Lattice study of the incommensurate ω phase transition in Zr-Nb alloys

The stability of the incommensurate omega phase has been studied in the scheme of the Landau-Lifshitz (L-L) free-energy model reformed for the weak first-order phase transition. It is revealed that the negative third-order term of the L-L expansion drives the transition and works, in competition with the second-harmonic term, to form the modulated omega phase; moreover, it functions to maintain soliton walls with constant width against temperature changes. The modulated omega phase is elucidated to have a microstructure with the sequence of subvariants-omega 1-omega 3-omega 2-separated by soliton walls of anti-omega structure. A series of primitive activation units of the modulated omega phase, which can be depicted in a phase diagram, is obtained in the Zr-20 wt% Nb-alloy system by analyzing the L-L free-energy function with the appropriate numerical calculations.