JP2006203070A - Lamination piezoelectric element - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a lamination piezoelectric element whereby the occurrence of cracks or the like extended in a lamination direction of a lamination body can be prevented. <P>SOLUTION: The lamination piezoelectric element 1 is provided with the lamination body 2, and the lamination body 2 is formed by laminating and sintering a plurality of piezoelectric bodies 3, a plurality of internal electrodes 4A, and a plurality of internal electrodes 4B. The internal electrodes 4A, 4B are alternately laminated via the piezoelectric body 3. A part overlapped with the internal electrodes 4A, 4B in the lamination body 2 is an active part P at which the piezoelectric body 3 is displaced when a voltage is applied between the internal electrodes 4A, 4B, and a part not overlapped with the internal electrodes 4A, 4B is an inactive part Q at which no piezoelectric body 3 is displaced. A plurality of low strength layers 5 with the density (strength) lower than that of the piezoelectric body 3 is provided to the inactive part Q of the lamination body 2 by each of a prescribed number of layers. The low strength layer 5 is formed with a piezoelectric ceramic material whose composition is the same as that of a piezoelectric ceramic material for forming the piezoelectric body 3. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a laminated piezoelectric element used in, for example, a fuel injection device.

As a conventional multilayer piezoelectric element, for example, as described in Patent Document 1, it has a multilayer body in which piezoelectric ceramic layers and internal electrodes are alternately stacked, and between adjacent internal electrodes in the multilayer body. One in which a stress relaxation layer is formed for each predetermined layer is known.
JP 2001-267646 A

  However, in the above prior art, the piezoelectric ceramic layer is formed of lead zirconate titanate or the like, and the stress relaxation layer is formed of a material mainly composed of lead titanate. That is, the piezoelectric ceramic layer and the stress relaxation layer are formed of materials having different composition systems. For this reason, since the shrinkage and expansion rates of the piezoelectric ceramic layer and the stress relaxation layer are different, when the laminate is fired, for example, the laminate is cracked or a crack extending in the stacking direction is induced in the active portion of the laminate. there is a possibility.

  An object of the present invention is to provide a multilayer piezoelectric element capable of preventing the occurrence of cracks and the like extending in the stacking direction of the multilayer body.

  The present invention is a multilayer piezoelectric element including a multilayer body obtained by alternately laminating and sintering a plurality of piezoelectric bodies and a plurality of internal electrodes including a first electrode and a second electrode. An active portion configured such that the first electrode and the second electrode overlap in the stacking direction of the stacked body, and an inactive configuration configured such that the first electrode and the second electrode do not overlap in the stacking direction of the stacked body The inactive portion is provided with a low-strength layer having a lower strength than the piezoelectric body, and the piezoelectric body and the low-strength layer are formed of a piezoelectric material having the same composition system. It is what.

  When manufacturing such a laminated piezoelectric element, a laminated body having a plurality of piezoelectric bodies, a plurality of internal electrodes, and a low-strength layer is obtained by firing. The low-strength layer is made of a piezoelectric material having the same composition as that of the piezoelectric body. For this reason, since the shrinkage and expansion rates of the piezoelectric body and the low-strength layer are equal, it is possible to prevent the laminate (sintered body) from being cracked, cracks extending in the stacking direction, and the like. In addition, since the piezoelectric material having the same composition system is used, an unnecessary reaction does not occur between the piezoelectric body and the low-strength layer, so that the formation of the piezoelectric body and the low-strength layer is hardly adversely affected. In the multilayer piezoelectric element thus manufactured, when a voltage is applied between the first electrode and the second electrode, an electric field is generated between them, and the piezoelectric body in the active portion of the multilayer body is displaced. At this time, stress concentrates on the inactive part of the laminate, but the inactive part is provided with a low-strength layer with lower strength than the piezoelectric body, so the stress on the inactive part is relieved by the low-strength layer. Will come to be. Accordingly, it is possible to prevent cracks extending in the stacking direction from occurring in the stacked body when the piezoelectric body is displaced.

  Preferably, the low strength layer is a layer having a density lower than that of the piezoelectric body. Thereby, a low intensity layer can be formed easily and reliably.

  At this time, the piezoelectric body and the low-strength layer are formed by a paste in which a substance containing a binder is mixed with a piezoelectric material, and the ratio of the amount of the binder to the piezoelectric material forming the low-strength layer forms the piezoelectric body. It is preferably larger than the ratio of the amount of the binder to the piezoelectric material. When the ratio of the amount of the binder to the piezoelectric material is increased in this way, holes are easily formed when fired, resulting in a low density. Therefore, even when a piezoelectric material having exactly the same composition is used as the piezoelectric material and the piezoelectric material of the low-strength layer, the density is higher than that of the piezoelectric body simply by increasing the ratio of the binder amount to the piezoelectric material forming the low-strength layer. A low-strength layer having a low thickness can be reliably formed.

  The piezoelectric body and the low-strength layer are formed by a paste in which a material containing a binder is mixed with a piezoelectric material, and the sintering temperature of the piezoelectric material forming the low-strength layer is that of the piezoelectric material forming the piezoelectric body. It may be higher than the sintering temperature. In this case, if the laminate is fired at a temperature between the sintering temperature of the piezoelectric material forming the piezoelectric body and the sintering temperature of the piezoelectric material forming the low-strength layer, the piezoelectric material forming the piezoelectric body is completely Even if sintered, the piezoelectric material forming the low-strength layer is in an unsintered state, so that the low-strength layer having a lower density than the piezoelectric body can be reliably formed.

  Preferably, the low-strength layer extends into the active part region. Thus, for example, when a crack occurs in the inactive portion of the laminate when the piezoelectric body is displaced in the active portion of the laminate, the crack is perpendicular to the stacking direction of the laminate along the low-strength layer. Since it becomes easy to enter, generation | occurrence | production of the crack extended in the lamination direction of a laminated body can be prevented more reliably.

  Further, preferably, a crack extending in a direction perpendicular to the stacking direction of the stacked body is formed in the low-strength layer. Even in such a configuration, for example, when a crack occurs in the inactive part of the laminate when the piezoelectric body is displaced in the active part of the laminate, the direction perpendicular to the stacking direction of the laminate along the low-strength layer Therefore, it is possible to more reliably prevent the occurrence of cracks extending in the stacking direction of the laminate.

  According to the present invention, it is possible to prevent a crack or the like extending in the stacking direction from occurring in the stacked body. As a result, the occurrence of cracks extending from the first electrode to the second electrode is avoided, so that the dielectric breakdown of the multilayer piezoelectric element can be prevented and the durability of the multilayer piezoelectric element can be improved.

  DESCRIPTION OF EMBODIMENTS Hereinafter, preferred embodiments of a multilayer piezoelectric element according to the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a perspective view showing an embodiment of a multilayer piezoelectric element according to the present invention. 2 is a side view of the multilayer piezoelectric element shown in FIG. 1, and FIG. 3 is a partially enlarged sectional view of the multilayer piezoelectric element shown in FIG. In each figure, the laminated piezoelectric element 1 of the present embodiment is used for a fuel injection device of an internal combustion engine mounted on an automobile, for example.

  The multilayer piezoelectric element 1 includes a quadrangular prism-shaped multilayer body 2. The multilayer body 2 is formed by laminating and sintering a plurality of piezoelectric bodies 3, a plurality of internal electrodes 4A, and a plurality of internal electrodes 4B. The dimension of the multilayer piezoelectric element 1 is, for example, about 10 mm × 10 mm × 35 mm. The thickness of the piezoelectric body 3 is about 80 to 100 μm per layer.

The piezoelectric body 3 is made of, for example, a piezoelectric ceramic material mainly composed of PZT (lead zirconate titanate). Examples of the composition of PZT include the following.
Pb0.999 [(Zn1 / 3 Nb2 / 3) 0.11 Ti0.425 Zr0.465] O ₃ + 0.2wt% Fe ₂ O ₃ + 0.2wt% Sb ₂ O ₃
As the powder characteristics of PZT, for example, the BET specific surface area is about 2.5 m ² / g, and the average particle size is about 0.6 μm. The sintering temperature of such PZT is about 950 ° C.

  The internal electrodes 4A and 4B are alternately stacked with the piezoelectric bodies 3 interposed therebetween. The internal electrode 4A is formed so as to be exposed from the inside of the side surface 2b of the multilayer body 2 to the opposite side surface 2a, and the internal electrode 4B is formed so as to be exposed from the inside of the side surface 2a of the multilayer body 2 to the side surface 2b. ing. Thereby, a part of the internal electrodes 4 </ b> A and 4 </ b> B is overlapped in the stacking direction of the stacked body 2. In the laminate 2, the portion where the internal electrodes 4A, 4B overlap is an active portion P where the piezoelectric body 3 is displaced when a voltage is applied between the internal electrodes 4A, 4B, and the portion where the internal electrodes 4A, 4B do not overlap ( The both end portions of the multilayer body 2 are inactive portions Q where the piezoelectric body 3 is not displaced when a voltage is applied between the internal electrodes 4A and 4B. The internal electrodes 4A and 4B are made of a conductive material containing Ag and Pd as main components, for example.

  In the inactive portion Q of the multilayer body 2, a plurality of low-strength layers 5 having a density (strength) lower than that of the piezoelectric body 3 are provided for each predetermined number of layers. These low-strength layers 5 are formed in the inactive portion Q of the stacked body 2 so as to extend into the region of the active portion P at a position between the internal electrodes 4A and 4B adjacent in the stacking direction of the stacked body 2. . Each low-strength layer 5 is formed from one edge to the other edge of each of the side surfaces 2a and 2b (see FIG. 1). The low-strength layer 5 is formed of a piezoelectric ceramic material having the same composition as that of the piezoelectric ceramic material forming the piezoelectric body 3.

  The low-strength layer 5 may contain cracks (slits) extending in the lateral direction of the stacked body 2 (direction perpendicular to the stacking direction of the stacked body 2). The crack extending in the lateral direction of the laminate 2 serves to reduce the stress applied to the inactive portion Q of the laminate 2 when the piezoelectric body 3 is displaced in the active portion P of the laminate 2.

  An external electrode 6A electrically connected to each internal electrode 4A is provided on the side surface 2a of the multilayer body 2, and an external electrode 6B electrically connected to each internal electrode 4B is provided on the side surface 2b of the multilayer body 2. Is provided.

  The external electrodes 6A and 6B are arranged on the outer side of the electrode portion 7 and the electrode portion 7 extending in the stacking direction of the stack 2 so as to cover a part of the side surfaces 2a and 2b of the stack 2, respectively. The electrode portion 8 extends in a wave shape in the stacking direction of the body 2. The electrode portion 8 is joined to the electrode portion 7 so as to have stretchability (flexibility) in the stacking direction of the stacked body 2. The electrode part 7 is made of a conductive material containing, for example, one of Ag, Au, and Cu as a main component. The electrode portion 8 is made of, for example, Cu and its alloy, Ni and its alloy, a flexible substrate, or the like.

  Next, a method for manufacturing the multilayer piezoelectric element 1 described above will be described with reference to FIG. First, a paste is prepared by mixing an organic binder resin, an organic solvent, and the like with ceramic powder containing PZT as a main component. Then, a plurality of ceramic green sheets 9 to be the piezoelectric bodies 3 are formed by applying the paste on a carrier film (not shown) by, for example, a doctor blade method.

  Subsequently, for example, a paste is prepared by mixing an organic binder resin, an organic solvent, and the like with a conductive material having a ratio of Ag: Pd = 85: 15. Then, the paste is screen-printed to form electrode patterns 10A corresponding to the internal electrodes 4A and electrode patterns 10B corresponding to the internal electrodes 4B on the upper surfaces of the separate green sheets 9.

  Subsequently, as in the method for forming the green sheet 9, a paste is prepared by mixing an organic binder resin, an organic solvent, and the like with ceramic powder mainly composed of PZT. Then, the low-strength layer is formed on a predetermined portion of the upper surface of the green sheet 9 different from the green sheet 9 on which the electrode pattern 10A is printed and the green sheet 9 on which the electrode pattern 10B is printed by screen printing the paste. 5 is formed. At this time, the ratio of the amount of the organic binder resin mixed with the ceramic powder is made larger than the ratio of the amount of the organic binder resin mixed with the ceramic powder forming the green sheet 9.

  Subsequently, the green sheet 9 on which the electrode pattern 10A is printed, the green sheet 9 on which the electrode pattern 10B is printed, and the green sheet 9 on which the ceramic layer 11 is printed are stacked in a predetermined order by a predetermined number of sheets. The green laminate 12 is produced by laminating the green sheets 9 on which the patterns 10A and 10B and the ceramic layer 11 are not printed on the outermost layer.

  Subsequently, the green laminate 12 is pressed in the laminating direction at a pressure of about 100 MPa while heating the green laminate 12 at a temperature of about 60 ° C., and then the green laminate 12 is cut into a predetermined dimension by, for example, a diamond blade. As a result, as shown in FIG. 4, the electrode patterns 10 </ b> A and 10 </ b> B and the ceramic layer 11 are exposed on the side surface of the green laminate 12.

  Subsequently, the cut green laminate 12 is placed on a setter, and the green laminate 12 is degreased (debinder) at a temperature of about 400 ° C. for about 10 hours, for example. Thereafter, the setter on which the degreased green laminate 12 is placed is placed in a mortar furnace, and the green laminate 12 is baked at a temperature of about 1000 ° C. for about 2 hours, for example. Thereby, the green laminated body 12 is shrink-sintered, and the above laminated body 2 is obtained as a sintered body.

  At this time, as described above, the ratio of the amount of the organic binder resin to the ceramic material forming the ceramic layer 11 is larger than the ratio of the amount of the organic binder resin to the ceramic material forming the ceramic green sheet 9. A hole is easily formed in the ceramic layer 12. For this reason, the ceramic layer 12 becomes the low-strength layer 5 having a density (strength) lower than that of the piezoelectric body 3.

  Here, since the ceramic layer 12 is formed of a ceramic material mainly composed of PZT having the same composition as the green sheet 9, the shrinkage rate of the ceramic layer 12 is equal to the shrinkage rate of the green sheet 9. Therefore, unlike the case where a material different from PZT, for example, a binder (resin paint) or PT (lead titanate) is applied or printed on the upper surface of the green sheet 9 and baked, the laminate 2 is cracked. There is almost no induction of cracks extending in the stacking direction in the stack 2. In addition, since the ceramic materials of the green sheet 9 and the ceramic layer 12 have the same composition, unnecessary reaction does not occur between the green sheet 9 and the ceramic layer 12. For this reason, it is prevented that a part of composition of the piezoelectric material 3 and the low-strength layer 5 is changed, and the low-strength layer 5 is formed so as to burn up cleanly as a whole.

  Subsequently, the external electrode 6A is formed on the side surface 2a of the multilayer body 2, and the external electrode 6B is formed on the side surface 2b of the multilayer body 2. Specifically, first, for example, a conductive paste containing Ag as a main component is screen-printed on the side surfaces 2a and 2b of the multilayer body 2, and then subjected to a baking process at a temperature of about 700 ° C., for example, to each of the side surfaces 2a and 2b. The electrode part 7 is formed. In addition, as a formation method of this electrode part 7, you may use sputtering method, an electroless plating method, etc. instead of baking. And the electrode part 8 extended in a wave shape is joined with the electrode part 7 in a several location, for example by soldering.

  Finally, for example, under a temperature of 120 ° C., a polarization process is performed by applying a predetermined voltage, for example, for 3 minutes so that the electric field strength with respect to the thickness of the piezoelectric body 3 becomes 2 kV / mm. In this polarization treatment, stress concentrates on the inactive portion Q of the laminate 2, but the inactive portion Q is provided with the low-strength layer 5 having a lower strength than other portions. Cracks extending in the lateral direction (direction perpendicular to the stacking direction of the stacked body 2) may enter the strength layer 5. Thus, the multilayer piezoelectric element 1 is completed.

  In such a laminated piezoelectric element 1, when a voltage is applied between the external electrodes 6A and 6B, a voltage is applied between the internal electrodes 4A and 4B connected to the external electrodes 6A and 6B. Thereby, an electric field is generated in the piezoelectric body 3 of the active part P sandwiched between the internal electrodes 4A and 4B, and the piezoelectric body 3 is displaced in the stacking direction of the stacked body 2.

  Here, since the low strength layer 5 is formed in the inactive portion Q of the multilayer body 2, for example, when the multilayer piezoelectric element 1 is used over a long period of time, the displacement of the piezoelectric body 3 of the active portion P causes When a crack that extends from the side surfaces 2 a and 2 b of the stacked body 2 to the inside of the stacked body 2 occurs, the crack extends along the low-strength layer 5 in the lateral direction of the stacked body 2. At this time, by forming the low-strength layer 5 in the region of the active portion P, cracks extending in the lateral direction of the multilayer body 2 are likely to occur when the piezoelectric body 3 is displaced. Further, as described above, when the low-strength layer 5 has cracks in advance, cracks extending in the lateral direction of the laminate 2 are more likely to occur. Accordingly, the stress applied to the other inactive portions Q when the piezoelectric body 3 is displaced is sufficiently relaxed, so that no cracks are generated in the stacking direction of the stacked body 2.

  Moreover, even if the electrode part 7 of the external electrodes 6A and 6B is cut at the position due to a crack in the low-strength layer 5, the wavy electrode part 8 is connected to the electrode part 7. The electrical connection between the internal electrode 4A and the external electrode 6A and the electrical connection between the internal electrode 4B and the external electrode 6B remain ensured.

  As described above, according to the present embodiment, the piezoelectric body 3 and the low-strength layer 5 of the multilayer body 2 are formed of the piezoelectric ceramic material having the same composition. Therefore, when the multilayer piezoelectric element 1 is manufactured, the multilayer body 2 is fired. It is possible to prevent the occurrence of cracks and cracks extending in the stacking direction. In addition, it is possible to prevent a crack extending in the stacking direction from occurring in the stacked body 2 when the stacked piezoelectric element 1 is driven. Therefore, the internal electrodes 4A and 4B are prevented from being short-circuited, and the dielectric breakdown of the multilayer piezoelectric element 1 can be avoided. As a result, the quality of the multilayer piezoelectric element 1 is improved.

  In the multilayer piezoelectric element 1 described above, a ceramic material mainly composed of PZT having the same composition as the material of the piezoelectric body 3 is used as the material of the low-strength layer 5, and the ratio of the amount of the organic binder resin to the ceramic material is set. By changing, the low strength layer 5 having a density lower than that of the piezoelectric body 3 was formed. However, the method for forming the low strength layer 5 is not particularly limited thereto.

For example, as the material of the low-strength layer 5, a ceramic material mainly composed of PZT having the same composition system as that of the piezoelectric body 3 and a sintering temperature higher than that of the piezoelectric body 3 may be used. In order to increase the sintering temperature of PZT, the composition of PZT itself may be changed, or PZT having larger powder (particles) than PZT forming piezoelectric body 3 may be used. Examples of the PZT include the following.
Pb [Ti0.47 Zr0.53] O ₃ + 0.5wt% Nb ₂ O ₅
As the powder characteristics of PZT, for example, the BET specific surface area is about 1.4 m ² / g, and the average particle size is about 1.5 μm. The sintering temperature of such PZT is about 1200 ° C.

  In this way, the low-strength layer 5 is formed of a ceramic material having a sintering temperature higher than that of the piezoelectric body 3, that is, a ceramic material having a low sintering property, thereby firing the green laminate 12 as shown in FIG. When performed at a temperature of about 0 ° C., the ceramic layer 11 becomes unsintered although the green sheet 9 is completely sintered. Therefore, the low-strength layer 5 having a sufficiently lower density than the piezoelectric body 3 can be formed without adjusting the amount of the organic binder resin with respect to the ceramic material.

  The present invention is not limited to the above embodiment. For example, the structure of the multilayer body 2 having the piezoelectric body 3, the internal electrodes 4A and 4B, and the low-strength layer 5 can be variously modified. Specifically, as shown in FIG. 5, the low-strength layer 5 may be formed at a position between the internal electrodes 4A and 4A adjacent to each other in the stacking direction of the stacked body 2 or between the internal electrodes 4B and 4B.

  In addition, as shown in FIG. 6, dummy electrodes 13 may be provided between the low-strength layers 5 formed at both end portions of the stacked body 2. When the laminate 2 having the dummy electrode 13 is manufactured, although not shown, a ceramic layer corresponding to the low-strength layer 5 and an electrode pattern corresponding to the dummy electrode 13 are printed on the upper surface of the ceramic green sheet. Thereafter, this green sheet and a green sheet with an electrode pattern may be laminated. By providing the dummy electrode 13 in the laminated body 2 in this manner, the adhesive force between the upper and lower piezoelectric bodies 3 sandwiching the dummy electrode 13 is reduced, so that cracks generated in the low-strength layer 5 are lateral along the dummy electrode 13. It will extend to. Thereby, the crack extended in the lamination direction of the laminated body 2 becomes still more difficult to produce.

  Further, as shown in FIG. 7, the low-strength layer 5 is formed at a position between the internal electrodes 4A and 4A adjacent to each other in the stacking direction of the multilayer body 2 or between the internal electrodes 4B and 4B. A dummy electrode 13 may be provided between the low-strength layers 5 formed in the portion.

  In addition, as shown in FIG. 8, the low-strength layer 5 may be formed entirely from one side surface of the laminate 2 to the other side surface. In this case, the crack that enters the low-strength layer 5 from the side surface of the laminate 2 extends in the lateral direction along the low-strength layer 5 as it is. Thereby, the crack extended in the lamination direction of the laminated body 2 becomes still more difficult to produce.

  In the multilayer piezoelectric element of the above embodiment, the low-strength layer 5 is formed so as to extend into the region of the active part P of the multilayer body 2. Of course, it does not matter if it is formed only.

  Furthermore, in the multilayer piezoelectric element of the above embodiment, the shape of the multilayer body 2 is a quadrangular prism shape, but may be other polygonal column shapes or cylindrical shapes. In addition, the position where the external electrodes 6A and 6B are provided on the side surface of the multilayer body 2 may be any position that does not contact each other.

1 is a perspective view showing an embodiment of a multilayer piezoelectric element according to the present invention. FIG. 2 is a side view of the multilayer piezoelectric element shown in FIG. 1. It is a partial expanded sectional view of the laminated body shown in FIG. It is a disassembled perspective view which shows the state after the cutting | disconnection of the green laminated body produced when manufacturing the lamination type piezoelectric element shown in FIG. It is a partial expanded sectional view which shows the modification of the laminated body shown in FIG. It is a partial expanded sectional view which shows the other modification of the laminated body shown in FIG. It is a partial expanded sectional view which shows the other modification of the laminated body shown in FIG. It is a partial expanded sectional view which shows the other modification of the laminated body shown in FIG.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Laminated piezoelectric element, 2 ... Laminated body, 3 ... Piezoelectric body, 4A ... Internal electrode (1st electrode), 4B ... Internal electrode (2nd electrode), 5 ... Low-strength layer, P ... Active part, Q ... Inactive part.

Claims (6)

A laminated piezoelectric element comprising a laminate formed by alternately laminating and sintering a plurality of piezoelectric bodies and a plurality of internal electrodes including first and second electrodes,
The stacked body includes an active portion configured such that the first electrode and the second electrode overlap each other in the stacking direction of the stacked body, and the first electrode and the second electrode are stacked in the stacking direction of the stacked body. And an inactive portion configured not to overlap with
The inactive portion is provided with a low-strength layer having a lower strength than the piezoelectric body,
The multilayer piezoelectric element, wherein the piezoelectric body and the low-strength layer are formed of a piezoelectric material having the same composition system.   The multilayer piezoelectric element according to claim 1, wherein the low-strength layer is a layer having a density lower than that of the piezoelectric body. The piezoelectric body and the low-strength layer are formed by a paste in which a material containing a binder is mixed with a piezoelectric material,
The multilayer piezoelectric element according to claim 2, wherein a ratio of the amount of the binder to the piezoelectric material forming the low-strength layer is larger than a ratio of the amount of the binder to the piezoelectric material forming the piezoelectric body. The piezoelectric body and the low-strength layer are formed by a paste in which a material containing a binder is mixed with a piezoelectric material,
The multilayer piezoelectric element according to claim 2, wherein a sintering temperature of the piezoelectric material forming the low-strength layer is higher than a sintering temperature of the piezoelectric material forming the piezoelectric body.   The multilayer piezoelectric element according to claim 1, wherein the low-strength layer extends into a region of the active part. The multilayer piezoelectric element according to claim 1, wherein a crack extending in a direction perpendicular to the stacking direction of the stacked body is formed in the low-strength layer.

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