3. For a 3-D space lattice, the relationships between the direct and reciprocal
lattices, in general, are obtained as follows:
Consider a unit cell of general lattice (Fig. 2.12) whose b-c plane has an area A
(= bÂc = bc sin a), then its volume is
V ¼ Area of the b À c plane  height ¼ A  d 100
Similarly,
V ¼ Area of the a À c plane  height ¼ B  d 010
¼ Area of the a À b plane  height ¼ C  d 001
So that, the magnitudes of the reciprocal lattice parameters are:
a
Ã
¼
2p
a
¼
2p
d 100
¼
2pA
V
¼ 2p
b  c
a:b  c
Similarly,
Fig. 2.11 Direct and reciprocal of 1-D and 2-D lattices
2.2 Construction of Reciprocal Lattice
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