114
5 Mechanical Properties
Table 5.1 Atomic masses (M B < M C ) of the constituents of various ternary compounds of type A(B,C), reduced mass
μ AC (5.48), fulfillment of the relation from (5.48) (‘+’: fulfilled, ‘−’: not fulfilled) and experimental mode behavior
(‘2’: two-mode, ‘1’: one-mode)
Alloy
A
B
C
M A
M B
M C
μ AC
Rel.
Modes
GaP 1−x As x
Ga
P
As
69.7
31.0
74.9
36.1
+
2
GaAs 1−x Sb x
Ga
As
Sb
69.7
74.9
121.8
44.3
−
1
CdS 1−x Se x
Cd
S
Se
112.4
32.1
79.0
46.4
+
2
Cd x Zn 1−x S
S
Zn
Cd
32.1
65.4
112.4
25.0
−
1
Mg x Zn 1−x O
O
Mg
Zn
16.0
24.3
65.4
12.9
−
1
Al x Ga 1−x N
N
Al
Ga
14.0
27.0
69.7
11.7
−
2(!)
Fig. 5.21 Phonon energies
of Cd x Zn 1−x S and
CdS 1−x Se x as a function of
the ternary composition.
Experimental data (solid
circles) are from [389],
dashed lines are guides to
the eye
x
Cd Zn S
x
1 - x
CdS
ZnS
360
340
320
300
280
260
240
220
-1
x
CdS Se
x
-
1
x
160
180
200
220
240
260
280
300
320
-1
CdS
CdSe
If the binary end components of a ternary alloy have different crystal structure, a transition between
the two occurs which is reflected in the phonon structure (energies and mode symmetries). As an
example, the optical phonon energies of Mg x Zn 1−x O are depicted in Fig. 5.22 (cmp. Fig. 3.43).
An example for the variation of phonon oscillator strength (as defined in (9.86)) with alloy composition is depicted in Fig. 5.23 for (Al,Ga)N [392].
5
5.2.9 Disorder
An example of local disorder are the localized vibrational modes due to a single defect. Here we
consider in our one-dimensional model random fluctuations of the model parameters. To that avail
we set up a numerical implementation of an one-dimensional chain with masses M 1 = M 2 = 1
and spring constants C 1 = C 2 , here C 2 = 2 C 1 . Now each mass varies randomly by a factor with a
5 The oscillator strengths f shown here have been calculated from the values S given in [392] divided by
5 Mechanical Properties
Table 5.1 Atomic masses (M B < M C ) of the constituents of various ternary compounds of type A(B,C), reduced mass
μ AC (5.48), fulfillment of the relation from (5.48) (‘+’: fulfilled, ‘−’: not fulfilled) and experimental mode behavior
(‘2’: two-mode, ‘1’: one-mode)
Alloy
A
B
C
M A
M B
M C
μ AC
Rel.
Modes
GaP 1−x As x
Ga
P
As
69.7
31.0
74.9
36.1
+
2
GaAs 1−x Sb x
Ga
As
Sb
69.7
74.9
121.8
44.3
−
1
CdS 1−x Se x
Cd
S
Se
112.4
32.1
79.0
46.4
+
2
Cd x Zn 1−x S
S
Zn
Cd
32.1
65.4
112.4
25.0
−
1
Mg x Zn 1−x O
O
Mg
Zn
16.0
24.3
65.4
12.9
−
1
Al x Ga 1−x N
N
Al
Ga
14.0
27.0
69.7
11.7
−
2(!)
Fig. 5.21 Phonon energies
of Cd x Zn 1−x S and
CdS 1−x Se x as a function of
the ternary composition.
Experimental data (solid
circles) are from [389],
dashed lines are guides to
the eye
x
Cd Zn S
x
1 - x
CdS
ZnS
360
340
320
300
280
260
240
220
-1
x
CdS Se
x
-
1
x
160
180
200
220
240
260
280
300
320
-1
CdS
CdSe
If the binary end components of a ternary alloy have different crystal structure, a transition between
the two occurs which is reflected in the phonon structure (energies and mode symmetries). As an
example, the optical phonon energies of Mg x Zn 1−x O are depicted in Fig. 5.22 (cmp. Fig. 3.43).
An example for the variation of phonon oscillator strength (as defined in (9.86)) with alloy composition is depicted in Fig. 5.23 for (Al,Ga)N [392].
5
5.2.9 Disorder
An example of local disorder are the localized vibrational modes due to a single defect. Here we
consider in our one-dimensional model random fluctuations of the model parameters. To that avail
we set up a numerical implementation of an one-dimensional chain with masses M 1 = M 2 = 1
and spring constants C 1 = C 2 , here C 2 = 2 C 1 . Now each mass varies randomly by a factor with a
5 The oscillator strengths f shown here have been calculated from the values S given in [392] divided by