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

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2nd Revise Page

Questions and Problems • 757

1.4

0.2 0.4 0.6

1.2

1.0

0.8

0.6

0.4

0.2

0.00 102030405060

Flux density,

B (tesla)

15,000

10,000

5,000

0

Flux density,

B (gauss)

Magnetic field strength, H (A/m)

Magnetic field strength, H (oersteds) Figure 18.29 Initial

magnetizationB-versus-H

curve for an iron-silicon alloy.

Magnetic Anisotropy

18.12The energy (per unit volume) required to

magnetize a ferromagnetic material to satu-

ration (Es) is defined by the following equa-

tion:

Es=

∫Ms

0

μ 0 HdM

H (A/m)

1.6

1.2

0.8

0.4

0

0

0.4

 60  40  20 20 40 60

0.8

1.2

1.6

B (tesla)

Figure 18.30 Complete magnetic

hysteresis loop for a nickel–iron alloy.

That is,Esis equal to the product ofμ 0 and

the area under anMversusHcurve, to the

point of saturation referenced to the ordinate

(orM) axis—for example, in Figure 18.17 the

area between the vertical axis and the magne-

tization curve toMs. EstimateEsvalues (in

J/m^3 ) for single-crystal iron in [100], [110],

and [111] directions.