Lecture 6 - Polarisation and Piezoelectricity Flashcards
What is the polar effect?
The polar effect is due to an asymmetry in positive and negative charge distribution in predominantly ionic materials. This effect is either intrinsic or can by applied by an external electric field.
How does an electric dipole appear?
This asymmetry caused by the polar effect gives rise to an electric dipole which we can define as q*r [C/m] where r a 3D vector.
What is Polarisation?
Polarisation is the total electric dipole moment per unit volume (Σqr)/V in [C/m²]
Polarisation represents charge that appears on the surface of a dielectric placed in an electric field, or strained mechanically or thermally.
Polarisation is the electric analogue to magnetisation.
What are Ferroelectrics/Electrets?
They are materials whose dipoles are aligned without an external field. (Intrinsically polar)
They exhibit spontaneous electrical polarisation analogous to ferromagnets, but can do so only below Tc (Curie temperature).
Applying an electric field changes the direction of this dipole moment because individual domains align with the applied field.
Ferroelectric materials are therefore used for piezoelectric or pyroelectric applications because we can control their axis of polarisation.
What is the Piezoelectric effect?
It’s the production of change in dielectric polarisation by the application of mechanical stress.
Conversely, applying an electric field to a piezoelectric material will cause a mechanical strain.
What are some applications of piezoelectric elements?
Passive Applications:
Hydrophones, microphones, phonographic pick-ups
Active Applications:
Buzzers, loudspeakers, depth sounders
What do we mean when we use piezoelectric materials in passive mode?
Passive mode means we apply mechanical stress on a piezoelectric material and utilise the current produced from it.
What do we mean when we use piezoelectric materials in active mode?
Active mode means we apply an electric field or current to a piezoelectric material to cause it to mechanically strain.
What are the piezoelectric equations of state?
P = χE +dσ S = cσ + dE
Where Variables P : Polarisation E : Electric Field S : Strain σ : Stress
And Constants
c : Elastic Constant
d : Piezoelectric Coefficient
χ : Electric Susceptibility
Explain the notation used for the piezoelectric effect
For the direct effect:
P_i=d_ijk*σ_jk
d is a rank 3 tensor => 27 independent piezoelectric coefficients
Due to symmetry we can reduce to only 6 stresses, three tensile and three shear, reducing d into 18 coefficients.
Pi =dij*σj
For the converse piezoelectric effect:
S_j=d_ij*E_i
What are the three piezoelectric modes of operation? How do we reduce to those alone?
Create piezoceramics that are thin plates leading to σ1,σ2,Ε1,Ε2 to be zero.
Useful coefficients left:
d31=d32
d33
d15=d24
Therefore we have three modes of operation:
Thickness Mode (d33) Longitudinal Mode (d31) Shear Mode (d15)
What is Thickness Mode of operation in piezoceramics?
Applied stress is in the same direction as polarisation for a thin plate
P3=d33*σ3
Therefore
Q=d33*F
We use thickness mode for passive applications such as underwater sound detection
What is Longitudinal Mode of operation in piezoceramics?
Applying stress parallel to x1 leads to change in polarisation along x3
P3=d31*σ1
Q/A = d31* F/a
where A area of surface perpendicular to x1 a area of surface perpendicular to x3 \_\_\_\_\_\_\_\_ | | | P | x3 | ↑ | ↑→ x1 |\_\_\_\_\_\_\_|
Passive Mode uses:
Microphones in telephone handsets
Active Mode uses:
Buzzers/Alarms
What is Shear Mode in piezoceramics?
A change in polarisation perpendicular to the polar axis where stress is applied σ5
P1= d15*σ5
This mode has the advantage that charges due to polarisation only appear under shear so any charge generation through the pyroelectric effect is ignored.
In passive applications, piezoceramics in shear mode are used for accelerometers
