A structure model for the incommensurately modulated phase, which involves modulated orientational ordering of BF_(4)^(-) together with modulated distortions and displacements of the morpholinium ions is reported. A mechanism is proposed for the phase transitions, whereby at low temperatures morpholinium cations are shaped around the tetrafluoroborate anion in order to optimize the interactions with one orientation of this anion and, thus, forcing BF_(4)^(-) into this orientation. This mechanism is essentially different from a pure order-disorder phase transition. It is supported by consideration of the transition entropy. The difference in configurational entropy between the disordered and incommensurate phases has been computed from the structure models. It is shown to be much smaller than the experimental transition entropy reported earlier. These features show that the order-disorder contribution is only a minor contribution to the transition entropy and that other factors, such as conformational changes, play a larger role in the phase transitions.