Steps and facets at the surface of soft crystals

Abstract:

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found.