Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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Revised Pages

18.7 Domains and Hysteresis • 737

Domain

wall

Figure 18.12 The gradual change in magnetic

dipole orientation across a domain wall. (From

W. D. Kingery, H. K. Bowen, and D. R.

Uhlmann,Introduction to Ceramics,2nd

edition. Copyright©c1976 by John Wiley &

Sons, New York. Reprinted by permission of

John Wiley & Sons, Inc.)

fraction. For an unmagnetized specimen, the appropriately weighted vector sum of

the magnetizations of all the domains is zero.

Flux densityBand field intensityHare not proportional for ferromagnets and

ferrimagnets. If the material is initially unmagnetized, thenBvaries as a function of

Has shown in Figure 18.13. The curve begins at the origin, and asHis increased, the

Bfield begins to increase slowly, then more rapidly, finally leveling off and becoming

independent ofH. This maximum value ofBis the saturation flux densityBs, and the

corresponding magnetization is the saturation magnetizationMs, mentioned previ-

ously. Since the permeabilityμfrom Equation 18.2 is the slope of theB-versus-H

curve, note from Figure 18.13 that the permeability changes with and is dependent on

H. On occasion, the slope of theB-versus-Hcurve atH=0 is specified as a material

property that is termed theinitial permeabilityμi, as indicated in Figure 18.13.

As anHfield is applied, the domains change shape and size by the movement

of domain boundaries. Schematic domain structures are represented in the insets

(labeled U through Z) at several points along theB-versus-Hcurve in Figure 18.13.

Initially, the moments of the constituent domains are randomly oriented such that

there is no netB(orM) field (inset U). As the external field is applied, the domains

that are oriented in directions favorable to (or nearly aligned with) the applied field

Magnetic field strength, H

Flux density,

B (or magnetization,

M

)

H = 0

H

H

H

H

V

U

W

X

Y

Z

H

0

Bs (Ms)

Figure 18.13 TheB-versus-Hbehavior for a

ferromagnetic or ferrimagnetic material that

was initially unmagnetized. Domain

configurations during several stages of

magnetization are represented. Saturation

flux densityBs, magnetizationMs, and initial

permeabilityμiare also indicated. (Adapted

from O. H. Wyatt and D. Dew-Hughes,

Metals, Ceramics and Polymers,Cambridge

University Press, 1974.)