Patent Publication Number: US-2023163325-A1

Title: Metal Support for Electrochemical Element, Electrochemical Element, Electrochemical Module, Electrochemical Device, Energy System, Solid Oxide Fuel Cell, and Method for Manufacturing Metal Support

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the United States national phase of International Application No. PCT/JP2019/014376 filed Mar. 29, 2019, and claims priority to Japanese Patent Application No. 2018-070340 filed Mar. 30, 2018, the disclosures of which are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a metal support for an electrochemical element, and the like. 
     Description of Related Art 
     Japanese Patent Application No. JP 2008-525967A (Patent Document 1) discloses the structure of a metal support for a metal-supported SOFC. The metal support disclosed in Patent Document 1 has a structure in which a metal foil having a thickness of about 15 μm is stacked on a metal mesh having a thickness of 200 μm or more obtained by weaving metal wire. 
     SUMMARY OF THE INVENTION 
     However, in the case of the structure of the metal support as disclosed in Patent Document 1, when an electrode layer is formed on the metal foil through, for example, screen printing, the metal foil becomes distorted along the unevenness of the metal mesh due to printing pressure of a squeegee because the metal foil has low strength. There is a problem in that it is difficult to form an electrode layer having a uniform thickness and few surface defects such as breakage and separation due to the distortion of the metal foil or the printing pressure of a squeegee being less likely to be uniformly applied. 
     The present invention was achieved in light of the aforementioned problem, and an object thereof is to provide a metal support for an electrochemical element and the like. This metal support for an electrochemical element is a metal support with reduced warping, and thus an electrode layer having a uniform thickness and reduced surface defects such as breakage and separation can be formed thereon. 
     Means for Solving Problem 
     Configuration 1 
     In a characteristic configuration of a metal support for an electrochemical element according to the present invention, 
     the metal support includes a plate face and having a plate shape as a whole, 
     the metal support is provided with a plurality of penetration spaces that pass through the metal support from a front face to a back face, the front face being a face to be provided with an electrode layer, 
     a region of the front face provided with the penetration spaces is a hole region, and 
     the metal support satisfies a condition that a warping degree is 1.5×10 −2  or less, 
     wherein the warping degree is determined by calculating a least square value through a least squares method using at least three points in the plate face of the metal support, calculating a first difference between the least square value and a positive-side maximum displacement value on a positive side with respect to the least square value and a second difference between the least square value and a negative-side maximum displacement value on a negative side that is opposite to the positive side with respect to the least square value, and dividing Da that is a sum of the first difference and the second difference by a maximum length Lmax of the plate face of the metal support that passes through a center of gravity to determine Da/Lmax, which is used as the warping degree. 
     With the above-mentioned characteristic configuration, regarding a plurality of points in the plate face of the metal support, the sum of the difference between the positive-side maximum displacement value and the least square value and the difference between the negative-side maximum displacement value and the least square value is calculated. When there are a plurality of points, the least square value is, for example, a straight line, a plane, or the like that is calculated from the plurality of points using the least squares method. For example, by adding the maximum displacement value on the positive side (positive-side maximum displacement value) with respect to the least square value, which is a straight line, a plane, or the like, to the maximum displacement value on the negative side (negative-side maximum displacement value) with respect to the least square value to determine Da, the warping degree of a metal support plate is determined. 
     With the above-mentioned characteristic configuration, by further dividing Da by the maximum length Lmax of the metal support, even the warping degrees of metal supports that are different in size can be compared based on a certain reference value. 
     By accurately calculating the warping degree of the metal support as described above and setting the warping degree to 1.5×10 −2  or less, an electrode layer having a uniform thickness and reduced surface defects such as breakage and separation can be formed on the metal support. If such an electrode layer having reduced surface defects can be formed, an electrolyte layer, a counter electrode layer, and the like that each have a uniform thickness and reduced surface defects such as breakage and separation can also be formed on the electrode layer. Accordingly, the layers can be formed with increased adhesion therebetween, and thus a high-performance electrochemical element is obtained. 
     Configuration 2 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     at least two points in the plate face of the metal support are located on at least one straight line passing through the center of gravity and are opposed to each other in the plate face of the metal support with the center of gravity being located at a center therebetween. 
     With the above-mentioned characteristic configuration, at least two points in the plate face of the metal support are located on at least one straight line passing through the center of gravity and opposed to each other in the plate face of the metal support with the center of gravity being located at the center therebetween. Accordingly, the least square value is calculated using points that are located in a direction away from each other relative to the center of gravity in the plate face. That is, the least square value is calculated using points scattered in the plate face rather than points in a localized region on the metal support. Accordingly, the least square value is calculated as a value relating to the shape of the plate face of the metal support. Using this least square value as a reference makes it possible to accurately calculate Da used as a reference for determining the warping degree of the metal support. 
     Configuration 3 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     when a plurality of straight lines are used as the straight line, the plurality of straight lines divide 360° by a predetermined angle around the center of gravity. 
     With the above-mentioned characteristic configuration, a plurality of straight lines passing through the center of gravity of the metal support radially extend while being away from each other by a predetermined angle around the center of gravity. Accordingly, the least square value is calculated based on points scattered over substantially the entire metal support. Using this least square value as a reference makes it possible to accurately calculate Da used as a reference for determining the warping degree of the metal support. It is preferable that the plurality of straight lines passing through the center of gravity of the metal support radially extend while being away from each other by an angle of 90° or less around the center of gravity because Da can be calculated more accurately, and it is more preferable that the straight lines radially extend while being away from each other by an angle of 60° or less. Also, it is preferable that the plurality of straight lines passing through the center of gravity of the metal support radially extend while being away from each other by an angle of 30° or more around the center of gravity because the warping degree can be easily measured. 
     Configuration 4 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     at least two points that are opposed to each other in the plate face of the metal support with the center of gravity being located at a center therebetween are located between a peripheral edge of the metal support and the hole region. 
     With the above-mentioned characteristic configuration, the least square value is calculated using at least two points located in a region between the peripheral edge of the metal support and the hole region, that is, in the peripheral edge portion of the metal support. In general, the warping degree of the peripheral edge portion is larger than that of the central portion in a metal support. When the area of a metal support is relatively small, a difference in the warping degree between the central portion and the peripheral edge portion in the metal support is not large, but when the area is increased, the peripheral edge portion is warped more greatly than the central portion. Accordingly, calculating Da based on points located in the peripheral edge portion makes it possible to accurately calculate Da and thus accurately calculate the warping degree of the metal support. 
     Configuration 5 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     at least two points that are opposed to each other in the plate face of the metal support with the center of gravity being located at a center therebetween are located between a peripheral edge of the metal support and the electrode layer to be formed on the metal support. 
     With the above-mentioned characteristic configuration, calculating Da based on points located much closer to the peripheral edge portion makes it possible to accurately calculate Da, and thus the warping degree of the metal support can be accurately calculated. 
     Configuration 6 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     the least square value is a least square plane calculated through a least squares method using at least four points in the plate face of the metal support. 
     With the above-mentioned characteristic configuration, a least square plane is calculated using at least four points in the plate face. Calculating Da based on differences from the least square plane also makes it possible to accurately determine the warping degree. 
     It is preferable that points located in a direction away from each other with respect to the center of gravity in the plate face are used as the above-mentioned at least four points in the plate face because a least square plane that approximates the shape of the plate face is calculated based on points scattered in the plate face. Also, it is preferable that a least square plane is calculated through the least squares method using five or more points in the plate face because more points in the plate face are used and thus Da can be accurately calculated. Also, it is preferable that a least square plane is calculated through the least squares method using twelve or less points in the plate face because the warping degree can be easily measured. 
     Configuration 7 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     each of front-side openings that are openings of the penetration spaces formed in the front face has a circular shape or a substantially circular shape having a diameter of 10 μm or more and 60 μm or less. 
     The above-mentioned characteristic configuration is favorable because the processing for forming the penetration spaces is facilitated, and the workability and cost of mass production can be improved. The front-side openings preferably have a circular shape or a substantially circular shape having a diameter of 10 μm or more, more preferably have a circular shape or a substantially circular shape having a diameter of 15 μm or more, and even more preferably have a circular shape or a substantially circular shape having a diameter of 20 μm or more. The reason for this is that employing such a configuration makes it possible to supply a sufficient amount of fuel gas (or air) to an electrode layer of the electrochemical element, and thus the performance of the electrochemical element can be further improved. Also, the front-side openings preferably have a circular shape or a substantially circular shape having a diameter of 60 μm or less, more preferably have a circular shape or a substantially circular shape having a diameter of 50 μm or less, and even more preferably have a circular shape or a substantially circular shape having a diameter of 40 μm or less. The reason for this is that employing such a configuration makes it easier to form the constitutional elements of the electrochemical element such as an electrode layer on the metal support provided with a plurality of penetration spaces while improving the strength of the metal support. 
     Configuration 8 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, 
     each of back-side openings that are openings of the penetration spaces formed in the back face has an area or a diameter larger than those of front-side openings that are openings of the penetration spaces formed in the front face. 
     The above-mentioned characteristic configuration is favorable because the processing for forming the penetration spaces is further facilitated, and the workability and cost of mass production can be improved. Moreover, this characteristic configuration is favorable because the ratio of the thickness of the entire metal support to the area of the front-side openings of the metal support can be increased, thus making it easy to form the constitutional elements of the electrochemical element such as an electrode layer on the metal support while ensuring sufficient strength. 
     Configuration 9 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, intervals between front-side openings that are openings of the penetration spaces formed in the front face are 0.05 mm or more and 0.3 mm or less. 
     The above-mentioned characteristic configuration is favorable because both the strength and the performance of the metal support can be increased. The intervals between the front-side openings are preferably 0.05 mm or more, more preferably 0.1 mm or more, and even more preferably 0.15 mm or more. The reason for this is that employing such a configuration makes it possible to further increase the strength of the metal support as well as makes it easier to form the constitutional elements of the electrochemical element such as an electrode layer on the metal support provided with a plurality of penetration spaces. Also, the intervals between the front-side openings are preferably 0.3 mm or less, more preferably 0.25 mm or less, and even more preferably 0.2 mm or less. The reason for this is that employing such a configuration makes it possible to supply a sufficient amount of fuel gas (or air) to the electrode layer of the electrochemical element, and thus the performance of the electrochemical element can be further improved. 
     Configuration 10 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, the metal support has a thickness of 0.1 mm or more and 1.0 mm or less. 
     The above-mentioned characteristic configuration is favorable because the strength of the entire metal support can be sufficiently maintained while penetration spaces are formed to have an appropriate size, thus making it possible to improve workability in mass production and reduce the material cost. The thickness of the metal support is preferably 0.1 mm or more, more preferably 0.15 mm or more, and even more preferably 0.2 mm or more. The reason for this is that employing such a configuration makes it possible to further facilitate handling in mass production while maintaining the strength of the metal support. The thickness of the metal support is preferably 1.0 mm or less, more preferably 0.75 mm or less, and even more preferably 0.5 mm or less. The reason for this is that employing such a configuration makes it possible to further reduce the material cost of the metal support while maintaining the strength of the metal support. 
     Configuration 11 
     In another characteristic configuration of the metal support for an electrochemical element according to the present invention, the metal support is made of a Fe—Cr based alloy. 
     With the above-mentioned characteristic configuration, the oxidation resistance and high-temperature strength of the metal support can be improved. Moreover, this characteristic configuration is favorable because the thermal expansion coefficient of the metal support can be set to be close to those of the materials of the constitutional elements of the electrochemical element such as an electrode layer and an electrolyte layer, which are formed on/over the metal support, thus making it possible to realize an electrochemical element having excellent heat-cycle durability. 
     Configuration 12 
     In a characteristic configuration of an electrochemical element according to the present invention, at least an electrode layer, an electrolyte layer, and a counter electrode layer are provided on/over the front face of the above-described metal support. 
     The electrochemical element in which at least an electrode layer, an electrolyte layer, and a counter electrode layer are provided on/over the front face of the above-described metal support is favorable because sufficient performance is ensured, and the workability and cost of mass production are improved. 
     Furthermore, this electrochemical element is favorable because the constitutional elements of the electrochemical element such as an electrode layer and an electrolyte layer are formed on/over the metal support having excellent strength, and therefore, the constitutional elements of the electrochemical element such as an electrode layer and an electrolyte layer can be formed as thin layers or thin films, thus making it possible to reduce the material cost of the electrochemical element. 
     Configuration 13 
     In a characteristic configuration of an electrochemical module according to the present invention, a plurality of the above-described electrochemical elements are arranged in an assembled state. 
     With the above-mentioned characteristic configuration, the plurality of the above-described electrochemical elements are arranged in an assembled state, thus making it possible to obtain an electrochemical module that is compact, has high performance, and has excellent strength and reliability, while also suppressing the material cost and processing cost. 
     Configuration 14 
     A characteristic configuration of an electrochemical device according to the present invention includes at least the above-described electrochemical module and a reformer, and includes a fuel supply unit that supplies fuel gas containing a reducing component to the electrochemical module. 
     The above-mentioned characteristic configuration includes the electrochemical module and the reformer and includes the fuel supply unit for supplying the fuel gas containing a reducing component to the electrochemical module, thus making it possible to use an existing raw fuel supply infrastructure such as city gas to realize an electrochemical device including the electrochemical module that has excellent durability, reliability, and performance. Also, it is easier to construct a system that recycles unused fuel gas discharged from the electrochemical module, thus making it possible to realize a highly efficient electrochemical device. 
     Configuration 15 
     A characteristic configuration of an electrochemical device according to the present invention includes at least the above-described electrochemical module and an inverter that extracts power from the electrochemical module. 
     The above-mentioned characteristic configuration is preferable because it makes it possible to boost, using an inverter, electrical output obtained from the electrochemical module that has excellent durability, reliability, and performance, or to convert a direct current into an alternating current, and thus makes it easy to use the electrical output obtained from the electrochemical module. 
     Configuration 16 
     A characteristic configuration of an energy system according to the present invention includes the above-described electrochemical device and waste heat utilization system that reuses heat discharged from the electrochemical device. 
     The above-mentioned characteristic configuration includes the electrochemical device and the waste heat utilization system that reuses heat discharged from the electrochemical device, thus making it possible to realize an energy system that has excellent durability, reliability, and performance as well as excellent energy efficiency. It should be noted that it is also possible to realize a hybrid system that has excellent energy efficiency by combination with a power generation system that generates power with use of combustion heat from unused fuel gas discharged from the electrochemical device. 
     Configuration 17 
     A characteristic configuration of a solid oxide fuel cell according to the present invention includes 
     the above-described electrochemical element 
     wherein a power generation reaction is caused in the electrochemical element. 
     With the above-mentioned characteristic configuration, the solid oxide fuel cell including the electrochemical element that has excellent durability, reliability, and performance can cause a power generation reaction, and thus a solid oxide fuel cell having high durability and high performance can be obtained. It should be noted that a solid oxide fuel cell that can be operated in a temperature range of 650° C. or higher during the rated operation is more preferable because a fuel cell system that uses hydrocarbon-based gas such as city gas as raw fuel can be constructed such that waste heat discharged from a fuel cell can be used in place of heat required to convert raw fuel to hydrogen, and the power generation efficiency of the fuel cell system can thus be improved. A solid oxide fuel cell that is operated in a temperature range of 900° C. or lower during the rated operation is more preferable because the effect of suppressing volatilization of Cr from a metal-supported electrochemical element can be improved, and a solid oxide fuel cell that is operated in a temperature range of 850° C. or lower during the rated operation is even more preferable because the effect of suppressing volatilization of Cr can be further improved. 
     Configuration 18 
     A characteristic configuration of a method for manufacturing a metal support according to the present invention is 
     a method for manufacturing the above-mentioned metal support, including 
     forming the plurality of penetration spaces passing through the metal support from the front face to the back face through laser processing, punching processing, etching processing, or a combination thereof. 
     With the above-mentioned characteristic configuration, the processing for forming the penetration spaces is facilitated, and the workability and cost of mass production can be improved. 
     Configuration 19 
     A characteristic configuration of the method for manufacturing a metal support according to the present invention includes a smoothing processing step. 
     The above-mentioned characteristic configuration is preferable because a metal support having a small warping degree is obtained through smoothing processing, thus making it easy to form an electrochemical element on the metal support. It is preferable to perform the smoothing processing such that the warping degree of a metal support is 1.5×10 −2  or less because it is easy to form an electrochemical element on the metal support. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG.  1    is a schematic diagram showing a configuration of an electrochemical element. 
         FIG.  2    is a schematic diagram showing configurations of electrochemical elements and an electrochemical module. 
         FIG.  3    is a schematic diagram showing configurations of an electrochemical device and an energy system. 
         FIG.  4    is a schematic diagram showing a configuration of an electrochemical module. 
         FIG.  5    shows a plan view and a cross-sectional view showing a structure of a metal support. 
         FIG.  6    is an explanatory diagram showing a method for calculating the warping degree of the metal support. 
         FIG.  7    is an explanatory diagram showing a method for calculating the warping degree of the metal support. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     First Embodiment 
     Hereinafter, an electrochemical element E and a solid oxide fuel cell (SOFC) according to this embodiment will be described with reference to  FIG.  1   . The electrochemical element E is used as a constitutional element of a solid oxide fuel cell that receives a supply of air and fuel gas containing hydrogen and generates power, for example. It should be noted that when the positional relationship between layers and the like are described in the description below, a counter electrode layer  6  side may be referred to as “upper portion” or “upper side”, and an electrode layer  2  side may be referred to as “lower portion” or “lower side”, with respect to an electrolyte layer  4 , for example. In addition, in a metal support  1 , a face on which the electrode layer  2  is formed is referred to as “front face  1   a ”, and a face on an opposite side is referred to as “back face  1   b”.    
     Electrochemical Element 
     As shown in  FIG.  1   , the electrochemical element E includes a metal support  1 , an electrode layer  2  formed on the metal support  1 , an intermediate layer  3  formed on the electrode layer  2 , and an electrolyte layer  4  formed on the intermediate layer  3 . The electrochemical element E further includes a reaction preventing layer  5  formed on the electrolyte layer  4 , and a counter electrode layer  6  formed on the reaction preventing layer  5 . Specifically, the counter electrode layer  6  is formed above the electrolyte layer  4 , and the reaction preventing layer  5  is formed between the electrolyte layer  4  and the counter electrode layer  6 . The electrode layer  2  is porous, and the electrolyte layer  4  is dense. 
     Metal Support 
     The metal support  1  supports the electrode layer  2 , the intermediate layer  3 , the electrolyte layer  4 , and the like, and maintains the strength of the electrochemical element E. That is, the metal support  1  serves as a support that supports the electrochemical element E. In this embodiment, the metal support  1  has a warping degree of 1.5×10 −2  or less, and the electrode layer  2  and the like are appropriately formed on the metal support  1 . 
     A material that has excellent electron conductivity, thermal resistance, oxidation resistance, and corrosion resistance is used as the material of the metal support  1 . Examples thereof include ferrite-based stainless steel, austenite-based stainless steel, and a nickel-based alloy. In particular, an alloy containing chromium is favorably used. In this embodiment, the metal support  1  is made of a Fe—Cr based alloy that contains Cr in an amount of 18 mass % or more and 25 mass % or less, but a Fe—Cr based alloy that contains Mn in an amount of 0.05 mass % or more, a Fe—Cr based alloy that contains Ti in an amount of 0.15 mass % or more and 1.0 mass % or less, a Fe—Cr based alloy that contains Zr in an amount of 0.15 mass % or more and 1.0 mass % or less, a Fe—Cr based alloy that contains Ti and Zr, a total content of Ti and Zr being 0.15 mass % or more and 1.0 mass % or less, and a Fe—Cr based alloy that contains Cu in an amount of 0.10 mass % or more and 1.0 mass % or less are particularly favorable. 
     The metal support  1  has a plate shape as a whole. The metal support  1  is provided with a plurality of penetration spaces  1   c  that pass through the metal support  1  from the front face  1   a , which is a face on which the electrode layer  2  is provided, to the back face  1   b . The penetration space  1   c  allows gas to permeate from the back face  1   b  of the metal support  1  to the front face  1   a  thereof. It should be noted that a configuration is also possible in which the plate-like metal support  1  is deformed into, for example, a box shape, a cylindrical shape, or the like through bending or the like and used. There is no limitation on the shape of the plate face (front face  1   a ) of the metal support  1 , and the plate face may also have a rectangular shape such as a square and a rectangle, a circular shape, or an elliptical shape. 
     A metal oxide layer  1   f  serving as a diffusion suppressing layer is provided on the surface of the metal support  1 . That is, the diffusion suppressing layer is formed between the metal support  1  and the electrode layer  2 , which will be described later. The metal oxide layer  1   f  is provided not only on the face of the metal support  1  exposed to the outside but also on the face (interface) that is in contact with the electrode layer  2 . The metal oxide layer  1   f  can also be provided on the inner faces of the penetration spaces  1   c . Element interdiffusion that occurs between the metal support  1  and the electrode layer  2  can be suppressed due to this metal oxide layer  1   f . For example, when ferrite-based stainless steel containing chromium is used in the metal support  1 , the metal oxide layer  1   f  is mainly made of a chromium oxide. The metal oxide layer  1   f  containing the chromium oxide as the main component suppresses diffusion of chromium atoms and the like of the metal support  1  to the electrode layer  2  and the electrolyte layer  4 . The metal oxide layer  1   f  need only have such a thickness that allows both high diffusion preventing performance and low electric resistance to be achieved. 
     The metal oxide layer  1   f  can be formed using various techniques, but it is favorable to use a technique of oxidizing the surface of the metal support  1  to obtain a metal oxide. Also, the metal oxide layer if may be formed on the surface of the metal support  1  by using a spray coating technique (a technique such as thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique such as a sputtering technique or PLD technique, or a CVD technique, or may be formed by plating and oxidation treatment. Furthermore, the metal oxide layer if may also contain a spinel phase that has high electrical conductivity, or the like. 
     When a ferrite-based stainless steel material is used to form the metal support  1 , its thermal expansion coefficient is close to that of YSZ (yttria-stabilized zirconia), GDC (gadolinium-doped ceria; also called CGO), or the like, which is used as the material of the electrode layer  2  and the electrolyte layer  4 . Accordingly, even if low and high temperature cycling is repeated, the electrochemical element E is not likely to be damaged. Therefore, this is preferable due to being able to realize an electrochemical element E that has excellent long-term durability. 
     Next, the warping degree of the metal support  1  will be described with reference to  FIGS.  6  and  7   . The warping degree is an index of to what extent the metal support  1  is warped with respect to a flat face. 
     In the metal support  1  shown in  FIG.  6   , a center of gravity G of the metal support  1  is determined. The center of gravity G is a point at which the primary moment around the center of gravity G is zero when it is assumed that the metal support  1  is not provided with a hole region g 1  and has a uniform thickness and uniform density. For example, when the plate face (front face  1   a ) of the metal support  1  has a rectangular shape such as a square or a rectangle, the center of gravity G is the intersection point of the diagonal lines. When the plate face has a circular shape, the center of gravity G is the center thereof. When the plate face has an elliptical shape, the center of gravity G is a point corresponding to the intersection point of the major axis and the minor axis. 
     Straight lines L 1  to L 4  indicate a plurality of straight lines that pass through the center of gravity G and radially extend. The straight lines L 1  to L 4  divide 360° by a predetermined angle around the center of gravity G. In  FIG.  6   , the straight lines L 1  to L 4  are drawn so as to be away from each other by 45°. It should be noted that the four straight lines L 1  to L 4  are drawn in this diagram, but the number of the straight lines L is not limited thereto and may also be one to three, or five or more. In addition, the angle dividing 360° is not limited to 45°, and may also be smaller than 45° or larger than 45°. 
     It is preferable that the plurality of straight lines passing through the center of gravity G of the metal support  1  radially extend while being away from each other by an angle of 90° or less around the center of gravity G because Da, which will be described later, can be calculated more accurately, and it is more preferable that the straight lines radially extend while being away from each other by an angle of 60° or less. Also, it is preferable that the plurality of straight lines passing through the center of gravity G of the metal support  1  radially extend while being away from each other by an angle of 30° or more around the center of gravity G because the warping can be easily measured. 
     In each of the straight lines L 1  to L 4 , two points P that are opposed to each other in the plate face of the metal support  1  with the center of gravity G being located at the center therebetween are extracted. The two points P that are opposed to each other are located in a region of a peripheral edge portion OP between the peripheral edge of the metal support  1  and the hole region g 1  ( FIG.  5   ). Here, eight points, namely points P 1   a  and P 1   b  on the straight line L 1 , points P 2   a  and P 2   b  on the straight line L 2 , points P 3   a  and P 3   b  on the straight line L 3 , and points P 4   a  and P 4   b  on the straight line L 4 , are extracted. 
     It should be noted that, in the description above, two points P that are opposed to each other with the center of gravity G being located at the center therebetween are extracted per straight line L, but three or more points P may also be extracted per straight line L. 
     The size of the hole region g 1  varies depending on the metal support  1 , and therefore, the size of the peripheral edge portion OP also varies depending on the metal support  1 . For example, the peripheral edge portion OP can be set to have a size of about 20% or less from the peripheral edge of the metal support  1 . For example, the peripheral edge portion OP corresponds to an area between the peripheral edge of the metal support  1  and the position away from the peripheral edge by about 20% or less of the distance between the peripheral edge of the metal support  1  and a straight line that passes through the center of gravity G and extends in parallel with the peripheral edge. Furthermore, the peripheral edge portion OP can be set to have a size of about 10% or less from the peripheral edge of the metal support  1 , and can also be set to have a size of about 5% or less from the peripheral edge of the metal support  1 . 
     The layers such as the electrode layer  2 , the intermediate layer  3 , the electrolyte layer  4 , the reaction preventing layer  5 , and the counter electrode layer  6  are placed on the metal support  1 . The peripheral edge portion OP may also correspond to an area between the outer edge of any of these layers and the peripheral edge of the metal support  1 . 
     Using the points P located in such a peripheral edge portion OP of the metal support  1  makes it possible to determine a least square plane a (least square value) (which will be described later) that is more typical of the shape of the metal support  1 . 
     The least square plane a is determined through the least squares method using the eight points P, namely the points P 1   a  to P 4   b , which has been extracted as mentioned above. The least square plane a is a plane that approximately indicates the range in which the points P 1   a  to P 4   b  are located. For example, the least square plane a is shown as a plane having a cross-section as shown in  FIG.  7   . 
     The positive-side maximum displacement value on the positive side (first side) with respect to the least square plane a, and the negative-side maximum displacement value on the negative side (second side) with respect to the least square plane a are determined. In this diagram, the point P 3   a  that is the farthest from the least square plane a on the positive side is a positive-side maximum displacement point, and the distance between the least square plane a and the point P 3   a  is taken as a positive-side maximum displacement value N1. Similarly, the point P 2   b  that is the farthest from the least square plane a on the negative side is a negative-side maximum displacement point, and the distance between the least square plane a and the point P 2   b  is taken as a negative-side maximum displacement value N2. 
     The difference between the positive-side maximum displacement point, which is the point P 3   a , and the least square plane a is taken as a first difference, and the first difference is the positive-side maximum displacement value N1. The difference between the negative-side maximum displacement point, which is the point P 2   b , and the least square plane a is taken as a second difference, and the second difference is the negative-side maximum displacement value N2. Da used as a reference for determining the warping degree of the metal support  1  is determined from the sum of the first difference and the second difference, namely the sum of the positive-side maximum displacement value N1 and the negative-side maximum displacement value N2. 
     Next, Da/Lmax, which is obtained by dividing Da by the maximum length Lmax of plate face of the metal support  1  is calculated as the warping degree. Here, as shown in  FIG.  6   , the lengths of the two sides of the metal support  1  having a rectangular shape are Lx and Ly, and the maximum length Lmax is determined as the square root of the sum of the square of Lx and the square of Ly. 
     In order to use the metal support  1  as a substrate for the electrochemical element E, the warping degree is preferably 1.5×10 −2  or less. The warping degree is more preferably 1.0×10 −2  or less, and the warping degree is even more preferably 5.0×10 −3  or less. As the warping degree is smaller, the electrode layer  2  and the like that each have a uniform thickness and reduced surface defects such as breakage and separation can also be formed on the metal support  1  as flat layers with increased adhesion therebetween. 
     Smoothing processing (e.g., leveler processing or annealing processing) may be performed in accordance with the warping degree of the metal support  1 . It should be noted that performing smoothing processing on a metal support  1  having a warping degree of greater than 1.5×10 −2  is favorable. 
     When the size of the hole region  1   g  is 5.0×10 2  mm 2  or more, performing smoothing processing makes it easy to reduce the warping degree of the metal support  1  and is thus preferable. When the size of the hole region  1   g  is 2.5×10 3  mm 2  or more, performing smoothing processing increases the effect of reducing the warping degree and is thus more preferable. 
     As described above, the least square plane a is calculated using the points P that are located in a direction away from each other relative to the center of gravity G in the plate face of the metal support  1 . For example, the points P are scattered over substantially the entire metal support  1 . Accordingly, the least square plane a is determined based on the points P scattered in the plate face as a plane that approximates the shape of the plate face of the metal support  1 . Thus, calculating Da based on differences from the least square plane and makes it possible to accurately determine the warping degree. 
     By further dividing Da by the maximum length Lmax of the metal support  1 , even the warping degrees of metal supports  1  that are different in size can be compared based on a certain reference value. For example, when the metal support  1  is relatively large, Da tends to increase, but when the metal support  1  is relatively small, Da tends to decrease. Accordingly, it is preferable to divide Da by the maximum length Lmax so as to be capable of comparing the warping degrees based on a certain value among metal supports  1  that are different in size. 
     By accurately calculating a warping degree of the metal support  1  as described above and setting the warping degree to 1.5×10 −2  or less, a flat metal support  1  with reduced warping can be obtained. Since the metal support  1  itself is flat, the electrode layer  2 , the electrolyte layer  4 , the counter electrode layer  6 , and the like can also be formed on the metal support  1  as flat layers. Accordingly, it is possible to suppress separation of these layers from the metal support  1 , a decrease in adhesion between these layers, breakage of these layers, and the like. 
     When a plurality of layers including the electrode layer  2 , the electrolyte layer  4 , the counter electrode layer  6 , and the like are formed on the metal support  1  to produce a cell, weight may be applied to the layers using a press or the like in order to bring the metal support  1  and the layers into more intimate contact with one another. As described above, the weight is substantially uniformly applied to the metal support  1  and the layers due to the reduced warping and flatness of the metal support  1 . Accordingly, when weight is applied to the layers using a press or the like, separation and breakage of the layers, separation of the layers from the metal support  1 , and the like are suppressed. Thus, a cell that has a uniform thickness, reduced surface defects such as breakage and separation, and increased adhesion between the layers can be produced. In addition, electrochemical reactions are efficiently performed between the layers, thus making it possible to improve the performance of the electrochemical element E. 
     It should be noted that the points P 1   a  to P 4   b  are located in the peripheral edge portion OP. The least square plane a is determined through the least squares method using such points P located in the peripheral edge portion OP. In general, the warping degree of the peripheral edge portion OP is larger than that of the central portion in the metal support  1 . For example, when the area of the metal support  1  is relatively small, a difference in the warping degree between the central portion and the peripheral edge portion OP in the metal support  1  is not large, but when the area is increased, warping of the metal support  1  increases from the central portion toward the peripheral edge portion OP. Accordingly, calculating Da based on the points P located in the peripheral edge portion OP makes it possible to accurately calculate Da including the information of the entire metal support  1 , and thus accurately calculate the warping degree of the metal support  1 . 
     It should be noted that, in the description above, the least square plane a is determined using the eight points, namely the points P 1   a  to P 4   b , but the least square plane a can be determined using at least four points located in the peripheral edge portion OP. In this case, it is preferable that points P located in a direction away from each other with respect to the center of gravity G in the plate face are used as the above-mentioned at least four points in the plate face because a least square plane a that approximates the shape of the plate face is calculated based on the points scattered in the plate face. 
     Also, it is preferable that the least square plane a is calculated through the least squares method using five or more points in the peripheral edge portion OP because more points in the plate face of the metal support  1  are used and thus Da can be accurately calculated. Also, it is preferable that the least square plane a is calculated through the least squares method using twelve or less points in the plate face because the warping degree can be easily measured. 
     Moreover, the least square plane a may also be determined based on any points located in the plate face of the metal support  1  other than the points P located in the peripheral edge portion OP. 
     Structures of Metal Support and Penetration Spaces 
     In the example shown in  FIG.  1   , the metal support  1  is constituted by a single metal plate. The metal support  1  can also be formed by stacking a plurality of metal plates. The metal support  1  can also be formed by stacking a plurality of metal plates that have the same thickness or substantially the same thickness. The metal support  1  can also be formed by stacking a plurality of metal plates that have different thicknesses. Hereinafter, examples of the structures of the metal support  1  and the penetration spaces  1   c  will be described with reference to the drawings. It should be noted that the metal oxide layer if is not shown. 
     An example in which the metal support  1  is constituted by a single metal plate will be described with reference to  FIG.  5   . As shown in  FIG.  5   , the metal support  1  is a plate-like member having a thickness T. That is, the metal support  1  has a plate shape as a whole. The metal support  1  is provided with the plurality of penetration spaces  1   c  that pass through the metal support  1  from the front face  1   a  to the back face  1   b . In the first example, the penetration spaces  1   c  are holes with a circular cross section. The cross section of each of the penetration spaces  1   c  may also have a rectangular shape, a triangular shape, a polygonal shape, or the like other than a circular shape or a substantially circular shape. Various shapes can be selected as long as the penetration spaces  1   c  can be formed and the functions of the metal support  1  can be maintained. These holes (penetration spaces  1   c ) are formed in the metal support  1  through laser processing, punching processing, etching processing, or a combination thereof. The central axes of these holes are orthogonal to the metal support  1 . It should be noted that the central axes of the holes (penetration spaces  1   c ) may be inclined to the metal support  1 . 
     The openings of the penetration spaces  1   c  formed in the front face  1   a  are referred to as “front-side openings  1   d ”. The openings of the penetration spaces  1   c  formed in the back face  1   b  are referred to as “back-side openings  1   e ”. Since the penetration spaces  1   c  are holes having a circular cross section, all of the front-side openings  1   d  and the back-side openings  1   e  have a circular shape. The front-side openings  1   d  and the back-side openings  1   e  may have the same size. The back-side openings  1   e  may be larger than the front-side openings  1   d . The diameter of each of the front-side openings  1   d  is taken as a “diameter D”. 
     As shown in  FIG.  5   , in the metal support  1 , the plurality of holes (penetration spaces  1   c ) are formed at positions corresponding to the lattice points of an orthogonal lattice at a pitch P (interval). The arrangement pattern of the plurality of holes (penetration spaces  1   c ) may be an orthorhombic lattice or an equilateral-triangular lattice other than the orthogonal lattice. The plurality of holes can be arranged at intersection points of the diagonal lines in addition to the lattice points. Various arrangement patterns can be selected as long as the penetration spaces can be formed and the functions of the metal support can be maintained. 
     A region of the front face  1   a  of the metal support  1  provided with the penetration spaces  1   c  is referred to as the “hole region  1   g ”. The hole region  1   g  is provided in a region of the metal support  1  excluding the vicinity of the outer peripheral region. The metal support  1  may be provided with a single hole region  1   g  or a plurality of hole regions  1   g.    
     The metal support  1  is required to have a strength that is sufficient to serve as a support for forming the electrochemical element E. The thickness T of the metal support  1  is preferably 0.1 mm or more, more preferably 0.15 mm or more, and even more preferably 0.2 mm or more. The thickness T of the metal support  1  is preferably 1.0 mm or less, more preferably 0.75 mm or less, and even more preferably 0.5 mm or less. 
     The diameter D of each of the front-side openings  1   d  is preferably 10 μm or more, more preferably 15 μm or more, and even more preferably 20 μm or more. The diameter D of each of the front-side openings  1   d  is preferably 60 μm or less, more preferably 50 μm or less, and even more preferably 40 μm or less. 
     The arrangement pitch P of the penetration spaces  1   c  (holes) is preferably 0.05 mm or more, more preferably 0.1 mm or more, and even more preferably 0.15 mm or more. The arrangement pitch P of the penetration spaces  1   c  (holes) is preferably 0.3 mm or less, more preferably 0.25 mm or less, and even more preferably 0.2 mm or less. 
     An area S of each of the front-side openings  1   d  of the penetration spaces  1   c  is preferably 7.0×10 −5  mm 2  or more, and preferably 3.0×10 −3  mm 2  or less. 
     Electrode Layer 
     As shown in  FIG.  1   , the electrode layer  2  can be provided as a thin layer in a region that is larger than the region provided with the penetration spaces  1   c , on the front face of the metal support  1 . When it is provided as a thin layer, the thickness can be set to approximately 1 μm to 100 μm, and preferably 5 μm to 50 μm, for example. This thickness makes it possible to ensure sufficient electrode performance while also achieving cost reduction by reducing the amount of expensive electrode layer material that is used. The region provided with the penetration spaces  1   c  is entirely covered by the electrode layer  2 . That is, the penetration spaces  1   c  are formed inside the region of the metal support  1  in which the electrode layer  2  is formed. In other words, all the penetration spaces  1   c  are provided facing the electrode layer  2 . 
     A composite material such as NiO-GDC, Ni-GDC, NiO—YSZ, Ni—YSZ, CuO—CeO 2 , or Cu—CeO 2  can be used as the material for forming the electrode layer  2 , for example. In these examples, GDC, YSZ, and CeO 2  can be called the aggregate of the composite material. It should be noted that it is preferable to form the electrode layer  2  using low-temperature calcining (not performing calcining treatment in a high temperature range of higher than 1100° C., but rather performing a wet process using calcining treatment in a low temperature range, for example), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Due to these processes that can be used in a low temperature range, a favorable electrode layer  2  is obtained without using calcining in a high temperature range of higher than 1100° C., for example. Therefore, this is preferable due to being able to prevent damage to the metal support  1 , suppress element interdiffusion between the metal support  1  and the electrode layer  2 , and realize an electrochemical element that has excellent durability. Furthermore, using low-temperature calcining makes it possible to facilitate handling of raw materials and is thus more preferable. 
     The inside and the surface of the electrode layer  2  are provided with a plurality of pores in order to impart gas permeability to the electrode layer  2 . 
     That is, the electrode layer  2  is formed as a porous layer. The electrode layer  2  is formed to have a denseness of 30% or more and less than 80%, for example. Regarding the size of the pores, a size suitable for smooth progress of an electrochemical reaction can be selected as appropriate. It should be noted that the “denseness” is a ratio of the material of the layer to the space and can be represented by a formula “1—porosity”, and is equivalent to relative density. 
     Intermediate Layer 
     As shown in  FIG.  1   , the intermediate layer  3  (intervening layer) can be formed as a thin layer on the electrode layer  2  so as to cover the electrode layer  2 . When it is formed as a thin layer, the thickness can be set to approximately 1 μm to 100 μm, preferably approximately 2 μm to 50 μm, and more preferably approximately 4 μm to 25 μm, for example. This thickness makes it possible to ensure sufficient performance while also achieving cost reduction by reducing the amount of expensive intermediate layer material that is used. YSZ (yttria-stabilized zirconia), SSZ (scandia-stabilized zirconia), GDC (gadolinium-doped ceria), YDC (yttrium-doped ceria), SDC (samarium-doped ceria), or the like can be used as the material of the intermediate layer  3 . In particular, ceria-based ceramics are favorably used. 
     It is preferable to form the intermediate layer  3  using low-temperature calcining (not performing calcining treatment in a high temperature range of higher than 1100° C., but rather performing a wet process using calcining treatment in a low temperature range, for example), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Due to these film formation processes that can be used in a low temperature range, an intermediate layer  3  is obtained without using calcining in a high temperature range of higher than 1100° C., for example. Therefore, it is possible to prevent damage to the metal support  1 , suppress element interdiffusion between the metal support  1  and the electrode layer  2 , and realize an electrochemical element E that has excellent durability. Furthermore, using low-temperature calcining makes it possible to facilitate handling of raw materials and is thus more preferable. 
     It is preferable that the intermediate layer  3  has oxygen ion (oxide ion) conductivity. It is more preferable that the intermediate layer  3  has both oxygen ion (oxide ion) conductivity and electron conductivity, namely mixed conductivity. The intermediate layer  3  that has these properties is suitable for application to the electrochemical element E. 
     Electrolyte Layer 
     As shown in  FIG.  1   , the electrolyte layer  4  is formed as a thin layer on the intermediate layer  3  so as to cover the electrode layer  2  and the intermediate layer  3 . The electrolyte layer  4  can also be formed as a thin film having a thickness of 10 μm or less. Specifically, as shown in  FIG.  1   , the electrolyte layer  4  is provided on both the intermediate layer  3  and the metal support  1  (spanning the intermediate layer  3  and the metal support  1 ). Configuring the electrolyte layer  4  in this manner and joining the electrolyte layer  4  to the metal support  1  make it possible to allow the electrochemical element to have excellent toughness as a whole. 
     Also, as shown in  FIG.  1   , the electrolyte layer  4  is provided in a region that is larger than the region provided with the penetration spaces  1   c , on the front face of the metal support  1 . That is, the penetration spaces  1   c  are formed inside the region of the metal support  1  in which the electrolyte layer  4  is formed. 
     The leakage of gas from the electrode layer  2  and the intermediate layer  3  can be suppressed in the vicinity of the electrolyte layer  4 . A description of this will be given. When the electrochemical element E is used as a constitutional element of a SOFC, gas is supplied from the back side of the metal support  1  through the penetration spaces  1   c  to the electrode layer  2  during the operation of the SOFC. In a region where the electrolyte layer  4  is in contact with the metal support  1 , leakage of gas can be suppressed without providing another member such as a gasket. It should be noted that, although the entire vicinity of the electrode layer  2  is covered by the electrolyte layer  4  in this embodiment, a configuration in which the electrolyte layer  4  is provided on the electrode layer  2  and the intermediate layer  3  and a gasket or the like is provided in its vicinity may also be adopted. 
     YSZ (yttria-stabilized zirconia), SSZ (scandia-stabilized zirconia), GDC (gadolinium-doped ceria), YDC (yttrium-doped ceria), SDC (samarium-doped ceria), LSGM (strontium- and magnesium-doped lanthanum gallate), or the like can be used as the material of the electrolyte layer  4 . In particular, zirconia-based ceramics are favorably used. Using zirconia-based ceramics for the electrolyte layer  4  makes it possible to increase the operation temperature of the SOFC in which the electrochemical element E is used compared with the case where ceria-based ceramics are used. For example, when the electrochemical element E is used in the SOFC, by adopting a system configuration in which a material such as YSZ that can exhibit high electrolyte performance even in a high temperature range of approximately 650° C. or higher is used as the material of the electrolyte layer  4 , a hydrocarbon-based raw fuel such as city gas or LPG is used as the raw fuel for the system, and the raw fuel is reformed into anode gas of the SOFC through steam reforming or the like, it is thus possible to construct a high-efficiency SOFC system in which heat generated in a cell stack of the SOFC is used to reform raw fuel gas. 
     It is preferable to form the electrolyte layer  4  using low-temperature calcining (not performing calcining treatment in a high temperature range of higher than 1100° C., but rather performing a wet process using calcining treatment in a low temperature range, for example), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Due to these film formation processes that can be used in a low temperature range, an electrolyte layer  4  that is dense and has high gas-tightness and gas barrier properties is obtained without using calcining in a high temperature range of higher than 1100° C., for example. Therefore, it is possible to prevent damage to the metal support  1 , suppress element interdiffusion between the metal support  1  and the electrode layer  2 , and realize an electrochemical element E that has excellent performance and durability. In particular, using low-temperature calcining, a spray coating technique, or the like makes it possible to realize a low-cost element and is thus preferable. Furthermore, using a spray coating technique makes it easy to obtain, in a low temperature range, an electrolyte layer that is dense and has high gas-tightness and gas barrier properties, and is thus more preferable. 
     The electrolyte layer  4  is given a dense configuration in order to block gas leakage of anode gas and cathode gas and exhibit high ion conductivity. The electrolyte layer  4  preferably has a denseness of 90% or more, more preferably 95% or more, and even more preferably 98% or more. When the electrolyte layer  4  is formed as a uniform layer, the denseness is preferably 95% or more, and more preferably 98% or more. When the electrolyte layer  4  has a multilayer configuration, at least a portion thereof preferably includes a layer (dense electrolyte layer) having a denseness of 98% or more, and more preferably a layer (dense electrolyte layer) having a denseness of 99% or more. The reason for this is that an electrolyte layer that is dense and has high gas-tightness and gas barrier properties can be easily formed due to such a dense electrolyte layer being included as a portion of the electrolyte layer even when the electrolyte layer has a multilayer configuration. 
     Reaction Preventing Layer 
     The reaction preventing layer  5  can be formed as a thin layer on the electrolyte layer  4 . When it is formed as a thin layer, the thickness can be set to approximately 1 μm to 100 μm, preferably approximately 2 μm to 50 μm, and more preferably approximately 3 μm to 15 μm, for example. This thickness makes it possible to ensure sufficient performance while also achieving cost reduction by reducing the amount of expensive reaction preventing layer material that is used. The material of the reaction preventing layer  5  need only be capable of preventing reactions between the component of the electrolyte layer  4  and the component of the counter electrode layer  6 . For example, a ceria-based material or the like is used. Materials that contain at least one element selected from the group consisting of Sm, Gd, and Y are favorably used as the material of the reaction preventing layer  5 . It is preferable that at least one element selected from the group consisting of Sm, Gd, and Y is contained, and the total content of these elements is 1.0 mass % or more and 10 mass % or less. Introducing the reaction preventing layer  5  between the electrolyte layer  4  and the counter electrode layer  6  effectively suppresses reactions between the material constituting the counter electrode layer  6  and the material constituting the electrolyte layer  4  and makes it possible to improve long-term stability in the performance of the electrochemical element E. Forming the reaction preventing layer  5  using, as appropriate, a method through which the reaction preventing layer  5  can be formed at a treatment temperature of 1100° C. or lower makes it possible to suppress damage to the metal support  1 , suppress element interdiffusion between the metal support  1  and the electrode layer  2 , and realize an electrochemical element E that has excellent performance and durability, and is thus preferable. For example, the reaction preventing layer  5  can be formed using, as appropriate, low-temperature calcining (not performing calcining treatment in a high temperature range of higher than 1100° C., but rather performing a wet process using calcining treatment in a low temperature range, for example), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. In particular, using low-temperature calcining, a spray coating technique, or the like makes it possible to realize a low-cost element and is thus preferable. Furthermore, using low-temperature calcining makes it possible to facilitate handling of raw materials and is thus more preferable. 
     Counter Electrode Layer 
     The counter electrode layer  6  can be formed as a thin layer on the electrolyte layer  4  or the reaction preventing layer  5 . When it is formed as a thin layer, the thickness can be set to approximately 1 μm to 100 μm, and preferably approximately 5 μm to 50 μm, for example. This thickness makes it possible to ensure sufficient electrode performance while also achieving cost reduction by reducing the amount of expensive counter electrode layer material that is used. A complex oxide such as LSCF or LSM, or a ceria-based oxide, or a mixture thereof can be used as the material of the counter electrode layer  6 , for example. In particular, it is preferable that the counter electrode layer  6  includes a perovskite oxide containing two or more elements selected from the group consisting of La, Sr, Sm, Mn, Co, and Fe. The counter electrode layer  6  constituted by the above-mentioned material functions as a cathode. 
     It should be noted that forming the counter electrode layer  6  using, as appropriate, a method through which the counter electrode layer  6  can be formed at a treatment temperature of 1100° C. or lower makes it possible to suppress damage to the metal support  1 , suppress element interdiffusion between the metal support  1  and the electrode layer  2 , and realize an electrochemical element E that has excellent performance and durability, and is thus preferable. For example, the counter electrode layer  6  can be formed using, as appropriate, low-temperature calcining (not performing calcining treatment in a high temperature range of higher than 1100° C., but rather performing a wet process using calcining treatment in a low temperature range, for example), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. In particular, using low-temperature calcining, a spray coating technique, or the like makes it possible to realize a low-cost element and is thus preferable. Furthermore, using low-temperature calcining makes it possible to facilitate handling of raw materials and is thus more preferable. 
     Solid Oxide Fuel Cell 
     The electrochemical element E configured as described above can be used as a power generating cell for a solid oxide fuel cell. For example, fuel gas containing hydrogen is supplied from the back surface of the metal support  1  through the penetration spaces  1   c  to the electrode layer  2 , air is supplied to the counter electrode layer  6  serving as a counter electrode of the electrode layer  2 , and the operation is performed at a temperature of 500° C. or higher and 900° C. or lower, for example. Accordingly, the oxygen O 2  included in air reacts with electrons e −  in the counter electrode layer  6 , thus producing oxygen ions O 2− . The oxygen ions O 2−  move through the electrolyte layer  4  to the electrode layer  2 . In the electrode layer  2 , the hydrogen H 2  included in the supplied fuel gas reacts with the oxygen ions O 2− , thus producing water H 2 O and electrons e − . With these reactions, electromotive force is generated between the electrode layer  2  and the counter electrode layer  6 . In this case, the electrode layer  2  functions as a fuel electrode (anode) of the SOFC, and the counter electrode layer  6  functions as an air electrode (cathode). 
     Method for Manufacturing Electrochemical Element 
     Next, a method for manufacturing the electrochemical element E will be described. 
     Electrode Layer Forming Step 
     In an electrode layer forming step, the electrode layer  2  is formed as a thin film in a region that is broader than the region provided with the penetration spaces  1   c , on the front face of the metal support  1 . The through holes of the metal support  1  can be provided through laser processing or the like. As described above, the electrode layer  2  can be formed using low-temperature calcining (a wet process using calcining treatment in a low temperature range of 1100° C. or lower), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Regardless of which technique is used, it is desirable to perform the technique at a temperature of 1100° C. or lower in order to suppress deterioration of the metal support  1 . 
     The following is a specific example of the case where low-temperature calcining is performed as the electrode layer forming step. 
     First, a material paste is produced by mixing powder of the material of the electrode layer  2  and a solvent (dispersion medium), and is applied to the front face of the metal support  1 . Then, the electrode layer  2  is obtained through compression molding (electrode layer smoothing step) and calcining at a temperature of 1100° C. or lower (electrode layer calcining step). Examples of compression molding of the electrode layer  2  include CIP (Cold Isostatic Pressing) molding, roll pressing molding, and RIP (Rubber Isostatic Pressing) molding. It is favorable to perform calcining of the electrode layer  2  at a temperature of 800° C. or higher and 1100° C. or lower. The order in which the electrode layer smoothing step and the electrode layer calcining step are performed can be changed. 
     It should be noted that, when an electrochemical element including an intermediate layer  3  is formed, the electrode layer smoothing step and the electrode layer calcining step may be omitted, and an intermediate layer smoothing step and an intermediate layer calcining step, which will be described later, may include the electrode layer smoothing step and the electrode layer calcining step. 
     It should be noted that lapping molding, leveling treatment, surface cutting treatment, surface polishing treatment, or the like can also be performed as the electrode layer smoothing step. 
     Diffusion Suppressing Layer Forming Step 
     The metal oxide layer if (diffusion suppressing layer) is formed on the surface of the metal support  1  during the calcining step in the above-described electrode layer forming step. It should be noted that it is preferable that the above-mentioned calcining step includes a calcining step in which the calcining atmosphere satisfies the atmospheric condition that the oxygen partial pressure is low because a high-quality metal oxide layer if (diffusion suppressing layer) that has a high element interdiffusion suppressing effect and has a low resistance value is formed. In a case where a coating method that does not include calcining is performed as the electrode layer forming step, a separate diffusion suppressing layer forming step may also be included. In any case, it is desirable to perform these steps at a temperature of 1100° C. or lower such that damage to the metal support  1  can be suppressed. The metal oxide layer if (diffusion suppressing layer) may be formed on the surface of the metal support  1  during the calcining step in an intermediate layer forming step, which will be described later. 
     Intermediate Layer Forming Step 
     In an intermediate layer forming step, the intermediate layer  3  is formed as a thin layer on the electrode layer  2  so as to cover the electrode layer  2 . As described above, the intermediate layer  3  can be formed using low-temperature calcining (a wet process using calcining treatment in a low temperature range of 1100° C. or lower), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Regardless of which technique is used, it is desirable to perform the technique at a temperature of 1100° C. or lower in order to suppress deterioration of the metal support  1 . 
     The following is a specific example of the case where low-temperature calcining is performed as the intermediate layer forming step. 
     First, a material paste is produced by mixing powder of the material of the intermediate layer  3  and a solvent (dispersion medium), and is applied to the front face of the metal support  1 . Then, the intermediate layer  3  is obtained through compression molding (intermediate layer smoothing step) and calcining at a temperature of 1100° C. or lower (intermediate layer calcining step). Examples of rolling of the intermediate layer  3  include CIP (Cold Isostatic Pressing) molding, roll pressing molding, and RIP (Rubber Isostatic Pressing) molding. It is favorable to perform calcining of the intermediate layer  3  at a temperature of 800° C. or higher and 1100° C. or lower. The reason for this is that this temperature makes it possible to form an intermediate layer  3  that has high strength while suppressing damage to and deterioration of the metal support  1 . It is more preferable to perform calcining of the intermediate layer  3  at a temperature of 1050° C. or lower, and more preferably 1000° C. or lower. The reason for this is that the lower the calcining temperature of the intermediate layer  3  is, the more likely it is to further suppress damage to and deterioration of the metal support  1  when forming the electrochemical element E. The order in which the intermediate layer smoothing step and the intermediate layer calcining step are performed can be changed. 
     It should be noted that lapping molding, leveling treatment, surface cutting treatment, surface polishing treatment, or the like can also be performed as the intermediate layer smoothing step. 
     Electrolyte Layer Forming Step 
     In an electrolyte layer forming step, the electrolyte layer  4  is formed as a thin layer on the intermediate layer  3  so as to cover the electrode layer  2  and the intermediate layer  3 . The electrolyte layer  4  may also be formed as a thin film having a thickness of 10 μm or less. As described above, the electrolyte layer  4  can be formed using low-temperature calcining (a wet process using calcining treatment in a low temperature range of 1100° C. or lower), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Regardless of which technique is used, it is desirable to perform the technique at a temperature of 1100° C. or lower in order to suppress deterioration of the metal support  1 . 
     It is desirable to perform a spray coating technique as the electrolyte layer forming step in order to form a high-quality electrolyte layer  4  that is dense and has high gas-tightness and gas barrier properties in a temperature range of 1100° C. or lower. In this case, the material of the electrolyte layer  4  is sprayed onto the intermediate layer  3  on the metal support  1 , and the electrolyte layer  4  is thus formed. 
     Reaction Preventing Layer Forming Step 
     In a reaction preventing layer forming step, the reaction preventing layer  5  is formed as a thin layer on the electrolyte layer  4 . As described above, the reaction preventing layer  5  can be formed using low-temperature calcining (a wet process using calcining treatment in a low temperature range of 1100° C. or lower), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Regardless of which technique is used, it is desirable to perform the technique at a temperature of 1100° C. or lower in order to suppress deterioration of the metal support  1 . It should be noted that leveling treatment, surface cutting treatment, or surface polishing treatment may be performed after the formation of the reaction preventing layer  5 , or pressing processing may be performed after wet formation and before calcining in order to flatten the top face of the reaction preventing layer  5 . 
     Counter Electrode Layer Forming Step 
     In a counter electrode layer forming step, the counter electrode layer  6  is formed as a thin layer on the reaction preventing layer  5 . As described above, the counter electrode layer  6  can be formed using low-temperature calcining (a wet process using calcining treatment in a low temperature range of 1100° C. or lower), a spray coating technique (a technique such as a thermal spraying technique, an aerosol deposition technique, an aerosol gas deposition technique, a powder jet deposition technique, a particle jet deposition technique, or a cold spraying technique), a PVD technique (e.g., a sputtering technique or a pulse laser deposition technique), a CVD technique, or the like. Regardless of which technique is used, it is desirable to perform the technique at a temperature of 1100° C. or lower in order to suppress deterioration of the metal support  1 . 
     In this manner, the electrochemical element E can be manufactured. 
     It should be noted that a configuration is also possible in which the electrochemical element E does not include both or either of the intermediate layer  3  (intervening layer) and the reaction preventing layer  5 . That is, a configuration is also possible in which the electrode layer  2  and the electrolyte layer  4  are in contact with each other, or a configuration is also possible in which the electrolyte layer  4  and the counter electrode layer  6  are in contact with each other. In this case, in the above-described manufacturing method, the intermediate layer forming step and the reaction preventing layer forming step are omitted. It should be noted that it is also possible to add a step of forming another layer or to form a plurality of layers of the same type one on top of another, but in any case, it is desirable to perform these steps at a temperature of 1100° C. or lower. 
     120-mm Square Test Piece 
     Comparative Example 1 
     A 120-mm square (120 mm×120 mm) crofer 22 APU metal plate having a thickness of 0.3 mm was provided with a plurality of penetration spaces  1   c  through laser processing in a 98-mm square (98 mm×98 mm) region around the center, and a metal plate (metal support  1 ) according to Comparative Example 1 was thus produced. The penetration spaces  1   c  were provided at positions corresponding to the lattice points of an orthogonal lattice. It should be noted that each of the front-side openings  1   d  had a diameter of 20 μm, and the pitch P was 200 μm. The maximum length Lmax was 16.97 cm. 
     Comparative Example 2 
     A metal plate (metal support  1 ) according to Comparative Example 2 in which the pitch P of the front-side openings  1   d  was 150 μm (each of the front-side openings  1   d  had a diameter of 25 μm) was produced in the same manner as in Comparative Example 1. 
     Working Example 1 
     A metal plate (metal support  1 ) according to Working Example 1 was produced by performing leveler processing on a metal plate (metal support  1 ) as that in Comparative Example 1 to smooth the metal plate. 
     Working Example 2 
     A metal plate (metal support  1 ) according to Working Example 2 was produced by performing annealing processing on a metal plate (metal support  1 ) as that in Comparative Example 2 to smooth the metal plate. 
     40-mm Square Test Piece 
     Working Example 3 
     A 40-mm square (40 mm×40 mm) crofer 22 APU metal plate having a thickness of 0.3 mm was provided with a plurality of penetration spaces  1   c  through laser processing in a 28-mm square (28 mm×28 mm) region around the center, and a metal plate (metal support  1 ) according to Working Example 3 was thus produced. The penetration spaces  1   c  were provided at positions corresponding to the lattice points of an orthogonal lattice. It should be noted that each of the front-side openings  1   d  had a diameter of 25 μm, and the pitch P was 150 μm. The maximum length Lmax was 5.66 cm. 
     Next, a paste to be used for the above-mentioned metal plates of Comparative Examples 1 and 2 and Working Examples 1 to 3 was produced by mixing 60 wt % of NiO powder and 40 wt % of YSZ powder and adding an organic binder and an organic solvent (dispersion medium) thereto. An attempt was made to form the electrode layer  2  through screen printing. In the case of Comparative Examples 1 and 2 and Working Examples 1 and 2, the screen printing was performed on a 105-mm square region around the center on the surface of the metal support  1 . In the case of Working Example 3, the screen printing was performed on a 30-mm square region around the center on the surface of the metal support  1 . 
     The warping degrees of the above-mentioned comparative examples and working examples were measured using the method described in the above-mentioned embodiment. In the comparative examples (Comparative Examples 1 and 2) and Examples 1 and 2, eight points that were located away from the peripheral edge of the metal support  1  by 5% of a distance between the peripheral edge of the metal support  1  and a straight line that passes through the center of gravity G and extends in parallel with the peripheral edge were used, and in Example 3, eight points that were located away from the peripheral edge of the metal support  1  by 15% of the above-described distance were used. Regarding the comparative examples and working examples, the result of whether or not the electrode layer  2  was formed was determined. Table 1 shows the measurement results and determination results. 
     Table 1 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 Determination  
               
               
                   
                   
                 Hole  
                   
                 Maximum  
                   
                   
                 (whether or not 
               
               
                   
                 Sample  
                 diameter 
                 Pitch 
                 straight line 
                 Da value 
                 Warping 
                 electrode layer  
               
               
                   
                 shape 
                 (μm) 
                 (μm) 
                 length L (cm) 
                 (mm) 
                 degree 
                 2 was formed) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Comp. 
                 12-cm  
                 20 
                 200 
                 16.97 
                 3.619 
                 2.1 × 10 −2   
                 No 
               
               
                 Ex. 1 
                 square 
                   
                   
                   
                   
                   
                   
               
               
                 Comp. 
                 12-cm  
                 25 
                 150 
                 16.97 
                 3.949 
                 2.3 × 10 −2   
                 No 
               
               
                 Ex. 2 
                 square 
                   
                   
                   
                   
                   
                   
               
               
                 Work. 
                 12-cm  
                 20 
                 200 
                 16.97 
                 1.451 
                 8.6 × 10 −3   
                 Yes 
               
               
                 Ex. 1 
                 square 
                   
                   
                   
                   
                   
                   
               
               
                 Work. 
                 12-cm  
                 25 
                 150 
                 16.97 
                 0.709 
                 4.2 × 10 −3   
                 Yes 
               
               
                 Ex. 2 
                 square 
                   
                   
                   
                   
                   
                   
               
               
                 Work. 
                  4-cm  
                 25 
                 150 
                 5.66 
                 0.659 
                 1.1 × 10 −2   
                 Yes 
               
               
                 Ex. 3 
                 square 
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     As is clear from the results shown in Table 1, in both of the comparative examples (Comparative Examples 1 and 2), the warping degree of the metal support  1  was large, and poor printing and surface defects such as separation and breakage occurred in the formed electrode layer  2 . Accordingly, an electrode layer  2  that can be used in the electrochemical element E could not be formed on the metal support  1 . In Comparative Example 1, which had the smallest warping degree among the comparative examples, the warping degree of the metal support  1  was 2.1×10 −2 . 
     On the other hand, in all of the working examples (Working Examples 1, 2, and 3), the warping degree of the metal support  1  was small, and surface defects such as breakage and separation were reduced. Accordingly, an electrode layer  2  that can be used in the electrochemical element E could be formed. In Working Example 3, which had the largest warping degree among these working examples, the warping degree of the metal support  1  was 1.1×10 −2 . 
     It was revealed from these results that, when the warping degree of the metal support  1  is 1.5×10 −2  or less, an electrode layer  2  having reduced surface defects such as breakage and separation can be formed on the metal support  1 . 
     It should be noted that, in Example 3, the intermediate layer  3 , the electrolyte layer  4 , the reaction preventing layer  5 , and the counter electrode layer  6  were formed after the electrode layer  2  had been formed, and the electrochemical element E was thus produced. In the produced electrochemical element E, fuel gas (30° C. humidified H 2 ) and air were supplied to the electrode layer  2  and the counter electrode layer  6 , respectively, and OCV (open circuit voltage), which is one of the indices of the power generation performance of a cell for a solid oxide fuel cell, was measured at an operation temperature of 750° C. As a result, the OCV of the electrochemical element E of Working Example 3 was 1.02 V. It was revealed from this result that the electrochemical element E of Working Example 3 had a large OCV (open circuit voltage) and was thus favorable. 
     Second Embodiment 
     An electrochemical element E, an electrochemical module M, an electrochemical device Y, and an energy system Z according to a second embodiment will be described with reference to  FIGS.  2  and  3   . 
     As shown in  FIG.  2   , in the electrochemical element E according to the second embodiment, a U-shaped member  7  is attached to the back face of the metal support  1 , and the metal support  1  and the U-shaped member  7  form a tubular support. 
     The electrochemical module M is configured by stacking a plurality of electrochemical elements E with collector members  26  being sandwiched therebetween. Each of the collector members  26  is joined to the counter electrode layer  6  of the electrochemical element E and the U-shaped member  7 , and electrically connects them. 
     The electrochemical module M includes a gas manifold  17 , the collector members  26 , a terminal member, and a current extracting unit. One open end of each tubular support in the stack of the plurality of electrochemical elements E is connected to the gas manifold  17 , and gas is supplied from the gas manifold  17  to the electrochemical elements E. The supplied gas flows inside the tubular supports, and is supplied to the electrode layers  2  through the penetration spaces  1  of the metal supports  1 . 
       FIG.  3    shows an overview of the energy system Z and the electrochemical device Y. 
     The energy system Z includes the electrochemical device Y, and a heat exchanger  53  serving as a waste heat utilization system that reuses heat discharged from the electrochemical device Y. 
     The electrochemical device Y includes the electrochemical module M, a desulfurizer  31  and a reformer  34  and includes a fuel supply unit that supplies fuel gas containing a reducing component to the electrochemical module M, and an inverter  38  that extracts power from the electrochemical module M. 
     Specifically, the electrochemical device Y includes the desulfurizer  31 , a water tank  32 , a vaporizer  33 , the reformer  34 , a blower  35 , a combustion unit  36 , the inverter  38 , a control unit  39 , a storage container  40 , and the electrochemical module M. 
     The desulfurizer  31  removes sulfur compound components contained in a hydrocarbon-based raw fuel such as city gas (i.e., performs desulfurization). When a sulfur compound is contained in the raw fuel, the inclusion of the desulfurizer  31  makes it possible to suppress the influence that the sulfur compound has on the reformer  34  or the electrochemical elements E. The vaporizer  33  produces water vapor (steam) from water supplied from the water tank  32 . The reformer  34  uses the water vapor (steam) produced by the vaporizer  33  to perform steam reforming of the raw fuel desulfurized by the desulfurizer  31 , thus producing reformed gas containing hydrogen. 
     The electrochemical module M generates power by causing an electrochemical reaction to occur with use of the reformed gas supplied from the reformer  34  and air supplied from the blower  35 . The combustion unit  36  mixes the reaction exhaust gas discharged from the electrochemical module M with air, and burns combustible components in the reaction exhaust gas. 
     The electrochemical module M includes a plurality of electrochemical elements E and the gas manifold  17 . The electrochemical elements E are arranged side-by-side and electrically connected to each other, and one end portion (lower end portion) of each of the electrochemical elements E is fixed to the gas manifold  17 . The electrochemical elements E generate power by causing an electrochemical reaction to occur between the reformed gas supplied via the gas manifold  17  and air supplied from the blower  35 . 
     The inverter  38  adjusts the power output from the electrochemical module M to obtain the same voltage and frequency as electrical power received from a commercial system (not shown). The control unit  39  controls the operation of the electrochemical device Y and the energy system Z. 
     The vaporizer  33 , the reformer  34 , the electrochemical module M, and the combustion unit  36  are stored in the storage container  40 . The reformer  34  performs reforming process on the raw fuel with use of combustion heat produced by the combustion of reaction exhaust gas in the combustion unit  36 . 
     The raw fuel is supplied to the desulfurizer  31  via a raw fuel supply passage  42 , due to operation of a booster pump  41 . The water in the water tank  32  is supplied to the vaporizer  33  via a water supply passage  44 , due to operation of a water pump  43 . The raw fuel supply passage  42  merges with the water supply passage  44  at a location on the downstream side of the desulfurizer  31 , and the water and the raw fuel, which have been merged outside of the storage container  40 , are supplied to the vaporizer  33  provided in the storage container  40 . 
     The water is vaporized by the vaporizer  33  to produce water vapor. The raw fuel, which contains the water vapor produced by the vaporizer  33 , is supplied to the reformer  34  via a water vapor-containing raw fuel supply passage  45 . In the reformer  34 , the raw fuel is subjected to steam reforming, thus producing reformed gas that includes hydrogen gas as a main component (first gas including a reducing component). The reformed gas produced in the reformer  34  is supplied to the gas manifold  17  of the electrochemical module M via a reformed gas supply passage  46 . 
     The reformed gas supplied to the gas manifold  17  is distributed among the electrochemical elements E, and is supplied to the electrochemical elements E from the lower ends, which are the connection portions where the electrochemical elements E and the gas manifold  17  are connected to each other. Mainly the hydrogen (reducing component) in the reformed gas is used in the electrochemical reaction in the electrochemical elements E. The reaction exhaust gas, which contains remaining hydrogen gas not used in the reaction, is discharged from the upper ends of the electrochemical elements E to the combustion unit  36 . 
     The reaction exhaust gas is burned in the combustion unit  36 , and combustion exhaust gas is discharged from a combustion exhaust gas outlet  50  to the outside of the storage container  40 . A combustion catalyst unit  51  (e.g., a platinum-based catalyst) is provided in the combustion exhaust gas outlet  50 , and reducing components such as carbon monoxide and hydrogen contained in the combustion exhaust gas are removed by combustion. The combustion exhaust gas discharged from the combustion exhaust gas outlet  50  is sent to the heat exchanger  53  via a combustion exhaust gas discharge passage  52 . 
     The heat exchanger  53  uses supplied cool water to perform heat exchange on the combustion exhaust gas produced by combustion in the combustion unit  36 , thus producing warm water. In other words, the heat exchanger  53  operates as a waste heat utilization system that reuses heat discharged from the electrochemical device Y. 
     It should be noted that instead of the waste heat utilization system, it is possible to provide a reaction exhaust gas using unit that uses the reaction exhaust gas that is discharged from (not burned in) the electrochemical module M. The reaction exhaust gas contains remaining hydrogen gas that was not used in the reaction in the electrochemical elements E. In the reaction exhaust gas using unit, the remaining hydrogen gas is used to perform heat utilization through combustion or power generation by a fuel cell and so on, thus achieving effective energy utilization. 
     Third Embodiment 
       FIG.  4    shows another embodiment of the electrochemical module M. The electrochemical module M according to a third embodiment is configured by stacking the above-described electrochemical elements E with cell connecting members  71  being sandwiched therebetween. 
     Each of the cell connecting members  71  is a plate-like member that has electrical conductivity and does not have gas permeability, and the upper face and the lower face are respectively provided with grooves  72  that are orthogonal to each other. The cell connecting members  71  can be formed using a metal such as stainless steel or a metal oxide. 
     As shown in  FIG.  4   , when the electrochemical elements E are stacked with the cell connecting members  71  being sandwiched therebetween, a gas can be supplied to the electrochemical elements E through the grooves  72 . Specifically, the grooves  72  on one side are first gas passages  72   a  and supply gas to the front side of one electrochemical element E, that is to say, the counter electrode layer  6 . The grooves  72  on the other side are second gas passages  72   b  and supply gas from the back side of one electrochemical element E, that is, the back face of the metal support  1 , through the penetration spaces  1   c  to the electrode layers  2 . 
     In the case of operating this electrochemical module M as a fuel cell, oxygen is supplied to the first gas passages  72   a , and hydrogen is supplied to the second gas passages  72   b . Accordingly, a fuel cell reaction progresses in the electrochemical elements E, and electromotive force and electrical current are generated. The generated power is extracted to the outside of the electrochemical module M from the cell connecting members  71  at the two ends of the stack of electrochemical elements E. 
     It should be noted that although the grooves  72  that are orthogonal to each other are respectively formed on the front face and the back face of each of the cell connecting members  71  in the third embodiment, grooves  72  that are parallel to each other can be respectively formed on the front face and the back face of each of the cell connecting members  71 . 
     Other Embodiments 
     (1) In the above-mentioned embodiments, the least square plane a is calculated through the least squares method using at least four points P that are located on a plurality of straight lines L passing through the center of gravity G of the metal support  1  and are opposed to each other in the plate face of the metal support  1  with the center of gravity G being located at the center therebetween. The warping degree is calculated based on the value Da, which is a difference between the positive-side maximum displacement value and the negative-side maximum displacement value that are obtained based on the least square plane a and are opposed to each other. However, the warping degree can also be calculated using the following methods. 
     (1-1) 
     A least square value αV determined through the least squares method using at least three points P that are randomly arranged in the plate face of the metal support  1  may be calculated. That is, instead of using a plurality of points P to calculate a least square plane a that typifies the plurality of points P, a least square value αV indicated by a straight line and the like that typifies the plurality of points P may be calculated. It should be noted that, in this embodiment and the other, the least square value αV encompasses a straight line, a plane (least square plane a), and the like that typify the plurality of points P, for example. 
     Based on the least square value αV, which is indicated by a straight line or the like, a first difference D 1  between the positive-side maximum displacement value on the positive side and the least square value αV and a second difference D 2  between the negative-side maximum displacement value on the negative side and the least square value αV are calculated, for example. Furthermore, as in the above-mentioned embodiments, the warping degree is calculated by dividing Da by the maximum length Lmax so as to be capable of comparing the magnitudes of the warping degrees based on a certain value even among metal supports  1  that are different in size. 
     With the method above, as in the above-mentioned embodiments, the warping degree of the metal support  1  can be accurately determined. 
     (1-2) 
     Also, a least square value αV may be calculated through the least squares method using at least three points P that are located on at least one straight line L passing through the center of gravity G of the metal support  1  and are opposed to each other in the plate face of the metal support  1  with the center of gravity G being located at the center therebetween. A method for calculating a warping degree based on the least square value αV is the same as the above-described method. 
     With the method above, the least square value αV is calculated using points P located in a direction away from each other with respect to the center of gravity G in the plate face. That is, the least square value αV is calculated based on points P scattered in the plate face rather than points located in a localized region on the metal support  1 . Accordingly, the least square value αV is calculated as a value relating to the shape of the plate face of the metal support  1 . Using this least square value αV as a reference makes it possible to accurately calculate Da used as a reference for determining the warping degree of the metal support  1 . 
     (1-3) 
     Also, a difference Dal between the positive-side maximum displacement value and the negative-side maximum displacement value may be determined using points P located at positions that are located on at least one straight line L passing through the center of gravity G of the metal support  1  and are opposed to each other in the plate face of the metal support  1  with the center of gravity G being located at the center therebetween. In the same manner as described above, the warping degree is calculated by dividing Dal by the maximum length Lmax. 
     In this case, the difference Dal may be calculated using a plurality of points P located on one straight line L or a plurality of points P located on a plurality of straight lines L. 
     (2) In the above-mentioned embodiments, Da is divided by the maximum length Lmax so as to be capable of comparing the warping degrees based on a certain value even among metal supports  1  that are different in size. However, a value obtained by dividing Da by the area of the plate face of the metal support  1  may also be used as the warping degree. Also, in this case, the magnitudes of the warping degrees can be compared based on a certain value and determined even among metal supports  1  that are different in size. 
     (3) In the above-mentioned embodiments, a plurality of straight lines L passing through the center of gravity G of the metal support  1  divide 360° by a predetermined angle. However, a plurality of straight lines L passing through the center of gravity G may also be away from each other at random angles. 
     (4) In the above-mentioned embodiments, the points P on the metal support  1  used to calculate Da are located in the region between the peripheral edge of the metal support  1  and the hole region  1   g , namely in the peripheral edge portion OP of the metal support  1 . However, the points P on the metal support  1  used to calculate Da need only be any points P on the metal support  1  and are not limited to the points P located in the peripheral edge portion OP. 
     (5) Although the electrochemical elements E are used in a solid oxide fuel cell in the above-mentioned embodiments, the electrochemical elements E can also be used in a solid oxide electrolytic (electrolysis) cell, an oxygen sensor using a solid oxide, and the like. 
     (6) In the above-mentioned embodiments, a composite material such as NiO-GDC, Ni-GDC, NiO—YSZ, Ni-YSZ, CuO—CeO 2 , or Cu—CeO 2  is used as the material of the electrode layer  2 , and a complex oxide such as LSCF or LSM is used as the material of the counter electrode layer  6 . With this configuration, the electrode layer  2  serves as a fuel electrode (anode) when hydrogen gas is supplied thereto, and the counter electrode layer  6  serves as an air electrode (cathode) when air is supplied thereto, thus making it possible to use the electrochemical element E as a cell for a solid oxide fuel cell. It is also possible to change this configuration and thus configure an electrochemical element E such that the electrode layer  2  can be used as an air electrode and the counter electrode layer  6  can be used as a fuel electrode. That is, a complex oxide such as LSCF or LSM is used as the material of the electrode layer  2 , and a composite material such as NiO-GDC, Ni-GDC, NiO—YSZ, Ni-YSZ, CuO—CeO 2 , or Cu—CeO 2  is used as the material of the counter electrode layer  6 . With this configuration, the electrode layer  2  serves as an air electrode when air is supplied thereto, and the counter electrode layer  6  serves as a fuel electrode when hydrogen gas is supplied thereto, thus making it possible to use the electrochemical element E as a cell for a solid oxide fuel cell. 
     It should be noted that the configurations disclosed in the above-described embodiments can be used in combination with configurations disclosed in other embodiments as long as they are compatible with each other. The embodiments disclosed in this specification are illustrative, and embodiments of the present invention are not limited thereto and can be modified as appropriate without departing from the object of the present invention. 
     INDUSTRIAL APPLICABILITY 
     The present invention can be applied to an electrochemical element and a cell for a solid oxide fuel cell. 
     DESCRIPTION OF REFERENCE SIGNS 
     
         
         
           
               1  Metal support 
               1   a  Front face 
               1   b  Back face 
               1   c  Penetration space 
               1   d  Front-side opening 
               1   e  Back-side opening 
               1   f  Metal oxide layer 
               1   g  Hole region 
               1   h  Unit region 
             T Thickness 
             D Inside diameter, diameter, hole diameter 
             P Pitch, interval 
             S Area (front-side opening) 
             A Aperture ratio 
               10  First metal plate 
               10   a  First front face 
               10   b  First back face 
               10   c  First penetration space 
               10   d  First front-side opening 
               10   e  First back-side opening 
               10   g  First hole region 
               10   h  First unit region 
             T 1  Thickness 
             D 1  Inside diameter, diameter, hole diameter 
             P 1  Pitch, interval 
             S 1  Area (front-side opening) 
             A 1  Aperture ratio 
               20  Second metal plate 
               20   a  Second front face 
               20   b  Second back face 
               20   c  Second penetration space 
               20   d  Second front-side opening 
               20   e  Second back-side opening 
             T 2  Thickness 
             D 2  Inside diameter, diameter, hole diameter 
             P 2  Pitch, interval 
             G Center of gravity 
             Y Electrochemical device 
             Z Energy system 
             α Least square plane 
             αV Least square value