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
This email address is being protected from spambots. You need JavaScript enabled to view it.
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
