Temperature driven $alpha$ to $beta$ phase-transformation in Ti, Zr and Hf from first principles theory combined with lattice dynamics

Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp to bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self consistent {it ab initio} lattice dynamical calculations (SCAILD), that the critical temperature for the hcp to bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free energy difference between the two phases. This opens up the possibility to study quantitatively, from first principles theory, temperature induced phase transitions.

textit{Ab initio} study of interacting lattice vibrations and stabilization of the $beta$-phase in Ni-Ti shape-memory alloy

Lattice dynamical methods used to predict phase-transformations in crystals typically evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the $beta$ structure when it appears as a high-temperature phase of the shape memory alloy (SMA) NiTi. Here it is shown by self consistent {it ab initio} lattice dynamical calculations (SCAILD) that the critical temperature for the pre-martensitic $R$ to $beta$ phase-transformation in NiTi can be effectively calculated with good accuracy, and that the $beta$-phase is a result primarily of the stabilizing interaction between different lattice vibrations.