Mechanisms of transition between 1q and 2q incommensurate phases in a two-dimensional crystal model

The two-dimensional elastically hinged molecule model of a crystal which contains two anharmonic terms was studied numerically. The results show that the Iq or 2q incommensurate phase can be stable depending on the parameters of the model. For example, in the sinusoidal incommensurate regime the Iq (2q) phase can be globally stable but in the domain-wall regime the situation can be opposite and the 1q <-> 2q (2q <-> 1q) transition can be expected. Another mechanism of the 1q <-> 2q phase transition stems from the softening of the dispersion surface simultaneously at two points of the Brillouin zone, (kappa(x),0) and (0,kappa(y)) In this case the 2q modulated phase can appear as a linear combination of the two Iq modulated phases. Under the assumption that the dispersion surface is slightly perturbed for some reason, the softening first occurs at one of the two points resulting in the Iq phase formation. Further changing of the external parameters leads to the softening at the second point and the 1q <-> 2q transition can take place. Both these mechanisms of the 1q <-> 2q phase transition were revealed and studied. [S0163-1829(98)07029-5].