Grain boundaries and the law of corresponding cones in smectics
M. Kléman1 - O.D. Lavrentovich2
1 Laboratoire de Minéralogie-Cristallographie (UMR
7590), Universités de Paris-VI & de Paris-VII, Case 115; 4
place Jussieu 75252 Paris cédex 05, France
2 Chemical Physics
Interdisciplinary Program and Liquid Crystal Institute, Kent State
University, Kent, Ohio 44242, USA
odl@lci.kent.edu
Received 21 June 1999 and Received in final form 10 September 1999
Abstract
Focal Conic Domains (FCDs) in smectic phases often
assemble according to a particular rule, experimentally discovered
by G. Friedel, the law of corresponding cones (l.c.c.).
This paper reports various results relating to this type of
association. First we show that a l.c.c. contact between 2 focal
conic domains has a vanishing energy, yielding metastable local
equilibrium. Then we use some projective properties of
conic sections to extend the celebrated Apollonian tiling, which
describes a tilt grain boundary (TiGB) of vanishing disorientation
made of toric focal conic domains, to any
TiGB. Finally we present a realistic model of the
energy of the
TiGB, which we compare to the energy
of a TiGB split into dislocations, and to the energy of a
curvature wall. This model explains why FCD tilings show
macroscopic zones not filled with FCDs.
PACS
61.30.Jf Defects
in liquid crystals - 61.72.Lk Linear defects: dislocation
disclinations - 61.72.Mm Grain and twin boundaries
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
