Biaxiality and temperature dependence of 3- and 4-layer intermediate smectic-phase structures as revealed by resonant X-ray scattering

High-resolution resonant X-ray diffraction experiments have been performed on free-standing films of two selenium-containing antiferroelectric liquid-crystal mixtures. Optical studies had indicated that both mixtures exhibit exceptionally wide intermediate phases, over a total range of > 9 K. Through the structural information obtained from the resonant scattering data, we confirm that the intermediate phases of these mixtures show both 3-layer and 4-layer structural periodicities. Moreover, due to the stability of these phases, we report for the first time the temperature dependence of both the helicoidal pitch and distortion angle in the 3-layer phases deduced using the resonant X-ray technique. Analysis using an extension of the theory set out by Levelut and Pansu (Levelut A-M. and Pansu B., Phys. Rev. E, 60 (1999) 6803) shows that over the temperature ranges measured, the pitch changes linearly as a function of temperature whilst the distortion angle remains constant.