Determination of thermodynamic properties of liquid Ag-In, Ag-Sb, Ag-Sn, In-Sb, Sb-Sn, Ag-In-Sb, Cu-In-Sn and Ag-In-Sn systems by Knudsen effusion Mass Spectrometry A. Popovic and L. Bencze* Jozef Stefan Institute, Jamova 39, SLO-1000 Ljubljana, Slovenia. *Eötvös Loránd University, Dept. of Physical Chemistry, H-1117 Budapest, Pázmány Péter sétány 1/A, Hungary

The scheme of a Knudsen cell - mass spectrometer system (FZ Jülich, Germany) < 20 KEMS laboratories over the world

ION SOURCE The scheme of single and double the Knudsen cells.

Determination of equilibrium vapour pressure by KEMS: Inghram, Chupka, 1955 where K is the (general) instrumental sensitivity constant I ij is the intensity of ion i originating from neutral species j  i is the isotopic abundance of ion i  i is the multiplier gain factor of ion i (sensitivity constant of the detector for ion i) - in multiplier current measurement mode only a i is the (spectral) abundance of ion i in the mass spectrum  i is the total ionisation cross section of species j at the actual electron energy (s i depends on j and the ionising electron energy) K can be determined by calibration using e.g. a reference substance (e.g.pure component) in the next or previous experiment, using internal standard inside the same cell, using isothermal long-term evaporation etc). p j *: pressure over the pure component

Determination of activities by KEMS: 1/ by direct pressure calibration (DPC) using pure metals as reference substances in subsequent experiments (the uncertainty can reach as high as 20% due to a the change of sensitivity constant day-by-day), 2/ using a proper internal standard (ISM) being in the same cell, 3/ using twin or multiple Knudsen cell technique (MKC) (some of the compartments are filled with the pure components), 4/ from the change of the oligomer (monomer, dimer, trimer etc.) composition in the vapour (this latter method can be applied in the only case if the metals vaporise in the form of oligomers, such as Sb(g), Sb 2 (g), Sb 3 (g), Sb 4 (g)), 5/ applying the mass spectrometric Gibbs-Duhem Ion Intensity Ratio Method (GD- IIRM) that is a modification of the well-known Gibbs-Duhem relationship with MS quantities (i.e. ion intensities), 6/ applying the isothermal evaporation method (IEM) /long-term or total/, / for ternary alloys, by applying Miki’ s or Tomiska’ s new KEMS methods for the determination of the constants in the power series expression of G E. (Miki: Redlich-Kister expression, Tomiska: TAP expression)

THERMODYNAMIC PROPERTIES OF MIXING Activities and the activity coefficients ---> chemical potential change of mixing, excess chemical potential ---->Gibbs energy change of mixing, excess Gibbs energy The uncertainty of  E i /  (  E i )/ is usually lower than +-1 kJ/mol (at 1400 K, assuming an error as factor 1.1 in the values of activities,  =1.11 kJ/mol is obtained) Temperature dependence of activities---> partial and integral enthalpy changes of mixing. Uncertainties:  (H E i )~1-2 kJ/mol for partial quantities but in case of wrong identification of the composition the uncertainty of the integral quantity (H E ) can reach as high as ~10 kJ/mol if the partial quantities depend on composition very sharply. The Gibbs-Duhem integration helps against this problem.

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BINARY SYSTEMS

Miki’s method supplemented by us for the calculation of all the 3 ternary L’s: where G E is the excess Gibbs free energy, expressed in terms of binary and ternary interaction parameters. where where I Cu / I Sn is the measured ion intensity ratio of Cu + to Sn + and C is a constant Redlich-Kister-Muggianu:

By rearranging and putting similar terms together we finally get that : The three ternary parameters can finally be found by solving the set of linear equations: where ’n’ is the number of the measured compositions. If n>4 the solution of the linear equation system should be replaced with a multiple regression problem. The method provides the three ternary parameters, and, as input parameters it needs the binary parameters (either from own experiments or from literature) and the measured ion intensity ratio at various compositions for the given temperature. Any ion intensity ratio can be used from the total 3 variations of a ternary systems.

The result for Cu-In-Sn, obtained from I Cu / I Sn of 23 compositions, is as follows: Fig1. Measured compositions.

Fig.2. Ternary parameters as a function of temperature, obtained in this work. Fig.3. Ternary parameters as a function of temperature by Liu et al..

Fig. 4. Comparison of indium activity data obtained from our own and Liu’ s ternary parameters, from our measured mass loss data and from the measured EMF data of Yamaguchi.

Fig.5. Comparison of the partial excess enthalpy of indium obtained from our own and Liu’ s ternary parameters, from the ion intensity of In vs. temperature directly and by assuming binary parameters only.

Fig.6a. Iso-curves of the integral excess Gibbs energy at 1173 K, evaluated using our own ternary parameters. Fig.6b. Iso-curves of the integral excess Gibbs energy at 1173 K, evaluated Liu’ s ternary parameters. G E of Cu-In-Sn

Fig.7a. Iso-curves of the integral excess enthalpy at 1400 K, evaluated using our own ternary parameters. Fig.7b. Iso-curves of the integral excess enthalpy at 1400 K, evaluated using Liu’ s ternary parameters H E of Cu-In-Sn

Two possibilities for getting ternary L’s: 1: 2: = 1: 2: X = X

Dataset I, Ag + /In + Dataset I, Ag + /Sn + Dataset II, Ag + /Sn + our evaluation with Miki’s Ag + /In + data G E of Ag-In-Sn

Activities in Ag-In-Sn

CONCLUSIONS 1. The uncertainties of the ternary Redlich-Kister L-parameters obtained from our Knudsen effusion mass spectrometric data depend on the number of compositions studied. 23 compositions seemed to be sufficient to reach rather low relative uncertainty (the case of Cu-In-Sn). Lower number of compositions (the case of Ag-In-Sn) increases the uncertainties of L’s but the uncertainties of G E and of the activities remain still low. 2. There is a complete mismatch (both in absolute values and temperature trends) between the ternary L-parameters of Cu-In-Sn obtained in this work and those assessed by Liu. This mismatch results in large difference between the values obtained in this work and by Liu in all thermodynamic quantities, in particular in the partial and integral excess enthalpies and excess Gibbs energies. 3. The G E and activity values of Ag-In-Sn obtained from our and Miki’ s KEMS data agree very well but the ternary L-values obtained from this two sources are different. The difference in L’s probably also could be decreased by increasing the compositions studied. 4. Any ion pair variation (e.g. Ag + /Sn + or Ag + /In + in Ag-In-Sn) in the mass spectrum can be chosen in principle for obtaining the thermodynamic properties. The different choices must provide the same values in case of good consistency.

Many thanks to the COST 531 leadership for the support of my STSMs. ACKNOWLEDGEMENTS Thank You for Your attention!