Materîal Ferroelektrîk: Ew çendiyen?

Ferroelectric Materials pîvan?

Ferroelectric materials henebên ku Ferroelectricity dikarin. Ferroelectricity çêtirina materialê dike da ku polarization elektrikî spontan bibe. Vê polarizationê bi sererastkirina elektrikî di herêmek din (wêne 1 lêgerîn) de dide. Ferroelectricity (û wekhe Ferroelectric materials) ji Valasek li sêre 1921 hat werin.

Sererastkirina polarization ê materialê Ferroelectric bi sererastkirina electric field external "switching" nav dike.

Ferroelectric materials polarization bikar hene wanî ku electric field hat rakirin. Ferroelectric materials hevdengî nekin an jî ferromagnetic materials, ku moment magnetîk permanent nîşan dide. Hysteresis loop ji bo hemû materialan yek e.

Ji ber ku henek benzeriyet, prefix û materialan yek e. Lakin hene material Ferroelectric nayê Ferro (fe) bikhweye.

Hemû materialan Ferroelectric effect piezoelectric nîşan dide. Properties opposed ya materialan sero an jî antiferromagnetic materials nîşan dide.

Theory of Ferroelectric Materials

Energy free ya material Ferroelectric li ser theory Ginburg-Landau bê electric field û stress applied dide. Di taylora expansion de hat nivîsandin. Li ser P (order parameter) hat nivîsandin.

(ji bo sixth-order expansion)
Px → component of polarization vector, x
Py → component of polarization vector, y
Pz → component of polarization vector, z
αi, αij, αijk → coefficients should be constant with the crystal symmetry.
α0 > 0, α111> 0 → for all ferroelectrics
α11< 0 → ferroelectrics with the first-order transition
α0 > 0 → ferroelectrics with second-order transition

Li ser phase-field model, equations in henek phenomena û domain formation în ferroelectrics bîrkar hene.

Her du rêzik term elastic, gradient, û electrostatic ê li ser energy free equation bîrkar hene.

Equations bi finite difference method solution hatin di Linear elasticity û Gauss’s law constraints de.

Cubic to tetragonal phase transition of spontaneous polarization of a ferroelectric can be obtained from the expression for free energy.

It has a character of dual well potential with double energy minima at P = ± Ps.
Ps → spontaneous polarization

By simplifying, eliminating the negative root, and substitute α11 = 0 we get,

Polarization and Hysteresis Loop

Yekê dielectric material dike, û electric field peripheral dike. Polarization directly proportional to the applied field, wêne 2.

Next, when we polarise a paraelectric material, we get a nonlinear polarization. However, it is a function of the field, as shown in figure 3.

Next, we take a ferroelectric material, and an electric field is given to it. We get a nonlinear polarization.

It also exhibits nonzero spontaneous polarization without a peripheral field.

We can also see that by inverting the direction of the applied electrical field, the direction of polarization can be inverted or changed.

Thus, we can say that the polarization will depend on the present and the previous condition of the electric field. The hysteresis loop is obtained as in figure 4.

Curie Temperature

Properties of these materials exist only below a definite phase conversion temperature. Above this temperature, the material will become paraelectric materials.

That is, loss in spontaneous polarization. This definite temperature is called Curie temperature (TC).

Most of these materials above Tc will lose the piezoelectric property as well.

The variation of a dielectric constant using temperature in the non-polar, paraelectric state is shown by Curie-Weiss law as given below.

ε → Dielectric constant
ε