Conductivity measurement method

Abstract

This electrical conductivity measuring method includes: a) a step for measuring a first complex impedance between a first detecting electrode (21) and a second detecting electrode (22) at a first frequency, in a state in which a liquid (LQ) is in contact with a protective layer (50) in such a way as to face each of the first and second detecting electrodes (21, 22) across the protective layer (50); b) a step for extracting a first extracted value from the first complex impedance in accordance with an extraction rule; c) a step for determining whether the first extracted value lies within an acceptable range; d) a step for determining an electrical conductivity of the liquid (LQ) on the basis of the first extracted value if the first extracted value is determined to lie within the acceptable range in step c); and e) a step for determining the electrical conductivity of the liquid (LQ) on the basis of a second extracted value extracted in accordance with the extraction rules from a second complex impedance at a second frequency, if the first extracted value is determined to lie outside the acceptable range in step c).

Description

[Technical Field]

[0001] The present invention relates to a method for measuring conductivity, and more particularly to a method for measuring the conductivity of a liquid using a conductivity sensor. [Background technology]

[0002] International Publication No. 2021 / 241628 (Patent Document 1) discloses a capacitance-type sensor. The sensor includes an insulating layer, a first detection electrode, a second detection electrode, and a protective layer. The first detection electrode is provided on the insulating layer. The second detection electrode is provided on the insulating layer at a distance from the first detection electrode and forms the capacitance together with the first detection electrode. The protective layer covers the first and second detection electrodes, has a thickness d that satisfies 1 μm≦d≦10 μm, and is made of zirconia or alumina.

[0003] Japanese Patent Application Laid-Open Publication No. 2019-109224 (Patent Document 2) discloses a compact conductivity sensor intended to be capable of measuring a wide range of liquid conductivity even when the measurement area is small. The conductivity sensor includes first and second electrodes, each having a surface area that determines the cell constant of the sensor. At least one of the electrodes is provided with switching means arranged to change the surface area of ​​each electrode, thereby changing the cell constant of the sensor. For example, the first and second electrodes include multiple finger electrodes. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2021 / 241628 [Patent Document 2] Japanese Patent Application Publication No. 2019-109224 Summary of the Invention [Problem to be solved by the invention]

[0005] A method for measuring the conductivity of a liquid with sufficient sensitivity over a wide conductivity range using a sensor having a configuration like that of Patent Document 1 has not been fully studied. For example, it is thought that the technology of Patent Document 2 does not anticipate the formation of a protective layer as disclosed in Patent Document 1. This is because the formation of a protective layer leads to the formation of capacitance between the electrode and the liquid, and according to Patent Document 2, the impedance of the electrode increases due to the effect of the capacitance at the interface between the electrode and the liquid, which is considered to be a problem in ensuring a wide measurement range of the conductivity of the liquid. Furthermore, Patent Document 2 only discloses using an inert conductive material as the electrode material as a means of avoiding chemical interaction between the electrode and the liquid, and does not mention the use of a protective layer as such a means. The reason for this is that patents This is thought to be because the technology of Document 2 does not anticipate the addition of a protective layer that would lead to an increase in impedance.

[0006] The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a conductivity measurement method that can measure the conductivity of a liquid with sufficient sensitivity over a wide conductivity range. [Means for solving the problem]

[0007] A first aspect is a conductivity measurement method for measuring the conductivity of a liquid using a conductivity sensor including an insulating layer, a first detection electrode provided on the insulating layer, a second detection electrode provided on the insulating layer at a distance from the first detection electrode, and a protective layer made of an insulator and covering the first detection electrode and the second detection electrode, a) measuring a first complex impedance between the first detection electrode and the second detection electrode at a first frequency with the liquid in contact with the protective layer so as to face each of the first detection electrode and the second detection electrode through the protective layer; b) extracting a first extracted value from the first complex impedance according to a predetermined extraction rule; c) determining whether the first extracted value is within a predetermined tolerance range; d) determining the conductivity of the liquid based on the first extracted value if it is determined in c) that the first extracted value is within the acceptable range; and e) if it is determined in c) that the first extracted value is outside the tolerance range, determining the conductivity of the liquid based on a second extracted value extracted in accordance with the extraction rule from a second complex impedance between the first detection electrode and the second detection electrode at a second frequency different from the first frequency, with the liquid in contact with the protective layer so as to face each of the first detection electrode and the second detection electrode via the protective layer; Equipped with.

[0008] A second aspect is the conductivity measurement method of the first aspect, in which the extraction rule corresponds to extracting a reactance component from a complex impedance.

[0009] A third aspect is the conductivity measurement method of the first aspect, wherein the extraction rule corresponds to extracting an admittance absolute value from a complex impedance.

[0010] A fourth aspect is a conductivity measurement method according to the second or third aspect, wherein, if the first extracted value is greater than the tolerance range in c), the second frequency is higher than the first frequency in e).

[0011] A fifth aspect is a conductivity measurement method according to any one of the second to fourth aspects, wherein, in c), if the first extracted value is smaller than the tolerance range, in e), the second frequency is lower than the first frequency.

[0012] A sixth aspect is the conductivity measurement method according to the first aspect, wherein the extraction rule corresponds to extracting an impedance absolute value from a complex impedance.

[0013] A seventh aspect is the conductivity measurement method of the sixth aspect, wherein, when the first extracted value is greater than the tolerance range in c), the second frequency is lower than the first frequency in e).

[0014] An eighth aspect is a conductivity measurement method according to the sixth or seventh aspect, wherein, if in c) the first extracted value is smaller than the tolerance range, in e) the second frequency is higher than the first frequency.

[0015] A ninth aspect is the conductivity measurement method according to any one of the first to eighth aspects, wherein the e) is e1) measuring the second complex impedance only if it is determined in c) that the first extracted value is outside the tolerance range. Includes:

[0016] A tenth aspect is the conductivity measurement method according to any one of the first to eighth aspects, f) measuring the second complex impedance before c). Further provided are:

[0017] An eleventh aspect is a conductivity measurement method according to any one of the first to tenth aspects, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, and the space width is 200 μm or less.

[0018] A twelfth aspect is a conductivity measurement method according to any one of the first to tenth aspects, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, and the line width is 500 μm or more.

[0019] A thirteenth aspect is a conductivity measurement method according to any one of the first to tenth aspects, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, and the space width is 200 μm or less and the line width is 500 μm or more.

[0020] A fourteenth aspect is the conductivity measurement method according to any one of the eleventh to thirteenth aspects, wherein at least one of the first frequency and the second frequency is a frequency on the order of 100 kHz.

[0021] A fifteenth aspect is a conductivity measurement method according to any one of the first to tenth aspects, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a first line-and-space pattern having a first space width and a second line-and-space pattern having a second space width different from the first space width.

[0022] A sixteenth aspect is the conductivity measurement method of the fifteenth aspect, wherein the first space width is 100 μm or less, and the second space width is greater than 100 μm.

[0023] A seventeenth aspect is the conductivity measurement method according to the fifteenth or sixteenth aspect, wherein the second space width is 10 to 70 times the first space width.

[0024] An 18th aspect is a conductivity measurement method according to any one of the 15th to 17th aspects, wherein the first line and space pattern and the second line and space pattern are adjacent to each other by sharing one line.

[0025] A nineteenth aspect is the conductivity measurement method according to any one of the first to eighteenth aspects, wherein the protective layer is made of zirconia or alumina and has a thickness of 1 μm or more and 10 μm or less.

[0026] A twentieth aspect is the conductivity measurement method according to any one of the first to nineteenth aspects, wherein the protective layer is made of a sintered body. [Effects of the Invention]

[0027] According to one embodiment, if a first extracted value from a first complex impedance between the first and second sensing electrodes at a first frequency is determined to be within an acceptable range, the conductivity of the liquid is determined based on the first extracted value, and if the first extracted value from the first complex impedance between the first and second sensing electrodes at a first frequency is determined to be outside the acceptable range, the conductivity of the liquid is determined based on a second extracted value from a second complex impedance at a second frequency. This ensures that the extracted value is sufficiently sensitive to the conductivity of the liquid over a wide conductivity range. Thus, the conductivity of the liquid can be measured with sufficient sensitivity over a wide conductivity range.

[0028] The above e) is e1) measuring the second complex impedance only if it is determined in c) that the first extracted value is outside the tolerance range. This allows the measurement of the second complex impedance to be omitted when it is not necessary.

[0029] The conductivity measurement method is f) measuring the second complex impedance before c). This eliminates the need to measure the second complex impedance after step c).

[0030] In the conductivity sensor, the first detection electrodes and the second detection electrodes may be alternately positioned to form a line-and-space pattern having a line width and a space width, and the space width may be 200 μm or less, which makes it easier to ensure a detectable range of conductivity down to lower values.

[0031] In the conductivity sensor, the first detection electrodes and the second detection electrodes may be alternately positioned to form a line-and-space pattern having a line width and a space width, and the line width may be 500 μm or more, which makes it easier to ensure a detectable range of conductivity up to a higher value.

[0032] In the conductivity sensor, the first detection electrodes and the second detection electrodes may be alternately positioned to form a line-and-space pattern having a line width and a space width, where the space width may be 200 μm or less and the line width may be 500 μm or more. This makes it easier to ensure a wide range of detectable conductivity, from lower values ​​to higher values. This effect is more easily achieved when at least one of the first frequency and the second frequency is on the order of 100 kHz.

[0033] In the conductivity sensor, the first detection electrodes and the second detection electrodes may be alternately positioned to form a first line-and-space pattern having a first space width and a second line-and-space pattern having a second space width different from the first space width. This improves the linearity of the extracted value over a wide conductivity range. Therefore, the conductivity range over which the conductivity of a liquid can be measured with sufficient sensitivity and linearity can be widened. The first space width may be 100 μm or less, and the second space width may be greater than 100 μm. The second space width may be 10 to 70 times the first space width. Each of the multiple lines constituting the first line-and-space pattern may have a line length of 1 mm or more, and each of the multiple lines constituting the second line-and-space pattern may have a line length of 1 mm or more. The first line-and-space pattern and the second line-and-space pattern may each include multiple spaces. Furthermore, the first line and space pattern and the second line and space pattern may be adjacent to each other by sharing one line.

[0034] The protective layer may be made of zirconia or alumina and have a thickness of 1 μm to 10 μm. In this case, although the capacitance formed by the protective layer between the first detection electrode and the second detection electrode and the liquid has a large effect on the measurement of the impedance between the first detection electrode and the second detection electrode, according to the above embodiment, even under this effect, the conductivity of the liquid can be measured with sufficient sensitivity over a wide conductivity range.

[0035] The protective layer may be made of a sintered body. This avoids a decrease in manufacturing efficiency during the manufacture of the conductivity sensor, which would be caused by forming a protective layer made of a non-sintered body. Furthermore, since the protective layer and the insulating layer are a sintered body as an integral structure, defects originating from the interface between them are less likely to occur. This improves properties such as chemical resistance and thermal shock resistance.

[0036] The objects, features, aspects, and advantages of the present invention will become more apparent from the following detailed description and the accompanying drawings. [Brief explanation of the drawings]

[0037] [Figure 1] FIG. 1 is a front view schematically showing the configuration of a measurement system having a conductivity sensor according to a first embodiment. [Figure 2] FIG. 2 is a schematic rear view of FIG. 1. [Figure 3] FIG. 3 is a schematic partial cross-sectional view taken along line III-III in FIGS. 1 and 2. [Figure 4] FIG. 4 is a schematic partial cross-sectional view taken along line IV-IV in FIGS. 1 and 2. [Figure 5] 5 is a schematic partial cross-sectional view showing the state during the implementation of the conductivity measurement method in the field of view of FIG. 4. FIG. [Figure 6] FIG. 6 is a circuit diagram showing an approximate equivalent circuit corresponding to FIG. 5. [Figure 7] 2 is a schematic front view showing the configuration of the conductivity sensor in the measurement system of FIG. 1, with the protective layer not shown. FIG. [Figure 8] FIG. 10 is a graph showing simulation results for 100 kHz and 1000 kHz regarding the relationship between the conductivity of a liquid and the capacitance value corresponding to the reactance component extracted from the complex impedance measured by the conductivity sensor. [Figure 9] FIG. 9 is a partially enlarged view of FIG. 8. [Figure 10] FIG. 1 is a schematic flow diagram of a conductivity measuring method according to the first embodiment. [Figure 11]3 is a partial cross-sectional view schematically showing a step in a method for manufacturing the conductivity sensor according to the first embodiment. FIG. [Figure 12] FIG. 10 is a schematic flow diagram of a conductivity measuring method according to a second embodiment. [Figure 13] FIG. 11 is a schematic front view showing the configuration of the conductivity sensor in the third embodiment, with the protective layer omitted. [Figure 14] FIG. 10 is a graph showing simulation results for different line and space pattern configurations for the relationship between the conductivity of a liquid and the absolute value of admittance extracted from the complex impedance at 1000 kHz measured by a conductivity sensor. [Figure 15] FIG. 10 is a graph showing simulation results for different line and space pattern configurations for the relationship between the conductivity of a liquid and the absolute value of admittance extracted from the complex impedance at 100 kHz measured by a conductivity sensor. DETAILED DESCRIPTION OF THE INVENTION

[0038] Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0039] <First Embodiment> (composition) FIGS. 1 and 2 are a front view and a rear view, respectively, schematically illustrating the configuration of a measurement system 500 having a conductivity sensor 101 according to the present embodiment. FIG. 3 is a schematic partial cross-sectional view taken along line III-III in FIGS. 1 and 2. FIG. 4 is a schematic partial cross-sectional view taken along line IV-IV in FIGS. 1 and 2. FIG. 5 is a schematic partial cross-sectional view showing the state of a conductivity measurement method being performed in the field of view of FIG. 4. FIG. 6 is a circuit diagram showing an approximate equivalent circuit corresponding to FIG. 5. FIG. 7 is a schematic front view showing the configuration of the conductivity sensor 101, with the protective layer 50 omitted. Note that in FIGS. 1 and 2, the liquid LQ whose conductivity is to be measured by the conductivity sensor 101 is shown by a virtual line. Also, FIG. 5 illustrates the liquid LQ. To facilitate understanding of the directional relationships between the drawings, an XYZ Cartesian coordinate system is shown in each drawing. In this embodiment, the direction Z corresponds to the vertically upward direction.

[0040] The measurement system 500 includes a conductivity sensor 101 and a measuring instrument 200. The conductivity sensor 101 is a sensor for measuring the conductivity of the liquid LQ. The conductivity sensor 101 includes an insulating layer 10, a first detection electrode 21, a second detection electrode 22, and a protective layer 50. The conductivity sensor 101 may further include a first pad electrode 31, a second pad electrode 32, a first via electrode 41, and a second via electrode 42. The conductivity sensor 101 generally includes an insulating base in which electrodes including the first detection electrode 21 and the second detection electrode 22 are embedded. The insulating base is made up of the insulating layer 10 and the protective layer 50. A first pad electrode 31 and a second pad electrode 32 are provided on the conductivity sensor 101 for electrical connection to the embedded electrodes from outside the conductivity sensor 101.

[0041] The insulating layer 10 is preferably made of a ceramic insulator, and more preferably made of the same material as the protective layer 50. The thickness of the insulating layer 10 is, for example, about 1 mm.

[0042] 3 to 5, the first detection electrode 21 is provided on one surface of the insulating layer 10. The second detection electrode 22 is provided on the same surface of the insulating layer 10 at a distance from the first detection electrode 21. The minimum distance between the first detection electrode 21 and the second detection electrode 22 is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less.

[0043] In the conductivity sensor 101, the first detection electrodes 21 and the second detection electrodes 22 may be alternately positioned to form a line-and-space (L / S) pattern PT, as shown in FIG. 7 . In the example shown in FIG. 7 , the line-and-space pattern PT has a length direction along the X direction and a width direction along the Z direction. The line length LL of the line-and-space pattern PT is preferably 1 mm or more and 20 mm or less. The line-and-space pattern PT is also formed by alternatingly positioning at least one line L1 (e.g., multiple lines L1 as shown in FIG. 7 ) of the first detection electrode 21 and at least one line L2 (e.g., multiple lines L2 as shown in FIG. 7 ) of the second detection electrode 22. The minimum distance between the line L1 and the line L2, i.e., the space width WS (also referred to as the “S dimension”) of the line-and-space pattern PT, is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less. The width of each of the lines L1 and L2, ie, the line width WL (also referred to as "L dimension") of the line and space pattern PT is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less.

[0044] The first detection electrode 21 and the second detection electrode 22 are preferably made of a high-melting-point metal that is resistant to oxidation, such as platinum, tungsten, or cobalt. The thickness of the first detection electrode 21 and the second detection electrode 22 is, for example, about 5 μm.

[0045] The protective layer 50 covers the first detection electrode 21 and the second detection electrode 22. Specifically, the protective layer 50 has a surface SF and a surface opposite the surface SF that faces the first detection electrode 21 and the second detection electrode 22. The protective layer 50 has a thickness d, which preferably satisfies 1 μm≦d≦10 μm, and more preferably 1 μm≦d≦5 μm. The protective layer 50 is made of an insulator. In particular, when the protective layer 50 is made of zirconia or alumina, the corrosion resistance and chemical resistance of the conductivity sensor 101 are enhanced. The protective layer 50 has a relative dielectric constant ε, preferably ε≧10. For example, an ε of approximately 30 can be obtained by using zirconia, and an ε of approximately 10 can be obtained by using alumina. Preferably, ε / d≧1 is satisfied. The protective layer 50 is preferably made of a sintered body, for example, from the viewpoint of manufacturing efficiency.

[0046] The protective layer 50 shown in FIGS. 1 and 3 to 5 is a single layer that continuously covers both the first detection electrode 21 and the second detection electrode 22 and does not have a particular pattern. In this case, the shape of the protective layer 50 can be simple. On the other hand, if a more complex shape of the protective layer is allowed, the protective layer may have some kind of pattern as a modified example. This pattern may have first and second portions that are separated from each other, with the first portion covering the first detection electrode 21 and the second portion covering the second detection electrode 22. In this case, the first and second portions of the protective layer 50 are separated by an area where the protective layer 50 is not provided.

[0047] The first pad electrode 31 is provided on the surface of the insulating layer 10 opposite to the one surface. The second pad electrode 32 is provided on the surface of the insulating layer 10 opposite to the one surface, spaced apart from the first pad electrode 31. The first via electrode 41 penetrates the insulating layer 10, and has one end connected to the first detection electrode 21 and the other end connected to the first pad electrode 31. The second via electrode 42 penetrates the insulating layer 10, and has one end connected to the second detection electrode 22 and the other end connected to the second pad electrode 32.

[0048] The measuring instrument 200 has a function of measuring a complex impedance and a function of extracting an extracted value from the complex impedance according to a predetermined extraction rule. The measuring instrument 200 may be a typical impedance analyzer, but may also be a measuring instrument with a simpler configuration as long as the measurement method described below can be implemented. The extraction rule may be to extract a reactance component, an admittance absolute value, or an impedance absolute value from the complex impedance.

[0049] Measuring instrument 200 is electrically connected to first pad electrode 31 and second pad electrode 32. Referring to the equivalent circuit of FIG. 6, complex impedance IMP is the complex impedance between first detection electrode 21 and second detection electrode 22 in the state shown in FIG. 5. In the state shown in FIG. 5, liquid LQ is in contact with protective layer 50 so as to face each of first detection electrode 21 and second detection electrode 22 through protective layer 50. The effects of the complex impedances of first pad electrode 31, first detection electrode 21, and the first via electrode 41 therebetween, and the complex impedances of second pad electrode 32, second detection electrode 22, and the second via electrode 42 therebetween on complex impedance IMP are almost negligible. Therefore, the complex impedance measured by measuring instrument 200 is essentially the complex impedance IMP between first detection electrode 21 and second detection electrode 22 (FIG. 6).

[0050] Complex impedance generally has a resistance component and a reactance component. In the configuration of this embodiment, the reactance component is mainly due to the capacitance value formed by the protective layer 50 and the liquid LQ being disposed in the electrical path between the first detection electrode 21 and the second detection electrode 22. Therefore, hereinafter, the reactance component may be referred to as the capacitance value.

[0051] FIG. 8 is a graph showing simulation results for 100 kHz and 1000 kHz regarding the relationship between the conductivity of the liquid LQ and the capacitance value corresponding to the reactance component extracted from the complex impedance measured by the conductivity sensor 101. Note that this simulation is for a conductivity sensor 101 having a line-and-space pattern PT with a line width WL = 50 μm and a space width WS = 50 μm. FIG. 9 is a partial enlarged view of FIG. 8. As can be seen from these graphs, the sensitivity of the capacitance value to the conductivity of the liquid LQ is excellent in the conductivity range of 1 to 200 μS / cm at a frequency of 100 kHz, and is excellent in the conductivity range of 10 to 800 μS / cm at a frequency of 1000 kHz.

[0052] Tables 1 and 2 below show simulation results under various conditions of detectable conductivity when a reactance component (essentially a capacitance value) is extracted from the complex impedance.

[0053] [Table 1]

[0054] [Table 2]

[0055] In this specification, the term "detectable conductivity" refers to a range of conductivity in which the gradient of the extracted value with respect to the conductivity (unit: μS / cm) (in other words, the differential coefficient of the extracted value with respect to the conductivity) is equal to or greater than the reference value. When the extracted value is the absolute admittance value (unit: S) or the reciprocal of the resistance component (unit: S), the reference value is 10 -10 , 10 -9 , 10 -8 , 10 -7[Unit: S / (μS / cm)]. Also, if the extracted value is a capacitance value [unit: F], the reference value is 10 -14 The frequency dependence of the "detectable conductivity" is [unit: F / (μS / cm)] when the extracted value is the absolute admittance value [unit: S] or the reciprocal of the resistance component [unit: S]. This is because the frequency dependence of measurement variability is large in such cases, and this is taken into account in determining a reasonable reference value. In Tables 1 and 2 above and other tables described below, the symbol "-" indicates that the detectable conductivity range is not found within the simulation range. For example, as the dimension L or measurement frequency increases, the change in the extracted value relative to a change in conductivity tends to decrease. If this tendency becomes excessive, it becomes difficult to detect the conductivity, in other words, to calculate the conductivity with sufficient accuracy.

[0056] Furthermore, a pair of values ​​described as "L / S" indicates a combination of a line width WL and a space width WS in a line and space pattern PT. Each of the line width WL and the space width WS may be 50 μm or more and 1000 μm or less as exemplified in Tables 1 and 2 above, but is not limited to this. The line width WL and the space width WS are the same in Table 1 above, but are different in Table 2 above.

[0057] In the results of Tables 1 and 2 above, the higher the frequency, the more the detectable conductivity tends to shift to a higher conductivity region.

[0058] FIG. 10 is a schematic flow diagram of a conductivity measurement method for measuring the conductivity of the liquid LQ using the conductivity sensor 101.

[0059] In step S101, in the state of FIG. 5, a first complex impedance between the first detection electrode 21 and the second detection electrode 22 at a first frequency is measured. In the state shown in FIG. 5, as described above, the liquid LQ is in contact with the protective layer 50 so as to face each of the first detection electrode 21 and the second detection electrode 22 via the protective layer 50. This measurement may be performed by a complex impedance measurement unit (not shown) included in the measuring instrument 200. The complex impedance measurement unit has a function of measuring complex impedance at a first frequency and a second frequency (described later). In other words, the function of measuring complex impedance is a function of applying an AC signal of the above frequency to the object to be measured and measuring the ratio and phase difference between the voltage and current of the AC signal.

[0060] In step S102, a first extracted value is extracted from the first complex impedance according to a predetermined extraction rule. This extraction may be performed by an extracting unit (not shown) included in measuring instrument 200. The extracted first extracted value may be stored in a storage unit (not shown) included in measuring instrument 200.

[0061] In step S200, it is determined whether the first extracted value is within a predetermined allowable range. This determination may be made by a determination unit (not shown) included in the measuring instrument 200. The allowable range may be determined by previously investigating the range in which the sensitivity of the extracted value to the conductivity of the liquid LQ is sufficiently high. Note that in the determination process of step S200, a provisional conductivity of the liquid LQ determined from the first extracted value may be used. In this case, the aforementioned range of detectable conductivity may be used as the allowable range. In other words, the determination process may be performed based on whether the provisional conductivity is within the range of detectable conductivity. Even in this case, the definitive (as opposed to provisional) conductivity is determined in a step described below.

[0062] If it is determined in step S200 that the first extracted value is within the allowable range, then in step S303, the conductivity of the liquid LQ is determined based on the first extracted value. This determination may be made based on a correspondence relationship between the extracted value and the conductivity that has been determined in advance. This correspondence relationship may be determined experimentally, for example. This determination may be made by a determination unit (not shown) included in the measuring instrument 200.

[0063] If it is determined in step S200 that the first extracted value is outside the allowable range, in steps S401 to S403, the conductivity of the liquid LQ is determined based on a second extracted value extracted in accordance with the extraction rules from the second complex impedance between the first detection electrode 21 and the second detection electrode 22 at a second frequency in the state shown in Fig. 5. Here, the second frequency is different from the first frequency.

[0064] Specifically, first, in step S401, a second complex impedance between the first detection electrode 21 and the second detection electrode 22 at a second frequency is measured in the state of Fig. 5. In this embodiment, the second complex impedance is measured only if it is determined in step S200 that the first extracted value is outside the allowable range. Therefore, in this embodiment, in measuring instrument 200, the determination unit causes the complex impedance measurement unit to start the measurement in step S401.

[0065] In step S402, a second extracted value is extracted from the second complex impedance in accordance with the extraction rule. This extraction may be performed by the extracting unit included in the measuring instrument 200.

[0066] In step S403, the conductivity of the liquid LQ is determined based on the second extracted value. decision may be performed by the determining unit included in the measuring instrument 200.

[0067] In this way, the conductivity of the liquid LQ is determined.

[0068] The storage unit, judgment unit, and decision unit may be realized by a control device (not shown). The control device may be configured by a general computer having an electric circuit. The general computer has a central processing unit (CPU), a read-only memory (ROM), a random access memory (RAM), a storage device, an input unit, a display unit, a communication unit, and a bus line connecting these units to each other.

[0069] Furthermore, in this embodiment, a method using two frequencies, a first frequency and a second frequency, has been described, but as a modification, more than two frequencies may be used as appropriate. In this case, it is determined whether the second extracted value extracted in step S402 is within a predetermined tolerance range for the second extracted value, and based on the determination result, a third complex impedance is measured at the third frequency, followed by extraction of the third extracted value, etc. In this way, the conductivity of the liquid LQ can be determined using the optimal frequency out of more than two frequencies.

[0070] Next, the relationship between the first frequency and the second frequency will be described below.

[0071] When the extraction rule corresponds to extracting a reactance component (capacitance value) from a complex impedance, if the first extracted value is greater than the allowable range in step S200, the second frequency may be higher than the first frequency in step S401. Also, if the first extracted value is smaller than the allowable range in step S200, the second frequency may be lower than the first frequency in step S401.

[0072] When the extraction rule corresponds to extracting an admittance absolute value from the complex impedance, if the first extracted value is greater than the tolerance range in step S200, the second frequency may be higher than the first frequency in step S401. If the first extracted value is smaller than the tolerance range in step S200, the second frequency may be lower than the first frequency in step S401. Regarding simulation results for the minimum and maximum detectable conductivity when the admittance absolute value is used as the extracted value, representative results are shown in Tables 3 and 4 below, and results when parameters are systematically changed are shown in Table 5 below.

[0073] [Table 3]

[0074] [Table 4]

[0075] [Table 5]

[0076] In a case where the extraction rule corresponds to extracting an impedance absolute value from a complex impedance, if the first extracted value in step S200 is greater than the allowable range, the second frequency in step S401 may be lower than the first frequency. Also, if the first extracted value in step S200 is smaller than the allowable range, the second frequency in step S401 may be higher than the first frequency. Since the simulation results when the admittance absolute value is used as the extracted value have already been shown in Tables 3 to 5 above, description of the simulation results when the impedance absolute value corresponding to the reciprocal of the admittance absolute value is used as the extracted value will be omitted.

[0077] (Manufacturing method) FIG. 11 is a partial cross-sectional view schematically showing one step in the method for manufacturing the conductivity sensor 101 according to the present embodiment.

[0078] 3 and 11, a laminate is prepared including a green sheet 10G that will become the insulating layer 10, a paste layer 21G that will become the first detection electrode 21, a paste layer 22G that will become the second detection electrode 22, a paste layer 31G that will become the first pad electrode 31, a paste layer 32G that will become the second pad electrode 32, a paste layer 41G that will become the first via electrode 41, and a paste layer 42G that will become the second via electrode 42. Each paste layer can be formed by printing a paste containing metal powder and ceramic powder onto the green sheet 10G. The green sheet 10G may be a single layer, or may be formed by stacking multiple green sheets.

[0079] A green sheet 50G that will become the protective layer 50 is pressure-bonded onto the above-mentioned laminate as shown by the arrow (FIG. 11). This pressure-bonding is preferably performed while heating.

[0080] Next, the laminate with the green sheet 50G pressed thereon is fired, thereby obtaining the conductivity sensor 101. In this case, the protective layer 50 is therefore made of a sintered body.

[0081] (effect) According to this embodiment, if it is determined in step S200 (FIG. 10) that the first extracted value is within the allowable range, the conductivity of the liquid LQ is determined based on the first extracted value in step S303, and if it is determined in step S200 (FIG. 10) that the first extracted value is outside the allowable range, the conductivity of the liquid LQ is determined based on the second extracted value from the second complex impedance at the second frequency in steps S401 to S403. This makes it possible to ensure sufficient sensitivity of the extracted value to the conductivity of the liquid LQ over a wide conductivity range. Therefore, it is possible to measure the conductivity of the liquid LQ with sufficient sensitivity over a wide conductivity range.

[0082] In this embodiment, step S401 is performed only when it is determined in step S200 that the first extracted value is outside the allowable range, thereby making it possible to omit step S401 when it is not necessary.

[0083] The space width WS of the line and space pattern PT (FIG. 7) is preferably 200 μm or less, and more preferably 100 μm or less. This makes it easier to ensure a detectable range of conductivity down to lower values. Furthermore, from the viewpoint of ease of manufacturing the detection electrode, the space width WS is preferably 30 μm or more, and more preferably 50 μm or more.

[0084] The line width WL of the line and space pattern PT (FIG. 7) is preferably 500 μm or more, more preferably 1000 μm or more. This makes it easier to ensure a higher range of detectable conductivity. In addition, from the viewpoint of miniaturizing the detection electrode, the line width WL is preferably 2000 μm or less, more preferably 1000 μm or less. Note that if the upper limit of the conductivity to be measured is 1000, μ As long as the line width WL is on the order of S / cm, there is little need to make the line width WL excessively larger than the values ​​mentioned here.

[0085] It is more preferable that both the space width WS and the line width WL conditions are satisfied. This makes it easier to ensure a wide range of detectable conductivity, from lower values ​​to higher values. This effect is more easily achieved when the measurement frequency (in other words, at least one of the first and second frequencies) is a frequency on the order of 100 kHz. Note that the order of 100 kHz is, in other words, 10 kHz, one digit lower. z The frequencies are between the order of magnitude of 1000 kHz and the order of 1000 kHz, and of course, frequencies of about 100 kHz (e.g., 100 k Hz ±10% of the frequency range. The same applies to other frequency orders.

[0086] The line length LL (FIG. 7) of the line and space pattern PT is preferably 1 mm or more and 20 mm or less. When the line length LL is 1 mm or more, the sensitivity of the conductivity sensor 101 can be increased. When the line length LL is 20 mm or less, the probability of defects due to adhesion of foreign matter on the line and space pattern PT can be reduced. Furthermore, when the line length LL is 20 mm or less, the size of the conductivity sensor 101 can be prevented from becoming excessively large.

[0087] The space width WS is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less. When the space width WS is 30 μm or more, the space width WS can be easily controlled using general multilayer ceramic technology. When the space width WS is 2000 μm or less (more preferably 1000 μm or less), it is possible to prevent the electrical coupling between the first detection electrode 21 and the second detection electrode 22 via the liquid LQ from becoming too weak, and therefore it is easy to prevent the sensitivity of the conductivity sensor 101 from becoming too weak.

[0088] When the protective layer 50 is made of zirconia or alumina and has a thickness d of 1 μm or more and 10 μm or less, the capacitance formed by the protective layer 50 between the first detection electrode 21 and the second detection electrode 22 and the liquid LQ significantly contributes to the impedance IMP (FIG. 6). However, according to this embodiment, even under this influence, the conductivity of the liquid LQ can be measured with sufficient sensitivity over a wide conductivity range. Note that while reducing the ε / d of the protective layer 50 can suppress this influence, the sensor sensitivity is likely to decrease due to the weakened electrical coupling between the first detection electrode 21 and the second detection electrode 22 and the liquid LQ. When high sensitivity is prioritized, the material for the protective layer 50 preferably has a high relative dielectric constant ε. From this perspective, zirconia or alumina is preferred, and zirconia is more preferred. On the other hand, in order to suppress the temperature dependence of the conductivity sensor 101, alumina is preferred over zirconia as the material for the protective layer 50. From the viewpoint of the heat resistance of the conductivity sensor 101 as well, alumina is more preferable than zirconia as the material for the protective layer 50.

[0089] The protective layer 50 may be made of a sintered body. This avoids a decrease in manufacturing efficiency during the manufacture of the conductivity sensor, which would be caused by forming a protective layer made of a non-sintered body. Furthermore, because the protective layer 50 and the insulating layer 10 are sintered bodies as an integrated structure, defects originating from the interface between them are less likely to occur. This improves properties such as chemical resistance and thermal shock resistance.

[0090] Both the insulating layer 10 and the protective layer 50 are preferably made of a ceramic insulator, and more preferably made of the same material. This reduces the difference in shrinkage rate during the firing process for manufacturing the conductivity sensor 101. Therefore, even if the thickness d of the protective layer 50 is relatively small, a pinhole-free protective layer 50 can be obtained. Therefore, the thickness d can be reduced while still fully achieving the effect of improving the corrosion resistance and chemical resistance of the protective layer 50.

[0091] The portion that becomes the protective layer 50 is preferably formed by pressing a green sheet 50G (FIG. 11). This makes it possible to obtain a pinhole-free protective layer 50 even if the thickness d of the protective layer 50 is relatively small, compared to when the portion is formed by applying a ceramic paste.

[0092] The first detection electrode 21 and the second detection electrode 22 are preferably made of a high-melting point metal, such as platinum, tungsten, or cobalt, which can prevent the electrodes from volatilizing or melting during the firing process for manufacturing the conductivity sensor 101.

[0093] <Embodiment 2> In the second embodiment, another method for measuring the conductivity of liquid LQ using a measurement system substantially similar to the measurement system 500 described in the first embodiment will be described. FIG. 12 is a schematic flow diagram of the conductivity measurement method in the present embodiment. Steps S101 and S102 are performed in the same manner as in the conductivity measurement method in the first embodiment (FIG. 10). However, in the second embodiment, unlike the first embodiment, steps S401 and S402 are performed before step S200. Therefore, in the second embodiment, unlike the first embodiment, in the measuring instrument 200, the complex impedance measurement unit starts the measurement in step S401 without relying on the determination unit.

[0094] In step S200, it is determined whether or not the first extracted value is within a predetermined allowable range, as in the above-described embodiment 1. If it is determined in step S200 that the first extracted value is within the allowable range, then in step S303, the conductivity of the liquid LQ is determined based on the first extracted value, as in the above-described embodiment 1. If it is determined in step S200 that the first extracted value is outside the allowable range, then in step S403, the conductivity of the liquid LQ is determined based on the second extracted value.

[0095] In this way, the conductivity of the liquid LQ is determined. According to the present embodiment, the second complex impedance has already been measured before step S200, and therefore does not need to be measured after step S200.

[0096] In this embodiment, a method using two frequencies, a first frequency and a second frequency, has been described. However, as a modification, more than two frequencies may be used as appropriate. In this case, before step S200, the complex impedance is measured at each of the more than two frequencies and an extracted value is extracted. Then, it is determined which of these multiple extracted values ​​should be used as the basis for determining the conductivity of the liquid LQ. In this way, the conductivity of the liquid LQ can be determined using the optimal one of the more than two frequencies.

[0097] Other features of the second embodiment are almost the same as those of the first embodiment, and therefore description thereof will not be repeated.

[0098] <Third Embodiment> In the following, a conductivity sensor 102 (FIG. 13) according to the third embodiment will be described, and the conductivity sensor 101 (FIG. 7) according to the first embodiment will be additionally described.

[0099] FIG. 13 is a schematic front view showing the configuration of a conductivity sensor 102 according to the present embodiment, with the protective layer 50 omitted. In the conductivity sensor 102, first detection electrodes 21 and second detection electrodes 22 are alternately positioned to form a first line-and-space pattern PTa having a first space width WSa and a second line-and-space pattern PTb having a second space width WSb different from the first space width WSa. Here, the second space width WSb is different from the first space width WSa. The first space width WSa may be 100 μm or less, and the second space width WSb may be greater than 100 μm. Furthermore, the second space width WSb may be 10 to 70 times the first space width WSa. FIG. 14 (described later) shows an example in which the second space width WSb is 20 times the first space width WSa. If the difference between the two needs to be relatively small, the second space width WSb may be 10 to 20 times the first space width WSa. Each of the first line-and-space pattern PTa and the second line-and-space pattern PTb may include multiple spaces. The first space width WSa (in terms of its lower limit) may be, for example, 15 μm or more, or 30 μm or more. The second space width WSb (in terms of its upper limit) may be, for example, 2000 μm or less, or 1000 μm or less.

[0100] 13, each of the line and space patterns PTa and PTb has a length direction along the X direction and a width direction along the Z direction. The first line and space pattern PTa is formed by alternating between at least one line (line L1a and line L1ab in FIG. 13) included in the first detection electrode 21 and at least one line (multiple lines L2a in FIG. 13) included in the second detection electrode 22. The second line and space pattern PTb is formed by alternating between at least one line (multiple lines L1b and line L1ab in FIG. 13) included in the first detection electrode 21 and at least one line (multiple lines L2b in FIG. 13) included in the second detection electrode 22.

[0101] The first line-and-space pattern PTa and the second line-and-space pattern PTb are adjacent to each other by sharing one line L1ab. In the example of FIG. 13, the line shared by the first line-and-space pattern PTa and the second line-and-space pattern PTb is line L1ab included in the first detection electrode 21, but as a modified example, it may be a line included in the second detection electrode 22. Also, a modified example in which there is no shared line may be used, in which case the first line-and-space pattern PTa and the second line-and-space pattern PTb may be separated from each other.

[0102] Each of the multiple lines constituting the first line-and-space pattern PTa, i.e., line L1a and line L2a, may have a line length LLa of 1 mm or more and 20 mm or less. Each of the multiple lines constituting the second line-and-space pattern PTb, i.e., line L1b and line L2b, may have a line length LLb of 1 mm or more and 20 mm or less. The line lengths LLa and LLb may be the same as each other, as shown in FIG. 13, or may be different from each other. The line L1ab shared by the first line-and-space pattern PTa and the second line-and-space pattern PTb may have the line length LLa or the line length LLb.

[0103] The lines L1a and L2a of the first line-and-space pattern PTa may have a common line width WLa, which is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less. The lines L1b and L2b of the second line-and-space pattern PTb may have a common line width WLb, which is preferably 30 μm or more and 2000 μm or less, and more preferably 30 μm or more and 1000 μm or less. The line width WLb may be larger than the line width WLa. The line L1ab may have the line width WLa or the line width WLb.

[0104] 14 is a graph showing the simulation results for different line and space pattern configurations regarding the relationship between the conductivity of the liquid LQ and the admittance absolute value extracted from the complex impedance at 1000 kHz measured by the conductivity sensor. In the figure, "50 / 50 μm + 1000 / 1000 μm" corresponds to the conductivity sensor 102 of the third embodiment (FIG. 13), in which the L / S of the first line and space pattern PTa is 50 / 50 μm and the L / S of the second line and space pattern PTb is 1000 / 1000 μm. Also, "50 / 50 μm" corresponds to the conductivity sensor 101 of the first embodiment (FIG. 7), in which the L / S of the line and space pattern PT is 50 / 50 μm. Furthermore, "1000 / 1000 μm" corresponds to the conductivity sensor 101 (FIG. 7) of the first embodiment described above, in which the L / S of the line and space pattern PT is 1000 / 1000 μm. Furthermore, "1000 / 50 μm" corresponds to the conductivity sensor 101 (FIG. 7) of the first embodiment described above, in which the line width WL is 1000 μm and the space width WS is 50 μm.

[0105] In the conductivity range shown in this graph, the sensitivity of the capacitance value to the conductivity of the liquid LQ is sufficiently high for the "50 / 50 μm" conductivity sensor 101 in a conductivity range of 6 μS / cm or more, and difficult to detect for the "1000 / 1000 μm" conductivity sensor 101 over the entire range. The "50 / 50 μm + 1000 / 1000 μm" conductivity sensor 102 is sufficiently high for a conductivity range of 10 μS / cm or more, and the "1000 / 50 μm" conductivity sensor 101 is sufficiently high for a conductivity range of 40 μS / cm or more. On the other hand, it is preferable that the conductivity sensor not only has a wide detectable range but also has high linearity. In this regard, the coefficient of determination R of the regression line in the conductivity range of 1 to 500 μS / cm is 2 are shown in Table 6 below.

[0106] [Table 6]

[0107] The conductivity sensor 101 with a 1000 / 50 μm diameter has the coefficient of determination R closest to 1. 2 It can be seen that the "50 / 50 + 1000 / 1000" conductivity sensor 102 has the highest linearity. Therefore, when high linearity is required, this conductivity sensor is considered to be the most desirable. On the other hand, the "50 / 50 + 1000 / 1000" conductivity sensor 102 is considered to have a relatively good balance between the wide range of detectable conductivity and the high linearity. Note that although the "1000 / 1000" conductivity sensor 101 has high linearity, it is unable to obtain a detectable conductivity range under these simulation conditions.

[0108] Table 7 below shows the simulation results for detectable conductivities at more different frequencies.

[0109] [Table 7]

[0110] In the results for "1000 / 50" in Table 7 above, the maximum detectable conductivity can be increased by using a somewhat higher frequency, but using an excessively high frequency actually decreases it. This is because, as the measurement frequency increases, the conductivity range with relatively high detection sensitivity shifts to higher conductivities, while the change in admittance (more generally, the change in the extracted value) becomes generally slower. From this perspective, it is often preferable that the measurement frequency be 100 kHz or less.

[0111] FIG. 15 is a graph showing simulation results for different line-and-space pattern configurations regarding the relationship between the conductivity of the liquid LQ and the admittance absolute value extracted from the complex impedance at 100 kHz measured by a conductivity sensor. As can be seen from these results, at 100 kHz, a configuration having an L / S dimension of "1000 / 50" (more generally, a configuration in which the L dimension is larger than the S dimension) has higher sensitivity and linearity over a wide conductivity range compared to configurations or combinations of configurations with the same L and S dimensions. From this perspective, the L dimension is preferably 2.5 times or more the S dimension, and may be 10 times or more the S dimension. However, to avoid excessive sensor size, the L dimension is set to, for example, 40 times or less the S dimension.

[0112] The method for measuring conductivity in the third embodiment is the same as that in the first or second embodiment, and therefore the description thereof will not be repeated.

[0113] This embodiment also improves the linearity of the extracted value over a wide range of conductivity, thereby widening the conductivity range over which liquid conductivity measurements can be performed with sufficient sensitivity and linearity.

[0114] The simulation results at frequencies of 1 kHz, 10 kHz, 100 kHz, and 1000 kHz shown in the above-described embodiments are expected to roughly reflect the characteristics at frequencies of 1 kHz, 10 kHz, 100 kHz, and 1000 kHz. In particular, according to the inventors' studies, the characteristics at frequencies of 1 kHz ±10%, 10 kHz ±10%, 100 kHz ±10%, and 1000 kHz ±10% are considered to be roughly the same as the characteristics disclosed above at frequencies of 1 kHz, 10 kHz, 100 kHz, and 1000 kHz.

[0115] Furthermore, in the simulation results shown in each embodiment, the characteristics at the dimensions L and S are considered to be approximately the same as the characteristics at the dimensions L±10% and the dimensions S±10%.

[0116] The above-described embodiments and modifications may be freely combined with each other. Although the present invention has been described in detail, the above description is illustrative in all respects and does not limit the present invention. It is understood that countless modifications not illustrated can be envisioned without departing from the scope of the present invention. [Explanation of symbols]

[0117] 10: Insulating layer 21: First detection electrode 22: Second detection electrode 31: First pad electrode 32: Second pad electrode 41: First via electrode 42: Second via electrode 50 :Protective layer 101, 102: Conductivity sensor 200: Measuring instruments 500: Measurement system PT: Line and space pattern PTa: First line and space pattern PTb: Second line and space pattern

Claims

1. 1. A conductivity measurement method for measuring the conductivity of a liquid using a conductivity sensor including: an insulating layer; a first detection electrode provided on the insulating layer; a second detection electrode provided on the insulating layer at a distance from the first detection electrode; and a protective layer made of an insulator and covering the first detection electrode and the second detection electrode, a) measuring a first complex impedance between the first detection electrode and the second detection electrode at a first frequency with the liquid in contact with the protective layer so as to face each of the first detection electrode and the second detection electrode through the protective layer; b) extracting a first extracted value from the first complex impedance according to a predetermined extraction rule; c) determining whether the first extracted value is within a predetermined tolerance range; d) determining the conductivity of the liquid based on the first extracted value if it is determined in c) that the first extracted value is within the acceptable range; e) if it is determined in c) that the first extracted value is outside the tolerance range, determining the conductivity of the liquid based on a second extracted value extracted in accordance with the extraction rule from a second complex impedance between the first detection electrode and the second detection electrode at a second frequency different from the first frequency, with the liquid in contact with the protective layer so as to face each of the first detection electrode and the second detection electrode via the protective layer; A conductivity measurement method comprising:

2. The conductivity measurement method according to claim 1 , wherein the extraction rule corresponds to extracting a reactance component from a complex impedance.

3. The conductivity measurement method according to claim 1 , wherein the extraction rule corresponds to extracting an admittance absolute value from a complex impedance.

4. 4. The conductivity measurement method according to claim 2, wherein if in step c) the first extracted value is greater than the tolerance range, in step e) the second frequency is higher than the first frequency.

5. 4. The conductivity measurement method according to claim 2, wherein if in step c) the first extracted value is smaller than the tolerance range, in step e) the second frequency is lower than the first frequency.

6. The conductivity measurement method according to claim 1 , wherein the extraction rule corresponds to extracting an impedance absolute value from a complex impedance.

7. 7. The conductivity measurement method according to claim 6, wherein, if in c), the first extracted value is greater than the tolerance range, in e), the second frequency is lower than the first frequency.

8. 7. The conductivity measurement method according to claim 6, wherein, if in c), the first extracted value is smaller than the tolerance range, in e), the second frequency is higher than the first frequency.

9. The above e) is e1) measuring the second complex impedance only if it is determined in c) that the first extracted value is outside the tolerance range. The conductivity measurement method according to any one of claims 1 to 3 and 6 to 8, comprising:

10. f) measuring the second complex impedance before c). The conductivity measurement method according to any one of claims 1 to 3 and 6 to 8, further comprising:

11. 9. The conductivity measurement method according to claim 1, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, and the space width is 200 μm or less.

12. 9. The conductivity measurement method according to claim 1, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, and the line width is 500 μm or more.

13. 9. The conductivity measurement method according to claim 1, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a line and space pattern having a line width and a space width, the space width being 200 μm or less, and the line width being 500 μm or more.

14. 14. The method of claim 13, wherein at least one of the first frequency and the second frequency is a frequency on the order of 100 kHz.

15. 9. The conductivity measurement method according to claim 1, wherein in the conductivity sensor, the first detection electrodes and the second detection electrodes are alternately positioned to form a first line-and-space pattern having a first space width and a second line-and-space pattern having a second space width different from the first space width.

16. 16. The conductivity measurement method according to claim 15, wherein the first space width is equal to or less than 100 μm, and the second space width is greater than 100 μm.

17. The conductivity measurement method according to claim 15, wherein the second space width is 10 times or more and 70 times or less than the first space width.

18. 16. The conductivity measurement method according to claim 15, wherein the first line-and-space pattern and the second line-and-space pattern are adjacent to each other by sharing one line.

19. 9. The electrical conductivity measuring method according to claim 1, wherein the protective layer is made of zirconia or alumina and has a thickness of 1 μm or more and 10 μm or less.

20. The electrical conductivity measuring method according to claim 1 , wherein the protective layer is made of a sintered body.

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