Ferro Electricity, Pyroelectricity, Electrical conductivity

1. Ferro Electricity
Ferro electricity refers to the creation of enormous value of induced dipole moment in
a weak electric field as well as existence of electric polarization even in the absence of
applied electric field.
Materials which exhibit electric polarization even in the absence of the applied electric
field are known as Ferro electric materials. These have permanent dipole moment in
each atom or molecule.
The dielectric constants of these materials are some three orders of magnitude larger
than that in ordinary dielectrics.
Examples-
• Lead titanate, PbTiO3
•Lead zirconate titanate (PZT)
•Lead lanthanum zirconate titanate (PLZT)

2. APPLICATIONS
• Thermistors
• Oscillators
• Non-volatile memory
• Filters
• Capacitors
• Light deflectors

3. Pyroelectricity
Pyroelectricity is an ability of the material to generate an electrical
signal when it is subjected to a thermal change. The pyro electric
coefficient λ is defined as the change in polarization per unit
temperature change of the specimen.
λ = dP/dT
For example- Barium Titanate

4. Applications
1. Passive Infrared Sensor
2. Infrared Thermometers
3. Laser Energy Sensors

5. Ferro electric hysteresis curve
Hysteresis of a magnetic material is a property by virtue of which the
flux density (B) of this material lags behind the magnetizing force (H).
D

6. In ferroelectric materials, the polarization P does not vary linearly with
electric field E.
The plot of P versus E in which the material is polarized in one direction
and then in opposite direction is called the hysteresis curve of the
specimen.

7. Electrical conductivity
Electrical conductivity is the measure of a material's ability to allow the
transport of an electric charge. Its SI is the siemens per meter, or, more
simply, Sm−1.
It is the ratio of the current density to the electric field strength.
The symbol for electrical conductivity is σ.
Electrical conductivity (σ) is the reciprocal of the electrical resistivity (ρ):
σ = 1/ρ
where resistivity for a material with a uniform cross section is:
ρ = RA/l
where R is the electrical resistance, A is the cross-sectional area, and l is
the length of the material

8. Some materials with good conductivity
• Silver
• Copper
• Gold
• Aluminium
• Zinc
• Nickel
• Brass

12. Thermal Conductivity
• It is the property of a material that indicates its ability to conduct
heat.
• It is represented by k and is measured in watts per kelvin per metre
(W·K−1·m−1).
• The reciprocal of thermal conductivity is thermal resistivity
There are four factors (kkk, AAA, that affect the rate at which heat is
conducted through a material. These four factors are included in the
equation below that was deduced from and is confirmed by
experiments.

13. The letter Q represents the amount of heat transferred in a time t, k is
the thermal conductivity constant for the material, A is the cross
sectional area of the material transferring heat, ΔT is the difference in
temperature between one side of the material and the other, and d is
the thickness of the material. These factors can be seen visually in the
diagram below.

14. Thermal expansion
Thermal expansion describes the tendency of an object to change in its area, volume and shape
to a shift in temperature through a transfer of heat.
Since thermal expansion leads to changes in dimension either in length or volume, therefore,
there are three types of thermal expansion namely – Linear expansion, Area expansion, and
Volume expansion.
Linear expansion occurs when there is a change in the length. Linear expansion formula is given
as,
Lo =original length,
α = length expansion coefficient,
L = expanded length,
ΔT = temperature difference,
ΔL = change in length.

15. Volume expansion occurs when there is a change in volume due to temperature.
Volume expansion formula is given as
Where,
Vo = original volume,
V = expanded volume,
αv = volume expansion coefficient,
ΔT = temperature difference,
ΔV = change in volume after expansion.

16. Area expansion occurs when there is any change in area due to temperature change. Area
expansion formula is given as,
Where,
A = original area,
ΔA = change in area,
αA = area expansion coefficient,
ΔT = temperature difference,
Ao = expanded area.

17. Example 1
A 5m long rod is heated to 40oC. If the length of the rod expands to 7m after some time,
calculate the expansion coefficient. Given room temperature is 30o C.
Solution:
Given:
Initial length Lo = 5 m,
Expanded length L = 7 m
Change in length Δ L = 7 – 5 = 2 m
Temperature difference Δ T = 40o C – 30o = 10o C
= 283 K
The linear expansion formula is given by,
ΔL / Lo = αL Δ T
∴ Length expansion coefficient is given by,
αL= ΔL /( Lo ×ΔT)
= 2 / 5 x 283
αL = 14 × 10-4 K-1.