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

Ch. 3.15 - Prob. 11KCPCh. 3.15 - Prob. 12KCPCh. 3.15 - Prob. 13KCPCh. 3.15 - Prob. 14KCPCh. 3.15 - Prob. 15KCPCh. 3.15 - Prob. 16KCPCh. 3.15 - Prob. 17KCPCh. 3.15 - Prob. 18KCPCh. 3.15 - Prob. 19KCPCh. 3.15 - Prob. 20KCPCh. 3.15 - Prob. 21KCPCh. 3.15 - Prob. 22KCPCh. 3.15 - Prob. 23KCPCh. 3.15 - Prob. 24AAPCh. 3.15 - Prob. 25AAPCh. 3.15 - Prob. 26AAPCh. 3.15 - Prob. 27AAPCh. 3.15 - Prob. 28AAPCh. 3.15 - Prob. 29AAPCh. 3.15 - Prob. 30AAPCh. 3.15 - Prob. 31AAPCh. 3.15 - Prob. 33AAPCh. 3.15 - A direction vector passes through a unit cube from...Ch. 3.15 - Prob. 36AAPCh. 3.15 - Prob. 37AAPCh. 3.15 - Prob. 38AAPCh. 3.15 - Prob. 41AAPCh. 3.15 - Prob. 42AAPCh. 3.15 - Prob. 43AAPCh. 3.15 - Prob. 44AAPCh. 3.15 - Prob. 45AAPCh. 3.15 - Prob. 46AAPCh. 3.15 - Prob. 47AAPCh. 3.15 - Rodium is FCC and has a lattice constant a of...Ch. 3.15 - Prob. 49AAPCh. 3.15 - Prob. 50AAPCh. 3.15 - Prob. 51AAPCh. 3.15 - Prob. 52AAPCh. 3.15 - Prob. 53AAPCh. 3.15 - Prob. 54AAPCh. 3.15 - Prob. 55AAPCh. 3.15 - Determine the Miller-Bravais direction indices of...Ch. 3.15 - Determine the Miller-Bravais direction indices of...Ch. 3.15 - Prob. 58AAPCh. 3.15 - Prob. 59AAPCh. 3.15 - Prob. 60AAPCh. 3.15 - Prob. 61AAPCh. 3.15 - Prob. 62AAPCh. 3.15 - Prob. 63AAPCh. 3.15 - Prob. 64AAPCh. 3.15 - Prob. 65AAPCh. 3.15 - Prob. 66AAPCh. 3.15 - Prob. 67AAPCh. 3.15 - Prob. 68AAPCh. 3.15 - Prob. 69AAPCh. 3.15 - Prob. 70AAPCh. 3.15 - Prob. 71AAPCh. 3.15 - Prob. 72AAPCh. 3.15 - Prob. 73AAPCh. 3.15 - Prob. 74SEPCh. 3.15 - Prob. 75SEPCh. 3.15 - Prob. 76SEPCh. 3.15 - Assuming that the volume of an HCP metal cell...Ch. 3.15 - Prob. 79SEPCh. 3.15 - Prob. 80SEPCh. 3.15 - Prob. 81SEPCh. 3.15 - Prob. 82SEPCh. 3.15 - Prob. 83SEPCh. 3.15 - Prob. 84SEPCh. 3.15 - Prob. 85SEPCh. 3.15 - Prob. 86SEPCh. 3.15 - Prob. 87SEPCh. 3.15 - Prob. 88SEPCh. 3.15 - Prob. 89SEPCh. 3.15 - Prob. 90SEPCh. 3.15 - Prob. 91SEPCh. 3.15 - Prob. 92SEPCh. 3.15 - Prob. 93SEPCh. 3.15 - Prob. 94SEPCh. 3.15 - Prob. 95SEPCh. 3.15 - Prob. 96SEP
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