Ab initio and CALPHAD-type thermodynamic investigation of the Ti-Al-Zr system

Abstract

Ti-Al based alloys have been widely used in the aeronautics and aerospace. Adding alloying element Zr can significantly improve their high-temperature endurance and corrosion resistance. To investigate the influence of the addition of element Zr on the properties of the Ti-Al system, ab initio calculations and the CALPHAD (CALculation of PHAse Diagrams) method were used to evaluate the Ti-Al-Zr ternary system. Ab initio calculations were carried out to calculate the formation enthalpies of intermetallic compounds and end-members. CALPHAD approach was employed to optimize the thermodynamic parameters based on experiments. The experimental data of phase equilibria at 1073, 1273, 1473, and 1573 K, as well as a vertical section of the Ti 3 Al-Ti + 5 wt.% Zr were used to assess this system. The thermodynamic parameters of the binary Ti-Al, Al-Zr and Ti-Zr systems were acquired from recent assessments, and the ternary ones were evaluated in the present work. The Ti-Al-Zr ternary dataset has been established and the calculated results are in close agreement with the experimental data on both thermodynamics and phase equilibria.

Critical Assessment of the Al-Ti-Zr System

“…Otherwise, all multiphase equilibria in the experimental section are reproduced in the modelling. At higher temperatures there is quite some discrepancy at 1200°C between the modelling [83] and experimental data in the Ti-corner, [23] while the match at 1300°C is somewhat better. Calculated phase boundaries at 800 and 1000°C of the vertical section [83] fit very well with those of the binary accepted here, with the sole exception for the a(Ti)/a(Ti) ?…”

“…Modelled [83] and experimentally determined [24] isothermal sections at 1000°C qualitatively match much better. Though, there are some differences in the solid solubility ranges of individual phases, most notably for Ti 3 Al, which has less solid solubility for Zr according to the modelling.…”

“…The major difference between the isothermal sections for 800°C, are that the experimental one shows phase equilibria between b(Ti,Zr) and Zr(Al,Ti) 2 , [25] while the calculations show that TiAl should be in equilibrium with Zr 4 Al 3 . [83] Therefore, multiphase equilibria in a wide range of compositions in the two isotherms are quite different from each other as discussed in (Ref 83). Which of the two versions is correct cannot be decided on the existing evidence.…”

“…Recently, CALPHAD-type and ab initio calculations were applied to establish isothermal sections at 800 and 1000°C, partial isothermal sections of the Ti-corner at 1000, 1200 and 1300°C and a vertical section along Ti-2.7 at.% Zr/Ti 3 Al. [83] Thermodynamic parameters from binaries were extracted from (Ref 41, 34,84) for Ti-Al, Al-Zr, and Ti-Zr, respectively. Experimental data from [23][24][25]52,74] have been used to optimize thermodynamic parameters using the CALPHAD approach.…”

First-principles and CALPHAD-type study of the Ir-Mo and Ir-W systems

“…Formation enthalpies obtained by the firstprinciples calculations can be considered as "experimental data" [26][27][28][29] when such data are unavailable. In the present work, the first-principles calculations were conducted in the Vienna ab initio simulation package (VASP) [30] with generalized gradient approximation (GGA) [31] proposed by Perdew et al [32] for the exchange and correlation contributions, and the valence electrons were treated by projector augmented plane-wave (PAW) potentials [33].…”