From dielectric spectroscopic study, a first-order ferroelectric phase tran
sition has been observed in ferroelectric smectic mixture CS-1013 having th
e phase sequence Cr-SmC*-SmA-N*-Iso. Frequency (100 Hz-10 MHz) and temperat
ure-dependent dielectric measurements have been performed on an electricall
y aligned sample (thickness 15 +/-1 mum) gold coated on glass plates. In th
e unidirectionally aligned sample, two dielectric relaxation modes (Goldsto
ne mode and soft mode) have been clearly observed in the ferroelectric SmC*
phase while only one relaxation mode (soft mode) is visualized in the para
electric SmA phase. Low-frequency molecular relaxation was also observed in
the smectic phases. The experimental results have also been analyzed at di
fferent temperatures and biasing voltages for an understanding of the dynam
ics of dielectric processes in the ferroelectric phase. Finally, we propose
d the "pseudospin" model for understanding the ferroelectric-antiferroelect
ric transition in liquid crystals. We associate the tilt angle theta and th
e pitch of the helix, respectively, with biaxial (b) and uniaxial (u) aniso
tropy parameters as fluctuating parameters around their stability limit (co
rresponding to the crystalline values). Here, the director acts as the pseu
dospin variable. This gives rise to a transverse Ising type (or anisotropic
Heisenberg model under the mean-field approximation). It is then shown tha
t such a model with fluctuations of (b) and (u) would explain the ferroelec
tric and antiferroelectric phase transitions in such liquid crystals. Using
Landau theory and the stability conditions, we have also shown, in brief,
the feasibility of different types of phase transitions in the ferroelectri
c liquid crystal system.