Theoretical Calculations of the Surface Tension of Liquid Transition Metals
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erfacial and surface properties of condensed matter phases are important from both fundamental and technological points of view.[1] Studies on surface properties and their relation to macro and microscopic phenomena have been done.[2–6] The surface energy and the work functions are the two most fundamental electronic properties of a metallic surface, and their determination is of great importance in the understanding of a wide range of surface phenomena. These two quantities can be calculated from the surface tension of liquid metals.[7] Based on the present experience, it may be argued that, for properties as difficult to assess experimentally as surface properties, theoretical calculations have reached a stage in which they may form the most consistent basis for a physical description of surface phenomena. The surface tension of liquid metals is an essential thermophysical property relating strongly to various phenomena associated with liquid metal processing operations. Many materials technologies are influenced by the surface tension of a liquid metal. In the field of process science, accurate and reliable data on the surface tension of all liquid metals are required.
FATHI AQRA, Associate Professor, University Teacher, and Researcher, and AHMED AYYAD, Assistant Professor, University Teacher, and Researcher, are with the Department of Chemistry, Faculty of Science and Technology, Hebron University, Hebron, West Bank, Palestine. Contact e-mail: [email protected] Manuscript submitted October 4, 2010. Article published online November 30, 2010. METALLURGICAL AND MATERIALS TRANSACTIONS B
The model of the surface tension of liquid metals must be accurate and universal. We recently have derived a theoretical equation for the calculation of surface tension of pure liquid metals, which was applied for pure liquid Ga.[8] In continuation to this work, it was considered worthwhile to increase the success of our equation by applying it to other liquid metals. Therefore, this article describes a theoretical calculation of the surface tension of pure liquid mercury as a function of temperature. In addition, the manuscript reports the calculation of the surface tension of various d-block metals at their melting points, such as Ti, Zr, Fe, Co, Ni, Cu, Zn, Cd, Ag, Au, Pd, and Pt. The obtained theoretical values are strictly compared with the experimental reported data. The theoretical consideration, here, is based on classical statistical thermodynamics formulation of Eyring and coworkers.[9–11] Their theory is focused on the assumption that the metal after melting acquires vacancies that are moving freely through the melt and that short-range order exists in the liquid.[9–11] The thermodynamic properties of the liquid metal may be calculated from the relationship between the Helmholtz free energy and the partition functions. Eyring has shown that this approach can predict the thermodynamic properties of numerous liquids and pure liquid metals. The Eyring’s approach in calculating the surface tension of a liquid metal was m
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