Abstract:
The present invention includes the following three types of piezoelectric porcelains. (1) In a piezoelectric porcelain having a composition of aPb[Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , the coefficients a, b and c (mol %) and the substitution rate X satisfy all the following conditions; 15≦a≦45, 32≦b≦45, 10≦c≦50 and 0.1≦X≦0.9. (2) In a piezoelectric porcelain having a composition of aPb[Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , the coefficients a, b and c (mol %) and the substitution rates X and Y satisfy all the following conditions; 15≦a≦45, 32≦b≦45, 10≦c≦50, 0.1≦X≦0.9, 0.1≦Y≦0.9 and Y-X≧0.05. (3) In a piezoelectric porcelain having a composition of aPb[Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , the coefficients a, b and c (mol %) and the substitution rates X and Y satisfy all the following conditions; 15≦a≦45, 32≦b≦45, 10≦c≦50, 0.2≦X≦0.9, 0.2≦Y≦0.9 and X-Y≧0.05.

Description:
BACKGROUND OF THE INVENTION 
     (1) Field of the Invention 
     The present invention relates to piezoelectric porcelains suitably for a member of a piezoelectric actuator, a piezoelectric buzzer and so on which utilize piezoelectric distortion. 
     (2) Related Art Statement 
     Lead zirconate titanate has a large piezoelectric distortion and can be used at a high temperature. Moreover, if a part of zirconate or titanate is substituted by the other elements, various kinds of properties can be obtained. Particularly, piezoelectric porcelains of three component series having composition of PbTiO 3  -PbZrO 3  -Pb(Mg 1/3  Nb 2/3 )O 3 , in which a part of zirconate or titanate is substituted by magnesium and niobium, has a relatively large piezoelectric constant d 31 . 
     Recently, in fields of precision machines, an optical instruments and so on, precise position control is needed. To this end, a piezoelectric element utilizing a piezoelectric distortion has been developed. As for such elements, a piezoelectric porcelain having a high piezoelectric constant d 31  is desired so as to make a distortion amount of the element larger. However, from the point of view mentioned above, a piezoelectric constant d 31  of the piezoelectric porcelain of three component series having a composition of PbTiO 3  -PbZrO 3  -Pb(Mg 1/3  Nb 2/3 )O 3  mentioned above is -225 pm/V and thus it is not sufficient for this purpose. 
     Further, in Japanese Patent Laid-Open Publication No. 3-40964, it is disclosed that an excellent property such as a piezoelectric constant d 31  =-307.9 pm/V can be realized in a piezoelectric porcelain of three component series having a composition of Pb(Mg 1/3  Nb 2/3 ) 0 .225 (Ni 1/3  Ta 2/3 ) 0 .15 Ti 0 .375 Zr 0 .25 O 3 . 
     However, in the piezoelectric porcelain having the composition disclosed in Japanese Patent Laid-Open Publication No. 3-40964, a Curie point is 177° C. which is very low. If the Curie point of the piezoelectric porcelain is low in a piezoelectric element, a limit of temperature, to which the piezoelectric porcelain is driven, becomes low. That is to say, if a Curie point of the piezoelectric porcelain is low, the following disadvantages occur. 
     Generally, since a piezoelectric porcelain after firing shows no piezoelectricity, it is necessary to perform a poling thereto under applying a DC voltage. However, if the piezoelectric porcelain after the poling mentioned above is once used at a temperature above a Curie point, the piezoelectric porcelain shows no piezoelectricity again. Therefore, it is necessary to perform a poling again for the piezoelectric porcelain. In this manner, the piezoelectric porcelain having a composition of Pb(Mg 1/3  Nb 2/3 )O 3  -Pb(Ni 1/3  Ta 2/3 )O 3  -PbTiO 3  -PbZrO 3  has a high piezoelectric property, but the use of the piezoelectric porcelain mentioned above is limited to low temperatures. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to eliminate the drawbacks mentioned above, and to provide a piezoelectric porcelain of three component series in which a piezoelectric constant d 31  is improved. 
     According to a first aspect of the invention, piezoelectric porcelains have a composition of aPb[Mg 1/3  (Nb 1-X  Ta X ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , coefficients a, b and c being mol % and a+b+c=100, wherein said coefficients a, b and c and a value X satisfy following conditions (1)˜(4); 
     
         15≦a≦45                                      (1) 
    
     
         32≦b≦45                                      (2) 
    
     
         10≦c≦50                                      (3) 
    
     
         0.1≦X≦0.9                                    (4). 
    
     Another object of the invention is to eliminate the drawbacks mentioned above, and to provide a piezoelectric porcelain in which a piezoelectric constant d 31  is improved and also a high Curie point can be maintained. 
     According to a second aspect of the invention, piezoelectric porcelains have a composition of aPb[(Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , coefficients a, b and c being mol % and a+b+c=100, wherein said coefficients a, b and c and a value X satisfy following conditions (21)˜(26); 
     
         15≦a≦45                                      (21) 
    
     
         32≦b≦45                                      (22) 
    
     
         10≦c≦50                                      (23) 
    
     
         0.1≦X≦0.9                                    (24) 
    
     
         0.1≦Y≦0.9                                    (25) 
    
     
         Y-X≧0.05                                            (26). 
    
     According to a third aspect of the invention, piezoelectric porcelains have a composition of aPb[(Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , coefficients a, b and c being mol % and a+b+c=100, wherein said coefficients a, b and c and a value X satisfy following conditions (41)˜(46); 
     
         15≦a≦45                                      (41) 
    
     
         32≦b≦45                                      (42) 
    
     
         10≦c≦50                                      (43) 
    
     
         0.2≦X≦0.9                                    (44) 
    
     
         0.2≦Y≦0.9                                    (45) 
    
     
         X-Y≧0.05                                            (46). 
    
     In the first aspect of the invention, the present inventors find that, in a piezoelectric porcelain having a composition of PbTiO 3  -PbZrO 3  -Pb(Mg 1/3  Nb 2/3 )O 3 , a relative dielectric constant of the piezoelectric porcelain is improved and a piezoelectric constant d 31  of the piezoelectric porcelain is improved extra-ordinarily by substituting a part of niobium by tantalum. 
     In this case, if a substitution rate X of tantalum with respect to niobium is not larger than 0.1, an effect of tantalum substitution does not appear so much. Moreover, if a value X is not smaller than 0.9, a Curie point of the piezoelectric porcelain decreases. 
     Further, if the value X is increased, a piezoelectric constant d 31  of the piezoelectric porcelain is improved gradually. Particularly, if the value X is larger than 0.3, it is effective for an improvement of the piezoelectric constant d 31 . Moreover, it is confirmed that, if the value X is smaller than 0.8, a Curie point of the piezoelectric porcelain becomes higher gradually. On this case, it is preferred that the coefficients a, b and c and the value X satisfy the following in equations (5)˜(8); 
     
         25≦a≦43                                      (5) 
    
     
         35≦b≦43                                      (6) 
    
     
         14≦c≦40                                      (7) 
    
     
         0.3≦X≦0.8                                    (8). 
    
     Furthermore, from the view point mentioned above, it is further effective if the value X is larger than 0.4, and a piezoelectric constant d 31  is most improved if the value X is near 0.6. However, if the value X is not larger than 0.7, a decrease of a Curie point becomes larger. Therefore, in this case, it is further preferred that the coefficients a, b and c and the value X satisfy the following conditions (9)˜(12); 
     
         30≦a≦42                                      (9) 
    
     
         37≦b≦40                                      (10) 
    
     
         18≦c≦33                                      (11) 
    
     
         0.4≦X≦0.6                                    (12). 
    
     Moreover, if up to 10 atomic % of Pb is substituted by one or more metal elements selected from a group of strontium, calcium and barium, it is possible to improve a piezoelectric constant d 31  more. If a substitution rate of the metal elements is larger than 3 atomic %, a piezoelectric constant d 31  is most improved. From this view point, it is further preferred if the substitution rate is larger than 4 atomic %. However, if the substitution rate is not smaller than 8 atomic %, a Curie point of a piezoelectric porcelain is decreased gradually. Therefore, it is preferred that the substitution rate is smaller than 8 atomic % and it is further preferred that the substitution rate is smaller than 7 atomic %. 
     In the second aspect of the invention, the present inventors find that, in a piezoelectric porcelain having a composition of Pb(Mg 1/3  Nb 2/3 )O 3  -Pb(Ni 1/3  Ta 2/3 )O 3  -PbTiO 3  -PbZrO 3 , both of a piezoelectric constant d 31  and a Curie point of the piezoelectric porcelain are improved by substituting a part of magnesium by nickel and by substituting a part of niobium by tantalum simultaneously. 
     In this case, if values X and Y satisfy Y-X≧0.05, a Curie point of the piezoelectric porcelain is improved, and also the piezoelectric porcelain having a particularly large piezoelectric constant d 31  can be obtained. 
     In this case, if the values X and Y become larger, a Curie point of the piezoelectric porcelain is decreased generally, and a piezoelectric constant d 31  thereof is improved. In addition, a piezoelectric constant d 31  becomes larger if the values X and Y are in a range of 0.3˜0.9, and it becomes even larger if the values X and Y are in a range of 0.4˜0.8. However, if the values X and Y are not smaller than 0.9, a Curie point is decreased abruptly. From the view point of a Curie point, it is preferred that the values X and Y are smaller than 0.8, and it is further preferred that the values of X and Y are smaller than 0.6. 
     Therefore, it is preferred that the coefficients a, b and c and the values X and Y satisfy the following in equations (27)˜(31); 
     
         25≦a≦43                                      (27) 
    
     
         35≦b≦43                                      (28) 
    
     
         14≦c≦40                                      (29) 
    
     
         0.3≦X≦0.8                                    (30) 
    
     
         0.3≦Y≦0.8                                    (31). 
    
     Moreover, it is further preferred that the coefficients a, b and c and the values X and Y satisfy the following in equations (32)˜(36); 
     
         30≦a≦42                                      (32) 
    
     
         37≦b≦40                                      (33) 
    
     
         18≦c≦33                                      (34) 
    
     
         0.4≦X≦0.6                                    (35) 
    
     
         0.4≦Y≦0.6                                    (36). 
    
     Further, it is necessary to set a difference between X and Y larger than 0.05. In this case, it is preferred to set the difference larger than 0.1 so as to increase a piezoelectric constant d 31 . Moreover, from the point of view of preventing a decrease of a Curie point, it is further preferred to set the difference smaller than 0.4. 
     Furthermore, if up to 10 atomic % of Pb is substituted by one or more elements selected from a group of strontium, calcium and barium, it is possible to improve a piezoelectric constant d 31  more. If a substitution rate of the metal elements is larger than 3 atomic %, a piezoelectric constant d 31  is most improved. From this point of view, it is further preferred if the substitution rate is larger than 4 atomic %. However, if the substitution rate is not smaller than 8 atomic %, a Curie point of a piezoelectric porcelain is decreased gradually. Therefore, it is preferred that the substitution rate is smaller than 8 atomic % and it is further preferred that the substitution rate is smaller than 7 atomic %. 
     In the third aspect of the invention, the present inventors find that, in a piezoelectric porcelain having a composition of Pb(Mg 1/3  Nb 2/3 )O 3  -Pb(Ni 1/3  Ta 2/3 )O 3  -pbTiO 3  -PbZrO 3 , both of a piezoelectric constant d 31  and a Curie point of the piezoelectric porcelain are improved by substituting a part of magnesium by nickel and by substituting a part of niobium by tantalum simultaneously. 
     In this case, if values X and Y satisfy X-Y≧0.05, a Curie point of the piezoelectric porcelain is improved, and also the piezoelectric porcelain having a particularly large piezoelectric constant d 31  can be obtained. 
     In this case, if the values X and Y become larger, a Curie point of the piezoelectric porcelain is decreased generally, and a piezoelectric constant d 31  thereof is improved. In addition, a piezoelectric constant d 31  becomes larger if the values X and Y are in a range of 0.3˜0.9, and it becomes even larger if the values X and Y are in a range of 0.4˜0.8. However, if the values X and Y are not smaller than 0.9, a Curie point is decreased abruptly. From the view point of a Curie point, it is preferred that the values X and Y are smaller than 0.8, and it is further preferred that the values of X and Y are smaller than 0.6. 
     Therefore, it is preferred that the coefficients a, b and c and the values X and Y satisfy the following conditions (47)˜(51); 
     
         25≦a≦43                                      (47) 
    
     
         35≦b≦43                                      (48) 
    
     
         14≦c≦40                                      (49) 
    
     
         0.3≦X≦0.8                                    (50) 
    
     
         0.3≦Y≦0.8                                    (51). 
    
     Moreover, it is further preferred that the coefficients a, b and c and the values X and Y satisfy the following conditions (52)˜(56); 
     
         30≦a≦42                                      (52) 
    
     
         37≦b≦40                                      (53) 
    
     
         18≦c≦33                                      (54) 
    
     
         0.4≦X≦0.6                                    (55) 
    
     
         0.4≦Y≦0.6                                    (56). 
    
     Further, it is necessary to set a difference between X and Y larger than 0.05. In this case, it is preferred to set the difference larger than 0.1 so as to increase a piezoelectric constant d 31 . Moreover, from the point of view of preventing a decrease of a Curie point, it is further preferred to set the difference smaller than 0.4. 
     Furthermore, if up to 10 atomic % of Pb is substituted by one or more elements selected from a group of strontium, calcium and barium, it is possible to improve a piezoelectric constant d 31  more. If a substitution rate of the metal elements is larger than 3 atomic %, a piezoelectric constant d 31  is most improved. From this point of view, it is further preferred if the substitution rate is larger than 4 atomic %. However, if the substitution rate is not smaller than 8 atomic %, a Curie point of a piezoelectric porcelain is decreased gradually. Therefore, it is preferred that the substitution rate is smaller than 8 atomic % and it is further preferred that the substitution rate is smaller than 7 atomic %. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graph showing a relation between a substitution rate X of tantalum with respect to niobium and a piezoelectric constant d 31  and a Curie point of a piezoelectric porcelain according to a first aspect of the invention in a piezoelectric porcelain of three component series having a composition of PbTiO 3  -PbZrO 3  -Pb(Mg 1/3  Nb 2/3 )O 3  ; 
     FIG. 2 is a graph illustrating a relation between a substitution rate Y and a piezoelectric constant d 31  and a Curie point of a piezoelectric porcelain according to a second aspect of the invention under such a condition that coefficients a, b and c are set in a range within the scope of the second aspect of the invention and also a substitution rate Y is varied from 0.0 to 1.0 while a substitute rate X is constant at 0.1; 
     FIG. 3 is a graph depicting a relation between a substitution rate X and a piezoelectric constant d 31  and a Curie point of a piezoelectric porcelain according to a third aspect of the invention under such a condition that coefficients a, b and c are set in a range within the scope of the third aspect of the invention and a substitution rate X is varied from 0.5 to 1.0 while a substitution rate Y is constant at 0.4; and 
     FIG. 4 is a graph showing a relation between the substitution X and a piezoelectric constant d 31  and a Curie point of the piezoelectric porcelain according to the third aspect of the invention under such a condition that the coefficients a, b and c are set in a range within the scope of the third aspect of the invention and the substitution rate X is varied from 0.2 to 1.0 while a substitution rate Y is constant at 0.2. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A method of producing piezoelectric porcelains according to the invention is not limited particularly. However, the following producing method is preferred. At first, raw materials of metal compound, preferably oxides, hydroxides or carbonates of metal elements are mixed in a ball mill or the like to obtain mixed powders having a composition within the scope of the invention. Then, the thus obtained mixed powders are calcined in the atmosphere at a temperature of 900° C.˜1100° C. to obtain a calcined body. The calcined body is crushed in the ball mill or the like and the crushed powders are pressed to obtain a formed body. Then, the thus obtained formed body is sintered at a temperature of 1200° C.˜1300° C. to obtain a sintered body. The thus obtained sintered body is worked to obtain a specimen having a predetermined dimension and a predetermined shape. Finally, electrodes are arranged on the specimen and the specimen with the electrodes is subjected to a poling for a piezoelectric porcelain. Of course, other producing methods can be applied freely in the present invention. 
     Hereinafter, experiments according to a first aspect of the invention will be explained. 
     EXPERIMENT 1 
     Raw material powders of PbO, MgO, Nb 2  O 5 , Ta 2  O 5 , TiO 2 , ZrO 2  were mixed in a ball mill for 24 hours to obtain mixed powders having compositions shown in a Table 1. The thus obtained mixed powders were calcined in the atmosphere at 1000° C. for 2 hours to obtain a calcined body. The thus obtained calcined body was crushed in the ball mill for 48 hours to obtain crushed powders. Then, the crushed powders were formed under a pressure of about 400 kg/cm 2  by means of a press machine to obtain a formed body having a diameter of 20 mm and a thickness of 5 mm. The thus obtained formed body was sintered at a temperature of 1200° C.˜1300° C. for 2 hours to obtain a sintered body. 
     The thus obtained sintered body was worked to obtain a plate-like specimen having dimensions of 12 mm (length)×3 mm (width)×1 mm (thickness). Then, silver electrodes were arranged on the planes of the specimen, and the specimen with the silver electrodes was subjected to a poling in such a manner that a DC voltage of 2 kV/mm was applied to the specimen in a silicone oil having a temperature of 80° C. With respect to the respective specimens after a poling, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 1 as well as coefficients a, b and c and a substitution rate X in a Pb[Mg 1/3  (Nb 1-X  Ta X ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , wherein the coefficients a, b and c were mol % and a sum of the coefficients a, b and c was 100. In sample Nos. 1˜17 in the Table 1, a substitution rate X of tantalum was varied while coefficients a, b and c were set in a range within the scope of the first aspect of the invention. 
     
                       TABLE 1______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________1     15     40     45   0   136     312   Comparative                                      example2     15     40     45   0.6 264     264   Present                                      invention3     15     35     50   0   107     284   Comparative                                      example4     15     35     50   0.6 240     236   Present                                      invention5     25     40     35   0   179     270   Comparative                                      example6     25     40     35   0.3 255     246   Present                                      invention7     25     40     35   0.7 293     214   Present                                      invention8     37.5   37.5   25   0   208     243   Comparative                                      example9     37.5   37.5   25   0.1 275     235   Present                                      invention10    37.5   37.5   25   0.4 336     211   Present                                      invention11    37.5   30     32.5 1.0 182     142   Comparative                                      example12    45     45     10   0   176     231   Comparative                                      example13    45     45     10   0.4 255     199   Present                                      invention14    45     32     23   0   194     213   Comparative                                      example15    45     32     23   0.3 250     189   Present                                      invention16    40     32     28   0   172     224   Comparative                                      example17    40     32     28   0.4 252     192   Present                                      invention______________________________________ 
    
     By comparing the differences between the sample Nos. 1 and 2, between the sample Nos. 3 and 4, between the sample No. 5 and the sample Nos. 6 and 7, between the sample No. 8 and the sample Nos. 9 and 10, between the sample Nos. 12 and 13, between the sample Nos. 14 and 15 and between the sample Nos. 16 and 17, it is understood that a piezoelectric constant d 31  is improved by substituting a part of niobium by tantalum. Moreover, as shown in the sample No. 11, if the substitution rate X was 1.0, it is understood that a piezoelectric constant d 31  is decreased and a Curie point is also decreased extraordinarily. 
     EXPERIMENT 2 
     In the same manner as experiment 1, specimens according to sample Nos. 18˜33 in a Table 2 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 2. 
     
                       TABLE 2______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________18    10     45     45   0.4 215     294   Comparative                                      example19    15     40     45   0.6 264     264   Present                                      invention20    15     35     50   0.6 240     236   Present                                      invention21    20     30     50   0.4 200     224   Comparative                                      example22    25     25     50   0.8 210     234   Comparative                                      example23    25     40     35   0.3 255     246   Present                                      invention24    25     40     35   0.7 293     214   Present                                      invention25    37.5   37.5   25   0.1 275     235   Present                                      invention26    27.5   37.5   25   0.4 336     211   Present                                      invention27    37.5   30     32.5 1.0 182     142   Comparative                                      example28    45     45     10   0.4 255     199   Present                                      invention29    50     32.5   17.5 0.4 254     163   Comparative                                      example30    50     32.5   17.5 0.1 202     187   Comparative                                      example31    55     40     5    0.4 214     159   Comparative                                      example32    45     32     23   0.3 250     189   Present                                      invention33    40     32     28   0.4 252     192   Present                                      invention______________________________________ 
    
     By comparing the a difference between the sample Nos. 18 and 19 in Table 2, it is understood that the sample No. 19 having a substitution rate X of 0.6 has an improved piezoelectric constant d 31 . by comparing the sample Nos. 20 and 21, it is understood that a piezoelectric constant d 31  is decreased extraordinarily if the coefficient b is not larger than 32. The same result is also shown in the sample No. 22. In the sample Nos. 23˜26, both of a piezoelectric constant d 31  and a Curie point were preferred. However, in the sample No. 27, since the substitution rate X is 1.0, a piezoelectric constant d 31  is decreased extraordinarily and a Curie point is also decreased. 
     By comparing sample Nos. 28 and 29, it is understood that a Curie point is decreased extraordinarily if the substitution rate X is not smaller than 45. Moreover, in the sample No. 30, since the substitution rate X is not smaller than 45, a Curie point is decreased extraordinarily and a piezoelectric constant d 31  is decreased as compared with the sample No. 29 in response to a decrease of the substitution rate X. In the sample No. 31, since the coefficient a is increased to 55 and the coefficient c is not larger than 10, a Curie point is particularly decreased. In the sample Nos. 32 and 33, both of a piezoelectric constant d 31  and a Curie point are preferred. 
     EXPERIMENT 3 
     In the same manner as experiment 1, according to sample Nos. 34˜44 in Table 3 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results were shown in Table 3. In this experiment 3, the substitution rate X of tantalum was varied from 0 to 1.0 gradually while the coefficients a, b and c were maintained constant. From the results shown in the previous experiments, it was understand that the coefficients a, b and c in the Table 3 were substantially most suitable values. Moreover, the results of this experiment 3 were shown in FIG. 1, which showed a relation between the substitution rate X and a piezoelectric constant d 31  or a Curie point. 
     
                       TABLE 3______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________34    37.5   37.5   25   0   208     243   Comparative                                      example35    37.5   37.5   25   0.1 275     235   Present                                      invention36    37.5   37.5   25   0.2 305     227   Present                                      invention37    37.5   37.5   25   0.3 322     219   Present                                      invention38    37.5   37.5   25   0.4 336     211   Present                                      invention39    37.5   37.5   25   0.5 344     203   Present                                      invention40    37.5   37.5   25   0.6 351     195   Present                                      invention41    37.5   37.5   25   0.7 342     187   Present                                      invention42    37.5   37.5   25   0.8 330     179   Present                                      invention43    37.5   37.5   25   0.9 312     171   Present                                      invention44    37.5   37.5   25   1.0 285     163   Comparative                                      example______________________________________ 
    
     From the results shown in the Table 3, it is understood that a piezoelectric constant d 31  is improved if the substitution rate X is larger than 0.1 and it is further improved if the substitution rate X is in a range of 0.3˜0.8, more preferably 0.4˜0.7. However, if the substitution rate X is not smaller than 0.7, a Curie point is particularly decreased. Therefore, it is preferred that the substitution rate X is smaller than 0.6. Moreover, in the case that the substitution rate X is 1.0 (i.e., all the niobium is substituted by tantalum), a piezoelectric constant d 31  is decreased and also a Curie point is decreased to a range under 170° C. as shown in the sample No. 44. 
     EXPERIMENT 4 
     In the manner as experiment 1, specimens according to sample Nos. 45˜54 in Table 4 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 4. In this experiment 4, SrCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Sr. 
     
                       TABLE 4______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________45    10     40     50   0.6 263     204   Comparative                                      example46    20     40     40   0.4 299     192   Present                                      invention47    25     50     25   0.4 242     206   Comparative                                      example48    25     30     45   0.5 237     142   Comparative                                      example49    37.5   47.5   15   0.6 273     153   Comparative                                      example50    37.5   37.5   25   0.0 272     183   Comparative                                      example51    37.5   37.5   25   0.3 325     159   Present                                      invention52    37.5   37.5   25   1.0 302     103   Comparative                                      example53    37.5   30     32.5 0.4 245     130   Comparative                                      example54    50     35     15   0.4 291     110   Comparative                                      example______________________________________ 
    
     From results shown in the Table 4, if the substitution rate X of tantalum is set in a range of 0.1˜0.9 under such a condition that the coefficients a, b and c are maintained constantly as shown in the Table 4, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 5 
     In the same manner as experiment 4, specimens according to sample Nos. 55˜64 in Table 5 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point measured. The measuring results are shown in Table 5. In this experiment 5, CoCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Ca. 
     
                       TABLE 5______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________55    10     40     50   0.6 270     194   Comparative                                      example56    20     40     40   0.4 306     182   Present                                      invention57    25     50     25   0.4 248     196   Comparative                                      example58    25     30     45   0.5 243     132   Comparative                                      example59    37.5   47.5   15   0.6 280     143   Comparative                                      example60    37.5   37.5   25   0.0 279     173   Comparative                                      example61    37.5   37.5   25   0.3 332     149   Present                                      invention62    37.5   37.5   25   1.0 309      93   Comparative                                      example63    37.5   30     32.5 0.4 252     120   Comparative                                      example64    50     35     15   0.4 298     100   Comparative                                      example______________________________________ 
    
     From the results shown in Table 5, if the substitution rate X of tantalum is set in a range of 0.1˜0.9 under such a condition that the coefficients a, b and c are maintained constant as shown in Table 5, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 6 
     In the same manner as experiment 4, specimens according to sample Nos. 65˜74 in Table 6 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in the Table 6. In this experiment 6, BaCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Ba. 
     
                       TABLE 6______________________________________                      CurieComposition      Piezoelectric                      pointSample a      b      c    X   constant d.sub.31                                (°C.)                                      Remarks______________________________________65    10     40     50   0.6 262     209   Comparative                                      example66    20     40     40   0.4 297     197   Present                                      invention67    25     50     25   0.4 241     211   Comparative                                      example68    25     30     45   0.5 236     147   Comparative                                      example69    37.5   47.5   15   0.6 272     158   Comparative                                      example70    37.5   37.5   25   0.0 270     188   Comparative                                      example71    37.5   37.5   25   0.3 323     164   Present                                      invention72    37.5   37.5   25   1.0 300     108   Comparative                                      example73    37.5   30     32.5 0.4 244     135   Comparative                                      example74    50     35     15   0.4 290     115   Comparative                                      example______________________________________ 
    
     From the results shown in Table 6, if the substitution rate X of tantalum is set in a range of 0.1˜0.9 under such a condition that the coefficients a, b and c are maintained constant as shown in the Table 6, it is possible to improve both a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 7 
     In the previous experiments, use was made of oxide powders as raw material powders. In this experiment 7, use was made of hydroxide powders or carbonate powders of metal elements rather than oxide powders, and specimens were prepared in the same manner as the previous experiments. With respect to the specimens, a piezoelectric constant d 31  and a Curie point were measured. As a result, the specimens according to this experiment 7 have substantially the same piezoelectric constant d 31  and a Curie point as those of the previous experiments. 
     As mentioned above, according to the first aspect of the invention, since a part of niobium in the piezoelectric porcelain having a composition of PbTiO 3  -PbZrO 3  -Pb(Mg 1/3  Nb 2/3 )O 3  is substituted by tantalum, a piezoelectric constant d 31  can be improved extraordinarily. 
     Hereinafter, experiments according to a second aspect of the invention will be explained. 
     EXPERIMENT 8 
     Raw material powders of PbO, MgO, NiO, Nb 2  O 5 , Ta 2  O 5 , TiO 2 , ZrO 2  were mixed in a ball mill for 24 hours to obtain mixed powders having compositions shown in Table 7. The thus obtained mixed powders were calcined in the atmosphere at 1000° C. for 2 hours to obtain a calcined body. The thus obtained calcined body was crushed in the ball mill for 48 hours to obtain crushed powders. Then, the crushed powders were formed under a pressure of about 400 kg/cm 2  by means of a press machine to obtain a formed body having a diameter of 20 mm and a thickness of 5 mm. The thus obtained formed body was sintered at a temperature of 1200° C.˜1300° C. for 2 hours to obtain a sintered body. 
     The thus obtained sintered body was worked to obtain a plate-like specimen having a dimensions of 12 mm (length)×3 mm (width)×1 mm (thickness). Then, silver electrodes were arranged on the planes of the specimen, and the specimen with the silver electrodes was subjected to a poling in such a manner that a DC voltage of 2 kV/mm was applied to the specimen in a silicone oil having a temperature of 80° C. With respect to the respective specimens after a poling, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 7 as well as coefficients a, b and c and substitution rates X and Y in aPb[Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , wherein the coefficients a, b and c were mol % and a sum of the coefficients a, b and c was 100. In sample Nos. 101˜118 in Table 7, substitution rates X and Y and the coefficients a, b and c were varied respectively. 
     
                       TABLE 7______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________101  10     45     45   0.2 0.4 217     284  Comparative                                        example102  15     40     45   0.3 0.7 260     241  Present                                        invention103  15     35     50   0   0.5 202     244  Comparative                                        example104  15     35     50   0.4 0.6 251     216  Present                                        invention105  20     30     50   0.6 0.9 206     154  Comparative                                        example106  25     25     50   0.1 0.1 163     285  Comparative                                        example107  25     40     35   0.3 0.7 310     199  Present                                        invention108  25     40     35   0.5 0.8 301     181  Present                                        invention109  37.5   37.5   25   0.5 1.0 304     138  Comparative                                        example110  37.5   37.5   25   0.2 0.5 345     193  Present                                        invention111  37.5   37.5   25   0.4 0.6 366     175  Present                                        invention112  37.5   30     32.5 0.9 1.0 168      97  Comparative                                        example113  45     45     10   0.3 0.4 268     184  Present                                        invention114  50     32.5   17.5 0.3 0.4 266     148  Comparative                                        example115  50     32.5   17.5 0.1 0.9 240     118  Comparative                                        example116  55     40     5    0.4 0.8 217     107  Comparative                                        example117  45     32     23   0.2 0.4 273     171  Present                                        invention118  40     32     28   0.3 0.4 266     177  Present                                        invention______________________________________ 
    
     If the sample Nos. 102, 103 and 104 are compared, it is understood that a piezoelectric constant d 31  is decreased extraordinarily in the sample No. 103 in which the substitution rate X is 0 i.e. no nickel exists. In the sample No. 105 in which the coefficient b is out of the scope of the second aspect of the invention, it is understood that a piezoelectric constant d 31  is decreased and a Curie point is also decreased. If the sample Nos. 106, 107 and 108 are compared, it is understood that a piezoelectric constant d 31  is decreased extraordinarily in the sample No. 106 in which the substitution rates X and Y are identical, but, in the sample Nos. 107 and 108 in which the coefficients a, b and c are same as those of the sample No. 106, a piezoelectric constant d 31  is larger than 300 pm/V. If the sample No. 109, 110, 111 and 112 are compared, it is understood that a Curie point is decreased extraordinarily in the sample No. 109 and thus the sample No. 109 has a problem for an actual use. In the sample No. 110 and 111, it is understood that both of a piezoelectric constant d 31  and a Curie point are improved. In the sample No. 112 in which no niobium exists, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased extraordinarily. 
     In the sample No. 113, it is understood that a piezoelectric constant d 31  is increased. In the sample Nos. 114, 115 and 116, it is understood that the coefficient a is larger than 50, but a Curie point is decreased extraordinarily. In the sample No. 117 and 118 having similar composition as that of the sample Nos. 114˜116, both of a piezoelectric constant d 31  and a Curie point are increased extraordinarily. 
     EXPERIMENT 9 
     In the same manner as the experiment 8, specimens according to sample Nos. 119˜132 in Table 8 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results were shown in Table 8. In the experiment 9, the substitution rates X and Y were varied while the coefficients a, b and c were maintained constant within the scope of the second aspect of the invention. 
     
                       TABLE 8______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________119  15     40     45   0.3 0.8 245     223  Present                                        invention120  15     40     45   0.8 0.8 225     208  Comparative                                        example121  15     35     50   0.2 0.6 247     226  Present                                        invention122  15     35     50   0.2 0.2 188     258  Comparative                                        example123  25     40     35   0.3 0.7 310     199  Present                                        invention124  25     40     35   0.7 0.7 303     179  Comparative                                        example125  37.5   37.5   25   0.1 0.9 299     166  Present                                        invention126  37.5   37.5   25   0.8 0.8 308     139  Comparative                                        example127  45     45     10   0.3 0.4 268     184  Present                                        invention128  45     45     10   0.7 0.7 269     140  Comparative                                        example129  45     32     23   0.1 0.6 296     160  Present                                        invention130  45     32     23   0.6 0.6 300     135  Comparative                                        example131  40     32     28   0.2 0.6 289     166  Present                                        invention132  40     32     28   0.6 0.6 294     146  Comparative                                        example______________________________________ 
    
     If the sample Nos. 119 and 120 are compared, it is understood that both of a piezoelectric constant d 31  and a Curie point are increased in the sample No. 119 in which the substitution rate Y is larger than the substitution rate X. If the sample Nos. 121 and 122 are compared, it is understood that a piezoelectric constant d 31  is increased extraordinarily in the sample No. 121 in which a substitution rate Y of tantalum is larger than that of the sample No. 122. If the sample Nos. 123 and 124 are compared, it is understood that both of a piezoelectric constant d 31  and a Curie point are improved largely in the sample No. 123 in which the substitution rate Y is larger than the substitution rate X. If the sample Nos. 127 and 128 are compared, it is understood that a Curie point is improved in the sample No. 127 according to the second aspect of the invention. If the sample Nos. 129 and 130 are compared, it is understood that a Curie point is decreased to a region under 150° C. in the sample No. 130. If the sample Nos. 131 and 132 are compared, it is understood that a Curie point is decreased to a region under 150° C. in the sample No. 132. 
     EXPERIMENT 10 
     In the same manner as experiment 8, specimens according to sample Nos. 133˜144 in Table 9 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 9. In the experiment 9, the coefficients a, b and c were varied while the substitution rate X was maintained at 0.2 and the substitution rate Y was maintained at 0.4. 
     
                       TABLE 9______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________133  10     40     50   0.2 0.4 222     270  Comparative                                        example134  15     40     45   0.2 0.4 243     270  Present                                        invention135  20     30     50   0.2 0.4 211     214  Comparative                                        example136  25     25     50   0.2 0.4 225     256  Comparative                                        example137  25     40     35   0.2 0.4 290     228  Present                                        invention138  37.5   37.5   25   0.2 0.4 328     201  Present                                        invention139  37.5   30     32.5 0.2 0.4 228     180  Comparative                                        example140  45     45     10   0.2 0.4 265     189  Present                                        invention141  50     32.5   17.5 0.2 0.4 263     153  Comparative                                        example142  55     40     5    0.2 0.4 219     149  Comparative                                        example143  45     32     23   0.2 0.4 273     171  Present                                        invention144  40     32     28   0.2 0.4 262     182  Present                                        invention______________________________________ 
    
     If the sample Nos. 135, 136 and 137 are compared, it is understood that piezoelectric constants d 31  of the sample Nos. 135 and 136, in which the coefficient b is not larger than 32, are decreased extraordinarily as compared with the sample No. 137. If the sample Nos. 138 and 139 are compared, it is understood that a piezoelectric constant d 31  of the sample No. 139, in which the coefficient b is not larger than 32, is decreased extraordinarily. If the sample Nos. 140˜144 are compared, it is understood that a Curie point of the sample No. 141, in which the coefficient a is larger than 45, is decreased largely as compared with that of the sample No. 140, 143 and 144 according to the second aspect of the invention. In the sample No. 142, in which the coefficient a is larger than 45 and the coefficient c is not larger than 10, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased extraordinarily. 
     EXPERIMENT 11 
     In the same manner as experiment 8, specimens according to sample Nos. 145˜155 in Table 10 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 10. In the experiment 11, the substitution rate Y was varied while the coefficients a, b and c were maintained constantly within the scope of the second aspect of the invention and the substitution rate X is maintained at 0.1. Moreover, a relation between the substitution rate Y and a piezoelectric constant d 31  or a Curie point is shown in FIG. 2. 
     
                       TABLE 10______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________145  37.5   37.5   25   0.1 0   221     238  Comparative                                        example146  37.5   37.5   25   0.1 0.1 235     230  Comparative                                        example147  37.5   37.5   25   0.1 0.2 307     222  Present                                        invention148  37.5   37.5   25   0.1 0.3 323     214  Present                                        invention149  37.5   37.5   25   0.1 0.4 340     206  Present                                        invention150  37.5   37.5   25   0.1 0.5 348     198  Present                                        invention151  37.5   37.5   25   0.1 0.6 356     190  Present                                        invention152  37.5   37.5   25   0.1 0.7 345     182  Present                                        invention153  37.5   37.5   25   0.1 0.8 333     174  Present                                        invention154  37.5   37.5   25   0.1 0.9 317     166  Present                                        invention155  37.5   37.5   25   0.1 1.0 268     158  Comparative                                        example______________________________________ 
    
     From the results shown in the Table 10, it is understood that, in the samples having the substitution rate Y of 0.2˜0.9, a piezoelectric constant d 31  is increased largely to a level of more than 300 pm/V and also a Curie point is increased to a level more than 166° C. In the sample No. 145 in which the substitution rate Y is 0, it is understood that a piezoelectric constant d 31  is decreased. Moreover, in the sample No. 155 in which the substitution rate Y is 1.0, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased largely. In the case that the substitution rate Y=0.1 (i.e. the substitution rate X is equal to the substitution rate Y), it is understood that a piezoelectric constant d 31  is decreased. Moreover, it is understood that a piezoelectric constant d 31  can be made more than 320 pm/V if the substitution rate Y is in a range of 0.3˜0.8 and also it can be made more than 340 pm/V if the substitution rate Y is in a range of 0.4˜0.7. Moreover, it is understood that, in order to obtain a Curie point greater than 190° C., it is necessary to limit the substitution rate Y to be smaller than 0.6. 
     EXPERIMENT 12 
     In the same manner as experiment 11, specimens according to sample Nos. 156˜166 in Table 11 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 11. In this experiment 12, CoCO 3  raw material powders were added in the mixed powders ad 5 atomic % of Pb was substituted by Ca. 
     
                       TABLE 11______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________156  10     40     50   0.6 0.8 249     148  Comparative                                        example157  20     40     40   0.4 0.6 343     146  Present                                        invention158  20     40     40   0.4 1.0 286     114  Comparative                                        example159  25     50     25   0.4 0.6 275     160  Comparative                                        example160  25     30     45   0.1 0.8 230     103  Comparative                                        example161  37.5   47.5   15   0.4 0.6 280     123  Comparative                                        example162  37.5   37.5   25   0.0 0.3 332     149  Comparative                                        example163  37.5   37.5   25   0.2 0.4 355     131  Present                                        invention164  37.5   37.5   25   0.7 0.7 354      82  Comparative                                        example165  37.5   30     32.5 0.4 0.6 273      84  Comparative                                        example166  50     35     15   0.3 0.7 310      61  Comparative                                        example______________________________________ 
    
     From the results shown in Table 11, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the second aspect of the invention while the coefficients a, b and c are also within the scope of the second aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 13 
     In the same manner as the experiment 11, specimens according to sample Nos. 167˜177 in a Table 12 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results were shown in Table 12. In this experiment 13, SrCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Sr. 
     
                       TABLE 12______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________167  10     40     50   0.6 0.8 243     158  Comparative                                        example168  20     40     40   0.4 0.6 335     156  Present                                        invention169  20     40     40   0.4 1.0 279     124  Comparative                                        example170  25     50     25   0.4 0.6 268     170  Comparative                                        example171  25     30     45   0.1 0.8 224     113  Comparative                                        example172  37.5   47.5   15   0.4 0.6 273     133  Comparative                                        example173  37.5   37.5   25   0.0 0.3 325     159  Comparative                                        example174  37.5   37.5   25   0.2 0.4 347     141  Present                                        invention175  37.5   37.5   25   0.7 0.7 347      92  Comparative                                        example176  37.5   30     32.5 0.4 0.6 266      94  Comparative                                        example177  50     35     15   0.3 0.7 303      71  Comparative                                        example______________________________________ 
    
     From the results shown in the Table 12, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the second aspect of the invention while the coefficients a, b and c are also within the scope of the second aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 14 
     In the same manner as experiment 11, specimens according to sample Nos. 178˜188 in Table 13 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 13. In this experiment 14, BaCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Ba. 
     
                       TABLE 13______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________178  10     40     50   0.6 0.8 242     163  Comparative                                        example179  20     40     40   0.4 0.6 334     161  Present                                        invention180  20     40     40   0.4 1.0 278     129  Comparative                                        example181  25     50     25   0.4 0.6 267     175  Comparative                                        example182  25     30     45   0.1 0.8 223     118  Comparative                                        example183  37.5   47.5   15   0.4 0.6 273     138  Comparative                                        example184  37.5   37.5   25   0.0 0.3 323     164  Comparative                                        example185  37.5   37.5   25   0.2 0.5 359     138  Present                                        invention186  37.5   37.5   25   0.7 0.7 346      97  Comparative                                        example187  37.5   30     32.5 0.4 0.6 265      99  Comparative                                        example188  50     35     15   0.3 0.7 302      76  Comparative                                        example______________________________________ 
    
     From the results shown in the Table 13, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the second aspect of the invention while the coefficients a, b and c are also within the scope of the second aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 15 
     In the previous experiments, use was made of oxide powders as raw material powders. In this experiment 15, use was made of hydroxide powders or carbonate powders of metal elements rather than oxide powders, and specimens were prepared in the same manner as the previous experiments. With respect to the specimens, a piezoelectric constant d 31  and a Curie point were measured. As a result, the specimens according to this experiment 15 have substantially same piezoelectric constant d 31  and a Curie point as those of the previous experiments. 
     As mentioned above, according to the second aspect of the invention, a piezoelectric constant d 31  and a Curie point can be improved extraordinarily. 
     Hereinafter, experiments according to a third aspect of the invention will be explained. 
     EXPERIMENT 16 
     Raw material powders of PbO, MgO, NiO, Nb 2  O 5 , Ta 2  O 5 , TiO 2 , ZrO 2  were mixed in a ball mill for 24 hours to obtain mixed powders having compositions shown in Table 14. The thus obtained mixed powders were calcined in the atmosphere at 1000° C. for 2 hours to obtain a calcined body. The thus obtained calcined body was crushed in the ball mill for 48 hours to obtain crushed powders. Then, the crushed powders were formed under a pressure of about 400 kg/cm 2  by means of a press machine to obtain a formed body having a diameter of 20 mm and a thickness of 5 mm. The thus obtained formed body was sintered at a temperature of 1200° C.˜1300° C. for 2 hours to obtain a sintered body. 
     The thus obtained sintered body was worked to obtain a plate-like specimen having a dimensions of 12 mm (length)×3 mm (width)×1 mm (thickness). Then, silver electrodes were arranged on the planes of the specimen, and the specimen with the silver electrodes was subjected to a poling in such a manner that a DC voltage of 2 kV/mm was applied to the specimen in a silicone oil having a temperature of 80° C. With respect to the respective specimens after a poling, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 14 as well as coefficients a, b and c and substitution rates X and Y in aPb[Mg 1-X  Ni X ) 1/3  (Nb 1-Y  Ta Y ) 2/3  ]O 3  -bPbTiO 3  -cPbZrO 3 , wherein the coefficients a, b and c were mol % and a sum of the coefficients a, b and c was 100. In sample Nos. 201˜218 in the Table 14, substitution rates X and Y and coefficients a, b and c were varied respectively. 
     
                       TABLE 14______________________________________                           CurieSam-  Composition     Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________201  10     45     45   0.6 0.2 216     280  Comparative                                        example202  15     40     45   0.6 0.5 269     242  Present                                        invention203  15     35     50   0.5 0   156     259  Comparative                                        example204  15     35     50   0.6 0.5 243     214  Present                                        invention205  20     30     50   0.6 0.3 211     202  Comparative                                        example206  25     25     50   0.2 0.2 192     272  Comparative                                        example207  25     40     35   0.7 0.3 278     211  Present                                        invention208  25     40     35   0.4 0.2 268     234  Present                                        invention209  37.5   37.5   25   1.0 0.5 294     153  Comparative                                        example210  37.5   37.5   25   0.8 0.2 283     187  Present                                        invention211  37.5   37.5   25   0.4 0.2 303     207  Present                                        invention212  38     30     33   1.0 0.5 193     132  Comparative                                        example213  45     45     10   0.4 0.3 258     187  Present                                        invention214  50     33     18   0.4 0.3 256     151  Comparative                                        example215  50     33     18   0.8 0.2 220     139  Comparative                                        example216  55     40     5    0.8 0.4 194     119  Comparative                                        example217  45     32     23   0.4 0.2 253     177  Present                                        invention218  40     32     28   0.5 0.2 246     183  Present                                        invention______________________________________ 
    
     In the sample No. 201, it is understood that the coefficient a is decreased and thus a piezoelectric constant d 31  is decreased. If the sample Nos. 202, 203 and 204 are compared, it is understood that a piezoelectric constant d 31  is decreased extraordinarily in the sample No. 203 in which the substitution rate Y is 0 (i.e. no tantalum exists tantalum). In the sample No. 205 in which the coefficient b is out of the scope of the third aspect of the invention, it is understood that a piezoelectric constant d 31  is decreased. If the sample Nos. 206, 207 and 208 are compared, it is understood that a piezoelectric constant d 31  is decreased extraordinarily in the sample No. 206 in which the substitution rates X and Y are identical, but, in the sample Nos. 207 and 208 in which the coefficients a, b and c are same as those of the sample No. 206, a piezoelectric constant d 31  is improved. If the sample Nos. 209, 210, 211 and 212 are compared, it is understood that a Curie point is decreased extraordinarily in the sample No. 209 in which the substitution rate X is 1.0 (i.e., no magnesium) exists and thus the sample No. 209 has a problem for an actual use. In the sample Nos. 210 and 211, it is understood that a piezoelectric constant d 31  is improved extraordinarily. In the sample No. 212 in which no magnesium exists, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased extraordinarily. 
     If the sample Nos. 213, 214 and 215 are compared, it is understood that a Curie point is decreased in the sample Nos. 214 and 215 wherein the coefficient a is larger than 45. Moreover, if the sample Nos. 216, 217 and 218 are compared, it is understood that a Curie point is decreased in the sample No. 216 wherein the coefficient a is larger than 45 and the coefficient c is not larger than 10. 
     EXPERIMENT 17 
     As is the same as the experiment 16, specimens according to sample Nos. 219˜232 in Table 15 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 15. In the experiment 17, the substitution rates X and Y were varied while the coefficients a, b and c were maintained constant within the scope of the third aspect of the invention. 
     
                       TABLE 15______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________219  15     40     45   0.7 0.5 255     237  Present                                        invention220  15     40     45   0.8 0.8 225     208  Comparative                                        example221  15     35     50   0.6 0.5 243     214  Present                                        invention222  15     35     50   0.7 0.7 227     193  Comparative                                        example223  25     40     35   0.8 0.3 262     206  Present                                        invention224  25     40     35   0.8 0.8 273     166  Comparative                                        example225  37.5   37.5   25   0.7 0.2 299     192  Present                                        invention226  37.5   37.5   25   0.7 0.7 339     152  Comparative                                        example227  45     45     10   0.7 0.3 249     172  Present                                        invention228  45     45     10   0.7 0.7 269     140  Comparative                                        example229  45     32     23   0.5 0.2 256     172  Present                                        invention230  45     32     23   0.5 0.5 290     148  Comparative                                        example231  40     32     28   0.6 0.3 261     170  Present                                        invention232  40     32     28   0.7 0.7 267     133  Comparative                                        example______________________________________ 
    
     If the sample Nos. 219 and 220 are compared, it is understood that both of a piezoelectric constant d 31  and a Curie point are increased in the sample No. 219 in which the substitution rate X is larger than the substitution rate Y. If the sample Nos. 221 and 222 are compared, it is understood that a piezoelectric constant d 31  and a Curie point are increased in the sample No. 121 in which the substitution rate X is larger than the substitution rate Y. If the sample Nos. 223 and 224 are compared, it is understood that a Curie point is largely decreased in the sample No. 224 in which the substitution rate X is equal to the substitution rate Y. If the sample Nos. 225 and 226 are compared, it is understood that a Curie point is largely decreased to a level of about 150° C. in the sample No. 226 in which the substitution rate X is equal to the substitution rate Y and thus the sample No. 226 has a problem for actual use. 
     If the sample Nos. 227 and 228 are compared, it is understood that a Curie point is largely decreased to a level under 150° C. in the sample No. 228 in which the substitution rate X is equal to the substitution rate Y and thus the sample No. 228 has a problem for an actual use. If the sample Nos. 229 and 230 are compared, it is understood that a Curie point is largely decreased in the sample No. 230 in which the substitution rate X is equal to the substitution rate Y. If the sample Nos. 231 and 232 are compared, it is understood that a Curie point is decreased to a region under 150° C. in the sample No. 232. 
     EXPERIMENT 18 
     As is the same as the experiment 16, specimens according to sample Nos. 233˜242 in Table 16 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 16. In the experiment 16, the coefficients a, b and c were varied while the substitution rate X was maintained at 0.5 and the substitution rate Y is was maintained at 0.3. 
     
                       TABLE 16______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________233  15     40     45   0.5 0.3 242     263  Present                                        invention234  20     30     50   0.5 0.3 209     207  Comparative                                        example235  25     25     50   0.5 0.3 223     249  Comparative                                        example236  25     40     35   0.5 0.3 290     221  Present                                        invention237  37.5   37.5   25   0.5 0.3 327     194  Present                                        invention238  37.5   30     32.5 0.5 0.3 224     173  Comparative                                        example239  45     45     10   0.5 0.3 261     182  Present                                        invention240  50     33     18   0.5 0.3 258     146  Comparative                                        example241  55     40     5    0.5 0.3 211     142  Comparative                                        example242  40     32     28   0.5 0.3 259     175  Present                                        invention______________________________________ 
    
     If the sample Nos. 233 and 234 are compared, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased in the sample No. 234 in which the coefficient b is not larger than 32. If the sample Nos. 235 and 236 are compared, it is understood that a piezoelectric constant d 31  is largely decreased in the sample No. 235 in which the coefficient b is 25. If the sample Nos. 237, 238 and 239 are compared, it is understood that both of a piezoelectric constant d 31  and a Curie point are decreased in the sample No. 238 in which the coefficient b is not larger than 32. If the sample Nos. 240, 241 and 242 are compared, it is understood that a Curie point is largely decreased as compared with that of the sample No. 242 in the sample No. 240 in which the coefficient a is larger than 45. Moreover, it is understood that both of a piezoelectric constant d 31  and a Curie point are extraordinarily decreased as compared with that of the sample No. 242 in the sample No. 241 in which the coefficient a is larger than 45 and the coefficient c is smaller than 10. 
     EXPERIMENT 19 
     As is the same as the experiment 16, specimens according to sample Nos. 243˜248 in a Table 17 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results were shown in the Table 17. In the experiment 19, the substitution rate X was varied in a range of 0.5˜1.0 while the coefficients a, b and c were maintained constant within the scope of the third aspect of the invention and the substitution rate Y is maintained at 0.4. Moreover, a relation between the substitution rate X and a piezoelectric constant d 31  or a Curie point is shown in FIG. 3. 
     
                       TABLE 17______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________243  37.5   37.5   25   0.5 0.4 312     186  Present                                        invention244  37.5   37.5   25   0.6 0.4 316     181  Present                                        invention245  37.5   37.5   25   0.7 0.4 306     176  Present                                        invention246  37.5   37.5   25   0.8 0.4 294     171  Present                                        invention247  37.5   37.5   25   0.9 0.4 383     166  Present                                        invention248  37.5   37.5   25   1.0 0.4 250     161  Comparative                                        example______________________________________ 
    
     From the results shown in Table 17, it is understood that a Curie point is extraordinarily decreased to a level of smaller than 170° C. if the substitution rate X is 1.0 Moreover, it is understood that a piezoelectric constant d 31  is largely improved if the substitution rate X is smaller than 0.9. Further, it is understood that piezoelectric constant d 31  is more largely improved to a level larger than 300 pm/V if the substitution rate X is smaller than 0.7. Furthermore, it is understood that a piezoelectric constant d 31  becomes larger than 310 pm/V if the substitution rate X is 0.5 or 0.6. 
     EXPERIMENT 20 
     In the same manner as experiment 16, specimens according to sample Nos. 249˜257 in Table 18 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in the Table 18. In the experiment 20, substitution rate X was varied in a range of 0.2˜1.0 while the coefficients a, b and c were maintained constant within the scope of the third aspect of the invention and the substitution rate Y is maintained at 0.2. Moreover, a relation between the substitution rate X and a piezoelectric constant d 31  or a Curie point is shown in FIG. 4. 
     
                       TABLE 18______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________249  37.5   37.5   25   0.2 0.2 263     217  Comparative                                        example250  37.5   37.5   25   0.3 0.2 299     212  Present                                        invention251  37.5   37.5   25   0.4 0.2 309     207  Present                                        invention252  37.5   37.5   25   0.5 0.2 312     202  Present                                        invention253  37.5   37.5   25   0.6 0.2 316     197  Present                                        invention254  37.5   37.5   25   0.7 0.2 306     192  Present                                        invention255  37.5   37.5   25   0.8 0.2 294     187  Present                                        invention256  37.5   37.5   25   0.9 0.2 283     182  Present                                        invention257  37.5   37.5   25   1.0 0.2 250     177  Comparative                                        example______________________________________ 
    
     From the results shown in Table 18, it is understood that a Curie point is extraordinarily decreased if the substitution rate X is 1.0. Moreover, it is understood that a piezoelectric constant d 31  is largely improved if the substitution rate X is smaller than 0.9. Further, it is understood that a piezoelectric constant d 31  is largely decreased in the sample No. 249 in which the substitution rate X is equal to the substitution rate Y. Moreover, it is understood that both of a piezoelectric constant d 31  and a Curie point are largely improved in the sample Nos. 250˜256 in which the substitution rate X is larger than the substitution rate Y. Particularly, it is understood that a piezoelectric constant d 31  is more largely improved to a level larger than 300 pm/V if the substitution rate X is in a range of 0.4˜0.7. Moreover, it is understood that a piezoelectric constant d 31  becomes larger than 310 pm/V if the substitution rate X is 0.5 or 0.6. 
     EXPERIMENT 21 
     In the same manner as experiment 16, specimens according to sample Nos. 258˜268 in a Table 19 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results were shown in the Table 19. In this experiment 21, SrCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Sr. 
     
                       TABLE 19______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________258  10     40     50   0.8 0.6 237     164  Comparative                                        example259  20     40     40   0.6 0.4 315     162  Present                                        invention260  20     40     40   1.0 0.4 256     142  Comparative                                        example261  25     50     25   0.6 0.4 249     176  Comparative                                        example262  25     30     45   0.8 0.1 177     134  Comparative                                        example263  37.5   47.5   15   0.6 0.4 254     139  Comparative                                        example264  37.5   37.5   25   0.2 0.0 286     173  Comparative                                        example265  37.5   37.5   25   0.4 0.2 326     147  Present                                        invention266  37.5   37.5   25   0.7 0.7 347      92  Comparative                                        example267  37.5   30     32.5 0.6 0.4 247     100  Comparative                                        example268  50     35     15   0.7 0.3 270     83   Comparative                                        example______________________________________ 
    
     From the results shown in Table 19, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the third aspect of the invention while the coefficients a, b and c are also within the scope of the third aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 22 
     As is the same as the experiment 16, specimens according to sample Nos. 269˜279 in Table 20 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 20. In this experiment 22, CoCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Ca. 
     
                       TABLE 20______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________269  10     40     50   0.8 0.6 244     154  Comparative                                        example270  20     40     40   0.6 0.4 322     152  Present                                        invention271  20     40     40   1.0 0.4 263     132  Comparative                                        example272  25     50     25   0.6 0.4 256     166  Comparative                                        example273  25     30     45   0.8 0.1 183     124  Comparative                                        example274  37.5   47.5   15   0.6 0.4 261     129  Comparative                                        example275  37.5   37.5   25   0.2 0.0 293     163  Comparative                                        example276  37.5   37.5   25   0.4 0.2 333     137  Present                                        invention277  37.5   37.5   25   0.7 0.7 354      82  Comparative                                        example278  37.5   30     32.5 0.6 0.4 254      90  Comparative                                        example279  50     35     15   0.7 0.3 277     73   Comparative                                        example______________________________________ 
    
     From the results shown in the Table 20, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the third aspect of the invention while the coefficients a, b and c are also within the scope of the third aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 23 
     In the same manner as experiment 16, specimens according to sample Nos. 280˜290 in Table 21 were prepared. With respect to the thus prepared specimens, a piezoelectric constant d 31  and a Curie point were measured. The measuring results are shown in Table 21. In this experiment 23, BaCO 3  raw material powders were added in the mixed powders and 5 atomic % of Pb was substituted by Ba. 
     
                       TABLE 21______________________________________                           CurieSam- Composition      Piezoelectric                           pointple  a      b      c    X   Y   constant d.sub.31                                   (°C.)                                        Remarks______________________________________280  10     40     50   0.8 0.6 236     169  Comparative                                        example281  20     40     40   0.6 0.4 313     167  Present                                        invention282  20     40     40   1.0 0.4 255     147  Comparative                                        example283  25     50     25   0.6 0.4 248     181  Comparative                                        example284  25     30     45   0.8 0.1 176     139  Comparative                                        example285  37.5   47.5   15   0.6 0.4 253     144  Comparative                                        example286  37.5   37.5   25   0.2 0.0 285     178  Comparative                                        example287  37.5   37.5   25   0.4 0.2 324     152  Present                                        invention288  37.5   37.5   25   0.7 0.7 346      97  Comparative                                        example289  37.5   30     32.5 0.6 0.4 246     105  Comparative                                        example290  50     35     15   0.7 0.3 269     88   Comparative                                        example______________________________________ 
    
     From the results shown in the Table 21, if the substitution rate X of nickel with respect to magnesium and the substitution rate Y of tantalum with respect to niobium are within the scope of the third aspect of the invention while the coefficients a, b and c are also within the scope of the third aspect of the invention, it is possible to improve both of a piezoelectric constant d 31  and a Curie point. 
     EXPERIMENT 24 
     In the previous experiments, use was made of oxide powders as raw material powders. In this experiment 24, use was made of hydroxide powders or carbonate powders of metal elements rather than oxide powders, and specimens were prepared in the same manner as the previous experiments. With respect to the specimens, a piezoelectric constant d 31  and a Curie point were measured. As a result, the specimens according to this experiment 24 have substantially same piezoelectric constant d 31  and a Curie point as those of the previous experiments. 
     As mentioned above, according to the third aspect of the invention, a piezoelectric constant d 31  and a Curie point can be improved extraordinarily.