Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Question
Chapter 16.13, Problem 62AAP
To determine

The theoretical value for the saturation magnetization and saturation induction for nickel.

Expert Solution & Answer
Check Mark

Answer to Problem 62AAP

The theoretical value for the saturation magnetization for nickel is 1.70×106A/m.

The theoretical value for the saturation induction for nickel is 2.14T.

Explanation of Solution

Write the expression to calculate saturation magnetization for nickel (Ms).

  Ms=(Atomic density)NμB                                                                                  (I)

Here, magnetic moment is N and Bohr magneton is μB.

Write the expression to calculate atomic density for nickel.

  Atomic density=nV=na3                                                                                            (II)

Here, number of atoms per unit cell is n, volume of the unit cell is V and lattice constant is a.

Write the expression to calculate saturation induction (Bs).

  Bsμ0Ms                                                                                                          (III)

Here, permeability constant is μ0.

Conclusion:

The magnetic moment of the nickel atom is considered to be 2Bohr magnetons.

Substitute 4atoms/unit cell for n and 0.352nm for a in Equation (II).

 Atomic density=4atoms/unit cell(0.352nm)3=4atoms/unit cell(0.352nm×1×109m1nm)3=9.171×1028atoms/m3

The value of Bohr magneton (μB) is taken to be 9.27×1024Am2.

Substitute 9.171×1028atoms/m3 for Atomic density, 2Bohr magnetons/atom for N and 9.27×1024Am2 for μB in Equation (I).

 Ms=(9.171×1028atoms/m3)(2Bohr magnetons/atom)(9.27×1024Am2)=1.70×106A/m

Thus, the theoretical value for the saturation magnetization for nickel is 1.70×106A/m.

The value of permeability constant (μ0) is taken to be 4π×107Tm/A.

Substitute 4π×107Tm/A for μ0 and 1.70×106A/m for Ms in Equation (III).

 Bs=(4π×107Tm/A)(1.70×106A/m)=2.14T

Thus, the theoretical value for the saturation induction for nickel is 2.14T.

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Chapter 16 Solutions

Foundations of Materials Science and Engineering

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