Grain Boundary Structure: a Signature of Phasons in Incommensurate Smectics

We consider tilt grain boundaries with small angle θ in an incommensurate smectic Aic liquid crystal with ordering wave numbers q1q2 and sample thickness h. We show that for qiθh<1, a limit readily accessible to experiment, such boundaries consist of arrays of dislocations whose spacing varies as h1/5θ-4/5. This is qualitatively different from the result h1/3θ-2/3 obtained by Nallet and Prost for periodic smectics. This behavior, which is a consequence of the existence of phasons, should serve as a decisive test of the incommensurate nature of these systems. © 1991 IOP Publishing Ltd.