Abstract
The problem of oxygen exchange at the interface between a gas and a liquid metal is treated for systems under a “vacuum” (Knudsen regime, pressures lower than 1 Pa), where, due to the large mean free path of gas molecules in a vacuum, transport processes in the gas phase have no influence on the total interphase mass exchange, which is controlled by interface phenomena and by oxygen partition equilibrium inside the liquid. Owing to the double contribution of molecular O2 and volatile oxides to the oxygen flux from the surface, non-equilibrium steady-state conditions can be established, in which no variations in the composition of the two phases occur with time, as the result of opposite oxygen exchanges. The total oxygen and metal evaporation rates are evaluated as a function of the overall thermodynamic driving forces, and an account of the transport kinetics is given by using appropriate coefficients. A steady-state saturation degree s r, is defined which relates the oxygen activity in the liquid metal to the O2 pressure imposed and to the vapour pressures of volatile oxides. When metals able to form volatile oxides are considered, pressures of molecular O2 higher than those defined under equilibrium conditions have to be imposed in the experimental set-up in order to obtain a certain saturation degree, as a consequence of the condensation of the oxide vapours on the reactor walls. Effective oxidation parameters are determined, which define the conditions leading the liquid to a definite steady-state composition under a “vacuum” when it is out of equilibrium. The effective value of the oxygen pressure which corresponds to the complete oxygen saturation of the metal, \(P_{O_{2,} s}^E \), is evaluated at different temperatures for the systems Si-O and Al-O. The results are represented as curves of \(P_{O_{2,} s}^E \) against T, which separate different oxidation regimes; these results agree well with the experimental data found in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a η :
-
activity of the component η in the liquid phase
- k η :
-
partial-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)
- K η :
-
global-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)
- M η :
-
molecular weight of the species η (g mol−1)
- N totM :
-
global metal flux between the gas and the condensed phase (mol cm−2 s−1)
- \(N_{O_2 }^{tot} \) :
-
global oxygen flux between the gas and the condensed phase (mol cm−2 s−1)
- P j :
-
partial pressure of the j th oxide (Pa)
- P M :
-
vapour pressure of the pure metal (Pa)
- \(P_{O_2 } \) :
-
partial pressure of molecular O2 (Pa)
- P tot :
-
total pressure (Pa)
- P EM :
-
effective metal-vapour pressure (Pa)
- \(P_{O_2 }^E \) :
-
effective oxidation pressure (Pa)
- R E :
-
effective evaporation ratio
- s :
-
actual value of the bulk-saturation degree
- s r :
-
value of the bulk-saturation degree in steady-state (regime) conditions
- T :
-
temperature in the system, far from the container wall (K)
- T w :
-
temperature of the container wall (K)
- x η :
-
molar fraction of the component η in the liquid phase
- α η :
-
condensation coefficient of the species η (cm−3/2)
- l:
-
a quantity evaluated for a liquid below the saturation point
- liq:
-
quantity in the bulk liquid
- s:
-
a quantity evaluated in conditions where the liquid metal is saturated with oxygen
- I:
-
a quantity in the interfacial liquid layer
References
C. H. P. Lupis “Chemical Thermodynamics of Materials” (Elsevier Publishers, Amsterdam, Holland, 1983).
J. F. Padday In “Surface & Colloid Science” Ed. E. Matijevic (Wiley Intersc., New York, 1969).
Ju. V. Naidich, in “Progress in Surface and Membrane Science” Vol. 14, Eds. D. A. Cadenhead and J. F. Danielli (Academic Press, New York, 1981).
E. Ricci and A. Passerone, Mater. Sci. Eng. A161 (1993), 31.
E. Ricci, A. Passerone, P. Castello and P. Costa, J. Mater. Sci. 29 (1994) 1833.
H. H. Kellogg, Trans. Met. Soc. AIME, 263 (1966), 602.
D. Beruto, L. Barco and G. Belleri, Ceramurgia International 1 (1975), 87.
C. Wagner, J. Appl. Phys. 29 (1958), 1295.
E. A. Gulbransen, K. F. Andrew and F. A. Brassart, J. Electrochem. Soc. 113 (1966), 834.
L. Brewer and G. M. Rosemblatt, Trans. Met. Soc. AIME 224 (1962), 1268.
O. Winkler and R. Bakish, “Vacuum Metallurgy” (Elsevier Publishers, Amsterdam, 1971).
R. Ohno in “Liquid Metals-Chemistry and Physics”, Chap. 2, Ed. S. Z. Beer (Marcel Dekker Inc., New York, 1972).
S. Otsuka and Z. Kozuka, Trans. Jpn. Inst. Met. 22 (1981), 558.
R. H. Lamoreaux, D. L. Hildebrand and L. Brewer, High Temp. Sci. 20 (1985), 37.
R. J. Ackermann and R. J. Thorn, in “Progress in Ceramic Science”, Vol. 1, Chap. 2, Ed. J. E. Burke (Pergamon Press, New York, 1961).
E. Ricci, A. Passerone and J. C. Joud, Surface Sci. 206 (1988), 533.
J. J. Brennan and J. A. Pask, J. Am. Cer. Soc. 51 (1968), 569.
L. Coudurier, J. Adorian, D. Pique and N. Eustathopoulos, Rev. Int. Hautes Temp. Refract. 21 (1984), 81.
V. Laurent, D. Chatain, C. Chatillon and N. Eusthopoulos, Acta Met 36 (1988), 1797.
O. Knacke, O. Kubaschewski and K. Hesselmann, “Thermo-chemical Properties of Inorganic Substances” Second Edition (Springer Verlag, Verlag Stahleisen m. b. H Dusseldorf, 1991).
C. Gelain, A. Cassuto and P. Le Goff, Oxidation of Metals 3 (1971), 139.
L. Goumiri and J. C. Joud, Acta Met. 30 (1982), 1397.
Y. Austin Chang and Ker-Chang Hsieh “ Phase Diagrams of Ternary Copper-Oxygen-Metal Systems” (ASM International, Metals Park, Ohio, 1989).
R. Colin, J. Drowart and G. Verhagen, Trans. Faraday Soc. 61, n. 511 Part 7 (1965), 1364.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Castello, P., Ricci, E., Passerone, A. et al. Oxygen mass transfer at liquid-metal-vapour interfaces under a low total pressure. JOURNAL OF MATERIALS SCIENCE 29, 6104–6114 (1994). https://doi.org/10.1007/BF00354549
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00354549