Mechanism of the transition between 1<Emphasis Type="Italic">q</Emphasis> and 3<Emphasis Type="Italic">q</Emphasis> phases in a two-dimensional crystal model

The previously proposed model of a crystal with rotational degrees of freedom is extended to the two-dimensional case. The model contains two nonlinear terms that allow for the stability of 1q, 2q, or 3q modulated phases, depending on the ratio between the model parameters. A numerical treatment is performed for the transition between the 1q and 3q phases that is characteristic of crystals with hexagonal symmetry. This model makes it possible to reconstruct the sequence of phase transitions occurring in quartz crystals upon cooling and offers a satisfactory explanation of the experimentally observed increase in the temperature range of existence of the 1q phase under external uniaxial loading.