Handbook of Electrical Steel

792 Pages·2021·31.685 MB·English

by  Goran Engdahl

HANDBOOK OF
ELECTRICAL
STEEL
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HANDBOOK OF
ELECTRICAL
STEEL
Göran Engdahl
The KTH Royal Institute of Technology, Sweden
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
1122000077__99778899881111222266991155__TTPP..iinndddd 22 2211//99//2211 88::1177 AAMM
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HANDBOOK OF ELECTRICAL STEEL
Copyright © 2022 by World Scientific Publishing Co. Pte. Ltd.
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September17,2021 13:33 HandbookofElectricalSteel-9inx6in b3998-fm pagev
Contents
Preface xvii
Concluding Remarks xxiii
Acknowledgements xxv
Chapter 1. A Brief Introduction to Magnetism
and Magnetic and Electric Fields 1
1.1 History of Magnetism . . . . . . . . . . . . . . . . . . . 1
1.2 Some Basic Electromagnetism . . . . . . . . . . . . . 3
1.2.1 The magnetic induction field. . . . . . . . . 3
1.2.2 The electric field . . . . . . . . . . . . . . . . 8
1.2.3 The electric dipole moment and the
displacement field . . . . . . . . . . . . . . . . 10
1.2.4 Magnetic moments . . . . . . . . . . . . . . . 12
1.2.5 Magnetic moments and the magnetizing
field . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.6 The magnetization field . . . . . . . . . . . . 17
1.2.7 The demagnetizing field . . . . . . . . . . . . 19
1.2.8 The Maxwell’s equations . . . . . . . . . . . 24
1.2.9 Magnetic field calculations . . . . . . . . . . 25
1.2.10 Material laws . . . . . . . . . . . . . . . . . . . 28
1.2.11 Electric and magnetic potentials . . . . . . 30
1.2.12 Electromotive and magnetomotive
forces . . . . . . . . . . . . . . . . . . . . . . . . 33
v
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vi Handbook of Electrical Steel
1.2.13 Dielectric and magnetic media
boundaries . . . . . . . . . . . . . . . . . . . . 37
1.2.14 The magnetic field outside and inside
magnetic materials . . . . . . . . . . . . . . . 42
1.2.15 Magnetic forces and magnetic energy . . . 45
1.2.16 Some thermodynamics of magnetic
materials . . . . . . . . . . . . . . . . . . . . . 56
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter 2. The Quantum Mechanical Nature
of Magnetic Material 61
2.1 Some Basic Quantum Mechanics . . . . . . . . . . . 67
2.2 Electron Spin and Orbitals . . . . . . . . . . . . . . . 72
2.3 The Free-Electron Model . . . . . . . . . . . . . . . . 82
2.4 Atomic Magnetism . . . . . . . . . . . . . . . . . . . . 89
2.4.1 The one-electron atom . . . . . . . . . . . . . 89
2.4.2 Addition of angular momenta
of the electrons . . . . . . . . . . . . . . . . . 95
2.4.3 Curie law of paramagnetism . . . . . . . . . 97
2.4.4 Pauli susceptibility . . . . . . . . . . . . . . . 98
2.4.5 Several electron atoms . . . . . . . . . . . . . 100
2.4.6 Spin–orbit coupling . . . . . . . . . . . . . . . 115
2.4.7 Theory of electronic magnetism . . . . . . . 117
2.5 Magnetism and Relativity . . . . . . . . . . . . . . . . 119
2.6 Zeeman Interaction . . . . . . . . . . . . . . . . . . . . 121
2.7 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . 124
2.8 Molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.8.1 Solid materials . . . . . . . . . . . . . . . . . . 140
2.9 Covalent solids . . . . . . . . . . . . . . . . . . . . . . . 141
2.9.1 Ionic crystals . . . . . . . . . . . . . . . . . . . 142
2.9.2 Hydrogen-bond solids . . . . . . . . . . . . . 143
2.9.3 Molecular solids . . . . . . . . . . . . . . . . . 143
2.9.4 Metals . . . . . . . . . . . . . . . . . . . . . . . 144
2.10 Magnetism of Electrons in Solids . . . . . . . . . . . 146
2.11 Some Basic Solid State Physics . . . . . . . . . . . . 147
2.11.1 Crystal lattices. . . . . . . . . . . . . . . . . . 147
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Contents vii
2.11.2 Miller indices and crystal directions . . . . 152
2.11.2.1 Some simple closed-packed
structures . . . . . . . . . . . . . . 156
2.11.3 Reciprocal space. . . . . . . . . . . . . . . . . 157
2.11.4 Brillouin zones . . . . . . . . . . . . . . . . . . 161
2.11.5 Band theory of solids . . . . . . . . . . . . . 163
2.11.5.1 General features of energy band
of electrons . . . . . . . . . . . . . 163
2.11.6 Electron motion in periodic structures . . 167
2.11.6.1 Energy band gaps
and overlap . . . . . . . . . . . . . 177
2.12 Electrical Conductivity . . . . . . . . . . . . . . . . . . 180
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Chapter 3. Ferromagnetism 187
3.1 Mean Field Theory . . . . . . . . . . . . . . . . . . . . 188
3.2 The Landau Theory . . . . . . . . . . . . . . . . . . . . 192
3.3 The Stoner Criterion . . . . . . . . . . . . . . . . . . . 194
3.4 Exchange Interactions . . . . . . . . . . . . . . . . . . 196
3.5 Other Ordered Magnetism. . . . . . . . . . . . . . . . 202
3.5.1 Antiferromagnetism . . . . . . . . . . . . . . 203
3.5.2 Ferrimagnetism . . . . . . . . . . . . . . . . . 205
3.5.3 Miscellaneous ordering. . . . . . . . . . . . . 208
3.5.3.1 Frustration. . . . . . . . . . . . . . 208
3.5.3.2 Amorphous magnets . . . . . . . 209
3.5.3.3 Spin glass . . . . . . . . . . . . . . 211
3.6 Crystal-field Interaction . . . . . . . . . . . . . . . . . 215
3.7 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . 217
3.7.1 Crystalline magnetic anisotropy . . . . . . . 217
3.7.2 Shape anisotropy . . . . . . . . . . . . . . . . 223
3.7.3 Induced anisotropy . . . . . . . . . . . . . . . 224
3.8 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . 224
3.8.1 Other magnetoelastic effects . . . . . . . . . 226
3.9 Ferromagnetic Domains . . . . . . . . . . . . . . . . . 227
3.9.1 Introduction . . . . . . . . . . . . . . . . . . . 227
3.9.2 Micromagnetic energies . . . . . . . . . . . . 231
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viii Handbook of Electrical Steel
3.9.2.1 Exchange energy . . . . . . . . . . 232
3.9.2.2 Anisotropy energy . . . . . . . . . 234
3.9.2.3 Demagnetizing energy . . . . . . 235
3.9.2.4 Strain energy . . . . . . . . . . . . 236
3.9.2.5 Magnetostriction energy . . . . . 237
3.9.2.6 Minimization of the
micromagnetic energy. . . . . . . 237
3.9.3 Domain walls . . . . . . . . . . . . . . . . . . . 240
3.9.3.1 The Bloch wall . . . . . . . . . . . 240
3.9.3.2 The N´eel wall . . . . . . . . . . . . 243
3.10 The Stoner–Wohlfarth Model. . . . . . . . . . . . . . 251
3.11 The Nucleation Field . . . . . . . . . . . . . . . . . . . 258
3.12 Domain-Wall Motion . . . . . . . . . . . . . . . . . . . 258
3.13 Examples of Real Hysteresis Loops . . . . . . . . . . 263
3.14 Long-Term Magnetization Features . . . . . . . . . . 268
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Chapter 4. Magnetic Materials 271
4.1 Soft Magnetic Materials . . . . . . . . . . . . . . . . . 273
4.1.1 Soft magnetic material characterizing
quantities . . . . . . . . . . . . . . . . . . . . . 273
4.1.1.1 Coercivity . . . . . . . . . . . . . . 275
4.1.1.2 Permeability. . . . . . . . . . . . . 275
4.1.1.3 Remanence . . . . . . . . . . . . . 278
4.1.1.4 Linearity and hysteresis . . . . . 279
4.1.1.5 Losses . . . . . . . . . . . . . . . . . 280
4.2 Available Materials . . . . . . . . . . . . . . . . . . . . 280
4.2.1 Soft magnetic material classification . . . . 280
4.2.2 Pure iron . . . . . . . . . . . . . . . . . . . . . 284
4.2.3 Conventional grain-oriented (CGO) SiFe
steel. . . . . . . . . . . . . . . . . . . . . . . . . 287
4.2.4 High permeability grain-oriented electrical
steel HiB . . . . . . . . . . . . . . . . . . . . . 291
4.2.5 Non-oriented electrical steel NO . . . . . . 294
4.2.6 Special iron-based alloys . . . . . . . . . . . 297
4.2.6.1 Rapid solidification . . . . . . . . 297
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Contents ix
4.2.6.2 The CVD process . . . . . . . . . 297
4.2.6.3 Alternative texture . . . . . . . . 299
4.2.6.4 Alternative to silicon . . . . . . . 300
4.2.7 Nickel and Cobalt-based alloys . . . . . . . 301
4.2.7.1 NiFe alloys . . . . . . . . . . . . . . 301
4.2.7.2 Permendur and Perminvar. . . . 304
4.2.8 Amorphous magnetic materials . . . . . . . 305
4.2.9 Nanocrystalline materials . . . . . . . . . . . 310
4.2.10 Soft ferrites . . . . . . . . . . . . . . . . . . . . 312
4.3 Hard Magnetic Materials . . . . . . . . . . . . . . . . 315
4.3.1 Hard magnetic material characterizing
quantities . . . . . . . . . . . . . . . . . . . . . 315
4.3.1.1 Remanent magnetization. . . . . 316
4.3.1.2 Saturation magnetization . . . . 316
4.3.1.3 Coercivity . . . . . . . . . . . . . . 316
4.3.1.4 The maximum energy
product . . . . . . . . . . . . . . . . 316
4.3.1.5 Squareness coefficient . . . . . . . 318
4.3.1.6 Orientation coefficient . . . . . . 320
4.3.1.7 Recoil curves and maximum
working field . . . . . . . . . . . . 320
4.3.1.8 The Curie temperature and
temperature coefficients . . . . . 321
4.4 Available Materials . . . . . . . . . . . . . . . . . . . . 322
4.4.1 Hard magnet classification . . . . . . . . . . 322
4.4.2 Alnico magnet alloys . . . . . . . . . . . . . . 327
4.4.3 Hard magnetic ferrites . . . . . . . . . . . . . 328
4.4.4 SmCo magnets . . . . . . . . . . . . . . . . . . 331
4.4.5 NdFeB magnets . . . . . . . . . . . . . . . . . 332
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Chapter 5. Characterization Methods 339
5.1 General Overview . . . . . . . . . . . . . . . . . . . . . 339
5.2 Material Characterization Approaches . . . . . . . . 343
5.2.1 Sheet characterization methods . . . . . . . 345
5.2.2 Ring core measurements . . . . . . . . . . . 347