Ferroelctricity

8/8/2019 Ferroelctricity

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Ferroelectricity Abdullah Khalil Hassan 70885

(Electric dipoles, polarization and

ferroelectric materials)

Prepared by

Abdullah Khalil Hassan

70885


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Ferroelectricity:-

Electric dipole:

It's a system of two charges that have the same magnitude but opposite in sign

separated by definite distance.

Electric dipole moment:

Is a measure of separation of positive and negative charges in a system of charges.

Where: M= Electric dipole moment.

q= Electric charge.

d= displacement vector in the direction from negative to positive charge.

The dipole moment of any array of charge (total dipole moment) that determines the

degree of polarity of the array:

Applying Electric field on the Electric diploe:

When an external electric field applied on the electric dipole a torque will be

subjected on the electric dipole with a magnitude:

This torque will rotate the electric dipole to make its dipole moment align with thedirection of the external field.


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Electric Polarization:

The total dipole moment per unit volume.

Also,

Where: = permittivity of free space (dielectric constant).

= electric susceptibility.E = external electric field.

Where the dielectric material is that has no free charges (i.e. all charges in this

material are bounded).

Electric susceptibility measure the response of the material to be polarized when an

external electric field applied, and is defined as electric polarization per unit electric

field.

Where:

Where: relative permittivity.

Permittivity of the material.


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Types of polarization:

1- Electronic polarization:Applying electric field will displace the center of positive (nucleus) and negative

(electrons) charges and induce a diploe moment called induced dipole moment thatgiven by:

Where: = constant of proportionality called electronic polarizability.But there is internal electric field that can reduce the applied electric field and given

by

2- Ionic (atomic) polarization:

Occurs in ionic crystals which have positive and negative ions that is arranged to give

zero net charges in the absence of electric field, but in the presence of electric field

the relative distance between the positive and negative ions increases giving a net

polarization (i.e. change in bond angels and inter atomic distances).

And the induced dipole moment is given by:

Where: ionic (atomic) polarizability.

3- Orientation polarization:It occurs in polar crystals in the absence of electric field dipoles are arranged

randomly giving a zero polarization, but in presence of electric field dipoles areoriented parallel to the field giving a net polarization.


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Materials classified as:

1- Insulators.2- Semiconductors.3- Conductors.4- Superconductors.

Insulators can be divided into:

a. Polar materials, materials that have permanent dipoles without applyingelectric field.

b. Non polar materials, materials that required an external electric field to behave electric dipoles.

Polar materials divided into:

a. Piezoelectr ic materials, materials in which the equilibrium position of ionschange when a stress applied on the sample, the applied stress will induce

polarization and this process known as piezoelectric effect.

b. Non piezoelectric materials, materials in which the equilibrium position ofions doesn't change when a stress applied on the sample.

Piezoelectric materials divided into:

a. Pyroelectric materials, materials in which the magnitude of the spontaneouspolarization depends on the temperature.

b. Non pyroelectric materials, materials in which the magnitude of thespontaneous polarization doesn't depend on the temperature.

Pyroelectric materials divided into:

a. Ferroelectric materials, pyroelectric materials which have spontaneouspolarization.

b. Non ferroelectric materials, pyroelectric materials that have no spontaneouspolarization.

Ferroelectric materials:Ferroelectricity is the phenomenon where spontaneous electric polarization of the

material takes place.

Properties of ferroelectric materials:

1- Domain and domain boundary:Ferroelectric materials is found to be divided into a number of ferroelectric domains.

Each domain contains a large number of dipoles that have the same direction. These

domains separated by domain boundary.


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Domains only differ in the polarization direction.

The domain walls have negligible length compared with the dimensions of the

domains.

If we apply an external electric field to the ferroelectric crystal, polarization takesplace in to processes:

1- For weak field:The volume of the domains that have polarization in the direction of the

applied field will grow in size on the expense of other domains.

2- For strong field:In this case a domain prefers to orient themselves in the direction of the

applied field.

2- Hysteresis loop:It gives a relation between the polarization and the electric field.

Where:

Ps = saturation polarization.

Pr = remnant polarization, the value of polarization when applied electric field

reduced to zero.


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Ec = coercive field, value of electric field required to reduce the polarization of the

material to zero.

3- Phase transition:Phase transition occurs at certain temperature called Curie temperature, at thistemperature the material transforms from ferroelectric phase into paraelectric phase,

where below this temperature the system will exhibit the ferroelectric property.

Near the Curie temperature the system behavior and electrical, mechanical and optical

properties changed.

Where the permittivity will have very high values near Curie temperature where its

value given by:

Where: C = Curie constant.

Tc = Curie temperature.

Types of phase transition:

1- First order phase transition, when the first derivative of the free energy,entropy and polarization with respect to temperature exhibit a discontinuity.

2- Second-order phase transitions, when there is continuity in the first derivativebut exhibit discontinuity in a second derivative of the free energy, entropy and

polarization with respect to temperature.

Applications of Ferroelectric Materials1. Capacitors A capacitor is an electronic component used for a number of

electronic circuits. It consists of 2 electrodes with a dielectric material in between. A

Ferroelectric Material is preferred for the manufacturing of a capacitor. Capacitors aregenerally formed by the Barium Titanate (BaTiO3) material. Where the internal

electric dipoles of a ferroelectric material are coupled to the material lattice so

anything that changes the lattice will change the strength of the dipoles (in other

words, a change in the spontaneous polarization). The change in the spontaneous

polarization results in a change in the surface charge. This can cause current flow in

the case of a ferroelectric capacitor even without the presence of an external voltage

across the capacitor.


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2. Storage memories SRAM and DRAM are volatile. EEPROM and CMOS require

a battery backup and are very costly. Ferroelectric Random Access Memory is non-

volatile as well as cheaper. FRAM is reliable as well.

3. Waveguides A waveguide is a device which controls the propagation of light

within the device. It carries the electromagnetic wave. The material used inside a

waveguide is a Ferroelectric Material.

4. Optical Memory Display Latest optical memory displays technologies are devised

using the Ferroelectric Material. PLZT is most preferred Ferroelectric Material for

this purpose.

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Ferroelctricity