Symmetry Rule of the Landau Free Energy in the Phonon-Originating Phase Transition

We propose a pseudopotential model of the Landau free energy. A novel symmetry rule is manifested in the microscopic description of the model. Followed by ab initio calculations, a method of analyzing the mechanism of a weakly first-order phase transition is established. The model is applied to the pre-\(\omega\) phase transition in Zr metal and in Zr–20% Nb (Zr–20Nb) alloy. The criterion is elucidated for the commensurate (C) \(\omega\)-to-incommensurate (IC) \(\omega\) phase transition by estimating the soliton (anti-\(\omega\) phase wall) formation energy of the IC\(\omega\) phase. The quantitative calculation of the reaction path in the thermodynamical potential field has explained the crystal structural difference of the pre-omega phase between Zr metal (C structure) and Zr–20Nb alloy (IC structure). The results of the phase stability are summarized in a energy-phase diagram.