The bcc (body-centered-cubic) phase to hcp (hexagonal-close-packed) phase transformation in certain elements and alloys is induced either by quenching or the application of pressure. Following the Burgers mechanism and through first-principles calculations we show that the bcc structure of Sc, Y, Ti, Zr, and Hf is unstable with respect to the shuffle of atoms rather than the shear. We therefore reduce the two-order-parameter (two-OP) Ginzburg-Landau (GL) free energy to an effective free energy in the shuffle OP. From the phonon dispersion experiments and the change of entropy at transition temperature we found the GL free energy coefficients for Ti and Zr. By using this information we obtain the domain wall width and energy for Ti and Zr.
|Physical Review B - Condensed Matter and Materials Physics
|Published - 2001