First-principles calculations of phase stability in the Ti–Zr–Si ternary system

First-principles calculations of the enthalpies of formation of ternary compounds with Fe2P-type (C22, hP9, P 6 ¯ 2 m , N°189) and Mn5Si3-type (D88, hP16, P63/mcm, N°193) structures have been performed in the Ti–Zr–Si system. At low temperature, two ternary compounds C22- Ti3Zr3Si3 and D88-Ti4Zr6Si3 are stable. The existence at high temperature of two solid solutions, (TiZr)5Si3 with the Mn5Si3-type structure and (TiZr)2Si with the Fe2P-type structure, is emphasized. The calculated isothermal section at 1323 K agrees well with the experimental results in the Ti-rich region.