Synchrotron X-ray study of the q-fold quasicrystalline symmetry of the smectic C twist grain boundary phase (TGB(c))

We report the first X-ray scattering investigation of spatial variations of the q-fold quasicrystalline symmetry (so-called commensurability) of well- aligned TGB(c) samples. A spatial resolution of 20 x 40 mu m(2) was achieve d using the ESRF microfocus beamline. The liquid crystal samples, contained between glass plates which were either parallel or in a wedge geometry, we re scanned in order (i) to probe the mosaicity and (ii) to continuously cha nge the balance between surface and volume effects. In the case of parallel plate cells, commensurability was observed everywhere throughout the sampl e, hence ruling out possible effects of mosaicity to explain the q-fold sym metry of the diffraction patterns previously reported when probed with a sp atial resolution of 1 x 1 mm(2) in rotating anode experiments. In the case of wedge cells, the evolution of X-ray patterns with thickness suggested th at commensurate lockin occurs for sufficiently thick samples with a width t hat is statistical.