Predictive Models for the Velocity of Sound in Liquid Metallic Elements at Their Melting-Point Temperatures
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970s, there has been renewed interest in the thermophysical properties of almost all liquid metallic elements, i.e., liquid metals, semimetals, and semiconductors such as silicon, following the advent of mathematical modeling techniques supported by powerful computers. Nowadays, computer simulation studies (e.g., the fluid flow in a vessel or the solidification of a metal, the calculations of the Reynolds, Prandtl, and Schmidt numbers, etc.) of materials-processing operations, based on mathematical models, are widely used as a very useful tool for improving liquid-metal-processing operations and product quality. As a matter of course, accurate and reliable data for the thermophysical properties of metallic liquids are indispensable, not only for the execution of computer simulations and the development of mathematical models[1,2] but also for the direct solution of industrial problems involving hightemperature processing operations.[1,2] For a clear understanding of the behavior and nature of metallic liquids, and further, for accurate predictions TAKAMICHI IIDA, Visiting Scholar, is with McGill University, and Professor Emeritus, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan. RODERICK GUTHRIE, Macdonald Professor, and Director, McGill Metals Processing Centre, is with McGill University, Montreal, PQ, Canada H3A 2A7. Contact e-mail: [email protected] Manuscript submitted February 13, 2009. Article published online July 31, 2009. METALLURGICAL AND MATERIALS TRANSACTIONS B
of their thermophysical properties, the velocity of sound is an essential basic thermophysical property: For example, it is well known that the velocity of sound is of great relevance to the compressibility and structure of metallic liquids. Furthermore, the authors’ recent studies[3–10] have proved that the models, in terms of a simple parameter revealed through data for the velocity of sound, provide very good agreement with experimental data for several thermophysical properties of liquid metallic elements; values calculated from the authors’ models fall, or almost fall, within the range of uncertainties in experimental data for high-melting-point or reactive metals. Even so, relatively few studies have been made of the velocity of sound in metallic liquids, in particular, from the standpoint of materials process science. In this article, the authors present accurately predictive models for the velocity of sound in liquid metallic elements at their melting-point temperatures. While multicomponent alloys are typically treated in liquidmaterials-processing operations, accurate and reliable data for the respective pure components of an alloy system are first needed[11–15] as a starting point. In addition, one must make investigations of element properties (e.g., the velocity of sound) in order to clearly understand the essence of a metallic liquid’s thermophysical properties. In the field of materials process science, both ‘‘accuracy’’ and ‘‘universality’’ are required of any model for predicting the thermophysical properties of liquid
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