Vaporization of high-lead silicate glasses (optical glasses SFS 1, SF 11, SF 5, F 2, etc.) at high temperatures, was investigated by means of thermo-gravimetry, chemical analysis, and X-ray diffraction. These glasses evaporated considerably at high temperatures, as compared with such glasses as alkali-silicate glasses. The major volatile component from the melts was PbO, and under the atmosphere containing more than 0.4% of SO
2, K
2O was also volatile. The rate of vaporization, with a few exceptions, was scarcely affected by the heating atmosphere.
The result of this investigation on the change of volatility with time did not obey the formulae proposed by Preston and Turner, Oldfield and Wright, and Barlow. This is probably attributed to the fact that the rates of vaporization of these glasses were governed not only by diffusion of volatile components within melts, but also by the rate of evaporation at the surface of the melts. Therefore, the solution of the diffusion equation with surface evaporation condition given by Crank, was applied here. It is expressed by the following equations: for semi-infinite media,
Mt=(
c2-
c0/
h){
eh2Dterfc
h√
Dt-1+2/√π
h√
Dt}……………………(1)
for limited plane sheet media,
Qt/
Q∞=1-_??_{2
L2e-β
n2Dt/
l2/β
n2(β
n2+
L2+
L)}…………………………………………(2)
In these equations,
Mt is the total amount of substance diffusing through the unit area of the surface during time
t;
h=α/
D, where α is a constant (here called an apparent surface evaporation rate constant);
D is the diffusion coefficient;
c0 and
c2 are the initial concentrations of the diffusing substance in atmosphere and in media, respectively; β
n are the positive root of the equation, β
n tan β
n=
L, where
L=
lα/
D;
l is the thickness of plane sheet; and
Qt/
Q∞ is the fraction of evaporation.
Both of the equations were found to be applicable to the vaporization of PbO from the molten glass. In early stages of the vaporization process,
D and α obtained by equation (1) showed a good agreement with these obtained by equation (2). Apparent activation energies for diffusion and surface evaporation, were about 40kcal/mole and 60-70kcal/mole, respectively. The physical meaning of the former was not clear, whereas the latter probably corresponded to the heat of evaporation of PbO. Thus, at higher temperatures the diffusion process tended to control the over-all process, whereas at lower temperatures the surface evaporation rate became predominant.
Both of
D and α depended on the composition. They became larger exponentially with increasing modifier oxide contents (PbO and K
2O).
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