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

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

Questions and Problems • 95

3.34What are the indices for the plane drawn in

the sketch below?

0.4 nm

0.4 nm

+x

+y

+z

0.2 nm

3.35Sketch within a cubic unit cell the following

planes:

(a)(012),

(b)(313),

(c)(101),

(d)(211).

3.36Determine the Miller indices for the planes

shown in the following unit cell:

A

B

+z

+x

+y

1

2

1

3

3.37Determine the Miller indices for the planes

shown in the following unit cell:

A

B

+z

+x

+y

1

2

1

2

3.38For each of the following crystal structures,

represent the indicated plane in the manner

of Figures 3.26 and 3.27, showing both anions

and cations:

(a)(111) plane for the diamond cubic crystal

structure, and

(b)(110) plane for the fluorite crystal struc-

ture.

3.39Below are shown three different crystallo-

graphic planes for a unit cell of some hypo-

thetical metal. The circles represent atoms:

(110) (101)

0.39 nm 0.32 nm 0.36 nm

0.30 nm

0.20 nm 0.25 nm

(011)

(a)To what crystal system does the unit cell

belong?

(b)What would this crystal structure be

called?

(c)If the density of this metal is 18.91 g/cm^3 ,

determine its atomic weight.

3.40Convert the (012) plane into the four-index

Miller–Bravais scheme for hexagonal unit

cells.

3.41Determine the indices for the planes shown in

the hexagonal unit cells below:

a 1

a 2

a 3

z

(a)

a 1

a 2

a 3

z

(b)

3.42Sketch the (2 1 ̄10) plane in a hexagonal unit ̄

cell.