Method of fabricating piezoelectric transducer with polymer element

A piezoelectric transducer having at least one active element consisting of a film of polymer material is disclosed. Electrodes are formed on the two principal faces of the film after polarization of the film. The film is endowed with piezoelectric properties under the sole action of an electric field oriented along the normal to its principal faces and without any need for preliminary stretching. The anisotropy induced as a result of this orientation is solely electrical.

BACKGROUND OF THE INVENTION 
This invention relates to piezoelectric transducers and may be extended to 
pyroelectric transducers as well, the active element of which is 
constituted by a polymer in sheet form. When subjected to a suitable 
treatment, said active element exhibits piezoelectric and pyroelectric 
properties which are similar to those possessed by certain classes of 
crystals. 
One of the first synthetic polymers to show clear evidence of piezoelectric 
and pyroelectric properties was polyvinylidene fluoride. In this case the 
treatment includes: (a) unidirectional drawing of a flat film of said 
polymer, (b) metallizing the faces of the drawn film and (c) subjecting 
the metallized faces to an electric field by connecting its metallized 
faces to an electric polarizing generator. The disadvantage of a flat film 
lies in the fact that its use is limited to transducers having developable 
shapes, that is shapes which are capable of being opened and flattened out 
upon a plane without stretching any element. Furthermore, the thinness of 
the films employed entails the need for stretching latter by means of a 
prestressing device. 
This disadvantage can be overcome by means of a thermoforming technique 
which makes it possible to obtain a non-developable self-supporting shape 
which consequently does not have any joint. The thermoforming operation is 
carried out at a temperature which results in stretching of the molecular 
chains since this stretching process is intended to produce a change of 
phase which makes the material polar. It is then an easy matter to induce 
electrical anisotropy by polarization. The electrodes are clearly formed 
after the polymer film has been given its final shape. 
The technique which includes inducing the polar phase by substantial 
drawing of the polymer makes it necessary to take precautions in order to 
prevent shrinkage of the drawn film or to prevent the shape obtained by 
thermoforming from shrivelling-up and thus losing its self-supporting 
properties. During operation, a polymer-film transducer must be capable of 
withstanding a temperature rise while retaining its shape, its dimensions 
and its conversion efficiency. 
In addition to the lack of dimensional stability resulting from the 
disturbing effect produced on the mechanical equilibrium by drawing 
performed above the melting temperature of the polymer, it should also be 
mentioned that the shapes usually obtained from polyvinylidene fluoride 
have relatively low mechanical compliance. 
In order to overcome these drawbacks, the invention provides a method of 
manufacture which essentially includes electrically polarizing a shaped 
product so as to retain its original elastic properties. This does not 
prevent development of piezoelectric and pryroelectric properties since 
the electrical anisotropy induced by the polarization is the only factor 
involved in the transducing action which takes place. By reason of the 
fact that only the desired anisotropy is electrical and that it is 
produced by an electric field having a direction perpendicular to the 
faces of the polymer film, the transducing action is related to the effect 
of certain crystal systems which have symmetry of revolution with respect 
to the normal to the faces of the manufactured product. 
BRIEF DESCRIPTION OF THE INVENTION 
The present invention relates to a piezoelectric transducer in which the 
active element comprises a film of polymer material provided on its two 
principal faces with electrodes forming a capacitor. The transducer is 
distinguished by the fact that the anisotropy induced in said material is 
solely electrical and results from a dipolar orientation in the direction 
of the normal to said principal faces. 
The invention is also directed to the method of manufacture of the 
transducer element as mentioned in the foregoing.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In FIG. 1, there can be seen a cylindrical element 14 made from a polymer 
material such as polyvinylidene fluoride (PVF.sub.2). The structure of 
PVF.sub.2 is composed of spheroidal crystal masses in an amorphous phase. 
The macroscopic mechanical properties are those of an isotropic substance. 
This polymer has three distinct crystalline forms .alpha., .beta. and 
.gamma.. The .alpha. form is the one obtained from the molten polymer. The 
molecular chains are wound in a helix 18 as shown at (a) in FIG. 2. It is 
observed that the .alpha. form has an arrangement of carbon atoms 16, 
hydrogen atoms 17 and fluorine atoms 15 such that the electric dipole 
moments compensate for each other along the chain. The .beta. form 
corresponds to a molecular chain as shown at (b) in FIG. 2. This .beta. 
form and the .gamma. form which is similar to this latter are less stable 
than the .alpha. form; they are characterized by a zigzag chain and by 
electric dipole moments in which the effects are added. 
The structure of the element 14 of FIG. 1 can therefore be designated 
schematically by a system of chains 4, 5, 6, 7, 8, 9, 10, 11 which 
represent at (a) a non-polar solid phase II (.alpha. phase) and by a few 
chains 12 and 13 which represent a highly polar solid phase I (.beta. and 
.gamma. phases). At (a), the polymer material has not been subjected to 
any stress after solidification so that, with respect to the system of 
axes XYZ, no direction of molecular chain has undergone any change with 
respect to the original arrangement. The element 14 shown at (a) in FIG. 1 
is endowed with good mechanical stability and can be considered as 
electrically isotropic from a macroscopic standpoint since it has not been 
electrically polarized. 
In order to establish piezoelectric and pyroelectric properties in 
polyvinylidene fluoride, it is a known practice to subject the element 14 
to substantial drawing which is intended to convert the non-polar phase II 
to a polar phase I. This mechanical action is illustrated at (b) in FIG. 1 
in which it is observed that the element 14 is drawn uniformly in the 
plane XY in circumferential tension .sigma.. The diameter of the element 
14 has increased and its thickness has decreased. 
One of the consequences of this drawing process, which is performed below 
the melting point of the polymer, is that the chains 5 to 13 have moved 
back to the direction of the plane XY, with the result that there exists 
at (b) a mechanical anisotropy which the element 14 did not possess at 
(a). Moreover, the initially spheroidal masses have assumed a lenticular 
shape within the amorphous phase. The other consequence is that certain 
non-polar chains 9, 10, 11 have become polar, which is readily apparent 
when comparing the structures (a) and (b) of FIG. 2. 
In order to produce the electrical anisotropy which is necessary for the 
appearance of piezoelectric and pyroelectric effects, another known 
practice consists in subjecting the drawn element 14 shown at (b) in FIG. 
1 to an electric field having a direction Z. To this end, the principal 
circular faces of the element 14 shown at (b) are coated with electrodes 
between which a direct-current high voltage is applied. When treated in 
this manner, the element 14 shown at (b) together with its electrodes 
forms a transducer element which produces a proportional electric voltage 
when heated or subjected to an external stress. Conversely, an electric 
voltage applied between its electrodes produces proportional mechanical 
deformations along the axis Z and in the plane XY. 
It is apparent from the foregoing that, in order to facilitate electrical 
polarization, this latter has been made dependent on a preliminary 
treatment which alters the mechanical isotropy of the polymer. This 
results in a lack of dimensional stability which entails the need to take 
precautions in order to prevent modification of the shape given to the 
transducer. 
In fact, the operation of a piezoelectric transducer of polymer material 
can be analyzed in simplified manner by adopting the general form of a 
transducer illustrated in FIG. 3 as a model. This non-developable form 
comprises a sheet 14 of polyvinylidene fluoride provided with electrodes 
19 and 20. An electric generator 21 connected to the electrodes 19 and 20 
induces a variation of polarization .delta. P to which there correspond in 
the case of the element 22 having a radius of curvature .rho. a 
deformation .delta. Z in thickness and associated transverse deformations; 
the Poisson coefficient .nu. of the material relates these deformations as 
illustrated by arrows to the direct deformation .delta. Z. During 
fabrication, an electrical polarization P has been established in the 
polymer material and is expressed by the relation: 
EQU P=N..mu..&lt; cos .theta.&gt; (1) 
where N represents the volume concentration of the dipoles carried by the 
molecular chains, 
.mu. represents the dipole moment, 
&lt; cos .theta.&gt; is a contribution factor which depends on the inclination 
.theta. of the dipole moment with respect to the axis Z. 
The piezoelectric effect which is characteristic of the thickness mode can 
be represented by a coefficient d=.delta.P/.delta.Z. Since .mu. and &lt; cos 
.theta.&gt; are constants, we have: 
EQU d=.mu..multidot.&lt; cos .theta.&gt;..delta.N/.delta.Z (2) 
which may be written in the form: 
EQU d=-.mu..multidot.&lt; cos .theta.&gt;/v.sup.2 .multidot.dv/dZ.multidot.n (3) 
where n represents the number of dipoles which take part in the 
polarization, v represents the volume of the element 22. 
Relation (3) may be written: 
EQU d=-P.multidot.1/v dv/dZ (4) 
and observing that the volume compliance s.sub.v is precisely equal to 
1/v.multidot.dv/dZ, the following simple result is obtained: 
EQU d=-P.multidot.s.sub.v (5) 
with, by definition: 
##EQU1## 
where E is the Young number of the polymer material. 
In regard to the pyroelectric effect, one may proceed in a similar manner 
by defining a coefficient 
EQU p=dP/dT 
where T is the temperature. 
We then obtain the simple relation: 
EQU p=P.multidot..alpha..sub.v (6) 
where .alpha..sub.v is the coefficient of volume thermal expansion. 
Relations (5) and (6) reflect in a summary but correct manner the 
piezoelectric and pyroelectric effects of polymer materials which have 
been subjected to electrical polarization P. 
A much more significant formulation is offered by the tensorial 
representation in conjunction with the notations employed in 
crystallography. By adopting the indices 1, 2 and 3 mentioned at (a) in 
FIG. 1, the method of fabrication by unidirectional drawing followed by 
polarization in polar phase results in a piezoelectric effect described by 
means of the tensor d.sub.ijk of rank three as follows: 
##EQU2## 
The variation of polarization dP.sub.i (vector) is related to the 
deformation dX.sub.jk (tensor of rank two) by the tensorial relation: 
EQU dP.sub.i =d.sub.ijk .multidot.dX.sub.jk 
The pyroelectric effect is defined by the following tensorial formula: 
EQU dPi=p.sub.i dT 
with dT temperature variation (scalar) 
##EQU3## 
A study of relations (7) and (8) shows that polyvinylidene fluoride 
(PVF.sub.2) which is drawn and subsequently polarized in accordance with 
the teachings of the present state of the technique is to be considered as 
falling into class 2 mm, which means that it behaves as a pyramidal 
orthorhombic crystal. The compliance tensor of order four of this class 
comprises nine differentiated coefficients. The mechanical equilibrium is 
highly disturbed and this explains the fact that the product obtained has 
a tendency to shrink or to shrivel-up. 
In order to have the advantage of favorable piezoelectric and pyroelectric 
properties without being exposed to the same drawbacks, the invention 
proposes to induce piezoelectric properties such that the coefficients 
d.sub.31 and d.sub.32 are equal as well as the coefficients d.sub.24 and 
d.sub.15. 
The piezoelectric effect obtained is therefore described by the tensor: 
##EQU4## 
The compliance tensor is: 
##EQU5## 
In fact, the polymer material has macroscopic mechanical properties which 
are those of an isotropic substance. 
However, an intermediate degree of anisotropy can also remain at the level 
of the crystalline masses. This corresponds to the isomorphism which 
characterizes transverse isotropy and the crystallographic classes 4 mm 
(pyramidal ditetragonal) and 6 mm (pyramidal dihexagonal). The two classes 
last named are advantageous when it is desired to obtain a pyroelectric 
transducer since the tensor P.sub.i is again of the form: 
##EQU6## 
It is useful to recall that all pyroelectric transducers are also 
piezoelectric transducers but the converse does not hold true. 
FIG. 4 illustrates the difference in operation of a piezoelectric 
transducer of cylindrical shape, depending on whether it is fabricated 
from a film of polymer material which has been subjected to a drawing 
operation or whether, on the contrary, the anisotropy induced is purely 
electrical. The transducer shown at (a) in FIG. 4 is fabricated from a 
flat film which has been drawn in the direction 24. This film is stretched 
over an elastic core 23 of cylindrical shape and thus assumes the shape 
shown in full lines when at rest. By applying an alternating-current 
voltage to the electrodes which cover the two principal faces of the film 
which is wound on the periphery of the core 23, an alternate radial 
expansion of the transducer is accordingly observed. Its cylindrical 
radiation surface vibrates between the shapes shown in dashed lines. It is 
observed that the volume displaced by the transducer is primarily due to 
the elongation which takes place in the direction 24. 
The transducer shown at (b) in FIG. 4 is fabricated in accordance with the 
invention by molding of the polymer material in the hot state. The shaped 
element thus obtained is made piezoelectric solely under the action of an 
electrical dipole orientation along the normal to the molded film. Said 
shaped element has the appearance of a cylindrical box having an open 
bottom end, a cylindrical wall 25 and an end-wall 28 which are formed in a 
single piece. The interior of said shaped element is empty since it is 
self-supporting. The element 25, 28 shown at (b) in FIG. 4 is coated 
externally and internally with electrodes. When an alternating-current 
voltage is applied to the electrodes, said element begins to vibrate both 
radially and axially. The volume swept by this vibration is illustrated by 
the two contours shown in dashed lines. The expansion uniformly affects 
both the cylindrical wall 25 and the end-wall 28 of the transducer; the 
circumferential deformations 26 and 29 associated with the axial 
deformation 27 and with the radial deformation 30 produce a variation in 
volume of the transducer, thereby causing radiation over the entire 
surface of this latter. The comparison which has just been mentioned is 
intended to show that piezoelectric properties induced in a film of 
polymer material solely as a result of suitable electrical polarization 
can be utilized just as readily as those which had been obtained up to the 
present time and called for preliminary drawing of the film. 
By reason of the fact that preliminary drawing of the polymer material has 
been dispensed with, the fabrication is appreciably simplified since it 
only comprises a shaping operation without drawing followed by an 
electrical polarization operation. 
In the most simple case, it is possible to start from a solution of 
PVF.sub.2 in a solvent such as dimethylformamide. By coating the surface 
of a mold with a layer of this solution and by evaporating the solvent at 
a temperature below 80.degree. C., a film of PVF.sub.2 in polar phase I is 
obtained. This film is then coated with electrodes on both faces. A high 
voltage is applied between the two electrodes in order to cause dipolar 
orientation in the direction of the normal to the faces. Since the 
PVF.sub.2 is in the polar phase I, there is no need whatsoever for any 
drawing operation in order to ensure that electrical polarization is 
readily established. Another mode of operation consists in shaping the 
PVF.sub.2 by means of a hot molding operation. When the PVF.sub.2 
solidifies from the molten state, the non-polar phase II is obtained. In 
this state of crystallization which corresponds to the crystallographic 
class 2/m, the material does not have a dipole moment .mu. (see the chain 
structure (a) of FIG. 2). However, it has been shown by experience that, 
on condition that an intense electric field of the order of 1 MV/cm or 
more is applied, there accordingly takes place a conversion from phase II 
to a polar phase which can be designated as a "pseudo I phase". This 
conversion takes place when electrical polarization of the molten polymer 
is carried out at room temperature or at a higher temperature. In order to 
produce a phase conversion, it is therefore possible to dispense with the 
drawing operation which had hitherto been considered necessary for 
electrical polarization of the molten PVF.sub.2. The fact that 
piezoelectric properties can be induced in the molten PVF.sub.2 solely 
under the action of a very intense electric field assumes considerable 
practical importance. 
An improvement can be made in this technique by fabricating the shaped 
element from a copolymer which associates molecular chains of 
polytetrafluoroethylene (PTFE) with the molecular chains of PVF.sub.2. In 
fact, this association in which the concentration of PTFE is within the 
range of a few % to approximately 30% gives rise to a polar phase having 
chains of the zigzagging type. This conversion can be understood by 
comparing the chains of PVF.sub.2 with those of PTFE which are illustrated 
respectively at (a) and (c) in FIG. 2. The molecular chain of PTFE does 
not have an electric dipole moment since fluorine atoms 15 have been 
substituted for all the hydrogen atoms 17 of the molecular chain of the 
polyethylene. Nevertheless, the molecular chain of PTFE is of the 
zigzagging type and can be linked to PVF.sub.2 chains. Linking has the 
effect of converting the helical chains of PVF.sub.2 to zigzagging chains 
which are similar to that shown at (b) in FIG. 2. By solidification from 
the molten state, the PVF.sub.2 -PTFE copolymer finally has a polar phase 
which is electrically polarized more readily than if PVF.sub.2 were the 
sole constituent. The use of the PVF.sub.2 -PTFE copolymer provides the 
advantage of substantially higher mechanical compliance than that obtained 
from PVF.sub.2 alone. The advantage of PTFE as linking agent lies in the 
fact that it has high oxidation resistance. 
Without departing from the field of the invention, other suitable 
copolymers may be mentioned. Starting from PVF or in other words polyvinyl 
fluoride, one of the copolymers PVF-PTFE and PVF-PVF.sub.2 can be employed 
as a base material. Another copolymer which is suitable for use is 
chlorinated polyethylene, the three constituents of which are polyethylene 
PE, polyvinyl chloride PVC and polyvinylidene chloride PVCl.sub.2. A polar 
material which is obtained from the molten state and is also worthy of 
mention is polychlorotrifluoroethylene PVClF.sub.3. 
In the case of materials which are polarizable in an electric field, PVC 
and PVF can be added to the PVF.sub.2 already mentioned and are 
essentially amorphous, whether they are obtained from the molten state or 
by evaporation of solvents such as cyclohexanone or dimethylformamide. 
The following table summarizes the properties of a few polymer and 
copolymer materials of interest for the preparation of piezoelectric 
elements. 
__________________________________________________________________________ 
copolymer 
copolymer 
Phase I 96% PVF.sub.2 
78% PVF.sub.2 
PVF.sub.2 4% PTFE 
22% PTFE 
PVF PVC Unit 
__________________________________________________________________________ 
s.sub.v 
4 .times. 10.sup.-9 
7 .times. 10.sup.-9 
5 .times. 10.sup.-9 
10.sup.-10 
10.sup.-10 
N.sup.-1 .multidot. m.sup.2 
p 3 to 6 .times.0 10.sup.-2 
2.2 .times. 10.sup.-2 
1.4 .times. 10.sup.-2 
1 to 2 .times. 10.sup.-2 
5 .times. 10.sup.-3 
C .multidot. m.sup.-2 
d 10 to 30 .times. 10.sup.-12 
7 .times. 10.sup.-12 
4 .times. 10.sup.-12 
1 to 5 .times. 10.sup.-12 
1 to 2 .times. 10.sup.-12 
C .multidot. N.sup.-1 
.alpha..sub.v 
1.5 .times. 10.sup.-4 
1.5 .times. 10.sup.-4 
1.5 .times. 10.sup.-4 
2 .times. 10.sup.-4 
2 .times. 10.sup.-4 
K.sup.-1 
p 1 to 3 .times. 10.sup.-5 
1 to 2 .times. 10.sup.-5 
1 to 2 .times. 10.sup.-5 
1 to 5 .times. 10.sup.-6 
1 to 2 .times. 10.sup.-6 
C .multidot. m.sup.-2 .multidot. 
K.sup.-1 
__________________________________________________________________________ 
The values indicated in the table are mean values of the quantities defined 
in the foregoing. The relations d=P.s.sub.v and p=P..alpha..sub.v lead 
only to values which are approximately equal to experimental values. 
Shaping of polymer materials can be carried out by all the methods employed 
in the plastics industry. 
In order to gain a clearer idea, it is possible by way of example to 
contemplate the manufacture of a loudspeaker diaphragm as shown in FIG. 6 
which is a view in isometric perspective. This diaphragm constitutes a 
complete electroacoustic transducer and comprises a sheet 35 of polymer to 
which a non-developable shape consisting of a bulge has been given. The 
shape of said bulge is obtained by making an equatorial cut in a toric 
surface. A flat annular flange forms the periphery of said bulge and its 
center is coplanar with the annular flange. In FIG. 6, the two principal 
faces of the diaphragm 35 are covered by electrodes 36 and 37 in order to 
form a capacitor. 
In order to construct a diaphragm having the shape illustrated in FIG. 6, 
one method which can be adopted by way of example consists in preparing a 
mold having two sections as shown in FIG. 5, which is a cross-sectional 
view taken in a meridian plane. Said mold is made up of two half-shells 
placed one above the other. The half-shell 31 is machined to form raised 
portions and the half-shell 32 is machined to form recessed portions so 
that, by fitting these two half-shells together, they delimit an internal 
space having the desired shape and thickness. An injection passage 33 
communicates with said internal space. By way of example, the passage 33 
is placed along the axis of revolution of the mold. By injecting molten 
polymer into the passage 33, the internal space can be completely filled 
and a molded diaphragm 35 can thus be obtained after solidification of the 
injected paste. 
By way of alternative, the hollow half-shell 32 can be employed alone and 
molding can be carried out by application of a preform of polymer in paste 
form. By means of an operation which consists in blowing hot air, the 
preform is caused to line the hollowed-out portion of the half-shell 32 
and solidifies in contact with the mold wall. 
It is also possible to adopt the compression molding technique. The 
powdered polymer is placed within a half-shell 32 which is heated to a 
value above the solidification temperature. The half-shell 31 then 
compresses the molten powder under a pressure of the order of 50 to 100 
kgs/cm.sup.2. The casting thus formed is then cooled under pressure. If 
only one of the half-shells 32 or 31 is employed, the castings can be 
obtained by projection of polymer powder onto the half-shell which is 
heated to a temperature above the solidification point. This coating 
operation can also be carried out by dipping in a concentrated solution of 
polymer. The coated half-shell is heated to a slight extent and placed 
within a vacuum enclosure or an air circulation chamber in order to permit 
rapid evaporation of the solvent. 
The thermoforming technique also comes within the scope of the invention on 
condition that the operation is carried out with a preform, said preform 
being heated to a temperature which rises above the solidification point; 
the two portions of the mold are then at a temperature below the 
solidification point. 
After completion of the molding operation, the diaphragm can be 
electrically polarized. To this end, said diaphragm must be coated with at 
least one conductive electrode. By way of example, a film of metal such as 
aluminum can be deposited in vacuo. It is also possible to adopt a 
non-electrolytic chemical deposition of metals such as copper, nickel and 
so forth. A silver paint can also be employed as a conductive coating. 
Finally, metallization can be obtained by means of the mold in the form of 
thin sheets pressed against the object during the molding stage. 
In FIG. 6, there can be seen the polarization technique with two electrodes 
formed on each side of the molded object 35. These electrodes 37 and 36 
are connected electrically to a voltage source 39. A protective resistor 
38 is provided in order to limit the current and to guard against any 
danger of breakdown. It is possible for example to employ a polarization 
voltage within the range of a few kV to 20 kV and a limiting resistor of 
10.sup.7 to 10.sup.9 ohms. The sample may or may not be heated during 
polarization. If it is heated, the heating technique can consist in 
immersing the sample in an oil having high dielectric strength such as 
those employed for the insulation of high-voltage transformers. 
Average conditions of polarization are as follows: 
polarizing electric field: 300 kV/cm to 2 MV/cm, 
polarization temperature: 60.degree. to 100.degree. C., 
duration of treatment: from a few seconds to a few tens of minutes. 
In FIG. 7, there is shown an installation for electrically polarizing a 
diaphragm 35 coated with a single electrode 44. This installation 
comprises a conductive bench 41. A conductive support 43 placed on the 
bench 42 serves as a seating for the diaphragm 35 and as a ground contact 
for the electrode 44. A column 46 supports and electrically connects a 
counter-electrode 45 to the cover 41. An electric generator 48 is 
connected to ground M and to the cover 41 by means of a protective 
resistor 49. A voltmeter 52 serves to measure the high voltage produced by 
the generator 48. Steps can be taken to ensure that the enclosure 53 is at 
atmospheric pressure, in which case polarization of the diaphragm 35 takes 
place by means of a corona discharge. It is also possible to reduce the 
pressure within the enclosure 53 by means of a vacuum pump 47. A neutral 
gas reservoir 50 fitted with a regulating valve 51 serves to obtain 
discharge conditions such as to permit formation of a plasma between the 
electrode 45 and the free surface of the diaphragm 35. 
When the polarization operation is completed, a conductive coating is 
deposited on the top face of the diaphragm 35 in order to form the final 
transducer element. 
By way of constructional example, a loudspeaker has been molded in 
accordance with the configuration shown in FIG. 6 with an annular flange 
having an external diameter of 110 millimeters and an internal diameter of 
75 millimeters; a flat central portion had a diameter of 25 millimeters 
and a projecting portion or bulge had a height of 7.5 millimeters. The 
molding operation was carried out by making use of the copolymer composed 
of 78% PVF.sub.2 -22% PTFE. 
An electroacoustic transducer of this type has been fabricated with a 
thickness of 300 microns and polarized at 75.degree. C. with an electric 
field of 300 kV/cm applied for a period of 15 minutes. 
By applying to this transducer a low-frequency alternating-current voltage 
of a few tens of volts, there has been obtained a characteristic curve 54 
of frequency response at a constant excitation voltage as illustrated in 
FIG. 8, where P.sub.a designates the acoustic pressure produced and f 
designates the frequency of the sound radiation emitted. 
The invention extends to all fields of application of piezoelectricity and 
pyroelectricity, in particular to electroacoustic devices, ultrasonic 
emitters and receivers employed in underwater acoustics, infrared sensors, 
ink-jet writing devices, devices for firing explosive charges, electric 
relays and electromechanical filters.