(d) Some Important Notations Used in B.Z
The names of certain points and directions of a B-Z (Fig. 2.25), commonly
used by experts are the following:
Г—Origin
W−Corner
L−Center of hexagonal faces
X−Center of square faces
Г ⟶ H denotes [100] direction and symbolized as Δ
Г ⟶ N denotes [110] direction and symbolized as R
Г ⟶ P denotes [111] direction and symbolized as
V
Solved Examples
Example 1 Construct B-Z corresponding to a given plane oblique lattice with a 6 ¼
b and c ¼ c
:
Solution: Given: Plane oblique lattice with a 6 ¼ b and c ¼ c
: Let us follow the
procedure given below:
(i) Draw a primitive cell in the given lattice.
(ii) Draw a normal to each axis and obtain a* and b* as
a
Ã
¼
2p
asinc
and b
Ã
¼
2p
asinc
(iii) Obtain the reciprocal lattice net and construct a W–S unit cell. This is the
required B-Z for the given primitive oblique lattice.
Fig. 2.25 Some important notations used in Brillouin zones
72
2 Unit Cell Construction
The names of certain points and directions of a B-Z (Fig. 2.25), commonly
used by experts are the following:
Г—Origin
W−Corner
L−Center of hexagonal faces
X−Center of square faces
Г ⟶ H denotes [100] direction and symbolized as Δ
Г ⟶ N denotes [110] direction and symbolized as R
Г ⟶ P denotes [111] direction and symbolized as
V
Solved Examples
Example 1 Construct B-Z corresponding to a given plane oblique lattice with a 6 ¼
b and c ¼ c
:
Solution: Given: Plane oblique lattice with a 6 ¼ b and c ¼ c
: Let us follow the
procedure given below:
(i) Draw a primitive cell in the given lattice.
(ii) Draw a normal to each axis and obtain a* and b* as
a
Ã
¼
2p
asinc
and b
Ã
¼
2p
asinc
(iii) Obtain the reciprocal lattice net and construct a W–S unit cell. This is the
required B-Z for the given primitive oblique lattice.
Fig. 2.25 Some important notations used in Brillouin zones
72
2 Unit Cell Construction