3.7 Alloys
65
Table 3.9 Calculated interaction parameter (at T = 800 K, 1 kcal/mol= 43.39 meV), miscibility-gap temperature
T mg and concentration x mg for various ternary alloys. Data for (In,Ga)N from [253], other data from [252]
Alloy
T mg
x mg
(0)
(0.5)
(1)
(K)
(kcal/mol)
(kcal/mol)
(kcal/mol)
Al x Ga 1−x As
64
0.51
0.30
0.30
0.30
GaP x As 1−x
277
0.603
0.53
0.86
1.07
Ga x In 1−x P
961
0.676
2.92
3.07
4.60
GaSb x As 1−x
1080
0.405
4.51
3.96
3.78
Hg x Cd 1−x Te
84
0.40
0.45
0.80
0.31
Zn x Hg 1−x Te
455
0.56
2.13
1.88
2.15
Zn x Cd 1−x As
605
0.623
2.24
2.29
2.87
In x Ga 1−x N
1505
0.50
6.32
5.98
5.63
Fig. 3.43 Calculated
energy vs. volume of the
formula unit for
Mg x Zn 1−x O in the
wurtzite (WZ), hexagonal
(HX) and rocksalt phase
(RS). The separations
between the three phase are
denoted by straight bold
lines. Adapted from [254]
0.6
0.5
0.4
0.3
0.2
0.1
0
Energy (eV)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Mg-concentration x
18
Volume (Å )
3
20
22
24
26
structure of Mg x Zn 1−x O has been calculated [254] as depicted in Fig. 3.43 (cmp. Fig. 2.4 for silicon).
The transition between wurtzite and rocksalt structure is predicted for x = 0.33.
3.7.3 Virtual Crystal Approximation
In the virtual crystal approximation (VCA) the disordered alloy AB x C 1−x is replaced by an ordered
binary compound AD with D being a ‘pseudoatom’ with properties that are configuration averaged
over the properties of the B and C atoms, e.g. their masses or charges. Such an average is weighted
with the ternary composition, e.g. the mass is M D = x M B + (1 − x)M C . For example, the A–D force
constant would be taken as the weighted average over the A–B and A–C force constants.
3.7.4 Lattice Parameter
In the VCA for an alloy a new sort of effective atom is assumed that has an averaged bond length that
depends linearly on the composition. Typically, Vegard’s law (3.27), which predicts that the lattice
constant of a ternary alloy A x B 1−x C depends linearly on the lattice constants of the binary alloys AC
65
Table 3.9 Calculated interaction parameter (at T = 800 K, 1 kcal/mol= 43.39 meV), miscibility-gap temperature
T mg and concentration x mg for various ternary alloys. Data for (In,Ga)N from [253], other data from [252]
Alloy
T mg
x mg
(0)
(0.5)
(1)
(K)
(kcal/mol)
(kcal/mol)
(kcal/mol)
Al x Ga 1−x As
64
0.51
0.30
0.30
0.30
GaP x As 1−x
277
0.603
0.53
0.86
1.07
Ga x In 1−x P
961
0.676
2.92
3.07
4.60
GaSb x As 1−x
1080
0.405
4.51
3.96
3.78
Hg x Cd 1−x Te
84
0.40
0.45
0.80
0.31
Zn x Hg 1−x Te
455
0.56
2.13
1.88
2.15
Zn x Cd 1−x As
605
0.623
2.24
2.29
2.87
In x Ga 1−x N
1505
0.50
6.32
5.98
5.63
Fig. 3.43 Calculated
energy vs. volume of the
formula unit for
Mg x Zn 1−x O in the
wurtzite (WZ), hexagonal
(HX) and rocksalt phase
(RS). The separations
between the three phase are
denoted by straight bold
lines. Adapted from [254]
0.6
0.5
0.4
0.3
0.2
0.1
0
Energy (eV)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Mg-concentration x
18
Volume (Å )
3
20
22
24
26
structure of Mg x Zn 1−x O has been calculated [254] as depicted in Fig. 3.43 (cmp. Fig. 2.4 for silicon).
The transition between wurtzite and rocksalt structure is predicted for x = 0.33.
3.7.3 Virtual Crystal Approximation
In the virtual crystal approximation (VCA) the disordered alloy AB x C 1−x is replaced by an ordered
binary compound AD with D being a ‘pseudoatom’ with properties that are configuration averaged
over the properties of the B and C atoms, e.g. their masses or charges. Such an average is weighted
with the ternary composition, e.g. the mass is M D = x M B + (1 − x)M C . For example, the A–D force
constant would be taken as the weighted average over the A–B and A–C force constants.
3.7.4 Lattice Parameter
In the VCA for an alloy a new sort of effective atom is assumed that has an averaged bond length that
depends linearly on the composition. Typically, Vegard’s law (3.27), which predicts that the lattice
constant of a ternary alloy A x B 1−x C depends linearly on the lattice constants of the binary alloys AC