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 $\mu$ is small compared to their surface tension $\gamma$, more precisely $\mu a<\gamma$ 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 P. Pieranski et al. Good agreement is found.

arXiv comment8 Pages, 1 Figure. To appear on Eur. Phys. Journal. B

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