Performance of a Modified Schytil Model for the Surface Tension of Liquid Metallic Elements at Their Melting Point Tempe
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TRODUCTION
KNOWLEDGE of the surface tension of metallic liquids is essential for understanding various materials processing concepts (e.g., refining, casting, melt spinning and extraction, crystal growth, welding, sintering, etc.). From the standpoint of materials process science, accurate and reliable data for the surface tension of metallic liquids are indispensable, not only for the execution of computer simulations and the development of mathematical models but also for the direct solution of industrial problems of high-temperature operations.[1–3] (pp. 109–46) Particularly, accurate data for the properties of almost all liquid metallic elements are first needed,[3–11](p. 89) even though practical materials are in general alloys. In addition, to seize the essence of the surface tension for a metallic liquid, experimental and theoretical work on liquid metallic elements should be made. In the area of materials process science, both accuracy and universality are required of any model for predicting the thermophysical properties (e.g., surface tension) of liquid metallic elements. Many papers on the surface tension of metallic liquids have been published in the clast 15 years or so.[12–23] However, they are still not satisfactory, with respect to both accuracy and universality of models, from the viewpoint of materials process TAKAMICHI IIDA, Visiting Professor and RODERICK GUTHRIE, Macdonald Professor of Metallurgy and Director, are with McGill Metals Processing Centre, 3610 University St, Montreal, Quebec, Canada H3A 2B2. Contact e-mail: [email protected] TAKAMICHI IIDA, Professor Emeritus, is with Osaka University, Osaka 565-0871, Japan. Manuscript submitted March 2, 2009. Article published online February 5, 2010. METALLURGICAL AND MATERIALS TRANSACTIONS B
science. Although the Skapski and the Schytil models for the surface tension of liquid metallic elements can be given in view of universality, the weakness of these models is that the agreement with experiment is not necessarily good. In the authors’ recent articles,[24,25] it was shown that a modified Skapski model in terms of a 1=2 common parameter, which is denoted by nE ; for the surface tension of liquid metallic elements at their melting point temperatures, performs well for many liquid metallic elements. In this article, the authors evaluate the performance of both the Schytil model and a modified Schytil model, which is now proposed by the authors, by comparing experimental values for the melting point surface tension of a large number of liquid metallic elements with those calculated from these two models, using relative standard deviations as a yardstick for comparison. Furthermore, the current authors indicate that values of the respective numeric factor for liquid metallic elements, which appear in the modified Schytil model, vary periodically with atomic number. II.
PERFORMANCE OF THE SCHYTIL MODEL
Schytil[26] presented a semiempirical model for the surface tension of liquid metallic elements at their melting point temperatures in terms of well-kn
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