3.7 Alloys
61
(a)
k y
k z
k x
X
R
M
S
Z
T
(b)
k y
k z
k x
W
K
L
U
X
X
(c)
k y
k z
k x
H
P
F
N
D
G
(d)
H
H
H
H
H
P
K
T
K
P
S
L
R
A
L
L
T'
S'
A
M
U
M
(e)
X
T
N
(f) k x
k y
k z
X
Y
Z
U
S
T
Fig. 3.38 Brillouin zones and special k points for the a primitive cubic (pc), (b) fcc, c bcc, and d hcp lattice. e Brillouin
zone for chalcopyrite structure with fcc Brillouin zone shown as dashed outline f Brillouin zone for orthorhombic lattice
with one quadrant shown with dashed lines
• They form an ordered (periodic) structure that is called a superlattice.
• They form a random alloy.
3.7.1 Random Alloys
Alloys for which the probability to find an atom at a given lattice site is given by the fraction of these
atoms (i.e. the stoichiometry), independent of the surrounding, are called random alloys. Deviations
from the random population of sites is termed clustering.
61
(a)
k y
k z
k x
X
R
M
S
Z
T
(b)
k y
k z
k x
W
K
L
U
X
X
(c)
k y
k z
k x
H
P
F
N
D
G
(d)
H
H
H
H
H
P
K
T
K
P
S
L
R
A
L
L
T'
S'
A
M
U
M
(e)
X
T
N
(f) k x
k y
k z
X
Y
Z
U
S
T
Fig. 3.38 Brillouin zones and special k points for the a primitive cubic (pc), (b) fcc, c bcc, and d hcp lattice. e Brillouin
zone for chalcopyrite structure with fcc Brillouin zone shown as dashed outline f Brillouin zone for orthorhombic lattice
with one quadrant shown with dashed lines
• They form an ordered (periodic) structure that is called a superlattice.
• They form a random alloy.
3.7.1 Random Alloys
Alloys for which the probability to find an atom at a given lattice site is given by the fraction of these
atoms (i.e. the stoichiometry), independent of the surrounding, are called random alloys. Deviations
from the random population of sites is termed clustering.