Landau free energy for a bcchcp reconstructive phase transformation
Abstract
We study the bcchcp phase transition in Ti and Zr with the use of firstprinciples 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 firstprinciples calculations, we show that the bcc structure is unstable with respect to the shuffle of atoms (TA_{1} Npoint 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 triplewell 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.
 Publication:

Physical Review B
 Pub Date:
 June 2001
 DOI:
 10.1103/PhysRevB.63.224114
 Bibcode:
 2001PhRvB..63v4114S
 Keywords:

 73.20.At;
 73.21.b;
 75.70.Ak;
 Surface states band structure electron density of states;
 Electron states and collective excitations in multilayers quantum wells mesoscopic and nanoscale systems;
 Magnetic properties of monolayers and thin films