Nature of incommensurate phases in real systems

Features of both incommensurate phases and incommensurate-to-commensurate transitions in K₂SeO₄and Ba₂NaNb₅O₁₅ have been analyzed on the basis of the Ginzburg-Landau theory, in which only the translation symmetry is taken into account. When only three higher-order distortion waves as well as the first-order wave are included, the theory reproduces incommensurate features obtained experimentally. This is an indication that the incommensurate phases in real systems never have the lowest free energy and are then characterized as an non-equilibrium state. Because the discommensuration interacts with structrual defects, the non-equilibrium state should be realized as a result of an interaction between the discommensuration and the defect involved in real systems.