Orientational and positional order in a tilted hexatic liquid-crystal phase

We present a synchrotron-x-ray study of the smectic-C (${\mathrm{S}}_{\mathrm{C}}$) and smectic-I (${\mathrm{S}}_{\mathrm{I}}$) phase in a single-domain freely suspended film. Weak bond-orientational order in the ${\mathrm{S}}_{\mathrm{C}}$ phase evolves continuously into the ${\mathrm{S}}_{\mathrm{I}}$ phase so that the two phases are not thermodynamically distinct. From a Fourier analysis we obtain the hexatic order parameter ${\mathrm{C}}_{6}$, the coefficient of cos6\ensuremath{\chi}. The higher , with ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{n}}$\ensuremath{\simeq}n+0.3n(n-1), in agreement with a scaling theory.