Structural Study of the Smectic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">C</mml:mi></mml:math>Twist Grain Boundary Phase

Abstract

We report the first three dimensional x-ray study of the recently discovered twist grain boundary smectic- $C$ phase $({\mathrm{TGB}}_{C})$. Unlike the predictions of the original Renn-Lubensky model for TGB phases (and the experimental observations in the untilted ${\mathrm{TGB}}_{A}$ phase), the smectic layers in the ${\mathrm{TGB}}_{C}$ phase are shown to be tilted with respect to the helical TGB axis by an angle approximately equal to the smectic- $C$ director tilt angle. The reciprocal lattice consists of either two rings of equispaced Bragg spots or uniform rings confirming the existence of both commensurate and incommensurate TGB phases.