Paper PII-18

Impact of Ternary Parameters

Schmid-Fetzer Rainer and Janz Andreas

University of Clausthal, Institute of Metallurgy, Robert-Koch-Str. 42

D-38678 Clausthal-Zellerfeld, Germany

The impact of using a ternary parameter L, defined by the excess Gibbs energy, G^exc= L·x₁·x₂·x₃, is elaborated. It is emphasized that this impact is very much counter-intuitive.

For example, the activity of Hg in the Bi-Sn-Hg system at 350°C along the section    x_Bi = x_Sn is shown as the solid line in Fig. 1, calculated without a ternary parameter (L=0). In this example, we have calculated a_Hg from the Redlich-Kister (Mugg ianu) extrapolation of the binary data, but that is completely unimportant for the following. We get the same impact of L for any other extrapolation scheme.

It is is not possible to push the activity curve a_Hg down (or up) for all alloys on that section by using any value of this simplest ternary L-parameter. An increase of a_Hg for x_Hg <0.5 always comes with a decrease of a_Hg for x_Hg >0.5 (or vice versa) and a_Hg (x_Hg=0.5) is constant for all values of L. This impact of L is very much against intuition, see Fig. 1.

Fig. 1: System Bi-Sn-Hg, section Bi:Sn = 1:1, T=350°C.

Bi

Sn

Hg

This is a general feature. In any ternary 1-2-3 system the ternary excess term L·x₁·x₂·x₃ leaves a₁ unchanged along the section x₁=0.5. The reason is that = L·x₂·x₃·(1-2x₁).

Conclusion: This ternary L-parameter should not be used as a fitting tool for phase diagrams without carefully checking its impact on activities. It is better to not use it at all, but rather improve on the binary descriptions.