The bcc (body-centered cubic) phase to hcp (hexagonal closed pack) phase transformation in certain elements (e.g. Ti) and alloys is induced either by quenching or application of pressure. To study domain walls in these materials we have extended the Landau model of Lindgård and Mouritsen by including a spatial gradient (Ginzburg) term of the scalar order parameter. Through first-principles calculations, we show that the bcc structure is unstable with respect to the shuffle of atoms rather than the shear. Therefore, we can reduce the multiple (two) order parameter (OP) Landau free energy (LFE) to an effective one OP (shuffle) potential, which is a reasonable approximation. In general, the effective LFE is a triple-well potential. From the variational derivative of the total free energy we obtain a static equilibrium condition. By solving this equation for different physical parameters and boundary conditions, we obtain different quasi-one-dimensional soliton-like solutions which correspond to four types of domain walls between the bcc phase and the hcp phase.
- Domain walls
- Landau-Ginzburg model
- Reconstructive phase transformations