ИСТИНА

Thermodynamic modeling allows to reduce time and material costs for the study of phase equilibria in multicomponent systems. To improve the reliability of predicting the phase composition and properties of phases, it is important to estimate the uncertainty of the parameters of CALPHAD models. The uncertainty of model parameters is due to various factors: the lack of experimental information to unambiguously determine the model parameters, the errors in the experimental data, as well as the uncertainty of the models themselves. The purpose of this study was to quantify the uncertainty of model parameters of fcc and melt in the binary Au–Pd and investigate its influence on the calculations of phase equilibria in the Ag–Au–Pd ternary. The liquidus and solidus temperatures, as well as the heats of melting of 6 alloys of the Au–Pd system, were determined by the DTA/DSC method. These results, together with the published data, were used to make a new thermodynamic description of the system. The emphasis was placed on new results of measurements of the solidus temperature and melting enthalpies by proper adjusting of data weights. Two models were tested for the melt: subregular and three-parameter Redlich-Kister expansion. The new assessment of Au–Pd system shows good agreement with both our and literature data. In particular, it does not exhibit the extremely unusual behavior of the calculated thermodynamic properties of the melt - a change in the sign of the excess Gibbs energy in the composition region near Pd, which was observed in previous calculations. The statistical jackknife method was used to estimate the uncertainties of two sets of phase model parameters obtained from the CALPHAD calculation of the Au–Pd system. Using the “probing” method, we assessed the influence of estimated uncertainty in the parameters of the fcc and melt models on the calculation of the corresponding equilibria in the ternary Ag–Au–Pd. To implement this approach, macros were prepared in the Thermo-Calc package. However, due to the very high labor consuming of this method, which involves repeating calculations with varying parameter values within appropriate limits, only 3-5 test points could be used during “probing” and calculations were performed only for a limited number of compositions and/or temperatures. By “probing” the uncertainty region of parameter values, the uncertainty of the calculated coordinates of phase equilibria in the Ag–Au–Pd system was estimated, which was approximately 0.02 mole fraction in composition and 5 K in temperature. Thus, in the studied ternary system, the scatter of the calculation results does not exceed the discrepancy between the various results of studying the bounding Au–Pd system. In addition, the fundamental need to take into account the mutual correlation of the phase model parameters obtained during optimization has been confirmed. In particular, the coefficients of the temperature dependence of the interaction parameters of both phase turn out to be nearly linearly depended: the modules of the correlation coefficients were 0.998-0.999 and more. This was also confirmed by the “probing” of areas of uncertainty, when any attempt to independently vary the enthalpy and entropy contributions to the interaction parameters leads to a sharp deterioration in the results. Thus, only one of each pair of parameters has a significant uncertainty interval, and the other is almost uniquely determined from the condition of a linear relationship.