Thermodynamic Characteristics of Binary Al–Hf Melts

Abstract

The thermodynamic characteristics of aluminum–hafnium melts are studied. The well-known (Δ_f$H_{{298}}^{0}$) thermodynamic properties are analyzed, and unknown ones (($S_{{298}}^{0}$), ($H_{{298}}^{0}$ – $H_{0}^{0}$), c_p(T), and c_p(liq)) are calculated for the congruently melting Al₃Hf, Al₂Hf, AlHf, and Al₂Hf₃ compounds. The standard formation enthalpies of these intermetallic compounds are taken from the literature, where they were calculated using semiempirical Miedema’s model and were –142.4, –134.1, –100.6, and –225 kJ/mol for each intermetallic compound, respectively. The calculation results are used for a thermodynamic simulation (TS) of Al–Hf melts. The thermodynamic simulation is performed using the TERRA software package. The composition and the thermodynamic characteristics of the melts are calculated using the model of ideal solutions of interaction products (ISIP). This model is used to study the thermodynamics of the liquid solutions in the aluminum–hafnium system. The simulation is carried out in an initial argon atmosphere at a total pressure of 10⁵ Pa. The studies are performed in the region of temperatures and compositions corresponding to the liquid state of this system (2100–2300 K). A comparison of the results with the results of ideal solution approximation simulation makes it possible to determine the excess integral thermodynamic characteristics (enthalpy, entropy, Gibbs energy) of the Al–Hf melts. The enthalpies of mixing are shown to decrease in absolute value as temperature increases. The values found in this work are compared with the well-known data on the integral enthalpies of mixing for aluminum melts containing other III–IV group transition elements (Sc, Ti, Zr). The formation of Al–Hf, Al–Sc, Al–Ti, and Al–Zr liquid alloys is found to be accompanied by significant heat release. The extreme integral enthalpy of mixing of an Al–Hf alloy is comparable with that of an Al–Ti alloy and is no higher than –32 kJ/mol in absolute value. The components of the Al–Sc and Al–Zr systems demonstrate a tendency toward a stronger interaction: ΔH_mix reaches –45 kJ/mol. The ISIP model used for TS makes it possible to describe the thermodynamic properties of the aluminum–hafnium melts.