Enthalpies of formation of the Ag- Au- Si, Ag- Au- Ge, and Ag- Au- Sn Ternary Liquid Alloys; experimental determinations
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I.
INTRODUCTION
IN the past few years the need for better materials has created an emphasis on materials containing a large number of components. In these cases, thermodynamic properties and the phase relationships in the system are important but it seems unlikely that systematic experimental investigations can be carried out in the near future to measure either thermodynamic properties or phase diagrams of systems involving more than two components. Therefore, researchers have emphasized the evaluation of the thermodynamic properties of solutions from the properties of the related binary solutions in multicomponent systems. This approach can help reduce the number of experiments to be carried out in the investigation of a system. Ansara has reviewed t1'21 the methods available to calculate thermodynamic properties of multicomponent systems from binary data. He discusses first the physical models (interaction models) which are derived from a physical principle. These are regular, quasi-chemical, and "surrounded atom" or "central atom theory" models, which deal mainly with binary solutions and, in general, cannot describe highly asymmetrical solutions. The Redlich-Kister equation I31 is the most commonly used mathematical expansion for solution properties in binary systems. In addition, a large number of mathematical methods is now available to expand or interpolate the binary solution data into a ternary system. These are the Wohl, 141 Krupkowski, tS} Bonnier, I6] Toop, [7] Kohler, [s] and Colinet [91 models. Ansara, however, offers the following cautions: "For these last four equations, great care should be taken with the binary data used. Significative differences may be expected for the partial values which can then be derived, and a modification of the shape of the phase diagram may then occur . . . . Although all of these equations have been applied with success to represent the thermodynamic properties of ternary systems, little work has been done on higher order systems. Complications can arise in represent-
ing the properties of quaternary solutions for which the four limiting ternary systems are well described but by two or three different types of equations. ''t~'21 In many cases, a ternary interaction term also must be used. This term can be obtained only by comparing the calculated values with the experimental values of the ternary system, and therefore it is not usable for predictions. The present model, the Hoch-Arpshofen model, was deduced from physical principles and is applicable to binary, ternary, and larger systems. {l~ It was derived originally by looking at complexes in the solution and at the strength of the bond between atoms A and B (the A - B bond), which depends on the presence of other atoms in the complex. Our consideration of the solution is the same as that of Guggenheim]12] who speaks of "treatment of quadruplets of sites forming regular tetrahedra" when treating regular solutions and superlattices. Guggenheim, however, always treats the strength of the A - B bond in the same way,
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