Reaney- Piezoelectric Ceramics Flashcards
Electrostriction
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
Piezoelectricity
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
Component of polarisation
Spontaneous and induced polarisation
So for electrostriction, x=Q(Ps+Pind)^2
P vs E hysteresis graph for ferroelectric
Normal hysteresis loop
Strain vs field hysteresis for ferroelectric
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
What structures show piezoelectricity?
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
What properties of a piezoelectric material are different in different directions?
Because the structure and properties are anisotropic by definition, piezoelectric coefficient, compliance, electric fields and strains are different in all the directions
Numbers in Tensor notation
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
Modes of deformation formulae
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
Effective electromechanical coupling coefficient
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
Behaviour of d33 under applied field
d33 vs E. Starts horizontal at some value. At 50kV/m then goes exponential increase
What causes increase in piezoelectric coefficients above a certain applied field or stress?
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.
When are there no 90° domain walls?
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
What is delay in onset of domain wall motion as function of applied field related to?
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
Describe ageing
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
Why is the polarisation of a virgin sample of a ceramic zero?
Random distribution of the orientation of grains. So need to pole a ceramic prior to measurements
How does poling work?
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.
What is PZT?
Lead zirconite titanate. Solid solution of PbZrO3 and PbTiO3. Is a piezoelectric ceramic
Tetragonal and rhombohedral structures of PZT
For tetragonal, polarisation vectors along <001> directions of pseudocube so there are 6 orientations.
For rhombohedral, polarisation along body diagonals so has 8 orientations
PZT(53/47)
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
Further advantages of PZT
Phase boundary largely independent of temperature and the movement of domains is relatively easy.
PZT phase diagram
See slide 23
Isovalent doping of PZT
On A-site using Sr, Ca or Ba. Lowers Curie temperature and increases d33 due to easier movement of domain walls.
Aliovalent doping of PZT
C have several effects depending on choice of dopant. Can have acceptor or donor dopants either on A-site or B-site
Acceptor doping of PZT
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
Donor doping of PZT
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
Manufacturing PZT
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
Resonance mode applications of piezoelectrics
Ultrasound, sonar, transformers, filters, motors
Conventional mode applications of piezoelectrics
Spark generators sensors (pressure, acceleration, strain), actuators.
Spar generator schematic slide 31. Two poled pieces brought together +to+ or -to- makes a spark
Actuator designs for piezoelectrics
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)
