Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-03 GTBL042-Callister-v2 September 6, 2007 15:33

94 • Chapter 3 / Structures of Metals and Ceramics

Companion Site)], generate (and print out)

a three-dimensional unit cell for lead oxide,

PbO, given the following: (1) The unit cell is

tetragonal witha=0.397 nm andc=0.502 nm,

(2) oxygen atoms are located at the following

point coordinates:

000 001

100 101

010 011

110 111

1

2

1

2

0

1

2

1

2

1

and (3) Pb atoms are located at the following

point coordinates:

1

2

00. 763 0

1

2

0. 237

1

2

10. 763 1

1

2

0. 237

Crystallographic Directions

3.25Sketch a monoclinic unit cell, and within that

cell a [101] direction.

3.26What are the indices for the direction in-

dicated by the vector in the sketch below?

0.5 nm

+y

0.4 nm

+z

0.3 nm

+x

3.27Within a cubic unit cell, sketch the following

directions:

(a)[102],

(b)[313],

(c)[212],

(d)[301].

3.28Determine the indices for the directions

shown in the following cubic unit cell:

A

1 2 1 2 1 3

1

3

2

3

2

3

B

C

D

1

2

1

, 2

1

2

1

, 2

+x

+y

+z

3.29For tetragonal crystals, cite the indices of di-

rections that are equivalent to each of the fol-

lowing directions:

(a)[011]

(b)[100]

3.30Convert the [001] direction into the four-

index Miller–Bravais scheme for hexagonal

unit cells.

3.31Determine the indices for the two directions

shown in the following hexagonal unit cell:

a 1

a 2

a 3

z

B

A

3.32Using Equations 3.7a, 3.7b, 3.7c, and 3.7d, de-

rive expressions for each of the three primed

indices set (u′,v′, andw′) in terms of the four

unprimed indices (u,v,t, andw).

Crystallographic Planes

3.33Draw an orthorhombic unit cell, and within

that cell a (021) plane.