A model for accurate predictions of self-diffusivities in liquid metals, semimetals, and semiconductors
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INTRODUCTION
KNOWLEDGE of diffusivities for various liquid metallic elements is needed for many fields of engineering. For example, for most metallurgical processes, heterogeneous chemical reactions play an important role. The rates of heterogeneous reactions are limited by the diffusion of the reactant species to reaction site interfaces. Similarly, many other processes, such as corrosion, crystal growth, and so forth, are governed by the rate of atomic diffusion. To investigate atomic diffusion phenomena in a liquid alloy system, accurate data for the self-diffusivities of the respective pure metal components of the system are first needed. However, experimental data for self-diffusivities of liquid metallic elements are extremely scarce, mainly because of a lack of specific radio-isotopes (i.e., tracers). At present, it would appear that experimental self-diffusivity data are available only for some 20 metallic elements. Numerous theoretical and semitheoretical studies of selfdiffusivity in liquid metals have been made over the past half-century.[1–9] However, the agreement obtained between theory and experiment for various liquid metallic elements is still not satisfactory from a practical standpoint. Accurate and reliable data for self-diffusivity in almost all liquid metallic elements are greatly needed from the standpoint of materials process science. In this article, the authors present an appropriate model, by combining the modified Stokes-Einstein formula with the authors’ model for melting-point viscosity, to accurately predict the self-diffusivities of various liquid metallic elements. The authors also propose a simple expression TAKAMICHI IIDA, Visiting Professor, is with McGill University, Montreal, QC, Canada H3A 2B2, and Emeritus Professor, Osaka University, 2-1, Yamadaoka, Suita, Osaka 565-0871, Japan. RODERICK GUTHRIE, MacDonald Professor of Metallurgy, and NAGENDRA TRIPATHI, Postdoctoral Fellow, are with McGill Metals Processing Centre, McGill University, Montreal, QC, Canada H3A 2B2. Contact e-mail: nagendra4@ yahoo.com Manuscript submitted February 7, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS B
based on melting-point temperature for the temperature dependence of the self-diffusivity of liquid metallic elements. Using this model, self-diffusivity data are predicted for liquid iron, cobalt, nickel, titanium, aluminum, magnesium, silicon, and so forth.
II.
MODEL FOR SELF-DIFFUSIVITY OF LIQUID METALLIC ELEMENTS
A. Melting-Point Self-Diffusivity Various models and equations for self-diffusivity in liquid metals have been presented.[1–9] Of these, the modified Stokes-Einstein formula[6] is the most satisfactory from an engineering point of view because it is simple and is in good agreement with self-diffusivity data for liquid metals. Recently, the authors presented a model, represented by the following equation, for accurate predictions of the melting-point viscosity of liquid metallic elements:[10,11] mm 5 C0
M 1=2 gm ðjT T m Þ1=2
[1]
where m is the viscosity, C0 is a constant that is appro
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