Thermodynamic calculation of the ternary TiAlNb system

Abstract

Phase equilibria of the ternary TiAlNb system are dominated by the large range of homogeneity of (β-Ti,Nb), the binary intermetallic compounds of the NbAl and TiAl systems and the formation of two ternary compounds. The available ternary experimental data, together with a thermodynamic extrapolation of the ternary system from the binary systems, have been used to calculate the ternary phase diagram. The model descriptions of the Gibbs energies of most of these compounds are given by the existing calculations of the binary systems. In order to model a phase which is present in only one binary system, but has a ternary homogeneity range, a hypothetical phase with the same structure was analytically described for each binary system. Such a phase would, of course, be metastable in the other binary systems. Constraints on the Gibbs energies of formation were derived from the crystal structures of the corresponding ordered compounds. These same constraints were employed for the corresponding phases in the ternary system. In a final optimization step, ternary parameters were introduced and adjusted to the available experimental data. The as-derived description of the ternary TiAlNb system can be used to estimate single or multiphase fields and thermodynamic quantities where no experimental data are yet available. It is also useful as an indicator of problem areas for which additional experimental data are required.