Using x-ray and optical methods we have probed the structural organization of an antiferroelectric twist grain boundary phase $\left(\mathrm{TGB}{C}_a\right)$ lying between the regular antiferroelectric smectic-$C$ $\left(\mathrm{Sm}{C}_a^{*}\right)$ and the smectic-$Q$ (Sm$Q$) or isotropic phase. We find that the twist axis is everywhere perpendicular to the local smectic layer normal and that the helical superstructure is incommensurate with the smectic layer structure. The twist grain boundaries consist of a periodic lattice of alternating $+1∕2$ and $-1∕2$ dispirations, i.e., unit screw dislocations in combination with half unit disclinations. The molecular tilt plane is alternatingly parallel and perpendicular to the twist axis. We find that the optically measured tilt angle in the $\mathrm{Sm}{C}_a^{*}$ phase is smaller than that measured by x rays, which is the opposite to what is found in the $\mathrm{Sm}{C}^{*}$ phase. This means that the core part tilts less than the end chains in the $\mathrm{Sm}{C}_a^{*}$ phase, while it tilts more in the $\mathrm{Sm}{C}^{*}$ phase. On entering the TGB phase a clear decrease is measured in the tilt angle. This is explained by the elastic influence from the disclinations, which appear in this phase.

• Received 4 October 2006

DOI:https://doi.org/10.1103/PhysRevE.76.011704