Dipole-dipole interactions and the ferroelectric-modulated and modulated-paraelectric phase transitions of NaNO2

We consider a body-centered orthorhombic lattice of reorientable point dipoles which interact with each other electrostatically. The lattice constants are those of NaNO₂, and the dipoles are able to reorient in the bc plane. Using a classical statistical mechanical formalism we find that when the temperature is increased from zero the system undergoes two phase transitions: the first from the ferroelectric to a modulated phase, and the second from the modulated to the totally disordered (paraelectric) phase. The mechanism giving rise to the ferroelectric-modulated phase transition can be described saying that in an intermediate temperature range a state where the entropy is distributed among the dipoles in a modulated way has less free energy than that where all the dipoles are equally disordered.