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The Science and Engineering

of Materials, 4thedDonald R. Askeland Pradeep P. Phul

Unit 8Magnetic Materials

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Objectives of Unit 8 To study the fundamental basis for

responses of certain materials to thepresence of magnetic fields.

To examine the properties andapplications of different types of magneticmaterials.

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Chapter Outline

8.1 Classification of Magnetic Materials 8.2 Magnetic Dipoles and Magnetic Moments 8.3 Magnetization, Permeability, and the

Magnetic Field

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Ferromagnetism Ferrimagnetism Diamagnetism

Section 8.1Classification of Magnetic Materials

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The magnetic behavior of materials can be traced to thestructure of atoms.

Bohr magneton- The strength of a magnetic moment ofan electron (B) due to electron spin.

Section 8.2

Magnetic Dipoles and Magnetic Moments

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2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.

Figure 8.1 Origin of magnetic dipoles: (a) The spin of the

electron produces a magnetic field with a direction dependenton the quantum number ms. (b) Electrons Electrons orbitingaround the nucleus create a magnetic field around the atom.

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Magnetic fields are generated bymovement of electric charges

A loop of electric currentgenerates a magnetic

dipole field

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A magnetic dipole Field lines run from

theNorthpole to theSouthpole

Field lines indicate thedirection of force thatwould be experiencedby a North magneticmonopole

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A bar magnet

A simple bar magnetbehaves like a magnetic

dipole

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Far field picture

Sometimes thedipoles are very

small compared withtheir spatial field ofinfluence

An electron, forexample

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Schematic representation

A magnetic dipole isoften represented

schematically as anarrow.

The head of thearrow is the Northpole.

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Flux density, B

Density of flux (orfield) linesdetermines forces

on magnetic poles Direction of flux

indicates directionof force on a North

poleB

A

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The relationship between the magneticfield and magnetization

When an electric current is passed through thecoil, a magnetic field H is produced, with thestrength of the field given by

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Section 8.3Magnetization, Permeability,

and the Magnetic Field

The magnetization M represents the increase in the fluxdensity due to the core material,

The first part of this equation is simply the effect of the appliedmagnetic field. The second part is the effect of the magnetic

material that is present

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Magnetic permeability- The ratio between inductance ormagnetization and magnetic field. It is a measure of theease with which magnetic flux lines can flow through a

material. Magnetization- The total magnetic moment per unitvolume.

Magnetic susceptibility- The ratio betweenmagnetization and the applied field.

Section 8.3Magnetization, Permeability, and the

Magnetic Field

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2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learningis a trademark used herein under license.

Figure 8.2 A current passing through a coil sets up a magneticfield Hwith a flux density B. The flux density is higher when amagnetic core is placed within the coil.

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H oersted B Gauss; 1 gauss/oersted

H A/m B Tesla (Webar/m2) 4 X 10-7 Webar/(A.m)

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Calculate the maximum, or saturation, magnetization that weexpect in iron. The lattice parameter of BCC iron is 2.866 .Compare this value with 2.1 tesla (a value of saturation fluxdensity experimentally observed for pure Fe.)

Example 8.1Theoretical and Actual Saturation

Magnetization in Fe

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Calculate the maximum, or saturation, magnetization that weexpect in iron. The lattice parameter of BCC iron is 2.866 .Compare this value with 2.1 tesla (a value of saturation fluxdensity experimentally observed for pure Fe.)

Example 8.1 SOLUTION

Based on the unpaired electronic spins, we expect each ironatom to have four electrons that act as magnetic dipoles. Thenumber of atoms per m3in BCC iron is:

Example 8.1Theoretical and Actual Saturation

Magnetization in Fe

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Example 8.1 SOLUTION (Continued)

The maximum volume magnetization (Msat) is the totalmagnetic moment per unit volume:

To convert the value of saturation magnetization Mintosaturation flux density Bin tesla, we need the value of 0M. Inferromagnetic materials 0M>> 0Hand therefore, B 0M.

Saturation induction in tesla = Bsat= 0Msat.

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Section 8.4Diamagnetic, Paramagnetic,

Ferromagnetic, Ferrimagnetic, andSuperparamagnetic Materials Diamagnetism- The effect caused by the magnetic

moment due to the orbiting electrons, which produces aslight opposition to the imposed magnetic field.(Negative magnetization, Negative Susceptibility, )

Superconductors are perfect diamagnets. In a diamagnetic material, the magnetization (M)

direction is opposite to the direction of applied field (H).

Ex. Cu, Ag, Si, Alumina, Superconductors (Xm= -1)Direction of M is opposite to H.

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Paramagnetism The net magnetic moment caused by the alignment of

the electron spins when a magnetic field is applied.(Dipoles do not interact).

The effect is lost as soon as the magnetic field isremoved.

(Positive magnetization, Positive Susceptibility).Titanium And copper alloys.

Ferromagnetic and ferrimagnetic materials above the Curie

temperature also exhibit paramagnetic behavior.

Ch t 20 M ti M t i l

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25 2011 Cengage Learning Engineering. All Rights Reserved. 20 - 25

Ferromagnetic Materials

Ferromagnetism

Alignment of the magnetic moments of atoms in the samedirection so that a net magnetization remains after the

magnetic field is removed. Susceptibility is given by the following equation known as the

Curie-Weiss law: Ferromagnetic behavior is caused by the unfilled energy

levels in the 3d level of atom.

whereC constant that depends upon the materialTc Curie temperatureT temperature above Tc

Chapter 20: Magnetic Materials

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Section 8.4Diamagnetic, Paramagnetic,

Ferromagnetic, Ferrimagnetic, andSuperparamagnetic Materials

Antiferromagnetism - Arrangement of magnetic

moments such that the magnetic moments of atoms orions cancel out causing zero net magnetization. The magnetic susceptibility is positive and small. In

addition, CoO and MnCl2 are examples ofantiferromagnetic materials.

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Figure 8.4 Thecrystal structure ofMn0 consists ofalternating layers of{111} type planes ofoxygen andmanganese ions. Themagnetic moments ofthe manganese ionsin every other (111)plane are oppositelyaligned.Consequently, Mn0 isantiferromagnetic.

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Ferrimagnetism- Magnetic behavior obtainedwhen ions in a material have their magneticmoments aligned in an antiparallel arrangementsuch that the moments do not completely cancel

out and a net magnetization remains. Ceramic materials ferrites. Curie- weiss

behavior. ferrites are used in many high-frequency

applications.

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Superparamagnetism (Liquid magnets/ Ferrofluids)

Grain size of ferromagnetic and ferrimagneticmaterials falls below a certain critical size, thesematerials behave as if they are paramagnetic.

The magnetic dipole energy of each particlebecomes comparable to the thermal energy. This small magnetic moment changes its direction

randomly.

if we produce iron oxide (Fe3O4) particles in a 3 to5 nm size, they behave as superparamagneticmaterials

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Figure 8.3 Theeffect of the corematerial on the fluxdensity. Themagnetic momentopposes the field indiamagneticmaterials.Progressivelystronger momentsare present inparamagnetic,

ferrimagnetic, andferromagneticmaterials for thesame applied field.

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We want to produce a solenoid coil that produces aninductance of at least 2000 gauss when a 10-mA currentflows through the conductor. Due to space limitations, thecoil should be composed of 10 turns over a 1 cm length.Select a core material for the coil.

Example 8.2Design/Materials Selection for a Solenoid

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l 8

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The magnetic field Hproduced by the coil.

The permeability of the core material must be:

The relative permeability of the core material must be at least:

From Table 8-4, we find that 4079 alloys has a maximumrelative permeability of 80,000 and might be a goodselection for the core material.

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Domains- Small regions within a single or polycrystallinematerial in which all of the magnetization directions arealigned.

Domains are regions in the material in which all of thedipoles are aligned in a certain direction.

Bloch walls- The boundaries between magnetic domains. Boundaries, called Bloch walls, separate the individual

magnetic domains.

Section 8.5Domain Structure andthe Hysteresis Loop

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Figure 8.5 (a) A qualitative sketch of magnetic domains in a

polycrystalline material. The dashed lines show demarcationbetween different magnetic domains; the dark curves show thegrain boundaries. (b) The magnetic moments in adjoiningatoms change direction continuously across the boundarybetween domains.

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When a magnetic field is imposed on the material, domainsthat are nearly lined up with the field grow at the expense ofunaligned domains.

Initially, the domains grow with difficulty, and relativelylarge increases in the field are required to produce even alittle magnetization.

The saturation magnetization, produced when all of thedomains are oriented along with the magnetic field, is the

greatest amount of magnetization that the material canobtain.

Section 8.5Movement of Domains in a

magnetic Field

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Figure 8.6 When a magnetic field is first applied to a magneticmaterial, magnetization initially increases slowly, then morerapidly as the domains begin to grow. Later, magnetization slows,as domains must eventually rotate to reach saturation. Notice thepermeability values depend upon the magnitude of H.

S i 8

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Saturation magnetization- When all of the dipoles have beenaligned by the field, producing the maximum magnetization.

Effect of Removing the Field.

Remanance- The polarization or magnetization that remains ina material after it has been removed from the field. Coercivity The magnetic field needed to bring the Induced

Magnetization to zero. Hysteresis loop- The loop traced out by magnetization in a

ferromagnetic or ferrimagnetic material as the magnetic field is

cycled.

Section 8.5Movement of Domains in a

magnetic Field

S i 8 5

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Hysteresis loop- The loop traced out by magnetization in aferromagnetic or ferrimagnetic material as the magnetic field iscycled.

Section 8.5Effect of Reversing the field

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Figure 8.7 (a) The ferromagnetic hysteresis M-H loop showing theeffect of the magnetic field on inductance or magnetization. Thedipole alignment leads to saturation magnetization (point 3), a

remanance (point 4), and a coercive field (point 5). (b) Thecorresponding B-H loop. Notice the end of the B-H loop, the B valuedoes not saturate since B = 0H+ 0M. (Source: Adapted fromPermanent Magnetism, by R. Skomski and J.M.D. Coey, p. 3, Fig. 1-1. Edited by J.M.D. Coey and D.R. Tilley. Copyright 899 Instituteof Physics Publishing. Adapted by permission.)

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Curie temperature- The temperature above (Tc) whichferromagnetic or ferrimagnetic materials becomeparamagnetic.

Section 8.6The Curie Temperature

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Figure 8.8 The effect of temperature on (a) the hysteresisloop and (b) the remanance. Ferromagnetic behaviordisappears above the Curie temperature.

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Soft Magnetic Materials - Ferromagnetic materials areoften used to enhance the magnetic flux density (B)produced when an electric current is passed through thematerial. Applications include cores for electromagnets,

electric motors, transformers, generators, and otherelectrical equipment. High saturation Magnetization High Permeability Small Coercive field

Small remanance Small Hysteresis loop Rapid Response to high Frequency magnetic field High Electrical resistivity

Section 8.7Applications of Magnetic Materials

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Figure 8.9 (a) Comparison of the hysteresisloops for three applications of ferromagneticand ferrimagnetic materials.

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Data StorageMaterials- Magnetic materials are used fordata storage.

Spintronics


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Permanent Magnets- Magnetic materials are used tomake strong permanent magnets

High Remanence High Permeability High Coercive Field Large Hysteresis Loop High Power Power- The strength of a permanent magnet as

expressed by the maximum product of the inductanceand magnetic field.


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Power- The strength of a permanent magnet asexpressed by the maximum product of the inductanceand magnetic field.


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Figure 8.10 (a) The largest rectangle drawn in the second or fourthquadrant of the B-Hcurve gives the maximum BHproduct. (BH)maxisrelated to the power, or energy, required to demagnetize the

permanent magnet. (b) Development of permanent magnetmaterials, maximum energy product is shown on the y -axis.(Source: Adapted fromPermanent Magnetism, by R. Skomski andJ.M.D. Coey, p. 23, Table 1-2. Edited by J.M.D. Coey and D.R. Tilley.Copyright 899 Institute of Physics Publishing. Adapted bypermission.)

Example 8 4

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Determine the power, or BHproduct, for the magnetic material

whose properties are shown in Figure 8.11.

Example 8.4Energy Product for Permanent Magnets

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Figure 8.11 The fourthquadrant of the B-Hcurvefor a permanent magneticmaterial (for Example 8.4)

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Several rectangles have been drawn in the fourth quadrantof the B-Hcurve. The BHproduct in each is:

Thus, the power is about 4.2 106gauss . oersted.

Example 8 6

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Calculate the force in kN for one square meter area of a

permanent magnet whose saturation magnetization is 1.61tesla.

Example 8.6Lifting Power of a Magnet

Example 8 6

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Calculate the force in kN for one square meter area of a

permanent magnet whose saturation magnetization is 1.61tesla.


We have been given the value of 0M= 1.61 tesla. We can

rewrite the equation that provides the force due to apermanent magnet as follows.

Example 8.6Lifting Power of a Magnet

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Magnetocrystalline anisotropy- In single crystals, thecoercivity depends upon crystallographic directioncreating easy and hard axes of magnetization.

Section 8.8Metallic and Ceramic Magnetic Materials

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Figure 8.12 Information can be stored or retrieved from amagnetic disk by use of an electromagnetic head. A current in thehead magnetizes domains in the disk during storage; the domainsin the disk induce a current in the head during retrieval.

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Figure 8.13 The initial magnetization curve for iron ishighly anisotropic; magnetization is easiest when the

directions are aligned with the field and hardest along[111]. (Source: FromPrinciples of ElectricalEngineering Materials and Devices, by S.O. Kasap, p.623, Fig. 8-24. Copyright 897 Irwin. Reprinted by

permission of The McGraw-Hill Companies.)

100

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Figure 8.14 Demagnetizing curves for Co5Sm and Co5Ce,representing a portion of the hysteresis loop.

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Figure 8.15 (a) The structure of magnetite, Fe304. (b) The

subcell of magnetite. The magnetic moments of ions in theoctahedral sites line up with the magnetic field, but themagnetic moments of ions in tetrahedral sites oppose thefield. A net magnetic moment is produced by this ionicarrangement.

Example 8.7

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Calculate the total magnetic moment per cubic centimeter in

magnetite. Calculate the value of the saturation flux density(Bsat) for this material.

Example 8.7Magnetization in Magnetite (Fe3O4)

Figure 8.15 (b) Thesubcell of magnetite.

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In the unit cell overall, there are eight subcells, so the totalmagnetic moment is 32 Bohr magnetons per cell. The size

of the unit cell, with a lattice parameter of 8.37 10-8cm,is:

The magnetic moment per cubic centimeter is:

This expression represents the magnetization Matsaturation (Msat). The value of Bsat 0Msatwill be =(4 10-7)(5.1 105) = 0.64 Tesla.

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Example 8.8

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Design a cubic ferrite magnet that has a total magneticmoment per cubic meter of 5.5 105A/m.

pDesign/Materials Selection

for a Ceramic Magnet

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Assuming that the addition of Mn ions does not appreciablyaffect the size of the unit cell, we find from Example 8-7

that:Letxbe the fraction of Mn2+ions that have replaced theFe2+ions, which have now been reduced to 1 -x. Then,the total magnetic moment is:

Therefore we need to replace 34.6 at% of the Fe2+ions withMn2+ions to obtain the desired magnetization.

ms-lec 31-36 unit 8 & 9

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