Landau free energy for a bcc-hcp reconstructive phase transformation

Mahdi Sanati, A. Saxena, T. Lookman, R. C. Albers

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


We study the bcc-hcp phase transition in Ti and Zr with the use of first-principles calculations. We have determined the complete energy surface from the bcc to hcp structure. The results are used to find an appropriate Landau free energy density for describing this transformation. The proposed Landau free energy density has two relevant order parameters: shear and shuffle. Through first-principles calculations, we show that the bcc structure is unstable with respect to the shuffle of atoms (TA1 N-point phonon) rather than the shear. Therefore, we reduce the two order parameter Landau free energy to an effective one order parameter (shuffle) potential, which is a reasonable approximation. In general, the effective Landau free energy is a triple-well potential. From the phonon dispersion data and the change in entropy at the transition temperature we find the free energy coefficients for Ti and Zr.

Original languageEnglish
Article number224114
Pages (from-to)2241141-2241147
Number of pages7
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number22
StatePublished - 2001


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