Effect of temperature and composition on surface tension in Fe-Ni-Cr alloys containing sulfur
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T~ -
8314T F, In [1 + k as e -AH~
[1] where o"~is the surface tension of the pure metal in N / m at a reference temperature T ~ A is a constant which expresses the variation of surface tension of pure metal at M.J. McNALLAN, Professor, is with the Department of Civil Engineering, Mechanics and Metallurgy, The University of Illinois at Chicago, Chicago, IL 60680. T. DEBROY, Professor, is with the Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802. Manuscript submitted October 17, 1990. METALLURGICAL TRANSACTIONS B
temperatures above the melting point in N / ( m K), F, is the surface excess in saturation in Kg m o l e / m 2, k is the entropy factor, as is the activity of sulfur in the alloy, and AH ~ is the enthalpy of segregation in K J / K g mole. It was recently demonstrated [4,5J that a simple arbitrary assumption of a single valued positive d t r / d T leads to an unrealistic weld pool aspect ratio, whereas the use of Eq. [1] results in reliable predictions. While mild steel can be adequately treated as a pure metal in which sulfur and oxygen are the only solute species which can influence the surface tension significantly, many important engineering alloys contain substantial quantities of alloying elements. The presence of these elements can also have a significant effect on the surface tension of the liquid metal and, as a consequence, on the welding behavior. An important group of such alloys is the austenitic stainless steels containing nickel, chromium, as well as smaller amounts of other elements. This article addresses the temperature and composition dependence of the surface tension of these alloys when sulfur is the primary surface-active impurity in the alloy. Fundamentally, surface tension or surface energy results from the fact that atoms near a free surface have partially unfilled coordination shells which requires that they be at higher energy states than the atoms in the bulk of the solution. In a multicomponent alloy, atoms whose energy state is affected least by the surface are segregated to the surface region, and this reduces the magnitude of the surface energy. In metallic solutions, the group VI elements, oxygen, sulfur, selenium, and tellurium, are strongly surface active in spite of their low solubilities and therefore exert the strongest influence on the surface tension of the solution. I61 Metallic alloying elements can also be surface active, but because the magnitudes of the energy changes associated with the segregation of these elements are smaller, larger amounts of metallic species must be present to produce the same change in the surface tension of the solution. A completely general formalism to determine surface tension of a multicomponent alloy containing a surfaceactive element would require a much more complex model than that represented by Eq. [ 1]. However, the behavior of some commercial alloys, such as stainless steel, may not require such a complex model, because in stainless steel, the principal metallic comp
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