Numerical Approach to Predicting Thermodynamic Properties of Ternary Al-Ni-Pt Alloys

Thermodynamic properties of ternary Al-Ni-Pt system, such as $\text{}^{ex}G_{AlNiPt},$ \mu_{Al(AlNiPt)},$ $\mu_{Ni(AlNiPt)},$ and $\mu_{Pt(AlNiPt)}$ at 1373 K were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting $\text{}^{ex}G_{AlNiPt} values was regarded as calculation of values of $\text{}^{ex}G$ function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of $\text{}^{ex}G$ on all legs of the triangle are known ($\text{}^{ex}G_{AlNi}$, $\text{}^{ex}G_{AlPt}$, $\text{}^{ex}G_{NiPt}$). This approach is contrary to finding the function value outside a certain area, if the function value inside this area is known. $\text{}^{ex}G$ and $L_{ijk}$ ternary interaction parameters in the Muggianu extension of the Redlich-Kister formalism are calculated numerically using the Mathematica program. The accepted values of the third component concentration $x_{x}$ differed from 0.01 to 0.1 mol fraction. Values of L parameters in the Redlich-Kister formula vary for different $x_{x}$ values, the $\text{}^{0}L_{AlNiPt}$ value in particular. Values of thermodynamic functions: $\text{}^{ex}G_{AlNiPt}$, $\mu_{Al(AlNiPt)}$, $\mu_{Ni(AlNiPt)}$ and $\mu_{Pt(AlNiPt)}$ do not differ significantly for different $x_{x}$ values. The choice of $x_{x}$ value does not influence the accuracy of calculations.