Abstract:
A method of making a print head ( 100 ) includes forming a body ( 110 ) having a closed base ( 120 ) and independent fluid containment compartments ( 220 ) formed about the closed base ( 120 ). A substantially planar piezoelectric transducer ( 80 ) comprising a slab ( 60 ) of piezoelectric material provides a means of enclosing each of the independent fluid containment compartments ( 220 ). Each of the independent compartments has operably associated therewith one of a plurality of first electrodes ( 20 ) arranged on a first surface ( 62 ) of the slab ( 60 ) of piezoelectric material and a portion of a second electrode ( 22 ) arranged on an opposite second surface ( 64 ). By applying a voltage to the first and second surface electrodes ( 20, 22 ) in a predetermined manner induces an electric field in a portion of the slab ( 60 ) of piezoelectric material and thereby forces fluid composition through the independent fluid containment compartment ( 220 ).

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is related to the following concurrently filed applications: (a) U.S. patent application Ser. No. 09/144,227 for “Ceramic Ink Jet Printing Element” by Dilip K. Chatterjee, Edward P. Furlani, and Syamal K. Ghosh; and (b) U.S. patent application Ser. No. 09/144,122 for “Dual Actuated Printing Element” by Dilip K. Chatterjee, Edward P. Furlani, and Syamal K. Ghosh; and, reference is made to commonly assigned U.S. patent application Ser. No. 09/071,485, filed May 1, 1998, entitled “Controlled Composition and Crystallographic Changes in Forming Functionally Gradient Piezoelectric Transducers” by Chatterjee et al; U.S. patent application Ser. No. 09/071,486, filed May 1, 1998, entitled “Functionally Gradient Piezoelectric Transducers” by Furlani et al; U.S. patent application Ser. No. 09/093,268, filed Jun. 8, 1998, entitled “Using Morphological Changes to Make Piezoelectric Transducers”, by Chatterjee et al; and U.S. patent application Ser. No. 09/120,995 filed Jul. 22, 1998, entitled “Piezoelectric Actuating Element For An Ink Jet Head And The Like”, by Furlani et al, the disclosures of which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to the field of printing and, more particularly, to a method of making a print head that utilizes a functionally gradient piezoelectric element. 
     BACKGROUND OF THE INVENTION 
     Piezoelectric ink jet elements are used in a wide range of microfluidic printing devices. Conventional ink jet elements utilize piezoelectric transducers that comprise one or more uniformly polarized piezoelectric elements with attached surface electrodes. The three most common transducer configurations are multilayer ceramic, monomorph or bimorphs, and flextensional composite transducers. To activate a transducer, a voltage is applied across its electrodes thereby creating an electric field throughout the piezoelectric elements. This field induces a change in the geometry of the piezoelectric elements resulting in elongation, contraction, shear or combinations thereof. The induced geometric distortion of the elements can be used to implement motion or perform work. In particular, piezoelectric bimorph transducers that produce a bending motion, are commonly used in micropumping devices. However, a drawback of the conventional piezoelectric bimorph transducer is that two bonded piezoelectric elements are needed to implement the bending. These bimorph transducers are typically difficult and costly to manufacture for micropumping applications (in this application, the word micro means that the dimensions of the element range from 100 microns to 10 mm). Also, when multiple bonded elements are used, stress induced in the elements due to their constrained motion can damage or fracture an element due to abrupt changes in material properties and strain at material interfaces. 
     Therefore, a need persists for an ink jet head that overcomes the aforementioned problems associated with conventional ink jet apparatus. 
     SUMMARY OF THE INVENTION 
     It is, therefore, an object of the present invention to provide a method of making a print head that utilizes a novel piezoelectric element. 
     It is another object of the invention to provide a method that utilizes a slab of piezoelectric material having a functionally gradient d-coefficient selected so that the material changes its geometry in response to an electric field in the slab. 
     Yet another object of the invention is to provide a method that enables any one of a plurality of independent fluid containment compartment to be activated for channeling fluid. 
     It is a feature of the invention that the method of making a print head includes the step of providing a plurality of independent fluid containment compartments each having a piezoelectric transducer having a functionally gradient d-coefficient for activating the flow of fluid therethrough. 
     To accomplish the several objects and advantages of the invention, there is provided a method of making a print head, comprising the steps of: 
     (a) forming a body having a closed base and a plurality of open independent fluid containment compartments formed about the base, each compartment having at least one inlet orifice and at least one outlet orifice; 
     (b) providing a substantially planar piezoelectric transducer comprising a slab of piezoelectric material having a first surface and an opposing second surface for enclosing said open independent fluid containment compartments, said piezoelectric material being provided having a functionally gradient d-coefficient selected so that said slab changes geometry in response to an applied voltage which produces an electric field in the slab; 
     (c) providing a plurality of first electrodes and a second electrode; 
     (d) arranging each one of said plurality of first electrodes on said first surface of said slab of piezoelectric material and said second electrodes on said second surface; 
     (e) arranging said piezoelectric transducer on said open independent fluid containment compartment such that each one of said plurality of first electrodes and a portion of said second electrode are operably associated with each one of said plurality of independent fluid containment compartments; 
     (f) providing a source of fluid composition in fluid communications with each one of said inlet orifices of each one of said independent fluid containment compartments; said source being arranged for channeling said fluid composition through an inlet orifice of said at least one of said plurality of independent fluid containment compartments; and, 
     (g) providing a source of power operably associated with each one of said first electrodes and said second electrode such that energizing any one of said plurality of first electrodes and said second electrode associated with any one of said independent fluid containment compartments enables said fluid composition to flow through said outlet orifice of one of said one independent fluid containment compartments. 
     An important advantage of the method of the present invention is that it provides for the utilization of a piezoelectric actuating element that comprises a single slab of piezoelectric material having a functionally gradient d-coefficient to implement droplet ejection, thereby eliminating the need for multilayered or composite piezoelectric structures. Moreover, a further advantage of the present method is that the slab of piezoelectric material provided for has a longer operational life span because it eliminates the stress induced fracturing that occurs in multilayered or composite piezoelectric transducers. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and objects, features and advantages of the present invention will become apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein: 
     FIG. 1 is a perspective view of the print head of the invention; 
     FIG. 2 is an exploded view of a portion of the print head of the invention; 
     FIG. 3 is a perspective view of a slab of piezoelectric material with a functionally gradient d 31  coefficient; 
     FIG. 4 is a plot of the piezoelectric d 31  coefficient across the width (T) of the slab of piezoelectric material of FIG. 3; 
     FIG. 5 is a plot of piezoelectric d 31  coefficient across the width (T) of a conventional piezoelectric bimorph transducer element, respectively; 
     FIG. 6 is a section view along line  6 — 6  of FIG. 3 illustrating the piezoelectric transducer before activation; 
     FIG. 7 is a section view taken along line  7 — 7  of FIG. 3 illustrating the piezoelectric transducer after activation; 
     FIG. 8 is a section view taken along line  8 — 8  of FIG. 3 illustrating the piezoelectric transducer after activation but under a opposite polarity compared to FIG. 7; 
     FIG. 9 is a perspective view of a single print element of the invention with a partial cut away section illustrating the internal fluid containment compartment; 
     FIGS. 10A,  10 B and  10 C are section views of a print element taken along line  10 A— 10 A,  10 B— 10 B,  10 C— 10 C, respectively, of FIG. 9 showing the print element in an unactivated, drop ejection, and ink refill state, respectively; and, 
     FIGS. 11A,  11 B and  11 C are section views of a print element taken along line  11 A— 11 A,  11 B— 11 B,  11 C— 11 C, respectively, of FIG. 9 showing the print element in an unactivated, drop ejection, and ink refill state, respectively. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Turning now to the drawings, and particularly to FIGS. 1,  2 , and  9 , the print head  100  of the present invention is illustrated. As depicted in FIGS. 1 and 2, print head  100  comprises a body  110 , a base  120 , and a piezoelectric actuating element  130 . The body  110  has a plurality of separate independent compartments, each defining a print element or head  100  (discussed further below), and each print head  100  having an inlet orifice  140  and outlet orifice  150 . Base  120  and piezoelectric actuating element  130  are fixedly attached to the body  110  in such a way so as to form a contiguous array of individual print elements  200  (see FIG.  9 ). 
     According to FIGS. 1 and 2, piezoelectric actuating element  130  comprises a slab  60  of piezoelectric material having opposed first and second surfaces  62  and  64 . A plurality of spaced first surface electrodes  20  is mounted on the first surface  62  of slab  60  of piezoelectric material. A second surface electrode  22  is mounted on opposed second surface  64  of slab  60  of piezoelectric material and extends substantially lengthwise along the second surface  64 . Each one of the plurality of first surface electrodes  20  is operably associated with one of the plurality of fluid containment compartments  220  (see FIG.  9 ). As illustrated in FIG. 1, power source  160 , with a plurality of first terminals  156 , connects to the plurality of first surface electrodes  20  via wires  162 . A second terminal  158  of power source  160  is electrically connected to the second surface electrode  22  via wire  164 . The power source  160  can impart a voltage of a specified polarity and magnitude to any one of the plurality of first surface electrodes  20 . Moreover, power source  160  may impart a predetermined voltage simultaneously to any number of the plurality of first surface electrodes  20  and a different voltage to the second surface electrodes  22  of piezoelectric actuating elements  130 . 
     Referring again to FIGS. 1 and 2, ink reservoir  170  is connected via fluid conduits  180  to inlet orifices  140  for supplying ink to the print head  100 . Print head  100  is adapted to receive ink from ink reservoir  170  which is in fluid communication with the inlet orifices  140 , and eject droplets of the ink onto a receiver (not shown) to form an image as will be described. 
     Body  110 , having a plurality of containment compartments  220 , of the printing element  100  can be manufactured by injection molding of plastics or ceramic composite materials, as described below. Advantages of having a body  110  made of such materials are that they are non-corrosive to the various ink compositions contained therein and they have sufficient flexural properties to squeeze ink out of the ink compartments with the aid of piezoelectric actuating element  130 . Those skilled in the art will appreciate that injection molding of plastics and ceramics to form intricate bodies is known in the art. Hence, during fabrication, inlet and outlet orifices  140 ,  150  of the body  110  can be formed either during the injection molding process or after the injection molding process by either mechanical drilling or laser assisted drilling. The base  120  of the body  110  can be made separately utilizing a plastic sheet and then attaching the base  120  to the body  110  utilizing an appropriate adhesive. Alternatively, base  120  and body  110  can be made together by an injection molding process. 
     Depicted in FIGS. 6-8, piezoelectric actuating element  130  is essentially a slab  60  of piezoelectric material having opposed first and second surfaces  62 ,  64 . Slab  60  is preferably made from ferroelectric materials such as PZT, PLZT, LiNbO 3 , LiTaO 3 , KNbO 3 , BaTiO 3  or from a mixture of these materials, most preferred being PZT (lead-zirconium-titanates). Skilled artisans will appreciate that the gradient in piezoelectric properties in these materials can be achieved either by varying the chemical composition of individual species, by changing the crystallographic nature of the piezoelectric phases, by modifying the morphological nature of the phases, or by combination of all the three procedures. The preferred direction of change in gradient of piezoelectric properties, particularly the d-coefficients in this present invention, is the thickness direction. The d-coefficients are constants of proportionality that relate the stresses induced in piezoelectric material to the electric field applied therein. The most preferred piezoelectric material for construction of print head  100  of the invention is PZT (lead-zirconium-titanates). These functionally gradient piezoelements are manufactured either by sequential dip coating, or by tape casting, or by cold pressing, or by injection molding, or by extrusion and subsequently sintering. 
     Referring again to FIG. 2, first and second surface electrodes  20 ,  22  are arranged on the first and second opposed surfaces  62 ,  64 , respectively, of the functionally gradient piezoelectric actuating element  130  in predetermined locations, preferably above the ink compartments. First and second surface electrodes  20 ,  22  may be affixed to their respective surfaces either by screen printing, or by chemical vapor deposition, or by physical vapor deposition of highly conducting elements such as gold, silver, palladium, or gold-palladium alloy. Preferably, after the first and second surface electrodes  20 ,  22  are affixed to the surfaces, piezoelectric actuating element  130  is then fixedly attached to the body  110  using some sort of adhesive material. 
     In a most preferred embodiment of this invention, the body  110  and the base  120  of the print head  100  can be made in conjunction by adopting injection molding of ceramic or ceramic composite materials such as tetragonal zirconia alloy or zirconia-alumina composites. These materials have sufficient toughness, corrosion resistance and wear and abrasion resistance (pigment particles in ink causes wear and abrasion in the ink compartment and outlet orifices) to be ideal candidates for print element  200 . In this embodiment, body  110  and the base  120  are made in the green ceramic form in one single step injection molding process using compounded zirconia alloy or compounded zirconia-alumina composites. The inlet and outlet orifices  140 ,  150  can be made in the body  110  either during the injection molding process or in a secondary step wherein a sacrificial member (not shown) is inserted at the desired locations of the green bodies. These sacrificial members (not shown) degenerates during the later sintering step. The piezoelectric actuating elements  130  are made by the methods described above. However, before sintering the green piezoelements, the electrodes are formed in desired locations of the elements adopting the methods described above. The next step in the manufacturing process is the alignment and positioning of the green ink jet body  110  with base  120  and the green piezoelectric actuating element  130  assemblage and sintering of the assemblage. During the sintering process, the electroded piezoelectric element and the body (with base) of the head bond together to form the print head  100 . The sacrificial elements (not shown), which were used to form the orifices degenerate during the sintering process forming the inlet and outlet orifices  140 ,  150 . 
     Referring to FIG. 3, a perspective view is shown of the slab  60  of piezoelectric material with a functionally gradient d 31  coefficient. As indicated, slab  60  of piezoelectric material has opposed first and second surfaces  62  and  64 . The width of the slab  60  of piezoelectric material is denoted by (T) and runs perpendicular to the first and second surfaces  62  and  64 , as shown in FIG.  3 . The length of slab  60  of piezoelectric material is denoted by (L) and runs parallel to the first and second surfaces  62  and  64 , as also shown in FIG.  3 . Slab  60  of piezoelectric material is poled perpendicularly to the first and second surfaces  62  and  64 , as indicated by polarization vector  70 . 
     Skilled artisans will appreciate that in conventional piezoelectric transducers the piezoelectric “d”-coefficients are constant throughout the slab  60  of piezoelectric material. Moreover, the magnitude of the induced sheer and strain are related to these “d”-coefficients via the constitutive relation as is well known. However, slab  60  of piezoelectric material used in the print head  100  of the invention is fabricated in a novel manner so that its piezoelectric properties vary in a prescribed fashion across its width as described below. The d 31  coefficient varies along a first direction perpendicular to the first surface  62  and the second surface  64 , and decreases from the first surface  62  to the second surface  64 , as shown in FIG.  4 . This is in contrast to the uniform or constant spatial dependency of the d 31  coefficient in conventional piezoelectric elements, illustrated in FIG.  5 . 
     In order to form the preferred slab  60  of piezoelectric material having a piezoelectric d 31  coefficient that varies in this fashion, the following method may be used. A piezoelectric block is coated with a first layer of piezoelectric material with a different composition than the block onto a surface of the block. Sequential coatings of one or more layers of piezoelectric material are then formed on the first layer and subsequent layers with different compositions of piezoelectric material. In this way, the piezoelectric element is formed which has a functionally gradient composition which varies along the width of the piezoelectric element, as shown in FIG.  4 . 
     Preferably, the piezoelectric materials used for forming the piezoelectric element is selected from the group consisting of PZT, PLZT, LiNbO 3 , LiTaO 3 , KNbO 3 , or BaTiO 3 . Most preferred in this group is PZT. For a more detailed description of the method, see commonly assigned U.S. Patent application Ser. No. 09/071,485, filed May 1, 1998, to Chatterjee et al; Ser. No. 09/071,486, filed May 1, 1998, to Furlani et al; and, Ser. No. 09/093,268, filed Jun, 8, 1998, to Chatterjee et al, hereby incorporated herein by reference. 
     Referring now to FIGS. 6-8, the piezoelectric transducer  80  is illustrated comprising slab  60  of piezoelectric material in the inactivated state, a first bending state and a second bending state, respectively. As previously mentioned, piezoelectric transducer  80  comprises a slab  60  of piezoelectric material with polarization vector  70 , and first and second surface electrodes  20  and  22  attached to first and second surfaces  62  and  64 , respectively. First and second surface electrodes  20  and  22  are connected to wires  24  and  26 , respectively. Wire  24  is connected to a switch  30  that, in turn, is connected to a first terminal of voltage source  40 . Wire  26  is connected to the second terminal of voltage source  40  as shown. 
     According to FIG. 6, the piezoelectric transducer  80  is shown with switch  30  open. Thus there is no voltage across the piezoelectric transducer  80  and it remains unactivated. 
     Referring now to FIG. 7, the piezoelectric transducer  80  is shown with switch  30  closed. In this case, the voltage (V) of voltage source  40  is impressed across the piezoelectric transducer  80  with the negative and positive terminals of the voltage source  40  electrically connected to the first and second surface electrodes  20  and  22 , respectively. Thus, the first surface electrode  20  is at a lower voltage than the second surface electrode  22 . This potential difference creates an electric field through the slab  60  of piezoelectric material causing it to contract in length parallel to its first and second surfaces  62  and  64 , respectively and perpendicular to polarization vector  70 . Specifically the change in length (in this case contraction) is given by S(z)=−(d 31 (z)V/T)×L as is well known. Since the functional dependence of the piezoelectric coefficient d 31 (z) increases with z as shown in FIG. 4, the lateral contraction S(z) of the slab  60  of piezoelectric material decreases in magnitude from the first surface  62  to the second surface  64 . Therefore, when the first surface electrode  20  is at a lower voltage than the second surface electrode  22 , the slab  60  of piezoelectric material distorts into a first bending state as shown. It is important to note that the piezoelectric transducer  80  requires only one slab  60  of piezoelectric material as compared to two or more elements for the prior art bimorph transducer (not shown). 
     According to FIG. 8, the piezoelectric transducer  80  is shown with switch  30  closed. In this case, the voltage V of voltage source  40  is impressed across the piezoelectric transducer  80  with positive and negative terminals of the voltage source  40  electrically connected to the first and second surface electrodes  20  and  22 , respectively. Thus, the first surface electrode  20  is at a higher voltage than the second surface electrode  22 . This potential difference creates an electric field through the slab  60  of piezoelectric material causing it to expand in length parallel to its first and second surfaces  62  and  64 , respectively and perpendicular to polarization vector  70 . Specifically, we define S(z) to be the change in length (in this case expansion) in the x (parallel or lateral) direction noting that this expansion varies as a function of z. The thickness of the piezoelectric actuating element  130  is given by T as shown in FIG. 6, and therefore S(z)=(d 31 (z) V/T)×L as is well known. The functional dependence of the piezoelectric coefficient d 31 (z) increases with z as shown in FIG.  4 . Thus, the lateral expansion S(z) of the slab  60  of piezoelectric material decreases in magnitude from the first surface  62  to the second surface  64 . Therefore, when the first surface electrode  20  is at a higher potential than the second surface electrode  22 , the slab  60  of piezoelectric material distorts into a second bending state as shown. 
     Referring again to FIG. 9, a perspective is shown of one of the contiguous array of print elements  200  of the invention. In this embodiment, the print element  200  comprises a body  110 , a base  120 , and a piezoelectric actuator  132 . The base  120  and piezoelectric actuator  132  are fixedly attached to the body  110  as shown, thereby forming a fluid containment compartment  220  that is shown in a partial cutaway view. As discussed previously, body  110  has an inlet orifice  140  (FIG. 2) and outlet orifice  150 . Piezoelectric actuator  132  is shown comprising slab  60  of piezoelectric material with opposed first and second surfaces  62  and  64 . As is understood, first surface electrode  20  is mounted on the first surface  62  of slab  60  of piezoelectric material and a second surface electrode  22  is mounted on the second surface  64  of slab  60  of piezoelectric material. Moreover, power source  240  is depicted having first and second terminals  250 ,  260  that are connected to the first and second surface electrodes  20  and  22 , respectively. An ink reservoir  170  is connected via fluid conduit  180  to inlet orifice  140  (FIG. 2) for supplying ink to the fluid containment compartment  220  of the print element  200 . A receiver  300  is positioned in front of the outlet orifice  150  for receiving ink drops  290  (as shown in FIGS. 11B and 11C) ejected from the print element  200  as will be described. 
     Referring now to FIGS. 10A,  10 B, and  10 C, and FIGS. 11A,  11 B, and  11 C, section views are shown of print element  200  taken along lines  10 A— 10 A,  10 B— 10 B,  10 C— 10 C, and  11 A— 11 A,  11 B— 11 B,  11 C— 11 C of FIG. 9, respectively. The ink in the fluid containment compartment  220  is indicated by the slanted lines  270 . FIGS. 10A and 11A show the print element  200  in an unactivated state. FIGS. 10B and 11B show the print element  200  during ink drop formation and ejection, and FIGS. 10C and 11C show the print element  200  during the ink refill stage. 
     According to FIGS. 10A and 11A, when the power source  240  is off, there is of course no voltage being applied to the first or second terminals  250  and  260 . Therefore, there exists no potential difference between the first and second surface electrodes  20  and  22  and the print element  200  is inactive. 
     According to FIGS. 10B and 11B, to pump a drop of ink  290  out of the fluid containment compartment  220  through the outlet orifice  150 , power source  240  provides a negative voltage to first terminal  250  and a positive voltage to second terminal  260 . Thus, the first surface electrode  20  is at a lower voltage than the second surface electrode  22 . This creates an electric field through the slab  60  of piezoelectric material causing it to contract in length parallel to the first and second surface electrodes  20  and  22 , as discussed above. Since the functional dependence of the piezoelectric coefficient d 31 (z) increases with (z) as shown in FIG. 4, the lateral contraction of the slab  60  of piezoelectric material decreases in magnitude from the first surface electrode  20  to the second surface electrode  22 , thereby causing the slab  60  of piezoelectric material to deform into a first bending state as shown in FIG.  7 . This, in turn, decreases the free volume of the fluid containment compartment  220  thereby increasing the pressure to such a level that a drop of ink  290  is ejected out through outlet orifice  150  and ultimately onto a receiver  300 . 
     With reference to FIGS. 10C and 11C, to draw ink into the fluid containment compartment  220  from the ink reservoir  170 , the power source  240  provides a positive voltage to first terminal  250  and a negative voltage to second terminal  260 . Thus, the first surface electrode  20  is at a higher voltage than the second surface electrode  22 . This potential difference creates an electric field through the slab  60  of piezoelectric material causing it to expand in length parallel to the first and second surface electrodes  20  and  22  as discussed above. Since the functional dependence of the piezoelectric coefficient d 31 (z) increases with (z) as shown in FIG. 4, the lateral expansion of the slab  60  of piezoelectric material decreases in magnitude from the first surface electrode  20  to the second surface electrode  22 , thereby causing the slab  60  of piezoelectric material to deform into a second bending state as shown in FIG.  8 . This, in turn, increases the free volume of the fluid containment compartment  220  thereby decreasing the pressure in the fluid containment compartment  220  so that it is less than in the ink reservoir  170 . Under this condition, ink flows from the ink reservoir  170  via the fluid conduit  180 , through the inlet orifice  140 , into the fluid containment compartment  220 . 
     The operation of the print head  100  can now be understood via reference to FIGS. 1,  2 ,  9 ,  10 A- 10 C, and  11 A- 11 C. To eject a drop of ink  290  out of one of the plurality of fluid containment compartments  220 , the power source  160  simultaneously imparts a voltage to the first surface electrode  20  that is operably associated with the respective fluid containment compartment  220 , and a different voltage to the second surface electrode  22  such that the respective first surface electrode  20  is at a lower voltage than the second surface electrode  22 . This creates an electric field through a portion of the slab  60  of piezoelectric material between the respective first surface electrode  20  and a portion of the second surface electrode  22 . As a result, slab  60  of piezoelectric material contracts in length parallel to the respective first surface electrode  20  and second surface electrode  22 , as discussed above. Since the functional dependence of the piezoelectric coefficient d 31 (z) increases with (z) as shown in FIG. 4, the lateral contraction of the portion of the slab  60  of piezoelectric material between the respective first surface electrode  20  and the second surface electrode  22  decreases in magnitude from the respective first surface electrode  20  to the second surface electrode  22 , thereby causing the portion of the slab  60  of piezoelectric material between the respective first surface electrode  20  and the second surface electrode  22  to deform into a first bending state as shown in FIG.  7 . This, in turn, decreases the free volume of the respective fluid containment compartment  220 . Simultaneously, the pressure of the ink in the respective fluid containment compartment  220  increases to such a level that a drop of ink  290  is ejected out through outlet orifice  150  of the respective fluid containment compartment  220 , and ultimately onto a receiver  300 . 
     Referring again to FIGS. 1 and 9, to initiate the flow of ink into one of the plurality of fluid containment compartments  220  of the print head  100  from ink reservoir  170 , power source  160  is activated to impart a voltage to one of the plurality of first surface electrodes  20  that is operably associated with a specified fluid containment compartment  220 . Simultaneously, a different voltage is imparted to the second surface electrode  22  by power source  160 , such that the respective first surface electrode  20  is at a higher voltage than the second surface electrode  22 . This creates an electric field through a portion of slab  60  of piezoelectric material between the first surface electrode  20  and a portion of the second surface electrode  22 . As a result of the electric field, slab  60  of piezoelectric material is caused to expand in length parallel to the respective first surface electrode  20  and second surface electrode  22 , as discussed above. Since the functional dependence of the piezoelectric coefficient d 31 (z) increases with (z) as shown in FIG. 4, the lateral expansion of the portion of the slab  60  of piezoelectric material between the respective first surface electrode  20  and the second surface electrode  22  increases in magnitude from the respective first surface electrode  20  to the second surface electrode  22 , thereby causing the portion of the slab  60  of piezoelectric material between the respective first surface electrode  20  and the second surface electrode  22  to deform into a second bending state as shown in FIG.  7 . This, in turn, increases the free volume of the respective fluid containment compartment  220  thereby decreasing the pressure in the respective fluid containment compartment  220  so that it is less than in the ink reservoir  170 . Under this condition, ink flows from the ink reservoir  170  via the fluid conduit  180 , through the inlet orifice  140 , into the respective fluid containment compartment  220 . 
     Therefore, the invention has been described with reference to a preferred embodiment. However, it will be appreciated that variations and modifications can be effected by a person of ordinary skill in the art without departing from the scope of the invention. 
     PARTS LIST 
       20  first surface electrode 
       22  second surface electrode 
       24  wire 
       26  wire 
       30  switch 
       40  voltage source 
       60  slab of piezoelectric material 
       62  first surface 
       64  second surface 
       70  polarization vector 
       80  piezoelectric transducer 
       100  print head 
       110  body 
       120  base 
       130  piezoelectric actuating element 
       132  piezoelectric actuator 
       140  inlet orifice 
       150  outlet orifice 
       156  first terminals 
       158  second terminal 
       160  power source 
       162  wires 
       164  wire 
       170  ink reservoir 
       180  fluid conduit 
       200  print element 
       220  fluid containment compartment 
       240  power source 
       250  first terminal 
       260  second terminal 
       270  slanted lines 
       290  drop or droplets of ink 
       300  receiver