Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337670845
Author: ASKELAND
Publisher: Cengage
Question
Book Icon
Chapter 3, Problem 3.61P
Interpretation Introduction

(a)

Interpretation:

The plane within the cubic cell for [11¯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 3.61P

The figure shows direction within a cubic cell unit for [11¯0]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  1

Explanation of Solution

Procedure to draw [11¯0] direction within cubic unit cell:

xyz
Reduction of Integer11¯0
Reduction of scale---
Projectiona-b0c

Coordinates of points are (100),(010),(000)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  2

Interpretation Introduction

(b)

Interpretation:

The plane within the cubic cell for [2¯2¯1] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers 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 3.61P

The figure show direction within a cubic cell unit for [2¯2¯1]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  3

Explanation of Solution

Procedure to draw [2¯2¯1] direction within cubic unit cell:

xyz
Reduction of Integer-2-21
Reduction of scale-1-112
Projection-a-b12 c

Coordinates of points are (200),(020),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  4

Interpretation Introduction

(c)

Interpretation:

The plane within the cubic cell for [410] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure show direction within a cubic cell unit for [410]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  5

Explanation of Solution

Procedure to draw [410] direction within cubic unit cell:

xyz
Reduction of Integer410
Reduction of scale1140
Projectiona14 b 0c

Coordinates of points are (400),(010),(000)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  6

Interpretation Introduction

(d)

Interpretation:

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

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure show direction within a cubic cell unit for [01¯2]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  7

Explanation of Solution

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

xyz
Reduction of Integer0-12
Reduction of scale0- 121
Projection0a- 12bc

Coordinates of points are (000),(010),(002)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  8

Interpretation Introduction

(e)

Interpretation:

The plane within the cubic cell for [3¯2¯1] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure show direction within a cubic cell unit for [3¯2¯1]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  9

Explanation of Solution

Procedure to draw [3¯2¯1] direction within cubic unit cell:

xyz
Reduction of Integer-3-21
Reduction of scale- 32112
Projection- 32 a-b12 c

Coordinates of points are (300),(020),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  10

Interpretation Introduction

(f)

Interpretation:

The plane within the cubic cell for [111¯] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure shows the plane within a cubic cell unit for [111¯]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  11

Explanation of Solution

Procedure to draw [111¯] 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, 1 indicates plane intersects at 1on y-axis and -1 indicates that plane intersects at 1 on negative direction on z-axis.
  3. Coordinates of points are (100),(010),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  12

Interpretation Introduction

(g)

Interpretation:

The plane within the cubic cell for [11¯1] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure show direction within a cubic cell unit for [11¯1]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  13

Explanation of Solution

Procedure to draw [11¯1] direction within cubic unit cell:

xyz
Reduction of Integer1-11
Reduction of scale1-11
ProjectionA-bc

Coordinates of points are (100),(010),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  14

Interpretation Introduction

(h)

Interpretation:

The plane within the cubic cell for [011¯] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure show direction within a cubic cell unit for [011¯]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  15

Explanation of Solution

Procedure to draw [011¯] direction within cubic unit cell:

xyz
Reduction of Integer01-1
Reduction of scale---
Projection0aB-c

Coordinates of points are (000),(010),(001¯)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  16

Interpretation Introduction

(i)

Interpretation:

The plane within the cubic cell for [030] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure shows the plane within a cubic cell unit for [030]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  17

Explanation of Solution

Procedure to draw [030] 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, 3 indicates plane intersects at 3 on y-axis and indicates that plane is parallel to z-axis.
  3. Coordinates of points are (000),(030),(000)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  18

Interpretation Introduction

(j)

Interpretation:

The plane within the cubic cell for [1¯21] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure shows the plane within a cubic cell unit for [1¯21]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  19

Explanation of Solution

Procedure to draw [1¯21] 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 negative direction of x-axis, 2 indicates plane intersects at 2 on y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (100),(020),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  20

Interpretation Introduction

(k)

Interpretation:

The plane within the cubic cell for [113¯] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure shows the plane within a cubic cell unit for [113¯]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  21

Explanation of Solution

Procedure to draw [113¯] 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, 1 indicates plane intersects at 1on y-axis and -3 indicates that plane intersects at 3 on negative direction on z-axis.
  3. Coordinates of points are (100),(010),(003)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  22

Interpretation Introduction

(l)

Interpretation:

The plane within the cubic cell for [04¯1] needs to be sketched.

Concept Introduction:

Miller indices are the groups of numbers which indicate the orientation of a group of numbers given directions within a crystal structure.

Expert Solution
Check Mark

Answer to Problem 3.61P

The figure shows the plane within a cubic cell unit for [04¯1]

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  23

Explanation of Solution

Procedure to draw [04¯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, -4 indicates plane intersects at 4 on negative direction of y-axis and 1 indicates that plane intersects at 1 on z-axis.
  3. Coordinates of points are (00),(040),(001)

  Essentials Of Materials Science And Engineering, Chapter 3, Problem 3.61P , additional homework tip  24

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Chapter 3 Solutions

Essentials Of Materials Science And Engineering

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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