Prediction of ordered omega phase formation by coupled replacive–displacive processes in Zr₃Al₂Nb and Zr₄AlNb alloy: a first-principles study

We report ab initio study of the formation of chemically ordered athermal ω phase (trigonal symmetry, space group , non-ideal ω, ω′) in Zr3Al2Nb and (trigonal symmetry, space group P3m1, ideal ω) in Zr4AlNb alloy by coupled replacive–displacive transformation mode. The phase stability of body-centred cubic (bcc), non-ideal ω (ω′) and ideal ω structures of Zr3Al2Nb and Zr4AlNb was examined by first-principles calculations with projector augmented wave potentials and generalized gradient approximations. Position of Nb atom in the bcc lattice was decided by examining several atomic configurations, and it was also shown that the stability of each configuration is directly related to the number of Zr–Al bonds. Among these configurations, the most stable bcc Zr3Al2Nb and Zr4AlNb configurations showed instability for atomic displacements leading to ω-type structure in our ground-state energy calculations. In order to estimate strengths of Zr–Al, Nb–Al and Zr–Nb bonds, the heats of the formation for several virtual compounds were calculated and we find that the strength of Zr–Al bonds is higher than Nb–Al and Zr–Nb bonds. It was also confirmed that the formation of the ω phase in Zr3Al2Nb and Zr4AlNb is a combined displacive–replacive transformation. Moreover, our mechanical stability analysis predicts that both ω′-Zr3Al2Nb and B82-Zr2Al are mechanically stable phases with very poor ductility. In contrast, less pronounced directional bonding in ω-Zr4AlNb indicates this alloy to be ductile.