Introduction to piezoelectricity
Amira Barhoumi Meddeb
01/11/2013
Lecture outline
• Part 1
–
–
–
–
Definition of piezoelectricity
Applications
History
Crystallography
• Part 2
– Constitutive equations in 1D
– Effect of mechanical/electrical boundary conditions
– Piezoelectric coupling coefficient
• Part 3
– Constitutive equations in 3D
– Common transducers modes
2
Definition of piezoelectricity
3
Piezo: From Greek “piezein” meaning “to press”
Stimulus (Stress or
electric field)
Piezoelectric
material
Response (Charge or
displacement)
Electro-mechanical coupling
4
Direct piezoelectric effect (sensor)
5
Converse piezoelectric effect (actuator)
6
Have a
spontaneous
polarization
http://electrons.wikidot.com/ferroelectrics
The spontaneous
polarization can
be reversed by an
electric field
7
Applications
8
Underwater sonar
http://www.noliac.com/Applications-8427.aspx
Quartz watches
http://www.innovateus.net/invention/invention-quartz-watch
Spark ignition systems -Lighter
http://global.kyocera.com/fcworld/charact/elect/piezo.html
9
AFM probe
(Shibata et al. 2003)
10-mm Squiggle motor
(cameras autofocus, optical zoom
assemblies)
http://electronicdesign.com/article/components/piezoelectri
c-motor-delivers-precise-positioning-i
Piezoelectric speakers
http://www.houseofjapan.com/electronics/murataannounces-mass-production-of-worlds-thinnest-waterproofpiezoelectric-speaker
10
Piezoelectric shoes
http://www.gizmag.com/piezoelectric-generator-shoes/14945/
Piezo-Streetlights
http://www.consumerinstinct.com/social-mediatechnology/piezoelectricity-walk-jump-dance-andgenerate-electricity/
Energy harvesting from railroads
http://www.pearltrees.com/#/N-fa=1608799&N-play=1&Ns=1_5340530&N-u=1_151990&N-p=47887453&N-f=1_5340530
11
Piezo-Highways
http://www.consumerinstinct.com/social-mediatechnology/piezoelectricity-walk-jump-dance-and-generateelectricity/
Piezoelectric based Jaguar E-type
http://www.ecofriend.com/designers-conceptualize-next-generationpiezoelectric-based-jaguar-type.html
Piezo-Clothes
http://www.consumerinstinct.com/social-mediatechnology/piezoelectricity-walk-jump-dance-and-generateelectricity/
12
Energy harvesting dance floor
http://www.robaid.com/tech/walk-over-sustainable-dance-club-floor-tiles-to-generate-power.htm
13
History of piezoelectricity
14
15
16
17
Crystallography
18
19
For piezoelectricity to happen, an asymmetry must exist in the crystal structure.
Ø Naturally occurring asymmetry: Quartz, Tourmaline (Single crystals)
Rhombohedral
(Trigonal)
Quartz crystal structure (Trigonal)
20
Ø Ferroelectrics:
² Piezoelectric ceramics: Barium titanate, Lead zirconate titanate (PZT), Lead
niobate (Polycrystalline)
² Piezoelectric polymers: Polyvinylidene fluoride (Semicrystalline)
21
Perovskite structure
ABO3
Ø BaTiO3 is the prototype ferroelectric that crystallizes in this structure. Other
important examples are PbTiO3 and Pb(ZrxTi1−x)O3
Ø This structure is a simple cubic unit cell with a large cation (A) on the corners, a
smaller cation (B) in the body center, and oxygens (O) in the center of the faces.
22
http://www.fujitsu.com/global/services/microelectronics/product/memory/fram/index.html
23
Piezoelectric polymers: PVDF
24
The role of ferroelectricity in piezoelectric materials
• In non-ferroelectric piezoelectric materials, the observed piezoelectric
response originates from atomic displacements within the individual unit
cells of the material.
• A similar piezoelectric response occurs in ferroelectric piezoelectrics as
well. It dominates as long as the domain configuration in the material
remains unaffected by the applied electric field or mechanical stress and
is called the intrinsic response.
25
Poling:
26
Temperature:
Curie Temperature (Tc) is the critical temperature beyond which a previously
ferroelectric material becomes paraelectric.
BaTiO3
http://electrons.wikidot.com/ferroelectrics
http://www.murata.com/products/capacitor/design/faq/mlcc/property/06_more.html
27
(a)
(b)
(P-E) hysteresis loops of (a) paraelectric phase {above Tc}
and (b) ferroelectric phase {below Tc)
28
Comparison of the most important piezoelectric material classes by
means of typical examples
29
Summary:
• The electromechanical properties of piezoelectric material are
related to the electric dipoles that exist in the molecular structure.
• Poling the polycrystalline material produces an alignment of the
electric dipoles.
• Application of an external field or application of a mechanical stress
will produce motion in the electric dipoles. This motion of the dipoles
gives piezoelectric materials their electromechanical properties.
30
Linear Constitutive Equations
1D
31
Mechanical behavior
S = sT
S: Strain [m/m]
s: Compliance [m2/N]
T: Stress [N/m2]
32
Example 1: Consider a material with an elastic compliance of 20 x 10-12m2/N
and a square cross-section with side length of 7 mm. Compute the strain
produced by the application of a 100 N load.
33
Dielectric behavior
Q
•
Capacitance is defined as the ability of two
conductors to store a charge Q when a
potential V is applied across them.
Co = Q/V = ε0A/d
– ε0 is the permittivity of free space
– A is the area of the conducting plates
– d is the distance between the two
plates
D = e0E
•
E=
d
V
t
Q’>Q
•
D = e .E
•
•
E
The resultant capacitance can then be
measured due to the dielectric:
C = εrε0A/d
The dielectric constant εr= ε/εo
The dielectric constant, or relative
permittivity, is the ratio of the amount of
electrical energy stored in a material by
an applied voltage, relative to that
stored in a vacuum.
34
D
E=V/d
e=e0 er
V
(εr)
D =εE
D: Electric displacement [C/m2]
e: Dielectric permittivity [F/m]
E: Electric field [V/m]
35
Example 2: Consider a parallel-plate capacitor having an area of 6.45x10-4 m2
(1 in2) and a plate separation of 2x10-3 m (0.08 in.) across which a potential of
10 V is applied. If a material having a dielectric constant of 6.0 is positioned
within the region between the plates, compute
(a) The capacitance
(b) The magnitude of the charge stored on each plate
(c) The dielectric displacement D
e0 =8.85*10-12 F/m
36
Mechanical behavior (Hooke’s Law)
S = sT
S: Strain
s: Compliance
T: Stress
Electrical behavior
D =εE
D: Electric displacement
e: Permittivity
E: Electric field
When the equations are combined:
! S $ ' s 0 *! T $
"
%=)
%
,"
# D & ( 0 ε +# E &
37
Electromechanical coupling in the constitutive equations?
Coupling terms
! S $ ' s 0 *! T $
"
%=)
%
,"
# D & ( 0 ε +# E &
38
Direct piezoelectric effect
At E=0 V/m
! S $ ' s 0 *! T $
"
%=)
%
,"
# D & ( d ε +# E &
39
Converse piezoelectric effect
At T=0 N/m2
! S $ ' s
"
%=)
# D & ( d
d *! T $
%
,"
ε +# E &
40
The total strain due to mechanical stress and applied electric field:
S = sT + d E
Strain
[m/m]
Elastic
compliance
[m2/N]
Stress
[N/m2]
Electric field
[V/m]
Piezoelectric
strain coefficient
[m/N]
Field variables
Material
properties
41
The total electric displacement due to mechanical stress and applied electric field:
D = d T +ε E
Electric
displacement
[C/m2]
Elastic
compliance
[m2/N]
Stress
[N/m2]
Electric field
[V/m]
Dielectric
permittivity
[F/m]
Field variables
Material
properties
42
Effect of boundary conditions
Short-circuit:
D = d T +ε E
S = sT + d E
To indicate that this measurement was
performed at zero electric field, the convention
is to use a superscript E to indicate that the
compliance was measured at E = 0.
S=sE T
43
Open-circuit:
S = sT + d E
D = d T +ε E = 0
dT
E =−
ε
S=
sD=
44
2 %
"
d
D
E
s = s $1− E '
# s ε&
The circled term quantifies the change in the mechanical compliance
as a function of the electrical boundary condition.
45
Example 3: PZT 5A4 from Piezo Systems, Inc. has the following properties:
c E = 62GPa
εr = 1800
d =390 *10 −12 C / N
Compute the percentage change in the mechanical compliance between the shortcircuit and open-circuit condition
e0 =8.85*10-12 F/m
46
47
How about ε?
! S $ ' sE
"
%=)
# D & )( d
*!
d , T $
"
%
T
ε ,+ # E &
2 %
"
d
ε S = ε T $1− E T '
# s ε &
Boundary condition:
T=0
Boundary condition:
S=0
48
2 %
"
d
D
E
s = s $1− E T '
# s ε &
2 %
"
d
S
T
ε = ε $1− E T '
# s ε &
k=
d
s Eε T
The piezoelectric coupling coefficient: Relates
to the “strength” of the electromechanical
coupling
d=0?
No coupling!
0<k2<1
49
Example 4: Compute the piezoelectric coupling coefficient, k, for the material
parameters listed in the previous example. Also compute k2 for the same material.
50
A better understanding of this table
Comparison of the most important piezoelectric material classes by
means of typical examples
51
Linear Constitutive Equations
3D
52
An electric field could be applied in each direction independently, therefore E is
a vector that consists of the electric field in the 1, 2, and 3 directions:
For stress, T and strain, S:
1. The face on which the stress/strain is acting
2. The direction of the stress/strain
There are a total of NINE
stress/strain components – 3
on each face
Symmetry in stress/strain
There are SIX stress/strain components which are independent
55
56
57
58
Most common piezoelectric materials are orthotropic materials which have a
compliance matrix of the form:
59
Most dielectric materials do not exhibit cross-coupling in the relationship between
electric field and electric displacement. This reduces the dielectric matrix to a
diagonal matrix:
The dielectric properties in the “11” and “22” directions are equal in most times
piezoelectric materials.
The symmetry in the crystal structure of most piezoelectric materials limits the
coupling to only subset of directions. The piezoelectric strain coefficients matrix is:
Piezoelectric strain coefficients matrix for a poled piezoelectric
! 0
0
0
#
d =# 0
0
0
#
#" d31 d31 d33
d31
0
d15
d15
0
0
0
0 $
&
0 &
&
0 &%
Indicates that the electrodes are
perpendicular to the 3-axis
Indicates that the piezoelectrically
induced strain or the applied stress
is in the 1-direction
62
Don Leo. SMART STRUCTURES/ACTIVE MATERIALS.
Many applications do not require the use of the full constitutive relationships to
analyze the problem. Most common modes:
’33’ mode
’31’ mode
E3≠0
E3≠0
T3≠0
T1≠0
S3≠0
S1≠0
64
‘33’ mode transducer
F: Force
X: Displacement
V: Voltage
Q: Charge
L: Length
w: Width
t: Thickness
65
X=f(F, V)?
Q=f(F,V)?
66
1/stiffness [m/N]
[m/V] or [C/N]
Capacitance [F]
67
‘31’ mode transducer
68
This is a data sheet from American Piezo Ceramics, Inc. listing the material parameters
of their line of products.
69
Example 5: Determine the displacement produced in the ‘3’ direction by applying
50 volts to a piezoelectric transducer with a length of 10mm, width of 3mm, and
thickness of 0.25 mm.
Assume that the resistance force is zero. Use the material parameters of APC 850.
70
Example 6: Compute the displacement in the ‘1’ direction of a transducer with a
length of 10 mm, width of 3 mm, and thickness of 0.25 mm. The applied voltage is
50 V and the resistance force is zero. Use the material parameters for APC 850.
71
Note that the transducer produces 350 nm of motion in the ‘1’
direction but only 20 nm of motion in the ‘3’ direction when subjected
to the same potential of 50 V.
The reason is that the motion in the ‘1’ direction is amplified by the
geometric dimensions L/t. Thus, we can design a transducer that
produces more motion in one dimension as compared to the other
dimension.
72
Selecting your piezoelectric system for the
required application
Geometry and dimensions
Control the dimension of your system to maximize the desired outcome (examples 5
&6)
Materials properties: with the focus being on piezoelectric and mechanical properties
73
Or one Can go the composite route!
Example of piezocomposite design goals for sonar transducer
Paramter
Desired value
Capacitance
Maximize
Acoustic impedance
Match to 1.5 Mrayls (water)
Electromechanoical coupling
Maximize
Electrical loss tangent
Minimize
Mechanical loss
Minimize
74
If we would want to built a piezoelectric system with high strain values:
Polymer nanocomposites could be a good choice
What matrix to use?
What nanoparticles to use?
Modeling
Ways to choose:
Experiments
75
References in Piezoelectricity
• W. Heywang, K. Lubitz and W. Wersing, Piezoelectricity: Evolution and future of a
technology, Springer, Berlin Germany 2008.
• W. Guyton Cady, Piezoelectricity: An intorduction to the theory and applications of
electromechanical phenomena in crystals, McGroaw-Hill Book Company, Inc., New
York, 1946.
• D. Damjanovic, Ferroelectric, dielectric and piezoelectric properties of ferroelectric
thin films and ceramics, Rep. Prog. Phys. 61 (1998) 1267-1324.
76