V ORTH ¼ 2V SH
The reverse relationships can be found by determining the inverse of the matrix
in Eq. 5.8, that is,
2 1 0
0 1 0
0 0 1
0
@
1
A
À1
¼
1
2
1 À1 0
0 2 0
0 0 2
0
@
1
A
Hence the inverse relationship (i.e., transformation from orthorhombic to simple
hexagon) is
h
k
l
0
@
1
A ¼
1
2
1 À1 0
0 2 0
0 0 2
0
@
1
A
H
K
L
0
@
1
A
ð5:9Þ
The same can be written as
h ¼
H
2
À
K
2
þ 0 L
k ¼ 0 H þ 1K þ 0 L
l ¼ 0 H þ 0 K þ 1 L
ð5:10Þ
where i ¼ À (h + k)
Fig. 5.2 Hexagonal and
orthorhombic axes
5.2 Transformation of Indices of Crystal Planes (Unit Cell)
183