A new order parameter model for the structural phase transitions in VO ₂ -based solid solutions

To describe the structural phase transitions P4₂/mnm(R) ↔ P2₁/c(M₁) ↔ P1(T) ↔ C2/m(M₂) observed experimentally in VO₂ and its solid solutions, the two-component order parameter model is newly proposed. We identify the space groups of 102 ordered phases induced by the 36 irreducible representations of the ten star channel groups related to six Lifshitz stars in the Brillouin zone of space group P4₂/mnm, and show that these are characterized by the invariant characteristic quantities of four image groups (L groups). In particular, it is shown that the two-component order parameter model transformed according to the two-dimensional irreducible representation T₂ of star channel group P4₂/mnm[k₁₆⁽¹⁾] is far more effective than the four-component one for describing the phase transitions observed experimentally in VO₂ and its solid solutions. The structurally stable Landau potential models with one to five varying parameters and invariant under the L₂⁸(4mm) group are suggested for the phenomenological studies based on the two-component order parameter model. By using the eighth-order Landau potential model with three varying parameters, the coefficient phase diagram and the temperature-concentration phase diagram are theoretically constructed, which are in good agreement with the experimental data of V_1-xAl_xO₂.