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

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

3.12 Point Coordinates • 65

0.40 nm

0.46 nm

(a)

0.48 nm

z

x

y

(b)

1

0.46 nm

0.12 nmM

N

O

P

1

4

1

2

z

x

y

0.20 nm

Solution

From sketch (a), edge lengths for this unit cell are as follows:a=0.48 nm,

b=0.46 nm, andc=0.40 nm. Furthermore, in light of the above discussion,

fractional lengths areq=^14 ,r=1, ands=^12. Therefore, first we move from

the origin of the unit cell (pointM)qa=^14 (0.48 nm)=0.12 nm units along

thexaxis (to pointN), as shown in the (b) sketch. Similarly, we proceedrb=

(1)(0.46 nm)=0.46 nm parallel to theyaxis, from pointNto pointO. Finally,

we move from this position,sc=^12 (0.40 nm)=0.20 nm units parallel to thez

axis to pointP, as noted again in sketch (b). This pointPthen corresponds to

the^14112 point coordinates.

EXAMPLE PROBLEM 3.8

Specification of Point Coordinates

Specify point coordinates for all atom positions for a BCC unit cell.

Solution

For the BCC unit cell of Figure 3.2, atom position coordinates correspond to

the locations of the centers of all atoms in the unit cell—that is, the eight corner

atoms and single center atom. These positions are noted (and also numbered)

in the following figure.

z

y

1

5

7

6

9

4

2 3

8

x

a

a

a