Frank's constant in the hexatic phase

Using videomicroscopy data of a two-dimensional colloidal system the bond-order correlation function G₆ is calculated and used to determine both the orientational correlation length ξ₆ in the liquid phase and the modulus of orientational stiffness, Frank’s constant F_A , in the hexatic phase. The latter is an anisotropic fluid phase between the crystalline and the isotropic liquid phase. F_A is found to be finite within the hexatic phase, takes the value 72/π at the hexatic↔isotropic liquid phase transition, and diverges at the hexatic↔crystal transition as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding.