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

TL;DR

This paper introduces a new first-principles method to accurately predict temperature-induced phase transitions in Ti, Zr, and Hf by calculating free energy differences without relying on harmonic phonon spectra.

Contribution

It develops an expression for free energy that overcomes harmonic approximation limitations and applies self-consistent ab initio lattice dynamics to predict phase transformation temperatures.

Findings

Successfully predicts critical temperatures for phase transformations.

Demonstrates effectiveness of the method on Ti, Zr, and Hf.

Provides a new tool for studying temperature-driven phase changes from first principles.

Abstract

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.