Abstract:
A laminated piezoelectric element ( 1 ) comprises a laminated piezoelectric element ( 1 ) piezoelectric layers ( 11 ) composed of a ceramic capable of expanding and contracting upon application of a voltage, and internal electrode layers ( 21   a  and  21   b ) that supply voltage to the piezoelectric layers, the internal electrode layers and piezoelectric layers being alternately provided, a first external electrode layer ( 31 ) provided on a side of the laminated piezoelectric element ( 1 ) and electrically connected with the internal electrode layers ( 21   a  and  21   b ), and a second external electrode layer ( 32 ) provided on a side of the laminated piezoelectric element ( 1 ) and electrically connected with the internal electrode layers ( 21   a  and  21   b ) via the first ecternal electrode layer wherein there are specific external electrode width relationships.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a laminated piezoelectric element used in, for example, an automobile fuel injection valve, a precision positioning apparatus of an optical apparatus, a driving element for prevention of vibration or an ink jet printer, and so forth. 
   2. Description of Related Art 
   Laminated piezoelectric elements, and particularly laminated piezoelectric elements used in automobile fuel injection valves, are required to ensure reliability over a broad temperature range extending from low temperatures to high temperatures. In environments in which they are subjected to such thermal shock, differences in thermal expansion between the piezoelectric element and external electrode provided on a side of the piezoelectric element cause thermal stress to be applied from the external electrode to the piezoelectric element resulting in the problem of the formation of cracks in the external electrode and the piezoelectric element. 
   Japanese Unexamined Patent Publications (Kokai) No. 2001-345490 and No. 8-242025 propose a laminated piezoelectric element that improves the durability of the external electrode by providing a plurality of external electrodes having different elongation percentages on a side of the piezoelectric element. In addition, Japanese Unexamined Patent Publication (Kokai) No. 2001-148521 proposes a laminated piezoelectric element that provides an external electrode on a side of the piezoelectric element, a solder layer that is narrower than the external electrode on the external electrode, and an external electrode layer connection lead wire that electrically connects the external electrode on the solder layer. As a result, thermal stress attributable to the difference in thermal expansion between the solder layer and piezoelectric element is not applied directly to the piezoelectric element due to the external electrode being wider than the solder layer. 
   However, the prior art described in JPP&#39;490 is susceptible to concentration of thermal stress generated in both ends of the external electrodes as the widths of the plurality of external electrodes are the same and, as the thermal stress applied to the piezoelectric element from the external electrodes is large, there was the problem of cracks forming in the external electrodes and piezoelectric element. In addition, in the prior art described in JPP&#39;521, as a solder layer is provided discontinuously relative to the direction of lamination of the piezoelectric, if cracks form at a plurality of locations in the external electrode not in contact with the solder layer due to the difference in thermal expansion between the solder layer and external electrode, sections appear in which there are electrical discontinuities between the locations where cracks have formed. In addition, if the cracks that have formed in the piezoelectric extend to the external electrode not in contact with the solder layer as well, sections similarly appear in which there are electrical discontinuities between the locations where cracks have formed. As a result, as a voltage cannot be applied to a portion of the piezoelectric element and the displacement of the piezoelectric element decreases, there is the problem that the characteristics change during the course of use. In addition, thermal stress is applied to the external electrode and piezoelectric element from both ends of the solder layer in the direction of lamination of the piezoelectric, resulting in the formation of cracks in the piezoelectric element. As the sites where cracks form are piezoelectric active sections and the direction in which the cracks spread is the direction of expansion and contraction of the piezoelectric element, the spreading of the cracks is promoted, thereby resulting in problems in terms of reliability. 
   SUMMARY OF THE INVENTION 
   An object of the present invention is to provide a laminated piezoelectric element capable of inhibiting the formation of cracks in an external electrode and piezoelectric element. 
   This and other objects of the present invention will be easily understood from the following detailed descriptions of the present invention. 
   In a first aspect of the present invention, a laminated piezoelectric element is provided that is provided with: a laminated piezoelectric element comprising piezoelectric layers composed of a ceramic capable of expanding and contracting upon application of a voltage, and internal electrode layers that supply voltage to the piezoelectric layers, the internal electrode layers and piezoelectric layers being alternately provided; a first external electrode layer provided on a side of the laminated piezoelectric element and electrically connected with the internal electrode layers; and, 
   a second external electrode layer provided on a side of the laminated piezoelectric element and electrically connected with the internal electrode layers via the first external electrode layer; wherein, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of the first external electrode layer is taken to be W 1 , and the width of the second external electrode layer is taken to be W 2 , the relationship exists in which W 1 &gt;W 2  and 2.5≦(W 2 /W 0 )×100≦60, the laminated piezoelectric element has a piezoelectric active section that expands and contracts when a voltage is applied, and the second external electrode layer is provided continuously in the direction of lamination of the piezoelectric layers in the piezoelectric active section. 
   According to this first aspect of the present invention, as the widths of the first and second external electrode layers are the same, thermal stress generated in both ends of each external electrode layer can be dispersed. In addition, as W 1 &gt;W 2 , thermal stress generated in the first external electrode layer is not applied directly to the piezoelectric body. In addition, if (W 2 /W 0 )×100 is 2.5 or more, a bonding strength can be secured which is capable of bonding a lead wire or electrode plate connected to the second external electrode layer with the second external electrode layer. In addition, if (W 2 /W 0 )×100 is 60 or less, a the thermal stress on the piezoelectric body can be held to a low level, the formation of cracks can be inhibited. In addition, if the second external electrode layer is provided continuously in the piezoelectric active section in the direction of lamination of the piezoelectric layers, the effect of thermal stress applied to the first external electrode and piezoelectric active section from both ends of the second external electrode layer in the direction of lamination of the piezoelectric body can be minimized. In other words, since both ends of the second external electrode layer in the direction of lamination of the piezoelectric are substantially not located on the piezoelectric active section, even if cracks form, they have little effect on the piezoelectric active section. On the other hand, in the case the second external electrode layer is provided discontinuously in the direction of lamination of the piezoelectric layers in the piezoelectric active section, thermal stress is applied to the first external electrode and the piezoelectric active section from both ends of the second external electrode layer in the direction of lamination of the piezoelectric, resulting in greater susceptibility to the formation of cracks in the piezoelectric active section. As the direction in which the cracks spread is consistent with the direction in which the piezoelectric active section expands and contracts, the spread of cracks is promoted thereby resulting in problems in terms of reliability. 
   Further, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0  and the width of the second external electrode layer is taken to be W 2 , a relationship should exist in which 5≦(W 2 /W 0 )×100≦30. In the case (W 2 /W 0 )×100 is less than 5, bonding strength between a lead wire or electrode plate and the first external electrode layer becomes inadequate. In addition, in the case (W 2 /W 0 )×100 exceeds 30, although the formation of cracks is inhibited, continuous effects cannot be adequately obtained. 
   Furthermore, according to the invention, when the thickness (after curing) of the first external electrode layer is taken to be T 1  and the thickness (after curing) of the second external electrode layer is taken to be T 2 , a relationship should exist in which 0.05≦(T 2 /T 1 )≦300. In the case T 2 /T 1  exceeds 300, as the thickness of the second external electrode layer is too large relative to the thickness of the first external electrode layer that acts to alleviate stress, its effect as a stress alleviating material becomes low, resulting in the formation of cracks. In addition, if T 2 /T 1  is less than 0.05, bonding strength of the lead wire or electrode plate with the second external electrode layer is inadequate. 
   Moreover, according to the invention, when the thickness (after curing) of the first external electrode layer is taken to be T 1  and the thickness (after curing) of the second electrode layer is taken to be T 2 , a relationship should exist in which 1≦(T 2 /T 1 )≦35. In the case where T 2 /T 1  exceeds 35, as the thickness of the second external electrode layer is too large relative to the thickness of the first external electrode layer that acts to alleviate stress, its effect as a stress alleviating material becomes low resulting in the formation of cracks. In addition, if T 2 /T 1  is less than 1, bonding strength of the lead wire or electrode plate with the second external electrode layer is inadequate. 
   In addition, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , it is preferable that W 0 ≦15 mm. In the case W 0  exceeds 15 mm, width W 2  of the second external electrode layer becomes 9.0 mm or more, and the thermal stress generated in the second external electrode layer exceeds the strength of the piezoelectric layers, thereby resulting in greater susceptibility to the formation of cracks in the piezoelectric. 
   In addition, according to the invention, if the first external electrode layer is composed of a metal comprising at least one selected from the group consisting of silver, palladium, platinum, copper, gold, nickel, tin, lead, zinc and bismuth as well as an alloy thereof, when the elastic modulus of the first external electrode layer is taken to be E 1  and the coefficient of linear expansion is taken to be α 1 , while elastic modulus of the second external electrode layer is taken to be E 2  and the coefficient of linear expansion is taken to be α 2 , if solder or an electrically conductive resin material is used for the second external electrode layer, as E 1 ×α 1  can be made to be smaller than E 2 ×α 2 , the first external electrode layer acts as a buffer layer that alleviates thermal stress in the second external electrode layer, thereby making it possible to alleviate thermal stress applied to the laminated piezoelectric element from the second external electrode layer. 
   In addition, according to the invention, if the second external electrode layer comprises solder or an electrically conductive resin material, if a lead wire or electrode plate is connected to the second external electrode layer, bonding strength of the lead wire or electrode plate with the second external electrode layer can be increased. 
   As has been described above, according to a first aspect of the present invention, a laminated piezoelectric element can be provided that realizes both secured bonding strength between a lead wire or electrode plate connected to the second external electrode layer and the second external electrode layer as well as inhibition of crack formation in the piezoelectric body. 
   In a second aspect of the present invention, a laminated piezoelectric element is provided that is provided with: a laminated piezoelectric element comprising piezoelectric layers composed of a ceramic capable of expanding and contracting upon application of a voltage, and internal electrode layers that supply voltage to the piezoelectric layers, the internal electrode layers and piezoelectric layers being alternately provided; a first external electrode layer provided on a side of the laminated piezoelectric element and electrically connected with the internal electrode layers; a second external electrode layer provided on a side of the laminated piezoelectric element and electrically connected with the internal electrode layers via the first external electrode layer; and, a third external electrode layer provided on a side of the laminated piezoelectric element and provided between the first external electrode layer and the second external electrode layer; wherein, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of the first external electrode layer is taken to be W 1 , the width of the second external electrode layer is taken to be W 2 , the width of the third external electrode layer is taken to be W 3 , the thickness (after curing) of the second electrode layer is taken to be T 2 , and the thickness (after curing) of the third external electrode layer is taken to be T 3 , the relationship exists in which W 1 &gt;W 3 &gt;W 2 , 2.5≦(W 2 /W 0 )×100≦60, and 0.05≦(T 2 /T 3 )≦300; and, the laminated piezoelectric element has a piezoelectric active section that expands and contracts when a voltage is applied, and the second external electrode layer is provided continuously in the direction of lamination of the piezoelectric layers in the piezoelectric active section. 
   According to this second aspect of the present invention, as the widths of the first through third external electrode layers are not the same, thermal stress generated in both ends of each external electrode layer can be dispersed. In addition, together with thermal stress generated in the second external electrode layer being alleviated by the first and third external electrode layers, thermal stress generated in the third external electrode layer can be alleviated by the first external electrode layer. In addition, if the relationship among the widths of the external electrode layer is such that W 1 &gt;W 3 &gt;W 2 , then thermal stress generated in the second or third external electrode layer is not applied directly to the piezoelectric. In addition, if (W 2 /W 0 )×100 is 2.5 or more, then bonding strength capable of bonding a lead wire or electrode plate connected to the second external electrode layer with the second external electrode layer can be secured. In addition, if (W 2 /W 0 )×100 is 60 or less, as thermal stress on the piezoelectric can be held to a low level, the formation of cracks can be inhibited. In addition, if the second external electrode layer is provided continuously in the piezoelectric active section in the direction of lamination of the piezoelectric layers, thermal stress applied to the first external electrode and piezoelectric active section from both ends of the second external electrode layer in the direction of lamination of the piezoelectric can be minimized. On the other hand, in the case the second external electrode layer is provided discontinuously in the piezoelectric active section in the direction of lamination of the piezoelectric layers, thermal stress is applied to the first external electrode and piezoelectric active section from both ends of the second external electrode layer in the direction of lamination of the piezoelectric, and cracks form easily in the piezoelectric active section. As the direction in which cracks spread is consistent with the direction of expansion and contraction of the piezoelectric active section, the spreading of cracks is promoted resulting in problems in terms of reliability. In addition, if T 2 /T 1  is set to be 300 or less, as the thickness of the second external electrode layer is excessively large relative to the thickness of the first external electrode layer, the first external electrode layer acts as a stress alleviating material thereby inhibiting the formation of cracks in the piezoelectric. In addition, if T 2 /T 1  is 0.05 or more, a bonding strength capable of bonding a lead wire or electrode plate connected to the second external electrode layer with the second external electrode layer can be secured. 
   Further, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of the second external electrode layer is taken to be W 2 , the thickness (after curing) of the second external electrode layer is taken to be T 2 , and the thickness (after curing) of the third external electrode layer is taken to be T 3 , a relationship should exist in which 5≦(W 2 /W 0 )×100≦30, and 1≦(T 2 /T 3 )≦35. In the case (W 2 /W 0 )×100 is greater than 30, the continuous effect of inhibiting crack formation in the piezoelectric cannot be obtained. In addition, in the case (W 2 /W 0 )×100 is less than 5, bonding strength between a lead wire or electrode plate and the second external electrode layer is inadequate. In addition, in the case T 2 /T 1  is greater than 35, as the thickness of the second external electrode plate is excessively large relative to the thickness of the first electrode plate acting as a stress alleviating material, its effect as a stress alleviating material decreases and cracks form in the piezoelectric. In addition, in the case T 2 /T 1  is less than 1, bonding strength between a lead wire or electrode plate and the second external electrode layer is inadequate. 
   Furthermore, according to the invention, if the first external electrode layer, the second external electrode layer, and the third external electrode layer are all of different materials, when the coefficient of linear expansion of the first external electrode layer is taken to be α 1  and its elastic modulus is taken to be E 1 , the coefficient of linear expansion of the second external electrode layer is taken to be α 2  and its elastic modulus is taken to be E 2 , and the coefficient of linear expansion of the third external electrode layer is taken to be α 3  and its elastic modulus is taken to be E 3  in particular, a relationship should exist in which E 1 ×α 1 &lt;E 3 ×α 3 &lt;E 2 ×α 2 . As a result, a material having high adhesive strength can be used for the material of the third external electrode layer that bonds a lead wire or electrode plate. As materials having high adhesive strength typically have a large elastic modulus, considerable thermal stress is applied to the piezoelectric. In the present invention, however, a material can be used for the material of the third external electrode layer that alleviates thermal stress generated in the second external electrode layer such that E 3 ×α 3 &lt;E 2 ×α 2 . In addition, if E 1 ×α 1 &lt;E 3 ×α 3 &lt;E 2 ×α 2 , thermal stress can be alleviated in a stepwise manner. 
   Moreover, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , it is preferable that W 0 ≦15 mm. If W 0  is greater than 15 mm, width W 2  of the second external electrode layer becomes 9.0 mm or more, and thermal stress generated in the second external electrode layer exceeds the strength of the piezoelectric layers, thereby resulting in greater susceptibility to crack formation in the piezoelectric. 
   In addition, according to the invention, if the first external electrode layer is composed of at least one metal selected from the group consisting of silver, palladium, platinum, copper, gold, nickel, tin, lead, zinc and bismuth, as well as an alloy thereof, when the elastic modulus of the first external electrode layer is taken to be E 1  and its coefficient of linear expansion is taken to be α 1 , and the elastic modulus of the second external electrode layer is taken to be E 2  and its coefficient of linear expansion is taken to be α 2 , as E 1 ×α 1  can be made to be smaller than E 2 ×α 2  in the case of using solder or an electrically conductive resin material for the second external electrode layer, the first external electrode layer acts as a buffer layer that alleviates thermal stress in the second external electrode layer, thereby making it possible to alleviate thermal stress applied to the laminated piezoelectric element from the second external electrode layer. 
   In addition, according to the invention, if the second external electrode layer and the third external electrode layer are composed of solder or an electrically conductive resin material, if a lead wire or electrode plate is connected to the second or third external electrode layer, the bonding strength of the lead wire or electrode plate with the second or third external electrode layer can be increased. 
   As described above, according to this second aspect of the present invention, a laminated piezoelectric element can be provided that realizes both secured bonding strength between a lead wire or electrode plate connected to the second external electrode layer and the second external electrode layer as well as inhibition of crack formation in the piezoelectric body. 
   In a third aspect of the present invention, a laminated piezoelectric element is provided that is provided with: a laminated piezoelectric element comprising piezoelectric layers composed of a ceramic capable of expanding and contracting upon application of a voltage, and internal electrode layers that supply voltage to the piezoelectric layers, the internal electrode layers and piezoelectric layers being alternately provided; and, a first external electrode layer provided on a side of the laminated piezoelectric element and electrically connected with the internal electrode layers; wherein, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , and the width of the first external electrode layer is taken to be W 1 , the relationship exists in which 2.5≦(W 1 /W 0 )×100≦60; and, the laminated piezoelectric element has a piezoelectric active section that expands and contracts when a voltage is applied, and the first external electrode layer is provided continuously in the direction of lamination of the piezoelectric layers in the piezoelectric active section. 
   According to this third aspect of the present invention, (W 1 /W 0 )×100 is 2.5 or more, and bonding strength capable of bonding a lead wire or electrode plate connected to the first external electrode layer with the first external electrode layer can be secured. In addition, if (W 1 /W 0 )×100 is 60 or less, as the thermal stress on the piezoelectric can be held to a low level, the formation of cracks can be inhibited. In addition, if the first external electrode layer is provided continuously in the piezoelectric active section in the direction of lamination of the piezoelectric layers, thermal stress applied to the piezoelectric active section from both ends of the first external electrode layer in the direction of lamination of the piezoelectric can be minimized. In other words, as both ends of the first external electrode layer in the direction of lamination of the piezoelectric are substantially not located on the piezoelectric active section, if cracks form they have little effect on the piezoelectric active section. On the other hand, in the case the first external electrode layer is provided discontinuously in the piezoelectric active section in the direction of lamination of the piezoelectric layers, thermal stress is applied to the piezoelectric active section from both ends of the first external electrode layer in the direction of lamination of the piezoelectric, and cracks form easily in the piezoelectric active section. As the direction in which cracks spread is consistent with the direction of expansion and contraction of the piezoelectric active section, the spreading of cracks is promoted resulting in problems in terms of reliability. 
   Further, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , and the width of the first external electrode layer is taken to be W 1 , a relationship should exist in which 5≦(W 1 /W 0 )×100≦30. In the case (W 1 /W 0 )×100 is greater than 30, the continuous effect of inhibiting crack formation in the piezoelectric cannot be obtained. In addition, in the case (W 1 /W 0 )×100 is less than 5, the bonding strength between a lead wire or electrode plate and the first external electrode layer is inadequate. 
   Furthermore, according to the invention, when the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination is taken to be W 0 , it is preferable that W 0 ≦15 mm. In the case W 0  exceeds 15 mm, width W 1  of the first external electrode layer becomes 9.0 mm or more, and the thermal stress generated in the second external electrode layer exceeds the strength of the piezoelectric layers, thereby resulting in greater susceptibility to the formation of cracks in the piezoelectric body. 
   Moreover, according to the invention, if the first external electrode layer is composed of a metal consisting of at least one among silver, palladium, platinum, copper, gold, nickel, tin, lead, zinc and bismuth, or an alloy thereof, there is less thermal stress and thermal stress applied to the piezoelectric can be reduced. 
   In addition, according to the invention, if the first external electrode layer is composed of solder of an electrically conductive resin material, in the case a lead wire or electrode plate is connected to the first external electrode layer, bonding strength of the lead wire or electrode plate with the first external electrode layer can be increased. 
   As described above, according to this third aspect of the present invention, a laminated piezoelectric element can be provided that realizes both a secure bonding strength between a lead wire or electrode plate connected to the first external electrode layer and the first external electrode layer as well as inhibition of crack formation in the piezoelectric body. 
   In addition, according to another aspect of the present invention, there is provided a fuel injection apparatus. When the piezoelectric element is used in the conventional fuel injection apparatus, reliability must be ensured over a broad temperature range extending from low temperatures to high temperatures. According to the present invention, even in environments in which a fuel injection apparatus is subjected to such thermal shock, a fuel injection apparatus can be provided that is resistant to changes in characteristics and maintains a high level of reliability for a long period of time because the formation of cracks in the piezoelectric element caused by thermal stress attributable to external electrodes can be inhibited. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1A to 1C  are each an explanatory drawing ( 1 ) showing the constitution of a laminated piezoelectric element according to a first embodiment of the present invention; 
       FIGS. 2A and 2B  are each an enlarged explanatory drawing of the essential portion of  FIG. 1 ; 
       FIGS. 3A and 3B  are each an enlarged explanatory drawing of the essential portion of the prior art laminated piezoelectric element; 
       FIGS. 4A to 4C  are each an explanatory drawing ( 2 ) showing the constitution of a laminated piezoelectric element according to a first embodiment of the present invention; 
       FIGS. 5A to 5C  are each an explanatory drawing ( 3 ) showing the constitution of a laminated piezoelectric element according to a first embodiment of the present invention; 
       FIGS. 6A to 6C  are each an explanatory drawing ( 4 ) showing the constitution of a laminated piezoelectric element according to a first embodiment of the present invention; 
       FIGS. 7A and 7B  are each an explanatory drawing ( 1 ) showing the constitution of a laminated piezoelectric element according to a second embodiment of the present invention; 
       FIG. 8  is an explanatory drawing ( 1 ) showing the constitution of a laminated piezoelectric element according to a third embodiment of the present invention; 
       FIGS. 9A and 9B  are each an explanatory drawing ( 2 ) showing the constitution of a laminated piezoelectric element according to a third embodiment of the present invention; 
       FIG. 10  is an explanatory drawing showing a constitution in which a laminated piezoelectric element according to the first to third aspects of the present invention is applied to a fuel injection apparatus; 
       FIGS. 11A to 11D  are each an explanatory drawing showing the method of defining the maximum width (W 0 ) of a laminated piezoelectric element according to the first to third aspects of the present invention in the direction perpendicular to the direction of lamination; 
       FIGS. 12A to 12C  are each an explanatory drawing showing the method of defining the widths (W 1 , W 2 , W 3 ) of external electrode layers in a laminated piezoelectric element according to the first to third aspects of the present invention; 
       FIGS. 13A to 13D  are each an explanatory drawing ( 1 ) showing other embodiments of a laminated piezoelectric element according to the first to third aspects of the present invention; 
       FIGS. 14A to 14D  are each an explanatory drawing ( 2 ) showing other embodiments of a laminated piezoelectric element according to the first to third aspects of the present invention; 
       FIGS. 15A to 15D  are each an explanatory drawing ( 3 ) showing other embodiments of a laminated piezoelectric element according to the first to third aspects of the present invention; 
       FIGS. 16A to 16D  are each an explanatory drawing ( 4 ) showing other embodiments of a laminated piezoelectric element according to the first to third aspects of the present invention; and 
       FIGS. 17A to 17D  are each an explanatory drawing ( 5 ) showing other embodiments of a laminated piezoelectric element according to the first to third aspects of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present invention will be further described with regard to the preferred embodiments thereof, referring to the accompanying drawings. 
   Embodiment 1 
   The following provides an explanation of the constitution of a first embodiment of the present invention referring to the drawings.  FIGS. 1A to 1C  are each an explanatory drawing showing a frontal view ( FIG. 1A ), a perspective view as viewed from arrow X in  FIG. 1A  ( FIG. 1B ), and a perspective view as viewed from arrow Y in  FIG. 1A  ( FIG. 1C ) of a laminated piezoelectric  1  of the present embodiment. As shown, laminated piezoelectric element  1  according to the present embodiment is, broadly speaking, provided with piezoelectric layers  11 , internal electrode layers  21   a  and  21   b,  first external electrode layer  31 , second external electrode layer  32  and lead wire  33 , and is roughly composed in the manner described below. Namely, laminated piezoelectric element  1  is alternately provided with a plurality of piezoelectric layers  11  composed of a PZT ceramic material that expands and contracts when a voltage is applied, and internal electrode layers  21  for supplying an applied voltage. A first electrode  31  is provided on the outer peripheral side of laminated piezoelectric element  1  that is electrically connected so that internal electrode layers  21   a  and  21   b  serve as different poles. Lead wire  33  is provided on first external electrode layer  31  via second external electrode layer  32 . 
   The following provides an explanation of the characteristics of a first aspect of the present invention.  FIGS. 2A and 2B  are each an enlarged view of the essential portion of laminated piezoelectric  1  according to the present embodiment.  FIG. 2A  is a schematic drawing, and  FIG. 2B  shows a section B that is encircled in  FIG. 2A . As shown, in a laminated piezoelectric  1  of the present embodiment, when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode  31  is taken to be W 1 , and the width of second external electrode  32  is taken to be W 2 , the relationship exists in which W 1 &gt;W 2  and 2.5≦(W 2 /W 0 )×100≦60. As a result, as the widths of first external electrode layer  31  and second external electrode layer  32  are not the same, thermal stress generated at both ends of first external electrode layer  31  and second external electrode layer  32  can be dispersed. In addition, as W 1 &gt;W 2 , thermal stress generated in second external electrode layer  32  is not applied directly to piezoelectric  11 . In addition, as there exists the relationship in which 2.5≦(W 2 /W 0 )×100≦60, and thermal stress applied to piezoelectric  11  can be alleviated, together with inhibiting the formation of cracks, bonding strength between lead wire  33  connected to second external electrode layer  32  and second external electrode layer  32  is adequate. In addition, it is more effective if the aforementioned relationship be such that 5≦(W 2 /W 0 )×100≦30 (the effects of this will be described later). 
   In addition, as second external electrode layer  32  is provided continuously in the direction of lamination of piezoelectric layers  11  in piezoelectric active section  1   a  that expands and contracts when a voltage is applied, the thermal stress applied to first external electrode layer  31  and piezoelectric  11  from both ends of second external electrode  32  in the direction of lamination of piezoelectric  11  can be minimized. 
   In addition, when the thickness (after curing) of first external electrode layer  31  is taken to be T 1 , and the thickness (after curing) of second external electrode layer  32  is taken to be T 2 , T 2 /T 1  is within the range of 0.05 to 300. As a result, as the thickness of second external electrode layer  32  is not excessively large relative to the thickness of first external electrode layer  31 , first external electrode layer  31  is able to act as a stress alleviating material and inhibit the formation of cracks in the piezoelectric. In addition, a bonding strength capable of bonding lead wire  33  connected to second external electrode layer  32  with second external electrode layer  32  can be secured. In addition, it is more effective if this relationship is such that 1≦(T 2 /T 1 )≦35 (the effects of this will be described later). 
   In addition, the maximum width W 0  of piezoelectric  11  in the direction perpendicular to the direction of lamination is 15 mm or less. As a result, width W 2  of second external electrode layer  32  is 9.0 mm or less, and thermal stress generated in second external electrode layer  32  does not exceed the strength of piezoelectric layers  11 , thereby making it difficult for cracks to form in piezoelectric layers  11 . 
     FIGS. 3A and 3B  are each an explanatory drawing for explaining the case in which width W 1  of first external electrode layer  31  and width W 2  of second external electrode layer  32  are the same.  FIG. 3A  is a schematic drawing, and  FIG. 3B  shows the manner of the formation of cracks at portion B that is encircled in  FIG. 3A . As shown, in laminated piezoelectric element  1  in which exists the relationship W 1 =W 2 , since stress generated at both ends of first external electrode layer  31  and second external electrode layer  32  is concentrated at piezoelectric  11 , cracks form easily in piezoelectric  11  as shown in crack  11   a.    
   The effects of a first aspect of the present invention will be explained in the following tables. Table 1 shows the relationship between W 1  and W 2  along with the results of measuring thermal stress on the piezoelectric for (W 2 /W 0 )×100 when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , and the width of second external electrode layer  32  is taken to be W 2 . As shown in Table 1, in the case the relationship between W 1  and W 2  is such that W 1 =W 2 , stress generated on the piezoelectric is the greatest, and the generated stress becomes smaller in the order of the case in which W 2 &gt;W 1  followed by the case in which W 1 &gt;W 2 . In addition, in the case W 1 &gt;W 2 , the smaller the value of (W 2 /W 0 )×100, the smaller the amount of stress generated on the piezoelectric. On the basis of this table, the stress generated on the piezoelectric can be seen to become smaller in the case W 1 &gt;W 2  and the smaller the value of (W 2 /W 0 )×100. 
   
     
       
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
                 
               Stress 
             
             
                 
               Relationship 
                 
               Generated on 
             
             
                 
               Between W1 
                 
               Piezoelectric 
             
             
               No. 
               and W2 
               (W2/W0) × 100 
               body (MPa) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               1 
               W1 = W2 
               42.0 
               76.2 
             
             
               2 
               W2 &gt; W1 
               42.0 
               70.0 
             
             
               3 
               W1 &gt; W2 
               60 
               50.4 
             
             
               4 
                 
               42 
               40.2 
             
             
               5 
                 
               35 
               30.3 
             
             
               6 
                 
               30 
               23.0 
             
             
               7 
                 
               24.9 
               20.4 
             
             
               8 
                 
               18.0 
               17.7 
             
             
               9 
                 
               10.0 
               15.2 
             
             
               10 
                 
               4.97 
               13.8 
             
             
               11 
                 
               0.98 
               10.1 
             
             
                 
             
           
        
       
     
   
   Table 2 shows the relationship between W 1  and W 2 , the number of cycles as an indicator of durability, and the results of measuring adhesive strength between second external electrode layer  32  and lead wire  33  for (W 2 /W 0 )×100 when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , and the width of second external electrode layer  32  is taken to be W 2 . The following provides an explanation of the test method. A liquid tank thermal shock tester for performing thermal shock tests was used in the durability test in the present embodiment. First, n (for example, 20) piezoelectric elements to be tested were placed in a sealed container. Next, the piezoelectric elements contained in the sealed container were immersed in a high-temperature liquid tank maintained at a temperature of 160° C. within the liquid tank thermal shock tester and held there for a predetermined amount of time (for example, 10 minutes). Next, the piezoelectric elements contained in the sealed container were immersed in a low-temperature liquid tank maintained at a temperature of −40° C. within the liquid tank thermal shock tester, and held there for a predetermined amount of time (for example, 10 minutes). The process of immersing in the high-temperature liquid tank and the process of immersing in the low-temperature liquid tank were defined as one cycle, and this cycle was repeated. The piezoelectric elements were removed from the liquid tank thermal shock tester when the number of cycles reached 100, 500, 1000 and 1500 cycles followed by confirmation of the formation of cracks in the piezoelectric elements. The piezoelectric elements were evaluated as GOOD in the case there were no cracks in any of the piezoelectric elements at this time, and evaluated as NG (No Good) if even one crack had formed. Here, in the case of using a laminated piezoelectric element according to the present embodiment in an automobile fuel injection apparatus, the result of the evaluation is preferably GOOD when the number of cycles is 1000 or more. In addition, an autographic apparatus for carrying out tensile strength tests on metal materials on so forth was used to measure adhesive strength between second external electrode layer  32  and lead wire  33  in the present embodiment. First, the lead wire was pulled at a constant speed with the autographic apparatus while adjusting the position of the piezoelectric element so that the direction of pulling by the autographic apparatus and the tangent between the piezoelectric element  1  and lead wire  33  were roughly horizontal. Next, the tensile strength when lead wire  33  was partially separated from the piezoelectric element was measured until lead wire  33  completely separated from piezoelectric element  1 , and the average value was defined as the adhesive strength of the lead wire. 
   As shown in Table 2, although sample no. 1 demonstrated the largest adhesive strength between second external electrode layer  32  and lead wire  33  among all the samples, it was evaluated as NG at 100 to 1500 cycles, thus indicating a problem with durability. Although sample nos. 2 and 3 were evaluated as GOOD at 100 and 500 cycles, they were evaluated as NG at 1000 and 1500 cycles. Although sample no. 4 was evaluated as GOOD at 100 and 1000 cycles, it was evaluated as NG at 1500 cycles. Sample nos. 5 to 7 were all evaluated as GOOD at 100 to 1500 cycles, and demonstrated satisfactory durability. Although sample no. 8 was evaluated as GOOD at 100 to 1500 cycles, the adhesive strength between second external electrode layer  32  and lead wire  33  was inadequate. 
   It was determined from this table that durability is satisfactory in the case of the relationship indicated in sample nos. 5 to 7. Here, the actual dimensions of each parameter in sample no. 5, for example, consisted of W 0 =8.4 mm, W 1 =1.6 mm and W 2 =4.0 mm. The present invention is not limited to the case of these dimensions, but rather in the case the relationship between W 1  and W 2  is such that W 1 &gt;W 2 , and in the case (W 2 /W 0 )×100 is within the range of 5 to 30, durability is satisfactory and adhesive strength between second external electrode layer  32  and lead wire  33  is adequate. 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 2 
             
           
           
             
                 
                 
             
             
                 
                 
                 
                 
               Avg. lead 
             
             
                 
               Relationship 
                 
               No. of Cycles 
               wire adhesive 
             
           
        
         
             
               No. 
               between W1 and W2 
               (W2/W0) × 100 
               100 
               500 
               1000 
               1500 
               strength (N) 
             
             
                 
             
           
        
         
             
               1 
               W2 &gt; W1 
               61.4 
               NG 
               NG 
               NG 
               NG 
               3.9 
             
             
               2 
               W1 &gt; W2 
               61.4 
               GOOD 
               GOOD 
               NG 
               NG 
               3.8 
             
             
               3 
                 
               40.3 
               GOOD 
               GOOD 
               NG 
               NG 
               3.3 
             
             
               4 
                 
               25.0 
               GOOD 
               GOOD 
               GOOD 
               NG 
               1.9 
             
             
               5 
                 
               19.0 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               1.3 
             
             
               6 
                 
               6.1 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               0.4 
             
             
               7 
                 
               7.0 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               0.3 
             
             
               8 
                 
               2.5 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               0.1 
             
             
                 
             
           
        
       
     
   
   Table 3 shows the number of cycles as an indicator of durability and the results of measuring adhesive strength between second external electrode layer  32  and lead wire  33  for the relationship between T 1  and T 2  when the thickness (after curing) of first external electrode  31  in piezoelectric  11  is taken to be T 1 , and the thickness (after curing) of second external electrode layer  32  is taken to be T 2 . The test method is the same as that of the previously described test method. As shown in Table 3, sample nos. 1 to 4 were all evaluated as GOOD at 100 to 1500 cycles, indicating satisfactory durability. Although sample no. 5 was evaluated as GOOD at 100 to 1000 cycles, it was evaluated as NG at 1500 cycles. Although sample no. 6 was evaluated as GOOD at 100 and 500 cycles, it was evaluated as NG at 1000 and 1500 cycles. 
   It was determined from this table that durability is satisfactory in the case of the relationship indicated in sample nos. 1 to 4. Here, the actual dimensions of each parameter in sample no. 3, for example, consisted of T 1 =0.015 mm and T 2 =0.15 mm. The present invention is not limited to the case of these dimensions, but rather if the relationship between T 1  and T 2  is such that T 2 /T 1  is within the range of 1 to 35, durability is satisfactory and adhesive strength between second external electrode layer  32  and lead wire  33  is adequate. 
   
     
       
             
             
           
             
             
             
           
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 3 
             
           
           
             
                 
                 
             
             
                 
               Avg. lead 
             
             
                 
               wire 
             
           
        
         
             
                 
               No. of Cycles 
               adhesive 
             
           
        
         
             
               No. 
               T2/T1 
               100 
               500 
               1000 
               1500 
               strength (N) 
             
             
                 
             
           
        
         
             
               1 
               0.05 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               0.3 
             
             
               2 
               5 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               0.4 
             
             
               3 
               10 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               1.5 
             
             
               4 
               20 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               3.2 
             
             
               5 
               40 
               GOOD 
               GOOD 
               GOOD 
               NG 
               5.0 
             
             
               6 
               200 
               GOOD 
               GOOD 
               NG 
               NG 
               6.1 
             
             
                 
             
           
        
       
     
   
   The following provides an explanation of other embodiments according to a first aspect of the present invention referring to  FIGS. 4A to 4C  to  FIGS. 6A to 6C .  FIGS. 4A to 4C  to  FIGS. 6A to 6C  are explanatory drawings showing a laminated piezoelectric element produced by laminating laminated piezoelectric units. The laminated piezoelectric element  1  shown in these drawings is roughly composed in the manner described below. Namely, laminated piezoelectric element  1  is composed of a plurality of piezoelectric units  1   u,  and the plurality of piezoelectric units  1   u  are laminated by means of piezoelectric unit bonding surfaces  1   b  composed of an adhesive. A first external electrode layer  31  is provided on the outer peripheral side of laminated piezoelectric element  1  that is electrically connected so that internal electrode layers  21   a  and  21   b  serve as different poles. Lead wire  33  is provided on first external electrode layer  31  via second external electrode layer  32 . 
   Furthermore, the plurality of piezoelectric units  1   u  may also be laminated without using piezoelectric unit bonding surfaces  1   b  composed of adhesive. 
   In the laminated piezoelectric element  1  shown in  FIGS. 4A to 4C , a second external electrode layer  32  is provided separated by piezoelectric unit bonding surfaces  1   b  and, as it is difficult for second external electrode layer  32  to conform to piezoelectric unit bonding surfaces  1   b,  in the case second external electrode layer  32  is composed of an electrically conductive resin, displacement in piezoelectric layers  11  is restricted by the adhesive component of the electrically conductive resin, thereby making it possible to prevent any decreases in the characteristics, the reliability and so forth. In addition, in comparison with the case of second external electrode layer  32  being provided across piezoelectric unit bonding surfaces  1   b,  as the bonding surface between second external electrode layer  32  and lead wire  33  bonded to second external electrode layer  32  is smaller, it is difficult to impair expansion and contraction of lead wire  33 . Furthermore, although first external electrode layer  31  is provided across piezoelectric unit bonding surfaces  1   b,  if the first external electrode layer  31  is composed of art clay silver, since this typically forms a film having a high viscosity, it is difficult to make it conform to piezoelectric unit bonding surfaces  1   b.    
   In the laminated piezoelectric element  1  shown in  FIGS. 5A to 5C , as second external electrode layer  32  is provided across piezoelectric unit bonding surfaces  1   b,  second external electrode layer  32  can be coated at once, thereby allowing the production of products at low cost. In addition, although first external electrode layer  31  is provided across piezoelectric unit bonding surfaces  1   b,  in the case first external electrode layer  31  is composed of art clay silver, as this typically forms a film having a high viscosity, it is difficult to make it conform to piezoelectric unit bonding surfaces  1   b.    
   In the laminated piezoelectric element shown in  FIGS. 6A to 6C , as second external electrode layer  32  is provided across piezoelectric unit bonding surfaces  1   b,  a second external electrode layer  32  can be coated at once, thereby allowing the production of products at low cost. In addition, as a first external electrode layer  31  is provided separated by piezoelectric unit bonding surfaces  1   b,  it is difficult to make it to conform to piezoelectric unit bonding surfaces  1   b.  In addition, the piezoelectric units can be individually produced and inspected prior to bonding the piezoelectric units, thereby making it possible to improve the productivity as a result of early detection of defective products. 
   In the laminated piezoelectric elements composed by bonding laminated piezoelectric units as shown in  FIGS. 4A to 4C  to  FIGS. 6A to 6C  as well, when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , and the width of second external electrode layer  32  is taken to be W 2 , W 1 &gt;W 2  and 2.5≦(W 2 /W 0 )×100≦60. As a result, as the widths of first external electrode layer  31  and second external electrode layer  32  are not the same, thermal stress generated in both ends of first external electrode layer  31  and second external electrode layer  32  can be dispersed. In addition, since W 1 &gt;W 2 , thermal stress generated in second external electrode layer  32  is not applied directly to piezoelectric  11 . In addition, as the relationship exists in which 2.5≦(W 2 /W 0 )×100≦60, thermal stress on piezoelectric  11  is alleviated and, together with the formation of cracks in the piezoelectric being inhibited, bonding strength between lead wire  33  connected to second external electrode layer  32  and second external electrode layer  32  is adequate. In addition, the relationship in which 5≦(W 2 /W 0 )×100≦30 is even more effective. (the effects of this will be described later.) In addition, as a second external electrode layer  32  is provided continuously in the direction of lamination of piezoelectric layers  11  in piezoelectric active section la that expands and contracts when a voltage is applied, thermal stress applied to first external electrode layer  31  and piezoelectric  11  from both ends of second external electrode layer  32  in the direction of lamination of piezoelectric  11  can be minimized. 
   Embodiment 2 
   The following provides an explanation of the constitution of a second embodiment of the present invention referring to the drawings.  FIGS. 7A and 7B  are each an explanatory drawing showing a laminated piezoelectric element according to a second embodiment of the present invention. As shown, laminated piezoelectric element  1  of the present embodiment has a first external electrode layer  31  provided on the outer peripheral side of a plurality of piezoelectric layers  11  composed of PZT ceramic that expands and contracts when a voltage is applied. A third external electrode layer  32   a  is provided on first external electrode layer  31 . A second external electrode layer  32   b  is provided on third external electrode layer  32   a.    
   This second aspect of the present invention is characterized in that, when the maximum width of laminated piezoelectric element  1  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , the width of second external electrode layer  32   b  is taken to be W 2 , the width of third external electrode layer  32   a  is taken to be W 3 , the thickness (after curing) of second external electrode layer  32   b  is taken to be T 2 , and the thickness (after curing) of third external electrode layer  32   a  is taken to be T 3 , the relationship exists in which W 1 &gt;W 3 &gt;W 2 , 5≦(W 2 /W 0 )×100≦30 and 1≦(T 2 /T 3 )≦35. In addition, first external electrode layer  31 , second external electrode layer  32   b  and third external electrode layer  32   a  are all made of different materials. In addition, when the elastic modulus of first external electrode layer  31  is taken to be E 1  and the coefficient of linear expansion is taken to be α 1 , the elastic modulus of second external electrode layer  32   a  is taken to be E 2  and the coefficient of linear expansion is taken to be α 2 , and the elastic modulus of third external electrode layer  32   a  is taken to be E 3  and the coefficient of linear expansion is taken to be α 3 , E 1 ×α 1 &lt;E 3 ×α 3 &lt;E 2 ×α 2 . 
   According to this second aspect of the present invention, as the widths of first external electrode layer  31 , second external electrode layer  32   b  and third external electrode layer  32   a  are not the same, thermal stress generated in both ends of each of these external electrode layers can be dispersed. In addition, together with thermal stress generated in second external electrode layer  32   b  being alleviated by first external electrode layer  31  and third external electrode layer  32   a,  thermal stress generated in third external electrode layer  32   a  can be alleviated by first external electrode layer  31 . In addition, as W 1 &gt;W 3 &gt;W 2 , thermal stress generated in second external electrode layer  32   b  and third external electrode layer  32   a  is not applied directly to piezoelectric  11 . In addition, as 5≦(W 2 /W 0 )×100≦30 and 1≦(T 2 /T 3 )≦35, thermal stress on piezoelectric  11  is alleviated and, together with the formation of cracks in piezoelectric  11  being inhibited, the bonding strength between lead wire  33  connected to second external electrode layer  32   b  and second external electrode layer  32   b  is adequate. 
   In addition, first external electrode layer  31 , second external electrode layer  32   b  and third external electrode layer  32   a  are all made of different materials. In addition, when the elastic modulus of first external electrode layer  31  is taken to be E 1  and the coefficient of linear expansion is taken to be α 1 , the elastic modulus of second external electrode layer  32   a  is taken to be E 2  and the coefficient of linear expansion is taken to be α 2 , and the elastic modulus of third external electrode layer  32   a  is taken to be E 3  and the coefficient of linear expansion is taken to be α 3 , the relationship exists in which E 1 ×α 1 &lt;E 3 ×α 3 &lt;E 2 ×α 2 . As a result, a material having high adhesive strength can be used for the material of second external electrode layer  32   b  that bonds a lead wire and electrode plate. As materials having high adhesive strength typically also have a large elastic modulus, considerable thermal stress is applied to piezoelectric  11 . In the present invention, however, a material for which the product of the elastic modulus and coefficient of linear expansion is small so as to enable thermal stress generated in second external electrode layer  32   b  to be alleviated can be used for the material of third external electrode layer  32   a.  In addition, since E 1 ×α 1 &lt;E 3 ×α 3 &lt;E 2 ×α 2 , thermal stress can be alleviated in a stepwise manner. 
   In addition, as a second external electrode layer  32   b  is provided continuously in the direction of lamination of piezoelectric layers  11  in piezoelectric active section  1   a  that expands and contracts when a voltage is applied, thermal stress applied to first external electrode layer  31 , third external electrode layer  32   a  and piezoelectric  11  from both ends of second external electrode  32   b  in the direction of lamination of piezoelectric  11  can be minimized. 
   In addition, the maximum width W 0  of piezoelectric  11  in the direction perpendicular to the direction of lamination is 15 mm or less. As a result, width W 2  of second external electrode layer  32   b  is 9.0 mm or less, thermal stress generated in second external electrode layer  32   b  does not exceed the strength of piezoelectric layers  11 , and it is difficult for cracks to form in piezoelectric layers  11 . 
   The effects of this second aspect of the present invention will be explained in the following tables. Table 4 shows the relationship between W 1 , W 2  and W 3  and the results of measuring the stress generated on the piezoelectric for (W 2 /W 0 )×100 and T 2 /T 3  when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , the width of second external electrode layer  32   b  is taken to be W 2 , the width of third external electrode layer  32   a  is taken to be W 3 , the thickness (after curing) of second external electrode layer  32   b  is taken to be T 2 , and the thickness (after curing) of third external electrode layer  32   a  is taken to be T 3 . As shown in Table 4, in the case the relationship among W 1 , W 2  and W 3  is such that W 1 =W 2 =W 3 , the stress generated on the piezoelectric is the greatest, and subsequently becomes smaller in the order of the case in which W 2 &gt;W 1  (two external electrode layers instead of three) and the case in which W 1 &gt;W 3 &gt;W 2 . In addition, in the case W 1 &gt;W 3  &gt;W 2 , the smaller the value of T 2 /T 3 , the smaller the stress generated on the piezoelectric. It can be understood from the table that, in the case the relationship among W 1 , W 2  and W 3  is such that W 1 &gt;W 3 &gt;W 2 , the smaller the value of T 2 /T 3 , the smaller is the stress generated on the piezoelectric. 
   
     
       
             
             
             
             
             
           
         
             
               TABLE 4 
             
             
                 
             
             
                 
                 
                 
                 
               Stress 
             
             
                 
               Relationship 
                 
                 
               generated on 
             
             
                 
               among W1, W2 
                 
                 
               piezoelectric 
             
             
               No. 
               and W3 
               (W2/W0) × 100 
               T2/T3 
               body (MPa) 
             
             
                 
             
           
           
             
               1 
               W2 &gt; W1 
               42.0 
               — 
               70.0 
             
             
                 
               (2 layers) 
             
             
               2 
               W1 &gt; W2 
               42.0 
               — 
               40.2 
             
             
                 
               (2 layers) 
             
             
               3 
               W1 = W2 = W3 
               42.0 
               5.0 
               80.1 
             
             
               4 
               W1 &gt; W3 &gt; W2 
               38.1 
               5.0 
               17.4 
             
             
               5 
                 
               38.1 
               8.3 
               20.4 
             
             
                 
             
           
        
       
     
   
   Table 5 shows the relationship among W 1 , W 2  and W 3 , the number of cycles as an indicator of durability, and the results of measuring adhesive strength between second external electrode layer  32   b  and lead wire  33  for (W 2 /W 0 )×100 and T 2 /T 3  when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0 , the width of first external electrode layer  31  is taken to be W 1 , the width of second external electrode layer  32   b  is taken to be W 2 , the width of third external electrode layer  32   a  is taken to be W 3 , the thickness (after curing) of second external electrode layer  32   b  is taken to be T 2 , and the thickness (after curing) of third external electrode layer  32   a  is taken to be T 3 . The remainder of the test method is the same as Embodiment 1. As shown in Table 5, all of the samples of nos. 1 to 3 were evaluated as GOOD at 100 to 1500 cycles, thus indicating a satisfactory durability. 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 5 
             
           
           
             
                 
                 
             
             
                 
               Material 
               Material 
                 
               Avg. lead 
             
           
        
         
             
                 
                 
               of second 
               of first 
                 
               wire 
             
             
                 
               Relationship 
               external 
               external 
                 
               adhesive 
             
             
                 
               among W1, W2 
               electrode 
               electrode 
               No. of cycles 
               strength 
             
           
        
         
             
               No. 
               and W3 
               (W2/W0) × 100 
               T2/T3 
               layer 
               layer 
               100 
               500 
               1000 
               1500 
               (N) 
             
             
                 
             
             
               1 
               W1 &gt; W3 &gt; W2 
               15.0 
               5.0 
               A 
               A 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               1.3 
             
             
               2 
                 
               15.1 
               8.3 
               A 
               A 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               1.8 
             
             
               3 
                 
               15.1 
               1.5 
               B 
               A 
               GOOD 
               GOOD 
               GOOD 
               GOOD 
               1.3 
             
             
                 
             
           
        
       
     
   
   The following provides an explanation of another embodiment according to this second aspect of the present invention. As the laminated piezoelectric element  1  shown in  FIG. 8  has roughly the same constitution as the laminated piezoelectric element  1  shown in the aforementioned  FIGS. 7A and 7B , an explanation is only provided of the difference between the two, namely the relationship of the widths of the external electrode layers. Namely, although the relationship exists in which W 1 &gt;W 3 &gt;W 2  in the laminated piezoelectric element  1  shown in  FIGS. 7A and 7B  when the width of first external electrode layer  31  is taken to be W 1 , the width of second external electrode layer  32   b  is taken to be W 2 , and the width of third external electrode layer  32   a  is taken to be W 3 , in the laminated piezoelectric element shown in  FIG. 8 , this relationship differs in that W 1 &gt;W 2 &gt;W 3 . However, the two are the same with respect to the following points. Namely, as the widths of first external electrode layer  31  and second external electrode layer  32   b  are not the same, thermal stress generated in both ends of first external electrode layer  31  and second external electrode layer  32   b  can be dispersed. In addition, as W 1 &gt;W 2 , thermal stress generated in second external electrode layer  32   b  is not applied directly to piezoelectric  11 . Accordingly, a laminated piezoelectric element  1  can be provided that is capable of inhibiting the formation of cracks in piezoelectric layers  11 . 
   Embodiment 3 
   The following provides an explanation of the constitution of a third embodiment of the present invention referring to the drawings.  FIGS. 9A and 9B  are each an explanatory drawing showing a laminated piezoelectric element according to a third embodiment of the present invention. As shown, laminated piezoelectric element  1  of the present embodiment is provided with a first external electrode layer  31  on the outer peripheral side of a plurality of piezoelectric layers  11  composed of PZT ceramic that expands and contracts when a voltage is applied. A lead wire  33  is provided on first external electrode layer  31 . 
   This third aspect of the present invention is characterized in that, when the maximum width of piezoelectric  11  in the direction perpendicular to the direction of lamination is taken to be W 0  and the width of first external electrode layer  31  is taken to be W 1 , a relationship exists in which 2.5≦(W 1 /W 0 )×100≦60. As a result, as a relationship exists in which 2.5≦(W 1 /W 0 )×100≦60, and thermal stress applied to piezoelectric  11  can be alleviated, together with inhibiting the formation of cracks, the bonding strength between lead wire  33  connected to first external electrode layer  31  and first external electrode layer  31  is adequate. In addition, the relationship in which 5≦(W 1 /W 0 )×100≦30 is even more effective. 
   In addition, as first external electrode layer  31  is provided continuously in the direction of lamination of piezoelectric layers  11  in piezoelectric active section la that expands and contracts when a voltage is applied, thermal stress applied to piezoelectric  11  from both ends of first external electrode layer  31  in the direction of lamination of piezoelectric  11  can be minimized. 
   In addition, the maximum width W 0  of piezoelectric  11  in the direction perpendicular to the direction of lamination is 15 mm or less. As a result, width W 1  of first external electrode layer  31  is 9.0 mm or less, thermal stress generated in first external electrode layer  31  does not exceed the strength of piezoelectric layers  11 , and it is difficult for cracks to form in piezoelectric layers  11 . 
   Embodiment 4 
     FIG. 10  is an explanatory drawing showing an example of using a laminated piezoelectric element of the present invention in a common rail fuel injection system of a diesel engine. As shown in  FIG. 10 , an injector  5  has an upper housing  52  that houses a drive unit in the form of the aforementioned laminated piezoelectric element  1 , and a lower housing  53  fixed to its lower edge in which an injection nozzle unit  54  is formed inside. 
   Upper housing  52  has a roughly cylindrical shape, and laminated piezoelectric element  1  is inserted and fixed inside a longitudinal hole  521  that is eccentric with respect to the central axis. A high-pressure fuel path  522  is provided in parallel with and to the side of longitudinal hole  521 , and its upper end is connected to an external common module (not shown) through fuel inlet tube  523  that protrudes from the upper side of upper housing  52 . 
   A fuel outlet tube  525  that is continuous with a drain path  524  protrudes from the upper side of upper housing  52 , and fuel that flows out from fuel outlet tube  525  is returned to a fuel tank (not shown). Drain path  524  passes through gap  50  between longitudinal hole  521  and drive unit (laminated piezoelectric element)  1 , and is continuous with a three-way valve  551  to be described later by a path (not shown) that extends downward through upper and lower housings  52  and  53  from this gap  50 . 
   An injection nozzle unit  54  is provided with a nozzle needle  541 , which slides vertically in a piston body  531 , and an injection port  543  that injects high-pressure fuel supplied from a fuel collector  542 , which is opened and closed by nozzle needle  541 , into each cylinder of the engine. Fuel collector  542  is provided around the intermediate portion of nozzle needle  541 , and the lower end of the aforementioned high-pressure fuel path  522  opens herein. Nozzle needle  541  receives fuel pressure in the direction of valve opening from fuel collector  542  while also receiving fuel pressure in the direction of valve closing from back pressure chamber  544  provided facing the upper end and, when the pressure of back pressure chamber  544  drops, nozzle needle  541  lifts, injection port  543  opens and fuel is injected. 
   The pressure of back pressure chamber  544  is regulated by three-way valve  551 . Three-way valve  551  employs a constitution that selectively connects back pressure chamber  544  with high-pressure fuel path  522  or drain path  524 . Here, it has a ball-shaped valve body that opens and closes a port that connects to high-pressure fuel path  522  or drain path  524 . This valve body is driven by the aforementioned drive unit  1  via a large diameter piston  552 , hydraulic chamber  553  and small diameter piston  554  arranged below it. 
   Laminated piezoelectric element  1  for an injector of the present embodiment is characterized in that there exists a relationship among the widths of each of the external electrode layers (W 1 , W 2  and W 3 ) as described in the aforementioned Embodiments 1 to 3 and a relationship of the widths of the external electrode layers (W 1 , W 2 ) to the maximum width (W 0 ) of the laminated piezoelectric element in the direction perpendicular to the direction of lamination. As a result, both the securing of bonding strength between a lead wire or electrode plate connected to the external electrode layer and the external electrode layer as well as an inhibition of crack formation in the piezoelectric can be realized. Accordingly, a laminated piezoelectric element  1  for an injector can be provided that can be used in harsh environments and which is highly reliable. 
   Production Method: 
   The following provides an explanation of the production method of laminated piezoelectric element  1  and its detailed structure. A laminated piezoelectric element  1  described herein can be produced using the well-known green sheet method. A powder such as lead oxide, zirconium oxide, titanium oxide, niobium oxide or strontium carbonate serving as the primary raw material of the piezoelectric material is weighed out to the desired composition in accordance with known methods. In addition, the aforementioned mixing ratio composition is prepared to be 1 to 2% richer than the stoichiometric ratio in consideration of evaporation of lead. This is then dry mixed with a mixer followed by calcining at 800 to 950° C. 
   Next, pure water and a dispersant are added to form a slurry followed by wet crushing with a ball mill. After drying and degreasing this crushed powder, a solvent, a binder, a plasticizer and a dispersant, and so forth, are added followed by mixing with a ball mill. Subsequently, the slurry is vacuum degassed and its viscosity is adjusted while agitating with an agitator in a vacuum device. 
   Next, the slurry is molded into a green sheet of a predetermined thickness by a doctor blade device. The resulting green sheet is either stamped out with a press or cut with a cutter to mold it to a predetermined size. 
   Next, a pattern is screen printed on one surface of the green sheet following molding with, for example, a silver and palladium paste composed of silver and palladium at a ratio (% by weight) of 7:3 (hereinafter, referred to as Ag/Pd paste). 
   A pattern having a slightly smaller surface than the surface of piezoelectric layers  11  is formed over substantially the entire surface of the green sheet to serve as piezoelectric sheet  11 , using the aforementioned Ag/Pd paste, to serve as internal electrode layers  21   a  and  21   b.  A section having no internal electrode layer  21   a  ( 21   b ) formed is provided on the other side in opposition to the surface of the green sheet. In other words, internal electrode layer  21   a  ( 21   b ) does not reach one end of the opposing side of the green sheet (section equivalent to side  101  or the opposing surface of laminated piezoelectric element  1 ), while internal electrode layer  21   a  ( 21   b ) does reach the other opposing end. 
   A predetermined number of laminated layers of green sheets, on which internal electrode layers  21   a  and  21   b  are formed in this manner, are prepared. 
   Next, these green sheets are then laminated. In the case of laminating green sheets on which internal electrode layers  21   a  and  21   b  are formed, they are laminated so that the sections where electrodes are not formed are alternately positioned on side  101  of laminated piezoelectric element  1  and its opposing side. As a result, internal electrode layer  21   a,  which is exposed by extending to green sheet side  101 , serves as the internal electrode of one pole, while internal electrode layer  21   b,  which is exposed by reaching the opposing side, serves as the internal electrode of the other pole. As a result, the laminate has the structure shown in  FIGS. 1A to 1C . 
   Next, after hot-pressing with a hot-water rubber press, the laminate is degreased at 400 to 700° C. with an electric furnace and then fired at a temperature of 900 to 1200° C. 
   Next, a silver paste for firing is screen printed onto the side of the aforementioned laminate followed by firing to form first external electrode layer  31 . First external electrode layer  31  is formed at the location where internal electrode layers  21   a  of one of the poles are exposed and has electrical continuity with each internal electrode  21   a.  First external electrode  31  provided on the opposing side (not shown) is formed at the location where internal electrode layers  21   b  of the other pole are exposed and has electrical continuity with each internal electrode layer  21   b.  Furthermore, although first external electrode layer  31  is composed of silver paste for baking in this example, it can also be formed by baking a paste composed of a metal consisting of at least one selected from palladium, platinum, copper, gold, nickel, tin, lead, zinc or bismuth, or an alloy thereof. In addition, it can also be formed with solder or by coating an electrically conductive resin. Next, a second external electrode layer ( 32 ,  32   b ) composed of an electrically conductive resin is coated on first external electrode layer  31  (this is not required in Embodiment 3, namely in the case of a single external electrode layer). Next, a third external electrode layer  32   a  composed of an electrically conductive resin is coated onto second external electrode layer  32   b  composed of an electrically conductive resin (this step is not required in Embodiment 1, namely in the case of using two external electrode layers). 
   Preferably, each external electrode layer should be made of a different material. Examples of materials that should be used for first external electrode layer  31  include materials that have a small difference in coefficient of linear expansion with piezoelectric  11  such as at least one metal selected from silver, palladium, platinum, copper, gold, nickel, tin, lead, zinc and bismuth, or an alloy thereof. Solder or an epoxy-based electrically conductive resin containing silver should be used for the second external electrode layer ( 32 ,  32   b ). If the second external electrode layer ( 32 ,  32   b ) is composed of an epoxy-based electrically conductive resin containing silver, the material of the third external electrode layer  32   a  should be a material for which the product of its elastic modulus and coefficient of linear expansion is intermediate to that of first external electrode layer  31  and second external electrode layer  32   b,  such as a material composed of a silicon-modified epoxy-based electrically conductive resin containing silver. As materials having high adhesive strength typically have a large elastic modulus, considerable thermal stress is applied to piezoelectric  11 . However, due to the effects of third external electrode layer  32   a,  a material having high adhesive strength can be used for the material of second external electrode layer  32   b  that bonds a lead wire or electrode plate. 
   Next, a lead wire  33  is bonded to the second external electrode layer ( 32 ,  32   b ). 
   Although the lead wire is typically bonded at the time of curing the second external electrode layer, bonding of the lead wire may also be carried out when curing of the third external electrode layer and second external electrode layer. 
   Next, laminated piezoelectric element  1  is placed in air or immersed in an insulating oil as necessary and a direct current voltage is applied via lead wire  33  between internal electrode layers  21   a  and  21   b  to polarize the piezoelectric layers  11  and obtain laminated piezoelectric element  1 . 
   General Precautions: 
   The following provides an explanation of the method for defining the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination (W 0 ), and the widths of each external electrode layer (W 1 , W 2  and W 3 ), in the first through third aspects of the present invention referring to  FIGS. 11A to 11D  to  FIGS. 13A to 13D . 
   An explanation is first provided of the method for defining the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination (W 0 ) in the first through third aspects of the present invention referring to  FIGS. 11A to 11D .  FIGS. 11A to 11D  are cross-sectional views of laminated piezoelectric elements in the direction perpendicular to the direction of lamination. In the laminated piezoelectric element  1  shown in  FIG. 11A , the shape of its cross-section is roughly square. At this time, the maximum width W 0  in this cross-section is the length of the line that connects two facing corners of the square. In the laminated piezoelectric element  1  shown in  FIG. 11B , the shape of its cross-section is roughly rectangular. At this time, the maximum width W 0  in this cross-section is the length of the line that connects two facing corners of the rectangle. In the laminated piezoelectric element  1  shown in  FIG. 11C , the shape of its cross-section is roughly an oval. At this time, the maximum width W 0  in this cross-section is the length of the axial line in the lengthwise direction of the oval. In the laminated piezoelectric element  1  shown in  FIG. 11D , the cross-section has two curved sections and has a shape in which the corresponding ends of the two curved sections are connected with straight lines (in the shape of a race track). At this time, the maximum width W 0  in this cross-section is the length of the line that connects the corresponding apices of the two curved sections. 
   Furthermore, the cross-sectional shape of the laminated piezoelectric element is not limited to the shapes shown in  FIGS. 11A to 11D , but rather may also be an octahedron or another polygon. 
   The following provides an explanation of the method for defining the widths of each external electrode layer (W 1 , W 2  and W 3 ) in the laminated piezoelectric elements of the first to third aspects of the present invention referring to  FIGS. 12A to 12C .  FIG. 12A  is a side view of laminated piezoelectric element  1 ,  FIG. 12B  is a cross-sectional view of laminated piezoelectric element  1  in the direction perpendicular to the direction of lamination, and  FIG. 12C  is a partial cross-sectional view of laminated piezoelectric element  1  in the direction perpendicular to the direction of lamination. The widths of each external electrode layer (W 1 , W 2 , W 3 ) are defined as the average values of the widths of each external electrode layer in piezoelectric active section  1   a  of laminated piezoelectric element  1 . In the laminated piezoelectric element  1  shown in  FIG. 12A , the width of external electrode layer  31  is not constant. At this time, the width of external electrode layer  31  is defined as the average value of the width of external electrode layer  31  at piezoelectric active section  1   a  of laminated piezoelectric element  1 . In the laminated piezoelectric elements  1  shown in  FIGS. 12B and 12C , external electrode layer  31  is provided extending across two surfaces. At this time, the width of external electrode layer  31  is defined as the average value of the minimum width between the intersecting points of normal lines A and B relative to the side of piezoelectric  11  and both ends of external electrode layer  31  (width between  31   a  and  31   b ). 
   As has been described above, according to the first to third aspects of the present invention, by defining the relationships between the widths of each external electrode layer (W 1 , W 2  and W 3 ) and the widths of the external electrode layers (W 1 , W 2 ) relative to the maximum width of the laminated piezoelectric element in the direction perpendicular to the direction of lamination (W 0 ), a laminated piezoelectric element can be provided that realizes both secure bonding strength between a lead wire or electrode plate connected to an external electrode layer and the external electrode layer as well as inhibition of crack formation in the piezoelectric. 
   Furthermore, the constitution applied to the present invention is not limited to the constitutions of the above-described embodiments provided the object of the present invention is able to be achieved. For example, the shape of each piezoelectric layer  11  is not limited to a quadrangle, but rather may also be a octagon or other polygon. In addition, the external electrode layers may formed by screen printing, deposition, mask-coating using a metal mask or coating with a dispenser. In addition, the materials of the external electrode layers may all be the same. In addition, the shape of the external electrode layers may be suitably changed, and as shown in  FIG. 13A  for example, external electrode layer  31 , which is provided continuously on the outer peripheral side of laminated piezoelectric element  1  in the direction of lamination of piezoelectric  11  at a piezoelectric active section that expands and contracts when a voltage is applied, may be separated at bonding surface  1   b  of the piezoelectric units, while the separated external electrode layer  31  may be provided mutually differently offset in the direction orthogonal to the direction of lamination of piezoelectric  11 . In addition, as shown in  FIG. 13B , an external electrode layer  31  may also be provided diagonally relative to axial line A in the direction of lamination of piezoelectric layers  11  on the outer peripheral side of laminated piezoelectric element  1 . In addition, as shown in  FIG. 13D , external electrode layer  31  may also be provided in a corrugated manner relative to axial line A in the direction of lamination of piezoelectric layers  11  on the outer peripheral side of laminated piezoelectric element  1 . In addition, as shown in  FIG. 13C , an external electrode layer  31  may also be provided in the shape of a circle. In addition, the electrode that supplies a voltage from an external power supply to an external electrode layer is not limited to a lead wire, but rather may also be a plate-like electrode  33  in the shape of a plate and having a plurality of openings as shown in  FIGS. 14A to 14D  to  FIGS. 16A to 16D . In addition, laminated piezoelectric element  1  may also be in the form of a laminated piezoelectric element in which indentations are provided in the side of piezoelectric layers  11 , to alleviate an internal stress caused by operation of laminated piezoelectric element  1 , as shown in  FIGS. 17A to 17D .