We know that the reciprocal of the coefficients of unit translation vectors are in
the ratio:
p
À1
: q
À1
: r
À1
¼ h : k : l ¼ 2 : 3 : 1
Therefore,
p : q : r ¼
1
2
:
1
3
: 1
Then, the ratios of the actual lengths of the intercepts are:
l 1 : l 2 : l 3 ¼ pa : qb : rc
¼ 1:2 Â
1
2
: 1:8 Â
1
3
: 2 Â 1
Since l 1 is given as 1.2Å, we therefore multiply the RHS by 2, so that
l 1 : l 2 : l 3 ¼ 1:2 : 1:2 : 4
) l 2 ¼ 1:2 ˚
A and l 3 ¼ 4 ˚
A
Example 6 In a cubic crystal, find the lengths of the intercepts made on three axes
by a plane with Miller indices 1 32
ð
Þ.
Solution: Given: A cubic crystal, so that a = b = c, plane with Miller indices 1 32
ð
Þ,
intercepts along three axes = ?
We know that the reciprocal of the coefficients of unit translation vectors are in
the ratio:
p
À1 : q
À1 : r
À1 = h : k : l = 1 : -3 : 2
Therefore,
p : q : r = 1 : -
1
3
:
1
2
Then, the ratios of the actual lengths of the intercepts are:
l 1 : l 2 : l 3 ¼ pa : qb : rc
¼ 6a : À2a : 3a ¼ 6 : À2 : 3
142
4 Unit Cell Representations of Miller Indices