Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 3.15, Problem 53AAP

(a)

To determine

The Miller-Bravais indices of the hexagonal crystal plane, a.

The Miller-Bravais indices of the hexagonal crystal plane, b.

The Miller-Bravais indices of the hexagonal crystal plane, c.

(a)

Expert Solution
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Answer to Problem 53AAP

The Miller-Bravais indices of the hexagonal crystal plane, a is (01¯10).

The Miller-Bravais indices of the hexagonal crystal plane, b is (101¯2).

The Miller-Bravais indices of the hexagonal crystal plane, c is (2¯200).

Explanation of Solution

For plane a the intercepts are a1=,a2=1,a3=1andc=.

For plane b the intercepts are a1=1,a2=,a3=1,andc=12.

And for plane c the intercepts are a1=12,a2=12,a3=andc=

Miller-Bravais Indices for Planes are shown in table.

 Planer InterceptsReciprocals of InterceptsMiller-Bravais Indices
Plane-a(,1,1,)(0,1,1,0)(01¯10)
Plane-b(1,,1,12)(1,0,1,2)(101¯2)
Plane-c(12,12,,)(2,2,0,0)(2¯200)

The Miller-Bravais indices of the hexagonal crystal plane, a is (01¯10).

The Miller-Bravais indices of the hexagonal crystal plane, b is (101¯2).

The Miller-Bravais indices of the hexagonal crystal plane, c is (2¯200).

(b)

To determine

The Miller-Bravais indices of the hexagonal crystal plane, a.

The Miller-Bravais indices of the hexagonal crystal plane, b.

The Miller-Bravais indices of the hexagonal crystal plane, c.

(b)

Expert Solution
Check Mark

Answer to Problem 53AAP

The Miller-Bravais indices of the hexagonal crystal plane, a is (011¯0).

The Miller-Bravais indices of the hexagonal crystal plane, b is (11¯01).

The Miller-Bravais indices of the hexagonal crystal plane, c is (11¯01).

Explanation of Solution

The coordinates of intercepts for plane-a is (,1,1,), the coordinates of intercepts for plane-b is (1,1,,1) and the coordinates of intercepts for plane-c is (1,1,,1).

For plane a the intercepts are a1=,a2=1,a3=1andc=.

For plane b the intercepts are a1=1,a2=1,a3=,andc=1.

And for plane c the intercepts are a1=1,a2=1,a3=andc=1.

Conclusion:

Miller-Bravais Indices for Planes are shown in table below.

PlanesPlaner InterceptsReciprocals of InterceptsMiller-Bravais Indices
Plane-a(,1,1,)(0,1,1,0)(011¯0)
Plane-b(1,1,,1)(1,1,0,1)(11¯01)
Plane-c(1,1,,1)(1,1,0,1)(11¯01)

The Miller-Bravais indices of the hexagonal crystal plane, a is (011¯0).

The Miller-Bravais indices of the hexagonal crystal plane, b is (11¯01).

The Miller-Bravais indices of the hexagonal crystal plane, c is (11¯01).

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Chapter 3 Solutions

Foundations of Materials Science and Engineering

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