Table Of ContentTopics in Applied Physics Volume 53
Topics in Applied Physics
Founded by Helmut K. V. Lotsch
I Dye Lasers 2nd Ed. Editor: F. P. Schlfer 32 Image Reconstruction from Projections
2 Laser Spectroscopy of Atoms Implementation and Applications
and Molecules. Editor: H. Walther Edilor: G. T. Herman
3 Numerical and Asymptotic Techniques 33 Electrets Editor: G. M. Sessler
in Elcctromagnetics Editor: R. Mittra 34 Nonlinear Methods of Spectral Analysis
2nd Edition. Editor: S. Haykin
Interactions on Metal Surfaces Editor: R. Gamer
35 Uranium Enrichment Editor: S. Villani
Mikbawer Spectroscopy Editor: U. Comer
36 Amorphous Semiconductors
Picture Processing and Digital Filtering
Editor: M. H. Brodsky
2nd Edition. Editor: T. S. lluang
37 Thermally Stimulated Relaxation in Solids
I Integrated Optics 2nd Ed. Editor: T. Tamir Editor: P. Br&mlich
x Light Scattering in Solids 2nd Edition 38 Charge-Coupled Devices Editor: D. F. Barbe
Editor: M. Cardona
39 Semiconductor Devices for Optical
9 Laser Speckle and Related Phenomena Communication. 2nd Ed. Editor: H. Kressel
Editor: J. C. Dainty
40 Display Devices Editor: J. I. Pankove
IO Transient Electromagnetic Fields 41 The Computer in Optical Research
Editor: L. B. Felsen Methods and Applications. Editor: B. R. Frieden
II Digital Picture Analysis Editor: A. Rosenfeld 42 Two-Dimensional Digital Signal Processing I
12 Turbulence 2nd Ed. Editor: P. Bradshaw Linear Filters. Editor: T. S. Huang
13 High-Resolution Laser Spectroscopy 43 Two-Dimensional Digital Signal Processing 11
Editor: K. Shimoda Transforms and Median Filters.
14 Laser Monitoring of the Atmosphere Editor: T. S. Huang
Editor: E. D. Hinkley 44 Turbulent Reacting Flows
I5 Radiationless Processes in Molecules Editors: P. A. Libby and F. A. Williams
and Condensed Phases. Editor: F. K. Fong 45 Hydrodynamic Instabilities and the Transition to
16 Nonlinear Infrared Generation Turbulence
Editor: Y.-R. Shen Editors: H. L. Swinney and J. P. Gollub
I7 Electroluminescence Editor: J. I. Pankove 46 Glassy Metals 1
I8 Ultrashort Light Pulses Editors: H.-J. Giintherodt and H. Beck
Picosecond Techniques and Applications 47 Sputtering by Particle Bombardment I
Editor: S. L. Shapiro Editor: R. Behrisch
I9 Optical and Infrared Detectors 2nd Ed. 48 Optical Information Processing
Editor: R. J. Keyes Fundamentals. Editor: S. H. Lee
20 Holographic Recording Materials 49 Laser Spectroscopy of Solids
Editor: H. M. Smith Editors: W. M. Yen and P. M. Seizer
21 Solid Electrolytes Editor: S. Geller 50 Light Scattering in Solids 11. Basic Concepts and
22 X-Ray Optics. Applications to Solids Instrumentation
Editor: H.-J. Queisser Editors: M. Cardona and G. Gfintherodt
23 Optical Data Processing. Applicalions 51 Light Scattering in Solids III. Recent Results
Editor: D. Casasent Editors: M. Cardona and G. Giintherodt
24 Acoustic Surface Waves Editor: A. A. Oliner 52 Sputtering by Particle Bombardment II
Sputtering of Alloys and Compounds, Electron
25 Laser Beam Propagation in the Atmosphere and Neutron Sputtering, Surface Topography
Editor: J. W. Strohbchn
Editor: R. Behrisch
26 Photoemission in Solids I. General Principles
53 Glassy Metals II. Atomic Structure and Dynamics,
Editors: M. Cardona and L. Ley
Electronic Structure, Magnetic Properties
27 Photoemission in Solids II. Case Studies Editors: H. Beck and H.-J. Giintherodt
Editors: L. Ley and M. Cardona
54 Light Scattering in Solids IV. Electronic Scattering,
28 Hydrogen in Metals 1. Basic Properties Spin Effects, SERS, and Morphic Effects
Editors: G. Alefeld and J. V61kl Editors: M. Cardona and G. Gijntberodt
29 Hydrogen in Metals II 55 The Physics of Hydrogenated Amorphous Silicon I
Application-Oriented Properties Structure, Preparation, and Devices
Editors: G. Alefeld and J. Vijlkl Editors: J.D. Joannopoulos and G. Lucovsky
30 Excimer Lasers 2nd Ed. Editor: Ch. K. Rhodes 56 The Physics of Hydrogenated Amorphous Silicon II
31 Solar Energy Conversion. Solid State Electronic and Vibrational Properties
Physics Aspects. Editor: B. 0. Seraphin Editors: J.D. Joannopoulos and G. Lucovsky
Metals Glassy
II
Atomic Structure dna Dynamics,
Electronic ,erutcurtS Magnetic seitreporP
Edited by H. Beck and H.-J. Gfintherodt
With Contributions by M. yon Allmen H. Beck
P. Chaudhari J. Durand P.H. Gaskell U. Gonser
H.-J. Gfintherodt R. Harris H.-U. Kiinzi
.P Oelhafen R. Preston H. Rudin J.F. Sadoc
F. Spaepen P.J. Steinhardt J.O. Strom-Olsen
J.-B. Suck C.N.J. Wagner
With 681 Figures
galreV-regnirpS
Berlin Heidelberg New York Tokyo 3891
Professor Dr. Hans Beck
Institut de Physique, Universit~ de Neuchfitel, ,1 Rue A.-L. Brequet,
CH-2000 Neuchgtel, Switzerland
Professor Dr. Hans-Joachim Gi~ntherodt
Institut fiir Physik, Universit/it Basel, 82, Klingelbergstral3e
CH-4056 Basel, Switzerland
ISBN 3-540-12787-9 Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN 0-387-12787-9 Springer-Verlag New York Heidelberg Berlin Tokyo
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
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© by Springer-Verlag Berlin Heidelberg 1983
Printed in Germany
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Monophoto typesetting, offset printing and bookbinding: Briihlsche Universit~itsdruckerei, Giessen
2153/3130-543210
Preface
The quantitative treatment of the physical properties of systems which do not
have long-range periodicity is an outstanding challenge in modern fundamental
research in solid-state physics. Metallic glasses offer the unique possibility to
study the disordered state of matter with metallic properties down to the very
lowest temperature. The experimental results obtained for various physical
quantities have greatly stimulated theoretical work in this domain.
On the other hand, some unusual properties of glassy metals, such as high
mechanical ductility, high magnetic permeability, low coercive forces, tem-
perature-independent resistivities and others, make them suitable for industrial
applications. Let us mention foils for magnetic shielding, which are already
available, and applications for transformer materials and tape-recorder heads,
which will soon be on the market. Thus not only physicists, but also
metallurgists, surface chemists, metal engineers and representatives of other
branches of science and development have a strong interest in these materials.
In this volume various experimentalists and theoreticians active in the
field present the state of the art in the following domains of the physics of
metallic glasses:
Structure determination (J. F. Sadoc and C. N.J. Wagner) and modelling
--
(P. H. Gaskell)
M6ssbauer spectroscopy (U. Gonser and R. Preston)
Mechanical properties (H.-U. K/inzi), defects (P. Chaudhari, F. Spaepen,
and P.J. Steinhardt), and vibrational dynamics (J.-B. Suck and H. Rudin)
Laser quenching (M. yon Alhnen)
Electron spectroscopy (P. Oelhafen) and electronic transport at low
temperature (R. Harris and J.O. Strom-Olsen)
Magnetic properties (J. Durand).
A more detailed characterisation of the various contributions is given in the
introductory chapter.
It is a pleasure to thank the authors of these contributions for their
collaboration and their effort to review their domain of research as thoroughly
and concisely as possible.
Neuch~ttel, Basel, April 1983 H. Beck • H.-J. Giintherodt
Contents
1. Introduction. By H. Beck and H.-J. Gfintherodt . . . . . . . . . . 1
1.1 Atomic Structure and Dynamics . . . . . . . . . . . . . . 2
1,2 Electronic Structure and Transport . . . . . . . . . . . . . 3
3.1 Magnetic Properties . . . . . . . . . . . . . . . . . . . . 3
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Models for the Structure of Amorphous Metals
By P.H. Gaskell (With 12 Figures) . . . . . . . . . . . . . . . 5
1.2 Conceptual Models for Amorphous Metals . . . . . . . . . . 7
2.1.1 Microcrystallite Models . . . . . . . . . . . . . . . 7
2.1.2 Dense Random-Packed Hard Sphere Models ...... 8
2.1.3 Amorphous or Noncrystallographi¢ Cluster Models . . l0
a) Noncrystallographic Clusters Based on Tetrahedral
Close Packing . . . . . . . . . . . . . . . . . . 01
b) Stereochemically Defined Models Based on Trigonal
Prismatic Packing . . . . . . . . . . . . . . . . . 21
2.1.4 Random and Designed Models: Similarities and Differences. 31
a) Characteristics of Dense Random-Packed and Stereo-
chemically Defined Models . . . . . . . . . . . . . 14
2.2 Experimental Investigations of the Local Structure of Transition
Metal-Metalloid Glasses . . . . . . . . . . . . . . . . . . 51
2.2.1 Chemical Short-Range Order Around the Metalloid:
M-M Avoidance . . . . . . . . . . . . . . . . . . 61
2.2.2 The Metalloid Coordination Number . . . . . . . . . . 71
2.2.3 The Breadth and Shape of the M-T Distribution .... 91
2.2.4 Macroscopic Physical Properties . . . . . . . . . . . . 20
2.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Modelling the Structure of T-M Glasses Using Random-Packed
and Stereochemically Defined Models . . . . . . . . . . . . 12
2.3.1 Construction of the Initial Model . . . . . . . . . . . 22
a) Random Monatomic Models . . . . . . . . . . . . 22
b) Diatomic Random Models . . . . . . . . . . . . . 23
c) Stereochemically-Defined Models . . . . . . . . . . 23
d) Dislocation Models . . . . . . . . . . . . . . . . 24
2.3.2 Refinement of the Zero-Order Model . . . . . . . . . . 24
a) Energy Minimisation . . . . . . . . . . . . . . . 24
viii Contents
2.3.3 Characterisation of the Topology . . . . . . . . . . . 27
a) Analysis of the Interstice Distribution . . . . . . . . 27
b) Voronoi Polyhedra . . . . . . . . . . . . . . . . 27
c) Local Structural Parameters . . . . . . . . . . . . 27
2.3.4 Anisotropy . . . . . . . . . . . . . . . . . . . . . 28
2.3.5 Validation of the Model: Calculation of Microscopic and
Macroscopic Properties . . . . . . . . . . . . . . . . 28
a) Bond Length Distributions: Termination Broadening 29
b) Thermal Broadening . . . . . . . . . . . . . . . 30
2.4 Models for Transition Metal-Metalloid Glasses . . . . . . . . 31
2.4.1 Dense Random-Packed Models for Binary Alloys .... 31
a) Correlation Functions . . . . . . . . . . . . . . . 31
b) Coordination Numbers and Analyses of Interstice
Distribution Functions . . . . . . . . . . . . . . 36
c) Density . . . . . . . . . . . . . . . . . . . . . 38
2.4.2 Stereochemically-Defined Models . . . . . . . . . . . 38
a) Correlation Functions . . . . . . . . . . . . . . . 38
b) Coordination Numbers, Density and Polyhedron Size
Distributions . . . . . . . . . . . . . . . . . . . 40
c) Extension to Other T-M Alloys . . . . . . . . . . . 42
2.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . 44
2.6 Postscript (July 1983) . . . . . . . . . . . . . . . . . . . 45
References . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3. X-Ray and Neutron Diffraction Experiments on Metallic Glasses
By J. F. Sadoc and C. N. J. Wagner (With 16 Figures) . . . . . . . 51
3.1 Introductory Comments . . . . . . . . . . . . . . . . . . 51
3.2 Diffraction Theory of Amorphous Materials . . . . . . . . . 52
3.2.1 Interference Functions . . . . . . . . . . . . . . . . 52
a) Debye Formula. . . . . . . . . . . . . . . . . . 52
b) Monatomic Glasses . . . . . . . . . . . . . . . . 53
c) Polyatomic Glasses - Partial Interference Functions . 53
d) Determination of the Partial Functions . . . . . . . 55
3.2.2 Radial Distribution Functions and Fourier Transform
Techniques . . . . . . . . . . . . . . . . . . . . . 57
a) Radial Distribution Functions . . . . . . . . . . . 57
b) Partial Radial Distribution Functions . . . . . . . . 58
c) Total Radial Distribution Functions . . . . . . . . . 59
3.2.3 The Bhatia-Thornton Formalism . . . . . . . . . . . 60
a) Number-Concentration Partial Functions . . . . . . 61
b) Properties of the Number-Concentration Partial
Functions . . . . . . . . . . . . . . . . . . . . 62
c) Chemical Short-Range Order in Binary Alloys
Generalized Warren Chemical Short-Range Order
(CSRO) Parameter . . . . . . . . . . . . . . . . 63
stnetnoC IX
3.3 Experimental Diffraction Methods . . . . . . . . . . . . . 65
3.3.1 Variable 20 X-Ray Method . . . . . . . . . . . . . . 66
3.3.2 Correction of the Measured X-Ray Intensities ...... 68
a) Measured Intensity . . . . . . . . . . . . . . . . 68
b) Absorption Correction A(20, E, E') and Polarization
Factor P(20) . . . . . . . . . . . . . . . . . . . 69
c) Atomic Scattering Factor and Multiple Scattering . 70
d) Normalization of the Scattered Intensity . . . . . . . 71
e) Spurious Effects Occurring in Fourier Transformation
Termination Effects . . . . . . . . . . . . . . . . 72
3.3.3 Neutron Diffraction . . . . . . . . . . . . . . . . . 74
a) Some Characteristic Properties of Neutrons ..... 74
b) Neutron Interaction with Matter . . . . . . . . . . 74
3.3.4 Neutron Scattering Amplitude . . . . . . . . . . . . . 75
a) Nuclear and Magnetic Scattering Amplitudes ..... 75
b) Polarized Neutron Beams . . . . . . . . . . . . . 75
c) Nonpolarized Neutron Beams . . . . . . . . . . . 76
d) Polarization Analysis . . . . . . . . . . . . . . . 76
3.3.5 Correction of the Measured Neutron Intensity ...... 77
a) Absorption Correction . . . . . . . . . . . . . . 77
b) Incoherent Scattering and Background . . . . . . . . 77
c) Multiple Scattering . . . . . . . . . . . . . . . . 77
d) Inelastic Scattering and Placzek Correction ...... 77
3.4 Structure of Metallic Glasses . . . . . . . . . . . . . . . . 78
3.4.1 Partial Functions of Metal-Metalloid Glasses ...... 78
a) Combination of X-Ray, Nuclear and Polarized Neutron
Diffraction Data for the Evaluation of the Structure of
an Amorphous Co8o-P2o Alloy . . . . . . . . . . . 78
b) Combination of X-Ray and Neutron Diffraction Data
for the Evaluation of the Structure of an Amorphous
Fe-B Alloy . . . . . . . . . . . . . . . . . . . 80
c) Combination of Three X-Ray Wavelengths Involving
Anomalous Dispersion Corrections of the X-Ray Scatter-
ing Factors for the Evaluation of Partial Functions . 80
3.4.2 Structure of Metal-Metal Glasses . . . . . . . . . . . 82
a) X-Ray and Neutron Structure Investigation of Amorphous
Transition Metal Rare-Earth Metal Alloys ...... 82
b) Isotopic Substitution in an Amorphous CusvZr43 Alloy
for the Determination of the Partial Functions from
Neutron Diffraction Data . . . . . . . . . . . . . 82
c) Isomorphous Substitution of Zr by Hf in Amorphous
Cu60Zr40 and Ni35Zr65 Alloys . . . . . . . . . . . 84
d) Combination of X-Ray and Neutron Scattering for the
Evaluation of Topological and Chemical Short-Range
Order in Ni-Ti Glasses . . . . . . . . . . . . . . 86
x Contents
e) Chemical Short-Range Order in Metal-Metal Glasses 88
3.4.3 Magnetic Structure Determination Using Neutron Diffraction 88
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4. M6ssbauer Spectroscopy Applied to Amorphous Metals
By U. Gonser and R. Preston (With 21 Figures) . . . . . . . . . 93
4.1 How M6ssbauer Spectra are Measured . . . . . . . . . . . 93
4.1.1 Source . . . . . . . . . . . . . . . . . . . . . . . 94
4.1.2 Absorber . . . . . . . . . . . . . . . . . . . . . . 94
4.1.3 Detector . . . . . . . . . . . . . . . . . . . . . . 95
4.1.4 Drive System . . . . . . . . . . . . . . . . . . . . 95
4.1.5 M6ssbauer Spectra . . . . . . . . . . . . . . . . . 96
4.1.6 Scattering Geometry . . . . . . . . . . . . . . . . . 97
4.2 M6ssbauer Parameters . . . . . . . . . . . . . . . . . . 98
4.2.1 Recoil-Free Fraction . . . . . . . . . . . . . . . . . 98
4.2.2 Thermal Shift . . . . . . . . . . . . . . . . . . . . 99
4.2.3 Hyperfine Interactions . . . . . . . . . . . . . . . . 99
a) Isomer Shift . . . . . . . . . . . . . . . . . . . 99
b) Magnetic Splitting . . . . . . . . . . . . . . . . 100
c) Quadrupole Splitting . . . . . . . . . . . . . . . 103
4.3 M6ssbauer Effect as a Microprobe . . . . . . . . . . . . . 104
4.4 M6ssbauer Spectra of Amorphous Metals . . . . . . . . . . 104
4.4.1 Effects Due to the Variation of Metalloid Atoms .... 105
4.4.2 Effects Due to the Variation of Metal Atoms . . . . . . 106
4.4.3 Hyperfine Field Distribution . . . . . . . . . . . . . . 107
4.4.4 Can the Atomistic Structure be Deduced from the Spectral
Structure? . . . . . . . . . . . . . . . . . . . . . 109
4.5 Magnetic Properties . . . . . . . . . . . . . . . . . . . . 115
4.5.1 External Static Fields . . . . . . . . . . . . . . . . 115
4.5.2 External Dynamic Fields . . . . . . . . . . . . . . . 117
4.5.3 Surface Fields (Scattering Method) . . . . . . . . . . . 118
4.6 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6.1 Use of Polarized 7-Radiation . . . . . . . . . . . . . 119
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 122
References . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5. Defects and Atomic Transport in Metallic Glasses
By P. Chaudhari, F. Spaepen, and P.J. Steinhardt (With 13 Figures). 127
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . 127
5.2 Experimental Studies in Atomic Transport Properties ..... 129
5.2.1 General Concepts . . . . . . . . . . . . . . . . . . 129
a) Types of Atomic Transport . . . . . . . . . . . . 129
b) Equilibrium and Isoconfigurational Properties .... 130
Contents XI
5.2.2 Viscosity . . . . . . . . . . . . . . . . . . . . . . 131
a) Experimental Conditions and Techniques . . . . . . 131
b) Equilibrium Measurements . . . . . . . . . . . . . 132
c) Isoconfigurational Measurements . . . . . . . . . . 132
d) Stress-Dependence of the Flow Rate . . . . . . . . . 134
5.2.3 Diffusion . . . . . . . . . . . . . . . . . . . . . . 135
a) Experimental Techniques . . . . . . . . . . . . . 135
b) Diffusivity of the "Smaller" Atoms . . . . . . . . . 135
c) Diffusivity of the "Large" Atoms . . . . . . . . . . 136
d) Scaling of Viscosity and Diffusivity . . . . . . . . . 137
5.2.4 Structural Relaxation . . . . . . . . . . . . . . . . 138
a) Kinetics of the Viscosity Increase . . . . . . . . . . 138
b) Kinetics of the Diff'usivity Decrease . . . . . . . . . 139
c) Relationship Between the Effects of Structural Relaxation
on Different Properties . . . . . . . . . . . . . . 139
5.2.5 Similarity Between the Defects Governing Diffusion
and Flow . . . . . . . . . . . . . . . . . . . . . . 139
5.3 Computer Simulation Studies of Defects and Atomic Transport. 140
5.3.1 General Concepts . . . . . . . . . . . . . . . . . . 140
5.3.2 Computer-Built Models . . . . . . . . . . . . . . . 141
5.3.3 Point Defects . . . . . . . . . . . . . . . . . . . . 142
a) Definition of a Point Defect in Glasses . . . . . . . 143
b) Static Relaxation . . . . . . . . . . . . . . . . . 144
c) Dynamic Relaxation . . . . . . . . . . . . . . . 146
5.3.4 Line Defects - Static Relaxation . . . . . . . . . . . . 151
a) Definition of Line Defects in Glasses . . . . . . . . 151
b) Introducing the Defects in Glasses . . . . . . . . . 152
c) Detection of Dislocation After Relaxation . . . . . . 153
d) Burgers Vector . . . . . . . . . . . . . . . . . . 160
5.3.5 Dynamic Relaxation Studies . . . . . . . . . . . . . 163
5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6. Mechanical Properties of Metallic Glasses
By H.-U. Kiinzi (With 16 Figures) . . . . . . . . . . . . . . . 169
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2 Elasticity of Metallic Glasses . . . . . . . . . . . . . . . . 170
6.2.1 Experimental Techniques . . . . . . . . . . . . . . . 171
6.2.2 Elastic Constants . . . . . . . . . . . . . . . . . . 173
6.2.3 Theoretical Considerations . . . . . . . . . . . . . . 176
6.2.4 Magnetoelastic Behaviour . . . . . . . . . . . . . . 179
a) Isotropic Effects . . . . . . . . . . . . . . . . . 180
b) Anisotropic Effects . . . . . . . . . . . . . . . . . 181
c) The AE Effect . . . . . . . . . . . . . . . . . . 183
d) Experimental Results for the AE Effect . . . . . . . 186
