Observations of the liquid-crystal analog of the Abrikosov phase

Freeze-fracture transmission electron micrographs of the smectic A* phase confirm the twist grain boundary model of Renn and Lubensky. The fracture surface has an undulating structure with a 0.5-micrometer helical pitch parallel to 4.1-nanometer smectic layers. The layers are disrupted by a lattice of screw dislocations oriented normal to the helical axis. Optical diffraction shows that rotation of smectic blocks occurs in discrete steps of about 17°; hence, the screw dislocations are 14 to 15 nanometers apart and the grain boundaries are 24 nanometers apart. These observations show that the SmA* phase is the liquid-crystal analog of the Abrikosov phase in superconductors.