Using video-microscopy data of a two-dimensional colloidal system the bond-order correlation function G6 is calculated and used to determine the temperature-dependence of both the orientational correlation length xi6 in the isotropic liquid phase and the Frank constant F_A in the hexatic phase. F_A takes the value 72/pi at the hexatic to isotropic liquid phase transition and diverges at the hexatic to crystal transition as predicted by the KTHNY-theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding.
@article{arxiv.cond-mat/0610332,
title = {Frank's constant in the hexatic phase},
author = {P. Keim and G. Maret and H. H. von Gruenberg},
journal= {arXiv preprint arXiv:cond-mat/0610332},
year = {2012}
}