JPH0878747A - Lamination-type piezoelectric body - Google Patents

Abstract

PURPOSE: To provide a lamination-type piezoelectric body which can positively join piezoelectric plates and at the same time prevent electrodes from being short-circuited. CONSTITUTION: In a lamination-type piezoelectric body with a plurality of laminated piezoelectric plates 11, a metal mesh 15 which is included between the piezoelectric plates 11 and at the same time is provided with a protruding part 17 for connection, and a conductive adhesive layer 13 which is included between the piezoelectric plates 11 and at the same time where the metal mesh 15 is buried, the metal mesh 15 laid out at both sides of the piezoelectric plate 11 is used as a metal mesh 19 for positive electrode and a metal mesh for negative electrode, at the same time the protruding parts 17 for connection of the metal mesh 21 for negative electrode are electrically connected, and the protruding parts 17 for connection of the metal mesh 21 for negative electrode are electrically connected.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a laminated piezoelectric material used for a precision positioning device such as an optical device or a drive element for preventing vibration.

[0002]

2. Description of the Related Art Conventionally, a number of methods for manufacturing a laminated piezoelectric body (laminated actuator) by laminating a plurality of piezoelectric plates have been disclosed (for example, Japanese Patent Publication No. 56-50434).
(See the official gazette). In particular, various methods of improving reliability have been disclosed because the bonding state greatly changes depending on the bonding method of the piezoelectric plates, the characteristics after stacking greatly vary, and the characteristics vary among the elements.

As a method of manufacturing a laminated piezoelectric actuator, there is a method of simultaneous firing. In this method by simultaneous firing, it is relatively easy to make the piezoelectric plate thin, and the applied electric field can be increased, so that low voltage high displacement is possible, but the piezoelectric plate material (for example, Pb (Zr
Ti) made of ceramics such as O ₃ ) and an internal electrode material for performing the co-firing, it is necessary to use a noble metal such as Pd or Pt, and the cost increases as the number of laminated layers increases. there were.

Therefore, in order to reduce the cost, a method of laminating and bonding the piezoelectric plates using some kind of conductive adhesive is disclosed in, for example, Japanese Patent Laid-Open No. 60-121784. This publication discloses a method in which a metal plate for an electrode having the same shape as the piezoelectric plate is sandwiched between the piezoelectric plates and bonded by the adhesive force of a conductive paste such as silver paste.

[0005]

However, in this method, since the electrode metal plate having the same shape as the piezoelectric plate is sandwiched between the piezoelectric plates, the bonding between the electrode metal plate and the piezoelectric plate is insufficient. There was a problem of becoming. Therefore, there is a problem that the probability of occurrence of peeling at the bonding interface increases as the number of stacked piezoelectric plates increases. As a result, there is a problem that the piezoelectric actuator peels off at the bonding interface during use and becomes unusable.

Further, during the lamination of the piezoelectric plates, the conductive paste is extruded by the metal plate for electrodes and sticks out to the side surface of the piezoelectric plates, and the metal plates forming the positive electrode and the negative electrode respectively interposed between the piezoelectric plates are separated from each other. There was a problem of short circuit.

It is an object of the present invention to provide a laminated piezoelectric body which can surely bond piezoelectric plates to each other and can prevent a short circuit between electrodes.

[0008]

The laminated piezoelectric body of the present invention comprises a plurality of laminated piezoelectric plates, a metal mesh interposed between the piezoelectric plates and having a connecting projection, and A laminated piezoelectric body having a conductive adhesive layer embedded between the piezoelectric plates and burying the metal mesh, wherein the metal meshes disposed on both sides of the piezoelectric plate are a positive electrode metal mesh and a negative electrode, respectively. And the connecting projections of the positive electrode metal mesh are electrically connected to each other, and the connecting projections of the negative electrode metal mesh are electrically connected to each other.

In such a laminated piezoelectric material, for example, a conductive paste is applied to both surfaces of a plurality of piezoelectric plates, the conductive adhesive layer paste is dried, and then a connecting protrusion is provided between the plurality of piezoelectric plates. And then pressurizing while bonding the plurality of piezoelectric plates to each other to form a conductive adhesive layer for embedding the metal mesh between the piezoelectric plates. With the metal mesh for the positive electrode and the metal mesh for the negative electrode arranged on both sides of the, the connecting projections of the metal mesh for the positive electrode are electrically connected to each other, and the metal mesh for the negative electrode is It is manufactured by electrically connecting the connecting protrusions.

The metal mesh used has conductivity, and for example, metals such as brass, copper and stainless steel are preferable. The thickness of the metal mesh is preferably such that the metal mesh is embedded in the paste for conductive adhesive layer in the state after bonding without any gap. For this purpose, the thickness of the metal mesh is the paste for conductive adhesive layer. It is desirable that the thickness is equal to or less than the thickness of. Further, the mesh diameter of the metal mesh can be used as long as it is 300 μm or less from the point of filling the paste into the mesh and the bonding force of the piezoelectric plate, and particularly preferably 100 μm or less.

As the piezoelectric material forming the piezoelectric plate, for example, a piezoelectric ceramic material containing lead titanate zirconate as a main component is used, but the piezoelectric material is not limited to this, and a ceramic having piezoelectricity. Any of them can be used. A piezoelectric material having a high piezoelectric strain constant d ₃₃ is desirable as the piezoelectric material forming the piezoelectric body.

Further, the laminated piezoelectric body of the present invention includes a plurality of laminated piezoelectric plates, a plurality of elongated metal plates which are respectively interposed between the piezoelectric plates and have a connecting projection, and the piezoelectric plates. What is claimed is: 1. A laminated piezoelectric body having a conductive adhesive layer which is interposed and which embeds the elongated metal plate, wherein the elongated metal plates disposed on both sides of the piezoelectric body are elongated metal plates for positive electrodes and negative electrodes, respectively. Elongated metal plate for electrical connection, the connecting protrusions of the elongated metal plate for the positive electrode are electrically connected to each other, and the connecting protrusions of the elongated metal plate for the negative electrode are electrically connected to each other. Is.

The metal plate has a width smaller than that of the piezoelectric plate, and its material and thickness are preferably the same as those of the metal mesh for the same reason.

[0014]

In the laminated piezoelectric material of the present invention, since the metal mesh as the electrode and the plurality of elongated metal plates are interposed between the piezoelectric plates, when the pressure is applied during the lamination, the conductive adhesive layer paste gets into the space between the metal meshes. , Or around the elongated metal plate to firmly bond the piezoelectric plates together.

Further, since the conductive adhesive layer paste enters between the metal meshes and the conductive adhesive layer paste enters around the elongated metal plate, the conductive adhesive layer paste is formed during the lamination of the piezoelectric plates. Can be suppressed from protruding to the side surface of the piezoelectric plate.

[0016]

The present invention will be described below with reference to the drawings.

FIG. 1 shows a laminated piezoelectric material of the present invention, and reference numeral 11 denotes a disk-shaped piezoelectric plate. The piezoelectric plate 11 is a sintered body containing Pb (ZrTi) O ₃ (hereinafter abbreviated as PZT) as a main component, and has a disc shape with a diameter of 20 mm and a thickness of 0.5 mm.

A plurality of piezoelectric plates 11 are laminated, and a conductive adhesive layer 13 made of, for example, Ag containing a glass component is formed between them. Inside the conductive adhesive layer 13, for example, brass is used. The metal mesh 15 made of metal is embedded. As shown in FIG. 2, these metal meshes 15 are formed with connecting projections 17 and project in the radial direction of the piezoelectric plate 11. In addition, as shown in FIG. 1, the connecting projections 17 have metal meshes 15 interposed between the piezoelectric plates 11 so as to alternately face each other by 180 degrees. The metal mesh 19 for the positive electrode and the metal mesh 21 for the negative electrode are formed depending on the position of the connecting protrusion 17. Then, the connecting projections 17 of the positive electrode metal mesh 19 are bent and electrically connected to each other, and the connecting projections 17 of the negative electrode metal mesh 21 are bent and electrically connected to each other. It is connected to the.

In such a laminated piezoelectric material, a conductive paste is applied to both surfaces of the piezoelectric plate 11, the conductive adhesive layer paste is dried, and then a space between the plurality of piezoelectric materials 11,
That is, the metal mesh 15 having the connecting protrusions 17 is interposed between the pastes, and then the pastes are heated and pressed to bond the plurality of piezoelectric plates 11 to each other. It is formed by forming the conductive adhesive layer 13 in which the mesh 15 is embedded.

Then, the connecting projections 17 of the positive electrode metal mesh 19 and the negative electrode metal mesh 21 sandwiching the piezoelectric plate 11 are connected. That is, it is manufactured by electrically connecting the connecting projections 17 of the positive electrode metal mesh 19 to each other and electrically connecting the connecting projections 17 of the negative electrode metal mesh 21 to each other.

The laminated piezoelectric material having the above structure is
Since the metal mesh 15 as an electrode is interposed between the piezoelectric plates 11, when pressure is applied during lamination, the conductive adhesive layer paste enters between the meshes of the metal mesh 15 and the piezoelectric plate 1
It is possible to firmly bond one to the other, prevent peeling at the interface that occurs due to repeated application of a high electric field, and improve the reliability of the laminated piezoelectric body.

Further, since the conductive adhesive layer paste enters between the metal meshes 15, the conductive adhesive layer paste is not pushed out by the piezoelectric plate 11 during the lamination of the piezoelectric plates 11 and does not stick out to the side surface. Metal mesh for electrodes 19
It is possible to prevent electrical connection between the connecting protrusion 17 and the connecting protrusion 17 of the negative electrode metal mesh 21, and to prevent a short circuit between the positive electrode metal mesh 19 and the negative electrode metal mesh 21. .

Further, since the mechanical loss at the joint can be reduced, the displacement hysteresis generated upon application of an electric field is small, the displacement amount after repeated use is small, and the long-life piezoelectric body is provided. be able to.

Example 1 Both sides of a sintered body containing PZT as a main component were ground to a diameter of 20.
A disk-shaped piezoelectric plate 11 having a thickness of 0.5 mm and a thickness of 0.5 mm was formed. An electroconductive Ag paste containing a glass component was printed on both main surfaces of the piezoelectric plate 11 so as to have a thickness of 40 to 60 μm, and then dried at 100 ° C. 50 μm thickness,
A brass mesh having a mesh diameter of 100 μm is punched out into a circular shape having a diameter of 20 mm having a connecting projection 17 of 2 mm × 2 mm as shown in FIG.
The metal mesh 15 was sandwiched between the piezoelectric plates 11, and 100 layers of the piezoelectric plates 11 were laminated to form a laminated piezoelectric body.

The connecting projection 17 of the metal mesh 15
Are placed in the same position every other layer, and the other is placed 180 degrees on the opposite side. For a piezoelectric body in which 100 layers of the piezoelectric plate 11 are laminated, light pressure is applied so as not to cause positional displacement, and then a weight of about 4 kg is placed on the top of the laminated body.
Pressure bonding was performed at 0 ° C. for 1 hour.

Next, as shown in FIG. 1, the connecting projection 17 protruding in the radial direction of the piezoelectric plate 11 is bent in the axial direction,
The connection protrusions 17 of the positive electrode metal mesh 19 are electrically connected to each other by connecting the adjacent connection protrusions 17 to each other, and the connection protrusions 17 of the negative electrode metal mesh 21 are electrically connected to each other. Connected to each other. This was subjected to polarization treatment by applying a DC voltage of 3 kv / mm for 30 minutes in silicon oil at 80 ° C.

As a result of applying a DC voltage of 200 V to the obtained laminated piezoelectric material, a displacement amount of 15 μm was obtained. Further, an AC electric field of 0V to + 200V is applied to the laminated piezoelectric body 1
As a result of applying at a frequency of 0 Hz, the number of times of application is 3 × 10 ⁸
This displacement amount was maintained up to times. On the other hand, in the conventional example in which a metal plate having the same shape as the piezoelectric plate is inserted as an electrode, the AC electric field of 0 V to +200 V is applied at a frequency of 10 Hz for 5 × 10 ⁶ times and peeling occurs at the lamination interface. Occurred, and the amount of displacement changed.

The amount of displacement was measured by fixing the sample on a vibration isolation table, attaching an aluminum foil to the upper surface of the sample, and averaging the values measured by a laser displacement meter at the central portion and the peripheral portion of the element. The value was evaluated.

Example 2 A sintered body containing PZT as a main component was polished on both sides to have a diameter of 15
A disk-shaped piezoelectric plate 11 having a thickness of 0.35 mm and a thickness of 0.35 mm was formed. An electrically conductive Ag paste containing a glass component was printed on both main surfaces of the piezoelectric plate 11 so as to have a thickness of 20 μm, and then dried at 120 ° C. A brass mesh having a thickness of 20 μm and a mesh diameter of 200 μm having a connecting projection 17 of 2 mm × 2 mm as shown in FIG.
The metal mesh 15 was created by punching into a circle of m. The metal mesh 15 was sandwiched between the piezoelectric plates 11, and 200 layers of the piezoelectric plates 11 were laminated to form a laminated piezoelectric body.

Incidentally, the connecting projection 17 of the metal mesh 15
Are placed in the same position every other layer, and the other is placed 180 degrees on the opposite side. For a piezoelectric body in which 200 layers of the piezoelectric plate 11 are laminated, light pressure is applied so as not to cause positional displacement, and then a weight of about 3 kg is placed on the top of the laminated body.
Pressure bonding was performed at 0 ° C. for 1 hour. Next, as shown in FIG. 1, the connecting projection 17 protruding outward from the piezoelectric plate 11 is bent in the axial direction, and is connected to the adjacent connecting projection 17 that has been left one layer, and the positive electrode metal mesh is formed. The connection projections 17 of 19 are electrically connected to each other, and the negative electrode metal mesh 2 is also provided.
The connecting protrusions 17 of No. 1 were electrically connected to each other. This was subjected to polarization treatment by applying a DC voltage of 2 kv / mm for 30 minutes in silicon oil at 80 ° C.

As a result of applying a DC voltage of 200 V to the obtained laminated piezoelectric material, a displacement amount of 31 μm was obtained. Further, an AC electric field of 0V to + 200V is applied to the laminated piezoelectric body 1
As a result of applying at a frequency of 0 Hz, the number of times of application is 3 × 10.
This displacement amount was maintained up to ⁸ times. On the other hand, in the conventional example in which a metal plate having the same shape as the piezoelectric plate is inserted as an electrode, the AC electric field of 0 V to +200 V is applied at a frequency of 10 Hz for 1 × 10 ⁶ times, and peeling occurs at the lamination interface. Occurred, and the amount of displacement changed. The amount of displacement was measured in the same manner as in Example 1 above.

Example 3 Both sides of a sintered body containing PZT as a main component were ground to form one side 10
A piezoelectric plate 11 formed of a square rectangular plate having a thickness of 0.3 mm and a thickness of 0.3 mm was formed. After printing an electrically conductive paste, for example, an Ag paste containing a glass component, on both main surfaces of the piezoelectric plate 11 to a thickness of 40 to 50 μm,
It was dried at 120 ° C. Thickness 40μm, mesh diameter 50
The brass mesh of μm is 2mm × 2m as shown in Fig. 3.
The metal mesh 15 was punched into a square shape having a connecting protrusion 17 of m and a side of 10 mm, sandwiched between the piezoelectric plates 11, and 300 layers of the piezoelectric plates were laminated to form a laminated piezoelectric body.

Incidentally, the connecting projection 17 of the metal mesh 15
Are placed in the same position every other layer, and the other is placed 180 degrees on the opposite side. For a laminated piezoelectric body in which 300 layers of piezoelectric plates are laminated, light pressure is applied so that no displacement occurs, and then a weight of about 2 kg is placed on the upper part of the laminated body,
Pressure bonding was performed at 00 ° C. for 1 hour. Next, as shown in FIG. 1, these connecting protrusions 17 that are exposed to the outside are bent in the axial direction, and are connected to the adjacent connecting protrusions 17 that have been placed further, and the positive electrode metal mesh 19 The connecting protrusions 17 were electrically connected to each other, and the connecting protrusions 17 of the negative electrode metal mesh 21 were electrically connected to each other. 80 ° C
Polarization treatment was performed by applying a direct current voltage of 2 kv / mm for 30 minutes in the silicon oil.

As a result of applying a DC voltage of 50 V to the obtained laminated piezoelectric material, a displacement amount of 12 μm was obtained. Further, an AC electric field of 0V to + 50V is applied to this laminated piezoelectric body for 10H.
As a result of applying at the frequency of z, this displacement amount was maintained until the number of applications was 7 × 10 ⁸ .

On the other hand, in the conventional example in which a metal plate having the same shape as the piezoelectric plate is inserted as an electrode, 0V to +5 is applied.
When the AC electric field of 0 V was applied at a frequency of 10 Hz for 2 × 10 ⁶ times, delamination occurred at the laminated interface and the displacement amount changed. The displacement amount was measured in the same manner as in Example 1 above.

Example 4 A diameter of 12 was obtained by polishing both surfaces of a sintered body containing PZT as a main component.
A disk-shaped piezoelectric plate 11 having a thickness of 0.3 mm and a thickness of 0.3 mm was formed. An electroconductive Ag paste containing a glass component was printed on both main surfaces of the piezoelectric plate 11 so as to have a thickness of 10 to 20 μm, and then dried at 100 ° C. 20 μm thickness,
A brass mesh having a mesh diameter of 100 μm is punched into a circle having a diameter of 12 mm having a connecting protrusion 17 of 2 mm × 2 mm as shown in FIG.
The metal mesh 15 was sandwiched between the piezoelectric plates 11, and 100 layers of the piezoelectric plates 11 were laminated to form a laminated piezoelectric body.

Incidentally, the connecting projection 17 of the metal mesh 15
Are placed in the same position every other layer, and the other is placed 180 degrees on the opposite side. For a piezoelectric body in which 100 layers of the piezoelectric plate 11 are laminated, light pressure is applied so that the displacement does not occur, and then a weight of about 2 kg is placed on the top of the laminated body,
Pressure bonding was performed at 0 ° C. for 30 minutes.

Next, as shown in FIG. 1, the connecting projection 17 protruding in the radial direction of the piezoelectric plate 11 is bent in the axial direction,
The connection protrusions 17 of the positive electrode metal mesh 19 are electrically connected to each other by connecting the adjacent connection protrusions 17 to each other, and the connection protrusions 17 of the negative electrode metal mesh 21 are electrically connected to each other. Connected to each other. This was subjected to polarization treatment by applying a DC voltage of 3 kv / mm for 30 minutes in silicon oil at 80 ° C.

As a result of applying a DC voltage of 100 V to the obtained laminated piezoelectric material, a displacement amount of 6 μm was obtained. Further, an AC electric field of 0V to + 100V is applied to this laminated piezoelectric body for 10 minutes.
As a result of applying at a frequency of Hz, this displacement amount was maintained up to 5 × 10 ⁸ times of application.

On the other hand, in the conventional example in which a metal plate having the same shape as the piezoelectric plate is inserted as an electrode, 0 V to +1
When the AC electric field of 00 V was applied at a frequency of 10 Hz for 2 × 10 ⁶ times, delamination occurred at the laminated interface and the displacement amount changed.

FIG. 4 shows another embodiment of the present invention.
Both sides of the sintered body containing PZT as the main component were polished to a diameter of 18
A disk-shaped piezoelectric plate 31 having a thickness of 0.35 mm and a thickness of 0.35 mm was formed.

An electrically conductive Ag paste containing a glass component was printed on both main surfaces of the piezoelectric plate 31 so as to have a thickness of 25 μm, and then dried at 100 ° C. As shown in FIG. 4, two elongated metal plates 33 having a width of 2 mm, a thickness of 25 μm, and a length of 20 mm are arranged in parallel on the paste 32 of the piezoelectric plate 31 and sandwiched between the piezoelectric plates 31 to form a piezoelectric plate. 31 to 1
A laminated piezoelectric body was formed by laminating 50 layers.

As shown in FIG. 1, the ends of the elongated metal plate 33 are arranged such that the connecting projections 37 are located at the same position every other layer and the other is located on the opposite side by 180 degrees. . The piezoelectric plate 31 in which 150 layers of the piezoelectric plate 31 were laminated was lightly pressed so as not to be displaced, and then a weight of about 3 kg was placed on the upper part of the laminated body and pressure-bonded at 650 ° C. for 1 hour. .

Next, as shown in FIG. 1, the connecting projection 37 protruding in the radial direction of the piezoelectric plate 31 is bent in the axial direction,
The connecting protrusions 37 of the positive electrode metal mesh 19 are electrically connected to each other by connecting to the adjacent connecting protrusions 37, and the connecting protrusions 17 of the negative electrode metal mesh 21 are electrically connected to each other. Connected to each other. This was subjected to polarization treatment by applying a DC voltage of 3 kv / mm for 30 minutes in silicon oil at 80 ° C.

With such a laminated piezoelectric material, it is possible to obtain substantially the same effects as in the above embodiment. Further, in this case, since the two elongated metal plates 33 are arranged in parallel, the piezoelectric plates 31 can be laminated in parallel.

As a result of applying a DC voltage of 300 V to the obtained piezoelectric laminate, a displacement amount of 35 μm was obtained. Further, as a result of applying an AC electric field of 0 V to +300 V at a frequency of 10 Hz to this laminated body, this displacement amount was maintained until the number of times of application was 2 × 10 ⁸ . On the other hand, in the conventional example in which a metal plate having the same shape as the piezoelectric plate is inserted as an electrode,
When the AC electric field of V to +300 V was applied at a frequency of 10 Hz for 1 × 10 ⁶ times, delamination occurred at the laminated interface and the displacement amount changed. The displacement amount was measured in the same manner as in Example 1 above.

In the above embodiment, the example in which the two elongated metal plates 33 are arranged in parallel between the piezoelectric plates 31 has been described, but the present invention is not limited to the above embodiment.
Three or more elongated metal plates may be arranged between the piezoelectric plates. Further, the elongated metal plates do not necessarily have to be arranged in parallel.

[0048]

As described in detail above, according to the present invention, since the metal mesh as the electrode is interposed between the piezoelectric plates,
When pressure is applied during lamination, the conductive adhesive layer paste will enter between the metal meshes, firmly bond the piezoelectric plates together, and prevent peeling at the interface caused by repeated application of a high electric field. The reliability of the piezoelectric body can be improved. The same applies to the case where an elongated metal plate having a width smaller than that of the piezoelectric plate is interposed between the piezoelectric plates as an electrode.

Further, since the conductive adhesive layer paste enters between the metal meshes and around the elongated metal plate, the conductive adhesive layer paste may be extruded by the piezoelectric plate during the lamination of the piezoelectric plates and stick out to the side surface. Therefore, it is possible to prevent a short circuit between metal meshes and a short circuit between elongated metal plates.

Further, according to the present invention, since the mechanical loss at the joint can be reduced, the displacement hysteresis generated when an electric field is applied is small, the displacement amount after repeated use is small, and the long life of the laminated piezoelectric element is small. The body can be provided.

[Brief description of drawings]

FIG. 1 is a side view showing a cylindrical laminated piezoelectric body of the present invention.

2 is a plan view showing the metal mesh of FIG. 1. FIG.

FIG. 3 is a plan view showing a square metal mesh.

FIG. 4 is a plan view showing a state in which two elongated metal plates are arranged in parallel on a piezoelectric plate.

[Explanation of symbols]

 11, 31 ... Piezoelectric plate 13 ... Conductive adhesive layer 15 ... Metal mesh 17, 37 ... Connection protrusion 19 ... Positive electrode metal mesh 21 ... Negative electrode metal mesh 33 ... Elongated metal plate

Claims (2)

[Claims] 1. A plurality of laminated piezoelectric plates, a metal mesh interposed between these piezoelectric plates and having a connecting projection, and a metal mesh interposed between the piezoelectric plates and embedded with the metal mesh. A laminated piezoelectric body having a conductive adhesive layer, wherein the metal meshes arranged on both sides of the piezoelectric plate are respectively a positive electrode metal mesh and a negative electrode metal mesh, and the positive electrode metal mesh A laminated piezoelectric body, characterized in that the connecting projections are electrically connected to each other, and the connecting projections of the negative electrode metal mesh are electrically connected to each other. 2. A plurality of laminated piezoelectric plates, a plurality of elongated metal plates each interposed between the piezoelectric plates and having a connecting projection, and an elongated metal plate interposed between the piezoelectric plates. In the laminated piezoelectric body having a conductive adhesive layer for embedding, the elongated metal plates arranged on both sides of the piezoelectric body are elongated metal plates for positive electrode and elongated metal plate for negative electrode, respectively, and A laminated piezoelectric body characterized in that the connecting projections of the elongated metal plate for the positive electrode are electrically connected to each other, and the connecting projections of the elongated metal plate for the negative electrode are electrically connected to each other.