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Application example:Dielectric properties of ceramic materials

Capacitor with air between plates Capacitor with a dielectric material

0d

AC ε =

d

A

d

AC 0κε ε ==

V

QC =

Polarization of a dielectric material (C/m2):

( )10 −= κ ε E P

V V

The reason why the capacitance increases is that the electric field E (=V/d)

polarizes the dielectric and produces an increase in the charge density stored inthe plates equal to the polarization P (=Q/A). 2

Polarization of a dielectric material

)/( 2

mC N P µ ⋅=

Electrical dipole

Electrical dipole moment:

If N

dipoles per unit volume, thepolarization:

)( mC r q ⋅⋅=

3

Polarization mechanisms

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Ej: H2O, good dielectric (κ=80)(orientation polarization)

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Dielectric constants of some materials

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Why does BaTiO3 have such a high κ?Introduction to perovskites

• Materials with chemical composition: ABX3

• Examples: CaTiO3, BaTiO3, PbTiO3, PbZrO3: technologically veryinteresting due to their dielectric, piezoelectric and pyroelectricproperties.

• Al high T, the crystalline structure of these compounds is:

Red: CÚBICA PRIMITIVA

Base: Ba2+: (½, ½, ½); Ti4+ (0,0,0); O2-: (½, 0, 0); (0, ½, 0), (0, 0, ½);

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• The smallest cations (Ti4+) occupy octahedral interstices [6], while theother cations (Ba2+) occupy dodecahedral interstices [12].

Example: Perovskites

[6]

[12]

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Example: Perovskites• From the cations in octahedral

interstices we derive that:• From the cations in octahedral

interstices, we see that:

( )OO r r r r +=+ ]6[]12[ 2

• Combining both equations:

It is very unlikely that this equation to apply exactly, and therefore,it is common for the cations to be able to move around in theirinterstices

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Phase transformations in BaTiO3

Example: BaTiO3

• At high T, the stable phase is cubic and the positions of the positive andnegative ions are symmetric.

• However, as the temperature decreases, the Ti4+ cations move in onedirection and the anions move in the opposite direction. As a result, atetragonal phase is formed by elongation of the unit cell in the [001]direction and contraction along the [100] and [010] directions.

• At lower T, there is a transition to an orthorrombic phase, when the Ti4+

cation moves in the <110> direction. At even lower T, the stable phase istrigonal, due to the movement of the Ti4+ cations in the <111> direction.

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Phase transformations

• BaTiO3

Ba

O

Ti

Ba

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Phase transformations

• BaTiO3

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Ferroelectricty, pyroelectricity and piezoelectricity

• A ferroelectric material shows an spontaneous polarization (in theabsence of an electric field). Ex: BaTiO3 at room temperature, due to therelative movement of the anions and the cations. The spontaneouspolarization disappears at T higher than 130ºC, due to the phasetransformation to the cubic phase in which the positions of the cations andthe anions is symmetric. As a consequence of the spontaneous

polarisation, the dielectric constant is very high.

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• A pyroelectric material is that in which a temperature variation induces achange in the spontaneous polarization of the material. Example: BaTiO3,the polarization depends on temperature because the movement of ions isalso dependent on the temperature.

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• A piezoelectric material is that in which a pressure variation induces achange in the electrical polarization of the material. The applied pressurecan induce the relative movement of anions and cations, and therefore, anspontaneous polarization. In the same way, an electric field can induce amovement of the anions and the cations, and therefore, a change in theshape of the crystal.

• That is, a piezoelectric material converts:

Electric energy↔ Mechanical energy

• Example: Quartz: it is not ferroelectric, but a pressure can induce anspontaneous polarization and viceversa.

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Applications• Ferroelectric materials, as dielectrics for capacitors: the capacitors

can be made 100-1000 smaller than with conventional dielectrics.

• Pyroelectric materials, very sensitive to small changes intemperature. They can be used as infrared radiation detectors, forinstance, for night vision goggles, anti-burglar detectors (capable of

detecting the infrared radiation emitted by a person), etc…

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Piezoelectricity Applications of piezoelectric materials:

• Watches/computer clocks: quartz (piezoelectric but not ferroelectric): anelectrical signal induces the mechanical vibration of a quartz bar (to itsresonance frequency). This frequency can be used to count time.

• Lighters: a pressure on a sheet of a (PbZr xTi1-xO3) can induce an electricapotential of 3 kV, enough to produce an arc discharge between two closely

spaced sheets and ignite the gas.• Actuators: a potential difference applied on a transducer can change its

shape and actuate a mechanism, for instance, a inkjet printer.(http://www.howstuffworks.com/inkjet-printer3.htm)

Lighter Inkjet printer

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