Thermodynamics of the Liquid {xCu + yAu + (1 - x- y)Ge}, (0.75 _< x -< 1, 0 _< y < 0.125) Alloys at 1550 K by Knudsen Effusion Mass Spectrometry M. MILLER and K.A. GINGERICH Partial pressures and thermodynamic activities in four liquid Cu-Au-Ge alloys from the compositional section XAu = XGe and Xcu >-- 0.75 have been determined by Knudsen effusion mass spectrometry (KEMS) at 1550 K. The experimental data were also used for the thermo- dynamical description of the terminal compositional region of these alloys with Xc, -> 0.75 using Darken's ternary quadratic formalism. The binary interaction parameters for Cu-Au and Cu-Ge as well as the limiting activity coefficients of Au and Ge in their solute alloys with Cu have been evaluated from literature data. The ternary interaction parameter in the alloys investigated was determined experimentally as -3.15 --- 0.36. These parameters enabled the determination of equations describing the activity coefficients and the excess Gibbs free energies for the limited ternary region with Xc, - 0.75 as a function of the alloy composition: lnfc~ = --2.10X2Au -- 5.73 X2o -- 3.15 XAuXco lnfA, = --2.07 + lnfc~ + 4.20 XA~ + 3.15 XCe lnfc~ = --3.62 + lnfc~ + 3.15 XA~ + 11.46 X~ Gem = R T ( - I n f c ~ - 2.07 XA~ -- 3.62 XC~) The activities obtained from Darken's model agree very well with those calculated from the partial pressures for the four alloys studied. All the alloy components show negative deviations from ideality. I. INTRODUCTION KNOWLEDGE of thermodynamic properties of al- loys is essential for establishing proper refining opera- tion procedures for metals and for the development of new alloys. For most ternary and multicomponent sys- tems, however, experimental data exist only for a lim- ited temperature and composition range. In these cases, the needed data can be interpolated to the proper con- ditions if the analytical descriptions of the thermo- dynamic properties are established. At present, systems with very different thermodynamic characteristics can be described using different models. For this purpose, sim- ple models, such as regular and quasichemical solution models m and polynomial descriptions of thermodynamic functions, [2'3] or sophisticated models, such as the inter- action parameter formalism [4] or the multi-sub-lattice model tSJ are in use. These models were reviewed in re- cent articles, tz,3,6,7J The advantage of simple models is that they are easy to handle and their physical meaning is easy to understand. However, because of this sim- plicity, some interactions cannot be accounted for by these models, sometimes resulting in significant errors. More advanced models containing more parameters and M. MILLER, Associate Professor, is with the Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Technical University of Wroclaw, 50-370 Wroclaw, Poland. K.A GINGERICH, Professor, is with the Department of Chemistry, Texas A & M University, College Station, TX 77843. Manuscript submitted June 1, 1993. polynoms can give more precise descriptions, but the pa- rameters lose their physical and chemical meaning. In the present study, the thermodynamic activities of four {xCu + yAu + (1 - x - y)Ge} (1) alloys were de- termined for the composition range x -> 0.75 along the compositional section y = (1 - x)/2. The aim of the study was to determine the thermodynamic properties of certain samples and, finally, the description of the data by Darken's ternary quadratic modelJ g] This model is able to predict ternary thermodynamics from a limited set of measurements, introducing the ternary interaction parameter in addition to the thermodynamic parameters of binary systems which have to be well established. The interaction parameters enabled the analytical description of activities in the alloys studied in the limited compo- sitional region of x -> 0.75 and 0 -< y -< 1. Knudsen effusion mass spectrometry (KEMS) was used as the experimental method. The measured ion cur- rents coming from the ionization of each component of the equilibrium vapors in the Knudsen cell are related to their partial pressures by the following equation: p, = kl~T/(o'~3,i) [11 where p/= partial pressure of the component i, k = cal- ibration constant of the mass spectrometer, T = tem- perature, 1~ = intensity of the i § ions formed upon ionization of atoms i measured in the mass spectrum, o'i = ionization cross section of the atoms i, and 71 = mul- tiplier gain for i § ions. Belton and Fruehan 19'~~ as well as Neckel and METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 25A, APRIL 1994--857