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

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

3.13 Crystallographic Directions • 67

z

y

x

[111]

[110]

[100]

Figure 3.22 The [100], [110], and [111] directions within a

unit cell.

EXAMPLE PROBLEM 3.9

Determination of Directional Indices

Determine the indices for the direction shown in the accompanying figure.

z

y

x

a

b

Projection on

y axis (b)

Projection on

x axis (a/2)

c

Solution

The vector, as drawn, passes through the origin of the coordinate system, and

therefore no translation is necessary. Projections of this vector onto thex,y,

andzaxes are, respectively,a/2,b, and 0c, which become^12 ,1, and 0 in terms of

the unit cell parameters (i.e., when thea,b, andcare dropped). Reduction of

these numbers to the lowest set of integers is accompanied by multiplication

of each by the factor 2. This yields the integers 1, 2, and 0, which are then

enclosed in brackets as [120].

This procedure may be summarized as follows:

xyz

Projections a/2 b 0 c

Projections (in terms ofa,b, andc)^1210

Reduction 1 2 0

Enclosure [120]