Calculations for displacive ω-phase transformations in Ti-Al alloys with Nb additions at finite temperature

We examine by means of first-principles calculations the bcc-like (bcc: body centered cubic) to omega-like phase transformations in Ti-Al alloys with Nb additions at finite temperature. To simulate the alloy we use different discrete atomic configurations in a six atom unit cell of the stoichiometry Ti3Al2Nb. Calculated ground state energies show an instability in the ternary Ti3Al2Nb alloy against the omega structure type atomic displacement. To better understand the role of entropy in the stability/instability of these systems, the first-principles calculations are extended to finite temperature by including various contributions to the free energy. In particular, the vibrational free energy is calculated within a quasiharmonic approximation. It is shown that the bcc structure is stabilized by the contribution of the low energy modes to the lattice entropy against omega type atomic displacements. We find that configurational entropy plays a major role in the omega to B8(2) transformation. Calculated lattice parameters and transition temperatures are found to be in excellent agreement with experiment.