Use of Thermodynamic Data to Determine Surface Tension and Viscosity of Metallic Alloys
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Thermodynamic Data to Determine Surface Tension and Viscosity of Metallic Alloys Toshihiro Tanaka, Klaus Hack, and Shigeta Hara Introduction During the last three decades, various t h e r m o d y n a m i c databases have been compiled to be applied mainly to the cal culation of phase diagrams of alloys, salts, and oxides.' The accumulation and assessment of thermodynamic data and phase-equilibrium information to establish those databases is sometimes called the CALPHAD (calculated phase diagram) approach. 2 The CALPHAD approach has been recognized as useful in various aspects of materials science and engineering. 1,2 In addition to the use of ther modynamic databases for the calculation of phase diagrams, it would be very desirable to apply them to the calculation of other physicochemical quantities, such as surface tension. By doing this, not only can the Utility of databases be enlarged, but also a deeper understanding of the physical properties in question can be reached. On the basis of the concepts just mentioned, we have applied those thermody namic databases to the calculation of the surface tension of liquid alloys and molten ionic mixtures.3"7 In these calculations, we have applied Butler's equation 8 for the surface tension of liquid alloys. In addi tion, we have modified Butler's equation to be extended to molten ionic mixtures by considering the relaxation structure in the surface. These approaches will lead us
MRS BULLETIN/APRIL 1999
to develop a multifunctional data-bank System that will be widely applicable in the evaluation of physicochemical prop erties of liquid alloys and molten ionic mixtures from thermodynamic data. In this article, we explain some physi cal modeis for the surface tension and viscosity of liquid alloys and molten ionic mixtures, in which thermodynamic data can be directly applied to evaluate these physical properties. In addition, the concept for the just-mentioned multifunc tional thermodynamic data-bank System will be described by demonstrating the simultaneous calculation of phase dia grams, surface tension, and viscosity of some alloys used for new, Pb-free soldering materials.
Butler's Equation for Calculating Surface Tension of A-B Binary Liquid Alloys
Several authors3'4'9-17 have proposed cal culations of surface tension of liquid al loys by employing thermodynamic data, as shown in Table I. Their principles are based on Butler's equation, 8 which is ex pressed for surface tension aof any A-B binary liquid alloy as follows: RT
(1 - Afp
'•A
- — GBE'B(T,NB)
(1)
Butler derived Equation 1 assuming an equilibrium between a bulk phase and a surface phase, which is regarded as a hypothetical independent phase. In Equa tion 1, R is the gas constant, T is the temperature, crx is the surface tension of pure liquid X, and Ax is the molar surface area in a monolayer of pure liquid X (X = A or B). A x can be obtained from LN0U3Vx2/\
(2)
where N 0 is Avogadro's number, and Vx is the molar volume of pure liquid X. L in Equation 2 is usually set to be
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