Polar Smectic subphases: phase diagrams, structures and Xray scattering

P. V. Dolganov, V. M. Zhilin, V. E. Dmitrienko^{+}, E. I. Kats^{*}
Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow Reg., Russia ^{+}A. V. Shubnikov Institute of Crystallography, 119333 Moscow, Russia ^{*}LaueLangevin Institute, F38042 Grenoble, France ^{*}L. D. Landau Institute for Theoretical Physics RAS, 117334 Moscow, Russia

PACS: 61.30.Eb, 64.70.Md, 68.10.Cr

Abstract
We analyze a discrete phenomenological model accounting for phase
transitions and structures of polar SmecticC^{*} liquid
crystalline phases. The model predicts a sequence of phases
observed in experiment: antiferroelectric SmC^{*}_{A} 
ferrielectric SmC^{*}_{FI1}  antiferroelectric SmC^{*}_{FI2}
(three and four layer periodic, respectively)  incommensurate
SmC^{*}_{α}  SmA. We find that in the threelayer
SmC^{*}_{FI1} structure both the phase and the module of the order
parameter (tilt angle) differ in smectic layers. This modulation
of the tilt angle (and therefore of the layer spacing d) must
lead to Xray diffraction at the wave vectors Q_{s}=2π s/d
( even for the nonresonant scattering.


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