  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.
