Orientational ordering in the chiral smectic-${\mathrm{C}}_{\mathrm{FI}2\mathrm{}}^{*}$ liquid crystal phase determined by resonant polarized $\mathrm{x}$-ray diffraction

High-resolution resonant polarized x-ray diffraction experiments near the sulfur K edge have been performed on free-standing liquid crystal films exhibiting the chiral smectic-${\mathrm{C}}_{\mathrm{FI}2\mathrm{}}^{*}$ phase. It is widely accepted that this phase has a four-layer repeat unit, but the internal structure of the repeat unit remains controversial. We report different resolved features of the resonant x-ray diffraction peaks associated with the smectic-${\mathrm{C}}_{\mathrm{FI}2\mathrm{}}^{*}$ phase that unambiguously demonstrate that the four-layer repeat unit is locally biaxial about the layer normal and that the measured angle, describing the biaxiality, is in good agreement with optical measurements.