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Ferroelectricity is a spontaneouselectric polarizationof a material that can be reversed by theapplication of an external electric field.[1][2]

The term is used in analogy to ferromagnetism, in which a material exhibits a permanentmagnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in1920 in Rochelle salt by Valasek[3]. Thus, the prefixferro, meaning iron, was used to describe theproperty despite the fact that most ferroelectric materials do not have iron in their lattice.

Contents[hide]

1 Polarization

2 Applications

3 Materials

4 Theory

5 See also

6 References

7 Further reading

8 External links

[edit] Polarization

Dielectric polarisation

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PZT closer in composition to lead titanate is preferred, whereas piezoelectric applications makeuse of the diverging piezoelectric coefficients associated with the morphotropic phase boundarythat is found close to 50/50 composition.

In 1979 Swedish Sven Torbjrn Lagerwall discovered ferroelectric liquid crystals incollaboration withNoel Clark. The technology allows the building of flat-screen monitors. Mass

production began in 1994 by Canon, who bought the licence.Ferroelectric crystals often show several transition temperaturesanddomain structure hysteresis,much as do ferromagnetic crystals. The nature of thephase transition in some ferroelectriccrystals is still not well understood.

The ferroelectric effect also finds use in liquid crystalphysics by incorporation of a chiral dopantinto an achiral smectic C matrix. These liquid crystals exhibit the Clark- Lagerwall effect[7] thatcauses a change from one bistable state to another upon switching of electric field direction.

[edit] TheoryBased on Ginzburg Landau theory, the free energy of a ferroelectric material, in the absence ofan electric field and applied stress may be written as a Taylor expansion in terms of the orderparameter,P. If a sixth order expansion is used (i.e. 8th order and higher terms truncated), thefree energy is given by:

where Px, Py, and Pz are the components of the polarization vector in the x, y, and z directions

respectively, and the coefficients, i,ij,ijkmust be consistent with the crystal symmetry. Toinvestigate domain formation and other phenomena in ferroelectrics, these equations are oftenused in the context of aphase field model. Typically, this involves adding a gradient term, anelectrostatic term and an elastic term to the free energy. The equations are then discretized onto agrid using the finite difference method and solved subject to the constraints ofGauss's law andLinear elasticity.

In all known ferroelectrics, 0 > 0 and 111 > 0. These coefficients may be obtainedexperimentally or from ab-initio simulations. For ferroelectrics with a first order phase transition,11 < 0 and 11 > 0 for a second order phase transition.

The spontaneous polarization,Ps of a ferroelectric for a cubic to tetragonal phase transition may

be obtained by considering the 1D expression of the free energy which is:

This free energy has the shape of a double well potential with two free energy minima at

, wherePs is the spontaneous polarization. At these two minima, the derivative of thefree energy is zero, i.e.:

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SincePx = 0 corresponds to a free energy maxima in the ferroelectric phase, the spontaneouspolarization,Ps, is obtained from the solution of the equation:

which is:

and elimination of solutions yielding a negative square root (for either the first or second order

phase transitions) gives:

If 111 = 0, using the same approach as above, the spontaneous polarization may be obtained as:

The hysteresis loop (Px versus Ex) may be obtained from the free energy expansion by adding an

additional electrostatic term, Ex Px, as follows:

Plotting Ex as a function of Px and reflecting the graph about the 45 degree line gives an 'S'

shaped curve. The centre part of the 'S' corresponds to a free energy local maximum(since

). Elimination of this region, and connection of the top and bottom portions of the'S' curve by vertical lines at the discontinuities gives the hysteresis loop.

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