Page 76 - Chalcogenide Glasses for Infrared Optics

54 Cha pte r T w o

39
Herzberg. The expressions involve atomic masses, bond lengths,
bond angles, and two force constants k and kδ. The kδ is a measure of
the restoring force opposing a change in the angle between the two
valence bonds. The magnitude is about 10 percent of the k value and
was assumed to be such in all the calculations. Interatomic distances
were taken to be the sum of the covalent radii. With the equations and
using Gordy’s rule, the vibrational frequencies for four molecular
gases typical of the four molecular configurations considered were
calculated and compared with observed frequencies. The four gases
were CO , SO , AsCl and SiCl . Agreement between observed and
2 2 3 4
calculated was poor except for the AsCl , X-Y pyramidal case. A
3 3
method better suited for polyatomic force constant prediction was
40
developed by Somayajulu. This method utilizes the elemental cova-
lent force constants and electronegativity to predict force constants.
The expression used is
K = (K K ) + ∆
1/2
AB AA BB
where ∆ = (X − X ) 1/2
A B
40
Tables for elemental force constants are given by Somayajulu.
Values for single, double, and triple bonds are given including con-
stants for hybridized orbitals such as sp , the tetrahedral structure.
3
For silicon and germanium two force constants are given, single
3
and sp tetrahedral. Both the X-Y linear and nonlinear molecules
2
have three vibrational modes. In both cases the ν wave number cor-
1
responds to the symmetric stretching vibration, ν corresponds to the
3
unsymmetric stretching mode, while the ν frequency is the bending
2
mode. The ν modes are not infrared active because of the molecule
1
symmetry but can be seen in Raman spectra. All four of the pyrami-
dal molecule modes are infrared active. The calculated frequencies
for pyramidal molecules in close agreement with observed has been
mentioned before.
The observed frequencies for Si-Te, Si-Se, Ge-Te, and Ge-S in each
case agree very well with the ν mode frequency calculated for the
1
nonlinear X-Y symmetric molecule. The vibrations for the As-S and
2
As-Se molecules are quite different. They both match the ν mode of
1
the pyramidal structure. The absorptions were found in binary glasses
but not observed when a group IVA element was present. Surpris-
ingly, the P-S and P-Se vibrations fit the X-Y nonlinear configuration
2
rather than the pyramidal configuration.
The differences may be related to the chemical differences between
arsenic and the other VA elements phosphorus and antimony. The
differences were pointed out while explaining glass forming tenden-
cies. Also, we should keep in mind the change in bonding that will