b
Ã
¼
2p
b
¼
2p
d 010
¼
2pB
V
¼ 2p
c  a
a:b  c
c
Ã
¼
2p
c
¼
2p
d 001
¼
2pC
V
¼ 2p
a  b
a:b  c
The exact relationships between the direct and reciprocal lattice parameters and
interaxial angles of primitive unit cells of various crystal systems are provided in
Table 2.2.
Solved Examples
Example 1 Using graphical construction, demonstrate the relation between a
two-dimensional direct lattice and its corresponding reciprocal lattice net.
Proof: Let us consider a monoclinic crystal system of 1st setting with the unique
2-fold axis along c-axis defined as a 6 ¼ b 6 ¼ c; a = b = 90° 6 ¼ c.
For simplicity, let us orient the unit cell in such a way that the c-axis is perpendicular to the plane of the paper. Hence, a- and b- axes lie in the plane of the
paper as shown in Fig. 2.13. Further, let us consider some of the (hk0) planes,
namely (100), (010), (110), (120) and (210) in the direct lattice unit cell which are
parallel to the c-axis and therefore their normal lie in the plane of the paper. Also,
we know that a crystal plane in 2-D is a line.
Fig. 2.12 Relationship
between crystal planes and
their reciprocal lattice points
52
2 Unit Cell Construction