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
Book Icon
Chapter 3, Problem 3.60P
Interpretation Introduction

(a)

Interpretation:

The plane within the cubic cell for [101] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [101].

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  1

Explanation of Solution

Procedure to draw [101] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices.
  2. Here, 1 indicates that plane intersects at 1 on x-axis, indicates plane is parallel to y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (100),(000),(001)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  2

Interpretation Introduction

(b)

Interpretation:

The plane within the cubic cell for [01¯0] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows direction in cubic cell unit at [01¯0]

Explanation of Solution

Procedure to draw [01¯0] direction within cubic unit cell:

xyz
Reduction of Integer01¯0
Reduction of scale---
Projection0a-b0c

Coordinates of points are (000),(010),(000)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  3

Interpretation Introduction

(c)

Interpretation:

The plane within the cubic cell for [122¯] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [122¯]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  4

Explanation of Solution

Procedure to draw [122¯] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices.
  2. Here, 1 indicates that plane intersects at 1 on x-axis, 2 indicates that plane intersects at 2 on y-axis and -2 indicates that plane intersects at 2 on negative direction of z-axis.
  3. Coordinates of points are (100),(020),(002)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  5

Interpretation Introduction

(d)

Interpretation:

The plane within the cubic cell for [301] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [301]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  6

Explanation of Solution

Procedure to draw [301] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, 3 indicates that plane intersects at 3 on x-axis, indicates plane is parallel to y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (300),(000),(001)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  7

Interpretation Introduction

(e)

Interpretation:

The plane within the cubic cell for [2¯01] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure. We have to show the directions and planes in the cubic cell as per the Miller index for each example.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [2¯01]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  8

Explanation of Solution

Procedure to draw [2¯01] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, -2 indicates that plane intersects at 2 on negative direction of x-axis, indicates plane is parallel to y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (200),(000),(001)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  9

Interpretation Introduction

(f)

Interpretation:

The plane within the cubic cell for [21¯3] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure. We have to show the directions and planes in the cubic cell as per the Miller index for each example.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [21¯3]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  10

Explanation of Solution

Procedure to draw [21¯3] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, 2 indicates that plane intersects at 2 on x-axis, -1 indicates plane intersects at 1 on negative direction of y-axis and 3 indicates that plane intersects at 3 on z-axis.
  3. Coordinates of points are (200),(010),(003)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  11

Interpretation Introduction

(g)

Interpretation:

The plane within the cubic cell for [01¯1¯] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [01¯1¯]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  12

Explanation of Solution

Procedure to draw [01¯1¯] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, indicates that plane is parallel to x-axis, -1 indicates plane intersects at 1 on negative direction of y-axis and -1 indicates that plane intersects at 1 on negative direction of z-axis.
  3. Coordinates of points are (000),(010),(001)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  13

Interpretation Introduction

(h)

Interpretation:

The plane within the cubic cell for [102] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [102]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  14

Explanation of Solution

Procedure to draw [102] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, 1 indicates that plane intersects at 1 on x-axis, indicates plane is parallel to y-axis and 2 indicates that plane intersects at 2 on z-axis.
  3. Coordinates of points are (100),(000),(002)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  15

Interpretation Introduction

(i)

Interpretation:

The plane within the cubic cell for [002] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows direction in cubic cell unit at [002]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  16

Explanation of Solution

Procedure to draw [002] direction within cubic unit cell:

xyz
Reduction of Integer002
Reduction of scale001
Projection0a0bc

Coordinates of points are (000),(000),(002)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  17

Interpretation Introduction

(j)

Interpretation:

The plane within the cubic cell for [13¯0] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [13¯0]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  18

Explanation of Solution

Procedure to draw [13¯0] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, 1 indicates that plane intersects at 1 on x-axis, -3 indicates plane intersects at 3 on negative direction of y-axis and indicates that plane is parallel to z-axis.
  3. Coordinates of points are (100),(000),(030)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  19

Interpretation Introduction

(k)

Interpretation:

The plane within the cubic cell for [2¯12] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure. We have to show the directions and planes in the cubic cell as per the Miller index for each example.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [2¯12]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  20

Explanation of Solution

Procedure to draw [2¯12] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, -2 indicates that plane intersects at -2 on negative direction of x-axis, 1 indicates plane intersects at 1 on y-axis and 2 indicates that plane intersects at 2 on z-axis.
  3. Coordinates of points are (200),(010),(002)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  21

Interpretation Introduction

(l)

Interpretation:

The plane within the cubic cell for [31¯2¯] needs to be sketched.

Concept Introduction:

Miller indices are a group of numbers which shows the orientation of the plane in given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.60P

The figure shows plane in cubic cell unit at [31¯2¯]

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  22

Explanation of Solution

Procedure to draw [31¯2¯] plane within cubic unit cell:

  1. Remove indices from parenthesis and taking reciprocals of the indices
  2. Here, 1 indicates that plane intersects at 1 on x-axis, indicates plane is parallel to y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (300),(010),(002)

  Essentials of Materials Science and Engineering, SI Edition, Chapter 3, Problem 3.60P , additional homework tip  23

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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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