Abstract
With the help of the synchrotron radiation facility LURE, we have studied the following mesogenic phase sequence : Smectic A1 (monolayered) - fluid antiphase with a rectangular 2D lattice - Smectic A2 (bilayered), we have shown the existence of two ribbon phases with rectangular lattices of different symmetries. Besides the centred rectangular phase already described (SÃ) in which the two kinds of antiphase domains have an equal weight, we have found a second phase with a simple rectangular lattice in which the relative weight of the two kinds of domains varies with temperature until the SA2 phase is reached. In the centred rectangular phase, the in-layer periodicity increases with decreasing temperature while it remains constant in the simple rectangular phase. The transition temperature between these two phases exhibits a hysteresis of a few degrees

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