Crystal Structure 1 3.1 Some Basic Concepts of Crystal Structure ...

Crystal Structure
Bragg Diffraction and Reciprocal Lattice Vectors
Fig. 3.15
Reciprocal Vectors
The reciprocal lattice of a Bravais lattice constructed by the set of primitive vectors, a, b
and c is one that has primitive vectors given by:
b c
c a
a b
A 2 B 2 C
a b c
a b c
2
a b c
(3.6)
Examples:
(1) Reciprocal lattice to simple cubic lattice
For sc lattice, we may choose the following set of primitive vectors:
a aˆ,
a aˆ,
a aˆ,
1
x
2
y
3
z
We may then determine the reciprocal lattice vectors b 1 , b 2 and b 3 using eqn. 3.6:
a2
a3
2
b 2 xˆ
1
.
3
a a
Similarly,
2
2
b yˆ
2
and b3
zˆ
a
a
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