Patent Publication Number: US-2021172903-A1

Title: Sensor element for gas sensor

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority from Japanese application JP 2019-222909, filed on Dec. 10, 2019, the contents of which is hereby incorporated by reference into this application. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a sensor element for a gas sensor, and, in particular, to a surface protective layer thereof. 
     Description of the Background Art 
     As a gas sensor for determining concentration of a desired gas component contained in a measurement gas, such as an exhaust gas from an internal combustion engine, a gas sensor that includes a sensor element made of an oxygen-ion conductive solid electrolyte, such as zirconia (ZrO 2 ), and including some electrodes on the surface and the inside thereof has been widely known. As the sensor element, a sensor element having an elongated planar shape and comprising a protective layer formed of a porous body (porous protective layer) in an end portion in which a part for introducing the measurement gas is provided has been known (see Japanese Patent Application Laid-Open No. 2016-65852, for example). 
     The protective layer is provided to the surface of the sensor element to secure water resistance of the sensor element when the gas sensor is in use. Specifically, the protective layer is provided to prevent, in a case where water droplets adhere to the surface of the sensor element in a state of being heated by a heater located inside the sensor element, water-induced cracking of the sensor element under the action of thermal shock caused by heat (cold) from the water droplets on the sensor element. 
     In a case where the protective layer is provided to the planar sensor element as disclosed in Japanese Patent Application Laid-Open No. 2016-65852, a portion of the protective layer farther from the heater tends to be more vulnerable to thermal shock than a portion of the protective layer closer to the heater, and thus water resistance might vary with location. 
     One possible measure is an increase in thickness of the protective layer to improve thermal shock resistance, but the increase in thickness leads to reduction in responsiveness and temperature rise performance of the sensor element. In particular, in a case where a gas inlet through which the measurement gas is introduced into the sensor element is provided in a leading end surface of the element, an excessive increase in thickness of the protective layer covering the gas inlet is not preferable as it leads to noticeable reduction in responsiveness. 
     SUMMARY 
     The present invention relates to a sensor element for a gas sensor, and is, in particular, directed to a configuration of a surface protective layer thereof. 
     According to the present invention, a sensor element for a gas sensor includes: an element base being a ceramic structure, the element base having an end surface having a gas inlet through which a measurement gas is introduced into the element base, and including a sensing part for sensing a gas component to be measured and a heater for heating the sensor element; and a leading-end protective layer disposed around an outer periphery of the element base in a predetermined range at least including the end surface, and being a porous layer including one or more unit layers, wherein the leading-end protective layer is provided on the end surface to satisfy 
     
       
         
           
             
               
                 1 
                 100000 
               
                
               
                 ∑ 
                 
                   
                     
                       T 
                       j 
                     
                     · 
                     
                       ρ 
                       j 
                     
                   
                   
                     L 
                     e 
                   
                 
               
             
             &gt; 
             
               0.05 
                
               
                   
               
                
               
                 ( 
                 
                   j 
                   = 
                   
                     1 
                     ~ 
                     n 
                   
                 
                 ) 
               
             
           
         
       
     
     where T j  (j=1 to n: n is a natural number) is a thickness in μm of a j-th unit layer of the leading-end protective layer from a side of the element base on the end surface, ρ i  is a porosity in % of the j-th unit layer, and L e  is a distance in mm from the heater to the end surface. 
     The thickness of a portion in which the gas inlet is provided of the leading-end protective layer surrounding a portion of the element base in which the temperature becomes high when the gas sensor is in use is thereby determined so that the porosity and the distance from the heater satisfy the predetermined inequality, so that good water resistance of the portion of the sensor element can be secured without causing reduction in responsiveness. 
     The sensor element preferably has an elongated planar shape, and the end surface is preferably a surface on a side of one leading end portion in a longitudinal direction of the sensor element. 
     In this case, in the sensor element including the element base having the gas inlet at a leading end thereof, good water resistance of the leading end portion can be secured without causing reduction in responsiveness. 
     It is thus an object of the present invention to provide a sensor element for a gas sensor including a protective layer having a thickness in accordance with desired water resistance on an end surface having a gas inlet. 
     These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic external perspective view of a sensor element  10 ; 
         FIG. 2  is a schematic view illustrating a configuration of a gas sensor  100  including a cross-sectional view taken along a longitudinal direction of the sensor element  10 ; 
         FIG. 3  illustrates the gas sensor  100  in a case where a leading-end protective layer  2  has a two-layer configuration of an inner leading-end protective layer  2   a  and an outer leading-end protective layer  2   b;    
         FIG. 4  is a flowchart of processing at the manufacture of the sensor element  10 ; 
         FIG. 5  illustrates a case where the leading-end protective layer  2  has the two-layer configuration, and has a non-uniform thickness; 
         FIG. 6  is a plot of a result of evaluation of water resistance according to Example 1 shown in Table 1 against a leading end thickness index value; and 
         FIG. 7  is a plot of a result of evaluation of water resistance according to Example 2 shown in Table 2 against the leading end thickness index value along with the result of evaluation according to Example 1. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     &lt;Overview of Sensor Element and Gas Sensor&gt; 
       FIG. 1  is a schematic external perspective view of a sensor element (gas sensor element)  10  according to an embodiment of the present invention.  FIG. 2  is a schematic view illustrating a configuration of a gas sensor  100  including a cross-sectional view taken along a longitudinal direction of the sensor element  10 . The sensor element  10  is a ceramic structure as a main component of the gas sensor  100  sensing a predetermined gas component in a measurement gas, and measuring concentration thereof. The sensor element  10  is a so-called limiting current gas sensor element. 
     In addition to the sensor element  10 , the gas sensor  100  mainly includes a pump cell power supply  30 , a heater power supply  40 , and a controller  50 . 
     As illustrated in  FIG. 1 , the sensor element  10  has a configuration in which one end portion of an elongated planar element base  1  is covered with a porous leading-end protective layer  2 . 
     As illustrated in  FIG. 2 , the element base  1  includes an elongated planar ceramic body  101  as a main structure, main-surface protective layers  170  are provided on two main surfaces of the ceramic body  101 , and, in the sensor element  10 , the leading-end protective layer  2  is further provided outside both an end surface (a leading end surface  101   e  of the ceramic body  101 ) and four side surfaces on a side of one leading end portion. The four side surfaces other than opposite end surfaces in the longitudinal direction of the sensor element  10  (or the element base  1 , or the ceramic body  101 ) are hereinafter simply referred to as side surfaces of the sensor element  10  (or the element base  1 , or the ceramic body  101 ). 
     The ceramic body  101  is made of ceramic containing, as a main component, zirconia (yttrium stabilized zirconia), which is an oxygen-ion conductive solid electrolyte. Various components of the sensor element  10  are provided outside and inside the ceramic body  101 . The ceramic body  101  having the configuration is dense and airtight. The configuration of the sensor element  10  illustrated in  FIG. 2  is just an example, and a specific configuration of the sensor element  10  is not limited to this configuration. 
     The sensor element  10  illustrated in  FIG. 2  is a so-called serial three-chamber structure type gas sensor element including a first internal chamber  102 , a second internal chamber  103 , and a third internal chamber  104  inside the ceramic body  101 . That is to say, in the sensor element  10 , the first internal chamber  102  communicates, through a first diffusion control part  110  and a second diffusion control part  120 , with a gas inlet  105  opening to the outside on a side of one end portion E 1  of the ceramic body  101  (the element base  1 ) (to be precise, communicating with the outside through the leading-end protective layer  2 ), the second internal chamber  103  communicates with the first internal chamber  102  through a third diffusion control part  130 , and the third internal chamber  104  communicates with the second internal chamber  103  through a fourth diffusion control part  140 . A path from the gas inlet  105  to the third internal chamber  104  is also referred to as a gas distribution part. In the sensor element  10  according to the present embodiment, the distribution part is provided straight along the longitudinal direction of the ceramic body  101 . 
     The first diffusion control part  110 , the second diffusion control part  120 , the third diffusion control part  130 , and the fourth diffusion control part  140  are each provided as two slits vertically arranged in  FIG. 2 . The first diffusion control part  110 , the second diffusion control part  120 , the third diffusion control part  130 , and the fourth diffusion control part  140  provide predetermined diffusion resistance to the measurement gas passing therethrough. A buffer space  115  having an effect of buffering pulsation of the measurement gas is provided between the first diffusion control part  110  and the second diffusion control part  120 . 
     An outer pump electrode  141  is provided on an outer surface of the ceramic body  101 , and an inner pump electrode  142  is provided in the first internal chamber  102 . Furthermore, an auxiliary pump electrode  143  is provided in the second internal chamber  103 , and a measurement electrode  145  as a sensing part for directly sensing a gas component to be measured is provided in the third internal chamber  104 . In addition, a reference gas inlet  106  which communicates with the outside and through which a reference gas is introduced is provided on a side of the other end portion E 2  of the ceramic body  101 , and a reference electrode  147  is provided in the reference gas inlet  106 . 
     In a case where a target of measurement of the sensor element  10  is NOx in the measurement gas, for example, concentration of a NOx gas in the measurement gas is calculated by a process as described below. 
     First, the measurement gas introduced into the first internal chamber  102  is adjusted to have a substantially constant oxygen concentration by a pumping action (pumping in or out of oxygen) of a main pump cell P 1 , and then introduced into the second internal chamber  103 . The main pump cell P 1  is an electrochemical pump cell including the outer pump electrode  141 , the inner pump electrode  142 , and a ceramic layer  101   a  that is a portion of the ceramic body  101  existing between these electrodes. In the second internal chamber  103 , oxygen in the measurement gas is pumped out of the element by a pumping action of an auxiliary pump cell P 2  that is also an electrochemical pump cell, so that the measurement gas is in a sufficiently low oxygen partial pressure state. The auxiliary pump cell P 2  includes the outer pump electrode  141 , the auxiliary pump electrode  143 , and a ceramic layer  101   b  that is a portion of the ceramic body  101  existing between these electrodes. 
     The outer pump electrode  141 , the inner pump electrode  142 , and the auxiliary pump electrode  143  are each formed as a porous cermet electrode (e.g., a cermet electrode made of ZrO 2  and Pt that contains Au of 1%). The inner pump electrode  142  and the auxiliary pump electrode  143  to be in contact with the measurement gas are each formed using a material having weakened or no reducing ability with respect to a NOx component in the measurement gas. 
     NOx in the measurement gas caused by the auxiliary pump cell P 2  to be in the low oxygen partial pressure state is introduced into the third internal chamber  104 , and reduced or decomposed by the measurement electrode  145  provided in the third internal chamber  104 . The measurement electrode  145  is a porous cermet electrode also functioning as a NOx reduction catalyst that reduces NOx existing in an atmosphere in the third internal chamber  104 . During the reduction or decomposition, a potential difference between the measurement electrode  145  and the reference electrode  147  is maintained constant. Oxygen ions generated by the above-mentioned reduction or decomposition are pumped out of the element by a measurement pump cell P 3 . The measurement pump cell P 3  includes the outer pump electrode  141 , the measurement electrode  145 , and a ceramic layer  101   c  that is a portion of the ceramic body  101  existing between these electrodes. The measurement pump cell P 3  is an electrochemical pump cell pumping out oxygen generated by decomposition of NOx in an atmosphere around the measurement electrode  145 . 
     Pumping (pumping in or out of oxygen) of the main pump cell P 1 , the auxiliary pump cell P 2 , and the measurement pump cell P 3  is achieved, under control performed by the controller  50 , by the pump cell power supply (variable power supply)  30  applying a voltage necessary for pumping across electrodes included in each of the pump cells. In a case of the measurement pump cell P 3 , a voltage is applied across the outer pump electrode  141  and the measurement electrode  145  so that the potential difference between the measurement electrode  145  and the reference electrode  147  is maintained at a predetermined value. The pump cell power supply  30  is typically provided for each pump cell. 
     The controller  50  detects a pump current Ip 2  flowing between the measurement electrode  145  and the outer pump electrode  141  in accordance with the amount of oxygen pumped out by the measurement pump cell P 3 , and calculates a NOx concentration in the measurement gas based on a linear relationship between a current value (NOx signal) of the pump current Ip 2  and the concentration of decomposed NOx. 
     The gas sensor  100  preferably includes a plurality of electrochemical sensor cells, which are not illustrated, sensing the potential difference between each pump electrode and the reference electrode  147 , and each pump cell is controlled by the controller  50  based on a signal detected by each sensor cell. 
     In the sensor element  10 , a heater  150  is buried in the ceramic body  101 . The heater  150  is provided, below the gas distribution part in  FIG. 2 , over a range from the vicinity of the one end portion E 1  to at least a location of formation of the measurement electrode  145  and the reference electrode  147 . The heater  150  is provided mainly to heat the sensor element  10  to enhance oxygen-ion conductivity of the solid electrolyte forming the ceramic body  101  when the sensor element  10  is in use. More particularly, the heater  150  is provided to be surrounded by an insulating layer  151 . 
     The heater  150  is a resistance heating body made, for example, of platinum. The heater  150  generates heat by being powered from the heater power supply  40  under control performed by the controller  50 . 
     The sensor element  10  according to the present embodiment is heated by the heater  150  when being in use so that the temperature at least in a range from the first internal chamber  102  to the second internal chamber  103  becomes 500° C. or more. In some cases, the sensor element  10  is heated so that the temperature of the gas distribution part as a whole from the gas inlet  105  to the third internal chamber  104  becomes 500° C. or more. These are to enhance the oxygen-ion conductivity of the solid electrolyte forming each pump cell and to desirably demonstrate the ability of each pump cell. In this case, the temperature in the vicinity of the first internal chamber  102 , which becomes the highest temperature, becomes approximately 700° C. to 800° C. 
     In the following description, from among the two main surfaces of the element base  1  (the ceramic body  101 ), a main surface (or an outer surface of the sensor element  10  having the main surface) which is located on an upper side in  FIG. 2  and on a side where the main pump cell P 1 , the auxiliary pump cell P 2 , and the measurement pump cell P 3  are mainly provided is also referred to as a pump surface  1   p , and a main surface (or an outer surface of the sensor element  10  having the main surface) which is located on a lower side in  FIG. 2  and on a side where the heater  150  is provided is also referred to as a heater surface  1   h . In other words, the pump surface  1   p  is a main surface closer to the gas inlet  105 , the three internal chambers, and the pump cells than to the heater  150 , and the heater surface  1   h  is a main surface closer to the heater  150  than to the gas inlet  105 , the three internal chambers, and the pump cells. 
     A plurality of electrode terminals  160  are formed on the respective main surfaces of the ceramic body  101  on the side of the other end portion E 2  to establish electrical connection between the sensor element  10  and the outside. These electrode terminals  160  are electrically connected to the above-mentioned five electrodes, opposite ends of the heater  150 , and a lead for detecting heater resistance, which is not illustrated, through leads provided inside the ceramic body  101 , which are not illustrated, to have a predetermined correspondence relationship. Application of a voltage from the pump cell power supply  30  to each pump cell of the sensor element  10  and heating by the heater  150  by being powered from the heater power supply  40  are thus performed through the electrode terminals  160 . 
     The sensor element  10  further includes the above-mentioned main-surface protective layers  170  ( 170   a  and  170   b ) on the pump surface  1   p  and the heater surface  1   h  of the ceramic body  101 . The main-surface protective layers  170  are layers made of alumina, having a thickness of approximately 5 μm to 30 μm, and including pores with a porosity of approximately 20% to 40%, and are provided to prevent adherence of any foreign matter and poisoning substances to the main surfaces (the pump surface  1   p  and the heater surface  1   h ) of the ceramic body  101  and the outer pump electrode  141  provided on a side of the pump surface  1   p . The main-surface protective layer  170   a  on the side of the pump surface  1   p  thus functions as a pump electrode protective layer for protecting the outer pump electrode  141 . 
     In the present embodiment, the porosity is obtained by applying a known image processing method (e.g., binarization processing) to a scanning electron microscope (SEM) image of an evaluation target. 
     The main-surface protective layers  170  are provided over substantially all of the pump surface  1   p  and the heater surface  1   h  except that the electrode terminals  160  are partially exposed in  FIG. 2 , but this is just an example. The main-surface protective layers  170  may locally be provided in the vicinity of the outer pump electrode  141  on the side of the one end portion E 1  compared with the case illustrated in  FIG. 2 . 
     &lt;Details of Leading-end Protective Layer&gt; 
     In the sensor element  10 , the leading-end protective layer  2  is provided around an outermost periphery of the element base  1  having a configuration as described above in a predetermined range from the one end portion E 1 . 
     The leading-end protective layer  2  is provided in a manner of surrounding a portion of the element base  1  in which the temperature becomes high (up to approximately 700° C. to 800° C.) when the gas sensor  100  is in use, in order to secure water resistance in the portion to thereby suppress the occurrence of cracking (water-induced cracking) of the element base  1  due to thermal shock caused by local temperature reduction upon direct contact of the portion with water. 
     In the present embodiment, as a result of repeating dropping of a predetermined amount of water onto the leading-end protective layer  2  until any abnormality of a pump current Ip 0  occurs before and after dropping, a maximum amount of dropped water not causing the abnormality of the pump current Ip 0  is defined as a critical water amount. Whether water resistance is good or not is determined based on the magnitude of a value of the critical water amount. In this case, the term “water resistance” can be used in the sense of the critical water amount. 
     In addition, the leading-end protective layer  2  is provided to secure poisoning resistance to prevent poisoning substances, such as Mg, from entering into the sensor element  10 . 
     The leading-end protective layer  2  is provided to cover the leading end surface  101   e  and the four side surfaces of the element base  1  on the side of the one end portion E 1  (around an outer periphery of the element base  1  on the side of the one end portion E 1 ). A portion of the leading-end protective layer  2  on a side of the leading end surface  101   e  is particularly referred to as a leading end portion  2   e , a portion of the leading-end protective layer  2  on the side of the pump surface  1   p  is particularly referred to as a pump surface portion  2   p , and a portion of the leading-end protective layer  2  on a side of the heater surface  1   h  is particularly referred to as a heater surface portion  2   h.    
     The leading-end protective layer  2  is made of alumina to have a porosity of 10% to 40%. The leading-end protective layer  2  is provided as a low thermal conductivity layer having a high porosity to have a function to suppress thermal conduction from the outside to the element base  1 . 
     The leading-end protective layer  2  is formed to have a thickness in light of a positional relationship among the two main surfaces (the pump surface  1   p  and the heater surface  1   h ) of the element base  1  as main formation target surfaces, the leading end surface  101   e  of the ceramic body  101  having the gas inlet  105 , and the heater  150  while securing water resistance of the sensor element  10 . Details thereof will be described later. 
     The leading-end protective layer  2  is formed by sequentially thermal spraying (plasma-spraying) a material therefor onto the element base  1 . This is to develop an anchoring effect between the element base  1  and the leading-end protective layer  2  to thereby secure bonding (adhesion) of the leading-end protective layer  2  to the element base  1 . 
     &lt;Case where Leading-End Protective Layer has Laminated Structure&gt; 
     While  FIG. 2  illustrates the sensor element  10  including the leading-end protective layer  2  as a single layer, the leading-end protective layer  2  may have a laminated structure in which two or more layers (unit layers) are laminated.  FIG. 3  illustrates the gas sensor  100  in a case where the leading-end protective layer  2  has a two-layer configuration of an inner leading-end protective layer  2   a  and an outer leading-end protective layer  2   b . In a case illustrated in  FIG. 3 , the inner leading-end protective layer  2   a  is the same layer as the leading-end protective layer  2  of the sensor element  10  illustrated in  FIG. 2 , and the outer leading-end protective layer  2   b  is provided to surround the inner leading-end protective layer  2   a.    
     The outer leading-end protective layer  2   b  is made of alumina, and has a smaller porosity of 10% to 40% than any other layer (the inner leading-end protective layer  2   a  in the case illustrated in  FIG. 3 ) located inside the outer leading-end protective layer  2   b . The leading-end protective layer  2  illustrated in  FIG. 3  thus has a configuration in which a layer having a lower thermal conductivity than the outer leading-end protective layer  2   b  is covered with the outer leading-end protective layer  2   b  having a smaller porosity than the layer. 
     As with the inner leading-end protective layer  2   a , the outer leading-end protective layer  2   b  is formed by sequentially thermal spraying (plasma-spraying) a material therefor. 
     In a case where the leading-end protective layer  2  has the laminated structure as described above, each unit layer is formed to have a thickness in light of the positional relationship among the pump surface  1   p , the heater surface  1   h , the leading end surface  101   e , and the heater  150  while securing water resistance of the sensor element  10 . As a result, the leading-end protective layer  2  has a total thickness in light of the positional relationship. 
     An underlying layer, which is not illustrated, may be formed between the element base  1  and the inner leading-end protective layer  2   a  to enhance adhesion of the inner leading-end protective layer  2   a . In contrast to the inner leading-end protective layer  2   a  and the like formed by thermal spraying after completion of the element base  1 , the underlying layer is formed simultaneously with the element base  1 . 
     &lt;Thickness of Each Portion of Leading-End Protective Layer&gt; 
     The thickness (the total thickness) of each portion of the leading-end protective layer  2  comprised in the sensor element  10  of the gas sensor  100  according to the present embodiment will be described next. In the present embodiment, the leading-end protective layer  2  is formed to have a thickness in light of the positional relationship among the pump surface  1   p , the heater surface  1   h , the leading end surface  101   e , and the heater  150  as described above. 
     A relationship between the thickness of the leading-end protective layer  2  on each of the side of the pump surface  1   p  and the side of the heater surface  1   h  and the location of the heater  150  will be described first. 
     The leading-end protective layer  2  is provided so that an inequality (1) below is satisfied in each of the pump surface portion  2   p  and the heater surface portion  2   h , where n (n is a natural number) is the number of unit layers constituting the leading-end protective layer  2 , T s,i  (i=1 to n) is the thickness in μm of the i-th unit layer from a side of the element base  1  (s=p in a case of the thickness of the pump surface portion  2   p , and  s =h in a case of the thickness of the heater surface portion  2   h ), ρ i  is the porosity in % of the i-th unit layer, and L s  is the distance in mm from the heater  150  to the main surface of the element base  1  (s=p in a case of the distance on the side of the pump surface  1   p , and  s =h in a case of the distance on the side of the heater surface  1   h ). 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       100000 
                     
                      
                     
                       ∑ 
                       
                         
                           
                             T 
                             
                               s 
                               , 
                               i 
                             
                           
                           · 
                           
                             ρ 
                             i 
                           
                         
                         
                           L 
                           s 
                         
                       
                     
                   
                   &gt; 
                   
                     0.1 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         s 
                         = 
                         
                           
                             p 
                              
                             
                                 
                             
                              
                             or 
                              
                             
                                 
                             
                              
                             
                               h 
                               : 
                               
                                   
                               
                                
                               i 
                             
                           
                           = 
                           
                             1 
                             ~ 
                             n 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In this case, good water resistance of the pump surface portion  2   p  and the heater surface portion  2   h  is secured. More particularly, water resistance of more than 6 μL can be obtained. A value on a left-hand side of the inequality is hereinafter referred to as a main surface thickness index value. 
     In a case where the number of unit layers is one (i=1) as in the sensor element  10  illustrated in  FIG. 2 , a subscript i in the inequality (1) may be omitted. In  FIG. 2 , T p,i =T p  and T h,i =T h . In  FIG. 3 , T p,1 =T p,1 , T h,1 =T h1 , T p,2 =T p2 , and T h,2 =T h2 . 
     The main surface thickness index value is known to have a positive correlation with water resistance. That is to say, the sensor element  10  having a greater main surface thickness index value has better water resistance on each of the side of the pump surface  1   p  and the side of the heater surface  1   h  of the sensor element  10 . More particularly, a term T s,i ·ρ i /L s  providing the main surface thickness index value is inversely proportional to the distance L s  from the heater  150  to the main surface of the element base  1 , and is proportional to the thickness T s,i  of the unit layer. The inequality (1) thus means that excellent water resistance of the pump surface portion  2   p  and the heater surface portion  2   h  can be obtained by providing the unit layers constituting the pump surface portion  2   p  and the unit layers constituting the heater surface portion  2   h  respectively on the side of the pump surface  1   p  and the side of the heater surface  1   h  so that each unit layer has a thickness in light of the distance L s  from the heater  150  to the main surface of the element base  1 . This is presumably because, as the distance between the heater  150  and each main surface of the element base  1  increases, a temperature difference inside the sensor element  10  increases, and thermal shock resistance is deteriorated. In a case of the sensor element  10  illustrated in each of  FIGS. 2 and 3 , the heater surface  1   h  is closer to the heater  150  than the pump surface  1   p  is, so that the heater surface portion  2   h  is formed to have a smaller thickness than the pump surface portion  2   p  to cause the heater surface portion  2   h  and the pump surface portion  2   p  to have equivalent water resistance. 
     On the other hand, an excessive increase in thickness of the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  in each of the pump surface portion  2   p  and the heater surface portion  2   h  is not preferable because a thermal load applied to the heater  150  at a temperature rise increases, and, as a result, the sensor element  10  can be cracked. From this perspective, the inner leading-end protective layer  2   a  preferably has a thickness of 800 μm or less, and the outer leading-end protective layer  2   b  preferably has a thickness of 400 μm or less in each of the pump surface portion  2   p  and the heater surface portion  2   h.    
     A relationship between the thickness of the leading-end protective layer  2  on a side of the leading end surface  101   e  having the gas inlet  105  and the location of the heater  150  will be described next. 
     The leading-end protective layer  2  is provided on the leading end surface  101   e  so that an inequality (2) below is satisfied, where n (n is a natural number) is the number of unit layers constituting the leading end portion  2   e  of the leading-end protective layer  2 , T j  (j=1 to n) is the thickness (a size in the longitudinal direction of the element) of the j-th unit layer from the side of the element body  1 , ρ j  is the porosity in % of the j-th unit layer, and L e  is the distance in mm from the heater  150  to the leading end surface  101   e . 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       100000 
                     
                      
                     
                       ∑ 
                       
                         
                           
                             T 
                             j 
                           
                           · 
                           
                             ρ 
                             j 
                           
                         
                         
                           L 
                           e 
                         
                       
                     
                   
                   &gt; 
                   
                     0.05 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         j 
                         = 
                         
                           1 
                           ~ 
                           n 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In this case, good water resistance of the leading end portion  2   e  of the leading-end protective layer  2  is secured. More particularly, water resistance of more than 5 μL can be obtained. A value on a left-hand side of the inequality is hereinafter referred to as a leading end thickness index value. 
     In a case of a single layer as illustrated in  FIG. 2 , the leading-end protective layer  2  satisfying the inequality (2) is achieved, for example, when: 
       300 μm≤ T   1 ≤500 μm;
 
       20%≤ρ 1 ≤30%; and
 
       0.35 mm≤ L   e ≤1.3 mm
 
     In a case of the two-layer configuration as illustrated in  FIG. 3 , the leading-end protective layer  2  satisfying the inequality (2) is achieved, for example, when: 
       300 μm≤ T   1 ≤850 μm;
 
       40%≤ρ 1 ≤80%;
 
       150 μm≤ T   2 ≤350 μm;
 
       15%≤ρ 2 ≤40%; and
 
       0.35 mm≤ L   e ≤1.3 mm
 
     As with the main surface thickness index value, the leading end thickness index value is known to have a positive correlation with water resistance. That is to say, the sensor element  10  having a greater leading end thickness index value has better water resistance on the side of the one end portion E 1 . More particularly, a term T j ·ρ j /L e  providing the leading end thickness index value is inversely proportional to the distance L e  from the heater  150  to the leading end surface  101   e , and is proportional to the thickness T j  of the unit layer on the side of the one end portion E 1 . The inequality (2) thus means that excellent water resistance of the leading end portion  2   e  can be obtained by providing the unit layers constituting the leading end portion  2   e  so that each unit layer has a thickness in light of the distance L e  from the heater  150  to the leading end surface  101   e . This is also presumably because, as the distance between the heater  150  and the leading end surface  101   e  increases, the temperature difference inside the sensor element  10  increases, and thermal shock resistance is deteriorated. 
     Viewed in another way, water resistance of the sensor element  10  is secured as long as the thickness of each unit layer is determined so that the inequality (1) is satisfied in each of the pump surface portion  2   p  and the heater surface portion  2   h , and the inequality (2) is satisfied in the leading end portion  2   e . It can thus be said that there is less need to provide the leading-end protective layer  2  having an extremely large thickness. In such a case, reduction in responsiveness and temperature rise performance becomes a concern. It can thus be said that the inequalities (1) and (2) are requirements to secure water resistance on the side of the main surfaces and on the side of the one end portion without causing reduction in responsiveness and temperature rise performance. 
     The leading-end protective layer  2  is preferably provided to have the two-layer configuration of the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  as illustrated in  FIG. 3 , and to satisfy an inequality (3) below. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       100000 
                     
                      
                     
                       ∑ 
                       
                         
                           
                             T 
                             j 
                           
                           · 
                           
                             ρ 
                             j 
                           
                         
                         
                           L 
                           e 
                         
                       
                     
                   
                   &gt; 
                   
                     0.18 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           j 
                           = 
                           1 
                         
                         , 
                         2 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In this case, better water resistance of the leading end portion  2   e  is secured. More particularly, water resistance of more than 10 μL can be obtained. 
     The leading-end protective layer  2  satisfying the inequality (3) is achieved, for example, when: 
       300 μm≤ T   1 ≤850 μm;
 
       40%≤ρ 1 ≤80%;
 
       150 μm≤ T   2 ≤350 μm;
 
       15%≤ρ 2 ≤40%; and
 
       0.35 mm≤ L   e ≤1.3 mm
 
     The leading-end protective layer  2  is more preferably provided on the leading end surface  101   e  to satisfy an inequality (4) below. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       100000 
                     
                      
                     
                       ∑ 
                       
                         
                           
                             T 
                             j 
                           
                           · 
                           
                             ρ 
                             j 
                           
                         
                         
                           L 
                           e 
                         
                       
                     
                   
                   &gt; 
                   
                     0.25 
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           j 
                           = 
                           1 
                         
                         , 
                         2 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In this case, extremely good water resistance of the leading end portion  2   e  is secured. More particularly, water resistance of more than 20 μL can be obtained. 
     The leading-end protective layer  2  satisfying the inequality (4) is achieved, for example, when: 
       300 μm≤ T   1 ≤850 μm;
 
       50%≤ρ 1 ≤80%;
 
       250 μm≤ T   2 ≤350 μm;
 
       15%≤ρ 2 ≤40%; and
 
       0.35 mm≤ L   e ≤1.3 mm
 
     As set forth above, in the sensor element according to the present embodiment, the thickness of a portion in which the gas inlet is provided of the leading-end protective layer surrounding a portion of the element base in which the temperature becomes high when the gas sensor is in use is determined to satisfy the inequality (2), so that good water resistance of the portion of the sensor element can be secured without causing reduction in responsiveness. 
     &lt;Process of Manufacturing Sensor Element&gt; 
     One example of a process of manufacturing the sensor element  10  having a configuration and features as described above will be described next.  FIG. 4  is a flowchart of processing at the manufacture of the sensor element  10  by taking, an example, a case where the leading-end protective layer  2  includes the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  as illustrated in  FIG. 3 . 
     At the manufacture of the element base  1 , a plurality of blank sheets (not illustrated) being green sheets containing the oxygen-ion conductive solid electrolyte, such as zirconia, as a ceramic component and having no pattern formed thereon are prepared first (step S 1 ). 
     The blank sheets have a plurality of sheet holes used for positioning in printing and lamination. The sheet holes are formed to the blank sheets in advance prior to pattern formation through, for example, punching by a punching machine. Green sheets corresponding to a portion of the ceramic body  101  in which an internal space is formed also include penetrating portions corresponding to the internal space formed in advance through, for example, punching as described above. The blank sheets are not required to have the same thickness, and may have different thicknesses in accordance with corresponding portions of the element base  1  eventually formed. 
     After preparation of the blank sheets corresponding to the respective layers, pattern printing and drying are performed on the individual blank sheets (step S 2 ). Specifically, a pattern of various electrodes, a pattern of the heater  150  and the insulating layer  151 , a pattern of the electrode terminals  160 , a pattern of the main surface protective layers  170 , a pattern of internal wiring, which is not illustrated, and the like are formed. Application or placement of a sublimable material (vanishing material) for forming the first diffusion control part  110 , the second diffusion control part  120 , the third diffusion control part  130 , and the fourth diffusion control part  140  is also performed at the time of pattern printing. In a case where the underlying layer is formed, a pattern to form the underlying layer is printed onto blank sheets to become an uppermost layer and a lowermost layer after lamination. 
     The patterns are printed by applying pastes for pattern formation prepared in accordance with the properties required for respective formation targets onto the blank sheets using known screen printing technology. A known drying means can be used for drying after printing. 
     After pattern printing on each of the blank sheets, printing and drying of a bonding paste are performed to laminate and bond the green sheets (step S 3 ). The known screen printing technology can be used for printing of the bonding paste, and the known drying means can be used for drying after printing. 
     The green sheets to which an adhesive has been applied are then stacked in a predetermined order, and the stacked green sheets are crimped under predetermined temperature and pressure conditions to thereby form a laminated body (step S 4 ). Specifically, crimping is performed by stacking and holding the green sheets as a target of lamination on a predetermined lamination jig, which is not illustrated, while positioning the green sheets at the sheet holes, and then heating and pressurizing the green sheets together with the lamination jig using a lamination machine, such as a known hydraulic pressing machine. The pressure, temperature, and time for heating and pressurizing depend on a lamination machine to be used, and these conditions may be determined appropriately to achieve good lamination. The pattern to form the underlying layer may be formed on the laminated body obtained in this manner. 
     After the laminated body is obtained as described above, the laminated body is cut out at a plurality of locations to obtain unit bodies eventually becoming the individual element bases  1  (step S 5 ). 
     The unit bodies as obtained are then each fired at a firing temperature of approximately 1300° C. to 1500° C. (step S 6 ). The element base  1  is thereby manufactured. That is to say, the element base  1  is generated by integrally firing the ceramic body  101  made of the solid electrolyte, the electrodes, and the main surface protective layers  170 . Integral firing is performed in this manner, so that the electrodes each have sufficient adhesion strength in the element base  1 . 
     After the element base  1  is manufactured in the above-mentioned manner, the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  are formed with respect to the element base  1 . The inner leading-end protective layer  2   a  is formed by thermal spraying powder (alumina powder) for forming the inner leading-end protective layer prepared in advance at a location of the element base  1  as a target of formation of the inner leading-end protective layer  2   a  to have an intended thickness (step S 7 ), and then firing the element base  1  on which an applied film has been formed in the above manner (step S 8 ). The alumina powder for forming the inner leading-end protective layer contains alumina powder having predetermined particle size distribution and a pore-forming material at a ratio corresponding to a desired porosity, and the pore-forming material is pyrolyzed by firing of the element base  1  after thermal spraying to suitably form the inner leading-end protective layer  2   a  having a high porosity of 40% to 80%. Known technology is applicable to thermal spraying and firing. 
     The inner leading-end protective layer  2   a  can be caused to have different thicknesses on the side of the pump surface  1   p , on the side of the heater surface  1   h , and on the side of the leading end surface  101   e , for example, by reduction in speed of thermal spraying, repeating of thermal spraying onto the same portion, and other methods at formation on a side on which the thickness is to be increased. 
     Upon formation of the inner leading-end protective layer  2   a , powder (alumina powder) for forming the outer leading-end protective layer similarly prepared in advance and containing alumina powder having predetermined particle size distribution is thermal sprayed at a location of the element base  1  as a target of formation of the outer leading-end protective layer  2   b  to have an intended thickness (step S 9 ) to thereby form the outer leading-end protective layer  2   b  having a desired porosity. The alumina powder for forming the outer leading-end protective layer does not contain the pore-forming material. Known technology is also applicable to the thermal spraying. Measures to be taken in a case where the outer leading-end protective layer  2   b  is caused to have different thicknesses on the side of the pump surface  1   p , on the side of the heater surface  1   h , and on the side of the leading end surface  101   e  are similar to those taken at formation of the inner leading-end protective layer  2   a.    
     In a case where the leading-end protective layer  2  is provided as a single layer as illustrated in  FIG. 2 , the above-mentioned step S 9  is unnecessary. 
     The sensor element  10  is obtained by the above-mentioned procedures. The sensor element  10  thus obtained is housed in a predetermined housing, and built into the body (not illustrated) of the gas sensor  100 . 
     &lt;Modifications&gt; 
     The above-mentioned embodiment is targeted at a sensor element having three internal chambers, but the sensor element is not necessarily required to have a three-chamber structure. That is to say, the sensor element may have one internal chamber or two internal chambers. 
     The above-mentioned embodiment is based on the assumption that the unit layers constituting the leading-end protective layer  2  have a uniform thickness in the leading end portion  2   e , but the thickness in the leading end portion  2   e  is sometimes not uniform depending on the shape of the leading-end protective layer  2 . One example of such a case is a case where the thickness T p  on the side of the pump surface  1   p  or the thickness T h  on the side of the heater surface  1   h  is intentionally caused to be different from the thickness T e  on the side of the leading end surface  101   e.    
       FIG. 5  illustrates a case where the leading-end protective layer  2  has the two-layer configuration, and has a non-uniform thickness. In such a case, after the size along the pump surface  1   p  of the element base  1 , the size along the heater surface  1   h  of the element base  1 , and the size at a location equidistant from the pump surface  1   p  and the heater surface  1   h  are specified, an average value of them may be used as a value of T j  in the above-mentioned inequalities (2) to (4). In a case illustrated in  FIG. 5 , equations below are satisfied: 
         T   1 =( T   1p   +T   1h   +T   1c )/3; and 
         T   2 =( T   2p   +T   2h   +T   2e )/3. 
     In the above-mentioned embodiment, after thermal spraying of the powder for forming the inner leading-end protective layer in the step S 7 , firing is performed in the step S 8 , and then thermal spraying of the powder for forming the outer leading-end protective layer is performed in the step S 9 . Firing in the step S 8  and thermal spraying in the step S 9 , however, may be performed in reverse order. 
     In the above-mentioned embodiment, the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  are each made of alumina, and the alumina powder is used as a thermal spraying material at formation of both of the layers, but they are not necessarily required to be made of alumina. The inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  may be made of metallic oxide, such as zirconia (ZrO 2 ), spinel (MgAl 2 O 4 ), and mullite (Al 6 O1 3 Si 2 ), in place of alumina. In this case, powder of the metallic oxide may be used as the thermal spraying material. 
     The above-mentioned embodiment is targeted at the sensor element  10  including the elongated planar element base  1  (the ceramic body  101 ) having the gas inlet  105  in the one end portion E 1  thereof, but, even in a case where the gas inlet  105  is located in a side portion of the sensor element  1 , similar effects to those obtained in the above-mentioned embodiment are expected as long as the inequalities (2) to (4) are satisfied. 
     EXAMPLES 
     Example 1 
     As Example 1, ten types of sensor elements  10  including leading-end protective layers  2  each being a single layer and having different thicknesses T 1  in the leading end portion  2   e  were manufactured, and water resistance in the leading end portion  2   e  of each of the sensor elements  10  was evaluated. 
     More particularly, two types of element bases  1  including an element base  1  having L p  of 0.91 mm, L h  of 0.41 mm, and L e  of 1.26 mm (hereinafter, a base sample a) and an element base  1  having L p  of 1.03 mm, L h  of 0.20 mm, and L e  of 0.38 mm (hereinafter, a base sample b) were prepared. 
     As for the leading-end protective layers  2  of the base sample a, the thickness T 1  in the leading end portion  2   e  was varied in seven levels of 50 μm, 100 μm, 150 μm, 200 μm, 300 μm, 400 μm, and 500 μm, and the porosity ρ 1  was varied in three levels of 20%, 25%, and 30%. 
     The leading-end protective layer  2  of the base sample b had a thickness T 1  in the leading end portion  2   e  of 380 μm, and had a porosity ρ 1  of 22%. 
     Water resistance was evaluated by applying a water droplet of 0.1 μL at a time to the side of the one end portion E 1  of the sensor element  10  while measuring the pump current Ip 0  through the main pump cell P 1  in a state of each of the sensor elements  10  being heated by the heater  150  to approximately 500° C. to 900° C., and specifying the maximum amount of water causing no abnormality in an output of measurement. 
     The distance L e  in each of the sensor elements  10 , the thickness T 1  and the porosity ρ 1  in the leading end portion  2   e  of the leading-end protective layer  2 , the leading end thickness index value calculated based on them, and the result of evaluation of water resistance are shown in Table 1 as a list.  FIG. 6  is a plot of the result of evaluation of water resistance according to Example 1 shown in Table 1 against the leading end thickness index value. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                   
                 LEADING-END 
                 LEADING END 
                 WATER 
               
               
                 L e   
                 PROTECTIVE LAYER 
                 THICKNESS 
                 RESISTANCE 
               
            
           
           
               
               
               
               
               
            
               
                 [mm] 
                 T 1  [μm] 
                 ρ 1  [%] 
                 INDEX VALUE 
                 [μL] 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1.26 
                 400 
                 25 
                 0.079 
                 6.8 
               
               
                 1.26 
                 100 
                 25 
                 0.020 
                 4.4 
               
               
                 1.26 
                 300 
                 25 
                 0.060 
                 5.7 
               
               
                 1.26 
                 50 
                 25 
                 0.010 
                 4.7 
               
               
                 1.26 
                 200 
                 25 
                 0.040 
                 5 
               
               
                 1.26 
                 150 
                 25 
                 0.030 
                 4.9 
               
               
                 0.38 
                 380 
                 22 
                 0.224 
                 16.0 
               
               
                 1.26 
                 500 
                 25 
                 0.099 
                 7.8 
               
               
                 1.26 
                 400 
                 20 
                 0.063 
                 5.8 
               
               
                 1.26 
                 300 
                 30 
                 0.071 
                 6.8 
               
               
                   
               
            
           
         
       
     
     As shown in Table 1, each of the sensor elements  10  having the leading end thickness index value satisfying the inequality (2) had water resistance of 5 μL or more. 
     It is understood from  FIG. 6  that the leading end thickness index value has a positive correlation with water resistance irrespective of the difference in size of the element base  1 , and it is also confirmed from  FIG. 6  that water resistance of more than 5 μL can be obtained when the leading end thickness index value exceeds 0.05. This indicates that water resistance is suitably secured in the one end portion E 1  of the sensor element  10  in which the gas inlet  105  is provided as long as the leading-end protective layer  2  is provided so that the leading end thickness index value satisfies the inequality (2). 
     Example 2 
     As Example 2, 12 types of sensor elements  10  each including the leading-end protective layer  2  having the two-layer configuration of the inner leading-end protective layer  2   a  and the outer leading-end protective layer  2   b  were manufactured, and water resistance in the leading end portion  2   e  of each of the sensor elements  10  was evaluated. 
     More particularly, two types of element bases  1  including the base sample a as in Example 1 and an element base  1  having L p  of 0.71 mm, L h  of 0.17 mm, and L e  of 0.39 mm (hereinafter, a base sample c) were prepared. 
     As for the inner leading-end protective layers  2   a  of the base sample a, the thickness T 1  in the leading end portion  2   e  was varied in seven levels of 350 μm, 400 μm, 500 μm, 600 μm, 650 μm, 800 μm, and 850 μm, and the porosity ρ 1  was varied in seven levels of 35%, 40%, 50%, 55%, 60%, 65%, and 80%. 
     On the other hand, as for the outer leading-end protective layers  2   b , the thickness T 2  in the leading end portion  2   e  was varied in three levels of 150 μm, 250 μm, and 350 μm, and the porosity ρ 2  was varied in three levels of 15%, 20%, and 25%. 
     The inner leading-end protective layer  2   a  of the base sample c had a thickness T 1  in the leading end portion  2   e  of 276 μm, and had a porosity ρ 1  of 16.2%. Furthermore, the outer leading-end protective layer  2   b  had a thickness T 2  in the leading end portion  2   e  of 232 μm, and had a porosity ρ 2  of 40.7%. 
     The distance L e  on the side of the leading end surface  101   e , the thickness T 1  and the porosity ρ 1  of the inner leading-end protective layer  2   a  (“FIRST PROTECTIVE LAYER” in Table 2), the thickness T 2  and the porosity ρ 2  of the outer leading-end protective layer  2   b  (“SECOND PROTECTIVE LAYER” in Table 2), the leading end thickness index value calculated based on them, and the result of evaluation of water resistance are shown in Table 2 as a list. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                   
                   
                   
                 LEADING  
                   
               
               
                   
                   
                   
                 END 
                   
               
               
                   
                 FIRST 
                 SECOND 
                 THICK- 
                 WATER 
               
               
                   
                 PROTECTIVE  
                 PROTECTIVE  
                 NESS 
                 RESIST- 
               
               
                 L e   
                 LAYER 
                 LAYER 
                 INDEX  
                 ANCE 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 [mm] 
                 T 1  [μm] 
                 ρ 1  [%] 
                 T 2  [μm] 
                 ρ 2  [%] 
                 VALUE 
                 [μL] 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1.26 
                 400 
                 50 
                 250 
                 25 
                 0.208 
                 14 
               
               
                 1.26 
                 650 
                 40 
                 250 
                 25 
                 0.256 
                 20 
               
               
                 1.26 
                 400 
                 40 
                 250 
                 25 
                 0.177 
                 11.2 
               
               
                 1.26 
                 500 
                 40 
                 250 
                 25 
                 0.208 
                 16.3 
               
               
                 0.39 
                 276 
                 16.2 
                 232 
                 40.7 
                 0.357 
                 20.4 
               
               
                 1.26 
                 800 
                 55 
                 250 
                 25 
                 0.399 
                 43.2 
               
               
                 1.26 
                 800 
                 35 
                 250 
                 25 
                 0.272 
                 30.9 
               
               
                 1.26 
                 800 
                 80 
                 250 
                 25 
                 0.558 
                 20 
               
               
                 1.26 
                 600 
                 60 
                 350 
                 25 
                 0.355 
                 25 
               
               
                 1.26 
                 850 
                 60 
                 250 
                 25 
                 0.454 
                 30 
               
               
                 1.26 
                 600 
                 60 
                 250 
                 15 
                 0.315 
                 20 
               
               
                 1.26 
                 350 
                 65 
                 150 
                 20 
                 0.204 
                 20 
               
               
                   
               
            
           
         
       
     
     As shown in Table 2, each of the sensor elements  10  had the leading end thickness index value satisfying the inequality (2), and had water resistance of 6 μL or more. 
       FIG. 7  is a plot of the result of evaluation of water resistance according to Example 2 shown in Table 2 against the leading end thickness index value along with the result of evaluation according to Example 1. As with  FIG. 6 , it is understood from  FIG. 7  that the leading end thickness index value has a positive correlation with water resistance irrespective of the difference in size of the element base  1 . This indicates that good water resistance is secured as long as each layer is provided so that the leading end thickness index value satisfies the inequality (2) even in a case where the leading-end protective layer  2  has the laminated structure of a plurality of unit layers. 
     In addition, it is confirmed from Table 2 and  FIG. 7  that, from among the sensor elements  10  of Example 2, each of the sensor elements  10  having the leading end thickness index value satisfying the inequality (3) has good water resistance of more than 10 μL, and, further, each of the sensor elements  10  having the leading end thickness index value satisfying the inequality (4) has extremely good water resistance of more than 20 μL. 
     While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications and variations can be devised without departing from the scope of the invention.