Determination of the Mixing Thermodynamic Properties of Liquid Ternary Alloys by Fitting the Knudsen Effusion Mass Spectrometric Data to the Redlich-Kister-Muggianu Sub-Regular Solution Model

Abstract

We discuss the vaporisation of four liquid ternary-alloy systems, namely, Cu-In-Sn, Ag-In-Sn, Al-Cu-Sn and Cu-Sb-Sn, on the basis of our previous Knudsen effusion mass spectrometric (KEMS) investigations of these systems. The thermodynamic activities and the thermodynamic functions (Gibbs energy, enthalpy, entropy) of mixing were determined using selected standard KEMS procedures (i.e., Simple Pressure Calibration Method (SPC), Oligomer Composition Change Method (OCC), Isothermal Evaporation Method (IEM) and Gibbs-Duhem Ion Intensity Ratio Method (GD-IIR)). In addition, the same thermodynamic quantities, as well as the so-called ternary interaction (L-) parameters, were also obtained from the composition dependence of the measured ion-intensity ratios using a new mathematical procedure (RKM-KEMS). The essence of this new procedure is the fitting of the measured intensity-ratio data were to the Redlich-Kister-Muggianu (RKM) sub-regular solution model, and this model is valid for many liquid ternary alloys, including the systems reviewed here. A full description of the mathematical derivation of RKM-KEMS is given in this work. The primary and intermediate data, obtained directly from the multiple-regression as output data, are the RKM ternary interaction L-parameters. From these quantities, the integral molar excess Gibbs energy, the excess chemical potentials, the activity coefficients and the activities were evaluated in this order. In addition, using the temperature dependence of activities, the integral and partial molar excess enthalpies and entropies could also be determined. The thermodynamic data obtained with the above-mentioned conventional KEMS methods and with the new RKM-KEMS procedure were compared and a good agreement was obtained for the systems studied.