Introduction to Magnetic Materials, 2nd edition

__Introduction to Magnetic Materials, 2nd Edition__ covers the basics of magnetic quantities, magnetic devices, and materials used in practice. While retaining much of the original, this revision now covers SQUID and alternating gradient magnetometers, magnetic force microscope, Kerr effect, amorphous alloys, rare-earth magnets, SI Units alongside cgs units, and other up-to-date topics. In addition, the authors have added an entirely new chapter on information materials. The text presents materials at the practical rather than theoretical level, allowing for a physical, quantitative, measurement-based understanding of magnetism among readers, be they professional engineers or graduate-level students.Content: Chapter 1 Definitions and Units (pages 1–21): Chapter 2 Experimental Methods (pages 23–86): Chapter 3 Diamagnetism and Paramagnetism (pages 87–114): Chapter 4 Ferromagnetism (pages 115–149): Chapter 5 Antiferromagnetism (pages 151–173): Chapter 6 Ferrimagnetism (pages 175–195): Chapter 7 Magnetic Anisotropy (pages 197–239): Chapter 8 Magnetostriction and the Effects of Stress (pages 241–273): Chapter 9 Domains and the Magnetization Process (pages 275–333): Chapter 10 Induced Magnetic Anisotropy (pages 335–357): Chapter 11 Fine Particles and Thin Films (pages 359–408): Chapter 12 Magnetization Dynamics (pages 409–438): Chapter 13 Soft Magnetic Materials (pages 439–476): Chapter 14 Hard Magnetic Materials (pages 477–504): Chapter 15 Magnetic Materials for Recording and Computers (pages 505–515): Chapter 16 Magnetic Properties of Superconductors (pages 517–526): Excerpt CHAPTER 1

DEFINITIONS AND UNITS

1.1 INTRODUCTION

The story of magnetism begins with a mineral called magnetite (Fe3O4), the first magnetic material known to man. Its early history is obscure, but its power of attracting iron was certainly known 2500 years ago. Magnetite is widely distributed. In the ancient world the most plentiful deposits occurred in the district of Magnesia, in what is now modern Turkey, and our word magnet is derived from a similar Greek word, said to come from the name of this district. It was also known to the Greeks that a piece of iron would itself become magnetic if it were touched, or, better, rubbed with magnetite.

Later on, but at an unknown date, it was found that a properly shaped piece of magnetite, if supported so as to float on water, would turn until it pointed approximately north and south. So would a pivoted iron needle, if previously rubbed with magnetite. Thus was the mariner's compass born. This north-pointing property of magnetite accounts for the old English word lodestone for this substance; it means "waystone," because it points the way.

The first truly scientific study of magnetism was made by the Englishman William Gilbert (1540–1603), who published his classic book On the Magnet in 1600. He experimented with lodestones and iron magnets, formed a clear picture of the Earth's magnetic field, and cleared away many superstitions that had clouded the subject. For more than a century and a half after Gilbert, no discoveries of any fundamental importance were made, although there were many practical improvements in the manufacture of magnets. Thus, in the eighteenth century, compound steel magnets were made, composed of many magnetized steel strips fastened together, which could lift 28 times their own weight of iron. This is all the more remarkable when we realize that there was only one way of making magnets at that time: the iron or steel had to be rubbed with a lodestone, or with another magnet which in turn had been rubbed with a lodestone. There was no other way until the first electromagnet was made in 1825, following the great discovery made in 1820 by Hans Christian Oersted (1775–1851) that an electric current produces a magnetic field. Research on magnetic materials can be said to date from the invention of the electromagnet, which made available much more powerful fields than those produced by lodestones, or magnets made from them.

In this book we shall consider basic magnetic quantities and the units in which they are expressed, ways of making magnetic measurements, theories of magnetism, magnetic behavior of materials, and, finally, the properties of commercially important magnetic materials. The study of this subject is complicated by the existence of two different systems of units: the SI (International System) or mks, and the cgs (electromagnetic or emu) systems. The SI system, currently taught in all physics courses, is standard for scientific work throughout the world. It has not, however, been enthusiastically accepted by workers in magnetism. Although both systems describe the same physical reality, they start from somewhat different ways of visualizing that reality. As a consequence, converting from one system to the other sometimes involves more than multiplication by a simple numerical factor. In addition, the designers of the SI system left open the possibility of expressing some magnetic quantities in more than one way, which has not helped in speeding its adoption.

The SI system has a clear advantage when electrical and magnetic behavior must be considered together, as when dealing with electric currents generated inside a material by magnetic effects (eddy currents). Combining electromagnetic and electrostatic cgs units gets very messy, whereas using SI it is straightforward.

At present (early twenty-first century), the SI system is widely used in Europe, especially for soft magnetic materials (i.e., materials other than permanent magnets). In the USA and Japan, the cgs–emu system is still used by the majority of research workers, although the use of SI is slowly increasing. Both systems are found in reference works, research papers, materials and instrument specifications, so this book will use both sets of units. In Chapter 1, the basic equations of each system will be developed sequentially; in subsequent chapters the two systems will be used in parallel. However, not every equation or numerical value will be duplicated; the aim is to provide conversions in cases where they are not obvious or where they are needed for clarity.

Many of the equations in this introductory chapter and the next are stated without proof because their derivations can be found in most physics textbooks.

1.2 THE cgs–emu SYSTEM OF UNITS

1.2.1 Magnetic Poles

Almost everyone as a child has played with magnets and felt the mysterious forces of attraction and repulsion between them. These forces appear to originate in regions called poles, located near the ends of the magnet. The end of a pivoted bar magnet which points approximately toward the north geographic pole of the Earth is called the north-seeking pole, or, more briefly, the north pole. Since unlike poles attract, and like poles repel, this convention means that there is a region of south polarity near the north geographic pole. The law governing the forces between poles was discovered independently in England in 1750 by John Michell (1724–1793) and in France in 1785 by Charles Coulomb (1736–1806). This law states that the force F between two poles is proportional to the product of their pole strengths p1 and p2 and inversely proportional to the square of the distance d between them:

F = k p1p2/d2. (1.1)

If the proportionality constant k is put equal to 1, and we measure F in dynes and d in centimeters, then this equation becomes the definition of pole strength in the cgs–emu system. A unit pole, or pole of unit strength, is one which exerts a force of 1 dyne on another unit pole located at a distance of 1 cm. The dyne is in turn defined as that force which gives a mass of 1 g an acceleration of 1 cm/sec2. The weight of a 1 g mass is 981 dynes. No name has been assigned to the unit of pole strength.

Poles always occur in pairs in magnetized bodies, and it is impossible to separate them. If a bar magnet is cut in two transversely, new poles appear on the cut surfaces and two magnets result. The experiments on which Equation 1.1 is based were performed with magnetized needles that were so long that the poles at each end could be considered approximately as isolated poles, and the torsion balance sketched in Fig. 1.1. If the stiffness of the torsion-wire suspension is known, the force of repulsion between the two north poles can be calculated from the angle of deviation of the horizontal needle. The arrangement shown minimizes the effects of the two south poles.

A magnetic pole creates a magnetic field around it, and it is this field which produces a force on a second pole nearby. Experiment shows that this force is directly proportional to the product of the pole strength and field strength or field intensity H:

F = kpH. (1.2)

If the proportionality constant k is again put equal to 1, this equation then defines H: a field of unit strength is one which exerts a force of 1 dyne on a unit pole. If an unmagnetized piece of iron is brought near a magnet, it will become magnetized, again through the agency of the field created by the magnet. For this reason H is also sometimes called the magnetizing force. A field of unit strength has an intensity of one oersted (Oe). How large is an oersted? The magnetic field of the Earth in most places amounts to less than 0.5 Oe, that of a bar magnet (Fig. 1.2) near one end is about 5000 Oe, that of a powerful electromagnet is about 20,000 Oe, and that of a superconducting magnet can be 100,000 Oe or more. Strong fields may be measured in kilo-oersteds (kOe). Another cgs unit of field strength, used in describing the Earth's field, is the ITLγITL (1γ = 10-5 Oe).

A unit pole in a field of one oersted is acted on by a force of one dyne. But a unit pole is also subjected to a force of 1 dyne when it is 1 cm away from another unit pole. Therefore, the field created by a unit pole must have an intensity of one oersted at a distance of 1 cm from the pole. It also follows from Equations 1.1 and 1.2 that this field decreases as the inverse square of the distance d from the pole:

H = p/d2. (1.3)

Michael Faraday (1791–1867) had the very fruitful idea of representing a magnetic field by "lines of force." These are directed lines along which a single north pole would move, or to which a small compass needle would be tangent. Evidently, lines of force radiate outward from a single north pole. Outside a bar magnet, the lines of force leave the north pole and return at the south pole. (Inside the magnet, the situation is more complicated and will be discussed in Section 2.9) The resulting field (Fig. 1.3) can be made visible in two dimensions by sprinkling iron filings or powder on a card placed directly above the magnet. Each iron particle becomes magnetized and acts like a small compass needle, with its long axis parallel to the lines of force.

The notion of lines of force can be made quantitative by defining the field strength H as the number of lines of force passing through unit area perpendicular to the field. A line of force, in this quantitative sense, is called a maxwell. Thus

1Oe = 1 line of force/cm2 = 1 maxwell/cm2.

Imagine a sphere with a radius of 1 cm centered on a unit pole. Its surface area is 4π cm2. Since the field strength at this surface is 1 Oe, or 1 line of force/cm2, there must be a total of 4π lines of force passing through it. In general, 4πp lines of force issue from a pole of strength p.

1.3 MAGNETIC MOMENT

Consider a magnet with poles of strength p located near each end and separated by a distance l. Suppose the magnet is placed at an angle θ to a uniform field H (Fig. 1.4). Then a torque acts on the magnet, tending to turn it parallel to the field. The moment of this torque is

(pH sin θ)(l/2) + (pH sin θ) (l/2) = pHl sinθ

When H = 1 Oe and θ = 90°, the moment is given by

m = pl, (1.4)

where m is the magnetic moment of the magnet. It is the moment of the torque exerted on the magnet when it is at right angles to a uniform field of 1 Oe. (If the field is nonuniform, a translational force will also act on the magnet. See Section 2.13.)

Magnetic moment is an important and fundamental quantity, whether applied to a bar magnet or to the "electronic magnets" we will meet later in this chapter. Magnetic poles, on the other hand, represent a mathematical concept rather than physical reality; they cannot be separated for measurement and are not localized at a point, which means that the distance l between them is indeterminate. Although p and l are uncertain quantities individually, their product is the magnetic moment m, which can be precisely measured. Despite its lack of precision, the concept of the magnetic pole is useful in visualizing many magnetic interactions, and helpful in the solution of magnetic problems.

Returning to Fig. 1.4, we note that a magnet not parallel to the field must have a certain potential energy Ep relative to the parallel position. The work done (in ergs) in turning it through an angle dθ against the field is

dEp = 2(pH sin θ)(l/2)dθ = mH sinθ dθ.

It is conventional to take the zero of energy as the θ = 90° position. Therefore,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5)

Thus Ep is -mH when the magnet is parallel to the field, zero when it is at right angles, and +mH when it is antiparallel. The magnetic moment m is a vector which is drawn from the south pole to the north. In vector notation, Equation 1.5 becomes

Ep = -m · H (1.6)

Equation 1.5 or 1.6 is an important relation which we will need frequently in later sections.

Because the energy Ep is in ergs, the unit of magnetic moment m is erg/oersted. This quantity is the electromagnetic unit of magnetic moment, generally but unofficially called simply the emu.

1.4 INTENSITY OF MAGNETIZATION

When a piece of iron is subjected to a magnetic field, it becomes magnetized, and the level of its magnetism depends on the strength of the field. We therefore need a quantity to describe the degree to which a body is magnetized.

Consider two bar magnets of the same size and shape, each having the same pole strength p and interpolar distance l. If placed side by side, as in Fig. 1.5a, the poles add, and the magnetic moment m = (2p)l = 2pl, which is double the moment of each individual magnet. If the two magnets are placed end to end, as in Fig. 1.5b, the adjacent poles cancel and m = p(2l ) = 2pl, as before. Evidently, the total magnetic moment is the sum of the magnetic moments of the individual magnets.

In these examples, we double the magnetic moment by doubling the volume. The magnetic moment per unit volume has not changed and is therefore a quantity that describes the degree to which the magnets are magnetized. It is called the intensity of magnetization, or simply the magnetization, and is written M (or I or J by some authors). Since

M = m/v, (1.7)

where v is the volume; we can also write

M = pl/v = p/v/l = p/A, (1.8)

where A is the cross-sectional area of the magnet. We therefore have an alternative definition of the magnetization M as the pole strength per unit area of cross section.

Since the unit of magnetic moment m is erg/oersted, the unit of magnetization M is erg/oersted cm3. However, it is more often written simply as emu/cm3, where "emu" is understood to mean the electromagnetic unit of magnetic moment. However, emu is sometimes used to mean "electromagnetic cgs units" generically.

It is sometimes convenient to refer the value of magnetization to unit mass rather than unit volume. The mass of a small sample can be measured more accurately than its volume, and the mass is independent of temperature whereas the volume changes with temperature due to thermal expansion. The specific magnetization σ is defined as

σ = m/w = m/vρ = M/ρ emu/g, (1.9)

where w is the mass and ρ the density.

Magnetization can also be expressed per mole, per unit cell, per formula unit, etc. When dealing with small volumes like the unit cell, the magnetic moment is often given in units called Bohr magnetons, μB, where 1 Bohr magneton = 9.27 × 10-21 erg/Oe. The Bohr magneton will be considered further in Chapter 3.

1.5 MAGNETIC DIPOLES

As shown in Appendix 1, the field of a magnet of pole strength p and length l, at a distance r from the magnet, depends only on the moment pl of the magnet and not on the separate values of p and l, provided r is large relative to l. Thus the field is the same if we halve the length of the magnet and double its pole strength. Continuing this process, we obtain in the limit a very short magnet of finite moment called a magnetic dipole. Its field is sketched in Fig. 1.6. We can therefore think of any magnet, as far as its external field is concerned, as being made up of a number of dipoles; the total moment of the magnet is the sum of the moments, called dipole moments, of its constituent dipoles.
(Continues...) Excerpted from Introduction to Magnetic Materials by B. D. Cullity. Copyright © 2009 by John Wiley & Sons, Ltd. Excerpted by permission of John Wiley & Sons.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site. INTRODUCTION TO MAGNETIC MATERIALS......Page 4 CONTENTS......Page 8 PREFACE TO THE FIRST EDITION......Page 16 PREFACE TO THE SECOND EDITION......Page 19 1.1 Introduction......Page 22 1.2.1 Magnetic Poles......Page 23 1.3 Magnetic Moment......Page 26 1.4 Intensity of Magnetization......Page 27 1.5 Magnetic Dipoles......Page 28 1.6 Magnetic Effects of Currents......Page 29 1.7 Magnetic Materials......Page 31 1.8 SI Units......Page 37 1.9 Magnetization Curves and Hysteresis Loops......Page 39 2.1 Introduction......Page 44 2.2.1 Normal Solenoids......Page 45 2.2.2 High Field Solenoids......Page 49 2.2.3 Superconducting Solenoids......Page 52 2.3 Field Production by Electromagnets......Page 54 2.4 Field Production by Permanent Magnets......Page 57 2.5.1 Hall Effect......Page 59 2.5.2 Electronic Integrator or Fluxmeter......Page 60 2.5.3 Other Methods......Page 62 2.6 Magnetic Measurements in Closed Circuits......Page 65 2.7 Demagnetizing Fields......Page 69 2.8 Magnetic Shielding......Page 72 2.9 Demagnetizing Factors......Page 73 2.10 Magnetic Measurements in Open Circuits......Page 83 2.11.1 Extraction Method......Page 87 2.11.2 Vibrating-Sample Magnetometer......Page 88 2.11.4 Image Effect......Page 91 2.12 Magnetic Circuits and Permeameters......Page 94 2.12.1 Permeameter......Page 98 2.12.2 Permanent Magnet Materials......Page 100 2.13 Susceptibility Measurements......Page 101 Problems......Page 106 3.2 Magnetic Moments of Electrons......Page 108 3.3 Magnetic Moments of Atoms......Page 110 3.5 Diamagnetic Substances......Page 111 3.6 Classical Theory of Paramagnetism......Page 112 3.7 Quantum Theory of Paramagnetism......Page 120 3.7.1 Gyromagnetic Effect......Page 123 3.7.2 Magnetic Resonance......Page 124 3.8.3 Rare-Earth Elements......Page 131 3.8.5 General......Page 132 Problems......Page 134 4.1 Introduction......Page 136 4.2 Molecular Field Theory......Page 138 4.3 Exchange Forces......Page 150 4.4 Band Theory......Page 154 4.5 Ferromagnetic Alloys......Page 162 4.6 Thermal Effects......Page 166 4.7 Theories of Ferromagnetism......Page 167 4.8 Magnetic Analysis......Page 168 Problems......Page 170 5.1 Introduction......Page 172 5.2.1 Above T(N)......Page 175 5.2.2 Below T(N)......Page 177 5.2.3 Comparison with Experiment......Page 182 5.3 Neutron Diffraction......Page 184 5.4 Rare Earths......Page 192 5.5 Antiferromagnetic Alloys......Page 193 Problems......Page 194 6.1 Introduction......Page 196 6.2 Structure of Cubic Ferrites......Page 199 6.3 Saturation Magnetization......Page 201 6.4 Molecular Field Theory......Page 204 6.4.1 Above T(c)......Page 205 6.4.2 Below T(c)......Page 207 6.4.3 General Conclusions......Page 210 6.5 Hexagonal Ferrites......Page 211 6.6.1 γ-Fe(2)O(3)......Page 213 6.6.3 Alloys......Page 214 6.7 Summary: Kinds of Magnetism......Page 215 Problems......Page 216 7.1 Introduction......Page 218 7.2 Anisotropy in Cubic Crystals......Page 219 7.3 Anisotropy in Hexagonal Crystals......Page 223 7.4 Physical Origin of Crystal Anisotropy......Page 225 7.5 Anisotropy Measurement......Page 226 7.5.1 Torque Curves......Page 227 7.5.2 Torque Magnetometers......Page 233 7.5.3 Calibration......Page 236 7.5.4 Torsion-Pendulum Method......Page 238 7.6.1 Fitted Magnetization Curve......Page 239 7.6.2 Area Method......Page 243 7.6.3 Anisotropy Field......Page 247 7.7 Anisotropy Constants......Page 248 7.8 Polycrystalline Materials......Page 250 7.9 Anisotropy in Antiferromagnetics......Page 253 7.10 Shape Anisotropy......Page 255 7.11 Mixed Anisotropies......Page 258 Problems......Page 259 8.1 Introduction......Page 262 8.2 Magnetostriction of Single Crystals......Page 264 8.2.1 Cubic Crystals......Page 266 8.2.2 Hexagonal Crystals......Page 272 8.3 Magnetostriction of Polycrystals......Page 275 8.4 Physical Origin of Magnetostriction......Page 278 8.5 Effect of Stress on Magnetic Properties......Page 279 8.6 Effect of Stress on Magnetostriction......Page 287 8.7 Applications of Magnetostriction......Page 289 8.8 ΔE Effect......Page 291 8.9 Magnetoresistance......Page 292 Problems......Page 293 9.1 Introduction......Page 296 9.2 Domain Wall Structure......Page 297 9.2.1 Néel Walls......Page 304 9.3.1 Bitter Method......Page 305 9.3.2 Transmission Electron Microscopy......Page 308 9.3.3 Optical Effects......Page 309 9.3.4 Scanning Probe; Magnetic Force Microscope......Page 311 9.4.1 Uniaxial Crystals......Page 313 9.4.2 Cubic Crystals......Page 316 9.5 Single-Domain Particles......Page 321 9.6 Micromagnetics......Page 322 9.7 Domain Wall Motion......Page 323 9.8 Hindrances to Wall Motion (Inclusions)......Page 326 9.9 Residual Stress......Page 329 9.11 Hindrances to Wall Motion (General)......Page 333 9.12.1 Prolate Spheroid (Cigar)......Page 335 9.12.2 Planetary (Oblate) Spheroid......Page 341 9.13 Magnetization in Low Fields......Page 342 9.14 Magnetization in High Fields......Page 346 9.15 Shapes of Hysteresis Loops......Page 347 9.16 Effect of Plastic Deformation (Cold Work)......Page 350 Problems......Page 353 10.1 Introduction......Page 356 10.2 Magnetic Annealing (Substitutional Solid Solutions)......Page 357 10.3 Magnetic Annealing (Interstitial Solid Solutions)......Page 366 10.4 Stress Annealing......Page 369 10.5 Plastic Deformation (Alloys)......Page 370 10.6 Plastic Deformation (Pure Metals)......Page 373 10.7 Magnetic Irradiation......Page 375 10.8 Summary of Anisotropies......Page 378 11.1 Introduction......Page 380 11.3 Coercivity of Fine Particles......Page 381 11.4.1 Fanning......Page 385 11.4.2 Curling......Page 389 11.5 Magnetization Reversal by Wall Motion......Page 394 11.6 Superparamagnetism in Fine Particles......Page 404 11.7 Superparamagnetism in Alloys......Page 411 11.8 Exchange Anisotropy......Page 415 11.9 Preparation and Structure of Thin Films......Page 418 11.10 Induced Anisotropy in Films......Page 420 11.11 Domain Walls in Films......Page 421 11.12 Domains in Films......Page 426 Problems......Page 429 12.2 Eddy Currents......Page 430 12.3 Domain Wall Velocity......Page 433 12.3.1 Eddy-Current Damping......Page 436 12.4 Switching in Thin Films......Page 439 12.5 Time Effects......Page 442 12.5.1 Time Decrease of Permeability......Page 443 12.5.2 Magnetic After-Effect......Page 445 12.5.3 Thermal Fluctuation After-Effect......Page 447 12.6 Magnetic Damping......Page 449 12.7.1 Electron Paramagnetic Resonance......Page 454 12.7.2 Ferromagnetic Resonance......Page 456 12.7.3 Nuclear Magnetic Resonance......Page 457 Problems......Page 459 13.1 Introduction......Page 460 13.2 Eddy Currents......Page 461 13.3.1 Transformers......Page 466 13.3.2 Motors and Generators......Page 471 13.4 Electrical Steel......Page 473 13.4.1 Low-Carbon Steel......Page 474 13.4.2 Nonoriented Silicon Steel......Page 475 13.4.3 Grain-Oriented Silicon Steel......Page 477 13.4.4 Six Percent Silicon Steel......Page 481 13.4.5 General......Page 482 13.5 Special Alloys......Page 484 13.5.2 Amorphous and Nanocrystalline Alloys......Page 487 13.5.4 Uses of Soft Magnetic Materials......Page 488 13.6 Soft Ferrites......Page 492 Problems......Page 497 14.1 Introduction......Page 498 14.2 Operation of Permanent Magnets......Page 499 14.3 Magnet Steels......Page 505 14.4 Alnico......Page 506 14.5 Barium and Strontium Ferrite......Page 508 14.6.1 SmCo(5)......Page 510 14.6.2 Sm(2)Co(17)......Page 511 14.6.3 FeNdB......Page 512 14.9 Ductile Permanent Magnets......Page 513 14.10 Artificial Single Domain Particle Magnets (Lodex)......Page 514 14.11 Bonded Magnets......Page 515 14.12.1 External Fields......Page 516 14.12.2 Temperature Changes......Page 517 14.13 Summary of Magnetically Hard Materials......Page 518 14.14.1 Electrical-to-Mechanical......Page 519 14.14.5 Force Applications......Page 522 14.14.6 Magnetic Levitation......Page 524 Problems......Page 525 15.2.1 Analog Audio and Video Recording......Page 526 15.3 Principles of Magnetic Recording......Page 527 15.3.2 AC Bias......Page 528 15.3.3 Video Recording......Page 529 15.4.1 Magnetoresistive Read Heads......Page 530 15.4.3 Digital Recording Media......Page 532 15.5 Perpendicular Recording......Page 533 15.7 Magneto-Optic Recording......Page 534 15.8.1 Brief History......Page 535 15.8.3 Future Possibilities......Page 536 16.1 Introduction......Page 538 16.2 Type I Superconductors......Page 540 16.3 Type II Superconductors......Page 541 16.4 Susceptibility Measurements......Page 544 16.5 Demagnetizing Effects......Page 546 APPENDIX 1: DIPOLE FIELDS AND ENERGIES......Page 548 APPENDIX 2: DATA ON FERROMAGNETIC ELEMENTS......Page 552 APPENDIX 3: CONVERSION OF UNITS......Page 554 APPENDIX 4: PHYSICAL CONSTANTS......Page 556 INDEX......Page 558 "B.D. Cullity wrote Introduction to Magnetic Materials explicitly for beginners, at the level of senior undergraduates or first-year graduate students. The material is presented at a practical level, allowing readers to develop a solid understanding of magnetic properties, quantities, and behavior. This new edition will be useful to students as well as engineers and scientists involved with magnetic phenomena, materials, and measurements. It crosses traditional disciplinary boundaries, covering topics in solid-state physics, materials science, electrical engineering, and computer science. It can serve as a basic learning and reference work for all those who need to understand the essentials of magnetic behavior."--Jacket