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Some mesogenic chiral compounds show a smectic Q phase just below the clearing point. The molecules are in a liquid state but they organized on a tridimensional lattice. At lower temperatures the only possible mesophase-mesophase transformation is towards an antiferroelectric smectic. Three different tetragonal and one hexagonal lattices have been identified. All these phases, except one, can be considered as crystalline arrays of twist grain boundaries inside an antiferroelectric smectic. The twist grain boundaries perpendicular to the smectic planes divide the smectic smcture in narrow sheets (their width compares to the molecular length), the smectic planes are twisted by an angle of x12 or of 1J3 on each side of a boundary and the successive sheets correspond to one another by a 41 or a 62 helical axis. The interface between two molecular layers is described by a mply periodic minimal surface.

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