Solution: Following the above said procedure, we have
(i)
Intercepts
3a
4b
∞
(ii)
Division by unit translation
3a
a = 3
4b
b = 4
∞
(iii)
Reciprocals
1
3
1
4
1
1
(iv)
After clearing fraction
4
3
0
⟹ The required Miller indices of the plane are (430).
Example 4 In an orthorhombic crystal with a: b: c = 1: 2: 5, a plane cuts intercepts
of 3Å, 4Å, and 5Å on its coordinate axes. Find the Miller indices of the plane.
Solution: Following the above said procedure, we have
(i)
Intercepts
3
4
5
(ii)
Division by unit translation
3
1 = 3
4
2 = 2
5
5 ¼ 1
(iii)
Reciprocals
1
3
1
2
1
(iv)
After clearing fraction
2
3
6
⟹ The required Miller indices of the plane are (236).
Example 5 In a crystal whose primitive translations are 1.2Å, 1.8Å and 2Å, a
plane with Miller indices (231) cuts an intercept of 1.2Å along the x-axis.
Determine the lengths of intercepts along y and z-axes.
Solution: Given: A plane with Miller indices (231), intercept along x-axis 1.2Å,
intercepts along y and z-axes = ?
Fig. 4.5 The position
coordinates of face-centered
atoms in a fcc unit cell
4.1 Miller Indices of Atomic Sites, Planes and Directions
141