Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
Solution and Answer Guide
ABBASCHIAN, PHYSICAL METALLURGY PRINCIPLES, 5E, 2025, 9798214001661;
CHAPTER 1: THE STRUCTURE OF METALS
PROBLEMS
1.1
Determine the direction indices for (a) line om, (b) line on, and (c) line op in the
accompanying drawing of a cubic unit cell.
Solution:
(a) The direction indices for line om are [111].
1
(b) The vector components of line on, in units of, a = 1, are , 1 and 0 along the x, y
2
and z axes respectively. The corresponding direction indices are accordingly [120].
2 1 1
(c) The components of line op are , , and . Thus the indices are [436].
3 2 1
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 1
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
1.2
Determine direction indices for lines (a) qr, (b) qs, and (c) qt.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 2
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
Solution:
(a) The direction indices of line qr are [001].
(b) The direction indices of line qs are [101].
1 1 1
(c) The direction indices of line qt along the x, y and z axes are , , and ,
2 4 1
yielding the indices 2 1 4 .
1.3
In this figure, plane pqr intercepts the x, y, and z axes as indicated. What are the
Miller indices of this plane?
Solution:
1 3 2
The intercepts of plane pqr with the three axes are , , and , with the
2 4 3
1 1
reciprocals , , so that the Miller indices of the plane are (12 8 9).
1/ 2
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 3
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
1.4
What are the Miller indices of plane stu?
Solution:
1 1
This plane has intercepts , –1 and , so that the Miller indices are 2 12 .
2 2
1.5
Write the Miller indices for plane vwx.
Solution:
On the assumption that parallel planes can be described by the same set of Miller
indices, this plane should have the same indices as plane (C) of Fig. 1.16, which are (111).
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 4
posted to a publicly accessible website, in whole or in part.
Chapter 1: The Structure of Metals
Solution and Answer Guide
ABBASCHIAN, PHYSICAL METALLURGY PRINCIPLES, 5E, 2025, 9798214001661;
CHAPTER 1: THE STRUCTURE OF METALS
PROBLEMS
1.1
Determine the direction indices for (a) line om, (b) line on, and (c) line op in the
accompanying drawing of a cubic unit cell.
Solution:
(a) The direction indices for line om are [111].
1
(b) The vector components of line on, in units of, a = 1, are , 1 and 0 along the x, y
2
and z axes respectively. The corresponding direction indices are accordingly [120].
2 1 1
(c) The components of line op are , , and . Thus the indices are [436].
3 2 1
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 1
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
1.2
Determine direction indices for lines (a) qr, (b) qs, and (c) qt.
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 2
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
Solution:
(a) The direction indices of line qr are [001].
(b) The direction indices of line qs are [101].
1 1 1
(c) The direction indices of line qt along the x, y and z axes are , , and ,
2 4 1
yielding the indices 2 1 4 .
1.3
In this figure, plane pqr intercepts the x, y, and z axes as indicated. What are the
Miller indices of this plane?
Solution:
1 3 2
The intercepts of plane pqr with the three axes are , , and , with the
2 4 3
1 1
reciprocals , , so that the Miller indices of the plane are (12 8 9).
1/ 2
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 3
posted to a publicly accessible website, in whole or in part.
, Solution and Answer Guide: Abbaschian, Physical Metallurgy Principles, 5e, 2025, 9798214001661;
Chapter 1: The Structure of Metals
1.4
What are the Miller indices of plane stu?
Solution:
1 1
This plane has intercepts , –1 and , so that the Miller indices are 2 12 .
2 2
1.5
Write the Miller indices for plane vwx.
Solution:
On the assumption that parallel planes can be described by the same set of Miller
indices, this plane should have the same indices as plane (C) of Fig. 1.16, which are (111).
© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or 4
posted to a publicly accessible website, in whole or in part.
