Temperature-driven α-to-β phase transformation in Ti, Zr and Hf from first-principles theory combined with lattice dynamics
Department of Physics and Astronomy, Division of Materials Theory Uppsala University Box 516, SE-751210, Uppsala, Sweden, EU
2 Institute of Electronic Engineering and Nanotechnologies, Academy of Sciences of Moldova Academiei 3/3, MD-2028 Chişinău, Moldova
3 Radboud University Nijmegen, Institute for Molecules and Materials - NL-6525 AJ Nijmegen, The Netherlands, EU
Accepted: 9 November 2011
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 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.
PACS: 64.70.kd – Metals and alloys / 63.20.kg – Phonon-phonon interactions / 63.20.Ry – Anharmonic lattice modes
© EPLA, 2011