The phase equilibria of the Ti–V–M (M = Si, Nb, Ta) ternary systems

Abstract

Eight Ti–V–Si ternary alloys were prepared to determine the phase equilibria associated with the Ti5Si4, Ti3Si and V6Si5 phases and the composition range of the ternary compound τ by means of X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA). The enthalpies of formation at 0 K for the end-members of the TiSi2, TiSi, Ti5Si4, Ti5Si3, Ti3Si, VSi2, V5Si3 and V3Si phases in the Ti–V–Si system were computed via first-principles calculations to supply necessary thermodynamic data for the modeling. The thermodynamic assessment of the Ti–V–M (M = Si, Nb, Ta) systems was carried out by the CALPHAD (CALculation of PHAse Diagrams) approach based the experimental data available in the literature and present work and theoretic values from the first-principles calculations. A set of self-consistent thermodynamic parameters for each ternary system was finally obtained. Some representative isothermal sections, vertical sections, liquidus and solidus surface projections were calculated. The calculated results indicated that almost all of the reliable experimental data were satisfactorily reproduced by the present modeling. The appropriate method can be chosen to study the ternary systems based on their phase equilibria.