0.0008

121.2

1170– 1270

after nitriding the Snoek peaks were not observed

7.7

other molybdenum alloys Mo–Nb(3) (wt%) 1

Mo–N–Re(47) (wt%)

≈435 ≈475 ≈625 423

1.5

0.5–2.1

1 1.5

Mo–N Mo–O(0.043) (wt%) Mo–N(0.06)– O(0.009) (wt%) Mo–C–N–O

70

425 4 531 11 Qm −1 = 0.0950 · CN ≈3 423 523 up to 20 ≈3 623 498 489–522 50

433–449

442 506 330–670

6.03

Mo–N

1.5 Mo–N(0.04) (wt%) Mo–N(up to 0.09) 5.5

SC 100

quen. from 2250◦ C

quen. from 2200◦ C

quen. from 1740◦ C SC

quen. from 2000◦ C

quen. from 1760◦ C quen. from 2130◦ C

Markin et al. (1987)

Gridnev et al. (1988)

Weller (1996, 2001) Yamane and Masumoto (1981) Grandini et al. (1996b) Piguzov et al. (1967)

Gridnev et al. (1988)

Yamane and Masumoto (1981) Haneczock et al. (1981, 1984)

4.7 Metals of the VIB Group 345

346

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.7.3 Tungsten and its Alloys In W and its alloys, the following internal friction eﬀects are observed: – – – – – –

Dislocation peaks (intrinsic peaks α, β, γ) Grain boundary peaks The Snoek relaxation due to C Peaks due to recrystallisation Peaks due to self-interstitials Eﬀects in the cemented carbides based on WC

W

W

W

W(99.8 and 99.999)

W

W

W

W W

composition

Tm (K)

Qm −1 (10−4 ) H (kJ mol−1 )

τ0 (s) mechanism state of specimen

reference

in deformed W, the following DP are observed (Fig. 2.20): (a) the α peak at 70 K (f = 45 kHz) and α peaks in the range 150–170 K (f = 1–45 kHz) which are believed to belong to diﬀusion of geometrical kinks in screw dislocations and to kink pair formation in non-screw dislocations, respectively. In very pure W the α peaks are observed at 46 and 87–95 K and the α peak at 158–170 K (f = 1.6 Hz); (b) β peaks in the range 250–500 K (f = 1.6 Hz–45 Hz) accounted for by dislocation interaction with intrinsic point defects; (c) γ peaks in the range 620–680 K (f = 1.3–1.6 Hz) accounted for by kink pair formation in screw dislocations ≈5 170 Chambers and CW 1.5 · 104 DP(α) DP(β) >450 – Schultz (1961) ≈5 ≈10−11 ≈160 DP(α) 23.1–24 Chambers and CW 1.2 · 104 Schultz (1962) 224 0.5 De Batist (1962) ≈100 CW DP ≈100 230 DP SC and PC PD ≈100 16.3 1060 DiCarlo and 10−13 PD ≈200 38.5 irr(d) 10−13 Townsend (1966) the peaks are absent in W(99.999) and caused by self-interstitials trapped at impurities 0.01–0.215 up to 1580– ≈540 Shestopal (1968a) recrystallisation peak 1650 4000 ≈4.5 irr(p) PD (5–20) · 105 ≈10 Townsend et al. (1969) ≈600 PD(int) 30 up to 0.7 ≈6.3 SC, irr(e) DiCarlo et al. the stress-induced ordering of the interstitial members of close Frenkel (1969) pairs

f(Hz)

Table 4.7.3. Tungsten and its Alloys (wt% if not speciﬁed diﬀerently)

4.7 Metals of the VIB Group 347

980

≈ 400

W

W(99.99) (RRR=8200)

W

W(RRR= 2400–20 000)

1900 2700 –

1535 2000 2780 423 613 ≈160 ≈260 ≈325 8

≈3 ≈8 ≈6 up to 0.8

Qm −1 (10−4 )

Tm (K) mechanism

DP(α) DP(β) DP(β) PD

primary recrystallisation GB 505 – –

τ0 (s) H (kJ mol−1 )

CW

CW

CW annl.

state of specimen

SC 100 the 110 split interstitials irr(n) 27 up to 1.7 – PD the 110 split interstitials trapped by impurity atoms PD(int) 8 ≈500 SC, irr(n) up to 1.5 ≈1.6 ≈10−14 PD(bi-int) ≈10−14 27 ≈5.4 up to 4 many minor peaks were observed also in the temperature range 7–310 K (at about 7, 12, 23, 34, 40.50 K, etc.). Some of them are attributed to interstitials trapped by impurity atoms and the others to interstitial clusters 70 ≈10 DP(α ) SC, CW 4.5 · 104 170 ≈20 DP(α) 220 ≈63.5 DP(β) 200–500 very broad peak – 800 – DP(γ)

0.7 0.5 0.3 1

W

W

f(Hz)

composition

Table 4.7.3. Continued

Rieu (1975b)

Okuda and Mizubayashi (1976)

Okuda and Mizubayashi (1975b,c)

DiCarlo (1974)

Grau and Szkopiak (1971)

Berlec (1970)

reference

348 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.5 · 104

300–900

1.3

1

1180

337

W

W

W

W(99.95)

W(RRR>8000)

W(RRR=32 000– 1.6 92 000)

W(RRR=50 000)

DP(α) DP(β) PD PD

≈0.3–0.4

28

DP(α) DP(γ)

0.33 1 ≈0.05

up to 30 70

180 620 2023 2203 148 260 8

70 DP(α ) 6.25 5 · 10−10 motion of kinks in non-screw dislocations 150 19.2 5 · 10−12 DP(α) kink pairs formation in non-screw dislocations 450–500 DP(β) 46 DP(α , α) 87–95 158–170 250–450 DP(β) 680 DP(γ) PD(int) 8 1.5 1.8 7 · 10−16 PD(bi-int) 27 1.8 5.5 7 · 10−15 100 up to 50 DP(α)

SC, irr(e)(2MeV) or irr(p)(20 MeV)

SC 111 SC 110 as-machined

SC, CW

SC, irr(n)

SC 110 CW

SC, CW

Tanimoto et al. (1996)

Duﬀy (1992)

Markin et al. (1987)

Schultz et al. (1985)

Mizubayashi and Okuda (1981)

Ziebart and Schultz (1983)

Rieu (1978)

4.7 Metals of the VIB Group 349

Tm (K) Qm (10−4 )

τ0 (s) H (kJ mol−1 ) mechanism state of specimen

relaxation in the binding Co phase ≈260 up to 120 800– 1000 Ru(1.5 wt%) and Cr(1.5 wt%) decrease the peak and increase the peak temperature

WC–Co(5–23)

0.2–5

quen. quen. + CW

the complex spectrum was observed which was not interpreted

reference

Bukatov et al. (1975a) Amman and Schaller (1987), Schaller et al. (1988) Bukatov et al. (1977) Schaller et al. (1985, 1988), Amman and Schaller (1987)

Grau and Szkopiak (1971)

SC, quen. from Schnitzel (1965) 2200◦ C Shchelkonogov et al. (1968)

WC–Co(5–15)

573 up to 65 146 673 ≈20 S(C) 188 W–C(up to 0.01) 0.4 588 40 172 653 up to 150 S(C) 197 Qm −1 = 1.5CC (CC in wt%) W–C(30), wt ppm 1 683 5 S(C) 683 – S(C) – 853 (non-relaxation peak) WC0.995 158 5 · 10−14 172 3 · 10−13 in the temperature range 300–1200 K peaks were not observed WC

1.1–1.5

the peak at 8 K is absent after irr(e), 2 MeV. The relaxation peak at about 28 K is due to the rotation motion of 110-defects which are presumed to be self-interstitial atoms trapped by vacancies

f(Hz)

Table 4.7.3. Continued

W–C W–C(0.007)

composition

−1

350 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

920–950

the peak may be due to dislocation movements in the cobalt phase and is associated with the “brittle to tough” transition

1

1

W–Re(0.66)

W–Ta(3)

WC–Co(11)– Cr(1.5) other tungsten alloys W–Re(20) 0.5

1253

1700 2270 1925 1703 primary recrystallisation secondary recrystallisation ≈900 510 GB

SC 100

annl. SC 100

CW

phases 1100 160 134.6 10−7 1220 370 WC + Co 192.3 10−9 1330 GB 320 192.3 10−9 – 1420 480 461.5 10−18 – 1600 810 471.2 10−15 the peak at 1100 K characterises the movement of partial dislocations in fcc cobalt. The peak at 1220 K is connected with a relaxation phenomenon in cobalt ≈950 0.85 up to 90 relaxation in the binding Co phase

1–2.3

WC–Co(10 vol.%) 1

WC–Co(11)

Markin et al. (1987) Markin et al. (1987)

Berlec (1970)

Schaller et al. (1985)

Schaller et al. (1992), Amman and Schaller (1994) Buss and Mari (2004)

4.7 Metals of the VIB Group 351

352

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.8 Metals of the VIIB group: Mn and Re In metals and alloys based on Mn and Re the following relaxation mechanisms have been observed: – – – – – –

Possible Zener relaxation in Mn–Cu Grain boundary relaxation in Re Twin boundary relaxation in Mn–Co–Cu, Mn–Cu Structural phase transformations (fcc → fct) in Mn–Al–Cu, Mn–Ni Martensitic transformation in Mn–Cu Magnetic phase transformation in Mn, Mn–Co–Cu, Mn–Ni

107

0.1

1000

200–300

1

0.1

1

Mn–Al(1–3)– Cu(10–40)

Mn–Al(2–3.6)– Cu(30–40) Mn–Al(3.8)– Cu(36.2)–Fe(3)– Ni(1.2)

Mn–Co(5–19)– Cu(5) (at.%)

Mn–Cu(9.3)

Mn–Cu(10)

Mn–Cu(10)

f(Hz)

Mn

Mn

composition

10−15

–

700 –

453

150

228

800

403–413

25

410 213

100

– 270

–

–

50

–

–

–

50

PhT(mag) PhT(mart)

–

– 10−11.6

PhT(mart)

PhT(mart) (twins)

twin boundaries in fct phase

–

twin boundaries in fct phase

–

10−14 –10−12 (twin boundaries)

Z

PhT (fcc→ fct)

10−13 –10−12 PhT (fcc→ fct)

additional IF peaks at 273 and 523 K

175.6

48–58

673

240–280

mechanism

PhT(mag) clusters in paramagnetic phase

τ0 (s) H (kJ mol−1 )

–

Qm −1 (10−4 )

300 (twin boundaries)

∼230 360–460

∼96 175

Tm (K)

–

–

–

–

–

state of specimen

Table 4.8. Metals of the VIIB group: Mn and Re (wt% if not speciﬁed diﬀerently)

Wang et al. (1988)

Wen et al. (1985)

Demin (1985)

Ito and Tsukishima (1985)

Ito and Tsukishima (1985)

Kˆe et al. (1987a)

Wen et al. (1985)

Rosen (1968a)

reference

4.8 Metals of the VIIB group: Mn and Re 353

Mn–Fe(24.7)– Cu(4) (at.%)

49–45

51.5

− 10 10−10.4

−11.5

4 · 10−14

τ0 (s) H (kJ mol−1 )

PhT(mart) twins

twins

mechanism

state of specimen

0.5

233 443 ∼280 390 95

Ito et al. (1981)

Udovenko et al. (2005)

Zaaroaui et al. (1983)

or¨ ok Hausch and T¨ (1977b) Sugimoto (1978) Wang et al. (1988)

reference

PhT(mar/twins) quen. 950◦ C Zhang et al. (2006) PhT(mar) + PhT(mag) PhT(mar) PhT(mag)

Z(?) 600 700–120 in addition to twin boundaries and PhT(mart) peaks PhT(mart) 1–2 333 68 600–800 333 PhT(mart) 55 PhT(mart) 1–2 452 25 600–800 448 PhT(mart) 14 PhT(mag) above PhT(mart) (see section “Magnetic Transformations” in Chap. 3) 200–300 ∼250 twin – boundaries

1

Mn–Fe–(14.6– 27.9)–Cu(5) (at.%) Mn–Fe(9.6)–Cu(5) 0.5 (at.%)

Mn–Cu(20)

Mn–Cu(25)

Mn–Cu(35–55)

1

273 230 50

Qm −1 (10−4 )

Mn–Cu(11.7) Mn–Cu(20–30)

Tm (K) 100–150

f(Hz)

Mn–Cu(11.7–44.6) 300–900 273

composition

Table 4.8. Continued

354 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

100–160

200 100

273

1673 210

107

1.1 1

Mn–Ni(14.3– 18.3) (at.%) Re Re Re(99.98) 607 – – –

twin boundaries

–

GB DP(B2 )

PhT(mag)

– –

373–473

1.3 –

PhT(mar) PhT(mag) PhT(fcc→ fct) – –

∼270 453 173–223 – – – 273 100–1 60–65 – walls of antiferromagnetic domains

Mn–Ni(9.7– 40) (at.%)

Mn–Ni(18.4) (at.%) 0.5

P P, CW

–

–

Schnitzel (1959) Fantozzi et al. (1982), CallensRaadschelders and De Batist (1974)

Ritchie et al. (1985) Hausch et al. (1983) Ritchie et al. (1985)

Ito et al. (1980) Hausch et al. (1983) Ito et al. (1981)

4.8 Metals of the VIIB group: Mn and Re 355

356

4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.9 Iron and Iron-Based Alloys Iron (Fe) based alloys and steels are the biggest table in this book. Presentation of all compositions in alphabetical order would lead to some disadvantages as very diﬀerent materials would appear as neighbours. Therefore, for the readers’ convenience, the Fe-based crystalline metallic materials are collected in the following ten groups: 4.9.1 4.9.2

Fe (“pure”), Fe–interstitial atoms (C, H, N), other elements (As, B, Ce, La, P, S, Y) <1%, and low carbon steels, 4.9.3 Fe–(<3%)Me–(C, N) and low alloyed steels (Me = metal), 4.9.4 Fe–Al alloys and steels (mainly bcc and bcc-based), 4.9.5 Fe–Al-based ternary and multi-component alloys (e.g., Fe–Al–Cr, Fe– Al–Ge, Fe–Al–Si etc.), 4.9.6 Fe–Co, –Ge, –Si, –Mo, –V, –W alloys, 4.9.7 Fe–Cr-based steels and alloys, 4.9.8 Fe–Mn-based steels and alloys, 4.9.9 Fe–Ni-based steels and alloys, 4.9.10 Other Fe-based multi-components alloys. Within each of these groups the alphabetical order is used. It is diﬃcult to classify some of the Fe-based alloys within the groups listed above, and some inconveniences are unavoidable. Nevertheless, this classiﬁcation helps to ﬁnd easier the regularities in anelastic phenomena in the Fe-based metallic materials.

mechanism state of specimen

Fe (high purity)

Fe (high purity)

Fe (pure) Fe (high purity)

Fe (Armco)

the scheme of DP peaks is presented in Chap. 2.3 three groups of the DP are observed: α – kinks at screw dislocations, α – thermal kinks at non-screw dislocations; γ – thermal kinks at screw dislocations; β1 and β2 – Hasiguti peaks, βα non-screw dislocations in an atmosphere of carbon atoms. DP(α) – 1000 CW 100–190 1.5–8 19.2 100–110 2–13 DP(βα ) 5.8 DP(β) 270–280 2–5 38.3 DP(γ) 380–420 13–20 – 793–823 600 irr(n) GB 15 – – irr(n) – 10−14 1.4 108 0.7 27 128 4 31 10−13.7 142 2.5 29 10−10.8 153 3.8 34 10−13.3 230 5 – – DP(α) CW 10−11 0.5 30 1–3 5.8 300 – DP(γ) – – irr(n) DP(β1 ) 32 DP(β2 ) 230 CW 2.5 · 10−12 DP(γ) 7.4 350 13–40 80–87.5 8 · 10−14

τ0 (s) H (kJ mol−1 )

Fe

Qm −1 (10−4 )

f(Hz)

composition

Tm (K)

Mizubayashi et al. (1985)

Hivert et al. (1977)

Pecherkina et al. (1976) Pavlov et al. (1982) Ketova et al. (1985) Grinnik et al. (1976) Diehl et al. (1977)

Magalas (1984a)

reference

In “pure” iron, i.e. iron with very low amount of any other dissolved elements, the dislocations (DP(α, β, γ)) and grain boundary peaks are observed Table 4.9.1. Fe (“pure”) (wt% if not speciﬁed diﬀerently)

4.9.1 Fe (“pure”)

4.9 Iron and Iron-Based Alloys 357

0.5–0.8

0.5

1.4 1.4 0.9 0.5

0.16

0.8–2.5

Fe(99.998)

Fe

Fe (puriﬁed)

Fe (pure)

Fe (C-free)

Fe(99.998)

f(Hz)

composition

12 17 22 30 323 623

160 335 30 130 300 305 25–50 250–285 220 238 245 30 45 27

Tm (K)

16 27 19 35 1.6 1.6

28 32 3–16 8 3 12 5 – 0.9 3.8 2.5 5 15 9

Qm (10−4 )

−1

–

– 10−14

4.7 25 158

3 · 10−14 3 · 10−15 – –

–

–

–

53 62 – –

–

–

τ0 (s) H (kJ mol−1 )

Table 4.9.1. Continued

DP(α4 ) DP(α3 ) DP(α2 ) DP(α1 ) – GB

DP(β1 ) DP(β1 ) DP(α)

DP(βα ) DP(βα ) DP(α) DP(βα ) DP(γ) DP(βγ ) DP(β1 ) DP(β2 ) –

mechanism

annl. 900◦ C

CW irr(n) annl. in H2 irr(n) irr(e) CW CW, irr(e) CW, irr(e) and annl. −33◦ C CW

annl. in H2 400◦ C CW

state of specimen

Gachechiladze et al. (1985)

San Juan et al. (1985b)

Ritchie et al. (1980)

Decker et al. (1979)

Hivert et al. (1978)

Ritchie et al. (1978)

reference

358 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe (cimp. <10 p.p.m.)

3.52 · 105 8.7 · 104

8.7 · 104

22.29 50.95 31.84 19.1

55 54.3 49.5 44.4

19.1 3.1

24.52 18.47

54.5 53.2

55.0 49

6.05

18

6.826

3.557 (revised)

6.826

0.673

2 · 10−13

2.5 · 10−11

2 · 10−13

– DP (kink migration) DP(α)

SC 731 εpl ≈ 0.84% at −195◦ C

SC 731 εpl ≈ 0.84% εpl ≈ 2.76% after 3 days after 11 years

SC 100 εpl ≈ 0.82% at 27◦ C

Pal-Val (1999), Natsik et al. (2004), Semerenko et al. (2002) Pal-Val et al. (1988)

Pal-Val and Kadeˇckova (1985); Pal-Val et al. (1986), Pal-Val et al. (1987) Pal-Val et al. (1988)

4.9 Iron and Iron-Based Alloys 359

Relaxation due to point defects: S(C, H, N), PD(C-vac) Dislocation intrinsic (DP(α, β, γ)) and dislocation-impurity (DES(C), SK(C,H,N)) peaks Grain boundary (GB) and impurity grain boundary (GBI) peaks

25

Fe (“steel”)

Fe–B(0.002)– C(0.003) Fe–B(0.005)– Ce(0.028)–C

0.8

Fe–As(0.22)–N, at% Fe2 B

1

1

≈1

0.8

Fe–As(0.22)–C

Fe (impurities: As, 2 C, Sn, Sb) Fe–As(0.14–0.4) 1

f(Hz)

composition

301–307 313 500 10 30 8.5

≈40

–

–

205–260

923–913 310 333 294 328 493

160

13 incl. bgr.

Qm −1 (10−4 )

810–900

293

Tm (K)

76.5 – –

– 88.8 – 80 134

243

–

–

–

–

–

–

ﬁrst report of IF peaks as a function of frequency – –

τ0 (s) H (kJ mol−1 )

PD(C/B) S(C) SK(C)

–

Oil quen. 880◦ C + annl. quen.

–

–

–

GBI S(C) PD(C/As) S(N) PD(N/As) PhT

–

Wire, diam. 1.0 mm

state of specimen

GB

transverse thermal currents

mechanism

Krishtal et al. (1970) Golovin et al. (1983a) Verner et al. (1976)

Bennewitz and R¨ otger (1936), after Zener et al. (1938) Ageev and Goryainov (1980) Shumilov et al. (1981, 1982) Kuzka et al. (1983)

reference

Table 4.9.2. Fe–Interstitial Atoms (C, H, N), Other Elements (As, B, Ce, La, P, S, Y) <1%, and Low Carbon Steels (wt% if not speciﬁed diﬀerently)

-

The following internal friction eﬀects are observed in this group:

4.9.2 Fe–Interstitial Atoms (C, H, N), Other Elements (As, B, Ce, La, P, S, Y) <1%, and Low Carbon Steels

360 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

3.5 50–100

54 83.7 ± 1 80

∼80 S(C)

S(C)

Fe–C or N(0.015) (at.%)

Fe–C(0.0025)

S(C) peak decreases linearly with increase in volume fraction of martensite ∼450 SK(C)(stable) ∼0.8 160 ∼10−12 91.34 312.5 S(C) 1 – 77.5 10−13.7 1.9 · 10−15 S(C) C–C Hz–kHz – – 83.37 interaction 82.5 if CC > 250 83.56 at ppm 84.90 280 313.46 10−4 –100 84.4 1.2 · 10−15 S(C) (1 Hz) 313 1.8 12–15 – – S(C) 473 9–11 SK(C) 330 100 1 – – S(C) 450–520 40–150 SK(C) 225–240 – 1.5 143 – DP(β2 )

Fe–C Fe–C Fe–C Fe–C(45), at.ppm Fe–C(250), at.ppm Fe–C(520), at.ppm Fe–C(600), at.ppm α-Fe–C(1000), at.ppm Fe–C(0.0007–0.2)

312.5

1.5 PD(C/vac)

S(C)

Fe–C

S(C) S(N)

1.9 · 10−15 S(C) 3.4 · 10−15 S(C)

–

–

−1 Q−1 C /CC ≈QN /CN = 1.75 · 10−5 at ppm−1 312 2150 per 1 78.2–80.1 (6–14) at.% 10−15

314 –

323

140

1

1 –

α-Fe–C α-Fe–C

≤1

≈1

α-Fe–C

313

α-Fe–C and α-Fe–N Fe–C

≈1

α-Fe–C

irr(e)

CW

CW

quen.

CW 13% – quen.

quen. from melting point

quen. from 720◦ C quen. from 1000◦ C – quen. 900◦ C, (1–4 h) Magn. ﬁeld 1.6 · 104 Am−1

Weller and Diehl (1980)

Magalas (1984b)

Magalas and Fantozzi (1996b) Golovin (1979)

Nowick and Berry (1972), Swartz et al. (1968) Blanter et al. (1982) Johnson (1965) Magalas (1996a) Diehl et al. (1981) Haneczock et al. (1993)

Weller (1996) Pascheto and Johari (1996) Walz et al. (1996)

Kulish et al. (1981)

Tanaka (1971)

4.9 Iron and Iron-Based Alloys 361

f(Hz) 27 225–232

Tm (K) 0.65 –

Qm (10−4 )

1

1 1

1.1 1.1 1.1 2

Fe–C(0.1)

Fe–C(0.12) Fe–C(0.1–0.53)

Fe–C(0.019) Fe–C(0.71) Fe–C(1.16) Fe–C(0.45) Steel 45 (Rus) Fe–C(0.7) Steel U7A (Rus)

1.7

≈1 314 313 545–580 470 311 470–480 483 493 493 430 540 480–495

483 18 32 45–105 40 0.3–150 25–45 15–25 66 92 5–15 40–50 4.5–21

≤20

–

10−11.6 –

–

–

80.5 82 – 151 – 136–160

–

–

–

5.5 · 10−15 10−14.2 – 10−15 –

–

recrystallisation – – and their clusters

–

4.8 58

τ0 (s) H (kJ mol−1 )

Table 4.9.2. Continued

390–410 10–100 590–610 8–20 870 – 1 1170 peaks caused by self interstitial atoms

1000

Fe–C(0.09)

Fe–C(0.05)

Fe–C(0.05)

Fe–C(0.03–0.04)

Fe–C(0.02) 133 Fe–C(0.03) (at.%) 1

composition

−1

S(C) DES(C) SK(C) SK(C) S(C) SK(C) SK(C) SK(C) in martensite DP SK(C) SK(C)

SK(C)

PhT(α → γ)

S(C) SK(C)

DP(α) DP(β2 )

mechanism

– quen. 730–800◦ C CW: 25–75% quen. 900◦ C and −196◦ C quen., CW, temp. CW, temp.

CW 69% + annl. <400◦ C CW

irr

– CW –

CW irr(n)

state of specimen

Primisler et al. (1978) Gavrilyuk et al. (1984)

oster et al. (1954) K¨ Iwasaki and Hashiguchi (1982) Piguzov et al. (1960)

Golter et al. (1987) Weller and Diehl (1975) Dadeshkeliane et al. (1975) Belbshenko et al. (1979) Moser and Pichon (1973), Moser et al. (1975) Golovin and Sarkisyan (1964) Magalas (1984b)

reference

362 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

14–18 30 380

14–110 – 5–9 8–15 30 2–4 5–9

490 480 483 99 133 198 265 470 240 30 300 313 490–500 540–550

1 2.5 ≈1000 1.09 3115 0.85 3910 0.9 1.4

Fe–(C + N) (<1 × 10−4 ) Fe–C(0.00011)– 1 N(0.00012)– O(0.00018) (at.%) Fe–C(0.35)– 4–5 Nb(0.16)–

58

5

7 75 – –

63

25

– 10−11 – –

–

–

–

2

–

–

DP(α) DP(γ) S(C) SK(C) PD(C/Nb)

SK(C) DP(β2 )

PhT(mag) in Fe3 C DP (in martensite) DP (in martensite)

SK(C)

SK(C)

quen., temp.

–

105–300

470–520

1

Fe–C(0.8) Steel U8A (Rus) Fe–C(0.9) Steel U9 (Rus) Fe–C(1) Steel U10 (Rus) Fe–C(1.2) Steel U12 (Rus) Fe–C(1.23)– Cr(0.64)–Mn(0.34) –

quen. from 800◦ C quen., temp.

Fe–C(0.71)

Gavrilyuk et al. (1981) quen.

CW

irr(n)

Bagramov et al. (2001) Tkalcec and Mari (2004) Tkalcec et al. (2006) Weller and Diehl (1977) Astie (1984)

Sarrak and Suvorova (1983) Gavrilyuk et al. (1976) Sudnik et al. (1974)

Krishtal and Golovin (1959) Shushaniya and Golovin (1961) Verner et al. (1976)

Mura et al. (1961)

quen. and CW

quen., temp. CW –

800◦ C

1.33 2.08 1.33 1.81 1

quen.

Fe–C(0.92)

–

136–186 7 · 10−16 – SK(C) 1.3 · 10−20 (H and τ0 depend on volume of retained austenite) 521 ≤150 SK(C)/FR(C) 528 ≤150 ≤140 501 163.4 – ≤140 505 SK(C) 500 8.5 – – SK(C) 490–510

1

Fe–C(0.71–0.93)

4.9 Iron and Iron-Based Alloys 363

Fe–H Fe–H

Fe–H

Fe–H

Fe–H

Fe–H Fe–H Fe–H Fe–H

500

1

Fe–C(0.8)– Zr(0.0125) Fe–C(0.8)– Ce(0.02) Fe–Ce(0.07)–N –

Qm −1 (10−4 ) – –

τ0 (s) H (kJ mol−1 ) SK(C)

mechanism quen.

state of specimen Verner et al. (1976)

reference

1

SK(C) – quen. 500 – Verner et al. (1976) – (Ce increases Qm −1 ) Kuzka et al. (1983) – – – 1.18 298 – – 301 S(N) 307 PD(N/Ce) Gibala (1967) – 8 · 104 48 S(H) 0.1–0.4 120 0.4–1 Lord (1967a) 12 107 1.5 DP(α) 26 CW 4–10 Dufrense et al. (1976) 5 10−9 –10−12.5 1 CW 50 DP(α) 30–40 Takita and – – 200–260 20–120 SK(H) Sakamoto (1976) 0.5 CW 10 DP(βH ) 1 Ritchie et al. (1979) – – 30 DP(α) 10 120 SK(H) 12 310 DP(γ) 4 – Q−1 jumps due to hydrogen melting in voids and microcracks (Golter and Shepilov 14–16 (1981), Wada and Sakamoto (1981), Golter et al. (1983), Golter and Roshchyupkin (1986)) 1 13.8 PhT(melt) 0.8 CW Golter and 32 0.6 DP(α) Shepilov (1981) 1 DP(β) 190–230 1.2–4.3 Kopylov et al. (1985) – 43.4 10−12 1 SK(H)I 110 CW 28 San Juan et al. 21 3.1 · 10−12 SK(H)II 155 (1985a) 22 35 1.8 · 10−13 mechanism: SK(H)I is due to double kinks at dislocations and hydrogen, SK(H)II is due to two hydrogen atoms clusters and dislocations

Tm (K)

f(Hz)

composition

Table 4.9.2. Continued

364 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1.5

301 428 455

∼30 ∼335 – – 1.15 S(N) and S(N/La) ∼10 ∼335 1.15 GB 570 – 0.73 257.69 ∼335 – S(N) and ∼30 1.18 ∼20 ∼330 1.18 S(N/Ce) ∼30 S(N) and ∼335 1.20 ∼25 S(N/Y) ∼330 1.21 all rare earth elements decrease and broaden the S(N) peak. Tendency to separate peak into two parts 445 1 Kuzka et al. (1983) – – – – PD

Fe–N–La(0.002) Fe–N–La(0.009) Fe–N–La(0.06) Fe–N–Ce(0.006) Fe–N–Ce(0.18) Fe–N–Y(0.049) Fe–N–Y(0.28)

Fe–N–Nb(0.037) (at.%) Fe–N–Nb(0.12) (at.%)

–

Fe–N(212), ppm

– – 103.2 107.1

76.923

138 –

–

–

– –

–

508 300 302–305 –

–

2.35 1

15 40 65 15 40–60 ∼100

300

1.1

Fe–N(0.004) (at.%) Fe–N(0.01) Fe–N(0.04)

S(N) PD PD

S(N) DES(N) SK(N) S(N) DES(N) S(N)

S(N)

290

1

Nowick and Berry (1972) Magalas and Gorczyca (1985) Smithells (1976) Magalas (1984b)

–

Ghilarducci et al. (1994) nitrogenised + Wern-bin et al. quen. (1981b)

quen.

annl. 550◦ C CW CW CW

–

Weller (1985)

–

Fe–N

Golter et al. (1987)

CW, ageing

1

S(H) DP(α) S(N)

Fe–N

0.05–0.25 – – 0.5–0.9 4.8 10−11.6 – 73.4–76.9 (5–18) · 10−15 – 77.5 5.3 · 10−15

14–22 27–32 296–298

157

Fe–H

4.9 Iron and Iron-Based Alloys 365

1

1

0.83

Fe–S(0.001)

Fe–S(0.02)

Fe–S(<0.02)–C

1

790 740 790 313

750

1020

1

Fe–P(0.027) (at.%) Fe–P(1.2) (at.%) Fe–Re(0.015–0.17) (at.%) Fe–Re(0.21) (at.%) Fe–Re(1.4–2.1) 1

530 640 560 650 773–790 950–1000 1020

1

Fe–P(0.009) (at.%)

Tm (K)

f(Hz)

composition

140 140 60 144

80

820–920

380 700 300–150 70–300 810

–

Qm (10−4 )

−1

280 – 209.3 69.8 –

–

–

–

180 230

–

–

–

–

206 – – 126 –

τ0 (s) H (kJ mol−1 )

Table 4.9.2 Continued

GBI GB GBI S(C)

GB

GBI

GB GBI GB GBI GB GBI GBI

mechanism

quen. 700◦ C

–

–

–

–

–

annl.

state of specimen

Shumilov et al. (1973)

Ashmarin et al. (1982, 1985a) Seleznev and Voronchikhin (1986) Shumilov et al. (1973, 1981)

Zhikharev and Shvedov (1980)

Bruver et al. (1976)

reference

366 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.8–1

Fe–As(0.05–0.15)– Mn(1.25–2.4) Fe–Co(≤1.0)–C

1

1–5

1000

1.5 0.8–1.4

Qm −1 (10−4 ) τ0 (s) H (kJ mol−1 )

470 40–50 –

–

Al decreases Qm −1 and increases the peak width 800–853 8–112 – – 870–988 5–355 Co has very little inﬂuence on Qm −1 , Tm Cr decreases Qm −1 – 330 – – 340 350 350 390 2 – – 585–620 62–9

Tm (K)

SK(C)

S(C) SK(C)

S(C)-type S(N) S(N/Cr)

GB GBI(As) S(C)-type

S(C)-type

mechanism

Chomakov (1978)

Sarrak et al. (1976)

quen. 950◦ C

Saitoh et al. (2004) Numakura et al. (1996a)

Shumilov et al. (1984) Saitoh et al. (2004)

Saitoh et al. (2004)

reference

quen. 1100◦ C

quen. 700◦ C quen. from diﬀerent temperatures

quen. 700◦ C

–

quen. 700◦ C

state of specimen

The Snoek eﬀect in Fe–C–Me alloys may be called diﬀerently in the cited literature, e.g. as Snoek, Snoek-type, s-i, or PD relaxation.

Fe–Cr(≤1.0)–C Fe–N(0.18) Fe–Cr(0.2)–N(0.16) Fe–Cr(0.5)–N(0.23) Fe–Cr(1.2)–N(0.29) Fe–Cr(<1)– C(0.4)–Steel 40X (Rus) Fe–Cr–Mn–C(0.2) (20XG) (Rus)

1.5

Fe–Al(≤0.43)–C

1.5

f(Hz)

Table 4.9.3. Fe–(<3%)Me–(C, N) and Low Alloyed Steels (Me = Metal) (wt% if not speciﬁed diﬀerently)

Relaxation due to point defects: S(C, N)1 , PD(C-vac) Dislocation intrinsic (DP) and dislocation-impurity (SK) peaks Grain boundary (GB) and impurity grain boundary (GBI) peaks Phase (martensitic) transformation (PhT(mart))

composition

-

The following internal friction eﬀects are observed in this group:

4.9.3 Fe–(<3%)Me–(C, N) and Low Alloyed Steels (Me = Metal)

4.9 Iron and Iron-Based Alloys 367

1000 1000

Fe–(Cu + 8%Fe)–C

Fe–(Cu–Zn)–C (iron–brass) Fe–Cu(1)–N (at.%)

4–5

1000

Fe–Mo(0.9)– C(0.03–0.05)

2.5

1

1

1.15 – 1.5 1

Fe–Mo(0.83)– C(0.35)

Fe–La(0.0036)–N (at.%) Fe–Mn–(≤0.96)–C Fe–Mn(0.99)– C(0.14) Fe–Mn(0.77)– C(0.20) Fe–Mn(0.6)– N(0.009) Fe–Mn(1.32)– N(0.0123) Fe–Mo(0.27)–C(1)

1000

Fe–Cr–Mn–W–C

1.85

f(Hz)

composition

438 483–490 540–550 390 473

480

300 490 370–420 510–570 370–380 520–550 303 320 297 301 Mn does ∼300 K ∼500 K ∼300 K ∼500 K smeared around ∼298

Tm (K) –

– – interphases matrix-ﬁller – – interphases matrix-filler – 75.3 80.1 – –

–

H (kJ mol−1 ) τ0 (s)

Table 4.9.3. Continued

1.3 2 1.6–2.5 10–12 –

2–16

–

–

83.7 101.7

–

–

–

–

–

–

–

–

–

not change Tm , decreases Qm −1 – – –

–

– threshold 15–30 6–10 2–10 ≤12 –

Qm (10−4 )

−1

Saitoh et al. (2004) Wagner et al. (1994)

Arkhangelskij et al. (1976b) Golovin et al. (1976) Golovin et al. (1987) Kuzka et al. (1983)

reference

CW

Golovin et al. (1978)

Gridnev et al. (1976) Gavrilyuk et al. (1981)

quen. 1373 K Kruk et al. (1994) + ageing 373 K

quen. 700◦ C quen. from 1250◦ C

–

–

composite

composite

quen.

state of specimen

PD(C/Mo/Mo) quen. SK(C) PD(C/Mo) S(C) quen. 1100◦ C PD(C/Mo)

S(C) – S(N) PD S(N) PD(N/La) S(C)–type S(C) SK(C) S(C) SK(C) S(N) composed of three peaks: at 280, 298, and 308 K SK(C)

S(C) SK(C) S(C)

mechanism

368 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.7 0.75

Fe–Sb(0.23)–C

Fe–Sb(0.23)–N (at.%) Fe–Si(≤0.83)–C Fe–Si(2)–Mn– C(0.2) 1.5 1090 2730

1000

1.5 1

7 4

156–118 –

35.6 121.2

76 84 96 113 116.5 127 above S(C) – 29.8

–

7.1 · 10−15 4 · 10−14 8.5 · 10−14 1.3 · 10−14 1.2 · 10−14 1.3 · 10−14 peak –

57

– 88.8 77.2 80.1 –

–

–

Pb melting in composite

308 – 333 294 – 328 Si decreases Qm −1 307 ≈10 320

600

P decreases Qm −1 538–473 80–15 307–318 1.5–8

∼210 ∼250

295 28–67 340–345 22–50 413–416 8–15 1500 607 15 2000 635 15 672 6 additional PD peaks are recorded ∼115 4 0.2 ∼170 15

0.85

Fe–P(≤0.21)–C Fe–P(0.007–0.24)– C(0.0017)– N(0.0018–0.012) Fe–Pb

Fe–Mo–N Fe–N(martensite)

Fe–Mo(5)–C(0.4)

Fe–Mo(0.94–2.64)– N(0.003–0.03)

S(C) PD(C/Sb) S(N) PD(N/Sb) S(C)–type dislocations around microcracks

Ph.T.(mart) kink-pairs (nonscrew) C-disloc. kink-pairs (screw) S(C)-type SK PD(N/?)

Kuzka et al. (1983) Saitoh et al. (2004) Golovin et al. (1975)

quen. 700◦ C heavily deformed

Golovin and Zuev (1976) Kuzka et al. (1983)

Saitoh et al. (2004) Ji et al. (1985)

Kuzka et al. (1983) Liu et al. (1997a)

Teplov (1985)

Soeno and Tsuchiya (1967)

–

–

–

quen. 700◦ C CW quen. 950◦ C

nitrogenised, martensite

– S(N) PD(N/Mo) PD(N/Mo/Mo) SK(?) quen. 1100◦ C

4.9 Iron and Iron-Based Alloys 369

f(Hz)

Fe–V(0.58)– C(0.35)

Fe–Sn(0.06) (at.%) Fe–Sn(0.5) (at.%) Fe–Sn(0.25)–C (at.%) Fe–Sn(0.25)–N (at.%) Fe–Re(0.048)–N (at.%) Fe–Ti(0.02–0.38) (at.%) Fe–Ti(2.1) (at.%) Fe–Ti(0.2– 1.7) (at.%) Fe–Ti(0.08)– C(0.55) Fe–Ti(<0.7)– N (at.%)

4–5

1–1.4

4–5

1 1

1

1.2

0.73

1 0.72

1

≈1000 Fe–Si(2.3)– C(3.6)–P(0.02) Fe–Si(2.3)– C(3.6)–P(0.08) (grey cast iron) – Fe–Se

composition

–

–

67 600 600 –

490 545–553 291–303 423 389–439 494–515 430 490 540 2.3 7.3 2.3

3–4 11–24 –

300–100 80–400 770 16–7

–

–

–

–

–

800 1000 833 950 960 308 358 294 335 306 314 800–850 950–940 980 230–180 –

–

–

– –

– 115 105 130 –

–

–

–

–

– – 60.5–48.0 –

–

– – 94.6 74.3 84 –

–

1.5

–

763

698

τ0 (s) H (kJ mol−1 )

Qm −1 (10−4 ) 2.5

Tm (K)

Table 4.9.3. Continued

SK(C) PD(C/Ti) S(N) PD PD PD(N/Ti) SK(C) – SK(C)

GB GBI GB GBI GBI S(C) PD(C/Sn) S(N) PD(N/Sn) S(N) PD(N/Re) GB GBI GBI DP(γ1 )

GBI(P)

mechanism

quen.

–

quen.

annl. CW

annl.

–

–

– –

–

–

annl. 760◦ C

state of specimen

Gavrilyuk et al. (1981)

Gavrilyuk et al. (1981) Kuzka et al. (1983)

Astie (1984)

Zhikharev and Shvedov (1980)

Kuzka et al. (1983)

Ashmarin et al. (1982) Ashmarin et al. (1985a)

Milman et al. (1981)

reference

370 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

2.5

87

100

0.85

Fe–V(0.34)–N

Fe–V(0.52)–N

Fe–V(0.46)– N(0.01) Fe–V(1.08)– N(0.32)

4–5

Fe–W(1.02)– C(0.35) Fe–W(1.25)–N

1000

1.2

Fe–W(4.4)– C(0.046)

Fe–Y(0.176)–N (at.%)

1

1000

Fe–W(0.5–0.76)– C(0.05)

1

451

0.89

Fe–V(0.68)–C (at.%) Fe–V(0.53–5.61)– C (at.%) Fe–V(2.1)–C(1)

360 390 294 298 9

–

3–4 3 –

25–37

392 500 565 298 336 380–390

–

8 10 ∼20 ∼15 30 42 –

7–14

–

–

∼340 ∼405 ∼410 ∼500 295 361 422 452 476 353– 359

305 355 350 382 480

76.7 83.9

72.4 80.1 77

–

83.9

76 93 117 126 132 74

∼90.38

86 – 81 – – S

– 10−15 nitriding at 673 K

–

–

–

–

–

–

–

PD(C/W/W) S(C) S(N) PD(N/Y)

PD(C/W)

SK(C) PD(C/W) PD

S(C)

quen. 730◦ C

–

–

quen. 1050◦ C

quen. 730◦ C

– 7.1 · 10−15 S(N) 6.4 · 10−15 PD(N/V) – PD (N/V/N/N) – PD(N/V/V) PD(N/V) – S(C) –

–

S(C) PD(C/V) PD(C/V) S(C) SK(C)

–

Kuzka et al. (1983)

Ageev and Morozyuk (1975) Golovin et al. (1978)

Ageev and Morozyuk (1975) Golovin et al. (1978) Gavrilyuk et al. (1981) Kuzka et al. (1983)

Soeno and Tsuchiya (1967) Chen et al. (1985)

Gridnev et al. (1976) Zgadzaj et al. (1981)

Kuzka et al. (1983)

4.9 Iron and Iron-Based Alloys 371

0.79 1 0.9 0.81 0.80 ∼1 ∼1 ∼1 ∼525 527 ∼0.7

Fe–Al(0.07)

Fe–Al(0.5–1)– N(0.001–0.005) Fe–Al(0.1) Fe–Al(0.2) Fe–Al(0.68) Fe–Al(1.54) Fe–Al(2.30) Fe–Al(3.0)

Fe–Al(3.8)

2

313

1.7

Fe–Al(0.003–0.106)– C(0.04) Fe–Al(0.006) 70 80 150–170 50–85 385 380 110 80 90 48 25 48 40

415

58–95

Qm −1 (10−4 )

PhT(ord) has the same meaning as PD(ord).

790 923 295 305 314 314 313 318 318 393 440 393 ∼330

315

f(Hz)

Tm (K)

–

∼81 ∼89

74 83 80.7 80.7

80.7

–

– – – – – –

–

τ0 (s) H (kJ mol−1 )

GB GBI S(N) PD(N/Al) S(C) S(C) S(C) S(C) S(C) S(C) PD(C/AL) S(C) S(C)

S(C)

S(C)

mechanism

973 K 973 K 993 K 993 K 993 K 1173 K

quen. 973 K

quen. quen. quen. quen. quen. quen.

quen. 973 K

quen. 993 K

state of specimen

Golovin and Golovina (2006a), Strahl (2006) Hotta and Iwana (1966)

aniche et al. J¨ (1966) Tanaka (1971) Tanaka (1971)

Rozanski and Lipinski (1977) aniche et al. J¨ (1966) Shumilov et al. (1981) Inokuchi (1975)

reference

Table 4.9.4. Fe–Al Alloys and Steels (Mainly bcc and bcc-Based (wt% if not speciﬁed diﬀerently)

Relaxation due to point defects: Snoek-type eﬀect S(C), point defects of diﬀerent types PD(C-vac, vac-vac), Zener peak (Z(Al)) Dislocation (DP), grain boundary (GB) peaks and peaks caused by phase (ordering) transformation (PhT(ord))2

composition (at.%)

-

The following internal friction eﬀects are observed in this group:

4.9.4 Fe–Al Alloys and Steels (Mainly bcc and bcc-Based)

372 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.79 1 ∼532 ∼1 1 ∼1 500 515 530 ∼1 ∼1.3

Fe–Al(7.9) Fe–Al(7.9) Fe–Al(7.9)

Fe–Al(8.0)

Fe–Al(11.7)

Fe–Al(10.8) Fe–Al(11.1)

Fe–Al(8.79) Fe–Al(10.6)

1 1.42 1.34 1.86 1.8 1.77

∼0.7

Fe–Al(7.2)

Fe–Al(6.6)

0.79 ∼1 400 416 2 ∼515

Fe–Al(4.0) Fe–Al(5.86) Fe–Al(6.6)

388 392 833 403 591 804

350 372 394 453 363 530 353 440 225 493 363 803

∼330 348 440 222 380 395 443 ∼347

15 11 5 112 30 27

50 45 0.4 55 45 17.8

125 18 33 83 47

135 55 29 2 80 55 90 20

99 100 241.3 98.1 – 221.1

274

91.3 45.2 –

90 95.2 ∼80.7 ∼90.4

89 45 – ∼81 ∼89.4 –

∼85.6

– 4.8 · 10−15 7.7 · 10−17 –

– – 3.7 · 10−19

– –

–

– – –

–

–

– – –

S(C) S(C) Z S(C) PD(C/vac) Z

S(C) S(C) S(C) PD(C/AL) S(C) SK S(C) S(C) DP S(C) S(C) Z

S(C) S(C) S(C) DP S(C) S(C) PD(C/AL) S(C)

quen. 1373 K

quen. quen.

quen. 1173 K quen. 993 K annl. 1523 K

quen. 1173 K

quen. 993 K

quen. 1273 K

quen. 1173 K

quen. 973 K quen.

quen. 993 K

quen. ≥1173 K

quen. 973 K quen. 993 K annl. 1173 K, furn. cooling

Tanaka (1971) Golovin et al. (2004b) Strahl (2006) Tanaka (1971) Tanaka and Sahashi (1971) Golovin et al. (1998c) Pozdova and Golovin (2003) Pavlova (2004)

Kulish et al. (1981)

Hotta and Iwana (1966) aniche et al. (1966) J¨ Golovin et al. (1998c) Strahl (2006)

aniche et al. (1966) J¨ Tanaka (1971) Golovin et al. (2004b) Strahl (2006)

4.9 Iron and Iron-Based Alloys 373

383 829 373 793 – 382 813 431 593 804 410 475 490 219 403 788 403 – 403 768

∼1 – ∼1 ∼1.3 – ∼1 ∼1.3 1.72 1.7 1.77 1 245 515 256 ∼1 ∼1.3 ∼1.3 ∼1 ∼1.3

Fe–Al(12.0) Fe–Al(12.8)

Fe–Al(13.3)

Fe–Al(14.0)

Fe–Al(14.2)

Fe–Al(14.7)

Fe–Al(17.0)

Fe–Al(18.9)

Fe–Al(16.9)

Fe–Al(16.0) Fe–Al(16.6)

Tm (K)

f(Hz)

composition (at.%)

20 62 20 73.0

150 12 33 20 90 60 3 13 52.6

30 47.4

110

50 35.7

30 36–60

Qm (10−4 )

−1

247

– 235

270

101 – 45

106 – 212

262

247

266

98.1 243

mechanism

Z

– 8 · 10−17 – 1.6 · 10−18

– 1.5 · 10−19

– –

–

– Z S(C) Z

S(C) PD(C/vac) Z S(C) S(C) – DP S(C) Z

– S(C) 1.5 · 10−18 Z

2 · 10−17

– S(C) 4.1 · 10−19 Z

– S(C) 5.3 · 10−17 Z

τ0 (s) H (kJ mol−1 )

Table 4.9.4. Continued reference

annl. at 1373–1573 K quen. 993 K annl. 1523 K

quen. 993 K annl. 1523 K

quen. 1273 K quen. from 1173 K

Tanaka (1971) Tanaka and Sahashi (1971)

Tanaka (1971) Tanaka and Sahashi (1971) Fischbach (1962)

Kulish et al. (1981) Golovin et al. (2004b)

quen. 1273 K Kulish et al. (1981) annl. 1573 K + Shyne and Sinnott static load (1960) quen. 993 K Tanaka (1971) annl. 1523 K Tanaka and Sahashi (1971) Fischbach (1962) annl. at 1373–1573 K quen. 993 K Tanaka (1971) annl. 1523 K Tanaka and Sahashi (1971) Pavlova (2004) quen. from 1373 K

state of specimen

374 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.9 0.9 1.99 1.81 210 327 10−4 –102

∼1 ∼1.3 – 1.29 1.09 1439 3700

Fe–Al(19.6)

Fe–Al(21.8)

Fe–Al(22.4)

Fe–Al(22.5)

523 970 ∼950

∼1000 950 ∼950

Fe–Al(24.8)

Fe–Al(24.25)

495 ∼280 433 775

593 630 ∼1 ∼1.3

434 796 524 545

650–800

428 778 444 778 494 248 300–400 670– 770 K 423 775

423 768

Fe–Al(24.25)

Fe–Al(23.9) Fe–Al(24.25)

Fe–Al(21.7)

Fe–Al(21.7)

∼1 ∼1.3

Fe–Al(19.3)

60 135 80

36 10 7.5 51.3

26 63 2.5 9.5

50–120

15 66.7

17 63 5 79 100 ∼10 8–20 50–90

6 81.3

255

96.5

228

101.9 56.7

230 222 112 232 108.6 103.8

111 228 113 224 105 ∼51 119 271 ± 6 238 ± 5 109 251

239

3.1 · 10−13 S(C) – GB 3.9 · 10−18 Z

– 5.2 · 10−17

S(C) DP S(C) Z

Z(cooling) Z(heating) S(C) Z S(C) S(C)

5 · 10−17 6 · 10−16 4.2 · 10−15 8 · 10−17 1.4 · 10−15 9 · 10−15 –

S(C) Z S(C) Z S(C) DP S(C) Z(in B2) Z(in D03 ) S(C) Z

5.2 · 10−15 7.8 · 10−17 4.2 · 10−15 8.2 · 10−17 – – ∼10−16 9 · 10−18 4 · 10−17 – 1.4 · 10−18

– S(C) 6.2 · 10−18 Z

annl. 1523 K

annl. 1273 K

annl. 1473 K SC, annl. 1473 K SC, annl. 1273 K quen. 993 K annl. 1523 K

annl. at 1373– 1573 K quen.

quen. 993 K annl. 1523 K

quen. 1123 K

quen. 1273 K quen. 1173 K quen. 1003 K

quen.

quen.

quen. 993 K annl. 1523 K

Golovin et al. (2004b) Tanaka (1971) Tanaka and Sahashi (1971) Hren (1963)

Pozdova and Golovin (2003) Nagy et al. (2002b), Nagy (2002a)

Golovin and Rivi`ere (2006a,b) Tanaka (1971) Tanaka and Sahashi (1971) Fischbach (1962)

Golovin et al. (2004b)

Tanaka (1971) Tanaka and Sahashi (1971) Pozdova and Golovin (2003)

4.9 Iron and Iron-Based Alloys 375

500 690 433 778 408 433 490 495 584 598 690 695 790 190–300 257 434 595 806 150 210 270 360 660–890

∼230

Fe–Al(25.8)

Fe–Al(25.3)

10−4 –102

∼1 ∼1.3 0.1 2.4 290 440 0.1 2.3 280 420 1.9 235 874 2.3 1.94 1.92 ∼2000

305–400

85

Fe–Al(25.0)– C(0.085) Fe–Al(25.1)

484

89

Fe–Al(24.9)

Tm (K)

f(Hz)

composition (at.%)

90 10 17 45.7 95 55 140 200 80 52 18 30 55 plateau 1–7 116 54 49 5 30 22 4 30–90

4.1–7.6

9.55

Qm (10−4 )

−1

–

211.5 ∼48 50.9 108.6 151.9 211.5 –

4 · 10−19 8 · 10−17

–

150 ± 2.8

286 ± 8 235 ± 2

– 2.8 · 10−17 –

–

1.4 · 10−13

229.8 106 ± 3

63.7–84.4

∼96

H τ0 (s) (kJ mol−1 )

Z(in D03 ) Z(in B2)

S(C) PD(C/vac) Z DP and self interstitial atoms

DP

Z

PD(C/vac)

antiphase dislocation S(C) PD(C/vac) S(C) Z S(C)

S(C)

mechanism

Table 4.9.4 Continued

quen. 1273 K

High-pressure torsion deformation

quen. 1323 K annl. quen. from 1273 K

quen. 1173–1523 K

soft quen. from 1273 K quen. + aged 543–723 K quen. 1273 K and irr(γ) quen. 993 K annl. 1573 K quen. 1173–1523 K

state of specimen

Golovin and Rivi`ere (2006a,b)

Pavlova (2004), Pavlova et al. (2005), Strahl (2006)

Tanaka (1971) Tanaka and Sahashi (1971) Pavlova (2004), Pavlova et al. (2005), Strahl (2006)

Rokhmanov et al. (1995), Rokhmanov (2001), Rokhmanov and Andronov (1999) Rokhmanov et al. (2006)

reference

376 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

495 673 – 433 785

562 546 –

∼1 ∼1.3

–

1–10 2 1.85 1.75 ∼1 ∼1.3

486

Fe–Al(26.6)

Fe–Al(27.1)

Fe–Al(28.3)

Fe–Al(29.0)

Fe–Al(30.0)

Fe–Al(30.0)

Fe–Al(27.1)

Fe–Al(26.6)

263

748 1023 790–830 453 610 800 438 780

500 720 906 190 580 536

314 318 306 ∼350 350 2109

Fe–Al(26.28)

489

238

Fe–Al(26.28)

1.5

35 820 40–130 100 105 90 8 50.0 53.8

–

2.4 · 10 1.9 · 10−13 1.2 · 10−15 – – 1.5 · 10−16

237 ± 9 99 157.7 – 223

– −17

– 3.1 · 10−16

1.5 · 10−17

–

10−16 1.6 · 10−12 8.4 · 10−14 3.2 · 10−15

2.2 · 10−16

–

–

220.2

102.9 135.6 237.4

∼75 ∼3 50 10 31.0

119 155 220 31 107 107.7

105.8

10 2 13.5 3.5 2 2.3

29

DP

disloc. GB Z PD PD(Al/sub) – S(C) Z

S(C) Z

S(C) PD(C/vac) Z

S(C) PD(C/vac) Z DP SK S(C)

S(C)

Tanaka (1971) Tanaka and Sahashi (1971) Golovin et al. (2004b)

quen. 993 K annl. 1523 K quen. 1273 K

Zhou et al. (2003b) Zhou et al. (2004)

Nagy et al. (2002b), Nagy (2002a) Golovin et al. (2004b) Shyne and Sinnott (1960) Tanaka (1971) Tanaka and Sahashi (1971) Wert (1955)

Golovin et al. (2004b) Nagy et al. (2002b) Nagy (2002a)

annl. 1173 K annl. 1173 K, air cooling

annl. 1273 K

quen. 993 K annl. 1523 K

quen. 1223–1323 K annl. 1573 K

furnace cooling

annl. + CW

SC annl. 1273 K SC annl. 1473 K

4.9 Iron and Iron-Based Alloys 377

8–36 kHz ∼20 kHz

811 788 282 – 67.5 – 1.79 1.69 1.61 51

3

2.4 2.28 2.16 3

–

0.01–10

Fe–Al(30.22)

Fe–Al(31.0)

Fe–Al(34.0)

Fe–Al(35.0)

Fe–Al(38.0)

Fe–Al(38.8)

Fe–Al(37.5)

Fe–Al(31.5)

Fe–Al(31.5)

Fe–Al(31.5)

f(Hz)

composition (at.%)

483 620 793

472 613 803 460 620

455 587

570–590 ∼800 ∼990 550 681 233 550 690 860 462 615 788 452

Tm (K)

40 70 10 ∼100

36 30 15 6 15

4 8

Qm −1 (10−4 ) 40–20 4 335 12 4 4 11.2 16 47.7 10 6.5 45 1.5

PD(Al/sub) – DP

10−15

276 ± 5

S(C) PD(C/vac) Z PD(vac) 2 jumps PD(vac) 4 jumps

–

4.9 · 10−15 3.4 · 10−15 7.4 · 10−17 ∼10−13

0.7 · 10−15

– 1.7 · 10−14 – 3.4 · 10−15 2.8 · 10−15 8 · 10−17 –

1.2 · 10−17 –

DP PhT(ord) Z S(C) PD(C/vac) DP S(C) S(C) Z S(C) PD(C/vac) Z antiphase dislocation (?) PD(vac) 2 jumps PD(vac) 4 jumps

mechanism

–

121 156 230 120 164

121 162.5

230 112.5 142 48 112.5 148–157 242.3 115 159 228 101.9

–

τ0 (s) H (kJ mol−1 )

Table 4.9.4 Continued

Rokhmanov (2000, 2001)

Golovin et al. (2004b)

Hermann et al. (1997)

reference

recrystallized, 1473 K

San Juan et al. (2006)

Pozdova (2001), Pozdova and Golovin (2003) quen. 1273 K Rokhmanov and + aged 573 K Golovin (2002) annl. ≤1370 K Schaefer et al. (1997), Damson (1998) quen. Pozdova (2001), Pozdova and Golovin (2003) annl. ≤1370 K Schaefer et al. (1997), Damson (1998) annl. 1173 K, Zhou et al. (2004) cooling in air

quen.

quen. 1223 K – quen. 1173 K quen. 1273 K, annl. 893 K

SC, annl. 1173 K

state of specimen

378 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

483 683 793

3

490 467 513 4 2.3

463 444

∼1

Fe–Al(45.0)

Fe–Al(45.0)

Fe–Al(50.0)

Fe–Al(43) Fe–Al(48) Fe–Al(53)

Fe–Al(50.0) Fe–Al(50.0)

475 618 789 425 575 475 650 575 725 385 ∼700 467 668 566 723

2.01 1.93 1.84 0.1

Fe–Al(40.0)

470 625

3

Fe–Al(39.0)

∼20 ∼80 ∼20

62.5 150 15 26 63 3 2 20 15 5 30 2.5 110 33 7

6 13

1.1 · 10−12 6.8 · 10−15 2.1 · 10−14

∼10−14 0.1 · 10−13 5 · 10−15 –

173 ± 19 117 173 – 101.0 160.6 169.2

0.7 · 10−15 10−14 –

4.3 · 10−15 3.5 · 10−15 8.4 · 10−17 –

10−14 0.2 · 10−15

120 158 226 118 162 128.8 163.5 –

114 172

PD(di-vac) PD(C/vac) PD(triple-vac)

S(C) PD(C/vac) Z S(C) PD(C/vac) PD(vac) 2 jumps PD(vac) 4 jumps S(C) PD(C/vac) DP GB PD(vac) 2 jumps PD(vac) 4 jumps S(C) PD(C/vac) quen. 1273 K

quen. 1273 K

heated 950 K annl. ≤1370 K

quen. 1273 K

annl. ≤1370 K

quen. 1523 K

quen. 1453 K

PD(vac) 2 jumps annl. at PD(vac) 4 jumps ≤1370 K

Golovin et al. (2004c) Schaefer et al. (1997), Damson (1998) Strahl and Golovin (2004a), Strahl (2006) Bonetti et al. (1996b) Schaefer et al. (1997), Damson (1998) Strahl (2006), Strahl and Golovin (2004a) Wu et al. (2006)

Schaefer et al. (1997), Damson (1998) Golovin et al. (2002)

4.9 Iron and Iron-Based Alloys 379

Relaxation due to point defects: Snoek-type eﬀect S(C), point defects of diﬀerent types PD(C-vac, C-Me), Zener peak (Z(Al,Me)) Dislocation (DP), grain boundary (GB) and impurity grain boundary (GBI) peaks

Fe–Al(5.1)– Cr(23.6) (at.%)

Fe–Al–Cr Fe–Al(5)–Cr(8– 36)–C Fe–Al(5)–Cr(15)– C(0.03)–Nb(0.73) Fe–Al(5)–Cr(15)– C(0.09)–Ti(0.47) Fe–Al(5)–Cr(25)– C Fe–Al(5)–Cr(25)

Fe–Al–Co Fe–Al(20)–Co(5) (at.%)

composition

2.6 · 10−17 Z 6.2 · 10−24 GB – S(C)

246 ± 13 393 ± 14 –

25 ∼40 ∼200 7

948 ∼570 ∼630 507

1 0.1–3.1 2.5

–

–

130 – –

GBI

PD(C/?)

PD(C/?)

540

–

1

–

10

GBI

DP S(C) – Z

530

–

–

mechanism

1

224–250

–

τ0 (s) H (kJ mol−1 )

–

10 35 100 25

Qm −1 (10−4 )

900–1010

230 440 503 830

Tm (K)

1

720 1.6 700 1.5

f(Hz)

annl. 1373–1473 K annl. 1273 K

–

quen. 1623 K

quen. 1623 K

–

quen. 1273 K

state of specimen

Zhou and Han (2003a) Pavlova (2004)

Gorokhova et al. (1986) Gorokhova et al. (1985, 1986) Belkin et al. (1987)

Belkin et al. (1987)

Golovin (2006b)

reference

Table 4.9.5. Fe–Al-Based Ternary and Multi-Component Alloys (e.g., Fe–Al–Cr, Fe–Al–Ge, Fe–Al–Si, etc.) (wt% if not speciﬁed diﬀerently)

-

The following internal friction eﬀects are observed in this group:

4.9.5 Fe–Al-Based Ternary and Multi-Component Alloys (e.g., Fe–Al–Cr, Fe–Al–Ge, Fe–Al–Si, etc.)

380 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe–Al(25)–Cr(25) (at.%)

Fe–Al(25)–Cr(8) (at.%) Fe–Al(25.0)– Cr(14.7) (at.%)

Fe–Al(25)–Cr(2.5) Fe–Al(25.6)– Cr(5.2) (at.%)

Fe–Al(5.4)– Cr(14.3)–C(0.01) Fe–Al(5.4)– Cr(14.3)– C(0.13) Fe–Al(5.5)–Cr (14.8)–C(0.03)– Nb(0.24)–Ti(0.36) Fe–Al(5.5)– Cr(26.8)–C(0.03)– Mn(0.3)–N(0.4) Fe–Al(13.9)– Cr(16) (at.%) 430 530–585 537 540

1

530 840 243 544 623 585 233 490–635 583–713 794 590–720 810 563 710 805 610 623–773

1.5

570 2.1 530 450 690 ∼2 ∼520 ∼2 ∼500 ∼2 1.55 220 1.45 2 ∼520

1

551

1

12 25 30 15 12 plateau plateau 20 plateau 30 5 15 30 10 plateau

60 35

3 8–10 240 <70

40

–

–

–

–

–

– – –

–

–

– – –

–

–

–

128 –

– 222

–

–

–

–

DP S(C) S(C) PD(C/Al/Cr) DP S(C) (∼585 K)+ PD(C/vac) Z S(C)+PD(C/vac) Z S(C) + PD(C/vac) Z S(C) S(C)+PD(C/vac)

PD(C/Cr)

PD(C/Cr/Cr) PD(C/Cr) S(C) PD(C/Cr)

S(C)

quen. 1273 K

quen. 1273 K

quen. 1273 K

quen. 1400 K quen. 1273 K

quen. 1273 K

annl. 1473 K quen. 1473 K

quen. 1623 K

quen. from 1623 K quen. 1623 K + temp.

Golovin et al. (2003b, 2005a)

Golovin et al. (2005a) Golovin et al. (2003b, 2005a)

Pavlova (2004) Golovin (2006b), Golovin et al. (2003b)

Golovin (2006b)

Belkin et al. (1984)

Gorokhova et al. (1985, 1986)

Gorokhova et al. (1985)

4.9 Iron and Iron-Based Alloys 381

Fe–Al(3)–Si(3)

Fe–Al–Si Fe–Al(1.6)–Si(3) 55 25 30 40

160–1100 ∼470 390 ∼440 160–1100

10 25

670 803

380 ∼430

∼500

Fe–Al(28)– ∼2 Cr(3.99)– Ti(0.83) (at.%) Fe–Al(31)–Cr(15) (at.%) 2.2 4

400 2.7 2.5 ∼380 2.4 10−4 –102

Fe–Al(28)–Cr(3) (at.%)

40 30 8 10 35 50 35 30 20–60

Qm −1 (10−4 )

500

480 633 806 213 476 650 523–673 815 700–830

∼2

Fe–Al(27)–Cr(2) (at.%)

Fe–Al(28)–Cr(2.65)

Tm (K)

f(Hz)

composition

–

state of specimen

PD(C/vac) Z

S(C)

quen. 1000–1273 K

quen. 1000–1273 K

quen. from 1173 K

quen. from 1373 K

quen. 1253 K S(C) PD(C/vac) Z quen. 1273 K DP S(C) PD(C/vac) S(C)+PD(C/vac) Z Z(in D03 ) quen. 850 K

mechanism

S(C) S(C/Al/Si) two-headed (S(C) and S(C/Al/Si)) peak S(C) S(C/Al/Si) two-headed (S(C) and S(C/Al/Si)) peak

–

–

2 · 10−19

276 ± 5 –

–

–

τ0 (s)

–

–

H (kJ mol−1 )

Table 4.9.5. Continued

Golovin and Golovina (2006), Pavlova (2004)

Golovin and Golovina (2006)

Golovin and Rivi`ere (2006b) Pozdova (2001), Pozdova and Golovin (2003) Golovin and Golovina (2006)

Golovin (2002)

Pozdova (2001), Golovin (2002)

reference

382 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe–Al(20)–Si(5) (at.%)

Fe–Al(12.5)–Si(12.5) (at.%)

Fe–Al(7.9)–Si(6.8) (at.%)

Fe–Al(5.5)–Si(9.6) (at.%)

Fe–Al(5)–Si(20) (at.%)

474

1000 413 480 1025 ∼435 500 575 705 ∼820 ∼935

∼2 1.6 670 ∼2 ∼2 527 1.75 505 ∼2 ∼2

413 513 580 213 273 1030 440 453 467 818 1025

485

1.95 490 1.9 535 523 ∼2 1.9 344 462 2 ∼2 –

247

–

–

GB S(C) + S(C/Al/Si)

PD(C/vac) DP

S(C)

– S(C)

1.3 · 10−17 Z GB

–

–

two-headed (S(C) and S(C/Al/Si)) peak 500 – – GB 7 – – S(C) 14 GB 50 14–28 – – S(C) 16 PD(C/vac) 4 5 10–15 242.2 5.2 · 10−18 Z GB

80

6 3 2 9 5 70 30 33 60 24 750

quen. >1173 K As cast

quen. 1250 K quen. 1053–1373 K

quen. 1173 K

quen. 1000–1273 K

quen. 1000–1273 K

quen. 1273 K

Golovin (2006b), Golovin et al. (2005b) Golovin et al. (2005b), Pavlova et al. (2006)

Golovin et al. (2005b) Golovin et al. (2005b)

Golovin (2006b), Pavlova et al. (2006)

Golovin (2006b), Pavlova et al. (2006)

4.9 Iron and Iron-Based Alloys 383

f(Hz)

Fe–Al(25)–Ta(2–6), at% ∼400 Fe–Al(10–23)–Zr(0.1–15), at%

other Fe–Al-based alloys 2 Fe–Al(25)–Mn(5) (at.%) 150 1.85 140 1.8 Fe–Al(25.9)–Nb(0.3) ∼2 (at.%) Fe–Al(25.9)–Ti(2) (at.%) ∼2 Fe–Al(25.9)–Ti(4) (at.%) ∼2

composition

H (kJ mol−1 )

τ0 (s) mechanism

S(C) 30 70 PD(C/vac) 7 10 Z 20 Z 25 and PD(C/vac) peaks both for 2 and 500 Hz – 10 Z –

Qm (10−4 )

Table 4.9.5. Continued

no S(C) and PD(C/vac) peaks ≤600 no S(C) and PD(C/vac) peaks

445 593 605 683 792 813 no S(C) 815

Tm (K)

−1

quen. 1273 K quen. 1070–1450 K

quen. 1273 K

quen. 1273 K

quen. 1173 K

state of specimen

Golovin (2006a), Golovin and Golovina (2006)

Golovin et al. (2004c) Golovin et al. (2004c, 2005a)

Golovin et al. (2005a)

reference

384 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

f(Hz)

1000

4–5

385–788 0.86 1000 1000

2.5 2.4

Fe–Co Fe–Co(0.9)–C(0.05)

Fe–Co(2.9)–C(0.35)

Fe–Co(3.5) (at.%)

Fe–Co(4.03)–N(0.02)

Fe–Co(4.5)–C(0.03)

Fe–Co(4.5)–C(0.05)

Fe–Co(4.6–7.2)–C(1) Fe–Co(30.0) (at.%)

360 510 362 392 570 480 370 4 5 2 30–160 6

–

180

– 3 9 6 ∼55

453 458 508 558 385–399 295

25

Qm −1 (10−4 )

390

Tm (K)

77.3 83.7 – – –

–

S(C/Co) S(C/Co) SK(C) SK(?) S(C)

S(C)

mechanism

– –

–

–

PD(C/Co) SK(C) S(C/Co) S(C) SK(C) SK(C) S(C)

9.5 · 10−15 S(N)

3 · 10−15

∼88 76.5

–

–

97.2 –

83.7

τ0 (s) H (kJ mol−1 )

reference

CW quen. 1273 K

quen. 1173 K

quen. 1173 K

quen. 1000–1100 K –

Golovin et al. (1978), Morozyuk and Kopteev (1981) Gridnev et al. (1976) Pavlova (2004)

Golovin and Golovina (2006) Soeno and Tsuchiya (1967) Ageev et al. (1979)

Golovin et al. (1978), Morozyuk and Kopteev (1981) quen., temper. Gavrilyuk et al. (1981)

quen. from 1173 K

state of specimen

Table 4.9.6. Fe–Co, –Ge, –Si, –Mo, –V, –W Alloys (wt% if not speciﬁed diﬀerently)

Relaxation due to point defects: Snoek-type eﬀect S(C, N), point defects of diﬀerent types PD(C-Me, vac-vac), Zener peak (Z)) Dislocation intrinsic (DP) and dislocation-impurity (SK) peaks, Grain boundary (GB) and impurity grain boundary (GBI) peaks, Phase (magnetic) transformation (PhT(mag)) peaks

composition

-

The following internal friction eﬀects are observed in this group:

4.9.6 Fe–Co, –Ge, –Si, –Mo, –V, –W Alloys

4.9 Iron and Iron-Based Alloys 385

1.3 2.5 0.5

Fe–Si(2.06)–C(1)

Fe–Si(2.84)–Sb(0.018)

∼1

3–12 800–300

∼873

4.7 10 2.3 80 800

–

–

208 238 215 246 –

– –

– 82.7 198

∼80 ∼70 – 10 40 28

83.7 –

77.3

–

–

–

–

– –

– 2. 10−15 10−13.5

–

–

τ0 (s) H (kJ mol−1 )

5 2

4

Qm −1 (10−4 )

463–493

805 920 820 950 ∼945

496 382 220–1240 369–397 1 770 800 427 585 3.7 585 416 683

Fe–Si(1.79)–Sb(0.10)

Fe–Si(1.08) (at.%)

Fe–Si Fe–Si(0.04) (at.%)

Fe–Ge(23) (at.%) Fe–Ge(28) (at.%)

Fe–Ge(15)

392 570

1000

(Fe)–Co(4.53)– Mn(0.21)–Si(0.11)– C(0.05) Fe–Ge Fe–Ge(∼3) at%

Tm (K) 362

f(Hz)

Fe–Co(4.53)–Mn(0.21)– 1000 Si(0.11)–C(0.05)

composition

Table 4.9.6. Continued

GBI

SK(C)

GB GBI GB GBI GBI

Z GB Z Z

S(C)

S(C) SK(C)

PD(C/Co)

mechanism

annl. 1123 K

CW

annl. 1123 K

–

quen. 1117 K quen. 1273 K

annl. 1273 K

quen. 1000–1273 K

quen. 1173 K

quen. 1173 K

state of specimen

Iwasaki and Fujimoto (1981) Gridnev et al. (1976) Iwasaki and Fujimoto (1981)

Zhikharev et al. (1978), Ashmarin et al. (1987)

Golovin and Golovina (2006) Borah and Leak (1974a) Golovin et al. (2006b,d)

Golovin et al. (1978), Morozyuk and Kopteev (1981) Golovin et al. (1978), Morozyuk and Kopteev (1981)

reference

386 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

40 30 5

∼800 ∼980 820 810

∼1 1 0.5

0.66

0.45 0.3 ∼1

∼1

–

Fe–Si(6)

Fe–Si(6.4) (at.%)

Fe–Si(7.7) (at.%)

Fe–Si(8) (at.%)

∼1

0.5

525

60

333–335 ∼473 955 960 958 337 305 327 353 ∼650

∼1

Fe–Si(3.16)– C(0.033) Fe–Si(3.50) (at.%) Fe–Si(4.50) (at.%) Fe–Si(6) (at.%) Fe–Si(5–6)–C Fe–Si(5.6)–C

Fe–Si(2.97)– C(0.03) Fe–Si(3)

4.4

8

20 5 175 185 183 – –

30 50 20 5 800

330 385 333–335 ∼473 ∼873

4–5

2 498 ∼1

10 10–14 1

300 540–595 490

800

Fe–Si(2.86)– C(0.07) Fe–Si(2.9)– C(0.35) Fe–Si(2.9) (at.%) –

– SK(C)

S(C)

–

281–297

241 ± 77 – 281–297

249 254 252 – 84 89 97 –

10−20 − 10−19 10−20 − 10−19 –

–

–

– – –

–

Z

Z

GBI PD(C/Si)(?) S(C) PD PD Superdisl. in ordered structure GB PhT(mag) Z

S(C/Si) SK(C) GBI

S(C) – – shoulder at high-temperature side PD(C/Si) SK(C) GBI – –

– 112–126 –

–

annl. 1373 K

annl. 1373 K

quen. 1273 K

quen. 1273 K + heating to 973 K

– – –

quen. 773–1473 K annl. at 1123 K quen. 773–1473 K –

quen. 1270 K

quen. 973 K, temp. 573K quen.

Nowick and Berry (1972)

Tanaka (1975a)

Lambri et al. (2004b)

Zhikharev et al. (1978), Ashmarin et al. (1987) Kuzka et al. (1983)

Iwasaki and Fujimoto (1981) Krishtal (1965)

Piguzov et al. (1977) Gavrilyuk et al. (1981) Golovin et al. (2005b) Krishtal (1965)

4.9 Iron and Iron-Based Alloys 387

Fe–V(0.62–2.6)– Mn(0.45)– C(0.036–0.05) Fe–W(0.5–4.4)– Mn(0.26–0.46)– C(0.04)

Fe–Mo(5.04)–C(0.16)

Fe–Mo(0.78–8.37)– C(0.019–0.37) Fe–Mo(0.86–1.67)– Mn(0.35–0.46)– C(0.05) Fe–Mo(2.16)–C(0.17)

Fe–Mo, Fe–V, Fe–W ≈30 ≈10 7–32 2 – 11 4 ∼0 4 2–8 –

9–37

∼1000 360 390 454

30 2 20 9 13 9 1

–

83.7 101.7 – 83 97 – 107 83.7 92.9 –

–

76.7 84 97.2

mechanism

PD(C/W/W) S(C) PD(C/W)

S(C) PD(C/V)

PD(C/Mo) SK(C) S(C) PD (C/Mo/Mo) SK S(C) and PD(C/Mo)

10−20 − 10−19 Z Z 1.6 · 10−20 – S(C) – Z DP – S(C)

–

–

281–297 296 –

Qm −1 H τ0 (s) (10−4 ) (kJ mol−1 )

310–503 ≈503 ∼1000 390 437 470 ∼1 39 180 39 235 ∼1000 370–390 437

≈1

810–815 ∼815 217 405 433 850 235 518

∼1 ∼1 527 2.3 507 2.1 560 530

Fe–Si(9.2–11.8) (at.%) Fe–Si(10.7) (at.%) Fe–Si(14) (at.%)

Fe–Si(25) (at.%)

Tm (K)

f(Hz)

composition

Table 4.9.6. Continued reference

Strahl and Golovin (2004a)

quen. 1173 K Golovin et al. (1978), Morozyuk et al. (1977) quen. Golovin et al. (1978), Morozyuk and Kopteev (1981), Morozyuk et al. (1977)

quen. Baranova and 1000–1300◦ C Golovin (1962) quen. 1173 K Ageev and Morozyuk (1975), Morozyuk et al. (1977) quen. Golovin and Golovin (1997)

quen. 1073 K

annl. 1373 K Tanaka (1975a) annl. 1373 K Golovin et al. quen. 1273 K (2004a)

state of specimen

388 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe66.2 –Cr33.8 Fe59.8 –Cr40.2 Fe52.1 –Cr47.9 Fe46.6 –Cr53.4 Fe40.2 –Cr59.8

(at.%) – (at.%) (at.%) (at.%) (at.%) 12 940

– 302.9 301.0 – 283.7 292.3

∼55 ∼80 ∼80 ∼75 ∼60

Fe–Cr(43.1) – 219

1

Fe–Cr(25.1–43.1) Fe–Cr(28) –

∼215 224–250 250–270 –

<40 ∼20–30 – 30

843–873 903–1013 820–840 ∼573

∼1 ∼1 1 38

Fe–Cr(18–38)

900 960

326–340

–

870

215 233–296

H (kJ mol−1 )

1

Qm −1 (10−4 )

Fe–Cr(10–25)

Tm (K)

– –

f(Hz)

Fe–Cr (binary bcc alloys) Fe–Cr(1.2) 1 833 Fe–Cr(5.2–27.6) 1 870–904

composition

Z GBI

Z GBI Z S(C)

Z

GB GBI

mechanism

1.5 · 10−20 2.0 · 10−20 – Z 3 · 10−18 1.4 · 10−18

– 10−12.5

– –

10−14 10−14 − 10−17.6 (5–50) · 10−21 –

τ0 (s)

SC 111 orientation

–

Hirscher and Ege (2002)

Barrand (1966)

Borah and Leak (1974b) Bogachev et al. (1975)

Sarrak et al. (1987)

Tanaka (1975b) – quen. 850–1000◦ C, annl. 1000◦ C quen. 800–1200◦ C

Barrand (1966)

reference

– –

state of specimen

Table 4.9.7. Fe–Cr-Based Steels and Alloys (wt% if not speciﬁed diﬀerently)

The following internal friction eﬀects are observed in this group: - Relaxation due to point defects: Snoek-type eﬀect S(C, N, H), point defects of diﬀerent types PD(H, C-Cr), FR(C, N), Zener peak (Z) - Dislocation intrinsic (DP) and dislocation-impurity (SK(C, H) and DEFR(C)) peaks, - Grain boundary (GB) and impurity grain boundary (GBI) peaks, - Phase transformation (PhT(α ↔ γ)) peaks

4.9.7 Fe–Cr-Based Steels and Alloys

4.9 Iron and Iron-Based Alloys 389

Fe–Cr(1.98)– C(0.16) Fe–Cr(2.5–6.8)– C(0.04) Fe–Cr(2.7)– C(0.35) Fe–Cr(6.2–27.9)–H (at.%) 4–5

6 · 10−14 3 · 10−15

83 96 83 100 –

– quen. 553◦ C quen. 853◦ C

–

SC (torsion)

state of specimen

Numakura et al. (1996a)

Soeno and Tsuchiya (1967) Kuzka et al. (1983)

Hirscher et al. (2000)

reference

SK(C) PD(C/Cr) –

–

SK(C)

CW

quen. 900◦ C

quen. 1100◦ C

Drapkin and Fokin (1980) Gavrilyuk et al. (1981) Asano and Shibata (1982)

S(C) and quen. diﬀerent Golovin et al. PD(C/Cr) or temperatures (1997b) PD(C/Cr/vac)

PD(N/Cr/Cr) PD(N/Cr) – S(N) S(N) and PD(N/Cr)

–

–

–

77 5.3 · 10−15 ∆ = HS(N–Cr) − HS(N) ≈20 kJ mol−1

67 84

488–493 6 – 545 3 500 230–250 6 73–75 (interaction of hydrogen with dislocations)

250 190/210 –/190 50/60 50 7 27 10 3.5–18

15–36 40

283.7 110 1.6 · 10−18 270.2 111 7.7 · 10−18 Z 281.7 100 1.7 · 10−18

∼35 ∼35 ∼35

mechanism

∼900 920 ∼990

τ0 (s)

H (kJ mol−1 )

Qm −1 (10−4 )

Tm (K)

280 315 (a few PD peaks) 1.3 302 1.3 302/325 1.3 286/320 1.3 ∼1 313 440 ∼1 313 440 1000 620 0.8

2.2 4.7 78

Fe47 –Cr53

Fe–Cr-interstitials Fe–Cr(0.23–1.4)– N(0.01) Fe–Cr(<2)–N (at.%) Fe–N(0.18) Fe–Cr(0.2),–N(0.16) Fe–Cr(0.5),–N(0.22) Fe–Cr(1.2)–N(0.29) Fe–Cr(0.91)–C(0.06)

f(Hz)

composition

Table 4.9.7. Continued

390 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

138.3

–

45

80 → 20

550

555 → 510

1.5 1.2

∼1

Fe–Cr(25)–(C + N)(0.05)

Fe–Cr(25)–C(0.007)– N(0.033)

2

548 490 550–570 no peaks

1

Fe–Cr(24.3)–C(0.03) Fe–Cr(24.3)–C(0.027)– N(0.02) Fe–Cr(24.5)–C–Ti(0.8)

Fe–Cr(24)–N(0.033)

–

132 ± 8 128 ∼110 ∼130 138

<100 80 5 8 80

∼548 545 ∼500 ∼560 ∼523

∼1 ∼1 ∼1 ∼1 ∼1

Fe–Cr(24)–C(0.01–0.12)

–

543

1 –

∼553

0.9

–

7 15 25 <80

–

–

– 50 132 7 107 – 50–8 127 between 300 and 750 K

–

–

–

– 134.1 – –

–

70–120 45

570 527

–

2 1.2

40–80

500–530

1

Fe–Cr(8.1–24.7)– C(0.03) Fe–Cr(13)–C(0.4) Fe–Cr(16)– (C + N)(0.05) Fe–Cr(16.6)–N(0.02) Fe–Cr(16.6)–N(0.04) Fe–Cr(16.6)–N(0.06) Fe–Cr(20)– (C + N)(0.05)

S(C, N)

S(C, N)

S(C) PD(C/Cr) S(C)

S(C) S(C) S(C)–Fe-rich S(C)–Cr-rich S(N)

S(C, N)

S(N)

FR(C) S(C, N)

S(C)

Golovin (1996, 1997), Golovin et al. (1997a) Sarrak et al. (1983)

Gorokhova et al. (1983) Zhabo (1984) Golovin (1996, 1997) Lebienvenu and Dubois (1981a)

Golovin et al. (1992) quen. Golovin (1996, 1997), Golovin et al. (1997a) quen. 1250◦ C Serzhantova et al. CW(ε ≤ 13%) (1997)

quen.

quen. 1250◦ C quen. 1250◦ C Suvorova and + annl. 475◦ C, Golovin (1985) 100 h ◦ quen. 1250 C Sarrak et al. (1983), Golovin et al. (1985), quen. 1250◦ C Golovin et al. (1992) quen. + aged

water quen.

quen. 1100◦ C

quen. 1200◦ C water quen.

quen. 1250◦ C

4.9 Iron and Iron-Based Alloys 391

4.2

4.8

∼900 ∼800

Fe–Cr(2)–C–Si(2) (70S2X2 Rus) Fe–Cr(4)–W(6)–Mo(5)– V(2)–C(0.88) (R6M5 Rus) Fe–Cr(4)–W(6)–Mo(5)– V(2)–C(0.97) ∼2

∼2

1.7

1070

133 201 – –

12 3 – 15–4

0.6

–

16

520– 570 520 780 1080 500– 510 1100

Fe–Cr(2)–C–Mo–V (15X2MFA Rus)

–

3–30

–

–

–

–

–

PhT(α − γ)

PhT(α − γ)

SK GB PhT(α → γ) SK(C)

SK

SK

S(C, N)

–

120.3 117.7 111.0 107.4

620

S(C, N)

S(C, N)

–

–

mechanism

–

44 → 17 38 20 32 10

575 → 515 483 473 447 433

Fe–Cr(35)–C(0.012)– ∼1 N(0.011) Fe–Cr(46)–(C + N)(0.05) 1 Fe–Cr(49)–(C + N)(0.05) 1 Fe–Cr(70)–(C + N)(0.01) 1 Fe–Cr(100)– 1 (C + N)(0.007) Fe–Cr-based ternary alloys Fe–Cr(<1)–C(0.4)– 1000 Mo(<1)–Si(<1)– V(<1) Fe–Cr(2)–C–Mo– 0.6 V(12X2MFA Rus)

140.9

τ0 (s) H (kJ mol−1 )

40

Qm (10−4 )

558

f(Hz) Tm (K)

Table 4.9.7. Continued

Fe–Cr(30)–(C + N)(0.05) 1

composition

−1

reference

annl. quen. + temp.

CW

or¨ ok Simpson and T¨ (1980) Shorshorov et al. (1998)

Strongin et al. (1980)

Strongin et al. (1984)

quen. 1000◦ C quen. 1000◦ C

Zharikov (1977) –

Golovin et al. (1992, 1997a), Golovin (1996) quen. 1250◦ C Serzhantova et al. CW(ε ≤ 13%) (1997) quen. Golovin (1996, 1997), Golovin et al. (1997a)

quen.

state of specimen

392 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe–Cr(14.39)–Al(5.4)– C(0.01) Fe–Cr(14.8)–Al(5.5)– C(0.03)–Nb(0.24)– Ti(0.4) Fe–Cr(15)–Al(5)– C+N(0.05) Fe–Cr(15)–Al(5)– C(0.13) Fe–Cr(15)–Al(4)– C(0.03)–N(0.009) Fe–Cr(15)–Al(5)– C(0.03)–Nb(0.73)

Fe–Cr(14.3)–Al(5.4)– C(0.13)

Fe–Cr(13)–Al(6)– Mo(2)–Ce(0.05)

Fe–Cr(8–36)–Al(5)–C Fe–Cr(8)–Al(4)– (C + N)(0.05) Fe–Cr(10.5)– Ni(0.85)– Mo(0.5). . . – C(0.17) (MANET)

540 537 545 523 → 503 530

1 ∼1 ∼1 ∼1 1

540

900–1010 447 380 453 500 560 621 650 710 723 897 963 430 530–585 537 551

1

1

1

0.67 0.59 0.55

∼250

1 1.2

250 87 50 → 12 10

48

–

≤70

–

PD(C, N/Cr, Al) PD(C/Cr, Al)

–

– –

PD(C/Cr)

S(C+N)

PD(C/Cr)

–

–

–

–

–

Z(Cr–Cr) GBI(Fe–Cr) GBI(Fe–Ce) PD(C/Cr/Cr) PD(C/Cr) S(C) S(C)

Several PD(C/Cr) type peaks

GBI S(C, N)

∼134

127

–

– 317.3 384.6

128 –

–

–

–

– –

224–250 111–119

– – ≤6 ≤4.5 ≤5.8 ≤0.5 ≤2 ≤0.9 ≤0.4 – ∼400 ∼100 3 8–10 240 40 Gorokhova et al. (1983)

annl. 700◦ C 2 hours quen. 1350◦ C and temp.

quen. 650–1250◦ C quen. 1250◦ C CW(ε ≤ 13%) quen. 1350◦ C

quen.

quen. 1350◦ C

Gorokhova et al. (1985, 1986)

Gorokhova et al. (1982) Serzhantova et al. (1997)

Golovin et al. (1992)

Gorokhova et al. (1985, 1986)

Gorokhova et al. (1983)

Wern-bin et al. (1981a)

quen. 1200◦ C diﬀer. cooling rate + annl.

quen. 1350◦ C

Belkin et al. (1987) Golovin et al. (1992), Golovin (1996) Gondi and Montanari (1994), Gondi et al. (1996)

– water quen.

4.9 Iron and Iron-Based Alloys 393

42–20 12 20–40

2–5 14–4 8–4 6

550 553–570 620 553–570

∼180 ∼205 ∼240 ∼305

1.2 0.9 0.9

1

0.5–2

1 180

∼500

0.9–1.5

5

280

695

263 5.5

590 ≈10 650 980–1150 170–280 1240 100

13

130

540

1

Qm −1 (10−4 )

Fe–Cr(15)–Al(5)– C(0.09)–Ti(0.47) Fe–Cr(16.6)–C(0.05)– H–Mo(2.3)–Ni(11.2) Fe–Cr(17)–C(0.05)– Ti(0.8) Fe–Cr(17.1)– C(0.095)–Mn(0.4)– Ni(0.24) Fe–Cr(17.1)–C(0.095)– Mn(0–41)–N(0.034)– Ni(0.24) Fe–Cr(17.1)–Mn(1.2)– Ni(7.2)–N(0.08)– Si(0.46)–C(0.06) Fe–Cr(17.2)–C(0.14)– Mn(14.6)–Ni(1.2)– N(0.36)+H2 Fe–Cr(17.5)– C(0.12)–Ni(8.8) Fe–Cr(17.6–18)– C(0.07–0.25)– Ni(11.5) Fe–Cr(17.8)–C(0.06)– Mn(2)–Mo(0.38)– Ni(7.9)–Si(0.5)

Tm (K)

f(Hz)

composition

–

295–335 260 –

–

72

SK

SK(C) SK(C)

CW

–

GB GBI DP

quen.

Austenised at 1050◦ C and cold roll. quen. 1050◦ C charged with hydrogen

quen. 1100◦ C

–

quen.

austenite

quen. 1350◦ C

state of specimen

FR(C)

peak in 6.4 · 10−14 austenite PhT(mart) – S(H)

–

–

S(C)

PD(H)

10−12 –

PD(C/Cr, Al)

mechanism

–

142.46

–

∼48.14

–

–

128

49

–

τ0 (s) H (kJ mol−1 )

Table 4.9.7. Continued

De Lima and De Miranda (1985)

Golovin et al. (1966) Gordienko and Tolmachev (1976)

Usui and Asano (1996)

Yoshida (1996)

Dubois et al. (1982)

Golovin et al. (1992) Dubois et al. (1982)

Asano et al. (1977)

reference

394 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

712 280

223 600–645 300 320

1

Fe–Cr(18)–C(0.02– 0.25)–Ni(11) Fe–Cr(18)–C–N– Ni(11) (X18N11 Rus) Fe–Cr(18.65)– C(0.046)–H– Mn(1.7)–Ni(9.2)– Si(0.58) Fe–Cr(18.9)– C(0.05)–Ni(8.6) 500

190–233 353 563–600 600–645

0.5

2–5 2–20 1 2

17–2 7 5–4 ≤ 7.4

49

(in fcc) –

–

–

∼155

2 → 13

665 → 640

∼1

1

147–152

7

740

50

1

1.5-4

228

1

Fe–Cr(18)–C–Ni(10) (X18N10 Rus)

Fe–Cr(17.8)–C(0.06)– H–Mn(2)–Mo(0.38)– Ni(7.9)–Si(0.5) Fe–Cr(18)–C(0.04– 0.08)–Mn(2)–N(0.8)– Ni(8) (X18H8AΛ2) Fe–Cr(18)–C(0.12)– Ni(9) PD(H)

10−12

–

–

–

–

PD(H)

DP FR PD(H) SK(H)

FR FR(C)

–

DEFR(C)

FR(N) (1.5– 1.9) · 10−12

–

austenite

– CW

Nitrogenised

quen. 1075◦ C

CW

quen. 1150◦ C CW(ε ≤ 27%)

quen. 1150◦ C

austenite

Asano et al. (1977)

Tolmacheva et al. (1976) Gordienko and Pozvonkov (1982) Igata et al. (1982b)

Golovin and Golovin (1996), Zharkov et al. (1996) Gordienko et al. (1985)

Banov and Parshorov (1980)

De Lima and De Miranda (1985)

4.9 Iron and Iron-Based Alloys 395

216

<80

823–873 950 823–873 950 796 936 986

Fe–Cr(24.6)– Ni(0.6)–Mn(0.57)– 1.5 Ti(0.8)–C(0.1) Fe–Cr(25)–Al(5)– 1 C(0.027) (X25Yu5 Rus) Fe–Cr(25)–Ti ∼1 ∼1 ∼1 ∼1 0.61 0.56 0.52

Fe–Cr(27)–Al(7)– Mo(2)–Ce(0.06)

Fe–Cr(27)–Al(5)

–

∼200 ∼50 ∼400 ∼120 250 – 346.2 384.6

250 212

– 298.08 – 375.00 – – 216–226 (segregations) 250 – – –

∼50 ∼500 – 18 28–40 200 25

802 905 963 530 830–870 950 948

∼1000

∼200 <80

48.1 48.1 57.7

∼0.5 ∼1.0 ∼1.5

∼200 ∼260 ∼325

Fe–Cr(19)– C(0.04)–Ni(9) (304L austenitic stainless steel) Fe–Cr(23)–Al(6)– Y(0.07)

–

–

– –

–

0.5 · 10−10 0.6 · 10−12

τ0 (s) H (kJ mol−1 )

f(Hz)

Qm −1 (10−4 )

composition

Tm (K)

Table 4.9.7. Continued

GBI Z(Cr–Cr) GBI(Fe–Cr) GBI(Fe–Ce)

GBI PD(sub)

PD(sub)

–

GBI GBI

Belkin et al. (1987)

Belkin et al. (1984)

Wern-bin et al. (1981a)

Igata et al. (1981b)

reference

Belkin et al. (1984) quen. 1000–1200◦ C quen. <1000 C quen. 1000–1200◦ C quen. <1000 C Wern-bin et al. annl. 700◦ C (1981a) 2 hours

annl. 700◦ C 2 hours –

CW

state of specimen

C at disloc. N at disloc. disl. + strong pinn. points Z(Cr–Cr) GBI(Fe–Cr) GBI(Fe–Y) PD(C/Cr/Cr)

mechanism

396 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

540

260 Fe–Mn(21) (at.%) ∼40 kHz ∼450 ∼373 Fe–Mn-interstitials Fe–Mn(1.12)– 1.3 282 315 N(0.03)–C(0.05) 420

(heat.) (cool.) (heat.) (cool.)

Tm (K)

Fe–Mn(14) (at.%) ∼40 kHz ∼530 ∼430 ∼500 ∼1.3 Fe–Mn(17.5) ∼350 Fe–Mn(17.5)– 1 570 Al(2.8)–C(0.45) 780 ≤650 Fe–Mn(20) 1000 150

Fe–Mn (binary) Fe–Mn(12) 2

f(Hz)

8 5 1.5

162 170 –

–

211.53 1.5 · 10−27 1 81.73 2 9.7 · 10−15 – ∼45 – ∼40 ≤60 134.08– – ≤40 150.84 4 (magnetic transformation in ε-phase (heating)) 18 (cooling) – – 79.8 1.3 · 10−25 2.2 59.61 1.8 1.3 · 10−14

–

H τ0 (s) (kJ mol−1 )

change in slope –

Qm −1 (10−4 )

reference

Azizov et al. (1966)

quen. 1000◦ C Gavrilyuk and Yakovenko (1998) quen. + CW Golovin et al. 15–55% (1966) Shishkov and Efros – (1989), Efros and Amigud (1986) annl. 1250◦ C De et al. (2002)

Parshorov and Weller (1985) annl. 1250◦ C De et al. (2002) –

state of specimen

PD(N/Mn/Mn) annl. S(C) PD(N/Mn)

PhT(γ → ε) PT(ε → γ) PT(γ → ε)

FR(C)/DP

PT(ε → γ) PT(γ → ε) PT(γ → ε)

PhT(ε ↔ γ)

mechanism

Table 4.9.8. Fe–Mn-Based Steels and Alloys (wt% if not speciﬁed diﬀerently)

Relaxation due to point defects: Snoek-type eﬀect S(C, N), point defects of diﬀerent types PD(C, N-Me), FR(C, N), Zener peak (Z)) Dislocation intrinsic (DP) and dislocation-impurity (SK) peaks, Grain boundary (GB) and impurity grain boundary (GBI) peaks, Phase (martensitic γ ↔ (PhT(mart)) and (magnetic, PhT(mag)) transformation peaks

composition

-

The following internal friction eﬀects are observed in this group:

4.9.8 Fe–Mn-Based Steels and Alloys

4.9 Iron and Iron-Based Alloys 397

Fe–Mn(3.5 – 7)– 1 C(0.04) Fe–Mn(13.7)–N(0.2) ∼1.8

4–5

≈100

1

1

80 36 160

287 300 520

0.5

Fe–Mn(1.73)– C(0.93) Fe–Mn(<2)–N (at.%) Fe–Mn(2)– N(0.0055)– C(0.2) Fe–Mn(2.26)– C(1.60) Fe–Mn(2.8)–C(0.35)

3–25

266–273

1

Fe–Mn(1.47)– C(0.13) Fe–Mn(1.5)–N

5 1 14–30

6–7.5 6 1.5 ≈40

∼510 ∼20 (heating)

490 540 510–475

280 313 413 440

several IF peaks

3 5 4–7 8 – 6

203 222–233 280 313 493 190

1

Fe–Mn(1.29)– N(0.006)–C(0.21)

Qm (10−4 )

f(Hz)

composition

Tm (K)

−1

–

–

–

–

–

75.5 81 –

65–72

–

–

–

–

–

–

–

–

–

–

–

τ0 (s) H (kJ mol−1 )

Table 4.9.8. Continued

PT(γ → ε)

PD(N/?) S PD(N/?) PhT(mag) in (Fe, Mn)3 C PD(C/Mn) SK(C) SK(C)

PD

Rokhmanov and Sirenko (1993) Gavrilyuk et al. (1981) Aliev et al. (1974a)

Pietrzyk et al. (1977)

Sarrak and Suvorova (1983) Kuzka et al. (1983)

Beloshenko et al. (1986) Solzbrenner and Carpenter (1976)

Pietrzyk et al. (1977)

quen. Gavrilyuk and 1000 CW+annl. Yakovenko (1998)

–

quen.

annl. ≈600◦ C

quen.

–

quen.

quen. 950◦ C

CW

PD(N/Mn) S SK DP PD (N/Mn/Mn) S(N) PD(N/Mn) SK(C)

–

state of speci- reference men

DP

mechanism

398 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1000

120 5 – 260 6 Fe–Mn-based ternary and multi-component alloys (see also in Fe–Cr-, 430–450 2.5–20 1 – – Fe–Mn(0.77)– Cr(0.22)–Si(0.3)– C(0.4) – – 2 420 1 Fe–Mn(0.83)– 2 520 Si(0.46)–V(0.68)– 1.5 600 C(0.06) 1000 420 – – – Fe–Mn(0.86)– Si(1.41)–C(3.29) 570–610 graphite Fe–Mn(1.13–1.3)– 1000 590 – – – Si(2.04 – 2.17)– C(0.15–0.19) 220 1 0.8 – – Fe–Mn(1.14)– 290 0.9 N(0.018)–V(0.1)– C(0.18) 313 3.7 160 130 650 – – Fe–Mn(1.18)–Cu(0.15)– interaction of C and H atoms with dislocations C(0.19)–H ((0.7–5) × 10−4 ) (at.%) 870–885 270–350 212–280 – 0.7 Fe–Mn(1.22)– Ce(0.028–0.83)– Si(0.31)–C(0.14) 1000 400 8 – – Fe–Mn(1.5)– 560 Si(0.5)–C(0.08) 13 1000 390 4 – – Fe–Mn(1.5)–Si(0.5)– V(0.18)–C(0.08) 540 7 490 1 1–10 – – Fe–Mn(1.61)–S(0.27)– Si(0.35)–V(0.1)–C(0.48)

Fe–Mn(20)–B(1)

quen. quen. annl. CW

–

PD(N/Mn) DP S(C) SK

GBI

CW

quen. 760◦ C

quen. 760◦ C

–

SK(C)

S(C) SK(C) S(C) SK(C) SK

Kriz (1973)

grey cast iron

Masse et al. (1985)

Strozheva and Fonshtein (1984)

Sheng et al. (1985)

Conophagos et al. (1971)

Efros and Amigud (1986)

Sergeev et al. (1977)

Rodzinyakova (1982)

quen. 1200◦ C temp.

PD(C/Si) PD(C/Mn) PD(C/V) S(C)

ε-phase PhT(magn) Efros and Amigud PhT(γ → ε) (1986) Fe–Ni- and Fe-complex alloys) Masse et al. (1985) SK(C) –

4.9 Iron and Iron-Based Alloys 399

30

475 480 320 870 620–670 970

1 1 1000

Fe–Mn(18)– Cr(4)–Ni(1)– V(0.32–2.56)– C(0.18+0.75)

645–670

400 23–120

255 70 400 150 602 → 595 2 → 15

1 1 ∼1

1000

25

486

1

Fe–Mn(13)– P(0.016–0.062)– C(1.1) (110G13L Rus) Fe–Mn(16)– Cr(9)–Si(5)–Ni(4) Fe–Mn(17)–Al(3)–C

15

513

1.7

Fe–Mn(2)–Cu(2)– Mo–C(0.2) Fe–Mn(3.5)–(Cr, V<1%)–C(0.04) Fe–Mn(5)–(Cr, V<1%)–C(0.04) Fe–Mn(7)–(Cr, V<1%)–C(0.04) Fe–Mn(12)–Cr(2) 25 25 18 50–70 70

0.8 0.9 3.7 500

220 290 313 780

1

Qm −1 (10−4 )

Fe–Mn(2)–Al(0.04)– V(0.1)–C(0.18)

Tm (K)

f(Hz)

composition

–

(cooling) (heating) ∼142

(heating) (cooling) – –

–

235–250

–

–

–

–

– –

Aliev et al. (1974b)

Normalis. at 900◦ C (martensite + retained austenite)

FR(C)

PhT(γ → ε) PhT(ε → γ) DEFR(C)

quen.

quen. 1150◦ C CW(ε ≤ 27%)

quen. 900◦ C

Golovin and Golovin (1996), Zharkov et al. (1996), Golovin et al. (1997c) Krshizh et al. (1980)

erez-S´ aez et al. (1994) P´

Shishkov and Efros (1989), Efros and Amigud (1986) Chizhenko et al. (1977)

Tavadze et al. (1985)

Efros and Amigud (1986)

reference

CW

quen. 1200◦ C normalis.

state of specimen

– PhT(ε → γ) PhT(γ → ε) PhT(α → γ) PhT (carbides) – –

SK(C) in martensite and FR(C) in austenite

–

–

DP DP S(C) GB

mechanism

–

τ0 (s) H (kJ mol−1 )

Table 4.9.8. Continued

400 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.5–1

Fe–Mn(29.4)– Cr(4.3)–Si(5.6) Fe–Mn(30)–Si(6)

Fe–Mn(32.2)– Si(6)–Cr(5.2)

Fe–Mn(30)–Si(6)– Cr(5)

– 0.5 0.5 ∼2

Fe–Mn(20)–Ti(3) Fe–Mn(26.4)– Si(6)–Cr(5) Fe–Mn(28)–Si(6)– Cr(5)

0.5

0.5 0.5 1

–

1000

Fe–Mn(20)–Nb(1)

Fe–Mn(20)–Co(2)

Fe–Mn(20)–Co(2)

463 323 393 393 393 473 393 573 423

330–350 520 210 350 500 120 270 200 437 273 238 275 238 406 430

(heating)

ε = 10%

110–50 35

(heating) (cooling) ε=0 ε = 2% ε = 5%

– (heating) (cooling) (cooling) (cooling) (heating) (heating) –

–

–

19.1 3.18 170 150 130–100

12–25 70 – 10 50 4 4 – 73 35 15 21 10 40 90

–

–

–

–

–

–

–

– –

–

Chen et al. (1999)

1100◦ C

Chen et al. (1999)

homogenised + Chou et al. (2000) Hot roll. + tensile-strained

Sato et al. (1988)

Yoshida and Otsuka (1994)

Chen et al. (1999)

Efros and Amigud (1986) Shishkov and Efros (1989)

CW

annl. 600◦ C, quen.

– 1100◦ C

–

γ-phase

PhT(γ → α ) disloc. relax. peak in γ phase 1100◦ C PT(γ → ε)

PhT(ε → γ)

PhT(γ → ε) PhT(ε → γ) PhT(γ → α )

PhT(magn) PhT(ε → γ) PhT(magn) PhT PhT PhT(ε → γ) PhT(γ → ε) PhT(γ → ε) PhT(γ → ε) PhT(ε → γ) PhT(AFM) PhT(MT) PhT(AFM) PhT(MT) PhT(ε → γ)

4.9 Iron and Iron-Based Alloys 401

f(Hz)

2

2.5

4–5

1000

Fe–Ni(3)–C(1)

Fe–Ni(3.07)–C

Fe–Ni(3.9)–C

Fe–Ni(25) (at.%) 0.5–5 0.5–5 (nanograined) 950 Fe–Ni(36) 960 (nanograined) Fe–Ni(50) 400 (nanograined) Fe–Ni-interstitials Fe–Ni(1.5)–C 1

Fe–Ni(20)

Fe–Ni (binary fcc alloys)

composition

390 2

1.3–2

8–48 2–15 3–12

310–315 460–480 480 480–490

4.5 3 10–90 250–400 14 30 30

Qm −1 (10−4 )

900 490 198 473 230 285 190

Tm (K)

–

–

–

–

–

–

–

–

–

–

(cooling) (heating) –

–

τ0 (s) H (kJ mol−1 )

state of specimen

S(C)

SK(C)

S(C) SK(C) SK(C)

quen. 950◦ C

quen. 900◦ C

CW

PhT(α → γ) – PhT(γ → α) PhT(MT) consolidated PhT(reverse MT) severely deformed HTP – n = 5, p = 1GPa

mechanism

Table 4.9.9. Fe–Ni-Based Steels and Alloys (wt% if not speciﬁed diﬀerently)

The following internal friction eﬀects are observed in this group: - Relaxation due to point defects: Snoek-type eﬀect S(C, N), point defects PD(H), FR(C, N), Zener peak (Z)) - Dislocation intrinsic (DP) and dislocation-impurity (SK(C, H), DEFR(C)) peaks, - Grain boundary (GB) and impurity grain boundary (GBI) peaks, - Phase (PhT(mart) and PhT(polym)) and (magnetic, PhT(mag)) transformation peaks

4.9.9 Fe–Ni-Based Steels and Alloys

Barmin et al. (1980) Gridnev et al. (1976) Gavrilyuk et al. (1981) Morozyuk and Kopteev (1981)

Golovin et al. (2005c) Golovin et al. (2006a)

Parshorov and Weller (1985) Wang et al. (2004a)

reference

402 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

∼1

Fe–Ni(24.7)–C(0.72)

518 518 460 128 120–125 218 253 423 500–518 433

1.2 1.2 1.2 1.2 1.5

1.2

453

1.2

Fe–Ni(24)–C(0.41)

Fe–Ni(19–27)– C(0.18–0.51)

Fe–Ni(19)–C(0.39)

Fe–Ni(19)–C(0.39)

∼10 10 66 167 210–130 580–470 520–450 167 5–10 ∼200

<80

1.2 443–453 70 IF peak due to internal stresses 1.2 280 3–30

–

–

5 · 10−17

75

−12

–

–

1.3 · 10

–

–

1.4 · 10−14

SK(C) in martensite FR(C) FR(C) SK(C) in martensite PhT(mart) – DP DP FR(C) SK(C)–type

PD(H)

DP

SK(C)–type

FR(C) S(C) SK(C) FR(C) SK(C)

S(N)

9.5 · 10−15 –

–

–

–

–

49

–

–

∼100

438

Fe–Ni(19)–C(0.39)

– – 140 100–103

–

– 10 15–24 5–10 16

570 360 440–460 530–580 518–548

1500– 2000 ∼1

–

2

76.5

120

0.85 295

–

no PD peaks were recorded

Fe–Ni(17–28)– C(0.23–0.75) Fe–Ni(18.4)–C(0.72)

Fe–Ni(11)–C(0.4) Fe–Ni(15)– C(0.02–0.69)

Fe–Ni(<5)–N (at.%) Fe–Ni(5)–N(0.02)

quen. 950–1150◦ C

quen. 1050◦ C

quen.

quen. 1050◦ C (28%M + A) quen. 1050◦ C quen. + liquid nitrogen

f.c.c.

–

quen. 1150◦ C

quen. 1100◦ C

quen. 1400◦ C quen. 900◦ C

–

–

Suvorova and Gvozdev (1978) Bugajchuk et al. (1992)

Prioul (1985)

Bugajchuk et al. (1992) Suvorova and Gvozdev (1978) Asano et al. (1975, 1977) Suvorova and Gvozdev (1978)

Teplov (1985)

Kuzka et al. (1983) Soeno and Tsuchiya (1967) Zhabo (1984) Bitjukov et al. (1977)

4.9 Iron and Iron-Based Alloys 403

1600

Fe–Ni(25–28)– C(0.23–0.3) Fe–Ni(30)–C(0.02) Fe–Ni(42)–C(0.02)

2 → 13

665 → 640 300 320 190–233 353 563–600

Fe–Ni(9.2)–Cr(18.7)– Mn(1.7)–Si(0.58)–H– C(0.046) Fe–Ni(10)–Cr(18)–C (X18N10 Rus) 1

1 2 17–2 7 5–4

∼155

0.5

280

500

49

7

740

–

(in fcc) –

147–152

50

1.5–4

228

72

5.5

–

–

–

10−12

FR

PD(H) SK(H) –

DEFR(C)

PD(H)

FR(N)

(1.5–1.9) · 10−12

CW

– CW

quen. 1150◦ C CW(ε ≤ 27%)

austenite

quen. 1150◦ C

austenite

PD(H)

–

quen. quen. 1150◦ C CW(ε ≤ 27%)

quen. 1100◦ C

state of specimen

CW

DP FR(C) PhT(mart) DEFR(C)

mechanism

DP

–

– 1.5 · 10−14 – –

τ0 (s) H (kJ mol−1 )

65.5 127 120 – 0.7 → 1.5 126

–

Qm (10−4 )

263

353 662 150 515

Tm (K)

Table 4.9.9. Continued

Fe–Ni-based ternary alloys Fe–Ni(7.9)–Cr(17.8)– 1 Mn(2)–Mo(0.38)– Si(0.5)–C(0.06) Fe–Ni(7.9)–Cr(17.8)– 1 Mn(2)–Mo(0.38)– Si(0.5)–H–C(0.06) Fe–Ni(8)–Cr(18)– 1 Mn(2)–C(0.04–0.08)– N(0.8) Fe–Ni(8.6)–Cr(18.9)– 712 C(0.05) Fe–Ni(9)–Cr(18)– ∼1 C(0.12)

1.5 ∼1

f(Hz)

composition

−1

Gordienko et al. (1985)

Golovin and Golovin (1996), Zharkov et al. (1996) Igata et al. (1982b)

Asano et al. (1977)

Banov and Parshorov (1980)

De Lima and De Miranda (1985)

De Lima and De Miranda (1985)

Prioul (1985) Golovin and Golovin (1996), Zharkov et al. (1996)

Teplov (1978)

reference

404 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

Fe–Ni(18)– Mo(1.5)–C(0.35) Fe–Ni(18)–Mo(4)– C(0.35)

Fe–Ni(16.04)– Co(5.2)–Mo(4.9)– C(0.02)

Fe–Ni(11)–Cr(18)– C(0.02–0.25) Fe–Ni(11)–Cr(18)–N–C (X18N11 Rus) Fe–Ni(11.2)–H– Cr(16.6)–Mo(2.3)– C(0.05) Fe–Ni(11.5)–Cr(17.6– 18)–C(0.07–0.25) Fe–Ni(15)–Mo(5.4)– C(0.025) Fe–Ni(16)–Co(5.2)– C(0.02) Fe–Ni(16)–Co(5)– C(0.020) Fe–Ni(16)–Mo(5)– C(0.025) Fe–Ni(16)–Co(5)– Mo(5)–C0.020) 2–5 2–20 13

170–280 100 6 1.5–2 11 20

10 8 2 5 24 20 25 23

223 600–645 280

980–1150 1240 530 600–620 340 440

440 530–540 600–620 320 470 533 573 533

1

1 1

1500–2000

1500–2000

1

1

0.5–2

695

1

7

≤7.4

600–645

1

1.4 · 10 1.3 · 10−14 1.4 · 10−14

140 98 107 102

−14

–

–

–

–

–

–

–

–

– –

–

10−12

–

295–335 260

49

–

SK – S(C) FR(C) SK(C) – SK(C)

SK(C)

SK(C)

GB GBI SKI DP SK(C)

DP FR PD(H)

FR(C)

quen. 1100◦ C

quen. 1100◦ C

cementation

quen. 900◦ C

aged martensite

quen. 900◦ C

–

austenite

nitrogenised

quen. 1075◦ C

Teplov (1978, 1985)

Bitjukov et al. (1977), Bitjukov and Chervinskij (1981)

Gordienko and Tolmachev (1976) Bitjukov et al. (1977)

Tolmacheva et al. (1976) Gordienko and Pozvonkov (1982) Asano et al. (1977)

4.9 Iron and Iron-Based Alloys 405

f(Hz)

Fe–Ni(24)–Mo(5)– –C(0.002) –C(0.018) –C(0.041) –C(0.069) –C(0.088) –C(0.2)

–

Fe–Ni(24)– Mn(0.5)–C(0.5) Fe–Ni(24)–Mo(4)– C(0.088)

1.9/∼700 1.9/∼700 1.9/∼700 1.9/∼700 1.9/∼700 1.9/∼700

∼1

1500–2000

Fe–Ni(24)–Mo(4)– C(0.3)

Fe–Ni(19.1)– 0.6–7.6 Mn(0.74)–C(0.51) 1.75 Fe–Ni(21)–Mo(3)– 1500–2000 C(0.5)

1.1–1.8 Fe–Ni(18.5)– Co(8.5)–Mo(4.9)– Ti(0.56)–C(0.01)

composition

1.6 → 5.5 141 → 136

580 → 560

208 183 173 143/∼100 133 178

14 45 44 45 12 4 30 40 2–8

125/12 –/4 180/3 40/IF jumps 25/– –/IF jumps

96.5 104 113 125 98 109 120 –

–

538 523 559 615 648 536 584 629 638

–

–

1.5 · 10−14 1.4 · 10−14 1.2 · 10−14 1.2 · 10−14 1.4 · 10−14 1.3 · 10−14 1.2 · 10−14 –

–

–

τ0 (s) H (kJ mol−1 )

10 20 ≤340 1450 47–5

Qm −1 (10−4 )

300 370 420–490 1050 120

Tm (K)

Table 4.9.9. Continued

CW quen. 1100◦ C CW

FR(C) SK(C) –

quen. 1150◦ C CW(ε ≤ 27%)

austenite

PhT(mart): if quen. 1150◦ C C < 0.04 isother. MT, if C > 0.04 athermal MT: increase in f decreases Q−1

DEFR(C) in fcc

DP

quen. 1100◦ C

quen. 1100◦ C

–

PhT(mart) PhT(polym) PhT(mag)

FR(C) SK(C) –

–

state of specimen

–

mechanism

Gordienko and Tolmachev (1976) Zharkov et al. (1996), Golovin et al. (1997c) Golovin et al. (1994, 1995), Golovin and Golovin (1996)

Rodrigues and Prioul (1985) Sarrak et al. (1980) Teplov (1978, 1985)

Chomka and Pastor (1983)

reference

406 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1600

1 1000

Fe–Ni(28)–Mn(1)–C

Fe–Ni(29)– Co(18)–C(0.02)

1–2

610–640

530 → 510 208 330–350 430–460 448 93–170 1.6 5 1 1 (jump in Q−1 ) – –

37.6 62.5–65.5 82–86.5 87 –

∼140

5 → 12

PhT(mag)

DP(X) DP S(C) PD(C/Ti) PhT(α ↔ γ)

4 · 10−14 7 · 10−14 1.7 · 10−14 2 · 10−14 – –

DEFR(C)

peak in martensite: C + twin boundaries DEFR(C) in f.c.c. PhT(mart) SK(C)

FR(C)

–

–

–

∼140 –

–

–

∼130

∼130

– 37

8 15 17 1→2

∼430 ∼430 ∼430 530 → 510 213 480

∼1 ∼1 ∼1 1–2 1000

2 3.3 4.3

530 525 523

∼1 ∼1 ∼1

Fe–Ni(24)–Mo(5)– –C(0.041) –C(0.069) –C(0.088) Fe–Ni(24)–Mo(5)– –C(0.041) –C(0.069) –C(0.088) Fe–Ni(24.5)– Mo(5)–C(0.002) Fe–Ni(24.5)– Mo(5)–C(0.002– 0.088) Fe–Ni(26)– Mo(4.5)–C(0.088) Fe–Ni(27)–Ti(2)–C

–

–

quen. 1150◦ C CW(ε ≤ 17%) quen. 1100◦ C

quen. 1150◦ C

quen. 1150◦ C+ cooled to −196◦ C quen. 1150◦ C CW(ε ≤ 17%)

quen. 1150◦ C

Blanter et al. (1980) Venzkunas et al. (1978)

Serzhantova et al. (1997) Seleznev and Voronchikhin (1986) Serzhantova et al. (1997) Teplov (1978)

Golovin et al. (1996b, 2000)

Golovin et al. (1996b, 2000)

4.9 Iron and Iron-Based Alloys 407

Fe–C(0.02)–Co(9.8)– Cr(10.5)–Mo(5.7)– Ni(7.5)

930

470 670 930 225 1020

1

1

1.1

470

1

60 – 920 100 300

920

–

2–10 2–7

130–180 273–283

500–1000

Qm −1 (10−4 ) 60 35

1.5

Fe–Al(5.5)–C(0.03)– Cr(26.8)–Mn(0.25)– N(0.4) Fe–Al(0.17)–C(0.31)– Cr(0.84)–Mn(0.84)– Si(1.1) Fe–B–C(0.35)–Cr– Mn(3) (35XG3P Rus) Fe–B–C(0.35)–Cr– Mn(3)–Ni (35HXG3P Rus) Fe–B–C(0.35)–Mn(3)– Ni (35HG3P Rus)

Tm (K) 530 840

f(Hz)

composition

– 77.5 – – –

–

–

–

– 222

– (interphase – – –

–

–

–

–

τ0 (s) H (kJ mol−1 )

SK boundaries) GB PhT(mart) PhT(polym)

GB

SK

DP(ß) DP(γ)

PD(C/Cr) (segregat.)

mechanism

–

–

–

quen. 800◦ C

CW

annl. 1200◦ C quen. 1200◦ C

state of specimen

Table 4.9.10. Other Fe-Based Multi-Components Alloys (wt% if not speciﬁed diﬀerently)

The following internal friction eﬀects are observed in this group: - Relaxation due to point defects: Snoek-type eﬀect S(C, N), point defects (PD and FR), Zener peak (Z)) - Dislocation intrinsic (DP(β, γ, H)) and dislocation-impurity (SK) peaks, - Grain boundary (GB) and impurity grain boundary (GBI) peaks, - Phase (PhT(mart) and PhT(polym)) and (magnetic, PhT(mag)) transformation peaks

4.9.10 Other Fe-Based Multi-Component Alloys

Badzoshvili et al. (1978), Tavadze et al. (1985) Chomka and Pastor (1983)

Badzoshvili et al. (1978) Tavadze et al. (1985)

Pavlov et al. (1983)

Gordienko et al. (1977)

reference

408 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

0.65 1.7 2

1

0.7 205 233 225–230 230 270–280

780 310–320 470–520 570 205

2 1.5

Fe–C–Cr(3)–Mn(3) Fe–C(0.2)–Cr–Mn(1) (20XG Rus) Fe–C(0.18)–Cr(1.17)– Mn(1.23) Fe–C–Cr–Mn–Mo–Ni Fe–C(0.4)–Cr–Mn(2)– Mo–Ni(2) (40XG2N2M Rus) 0.7

313

1

Fe–C(0.4)–Cr(13)– Mn(18) (40X13G18 Rus)

Fe–C(0.04)–Cr(18.3)– Mn(1.75)–Mo(2.16)– Ni(14.3)–Si(0.39) Fe–C(0.04)–Cr(18.3)– Mn(1.75)–Mo(2.16)– Ni(14.3)–Si(0.39)–H

230 300 330 480 537 611 675–690 470

200 280

550

538–661

Fe–C(0.08)–Cr(24.8)– H–Mn(1.6)–Ni(20.2)– Si(0.7)

Fe–C(0.08)–Cr(24.8)– Mn(1.63)–Mo(0.13)– Ni(20.2)–Si(0.7)–H

35 40 5–10 10–50 30

480 1–8 10–100 20–100 16

6

1.5 2–8 2 10 18 2 30–90 40–50

0.4 3–30

–

DP –

GB S(C) SK FR DP

– –

–

S(C)

PD(H/?) PD(H) DP(H/dis.) – FR(C) FR(N) PhT(α ↔ γ) SK(C)

–

– –

–

–

– – 1.3 · 10−12 PD(H)

(hydrogenised)

–

235–250 –

85

– –

–

– (in fcc)

– 49

CW

CW

CW

– quen.

–

– quen. 950◦ C

quen.

CW

– f.c.c.

Zielinski and Lunarska (1985), Zielinski (1985) Zielinski (1985), Zielinski and Lunarska (1985) Astafev et al. (1978)

Asano et al. (1977) Zhabo (1984), Golovin et al. (1983b, 1985)

Dowda et al. (1977)

Zoidze et al. (1985) Sarrak et al. (1976)

Verner et al. (1978)

Asano and Oshima (1982)

Asano et al. (1975, 1977)

4.9 Iron and Iron-Based Alloys 409

Fe–C(0.03)–Cr(18–20)– Mn(1–10)–N (0.16–0.38)– Ni(7–16) Fe–C(0.044)–Cr(18.7)– Mn(1.7)–N(0.02)– Ni(2.9)–Si(0.58) Fe–C(0.04–0.08)–Cr(18)– Mn(14)–N(0.2–0.8)–V Fe–C(0.4)–Cr(13)– Mn(1.8)–N(0.4)–V(0.6– 2.8) Fe–C(0.08)–Cr(24.8)– Mn(1.6)–Ni(20.2)–Si(0.7) Fe–C(0.38)–Cr(1.33)– Mn(0.53)–Si(0.25) Fe–C(0.04)–Cr(11)– Mn(0.12)–Si(0.1) Fe–C(0.1)–Cr(24.6)– Mn(0.57)–Ni(0.6)–Ti(0.8)

1

Fe–C(0.04)–Cr(2)– Mn(7)–Mo–V Fe–C(0.1 + 0.77)– Cr(2)–Mn(5)–Mo–V

0.7 0.3 32

325 360 620

500

1

610 390 620 530 830–870 950

550 1000 1000 1.5

480 553–583 600–683 320

8 12 18 28–40 200

4–12

2 15–19 8.5–3 2.5

2–5

590–740

1

τ0 (s) H (kJ mol−1 )

FR(N)

– 2 · 10−12

– 216–226 250

–

–

–

–

–

–

CW

quen. 1050◦ C

annl.

annl.

state of specimen

– S(C) quen. 1110◦ C SK(C) PD(C/Cr/Cr) – (segregat.) GBI

SK(C)

quen., CW

quen.

DP(C, N/dis.) quen. 1150◦ C FR

(relaxation in γ-phase)

–

SK FR FR

mechanism

C and stacking faults – – – FR – – DP

88 150

–

–

40 – – 12 20 – – (carbide boundaries)

Qm −1 (10−4 )

1 670– 630 1.5

433–473 570–670 510–470 250–200

f(Hz) Tm (K)

composition

Table 4.9.10. Continued

Asano and Oshima (1982) Lyubchenko and Stanovskij (1985) Drapkin and Fokin (1980) Belkin et al. (1984)

Verner et al. (1978)

Banov and Parshorov (1980)

Igata et al. (1982c)

Simonova et al. (1977)

Arkhangelskij et al. (1976a)

Aliev et al. (1974a)

reference

410 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1 Fe–C(0.4)–Cr(∼1)– Mo(∼1)–Ni(∼1)–Si(∼1) Fe–C–Cr–Mo–Ni–V 1.3 – 2–6

490–530 490

65 2 3 2

∼250 310 510 570–630

∼1

1.7

1.5 3

∼580 ∼400

0.8

Fe–C(0.35)–Cr(3)– Mo(∼1)–Ni(∼1) (35X3NM Rus) Fe–C(0.01)–Cr(12)– Mo(4)–Ni(9)

Fe–C(0.15)–Cr(2)– Mo(∼1)–Ni(∼1)– P(0.01)(15X2NMPA RUS)

50 30 – 340

473 790 920 710

36

Fe–C(0.14)–Cr(15)– Mo(3)–N–Ni(4)

–

–

155–180

–

145

–

–

2 – 6 – – slope changes

310 353 300 490

Fe–C(0.18)–Cr(1.17)– 0.65 Mn(1.23)–Ti Fe–C(1)–Cr(∼1)– 1000 Mn(∼1)–W(∼1.5) (XVG Rus) Mikhajlov et al. (1989)

quen. 1070◦ C

SK SK

–

quen.

–

Goryushin et al. (1976) Arkhangelskij et al. (1976b)

Astafev et al. (1978)

Golovin et al. (1999, 2000)

Luarsabishvili et al. (1980)

Arkhangelskij et al. (1976b)

quen.

CW

Dowda et al. (1977)

–

quen. 1150◦ C FR SK(C) in martensite PhT(isoth. mart) S(C) – SK GBI(P)

SK FR PhT(α → γ) PhT

S(C) PD(C/Ti) S(C) SK(C)

–

–

–

–

–

–

–

4.9 Iron and Iron-Based Alloys 411

Fe–Cr(18)–Mn(2)– N(0.8)–Ni(8) Fe–C(0.5)–Mn(0.5)– Ni(24)

Fe–Cr(19)–Mn(10)– N(0.38)–Ni(7)

Fe–Cr(15)–H–Mn(12) Fe–Cr(18)–Mn(14)– N(0.3–0.6) Fe–Cr(18)–Mn(7)– N(0.8) Fe–C(0.4)–Cr(13)– Mn(18)–N(0.39) Fe–C(0.4)–Cr(13)– Mn(18)–N(0.55)

Fe–C(0.07)–Cr(16)–Nb– Ni(07X16N4B Rus)

composition

–

1

1

1

1

12

695 1

0.5

22 40 270 2.3 8–25

Qm −1 (10−4 )

49 142

–

138

– 10−13

–

τ0 (s) H (kJ mol−1 )

580 8 120 2 · 10−13 690 17 – – 583 2.3 – – 613 0.1 476 11 – – 538 29 606 10 600–620 ≤5.5 – – 720 ≤4 (split of the FR peak due to Mn and Cr) 740 7 147 1.5 · 10−12 710 35 152 1.9 · 10−12 638 2–8 – –

540 820 1030 310 630–620

f(Hz) Tm (K)

Table 4.9.10. Continued

DP

PD(N/?)

FR(N) – FR(C) FR(N) – FR(C) FR(N) FR FR

SK GB PhT(α → γ) PD(H/H) FR(N)

mechanism

Banov and Parshorov (1980) Gordienko and Tolmachev (1976)

Gordienko et al. (1977)

quen. 1050◦ C aged 750◦ C quen. 1150◦ C quen. CW austenite

Verner et al. (1978)

Asano (1985) Banov et al. (1978a,b) Banov et al. (1978a,b) Verner et al. (1978)

Maksimovich et al. (1981)

of reference

quen.

quen. ageing

quen. 1130◦ C

Austenite quen. 1130◦ C

quen. 1050◦ C

state specimen

412 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

4.10 Co, Ni and their Alloys

413

4.10 Co, Ni and their Alloys In Co, Ni and their alloys the following internal friction eﬀects have been observed: – – – – – – – – – – – – – –

Dislocation Bordoni peaks in pure Ni Dislocation Hasiguti peaks in Co–O, pure Ni Eﬀects of cold work and ferromagnetism in Ni Point defect relaxation in Co–C, Co–N, Ni–C, Ni–Al–C and other alloys, in particular with H Divacancy reorientation in NiAl (B2) Dumb-bell interstitial reorientation in Ni Reorientation of C-pairs in Ni–C; Zener relaxation in Ni3 Al Diﬀusion eﬀects in Ni3 Al and related superalloys Grain boundary relaxation peaks in Co, pure Ni, Ni–Cr, –Zr, –Mo, –Ta, –Ti Phase transformations (magnetic) in Co–O and in Ni–Zn ﬁlms; Phase transformations (martensitic and intermediate phase) in Ni–Mn–Ga Phase transformations (polymorphic, α → β) in Co, Co–Nb, Co–Ni, Co–Re Recrystallisation in Co, Co–Fe, Co–Tb For amorphous alloys see Table 5.2

0.7–6

1

105

Co(99.99)

Co

Co(99.95)

(1–16) · 103

1000

1.3

1.5 – 18

Co–C Co–5Fe

Co–0.69N

Co–1Nb

Co–(2–23)Ni

Co(99.7)

1

f(Hz)

Co(99.99)

Co

composition

215 263 297 810 860 610 − 420 700 − 580 620 − 410

450 550 573 673 553 650

670 750 600 660 560 620 − 640

Tm (K)

600 50 <20 <400

2

20 20

450

100 200

<400

Qm −1 (10−4 )

40.6 31 36.8

159

H (kJ mol−1 )

τ0 (s)

heating heating cooling

state of specimen

PhT(α → β) PhT(α → β) PhT(polym.) PhT(polym.) PhT(polym.)

PD (N/dis)(?)

heating heating cooling

CW CW

GB(?) PhT(α ↔ β) recrystallisation CW PhT (α → β) PD (C/C) quen. 1050◦ C recrystallisation CW

PhT(α → β) PhT (α → β) PhT(α → β) PhT(α → β) PhT(β → α) PhT(α ↔ β)

mechanism

Table 4.10. Co, Ni and their Alloys (wt.% if not speciﬁed diﬀerently)

Sharshakov et al. (1975) Belko et al. (1969a)

Sidorov et al. (1978) Boyarskij et al. (1986) Bouquet and Dubois (1975) Smithells (1976) Bouquet and Dubois (1975) Smithells (1976)

Beloshenko et al. (1978)

Bidaux et al. (1985)

reference

414 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

3 · 104

2 · 104

Ni(99.7)

0.29

0.2

Ni(99.7)

Ni(99.999)

0.3 0.6 0.088 0.971

1.3

Co–5Re

Ni Ni(99.999) Ni(99.88) Ni(99.999)

3

Co–37Ni Co–50at.%O

78–101

81 including magnetic measurem. 73.3 78.1

50 20 2 · 10−13

(5 · 10−14 ) PD(int), disloc. PD dumb-bell interst. rotation DP(PD)

Q−1 decreases in paramagnetic state Q−1 decreases in paramagnetic state DP(int) 3 × 10−16 50 29 PhT(mag) 150 PhT(polym.) PhT(polym.)

2 · 10−15 260 292 7 · 10−15 342 PD(interstitial) 360 100 dumb-bell 322 PD(interstitial) 382 100 dumb-bell dependence on deform., annealing, amplitude 138 DP(B1 ) 10–175 248 50 DP(B2 ) peak height varying with deformation, annealing, grain size ≈22 143 DP(B1 ) ≈20 243 DP(B2 ?) peak height varying with deformation, annealing, orientation

365 370 333 348

1370–1300 1140 109 253 840 900

SC, CW

CW

SC

PC, annl.

Venkatesan and Beshers (1970), Beshers and Gottschall (1975)

Sommer and Beshers (1966)

Seeger and Wagner (1965)

PC, CW(4%) Turner and PC, CW(19%) De Batist (1964) PC, CW(15%) Wagner et al. (1964)

Belko et al. (1969b) Belko et al. (1969b) Postnikov et al. (1976) Sharshakov et al. (1975)

4.10 Co, Ni and their Alloys 415

115 PC, 10–60 10.6 4.4 · 10−14 DP(B1 ) non140 15.9 4.3 · 10−14 dissoc. disloc. 200 DP(B1 ) on 2–50 37.6 10−14 260 41.5 7.1 · 10−14 dissociat. disloc. peak height varying with deformation, annealing, magnetic ﬁeld PC, 330 zero applied magnetic ﬁeld ferromagn. 200 appl. magn. ﬁeld 39 kA/m peak PC, 120 zero applied magnetic ﬁeld DB(B1 ) 120 appl. magn. ﬁeld 39 kA/m 17.4 10−10 DP(B1 ) PC, 38 15–7 4.92 10−7 DP(B2 ) 85 30–12 17.4 10−10 240 30–18 280 36–18 PD(self-interst.) 350 30–23 120 25 125 37 DP(B2 ) 135 43

3 · 104

2.2

3.1 · 104

Ni(99.99), Ni(99.95)

Ni(99.99)

Ni(99.95)

CW

(0.7–4) · 106

DP(P1 ) DP(P2 ) DP(P3 ) GB

Ni(99.998)

340

5 · 10−14 3 · 10−11 10−12 3.7 · 10−24

1.4

30 52 69 306

Ni(99.993)

Cordea and Spretnak (1966) Besson and Boch (1978), Besson and Petit (1979)

Hasiguti et al. (1962)

reference

CW, annl. Tanaka et al. (1981a)

CW(1.6%) Tanaka et al. (1980b) CW(3.2%)

CW

state of specimen

130 350 375 700

mechanism

720

τ0 (s) H (kJ mol−1 )

Ni(99.99)

Qm −1 (10−4 )

f(Hz)

composition

Tm (K)

Table 4.10. Continued

416 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

10

0.1

NiAl (B2)

10

Ni3 Al(γ − γ )

Ni3 Al + Co, Cr, . . . (AM 1)

0.1

10−4 –70

1197 1220 1253 1250

870 1050 887 937 956 1000

45 115 >220 250

102 –104

Ni microcryst grain size 100 nm

Ni nanocryst. gr. size 10–30 nm Ni–Al(24.5) (at.%) Ni–Al(25.1) (at.%) Ni–Al(25.8) (at.%) Ni–Al(26.1) (at.%) Ni–Al(26.4) (at.%) Ni3 Al(γ )

725

1

Ni(99.99)

100 175 240

320 ≈50 27 58 67 45

7 → 3.5 → 1.5 13 → 7 → 3 9.5 → 8.5 → 6 10 → 45

280

318 264 257 257 257 297 347–405

4.9 14.5 46.3 45.3

134

dislocation movement DP(B1 ) DP(B2 ) DP (Hasiguti?) diﬀusion along f. grain boundaries PD(Al)

disloc. climb by vacancies

2.0 · 10−18 1.6 · 10−16 4.3 · 10−16 4.0 · 10−16 3.7 · 10−16 Z 4 · 10−18 3 · 10−18–32 diﬀusion of Ni thermoelastic eﬀect due to chemical gradient between γ and γ phases

1.8 · 10−9 5 · 10−4 1.7 · 10−13 2 · 10−13

10−11

Numakura and Nishi (2006)

SC

PC, nonperiodic (grain size 100 µm) Hirscher et al. (1996)

SC (L12 order) Gadaud and Chakib (1993) SC superalloy Gadaud and periodic distrib. Rivi`ere (1996) of precipitates (1 µm)

annl. 1273 K

→CW

Rivi`ere et al. (1985) CW → Zolotukhin et al. annl. 300◦ C → (1996) annl. 800◦ C

4.10 Co, Ni and their Alloys 417

1283 1343 1300 1343

4 · 103

Ni3 Al near γ matrix material 4 · 103

1293

4 · 103

Ni(79)–Al(7)–Mo(14) (R 4) Ni3 Al 299 260 273

297 257

550 420 1293 1373

0.5 0.9 4 · 103 5 · 104

Ni–Al(2)–C(0.5)

Ni(61,1)–Al(5.7)–Cr, Re, W, Mo, Co, Ta (CMSX–4)

232

900–1000 3–88 950 3

10

5 · 10−16 10−13 10−15

Hermann et al. (1996)

Al diﬀusion on Al or Ni sites, antisite atoms Ni diﬀusion on Ni sublattice other diﬀusion mechanism Al diﬀusion Ni diﬀusion other diﬀusion mechanism

PC, near γ, precipitation-free

SC, L12 (near γ )

SC (γ + < 5%γ )

SC (γ + 70%γ )

Brossmann et al. (2000)

Schaible et al. (1999)

reference

10−16 10−13

SC, PC SC

SC, various orientations

state of specimen

Smithells (1976)

mechanism

3.3 · 10−16 PD (reorient. of divacanies on Ni sublattice PD (thermal and 3.7 · 10−15 structural vac., antisite atoms PD(S)

τ0 (s) Qm −1 H (10−4 ) (kJ mol−1 )

Ni47–59 Al53–4 (B2) Ni53 Al47

Tm (K) 235

f(Hz)

Ni50−x Al50+x (B2)

composition

Table 4.10. Continued

418 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

42.3–43.2

10−12 –10−14 PD(H)

1.3 · 10−14 1.1 · 10−16

247 282

55 55

240–260 10–20 265–225

annl. 964 K annl. 1073 K

9.6 · 10−16 3.2 · 10−16

249 257

30 30

Ni–C(1.87)– 500 Cr(20)–Fe(46)–H

heating annl. 1073 K

1.5 · 10−16 4 · 10−16

278 270

PD(S) quen. PD (reorientat. SC, 111 stress axis of C-pairs) SC, 100 axis heating annl. 1073 K

PD (reorientat. PC of C-pairs

SC, PC

0 60–120 120

865

3.6 · 10−16

3.6 · 10−16

DP and PD

149

34.8

∼10−15 286 (PC) 288 SC 111

20–30

Ni(44.7)–Co(23.2)– 0.016 Cr(19.2)–Al(8.1)– Y(0.5)–Ta(4.3) Ni(52.7)–Co(16.5)– Cr(10.2–Al(17.0)– Ta(3.6) (wt%) (β phase) Ni(39.4)Co(26.0)– Cr(25.4)–Al(5.1)– Ta(1.2), wt% (γ phase)

Ni–C Ni–C

532 740 500 520

1.6 4 · 104 0.5 1

100 80111 40110 10001 8.2 0.57

Ni(99.99)–C(0.5) (wt%)

∼980

0.6–2.5

Ni75 Al24 Ta

Seki and Asano (1984)

Gadaud et al. (1993)

Smithells (1976) Numakura et al. (1996a)

Diamond and Wert (1967)

Mourisco et al. (1996)

4.10 Co, Ni and their Alloys 419

2

1

1

Ni–Mn(24.3)– Ga(26), at.%

Ni(51)–Mn(25)– Ga(24) (at.%)

Ni(51)–Mn(31)– Ga(18) (at.%)

Ni–Cr(20–33) (at.%) 2300 400

193 (cool) ∼1600 ∼1000 208 Qm −1 depends on heating rate ∼400 393 (c) ∼1000 423 (h)

140 240

10−14

annl. 1323/1173 K PC, gr.size 80 µm

state of specimen

PhT(mart)

PhT(mart)

SC and PC; annl. 1200 K PhT(mart) SC PhT(intermediate phase)

PD(C)

∼1100 0.3–3 200–700 heat./cool. hysteresis GB suppressed by Cr7 C3 GB particles: dissolution/precipitation hysteresis ∼950 10–30 Z 0.3–3 280

1.68

Ni–Cr(8.6–33) (at.%)

2–10

800–1070 GB 2 ≤400 ∼1100 heat./cool. hysteresis 1.4 GB depending on number of thermal cycles under oxygen contamination

600–650

Ni–Cr(0.5–19.5) Ni–Cr(20)

mechanism

0.3–3.0

τ0 (s) H (kJ mol−1 )

Ni–Cr(16.8)– Fe(8.1)–C(0.04)

Qm −1 (10−4 )

f(Hz)

composition

Tm (K)

Table 4.10. Continued

Segu´ı et al. (2004)

Segui et al. (1996), Cesari et al. (1997) Segu´ı et al. (2004)

Cao et al. (1994)

Cao et al. (1994, 1996)

Smithells (1976) Cao et al. (1993)

Ivanchenko et al. (2006)

reference

420 4 Internal Friction Data of Crystalline Metals and Alloys (Tables)

1

433 (c) 463 (h) 550

∼600 ∼700 0.1

720 5 870–970 Ni–Cr(3.5) ∼2.7 1023 450 Ni–Cr(13) ∼2.7 1048 360 Ni–Cr(22) ∼2.7 1093 370 Ni–Mo(1) ∼2.7 1103 530 Ni–Mo(5) ∼2.7 1130 400 Ni–Mo(10) ∼2.7 1156 200 Ni–Ta(0.2) ∼2.7 1083 640 Ni–Ta(2.2) ∼2.7 1133 680 Ni–Ti(0.9) ∼2.7 1013 470 Ni–Ti(2.7) ∼2.7 1048 440 Ni–Ti(6.9) ∼2.7 1040 200 for Ni–Ti-based alloys see Ti–Ni (Table 4.5)

106 –109 Ni–Zn ﬁlm (Ni0.4 Zn0.6 Fe2 O4 ) Ni–Zr(0.1–0.5) 1

Ni(58)–Mn(16)– Ga(26) (at.%)

2.79 2.88 2.96 3.1 3.24 3.32 3.1 3.2 2.83 2.88 2.92

GB 2 · 10−13 1 · 10−14 2 · 10−14 1 · 10−15 1 · 10−15 0.9 · 10−15 1 · 10−15 4 · 10−15 1.6 · 10−15 2.5 · 10−15 0.8 · 10−15

GB

PhT(mag)

PhT(mart)

Gridnev and Kushnareva (1990)

Smithells (1976)

Murthy (2002)

Segu´ı et al. (2004)

4.10 Co, Ni and their Alloys 421

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Index

α (primary) relaxation, 98, 102, 104–106, 110 activation energy spectrum model, 101, 107 activation enthalpy, 6 activation parameters for Bordoni relaxation, 55, 60, 61 for Finkelshtein–Rosis rel., 28, 29 for grain boundary rel., 78–82 for Hasiguti relaxation, 52, 53, 55, 62–64 for quasicrystals, 116, 117 for Snoek relaxation, 15–18 for Snoek–K¨ oster relaxation, 68–71 for Zener relaxation, 33–35 allotropic transformation, 129 amorphous alloys, 42–48, 97–113 amorphous structures, 96–113 amplitude dependence of IF (general), 7, 8, 51, 77 by dislocations (deformation), 136–142 by martensitic transformation, 125 in amorphous alloys, 113 anelastic relaxation, 3 due to dislocations, 50–77 due to magnetic eﬀects, 144–148 due to point defects, 11–49 due to thermelasticity, 87–95 hydrogen-induced, 37–48 mechanisms (in general), 11, 12 of non-equilibrium grain boundaries, 84

approximants, 113, 119 Arrhenius equation, 5, 107 athermal long-range interaction, 141 attempt frequency, 6 attenuation coeﬃcient, 10 β (secondary) relaxation, 98, 106, 110, 111 background high temperature b.gr., 51, 76, 77, 116 low temperature b.gr., 51, 74, 116 Bergman clusters, 118 Bordoni peak, 51–61 activation parameters, 55, 60, 61 annealing eﬀect, 57 crystal orientation eﬀect, 57 deformation eﬀect, 52 impurity eﬀect, 56 in bcc metals, 51, 52, 54–56 in fcc metals, 51, 52, 55, 57 in hcp metals, 51, 53, 55 irradiation eﬀect, 57 lattice eﬀect, 58 mechanism, 58–61 relaxation parameters, 55, 59–61 relaxation time, 59, 60 signature, 61 bulk metallic glasses, 100, 104 cellular metallic materials, 154 chemical short range order, 101 climb of jogs, 51, 74, 75, 80

536

Index

complex structures, 95, 119 concentrated solid solutions, 27, 42 coupled processes, 46 coupling model, 71, 98 crystallisation peak, 103 Cu-based MT-alloys, 126 cyclic loading, 144 damping by magnetic transformations, 130–132 hysteretic d., 7, 137, 145 macroeddy current d., 145 magnetoelastic d., 145–147 microeddy current d., 145 non-linear d., 7 viscous d., 7 damping capacity, 1, 8 Debye relaxation peak, 5, 6, 88, 93, 101, 146 decagonal quasicrystals, 113, 117 deformation peaks in amorphous structures, 111–119 in crystals, 50, 136–144 devitriﬁcation, 84, 117 diﬀusion, 101, 111 of point obstacles, 138 dilute alloys, 26 directed diﬀusion, 11 directional structural relaxation, 97, 102, 103, 111 dislocation breakaway, 138 dislocation climb (jogs), 50, 51, 74, 75, 80 dislocation concept for amorphous structures, 112 dislocation drag, 137 dislocation-enhanced Finkelsthein– Rosin eﬀect, 73 dislocation-enhanced Snoek eﬀect, 51, 53, 54, 71–73 dislocation in quasicrystals, 114 dislocation interaction with foreign solute atoms, 51 with intrinsic point defects, 50 dislocation movement controlled by diﬀusion, 76, 77, 84 thermally activated, 139 dislocation relaxations, 50–77, 79, 136–144

dislocation string model, 68, 139, 140 dislocations, 50, 68, 79, 138 dislocations at precipitates, 135 dislocations moving with Cottrellatmospheres, 76, 128 displacement chains, 101 double kink nucleation, 58 dynamic hysteresis, 5 dynamic modulus, 4 elastic dipole, 12–14, 21–23, 114 experimental techniques, 8–10 fatigue, 142–144 Fe-based MT-alloys, 127 Fermi–Dirac statistics, 41 ﬁctive temperature, 99 Finkelshtein–Rosin relaxation, 28–30 fragility parameter, 98 free volume, 101, 112 glass transition, 97, 104–110 Gorsky relaxation, 11, 38, 88, 96 intercrystalline G.r., 45, 88 relaxation strength, 38 relaxation time, 39 grain boundary dislocations, 80 grain boundary migration, 83 grain boundary relaxation, 75, 78–82, 84 activation parameters, 81, 82 eﬀect of misorientation, 81 non-equilibrium gr.b., 84 grain boundary sliding, 76, 79, 84 models, 81 Granato–L¨ ucke plot, 140 Guinier–Preston zones, 134 Hasiguti peaks, 51–53, 55, 62–64, 138 activation parameters, 55, 64 annealing eﬀect, 63 deformation eﬀect, 62 impurity eﬀect, 63 in bcc metals, 54 in fcc metals, 52 in hcp metals, 53 lattice eﬀect, 62 mechanisms, 63, 64 signatures, 64

Index Hidamets with, 148–155 easily moveable dislocations, 153 extremely high H concentr., 154 highly heterogeneous struct., 152 magnetic domains, 153 nanostructure, 154 porous cellular structure, 154 thermoelastic martensite, 152 hierarchically constrained dynamics, 100 high temperature background, 76 high-damping materials (Hidamets), 147–155 hydride precipitation/dissolution, 47, 136 hydrogen as a probe, 118 hydrogen peaks in amorphous structures, 111 in quasicrystals, 115, 116, 118 hydrogen storage, 115 hyperlattice construction of quasicrystals, 113, 114 hysteretic eﬀects by athermal interaction, 141 by dislocation breakaway, 138, 141 by phase transformations, 121–136 by plastic deformation, 51 in fatigue, 142 icosahedral quasicrystals, 42, 113, 118, 119 ideal Hookean elastic solid, 2 ideal Newtonian viscous ﬂuid, 2 intercrystalline Gorsky relaxation, 45, 88 interface movement diﬀusion-controlled, 136 interface relaxation, 135 intermetallic compounds, 35, 42, 81 internal friction (IF) background at high temperatures, 51, 76, 77 at low temperatures, 51, 74 at medium temperatures, 74–76 internal friction (IF) experiments, 8–10 interstitial atoms, 51, 65 interstitialcy theory, 101 intracrystalline thermoelast. rel., 90 inverse Hall–Petch relation, 84

537

irreversible structural relaxation, 100, 102, 107 isothermal Martensitic transf., 122, 128 kink model parameters, 60, 61 kink pair nucleation model, 59, 69 kinks in dislocations, 50, 51, 55, 59, 69, 74, 76 Kohlrausch–Williams–Watts fct., 98, 100, 101 KWW exponent, 108, 110 λ-tensor, 12, 14, 21–23 linear viscoelasticity, 2 loss angle, 4 loss compliance, 106 loss factor, 1 loss modulus, 4, 105 loss tangent, 4 low energy excitations, 111 low temperature background, 51, 74, 116 Mackay clusters, 118 macro-eddy current damping, 145 magnetic transformations, 130–132 magnetic transition damping, 145 magneto-elastic coupling, 144 magneto-elastic hysteretic damping, 145–147 magnetomechanical damping, 144–147 in amorphous structures, 113 magnetostriction, 144 martensitic transformation, 121–130 athermal m.t., 122 intrinsic m.t. eﬀect, 123 isothermal m.t., 123, 128 magnetic ﬁeld dedendence, 125, 126 non-transient m.t. eﬀect, 123 thermoelastic m.t., 122 transient m.t. eﬀect, 123 Maxwell model, 2, 102, 104, 111 mechanical spectroscopy, 2, 8 melting, 132, 133 metadislocations, 119 metallic glasses, 97–113 Fe-based m.g., 148 micro-eddy current damping, 145 microplasticity, 74

538

Index

modulus absolute dynamic m., 4 loss m., 4 storage m., 4 nanocrystalline materials, 82–86 nano-quasicrystalline structures, 115, 118 nanostructured materials, 83, 154 Newtonian viscous ﬂow, 2, 106 Niblett–Wilks peak, 51–54 NiTi-based MT-alloys, 125, 126 non-crystalline structures, 95, 96, 113 non-equilibrium grain boundaries, 84 non-resonant vibrating-reed techn., 107 ordered solid solutions, 35, 42, 81 paddle oscillators, 95, 107 phase transformations, 121–133 phason defects, 114 phason ﬂip, 114 phason wall, 114 phasons in quasicrystals, 113, 114, 116 phonon relaxation eﬀects, 50 pipe diﬀusion, 74, 81 plastic deformation, 54, 56, 62, 65, 111, 114 severe pl. d., 84, 86 of metallic glasses, 103 point defect relaxation, 11–49 by interstitials in bcc (Snoek), 12–27 by interstitials in fcc, 28–30 by interstitials in hcp, 30–32 by intrinsic point defects, 48 by solute atom pairs, 33–36 polycluster model, 112 polymorphic transformation, 129, 130 polytetrahedral structures, 44 porous metals, 94 precipitation at dislocations, 134 continuous/discontinuous, 135 of hydrides, 47, 136 strengthening, 115 precipitation/dissolution, 133–136 primary (main, α) relaxation, 98, 102, 104–106, 110

quality factor, 1, 9 quasicrystals, 42, 49, 96, 113–118 quasiperiodic crystals, 96 quasiperiodic order, 113 quasi-static tests, 8 reinforcing microparticles, 85 relaxation at interfaces, 135 within precipitates, 135 relaxation by interstitials in bcc metals, 12–27 in fcc metals, 28–30 in hcp metals, 30–32 relaxation centres, 101, 102, 111 relaxation spectra, 6 relaxation strength, 4 for Bordoni relaxation, 59 for dislocation breakaway, 139 for Gorksy relaxation, 38 for Snoek relaxation, 17–24 for thermoelastic eﬀect, 88, 91 for Zener relaxation, 33 relaxation time, 4, 33 for Bordoni relaxation, 59, 60 for glasses, 99, 100 for Gorsky relaxation, 39, 40 for grain boundary rel., 78 for grain boundary sliding, 80 for precipitation damping, 133 for Snoek relaxation, 15–18 for Snoek–K¨ oster relaxation, 68–71 for thermoelastic eﬀect, 88 limit relaxation time, 6, 7 reorientation, 12–23 resonant experiments, 9 reversible structural relaxation, 102, 107 rheological models, 2 secondary (β) relaxations, 98, 106, 110, 111 selection rules for anelasticity, 12, 13 self-interstitials, 48, 49, 101 severe plastic deformation, 84, 86 shape memory alloys, 42, 122, 125, 127, 154 shear band deformation, 103, 112, 113 short-range order, 101

Index chemical, 101 topological, 101 Snoek relaxation, 12–27 activation parameters, 16, 18 concentration dependence, 19, 20 grain size dependence, 24, 25 orientation dependence, 17–19 Snoek–K¨ oster peaks, 46, 53, 138 activation parameters, 68, 70, 71 annealing eﬀect, 65 eﬀect of interstitial conc., 65 eﬀect of substitutional atoms, 68 mechanisms, 68–71 peak temperatures, 66, 67 relaxation time, 68, 71 Snoek–K¨ oster relaxation, 46, 51, 65–71 in bcc metals, 51, 54, 65–68 in hcp metals, 53 Snoek-type relaxation, 14, 24–27, 96, 113 hydrogen-induced, 40–46, 96, 111, 113 in amorphous alloys, 40–46, 96, 113 in concentrated alloys, 27 in dilute alloys, 26 speciﬁc damping capacity, 150, 151 speciﬁc damping index, 150 spin density waves, 132 standard anelastic solid, 4 storage modulus, 4, 105 stretched exponential fct., 98, 100 structural relaxation irreversible str. r., 100, 107 of amorphous metals, 97–113 of nanocrystalline metals, 85

539

reversible str. r., 101, 107 structurally complex alloy phases, 119 subresonant experiments, 9 substitutional solute atoms, 51, 68 superconducting transition, 133 thermal activation, 5, 6 thermoelastic damping in amorphous structures, 96, 103, 116 in heterogeneous materials, 94 in micro-systems, 95 thermoelastic martensite, 87, 122 thermoelastic relaxation, 87–95 topological short range order, 101 transient internal friction, 110 tunneling states, 51 at dislocations, 74 for hydrogen, 41 in amorphous structures, 111, 116 twin boundary relaxation, 47, 82 ultraﬁne grained materials, 86 vacancies, 48 viscosity, 98, 102 viscous damping, 104 viscous ﬂow, 102, 106 Vogel–Fulcher–Tammann eq., 98 Voigt–Kelvin model, 2 wave-propagation experiments, 10 Zener relaxation, 32–36 in precipitating alloys, 134 inﬂuence of ordering, 35 Zener-type relaxation, 45

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