Phase Diagrams of Crystals with One-Dimensional Modulated Phases Induced by 2d Active Representations

TL;DRAbstract

A one-dimensional model of particles with a displacive degree of freedom for crystals possessing incommensurate phases which arise as a result of the condensation of either real two-dimensional or complex one-dimensional irreducible representations, has been proposed. For these representations all invariants of the free energy expansion can be divided to four general forms. For the active irreducible representations for which the invariants belong to the first form a complete list of invariants is derived. In this case the incommensurate modulation propagates along the symmetry axis and for such crystals a proposed one-dimensional model may be a good approach to describe the main features of the devil's staircase curve. The particles of the model interact with harmonic and anharmonic terms. The last ones may contain an additional third order term provided a soft phonon branch has a symmetry r 1 . The calculated phase diagrams show sequences of the incommensurate and commensurate one-di

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