Bond-orientational order, dislocation loops, and melting of solids and smectic-Aliquid crystals

A three-dimensional solid with an equilibrium concentration of unbound dislocation loops displays a resistance to torsion not present in isotropic liquids. There is residual bond-angle order analogous to that found in the two-dimensional hexatic phase. A bulk phase with bond orientational order may be observable in supercooled liquids. Such a phase would display an angular modulation in monodomain x-ray-diffraction patterns, and would give rise to an intrinsic asymmetry in the limits of supercooling and superheating. Bond-angle order may also be present in glasses. A dislocation-loop mechanism for the smectic-$A$—to-nematic transition implies anisotropic scaling and fixes the ratio of the transverse and longitudinal correlation length exponents.