Grain boundary structure: a signature of phasons in incommensurate smectics

Abstract

We consider tilt grain boundaries with small angle θ in an incommensurate smectic A_ic liquid crystal with ordering wave numbers q₁, q₂ and sample thickness h. We show that for q_iθh ≪ 1, a limit readily accessible to experiment, such boundaries consist of arrays of dislocations whose spacing varies as h^⅕θ^-4/5. This is qualitatively different from the result h^1/3θ^-⅔ 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.