The β-phase (body-centered cubic: b.c.c.) to ω-phase transformation in certain elements (e.g. Zr) and alloys (e.g. Zr-Nb) is induced either by quenching or application of pressure. The ω-phase is a metastable state and usually coexists with the β-matrix in the form of small particles. To study the formation of domain walls in these materials we have extended the Landau model of Cook for the ω-phase transition by including a spatial gradient (Ginzburg) term of the scalar order parameter. In general, the Landau free energy is an asymmetric double-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 obtained different quasi-one-dimensional soliton-like solutions. These solutions correspond to three different types of domain walls between the ω-phase and the β-matrix. In addition, we obtained soliton lattice (domain wall array) solutions, calculated their formation energy and the asymptotic interaction between the solitons.
- Asymmetric double-well potential
- Domain wall arrays and interaction
- Ginzburg-Landau model
- ω-phase transformation