Page 66 - Chalcogenide Glasses for Infrared Optics

44 Cha pte r T w o

This equation has been applied to the study of bonding in organic
36
and inorganic compounds including oxide glasses. For a molecular
compound of the form A B C , where x, y, and z are the atomic frac-
x y z
tions of the constituents A, B, and C, the molar refraction becomes
R = xR + yR + zR
A B C
where R , R and R are the atomic (or ionic) refraction values result-
A B, C
ing from their presence in the molecule. The approach applies well to
the covalent bonded chalcogenide glasses so that single values for
each element can be determined and used in many different glass
compositions. The atomic refraction values should be close to the
cube of their accepted covalent radii. Calculating directly from
accepted covalent radii would yield low values because the atomic
spheres are loosely packed. Amorphous selenium was chosen as the
starting point in calculating atomic refraction values for use with
chalcogenide glasses.Using available experimental data. The atomic
refraction for selenium was calculated and used as a reference. The
index wavelength chosen was 5 µm. The atomic refractions for silicon,
germanium, phosphorus, arsenic, sulfur, and tellurium were calcu-
lated from the cube of their covalent radii and normalized to selenium.
From these atomic refraction literature-derived values, the molar
refractions for the 28 glass compositions used in the density plot of
Fig. 2.15 were calculated and compared to the measured values.
Agreement was ±4.1 percent. The results are given in Table 2.5.
Another approach that yielded better agreement was to treat the glass
formulas of atomic refraction values for glasses with different con-
centrations of the same elements as simultaneous equations and solve
directly for the experimental atomic refraction values of each con-
stituent element. When the 28 glass compositions were recalculated,
the agreement with experimental values was ±1.1 percent. Table 2.6
lists the atomic refraction values determined from the literature and
from solving the simultaneous equations. Values from glasses based
on S, Se, and Te are given for comparison.
An illustration of the worth of the method follows: The refrac-
tive index for chalcogenide glasses at 5 µm can be calculated within
a few percent by using the density vs. molecular weight plot in
Fig. 2.15 and the atomic refraction values in Table 2.6 to calculate
molar refraction:

R = xR + yR + zR
A B C
2
2
Then solve for N from R = (N – 1)/(N + 2) × molecular weight/density.
This procedure was applied to 20 As-Se-Te glasses reported by
5
Jerger and Billian at Servo Corporation. The accurate values they
reported and the values estimated agreed within +3 percent. The results

are shown in Table 2.7.