PIEZOCERAMIC
APPLICATIONDATA
P
IEZ O
S
Y ST EMS
, I
NC
.
186 Mssachusetts Avenue Cambridge, MA02139 Te: (617) 547-1777 Fax: (617) 354-2200 Web wwwpezocom E-mail: sales@pezocom
The piezoelectric constants relating
the mechanical strain produced by an
applied electric field are termed the
strain constants, or the “d” coeffi-
cients. The units may then be
expressed as meters per meter, per
volts per meter (meters per volt).
It is useful to remember that large d
ij
constants relate to large mechanical
displacements which are usually
sought in motional transducer
devices. Conversely, the coefficient
may be viewed as relating the charge
collected on the electrodes, to the
applied mechanical stress.d
33
applies
2
1
3
P
+
–
2
1
3
P
+
–
Q or V
F
–
+
P
+
–
Q or V
–
F
+
P
+
–
Q or V
–
F
+
P
+
–
Figure - 1a
Figure - 1b
Figure - 2a
Figure - 2b
Figure - 2c
When a piezoceramic element is
stressed electrically by a voltage, its
dimensions change.
stressed mechanically by a force, it
generates an electric charge. If the
electrodes are not short-circuited, a
voltage associated with the charge
appears.
When it is
A piezoceramic is therefore capable
of acting as either a sensing or trans-
mitting element,or both. Since piezo-
ceramic elements are capable of gen-
erating very high voltages, they are
compatible with today’s generation of
solid-state devices — rugged, com-
pact,reliable,and efficient.
The following text describes the ter-
minology of piezoceramics and the
relationship among variables for func-
tional applications.
Relationships between applied forces
and the resultant responses depend
upon: the piezoelectric properties of
the ceramic;the size and shape of the
piece;and the direction of the electri-
cal and mechanical excitation.
To identify directions in a piezoce-
ramic element, three axes are used.
These axes, termed 1, 2 and 3, are
analogous to X,Y and Z of the classi-
cal three dimensional orthogonal set
of axes (Figure 1a)
The polar or 3 axis is taken parallel to
the direction of polarization within
the ceramic. This direction is estab-
lished during manufacturing by a high
DC voltage that is applied between a
pair of electroded faces to activate
the material. The polarization vector
“P” is represented by an arrow point-
ing from the positive to the negative
poling electrode. In shear operations,
these poling electrodes are later
removed and replaced by electrodes
deposited on a second pair of faces.
In this event,the 3 axis is not altered,
but is then parallel to the electroded
RELATIONSHIPS
faces found on the finished element
(Figure 1b). When the mechanical
stress or strain is shear,the subscript
5 is used in the second place.
Piezoelectric coefficients with double
subscripts link electrical and mechan-
ical quantities.
The first subscript
gives the direction of the electrical
field associated with the voltage
applied,or the charge produced. The
second subscript gives the direction
of the mechanical stress or strain.
Several piezoceramic material con-
stants may be written with a “super-
script” which specifies either a
mechanical or electrical boundary
condition. The superscripts are T, E,
D and S,signifying:
T = constant stress
= mechanically free
E = constant field = short circuit
D = constant electrical displacement
= open circuit
S = constant strain
= mechanically clamped
As an example, K
T3
expresses the
relative dielectric constant (K), mea-
sured in the polar direction (3) with
no mechanical clamping applied.
"D" CONSTANT
d =
strain developed
applied electric field
IN T R
O D U C T IO N
T
T
O P IE Z O E L E C T R IC IT Y
47
CATALOG #3, 1998