Reaney- Piezoelectric Ceramics

Question 1

Electrostriction

Answer 1

All materials undergo a small change in dimensions when subject to an electric field. If the strain is proportional to the square of the field, this is electrostriction.
x=QP^2
x is strain, Q is electrostrictive coefficient, P is polarisation

Question 2

Piezoelectricity

Answer 2

Some materials develop an electric polarisation when subject to strain through an applied stress. This is directly proportional to applied field. Reverse of electrostriction.
x=dE (converse/indirect), P=dX (direct)
E is field, X is stress, d is piezoelectric coefficient

Question 3

Component of polarisation

Answer 3

Spontaneous and induced polarisation

So for electrostriction, x=Q(Ps+Pind)^2

Question 4

P vs E hysteresis graph for ferroelectric

Answer 4

Normal hysteresis loop

Question 5

Strain vs field hysteresis for ferroelectric

Answer 5

Butterfly shape that crosses origin. Curved wing bottoms under x axis. Vertically straight sides up to some positive strain. Sharp corner so diagonally back down to origin. See slide 6

Question 6

What structures show piezoelectricity?

Answer 6

Noncentrosymmetric structures. 21 point groups of the 32 are noncentrosymmetric and 20 exhibit piezoelectricity. The other (432) by chance has symmetry characteristics that combine to give no net piezoelectric effect. All ferroelectric materials piezoelectric

Question 7

What properties of a piezoelectric material are different in different directions?

Answer 7

Because the structure and properties are anisotropic by definition, piezoelectric coefficient, compliance, electric fields and strains are different in all the directions

Question 8

Numbers in Tensor notation

Answer 8

The 3D axes are labelled 1, 2 and 3. Plane between 1 and 2 is 4. Plane between 2 and 3 is 5. Plane between 1 and 3 is 6

Question 9

Modes of deformation formulae

Answer 9

Δl3/l3=x3=d33E3 (commonly used)
Δl1/l1=d31E3
tanα=x5=d15E1 (shear)
Hydrostatic pressure: ΔP=d(h)X
Where d sub h =d33+2d31

Question 10

Effective electromechanical coupling coefficient

Answer 10

keff. Measure of how much applied electrical energy is converted into strain.
For direct effect: keff=mechanical energy converted to electrical energy/input mechanical energy
Or: keff=electrical energy converted to mechanical energy/input electrical energy
Can reach 90% for advanced materials

Question 11

Behaviour of d33 under applied field

Answer 11

d33 vs E. Starts horizontal at some value. At 50kV/m then goes exponential increase

Question 12

What causes increase in piezoelectric coefficients above a certain applied field or stress?

Answer 12

Onset of motion of domain walls. 180° ones don’t contribute as no net change in dimension when they move. For 90° domain walls, growth of domains favourably oriented with respect to applied field or stress will result in net change in dimensions. Extrinsic piezoelectric properties.

Question 13

When are there no 90° domain walls?

Answer 13

Materials whose paraelectric-ferroelectric phase transition only has loss of centrosymmetry, LiNbO3. So d33 not affected by increasing applied field or stress and piezo properties intrinsic

Question 14

What is delay in onset of domain wall motion as function of applied field related to?

Answer 14

The strain energy associated with the domain which is related to the force or field necessary to cause it to move. Means as domain walls oscillate in sinusoidal field or stress, some electrical energy converted into heat and the dielectric loss can increase

Question 15

Describe ageing

Answer 15

Motion of domain walls gradually becomes more difficult with an increasing number of cycles because of the formation of lattice defects which will try to pin the domain walls

Question 16

Why is the polarisation of a virgin sample of a ceramic zero?

Answer 16

Random distribution of the orientation of grains. So need to pole a ceramic prior to measurements

Question 17

How does poling work?

Answer 17

Apply static field of 1-4MV/m for a period of several minutes at elevated temperatures. Single crystals may also have to be poled as they usually possess a multidomain state.

Question 18

What is PZT?

Answer 18

Lead zirconite titanate. Solid solution of PbZrO3 and PbTiO3. Is a piezoelectric ceramic

Question 19

Tetragonal and rhombohedral structures of PZT

Answer 19

For tetragonal, polarisation vectors along <001> directions of pseudocube so there are 6 orientations.
For rhombohedral, polarisation along body diagonals so has 8 orientations

Question 20

PZT(53/47)

Answer 20

This composition sits on the morphotropic phase boundary between tetragonal and rhombohedral structures. Now 14 possible directions of polarisation in every grain so easy to pole. Also a metastable monoclinic structure often present at the boundary to allow even greater motion of domain walls. Coupling coefficients maximised

Question 21

Further advantages of PZT

Answer 21

Phase boundary largely independent of temperature and the movement of domains is relatively easy.

Question 22

PZT phase diagram

Answer 22

See slide 23

Question 23

Isovalent doping of PZT

Answer 23

On A-site using Sr, Ca or Ba. Lowers Curie temperature and increases d33 due to easier movement of domain walls.

Question 24

Aliovalent doping of PZT

Answer 24

C have several effects depending on choice of dopant. Can have acceptor or donor dopants either on A-site or B-site

Question 25

Acceptor doping of PZT

Answer 25

Create vacancies on oxygen sublattice which are highly mobile compared to cation vacancies. Associated with low εr, tanδ, d33, s, and no pronounced ageing.
MnO=Mn(Ti)’’+Oo+vo••
Highly mobile vo•• stabilise polarisation and thus the domain structure reducing most of the properties that are enhanced by domain wall motion. Termed hard PZTs

Question 26

Donor doping of PZT

Answer 26

Create vacancies on cation sublattice. Associated with high εr, tanδ, d33, s and less ageing.
LaO3=2La(Pb)• +3Oo +v(Pb)’’
V(Pb)’’ enhance possibility of domain wall motion by reducing diffusion of O vacancies. Often donor doping combined with isovalent dopant such as Sr to increase d33 at expense of Tc. Termed soft PZTs

Question 27

Manufacturing PZT

Answer 27

Almost always mixed oxide route. Density must be close to maximum to get hugest piezoelectric responses. Excess PbO commonly used to compensate for PbO-loss during sintering. Electrodes normally silver paint fired at 600-800C

Question 28

Resonance mode applications of piezoelectrics

Answer 28

Ultrasound, sonar, transformers, filters, motors

Question 29

Conventional mode applications of piezoelectrics

Answer 29

Spark generators sensors (pressure, acceleration, strain), actuators.
Spar generator schematic slide 31. Two poled pieces brought together +to+ or -to- makes a spark

Question 30

Actuator designs for piezoelectrics

Answer 30

See slide 32 diagrams. Bimorph has piezoelectric either side of central piece of metal (top and bottom). Get a signal or generate energy from plate attached to it moving (wobbling)