Journal of Materials Science

, Volume 29, Issue 23, pp 6104–6114 | Cite as

Oxygen mass transfer at liquid-metal-vapour interfaces under a low total pressure

  • P. Castello
  • E. Ricci
  • A. Passerone
  • P. Costa


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 sr, 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.


Oxygen Exchange Oxygen Flux Saturation Degree Oxygen Mass Transfer Volatile Oxide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



activity of the component η in the liquid phase


partial-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)


global-transport coefficients for the mass transfer of the component η (mol s g−1 cm−1)


molecular weight of the species η (g mol−1)


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)


partial pressure of the jth oxide (Pa)


vapour pressure of the pure metal (Pa)

\(P_{O_2 } \)

partial pressure of molecular O2 (Pa)


total pressure (Pa)


effective metal-vapour pressure (Pa)

\(P_{O_2 }^E \)

effective oxidation pressure (Pa)


effective evaporation ratio


actual value of the bulk-saturation degree


value of the bulk-saturation degree in steady-state (regime) conditions


temperature in the system, far from the container wall (K)


temperature of the container wall (K)


molar fraction of the component η in the liquid phase


condensation coefficient of the species η (cm−3/2)



a quantity evaluated for a liquid below the saturation point


quantity in the bulk liquid


a quantity evaluated in conditions where the liquid metal is saturated with oxygen


a quantity in the interfacial liquid layer


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  1. 1.
    C. H. P. Lupis “Chemical Thermodynamics of Materials” (Elsevier Publishers, Amsterdam, Holland, 1983).Google Scholar
  2. 2.
    J. F. Padday In “Surface & Colloid Science” Ed. E. Matijevic (Wiley Intersc., New York, 1969).Google Scholar
  3. 3.
    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).Google Scholar
  4. 4.
    E. Ricci and A. Passerone, Mater. Sci. Eng. A161 (1993), 31.CrossRefGoogle Scholar
  5. 5.
    E. Ricci, A. Passerone, P. Castello and P. Costa, J. Mater. Sci. 29 (1994) 1833.CrossRefGoogle Scholar
  6. 6.
    H. H. Kellogg, Trans. Met. Soc. AIME, 263 (1966), 602.Google Scholar
  7. 7.
    D. Beruto, L. Barco and G. Belleri, Ceramurgia International 1 (1975), 87.CrossRefGoogle Scholar
  8. 8.
    C. Wagner, J. Appl. Phys. 29 (1958), 1295.CrossRefGoogle Scholar
  9. 9.
    E. A. Gulbransen, K. F. Andrew and F. A. Brassart, J. Electrochem. Soc. 113 (1966), 834.CrossRefGoogle Scholar
  10. 10.
    L. Brewer and G. M. Rosemblatt, Trans. Met. Soc. AIME 224 (1962), 1268.Google Scholar
  11. 11.
    O. Winkler and R. Bakish, “Vacuum Metallurgy” (Elsevier Publishers, Amsterdam, 1971).Google Scholar
  12. 12.
    R. Ohno in “Liquid Metals-Chemistry and Physics”, Chap. 2, Ed. S. Z. Beer (Marcel Dekker Inc., New York, 1972).Google Scholar
  13. 13.
    S. Otsuka and Z. Kozuka, Trans. Jpn. Inst. Met. 22 (1981), 558.CrossRefGoogle Scholar
  14. 14.
    R. H. Lamoreaux, D. L. Hildebrand and L. Brewer, High Temp. Sci. 20 (1985), 37.Google Scholar
  15. 15.
    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).Google Scholar
  16. 16.
    E. Ricci, A. Passerone and J. C. Joud, Surface Sci. 206 (1988), 533.CrossRefGoogle Scholar
  17. 17.
    J. J. Brennan and J. A. Pask, J. Am. Cer. Soc. 51 (1968), 569.CrossRefGoogle Scholar
  18. 18.
    L. Coudurier, J. Adorian, D. Pique and N. Eustathopoulos, Rev. Int. Hautes Temp. Refract. 21 (1984), 81.Google Scholar
  19. 19.
    V. Laurent, D. Chatain, C. Chatillon and N. Eusthopoulos, Acta Met 36 (1988), 1797.CrossRefGoogle Scholar
  20. 20.
    O. Knacke, O. Kubaschewski and K. Hesselmann, “Thermo-chemical Properties of Inorganic Substances” Second Edition (Springer Verlag, Verlag Stahleisen m. b. H Dusseldorf, 1991).Google Scholar
  21. 21.
    C. Gelain, A. Cassuto and P. Le Goff, Oxidation of Metals 3 (1971), 139.CrossRefGoogle Scholar
  22. 22.
    L. Goumiri and J. C. Joud, Acta Met. 30 (1982), 1397.CrossRefGoogle Scholar
  23. 23.
    Y. Austin Chang and Ker-Chang Hsieh “ Phase Diagrams of Ternary Copper-Oxygen-Metal Systems” (ASM International, Metals Park, Ohio, 1989).Google Scholar
  24. 24.
    R. Colin, J. Drowart and G. Verhagen, Trans. Faraday Soc. 61, n. 511 Part 7 (1965), 1364.CrossRefGoogle Scholar

Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • P. Castello
    • 1
  • E. Ricci
    • 1
  • A. Passerone
    • 1
  • P. Costa
    • 2
  1. 1.Istituto di Chimica Fisica Applicata del Materiali del C.N.R.GenovaItaly
  2. 2.Istituto di Scienza e Tecnologie ChimicheFacoltà di Ingegneria dell'Università di GenovaGenovaItaly

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