Abstract:
A ternary polycrystalline material based on lead hafnate (PbHfO 3 ) and having improved dielectric, piezoelectric, and/or thermal stability properties. The Pb(Hf,Ti)O 3  based material can exhibit enhanced electromechanical coupling factors when compared to PZT based ceramics and can be used as high performance actuators, piezoelectric sensors and/or ultrasonic transducers. The ternary polycrystalline material can have a perovskite crystal structure with an ABO 3  formula and can be characterized by a substitution of heterovalent acceptor and donor ions at A or B (Zr/Hf) sites.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority of U.S. Provisional Application 61/581,365, filed Dec. 29, 2011, the contents of which are incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention is related to a piezoelectric material, and in particular, a high performance polycrystalline piezoelectric material based on lead hafnate. 
       BACKGROUND OF THE INVENTION 
       [0003]    For the past 60 years, perovskite Pb(Zr x Ti 1-x )O 3  (PZT) piezoelectric ceramics have dominated the commercial market of piezoelectric sensors, actuators and medical ultrasonic transducers due to their high dielectric, piezoelectric and electromechanical coupling factor properties. In addition, the properties of PZT piezoelectric ceramics can be further modified with different additives and/or dopants. In particular, PZT piezoelectric ceramics with compositions in the vicinity of a morphotropic phase boundary (MPB) that separates a rhombohedral phase from a tetragonal ferroelectric phase can exhibit anomalously high dielectric and piezoelectric properties. The high properties are the result of enhanced polarizability from the coupling between two equivalent energy states, i.e. between a tetragonal phase and a rhombohedral phase, which allows optimum domain reorientation during poling. 
         [0004]    Numerous PZT formulations/compositions have been engineered for specific characteristics that enhance their use in many applications. For example, Tables I and II list the properties of commercially available soft PZT ceramics, and  FIGS. 1 and 2  provide plots of dielectric permittivity and piezoelectric coefficient d 33  versus Curie temperature (T C ) for such materials. As shown by the data, polycrystalline materials with higher Curie temperatures generally possess lower dielectric and piezoelectric properties. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 Piezoelectric, dielectric and ferroelectric 
               
               
                 properties of commercial PZT5A type ceramics. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 P r   
                   
               
               
                   
                 d 33   
                 k p   
                   
                 tanδ 
                 T C   
                 (μC/ 
                 E C   
               
               
                 PZT5H 
                 (pC/N) 
                 (%) 
                 ε r   
                 (%) 
                 (° C.) 
                 cm 2 ) 
                 (kV/cm) 
               
               
                   
               
               
                 TRS200HD 1   
                 400 
                 0.66 
                 2000 
                 1.8 
                 340 
                 / 
                 / 
               
               
                 3195STD 2   
                 350 
                 0.63 
                 1800 
                 1.8 
                 350 
                 39 
                 14.9 
               
               
                 3295HD 2   
                 390 
                 0.65 
                 1900 
                 1.8 
                 350 
                 39 
                 12.0 
               
               
                 PIC255 3   
                 400 
                 0.62 
                 1750 
                 2.0 
                 350 
                 / 
                 / 
               
               
                 PIC155 3   
                 360 
                 0.62 
                 1450 
                 2.0 
                 345 
                 / 
                 / 
               
               
                 PKI502 4   
                 425 
                 0.60 
                 2000 
                 1.5 
                 350 
                 / 
                 / 
               
               
                 PZ23 5   
                 328 
                 0.52 
                 1500 
                 1.3 
                 350 
                 / 
                 / 
               
               
                 PZ27 5   
                 425 
                 0.59 
                 1800 
                 1.7 
                 350 
                 / 
                 / 
               
               
                 PZT5A1 6   
                 410 
                 0.62 
                 1875 
                 2.0 
                 370 
                 / 
                 / 
               
               
                 PZT5A3 6   
                 374 
                 0.60 
                 1700 
                 2.0 
                 365 
                 / 
                 / 
               
               
                   
               
               
                   1 TRS Technologies; 
               
               
                   2 CTS; 
               
               
                   3 PIceramic; 
               
               
                   4 Piezo-kinetics; 
               
               
                   5 Ferroperm; 
               
               
                   6 Morgan. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 Piezoelectric, dielectric and ferroelectric 
               
               
                 properties of commercial PZT5H type ceramics. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 P r   
                   
               
               
                   
                 d 33   
                 k p   
                   
                 tanδ 
                 T C   
                 (μC/ 
                 E C   
               
               
                 PZT5H 
                 (pC/N) 
                 (%) 
                 ε r   
                 (%) 
                 (° C.) 
                 cm 2 ) 
                 (kV/cm) 
               
               
                   
               
               
                 TRS610HD 1   
                 690 
                 0.70 
                 3900 
                 1.8 
                 210 
                 / 
                 / 
               
               
                 CTS3203STD 2   
                 550 
                 0.69 
                 3250 
                 2.0 
                 235 
                 37 
                 10.6 
               
               
                 CTS3203HD 2   
                 650 
                 0.70 
                 3800 
                 2.0 
                 225 
                 39 
                  8.0 
               
               
                 PIC151 3   
                 500 
                 0.62 
                 2400 
                 2.0 
                 250 
                 / 
                 / 
               
               
                 PIC153 3   
                 600 
                 0.62 
                 4200 
                 3.0 
                 185 
                 / 
                 / 
               
               
                 PKI532 4   
                 490 
                 0.63 
                 2700 
                 2.0 
                 220 
                 / 
                 / 
               
               
                 PKI552 4   
                 600 
                 0.67 
                 3400 
                 2.2 
                 200 
                 / 
                 / 
               
               
                 PZ21 5   
                 640 
                 0.60 
                 3980 
                 1.6 
                 218 
                 / 
                 / 
               
               
                 PZ29 5   
                 570 
                 0.64 
                 2870 
                 1.6 
                 235 
                 / 
                 / 
               
               
                 PZT5H1 6   
                 620 
                 0.60 
                 3400 
                 1.8 
                 200 
                 / 
                 / 
               
               
                 PZT5H2 6   
                 590 
                 0.65 
                 3400 
                 2.5 
                 195 
                 / 
                 / 
               
               
                   
               
               
                   1 TRS Technologies; 
               
               
                   2 CTS; 
               
               
                   3 PIceramic; 
               
               
                   4 Piezo-kinetics; 
               
               
                   5 Ferroperm; 
               
               
                   6 Morgan. 
               
             
          
         
       
     
         [0005]    It is appreciated that innovations in electronic devices have been the driving force for new developments in piezoelectric ceramics. In fact, and in order to meet the newly developed electromechanical devices, materials with Curie temperatures equivalent to heretofore developed materials but with higher dielectric and piezoelectric properties, and/or materials with similar dielectric and piezoelectric properties but higher Curie temperatures, are desired. 
         [0006]    In addition to the above, the electromechanical coupling factor—the square of which is closely related to output power density—is known to be an important material parameter in ultrasonic transducer applications and the dielectric variation for prior art PZT based materials is relatively broad and on the order of 2000-8000 ppm/° C. Therefore, a new polycrystalline piezoelectric material with increased electromechanical coupling factor and reduced dielectric variation would also be desirable. 
       SUMMARY OF THE INVENTION 
       [0007]    Ternary polycrystalline materials based on lead hafnate (PbHfO 3 ) and having improved dielectric, piezoelectric, and/or thermal stability properties are provided. In addition, the PbHfO 3  based materials can exhibit enhanced electromechanical coupling factors when compared to PZT based ceramics. The inventive materials can be used as high performance actuators, piezoelectric sensors and/or ultrasonic transducers. 
         [0008]    In particular, the ternary polycrystalline materials provide piezoelectric ceramic materials based on lead hafnium titanate, e.g. PbHfO 3 —PbTiO 3  (PHT), that have a perovskite crystal structure with an ABO 3  formula and are characterized by a substitution of heterovalent acceptor and donor ions at Zr/Hf sites. In addition, Pb(M I   3+ ,M II   5+ )O 3 —PHT ternary systems are provided that have: (1) equivalent Curie temperatures as prior art PZT based ceramics but exhibit higher dielectric and piezoelectric properties when compared thereto; and/or (2) comparable dielectric and piezoelectric properties as prior art PZT based ceramics but exhibit higher Curie temperatures when compared thereto. 
         [0009]    In some instances, the ternary polycrystalline materials have a formula of Pb 1-x M x  [(M I ,M II )O 3 ] 1-y-z Hf z Ti y O 3 , where M is Ba 2+ , Ca 2+ , Sr 2+ , La 3+  and the like; M I  is Mg 2+ , Zn 2+ , Ni 3+ , Yb 3+ , Sc 3+ , In 3+  and the like; M II  is Nb 5+ , Ta 5+ , Sb 5+  and the like; x is greater than or equal to 0.0 and less than 0.2; y is greater than 0.3 and less than 0.7; and z is greater than 0.3 and less than 0.7. In other instances, the ternary piezoelectric polycrystalline material has a formula of Pb 1-x M x  [(M I   3+ ,M II   5+ )O 3 ] 1-y-z Hf z Ti y O 3 , where Hf  4+  or Ti 4+  ions are at least partially replaced with donor dopants or acceptor dopants. The donor dopants can be Nb 5+ , Ta 5+ , W 5+  and the like and the acceptor dopants can be Fe 2+,3+ , Co 2+,3+ , Mn 2+,3+  and the like. 
         [0010]    The inventive material can have a Curie temperature in the range of 180° C. to 280° C. and a piezoelectric coefficient d 33  greater than 600 pC/N, a Curie temperature of greater than 300° C. and a piezoelectric coefficient d 33  greater than 500 pC/N, a Curie temperature in the range of 260-300° C. and a piezoelectric coefficient d 33  in the range of 450-680 pC/N, and/or a Curie temperature greater than 120° C. and a piezoelectric coefficient d 33  greater than 800 pC/N. In addition, the material can have electromechanical coupling k 33  greater than or equal to 78-80%. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is a graphical plot illustrating dielectric permittivity as a function of Curie temperature for PZT piezoelectric ceramics; 
           [0012]      FIG. 2  is a graphical plot illustrating piezoelectric coefficient d 33  as a function of Curie temperature for PZT piezoelectric ceramics; 
           [0013]      FIG. 3  is a graphical plot illustrating Curie temperature versus amount of PMN for pellets having a composition formula of (1-x)Pb(Hf 1-y Ti y )O 3 -xPMN with various levels of lead titanate (PT); 
           [0014]      FIG. 4  is an isothermal map of Currie temperature (T C ) for (1-x)Pb(Hf 1-y Ti y )O 3 -xPMN; 
           [0015]      FIG. 5   a  is a graphical plot illustrating piezoelectric coefficient d 33  as a function of PMN content; 
           [0016]      FIG. 5   b  is a graphical plot illustrating planar electrochemical coupling k p  as a function of PMN content; 
           [0017]      FIG. 6  is a graphical plot with data from the inventive materials shown in Tables III-V superimposed on data shown in  FIG. 1 ; 
           [0018]      FIG. 7  is a graphical plot with data from the inventive materials shown in Tables III-V superimposed on data shown in  FIG. 2 ; and 
           [0019]      FIG. 8  is a graphical plot of electromechanical coupling factor squared (k 33   2 ) as a function of Currie temperature for prior art PZT based ceramics and the inventive PHT based ceramics disclosed herein. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0020]    Inventive lead hafnium titanate-lead magnesium niobate (PHT-PMN) ternary ceramics with compositions of (1-x)Pb(Hf 1-y Ti y )O 3 -xPb(Mg 1/3 Nb 2/3 )O 3  ((1-x)Pb(Hf 1-y Ti y )O 3 -xPMN, x=0˜0.5, y=0.515˜0.7) are provided. For example and for illustrative purposes only, an example of how typical PHT-PMN ternary ceramics according to one or more embodiments of the present invention were produced and associated properties are described below. 
         [0021]    The inventive materials were prepared using a two-step precursor method. Raw materials of MgCO 3  (99.9%, Alfa Aesar, Ward Hill, Mass.), Nb 2 O 5  (99.9%, Alfa Aesar), HfO 2  (99.9%, Alfa Aesar) and TiO 2  (99.9%, Ishihara, San Francisco, Calif.) were used to synthesize columbite precursors of MgNb 2 O 6  and Hf 0.45 Ti 0.55 O 2  at 1000° C. and 1200° C., respectively. Thereafter, Pb 3 O 4  (99%, Alfa Aesar) and the MgNb 2 O 6  and Hf 0.45 Ti 0.55 O 2  percursor powders were batched stoichiometrically by wet-milling in alcohol for 24 hours (h). Dried mixed powders of the Pb 3 O 4 , MgNb 2 O 6  and Hf 0.45 Ti 0.55 O 2  were then calcined at 800° C. for 4 h to produce synthesized powders which were subsequently vibratory milled in alcohol for 12 h. The synthesized powders were then granulated and pressed into pellets having a 12 mm diameter, followed by a binder burnout at 550° C. and sintering in a sealed crucible at 1250° C. In order to minimize PbO evaporation during sintering, PbZrO 3  was used as a lead (Pb) source in the sealed crucible. 
         [0022]    Sintered pellets were tested for temperature dependence of dielectric permittivity with  FIG. 3  illustrating Curie temperature (T C ) versus amount of PMN for pellets having a composition formula of (1-x)Pb(Hf 1-y Ti y )O 3 -xPMN with various levels of lead titanate (PT). As shown in the figure, increasing the PMN content resulted in a monotonic T C  decrease from 360-285° C., 340-270° C., 320-255° C., 328-243° C. and 234-186° C. for the different PT levels corresponding to y=0.515, 0.534, 0.555, 0.574 and 0.7, respectively. Furthermore, with increasing PMN content, the ternary solid solution exhibited more relaxor-like characteristics, showing broadened dielectric peaks and dispersive dielectric behavior with respect to frequency. 
         [0023]    Based on the above results, an isothermal map of Currie temperature (T C ) for (1-x)Pb(Hf 1 -y Ti y )O 3 -xPMN was developed and is shown in  FIG. 4 . It is appreciated that along the MPB line from the PH-PT side towards the PMN-PT side, T C  gradually decreases from 325° C. to 200° C. It is appreciated that this decrease in T C  could be due to an increase of PMN content in the sintered pellets that were tested. 
         [0024]    The dielectric, piezoelectric and electromechanical properties of all studied (1-x)Pb(Hf 1-y Ti y )O 3 -xPMN compositions are summarized in Table III. In addition, the piezoelectric coefficient d 33  and planar electromechanical coupling k p  as a function of PMN are shown in  FIGS. 5   a  and  5   b , respectively. As shown in the figures, optimum piezoelectric and electromechanical properties where exhibited for specific compositions and it is appreciated that the optimum properties could be due to enhanced polarizability arising from coupling between tetragonal and rhombohedral phases. In addition, the optimum piezoelectric and electromechanical properties were achieved for the composition 0.8Pb(Hf 0,445 Ti 0,555 )O 3 -0.2Pb(Mg 1/3 Nb 2/3 )O 3 , with dielectric permittivity ε r , piezoelectric coefficient d 33 , planar electromechanical coupling k p  and T C  being on the order of 2870, 680 pC/N, 70% and 276° C., respectively. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE III 
               
             
             
               
                   
               
               
                 Piezoelectric, dielectric and ferroelectric properties of (1 − 
               
               
                 x)Pb(Hf 1−y Ti y )O 3 - x PMN ternary ceramics. 
               
             
          
           
               
                   
                 d 33   
                 k p   
                   
                 tanδ 
                 T C   
                 P r   
                 E C   
               
               
                 (1 − x)Pb(Hf 1−y Ti y )O 3 - x PMN 
                 (pC/N) 
                 (%) 
                 ε r   
                 (%) 
                 (° C.) 
                 (μC/cm 2 ) 
                 (kV/cm) 
               
               
                   
               
             
          
           
               
                 y = 0.515 
                 x = 0 
                 210 
                 37 
                 1220 
                 1.1 
                 360 
                 13 
                 13.2 
               
               
                   
                 x = 0.05 
                 280 
                 41 
                 1560 
                 1.6 
                 333 
                 25 
                 11.9 
               
               
                   
                 x = 0.1 
                 430 
                 62 
                 1100 
                 2.1 
                 306 
                 37 
                 8.8 
               
               
                   
                 x = 0.15 
                 330 
                 58 
                 870 
                 2.4 
                 285 
                 39 
                 8.3 
               
               
                 y = 0.534 
                 x = 0.05 
                 190 
                 32 
                 1350 
                 1.4 
                 340 
                 18 
                 14.4 
               
               
                   
                 x = 0.1 
                 450 
                 58 
                 2030 
                 1.4 
                 312 
                 32 
                 15 
               
               
                   
                 x = 0.15 
                 600 
                 69 
                 2330 
                 1.9 
                 291 
                 40 
                 9.4 
               
               
                   
                 x = 0.2 
                 320 
                 59 
                 960 
                 2.2 
                 271 
                 36 
                 8.1 
               
               
                 y = 0.555 
                 x = 0.1 
                 360 
                 37 
                 1300 
                 1.4 
                 321 
                 23 
                 17.3 
               
               
                   
                 x = 0.15 
                 430 
                 57 
                 2120 
                 1.4 
                 296 
                 32 
                 15.2 
               
               
                   
                 x = 0.18 
                 580 
                 65 
                 2770 
                 1.5 
                 286 
                 37 
                 11.3 
               
               
                   
                 x = 0.19 
                 640 
                 68 
                 2810 
                 1.5 
                 278 
                 40 
                 10.3 
               
               
                   
                 x = 0.2 
                 680 
                 70 
                 2870 
                 1.7 
                 276 
                 40 
                 9.9 
               
               
                   
                 x = 0.21 
                 590 
                 69 
                 2040 
                 1.6 
                 271 
                 42 
                 9.3 
               
               
                   
                 x = 0.22 
                 490 
                 68 
                 1630 
                 1.8 
                 268 
                 40 
                 8.4 
               
               
                   
                 x = 0.25 
                 340 
                 60 
                 1020 
                 2.2 
                 255 
                 38 
                 7.9 
               
               
                 y = 0.574 
                 x = 0.1 
                 160 
                 32 
                 1050 
                 1.3 
                 328 
                 22 
                 19.9 
               
               
                   
                 x = 0.15 
                 300 
                 49 
                 1550 
                 1.2 
                 304 
                 31 
                 19.4 
               
               
                   
                 x = 0.2 
                 440 
                 58 
                 2360 
                 1.4 
                 283 
                 34 
                 13.3 
               
               
                   
                 x = 0.24 
                 670 
                 69 
                 2960 
                 1.4 
                 263 
                 41 
                 9.5 
               
               
                   
                 x = 0.25 
                 640 
                 65 
                 2470 
                 1.6 
                 262 
                 38 
                 9.3 
               
               
                   
                 x = 0.26 
                 580 
                 65 
                 1900 
                 1.6 
                 / 
                 41 
                 8.6 
               
               
                   
                 x = 0.3 
                 230 
                 48 
                 1120 
                 2.2 
                 243 
                 28 
                 7.1 
               
               
                 y = 0.7 
                 x = 0.4 
                 330 
                 46 
                 2360 
                 0.8 
                 234 
                 26 
                 10.7 
               
               
                   
                 x = 0.45 
                 390 
                 54 
                 2050 
                 1.1 
                 213 
                 30 
                 7.3 
               
               
                   
                 x = 0.47 
                 540 
                 66 
                 2090 
                 1.3 
                 201 
                 37 
                 7 
               
               
                   
                 x = 0.5 
                 400 
                 60 
                 1420 
                 1.8 
                 186 
                 36 
                 5.9 
               
               
                   
               
             
          
         
       
     
         [0025]    The main properties of other systems, such as (1-x)Pb(Hf 1-y Ti y )O 3 -xPb(Ni 1/3 Nb 2/3 )O 3  (PHT-PNN), (1-x)Pb(Hf 1-y Ti y )O 3 -xPb(Sc 0.5 Nb 0.5 )O 3  (PHT-PSN) and (1-x)Pb(Hf 1-y Ti y )O 3 -xPb(Zn 1/3 Nb 2/3 )O 3  (PHT-PZN), are given in Tables IV and V below, respectively. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE IV 
               
             
             
               
                   
               
               
                 Piezoelectric, dielectric and ferroelectric properties of (1 − 
               
               
                 x)Pb(Hf 1−y Ti y )O 3 - x PNN ternary ceramics. 
               
             
          
           
               
                   
                 d 33   
                 k p   
                   
                 loss 
                 T C   
                 Pr 
                 E c   
               
               
                 Samples 
                 (pC/N) 
                 (%) 
                 K 
                 (%) 
                 (° C.) 
                 (μC/cm 2 ) 
                 (kV/cm) 
               
               
                   
               
             
          
           
               
                 y = 0.55 
                 x = 
                 5 
                 160 
                 35 
                 1050 
                 1.0 
                 337 
                 10 
                 12 
               
               
                   
                   
                 10 
                 280 
                 43 
                 1400 
                 1.2 
                 310 
                 16 
                 12 
               
               
                   
                   
                 15 
                 340 
                 49 
                 1830 
                 1.8 
                 280 
                 24 
                 10.7 
               
               
                   
                   
                 18 
                 495 
                 61 
                 2140 
                 1.7 
                 260 
                 29 
                 8 
               
               
                   
                   
                 19 
                 470 
                 61 
                 1970 
                 1.6 
                 256 
                 28 
                 7.5 
               
               
                   
                   
                 20 
                 435 
                 61 
                 1870 
                 1.8 
                 250 
                 31 
                 7.5 
               
               
                   
                   
                 22 
                 380 
                 60 
                 1250 
                 1.7 
                 238 
                 34 
                 7.3 
               
               
                   
                   
                 25 
                 350 
                 60 
                 1180 
                 1.8 
                 222 
                 36 
                 7.2 
               
               
                 y = 0.57 
                 x = 
                 10 
                 170 
                   
                 1030 
                 1.1 
                 — 
               
               
                   
                   
                 15 
                 250 
                 39 
                 1280 
                 1.4 
                 292 
                 19 
                 13.7 
               
               
                   
                   
                 19 
                 350 
                 47 
                 1950 
                 1.5 
                 266 
                 21 
                 10.2 
               
               
                   
                   
                 20 
                 360 
                 49 
                 2000 
                 1.5 
                 257 
                 23 
                 10.2 
               
               
                   
                   
                 21 
                 420 
                 57 
                 2100 
                 1.55 
                 252 
                 27 
                 9.8 
               
               
                   
                   
                 22 
                 480 
                 57 
                 2600 
                 1.77 
                 246 
                 28 
                 9 
               
               
                   
                   
                 23 
                 550 
                 65 
                 2650 
                 1.8 
                 240 
                 32 
                 8.8 
               
               
                   
                   
                 25 
                 595 
                 66 
                 2200 
                 1.66 
                 229 
                 34 
                 7.6 
               
               
                   
                   
                 20 
                 320 
                 50 
                 2000 
                 1.2 
                 260 
                 24 
                 11.5 
               
               
                   
                   
                 22 
                 410 
                 54 
                 2390 
                 1.3 
                 250 
                 28 
                 10.1 
               
               
                   
                   
                 23 
                 460 
                 57 
                 2600 
                 1.38 
                 244 
                 29 
                 9.8 
               
               
                   
                   
                 24 
                 530 
                 61 
                 2850 
                 1.4 
                 235 
                 31 
                 9.4 
               
               
                   
                   
                 25 
                 610 
                 65 
                 3000 
                 1.5 
                 234 
                 33 
                 8.6 
               
               
                   
                   
                 26 
                 650 
                 68 
                 2950 
                 1.6 
                 227 
                 35 
                 8.5 
               
               
                   
                   
                 26.5 
                 630 
                 67 
                 2430 
                 1.5 
                 225 
                 35 
                 8.4 
               
               
                   
                   
                 27 
                 660 
                 68 
                 2200 
                 1.35 
                 221 
                 37 
                 7.5 
               
               
                   
                   
                 28 
                 530 
                 65 
                 2270 
                 1.5 
                 215 
                 36 
                 7 
               
               
                   
                   
                 30 
                 460 
                 64 
                 2000 
                 1.7 
                 204 
                 36 
                 6.4 
               
               
                 y = 0.60 
                 x = 
                 25 
                 570 
                 63 
                 3200 
                 1.46 
                 225 
                 29 
                 9.5 
               
               
                   
                   
                 28 
                 650 
                 67 
                 3450 
                 1.5 
                 220 
                 31 
                 9 
               
               
                   
                   
                 29 
                 700 
                 69 
                 3610 
                 1.7 
                 214 
                 32 
                 8.3 
               
               
                   
                   
                 30 
                 765 
                 70 
                 3800 
                 2.0 
                 210 
                 32 
                 7.4 
               
               
                   
                   
                 30.5 
                 795 
                 71 
                 3600 
                 2.0 
                 206 
                 33 
                 7.2 
               
               
                   
                   
                 31 
                 760 
                 71 
                 3250 
                 2.0 
                 203 
                 34 
                 7.2 
               
               
                   
                   
                 31.5 
                 730 
                 71 
                 2940 
                 1.8 
                 — 
                 35 
                 6.9 
               
               
                   
                   
                 32 
                 690 
                 70 
                 2880 
                 1.75 
                 199 
                 34 
                 6.6 
               
               
                   
                   
                 33 
                 640 
                 68 
                 2350 
                 1.75 
                 191 
                 34 
                 6.2 
               
               
                 y = 0.70 
                 x = 
                 30 
                 300 
                 47 
                 1900 
                 1.4 
                 208 
                 25 
                 12.5 
               
               
                   
                   
                 40 
                 445 
                 51 
                 2700 
                 1.3 
                 184 
                 26 
                 9 
               
               
                   
                   
                 42 
                 540 
                 55 
                 3600 
                 1.65 
                 168 
                 26 
                 6 
               
               
                   
                   
                 44 
                 650 
                 58 
                 4500 
                 1.85 
                 155 
                 26 
                 6.7 
               
               
                   
                   
                 45 
                 725 
                 60 
                 4950 
                 1.98 
                 151 
                 26 
                 6.5 
               
               
                   
                   
                 46 
                 800 
                 61 
                 5500 
                 1.8 
                 145 
                 27 
                 5.6 
               
               
                   
                   
                 47 
                 865 
                 63 
                 5830 
                 2.3 
                 138 
                 27 
                 5.1 
               
               
                   
                   
                 48 
                 940 
                 65 
                 5240 
                 2.4 
                 120 
                 27 
                 3.8 
               
               
                   
                   
                 49 
                 970 
                 65 
                 6000 
                 2.5 
                 — 
                 27 
                 4.2 
               
               
                   
                   
                 50 
                 930 
                 65 
                 5930 
                 2.38 
                 — 
                 27 
                 4.3 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE V 
               
             
             
               
                   
               
               
                 Piezoelectric, dielectric and ferroelectric properties 
               
               
                 of (1 − x)Pb(Hf 1−y Ti y )O 3 - x PSN and 
               
               
                 (1 − x)Pb(Hf 1−y Ti y )O 3 - x PZN ternary ceramics. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Pr 
                   
               
               
                 Materials 
                 d 33   
                 k p   
                   
                 loss 
                 T C   
                 (μC/ 
                 E c   
               
             
          
           
               
                 y 
                 x 
                 (pC/N) 
                 (%) 
                 K 
                 (%) 
                 (° C.) 
                 cm 2 ) 
                 (kV/cm) 
               
               
                   
               
             
          
           
               
                   
                 (1 − x)Pb(Hf 1−y Ti y )O 3 - x PSN 
               
             
          
           
               
                 0.60 
                 0.20 
                 550 
                 65 
                 2420 
                 1.5 
                 325 
                 38 
                 10.6 
               
               
                 0.575 
                 0.175 
                 600 
                 71 
                 2220 
                 1.6 
                 325 
                 43 
                 9.4 
               
               
                 0.55 
                 0.12 
                 590 
                 70 
                 2250 
                 1.6 
                 334 
                 43 
                 9.5 
               
               
                 0.55 
                 0.125 
                 560 
                 67 
                 1950 
                 1.7 
                 330 
                 41 
                 9.2 
               
             
          
           
               
                   
                 (1 − x)Pb(Hf 1−y Ti y )O 3 - x PZN 
               
             
          
           
               
                 0.519 
                 0.20 
                 500 
                 70 
                 1650 
                 2.0 
                 292 
                 42 
                 9.1 
               
               
                 0.525 
                 0.20 
                 530 
                 69 
                 2060 
                 2.0 
                 295 
                 41 
                 10.3 
               
               
                 0.525 
                 0.25 
                 510 
                 68 
                 1900 
                 2.0 
                 280 
                 41 
                 9.9 
               
               
                 0.539 
                 0.225 
                 570 
                 68 
                 2300 
                 2.0 
                 292 
                 38 
                 11.6 
               
               
                   
               
             
          
         
       
     
         [0026]    In order to provide a clearer view of the enhanced properties exhibited by the inventive materials,  FIGS. 6 and 7  are plots of data from Tables III-V above compared to the data shown in  FIGS. 1 and 2 . The data from Tables III-V are labeled as PHT based ceramics, versus the data from  FIGS. 1 and 2  which are labeled as PZT based ceramics. As shown in the figures, a comparable dielectric permittivity with significant higher d 33  coefficient is exhibited by the inventive materials compared to heretofore polycrystalline piezoelectric materials. In addition,  FIG. 8  provides a plot of the electromechanical coupling factor squared (k 33   2 ) as a function of T C  for prior art PZT based ceramics and the inventive PHT based ceramics. Again, a significant improvement in output power density is expected by the ternary PHT polycrystalline piezoelectric materials disclosed herein. 
         [0027]    The invention is not restricted to the illustrative examples and embodiments described above. The examples are not intended as limitations on the scope of the invention. Methods, apparatus, compositions, and the like described herein are exemplary and not intended as limitations on the scope of the invention. Changes therein and others will occur to those skilled in the art and, as such, the specification and the appendices should be interpreted broadly.