Landau Model for Commensurate-Commensurate Phase Transitions in Uniaxial   Improper Ferroelectric Crystals
  We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter representing the local polarization. The corresponding phase diagram has the structure of harmless staircase, with the allowed wave numbers obeying the Farey tree algorithm. Among the stable commensurate phases only those with periods equal to odd number of lattice constants have finite macroscopic polarizations. These results are in excellent agreement with experimental findings in some A2BX4 compounds. 
M. Latkovic, A. Bjelis and V. Dananic