Performance of a Modified Skapski Model for the Surface Tension of Liquid Metallic Elements at Their Melting-Point Tempe
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THE surface tension of liquid metals is an essential thermophysical property relating deeply to various phenomena associated with liquid metal processing operations. Many materials technologies, such as smelting, refining, casting, crystal growth, brazing, sintering, zone melting, and fiber formation, are greatly influenced by the role played by the surface tension of a liquid metal. Accurate and reliable data on the surface tension of almost all liquid metallic elements, i.e., liquid metals, semimetals, and semiconductors, are needed in the field of materials process science. Consequently, both ‘‘accuracy’’ and ‘‘universality’’ are the necessary conditions for any model of the surface tension of liquid metallic elements. Over the past 100 years or more, numerous attempts have been made to describe the surface tension of a liquid metal in terms of basic physical quantities or material properties.[1,2] A considerable number of research articles on the surface tension of liquid metallic elements have been reported even in the last 10 years or so and some recent articles are referenced.[3–17] However, it is still difficult to identify a truly successful model for which both accuracy and universality apply. Although only a TAKAMICHI IIDA, Visiting Scholar, is with the McGill Metals Processing Center, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2, and is Professor Emeritus, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan. RODERICK GUTHRIE, Macdonald Professor and Director, is with the McGill Metals Processing Center, McGill University. Contact e-mail: [email protected] Manuscript submitted February 27, 2009. Article published online October 17, 2009. METALLURGICAL AND MATERIALS TRANSACTIONS B
few models, for example, the Skapski[1,2,14–19] and Schytil[1–4,17,20,21] models, are virtually universal, the weakness of these models is that agreement with the experiment is not necessarily satisfactory from the standpoint of materials process science. In view of this, the authors[22] presented a modified Skapski model, in which a common parameter n1/2 E , revealed through data for the velocity of sound, was introduced to improve predictions. In this work, the authors now evaluate the performances of both the Skapski and the modified Skapski models by comparing calculated values from these two models and the experimental values for the meltingpoint surface tension of a large number of liquid metallic elements, using a relative standard deviation as a yardstick for quantifying their predictive capabilities. Furthermore, the authors point out that the values of the proportionality factors of the respective liquid metallic elements in the modified Skapski model vary periodically with the atomic number.
II.
PERFORMANCE OF THE SKAPSKI MODEL
Skapski[18] proposed a semiempirical model for the surface tension of liquids based on their molar enthalpies of sublimation Dgs H0 at 0 K. The Skapski model is given by the equation cm ¼ Q
Dgs H0 2=3
Vm
½1
where c is the surface tension, Q is a n
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