A new methodology to obtain accurate models for ferroelectrics withapplication to BaTiO3
Vu-Quoc, L.; Srinivas, V.
Dielectrics and Electrical Insulation, IEEE Transactions on
Volume 1, Issue 2, Apr 1994 Page(s):196 - 212
Digital Object Identifier 10.1109/94.300252
Summary:A new methodology based on semi-infinite optimization is proposed
to obtain accurate yet simple phenomenological models for ferroelectric
single crystals. The phenomenological models for ferroelectrics start
with a Taylor series expansion of the governing thermodynamic potential,
the elastic Gibbs function, in terms of the independent variables. The
coefficients of the appropriately truncated series are determined, based
on the experimental properties of the crystal. However, there is to date
no method to determine the coefficients for an accurate correlation to
the experimental measurements. To this end, a semi-infinite optimization
problem is formulated, aiming at minimizing the error between the
analytical model and experiments in terms of permittivity coefficients
and spontaneous polarization. A model in the cubic and the tetragonal
phases for barium titanate (BaTiO3) single crystals for a
particular choice of experimental measurements is used to demonstrate
the workability of the proposed methodology. The resulting optimization
problem has an infinity of inequality constraints. The optimal solution
to the proposed semi-infinite optimization problem when used in the
model, accurately predicts the ferroelectric properties of BaTiO3
single crystals such as phase transitions, spontaneous
polarization, permittivity, the range of temperature in the cubic and
the tetragonal phase. The proposed methodology is not limited by the
complexity of the phenomenological model, or the choice of the
experimental measurements. Furthermore, the proposed methodology can be
generalized to model ferroelastic materials
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