The Vaporization Coefficient of Silica
Authors: Ingersoll Nolan , Costa Gustavo , Jacobson Nathan S. 
Published: February 2020

Free surface or Langmuir evaporation of a solid oxide often leads to a vapor flux that 1-4 orders of magnitude lower than that calculated from equilibrium vapor pressures [1]. This factor is termed the “vaporization coefficient” and clearly has a large impact on determining vaporization rates.

The most common method of measuring vaporization coefficients is to measure the vapor flux from a free surface and compare it to the vapor flux calculated from equilibrium vapor pressures.  In this study, we used a vacuum thermogravimetric analyzer (TGA) to measure the vapor flux from a silica coupon.  Initially we had deposition on the coupon of W and Ta oxides from the furnace element and heat shields.  This problem was eliminated with a graphite tube surrounding the coupon.  The coupons were amorphous, however the temperatures of vaporization (1475 to 1675°C) induced surface crystallization to a surface layer of cristobalite.  This was verified with x-ray diffraction (XRD) and scanning electron microscopy (SEM).

Thermodynamically, the vaporization of SiO2(cristobilite) leads SiO2(g), SiO(g), O2(g), O(g).  The pressures were calculated from a free energy minimization code [2] and converted to vapor fluxes with the Hertz-Knudsen-Langmuir equation. These calculated fluxes were compared to the measured fluxes and the vaporization coefficient is simply the quotient of the two.  These data are given in Table 1 below.

Table 1. Vaporization coefficients obtained by comparison of free surface vapor flux to calculated flux.

Temperature (°C)
J(calculated)
J(measured)

Vaporization Coefficient

 
mg/cm2-hr
mg/cm2-hr

 

1475
3.797459
0.0168

4.42E-03

1525
10.20388
0.0451

4.42E-03

1575
25.95741
0.1421

5.47E-03

1625
62.79001
0.3606

5.74E-03

1675
144.9916
0.7064

4.87E-03

Other investigators have determined the vaporization coefficient for silica with the Knudsen cell method and variation of the orifice geometry [3].  This method is discussed and results for silica [4-7].  The two methods will be discussed as well as differences and similarities in the results.

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3.            Paule, R.C. and J.L. Margrave, Free-Evaporation and Effusion Techniques, in The Characterization of High-Temperature Vapors, J.L. Margrave, Editor. 1967, John Wiley & Sons: New York.

4.            Firsova, L. and A.N. Nesmeyanov, Determination of the Coefficients of Condensation of Lithium, Beryllium, Boron, Silicon and Lead Oxides. Zhur. Fiz. Khim., 1960. 34.

5.            Shornikov, S.I., I.Y. Archakov, and M.M. Shults, Mass-spectrometric study of evaporation and thermodynamic properties of silicon dioxide - II. Determination of partial coefficients of silicon dioxide evaporation. Zhurnal Obshchei Khimii, 1999. 69(2): p. 197-206.

6.            Nagai, S.I., et al., Knudsen Effusion Study of Silica. Journal of the Chemical Society-Faraday Transactions I, 1973(9): p. 1628-1634.

7.            Rocabois, P., C. Chatillon, and C. Bernard, Vapor-Pressure and Evaporation Coefficient of SiO(Amorphous) and SiO2(S)+Si(S) Mixtures by the Multiple Knudsen Cell Mass-Spectrometric Method. Revue Internationale Des Hautes Temperatures et Des Refractaires, 1992. 28(2): p. 37-48.