Example 2 Show the planes 1 1 1
ð
Þ and 1 11
ð
Þ in a cubic unit cell. Draw the line of
along their intersection. Assign the Miller indices of direction to the line.
Solution: Construct a cubic unit cell. Select its origin and the three crystallographic
axes. Now, imagine the origin to be at O′ and draw 1 1 1
ð
Þ plane. Next, imagine the
origin to be at O′′ and draw 1 1 1
ð
Þ plane. Common direction of the two planes is
shown as AB or BA (Fig. 4.7) whose Miller indices are: [101] or 10 1
½
Š:
Example 3 Show (100), (110) and (111) planes in different bcc unit cells and list
the position coordinates of the atoms whose centers are intersected by each of the
three planes.
Solution: Construct three bcc unit cells, select their origin and the three crystallographic axes. Follow the above said procedure and draw the given planes within
the unit cells as shown in Fig. 4.8.
(a) The position coordinates of the atoms whose centers are intersected by the
(100) plane are: [[100]], [[110]], [[101]] and [[111]]. They are shown in
Fig. 4.8a.
(b) The position coordinates of the atoms whose centers are intersected by the
(110) plane are: [[100]], [[010]], [[011]], [101]] and
1
2
1
2
1
2
 Ã
Â
Ã
. They are shown in
Fig. 4.8b.
(c) The position coordinates of the atoms whose centers are intersected by the
(111) plane are: [[100]], [[010]], and [[001]]. They are shown in Fig. 4.8c.
Fig. 4.7 1 1 1
ð Þ, 1 11
ð
Þ planes
Fig. 4.8 Position coordinates intersected by a (100) plane, b (110) plane, and c (111) plane
146
4 Unit Cell Representations of Miller Indices