Essentials of Materials Science and Engineering, SI Edition
Essentials of Materials Science and Engineering, SI Edition
4th Edition
ISBN: 9781337672078
Author: ASKELAND, Donald R., WRIGHT, Wendelin J.
Publisher: Cengage Learning
Question
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Chapter 3, Problem 3.62P
Interpretation Introduction

(a)

Interpretation:

The direction within the hexagonal unit cell for  [1 1¯ 0] needs to be sketched.

Concept Introduction:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [h,k,i,l]. The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the direction within the hexagonal unit cell for  [1 1¯ 0]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  1

Explanation of Solution

Procedure for drawing direction for  [1 1¯ 0] :

  1. First draw empty hexagonal unit cell.
  2. There is no displacement along a1 direction as coordinate is zero.
  3. Draw the line in a2 direction by 1 unit.
  4. Draw the line in opposite direction of a3 by 1¯ units.
  5. There is no displacement along z-axis direction as coordinate is zero.
  6. Then join the origin to the point to obtain desired direction

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  2

Interpretation Introduction

(b)

Interpretation:

The direction within the hexagonal unit cell for  [1 1 2¯ 0] needs to be sketched.

Concept Introduction:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [h,k,i,l]. The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the direction within the hexagonal unit cell for  [1 1 2¯ 0]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  3

Explanation of Solution

  [1 1 2¯ 0]

Procedure for drawing direction for  [1 1 2¯ 0] :

  1. First draw empty hexagonal unit cell.
  2. Draw the line in direction of a1 by 1 units which indicates 1.
  3. Draw the line in a2 direction by 1 unit.
  4. Draw the line in opposite direction of a3 by 2¯  units.
  5. There is no displacement along z-axis direction as coordinate is zero.
  6. Then join the origin to the point to obtain desired direction

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  4

Interpretation Introduction

(c)

Interpretation:

The direction within the hexagonal unit cell for  [ 1¯ 01 1] needs to be sketched.

Concept Introducton:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [h,k,i,l]. The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the direction within the hexagonal unit cell for  [ 1¯ 01 1]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  5

Explanation of Solution

Procedure for drawing direction for  [ 1¯ 01 1] :

  1. First draw empty hexagonal unit cell.
  2. Draw the line in opposite direction of a1 by 1 unit which indicates 1¯  .
  3. There is no displacement along a2 direction as coordinate is zero.
  4. Draw the line in direction of a3 by 1 unit which indicates 1.
  5. Draw the line in direction along z-axis by 1 unit which indicates 1.
  6. Then join the origin to the point to obtain desired direction.

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  6

Interpretation Introduction

(d)

Interpretation:

The direction within the hexagonal unit cell for [0 0 0 3] needs to be sketched.

Concept Introduction:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [h,k,i,l]. The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the plane within the hexagonal unit cell for  [ 0003]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  7

Explanation of Solution

Procedure for drawing planes for  [ 0003] :

  1. Converting four index miller indices of  [ 0003]. into three indices.
  2. (hkil)= (0003)h=0k=0i=0l=3
  3. Now taking reciprocals of plane and putting lattice parameters
  4. a1=a2=a3=z=3a

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  8

Interpretation Introduction

(e)

Interpretation:

The direction within the hexagonal unit cell for [1¯ 0 1 0] needs to be sketched.

Concept Introduction:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [hkil] The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the plane within the hexagonal unit cell for  [ 1¯1 0]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  9

Explanation of Solution

Procedure for drawing planes for  [ 1¯1 0] :

  1. Converting four index miller indices of  [ 1¯1 0]. into three indices.
  2. (hkil)= (1¯010)h=1¯k=0i=1l=0
  3. Now taking reciprocals of plane and putting lattice parameters
  4. a1=aa2=a3=az=

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  10

Interpretation Introduction

(f)

Interpretation:

The direction within the hexagonal unit cell for  [011¯1] needs to be sketched.

Concept Introduction:

Miller indices at plane pass through the three points at edges of the hexagonal lattice. It has a four-digit system [h,k,i,l]. The additional indices are used to show the direction in three-dimensional vector.

Expert Solution
Check Mark

Answer to Problem 3.62P

Figure shows the plane within the hexagonal unit cell for  [011¯1]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  11

Explanation of Solution

Procedure for drawing planes for  [011¯1] :

  1. Converting four index miller indices of  [011¯1]. into three indices.
  2. (hkil)= (011¯1)h=0k=1i=1¯l=1
  3. Now taking reciprocals of plane and putting lattice parameters
  4. a1=a2=aa3=az=a

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.62P , additional homework tip  12

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Chapter 3 Solutions

Essentials of Materials Science and Engineering, SI Edition

Ch. 3 - Prob. 3.11PCh. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Prob. 3.16PCh. 3 - Prob. 3.17PCh. 3 - Prob. 3.18PCh. 3 - Prob. 3.19PCh. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Prob. 3.23PCh. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48PCh. 3 - Prob. 3.49PCh. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54PCh. 3 - Prob. 3.55PCh. 3 - Prob. 3.56PCh. 3 - Prob. 3.57PCh. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - Prob. 3.62PCh. 3 - Prob. 3.63PCh. 3 - Prob. 3.64PCh. 3 - Prob. 3.65PCh. 3 - Prob. 3.66PCh. 3 - Prob. 3.67PCh. 3 - Prob. 3.68PCh. 3 - Prob. 3.69PCh. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - Prob. 3.72PCh. 3 - Prob. 3.73PCh. 3 - Prob. 3.74PCh. 3 - Prob. 3.75PCh. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - Prob. 3.79PCh. 3 - Prob. 3.80PCh. 3 - Prob. 3.81PCh. 3 - Prob. 3.82PCh. 3 - Prob. 3.83PCh. 3 - Prob. 3.84PCh. 3 - Prob. 3.85PCh. 3 - Prob. 3.86PCh. 3 - Prob. 3.87PCh. 3 - Prob. 3.88PCh. 3 - Prob. 3.89PCh. 3 - Prob. 3.90PCh. 3 - Prob. 3.91PCh. 3 - Prob. 3.92PCh. 3 - Prob. 3.93PCh. 3 - Prob. 3.94PCh. 3 - Prob. 3.95PCh. 3 - Prob. 3.96PCh. 3 - Prob. 3.97PCh. 3 - Prob. 3.98PCh. 3 - Prob. 3.99PCh. 3 - Prob. 3.100PCh. 3 - Prob. 3.101DPCh. 3 - Prob. 3.102DPCh. 3 - Prob. 3.103CPCh. 3 - Prob. 3.104CP
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