Method of measuring relative dielectric constant of dielectric substance of powders, cavity resonator used in the same, and application apparatus

BACKGROUND OF THE INVENTION

0001The present invention relates to a method of measuring a relative dielectric constant of a dielectric substance of powders and, more particularly, a method of measuring a relative dielectric constant of powders capable of measuring a relative dielectric constant of a dielectric substance of powders with high precision even in a high-frequency band in excess of several GHz.

0002With improvements in the performance of various radio equipments, high-frequency ceramics dielectric substances of higher performance are requested. Normally the ceramics dielectric substances are used in the form of sintered products that are obtained by sintering the powder dielectric substance. Also, the composite dielectric substance in which the powder dielectric substance and the resin, or the like are mixed in various ratios is employed as the circuit parts. As a result, upon developing the high-frequency ceramics dielectric substance, it is necessary and indispensable to measure a relative dielectric constant of the dielectric substance in its powder state as the dielectric property of such dielectric substance.

0003For example, as disclosed in <patcit id="pcit0001" dnum="JP3127623B"><text>Japanese Patent No.3127623</text></patcit>, and the like, powders whose relative dielectric constant is to be measured are sealed in the vessel in which a pair of electrodes are arranged to oppose to each other at a predetermined interval, and then the relative dielectric constant of the powders is measured. Then, the relative dielectric constant of a mixed substance consisting of the powders and a liquid is measured by applying a voltage between a pair of electrodes, and then the relative dielectric constant of the powders is calculated based on the measured relative dielectric constant of the mixed substance.

0004However, in the method of measuring the relative dielectric constant of the powders in the prior art, the presence of the stray capacitance and the stray reactance cannot be ignored when the relative dielectric constant of the powders is to be measured in the high-frequency band in excess of several GHz. As a result, such a problem existed that the resonation of the overall measuring system is caused and thus it is unfeasible to measure the relative dielectric constant of the powders with high precision.

SUMMARY OF THE INVENTION

0005Therefore, it is an object of the present invention to provide a method of measuring a relative dielectric constant of powders, capable of measuring a relative dielectric constant of powders with high precision even in a high-frequency band in excess of several GHz.

0006According to the present invention, this object is solved by a method according to claim 1. Embodiments of the present invention are defined in the dependent claims.

0007A method of measuring a relative dielectric constant of powders comprising the steps of calculating a relative dielectric constant of a mixed substance consisting of powders and a liquid medium, and then calculating the relative dielectric constant of the mixed substance or a relative dielectric constant of the liquid medium as the relative dielectric constant of the powders when the relative dielectric constant of the mixed substance becomes equal to the relative dielectric constant of the liquid medium is also disclosed.

0008A method of measuring a relative dielectric constant of powders comprising the steps of sealing a mixed substance consisting of the powders and a liquid medium in a resonator, then inputting an electromagnetic wave into the resonator, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the relative dielectric constant of the mixed substance and a relative dielectric constant of the liquid medium is also disclosed.

0009A method of measuring a relative dielectric constant of powders comprising the steps of inputting an electromagnetic wave into a vessel in which a mixed substance consisting of the powders and a liquid medium is filled, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the relative dielectric constant of the mixed substance and a relative dielectric constant of the liquid medium is also disclosed.

0010Calculation of the relative dielectric constant of powders can be executed by calculating the relative dielectric constant of the mixed substance or the relative dielectric constant of the liquid medium as the relative dielectric constant of the powders when the relative dielectric constant of the mixed substance becomes equal to the relative dielectric constant of the liquid medium.

0011A procedure of detecting a point of time when the relative dielectric constant of the mixed substance becomes equal to the relative dielectric constant of the liquid medium is executed by measuring the relative dielectric constant of the mixed substance while changing gradually the relative dielectric constant of the liquid medium. The liquid medium can contain a liquid, or a liquid and a powder dielectric substance, or a liquid, a powder dielectric substance, and a dispersing agent.

0012A method of measuring a relative dielectric constant of powders which comprises the steps of sealing a mixed substance consisting of powders and a liquid medium in a resonator, then inputting an electromagnetic wave into the resonator, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the calculated relative dielectric constant of the mixed substance and a volume ratio of the powders in the mixed substance is also disclosed.

0013A method of measuring a relative dielectric constant of powders which comprises the steps of inputting an electromagnetic wave into a vessel in which a mixed substance consisting of powders and a liquid medium is filled, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the calculated relative dielectric constant of the mixed substance and a volume ratio of the powders in the mixed substance is also disclosed.

0014The relative dielectric constant of the liquid medium can be 0.5 times or more the relative dielectric constant of a powder composition. The relative dielectric constant of the liquid medium can be 0.5 times to 2.0 times the relative dielectric constant of a powder composition.

0015The liquid medium can contain a liquid, or a liquid and a powder dielectric substance, or a liquid, a powder dielectric substance, and a dispersing agent. Calculation of the relative dielectric constant of powders can be executed by using the logarithmic mixture rule or the Lichtenecker-Rother's Formula.

0016A cavity resonator in which at least one opening portion into which a measured dielectric substance is inserted is formed in a center portion of the cavity resonator in an axis direction and also a supporter is formed on an outside of the opening portion, wherein a relationship h/d between a length d of the opening portion and a length h of the supporter is set to 0.5 or more. Thus, leakage of the electromagnetic wave from the resonator can be suppressed.

0017A cavity resonator which is used in a method of measuring a relative dielectric constant of powders that comprises the steps of sealing a mixed substance consisting of powders and a liquid medium in a resonator, then inputting an electromagnetic wave into the resonator, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the relative dielectric constant of the mixed substance and a relative dielectric constant of the liquid medium, and in which at least one opening portion into which a measured dielectric substance is inserted is formed in the cavity resonator and also a supporter is formed on an outside of the opening portion, wherein a relationship h/d between a length d of the opening portion and a length h of the supporter is set to 0.5 or more. Thus, the cut-off structure can be obtained by preventing the leakage of the electromagnetic wave from the opening portion of the resonator.

0018A cavity resonator which is used in a method of measuring a relative dielectric constant of powders comprising the steps of sealing a mixed substance consisting of powders and a liquid medium in a resonator, then inputting an electromagnetic wave into the resonator, then calculating a relative dielectric constant of the mixed substance based on a response of the electromagnetic wave, and then calculating a relative dielectric constant of the powders from the calculated relative dielectric constant of the mixed substance and a volume ratio of the powders in the mixed substance, and in which at least one opening portion into which a measured dielectric substance is inserted is formed in the cavity resonator and also a supporter is formed on an outside of the opening portion, wherein a relationship h/d between a length d of the opening portion and a length h of the supporter is set to 0.5 or more. Thus, the cut-off structure can be obtained by preventing the leakage of the electromagnetic wave from the opening portion of the resonator, and the resonant frequency and the unloaded Q value of the resonator can be measured stably.

0019Also, the dielectric substance measuring system for inserting the rod-like-shaped dielectric substance into the cavity resonator, then measuring the resonant frequency and the unloaded Q value of the cavity resonator, and then measuring the relative dielectric constant and the dielectric loss tangent of the inserted rod-like dielectric substance based on the measured results is implemented.

0020Also, the resonator or the filter that can attain the intended resonance characteristic by inserting the rod-like-shaped dielectric substance into the cavity resonator is implemented.

0021According to the measuring method of the present invention, it is possible to provide a method of measuring a relative dielectric constant of powders, which is able to measure a relative dielectric constant of powders with high precision even in the high-frequency band in excess of several GHz. Also, it is possible to provide a method of measuring a relative dielectric constant of powders, which is able to measure a relative dielectric constant of powders of the high relative dielectric constant with high precision. Also, according to the second measuring method which is not part of the present invention, it is possible to provide a method of measuring a relative dielectric constant of powders, which is able to prevent degradation of a measuring precision caused when the relative dielectric constant of powders is detected by the extrapolation, by selecting a liquid medium having a value of the relative dielectric constant that is close to a value the relative dielectric constant of the detected powders. In addition, improvement of a measuring precision of the relative dielectric constant of powders can be achieved by calculating the relative dielectric constant of powders by using the logarithmic mixture rule or the Lichtenecker-Rother's Formula. Also, in the cavity resonator that can be used to measure the relative dielectric constant of powders in the present invention, at least one opening portion into which the measured dielectric substance is inserted is formed in the center portion in the axis direction and also the supporter is formed on the outside of the opening portion. In this cavity resonator, the optimum length of the supporter can be obtained by setting a relationship h/d between the length d of the opening portion and the length h of the supporter to 0.5 or more. In this case, the cavity resonator is not limited to the application of powders, and can be applied to any measured sample if such measured sample is formed of the dielectric substance. Also, it is feasible to implement a dielectric substance measuring system that inserts the rod-like-shaped dielectric substance into the cavity resonator, then measures the resonant frequency and the unloaded Q value of the cavity resonator, and then measures the relative dielectric constant and the dielectric loss tangent of the inserted rod-like dielectric substance based on the measured results. Also, it is feasible to implement the resonator or the filter that can attain the target resonance characteristic by inserting the rod-like-shaped dielectric substance into the cavity resonator. <ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">FIG.1</figref> is a block diagram of a measuring system for executing a method of measuring a relative dielectric constant of powders according to preferred embodiments of the present invention.</li><li><figref idref="f0002">FIG.2</figref> is a schematic perspective view of a dielectric substance sealing apparatus 4.</li><li><figref idref="f0003">FIG.3</figref> is a schematic sectional view, taken along an X-X line, of the dielectric substance sealing apparatus 4 shown in <figref idref="f0002">FIG.2</figref>.</li><li><figref idref="f0004">FIG. 4</figref> is a graph showing a relationship between a relative dielectric constant of a liquid medium and a relative dielectric constant of a mixed substance 18.</li><li><figref idref="f0004">FIG.5</figref> is a graph showing another relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18.</li><li><figref idref="f0005">FIG.6</figref> is a graph showing a relationship between a volume ratio of powders and the relative dielectric constant of the mixed substance 18.</li><li><figref idref="f0005">FIG.7</figref> is a schematic view showing a fluidizing apparatus 38A using a pump.</li><li><figref idref="f0006">FIG.8</figref> is a sectional view of a measuring system for executing a method of measuring the relative dielectric constant of powders according another preferred embodiment of the present invention.</li><li><figref idref="f0006">FIG.9</figref> is a schematic view showing a fluidizing apparatus 38B using stirring blades.</li><li><figref idref="f0007">FIG.10</figref> is a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 in Example 1.</li><li><figref idref="f0007">FIG.11</figref> is a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 in Example 2.</li><li><figref idref="f0008">FIG.12</figref> is a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 in Example 3.</li><li><figref idref="f0008">FIG.13</figref> is a graph showing a relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 4.</li><li><figref idref="f0008">FIG.14</figref> is a graph showing another relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 4.</li><li><figref idref="f0009">FIG.15</figref> is a graph showing a relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 5.</li><li>[<figref idref="f0009">FIG.16] FIG.16</figref> is a graph showing another relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 5.</li><li><figref idref="f0010">FIG.17</figref> is a graph showing a relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 6.</li><li><figref idref="f0010">FIG.18</figref> is a graph showing another relationship between the volume ratio of powders and the relative dielectric constant of the mixed substance 18 in Example 6.</li><li><figref idref="f0011">FIG.19</figref> is a view showing a configuration of a cylindrical cavity resonator used in the measurement of the relative dielectric constant of powders in the present invention.</li><li><figref idref="f0012">FIG.20</figref> is a view explaining a distribution of an electric field in the cylindrical cavity resonator.</li><li><figref idref="f0013">FIG. 21</figref> is a view showing a cut-off frequency of a supporter portion of the cylindrical cavity resonator.</li><li><figref idref="f0014">FIG.22</figref> is a view showing conditions required for a resonator shape to execute a simulation to derive the optimum value of the supporter of the cylindrical cavity resonator.</li><li><figref idref="f0015">FIG.23</figref> is a view showing results of the simulation.</li><li><figref idref="f0016">FIG.24</figref> is a view explaining a difference caused due to the relative dielectric constant ε of a measured dielectric substance.</li><li><figref idref="f0017">FIG.25</figref> is a view explaining a difference caused due to a height H of the resonator.</li><li><figref idref="f0018">FIG.26</figref> is a view explaining a difference caused due to a diameter d of an insertion hole of the dielectric substance.</li></ul>

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

0022Detailed explanation will hereinafter be made of preferred embodiments of the present invention with reference to the accompanying drawings. <figref idref="f0001">FIG.1</figref> is a block diagram of a measuring system for implementing a method of measuring a relative dielectric constant of powders according to preferred embodiments of the present invention.

0023As shown in <figref idref="f0001">FIG.1</figref>, a measuring system 2 includes a dielectric substance sealing apparatus 4, a network analyzer 6, and a processing unit 8.

0024The dielectric substance sealing apparatus 4 is an apparatus in which a mixed substance consisting of powders whose relative dielectric constant is to be measured and a liquid medium is sealed.

0025The network analyzer 6 is constructed to input the electromagnetic wave into the dielectric substance sealing apparatus 4 and output to the processing unit 8 the measured result of the electromagnetic wave that is output from the dielectric substance sealing apparatus 4 in response to the input of the electromagnetic wave.

0026The processing unit 8 is constructed to calculate the relative dielectric constant of the powders based on the measured result that is output from the network analyzer 6.

0027<figref idref="f0002">FIG.2</figref> is a schematic perspective view of the dielectric substance sealing apparatus 4, and <figref idref="f0003">FIG.3</figref> is a schematic sectional view, taken along an X-X line, of the dielectric substance sealing apparatus 4 shown in <figref idref="f0002">FIG.2</figref>.

0028As shown in <figref idref="f0002">FIG.2</figref>, the dielectric substance sealing apparatus 4 includes a cavity resonator 10, a tube 12, a syringe 14a and a syringe 14b.

0029As shown in <figref idref="f0003">FIG. 3</figref>, a hole 16a and a hole 16b through which the tube 12 is passed are formed in center portions of upper and lower surfaces of the cavity resonator 10. Also, a connector 20a and a connector 20b both are connected to the network analyzer 6 are formed on a side surface of the cavity resonator 10. A loop antenna 22a and a loop antenna 22b are formed on top end portions of the connector 20a and the connector 20b respectively. The tube 12 is used to seal a mixed substance 18 consisting of the powders and the liquid medium in the cavity resonator 10. In this case, it is preferable that the tube 12 should be formed of the material such as tetrafluoroethylene, or the like with a low dielectric constant and a small loss. The syringe 14a and the syringe 14b are used to inject the mixed substance 18 into the tube 12 and also fluidize the mixed substance 18 in the tube 12.

0030In the measuring system 2 constructed as above, the relative dielectric constant of the powders is measured as described in the following. First, a first measuring method out of the method of measuring the relative dielectric constant of powders will be explained hereunder.

0031In the first measurement of the relative dielectric constant of powders, first either a liquid such as water, alcohol, or the like or a mixed substance in which water, alcohol, and the like are mixed is prepared as the liquid medium. The relative dielectric constant of this liquid medium can be changed if a ratio of the mixed liquid is changed. The relative dielectric constant of the liquid medium is measured by using the publicly-known liquid-medium relative-dielectric-constant measuring method such as the cavity resonator method, the S-parameter method, the capacitance method, or the like.

0032Then, the mixed substance 18 in which the powders as the measured object are mixed into the liquid medium is filled into the syringe 14a and the syringe 14b. Then, the syringe 14a is inserted into the tube 12, and then the mixed substance 18 is injected from the syringe 14a into the tube 12. Then, the syringe 14b is inserted into the tube 12 when the mixed substance 18 is filled in the tube 12. In this case, it is preferable that, upon blending the powders and the liquid medium, the dispersing agent should be mixed into the liquid medium to accelerate the dispersion of powders into the liquid medium.

0033The mixed substance 18 injected into the tube 12 is fluidized in the tube 12 by moving pistons of the syringe 14a and the syringe 14b. The powders are diffused uniformly in the liquid medium by fluidizing the mixed substance 18 in the tube 12. As a result, improvement of a measuring precision of the relative dielectric constant of the powders can be achieved.

0034Then, the electromagnetic wave fed from the network analyzer 6 is input into the inside of the cavity resonator 10 from the loop antenna 22a. In response to the input of the electromagnetic wave, the electromagnetic wave fed from the cavity resonator 10 is output to the network analyzer 6 via the loop antenna 22b. In the network analyzer 6, a resonant frequency of the cavity resonator 10 is measured by using the electromagnetic wave that is output from the cavity resonator 10 to the network analyzer 6. As the measured result, the resonant frequency is output from the network analyzer 6 to the processing unit 8. Then, the relative dielectric constant of the mixed substance 18 is calculated by the processing unit 8.

0035In this manner, the relative dielectric constant of the mixed substance 18 at a predetermined volume ratio of powders can be calculated by the processing unit 8.

0036Then, while changing gradually the relative dielectric constant of the liquid medium at the same volume ratio of powders, the relative dielectric constant of the mixed substance 18 with respect to the relative dielectric constant of each liquid medium is calculated by the processing unit 8.

0037A graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 is made in the processing unit 8.

0038<figref idref="f0004">FIG.4</figref> is a graph showing the relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18. Also, in <figref idref="f0004">FIG.4</figref>, an abscissa denotes the relative dielectric constant of the liquid medium and an ordinate denotes the relative dielectric constant of the mixed substance 18. Also, an auxiliary line representing respective points at which a value of the relative dielectric constant (ε s) of the mixed substance 18 becomes equal to a value of the relative dielectric constant (ε 1) of the liquid medium, i.e., ε s = ε 1, is depicted.

0039The relative dielectric constant of the liquid medium is equal to the relative dielectric constant of the mixed substance 18 at an intersection point between a curve indicating the relative dielectric constant of the mixed substance 18 with respect to the relative dielectric constant of the liquid medium and the auxiliary line. The event that the relative dielectric constant of the liquid medium is equal to the relative dielectric constant of the mixed substance 18 is limited to the case that the relative dielectric constant of the liquid medium is equal to the relative dielectric constant of the powders. As a result, in <figref idref="f0004">FIG.4</figref>, the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18, both having the same value, at the intersection point between the curve and the auxiliary line yield the relative dielectric constant of the powders.

0040In <figref idref="f0004">FIG. 4</figref>, the relative dielectric constant of the powders is derived from the intersection point between the curve indicating the relative dielectric constant of the mixed substance 18 with respect to the relative dielectric constants of the liquid media that are estimated respectively based on the detected relative dielectric constant of the mixed substance 18, i.e., the relative dielectric constant of the mixed substance 18 that is derived by interpolating a plurality of measuring points of the mixed substance 18, and the auxiliary line.

0041<figref idref="f0004">FIG.5</figref> is a graph showing another relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18. Also, in <figref idref="f0004">FIG.5</figref>, an abscissa denotes the relative dielectric constant of the liquid medium and an ordinate denotes the relative dielectric constant of the mixed substance 18. Also, an auxiliary line representing respective points at which a value of the relative dielectric constant (<i>ε</i> s) of the mixed substance 18 becomes equal to a value of the relative dielectric constant (ε 1) of the liquid medium, i.e., ε s = ε 1, is depicted.

0042Unlike <figref idref="f0004">FIG.4, FIG.5</figref> shows the method of deriving the relative dielectric constant of the powders when the relative dielectric constant of the powders cannot be detected from the intersection point between the curve indicating the detected relative dielectric constant of the mixed substance 18 and the relative dielectric constant of the mixed substance 18 obtained by the interpolation, i.e., the relative dielectric constant of the mixed substance 18 within the interpolation range, and the auxiliary line. More concretely, as shown in <figref idref="f0004">FIG.5</figref>, the relative dielectric constant of the mixed substance 18 out of the interpolation range is estimated based on the relative dielectric constant of the mixed substance 18 within the interpolation range. In other words, the relative dielectric constant of the powders is detected from the intersection point between the curve of the relative dielectric constant of the mixed substance 18, which is derived by executing the extrapolation based on a plurality of measuring points of the mixed substance 18, and the auxiliary line.

0043As explained above, according to the present embodiment, the relative dielectric constant of the powders can be detected by detecting the point at which the relative dielectric constant of the mixed substance 18 becomes equal to the relative dielectric constant of the liquid medium. As a result, the relative dielectric constant of powders can be detected with high precision.

0044Next, a second measuring method not being part of the present invention out of the method of measuring the relative dielectric constant of powders will be explained hereunder. In this measurement of the relative dielectric constant of powders, first a liquid medium such as an ion-exchange water, or the like is prepared. Then, the mixed substance 18 in which the powders as the measured object are mixed into the liquid medium is filled in the syringe 14a and the syringe 14b. Then, the syringe 14a is inserted into the tube 12, and then the mixed substance 18 is injected from the syringe 14a into the tube 12. Then, the syringe 14b is inserted into the tube 12 when the mixed substance 18 is filled in the tube 12. In this case, it is preferable that, upon blending the powders and the liquid medium, the dispersing agent should be mixed into the liquid medium to accelerate the dispersion of the powders into the liquid medium.

0045The mixed substance 18 injected into the tube 12 is fluidized in the tube 12 by moving the pistons of the syringe 14a and the syringe 14b. The powders are diffused uniformly in the liquid medium by fluidizing the mixed substance 18 in the tube 12. As a result, improvement of a measuring precision of the relative dielectric constant of the powders can be achieved.

0046Then, the electromagnetic wave fed from the network analyzer 6 is input into the inside of the cavity resonator 10 from the loop antenna 22a. In response to the input of the electromagnetic wave, the electromagnetic wave fed from the cavity resonator 10 is output to the network analyzer 6 via the loop antenna 22b. In the network analyzer 6, the resonant frequency of the cavity resonator 10 in a TM₀₁₀ mode is measured by using the electromagnetic wave that is output from the cavity resonator 10 to the network analyzer 6. As the measured result, the resonant frequency is output from the network analyzer 6 to the processing unit 8. Then, the relative dielectric constant of the mixed substance 18 is calculated by the processing unit 8.

0047In this way, the relative dielectric constant of the mixed substance 18 at a predetermined volume ratio of powders can be calculated by the processing unit 8. In this case, processing procedures executed up to now are similar to those in the above first measuring method.

0048Then, in order to improve a measuring precision of the relative dielectric constants of the powders, the relative dielectric constant of the mixed substance 18 is derived by the processing unit 8 while changing gradually the volume ratio of the powders occupied in the mixed substance 18 that is injected into the tube 12.

0049Then, the processing unit 8 applies the formula such as the logarithmic mixture rule, the Lichtenecker-Rother's Formula, or the like, which is used to calculate the relative dielectric constants of powders from the relative dielectric constant of the mixed substance 18, to the relative dielectric constant of the mixed substance 18 calculated in this manner to calculate the relative dielectric constants of powders.

0050A graph showing a relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 is made in the processing unit 8.

0051<figref idref="f0005">FIG.6</figref> is a graph obtained by fitting the logarithmic mixture rule to a relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. In <figref idref="f0005">FIG.6</figref>, an abscissa denotes the volume ratio of powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0052In <figref idref="f0005">FIG.6</figref>, the fact that the volume ratio of the powders is 1.0 signifies that the liquid medium is not present in the mixed substance 18 and merely the powders are present. Therefore, a value of the relative dielectric constant obtained when the volume ratio of the powders is 1.0 corresponds to the relative dielectric constant of the powders. Thus, the relative dielectric constant of the powders is detected by reading the value of the relative dielectric constant obtained when the volume ratio of powders is 1.0 from the curve shown in <figref idref="f0005">FIG.6</figref>.

0053The curve shown in <figref idref="f0005">FIG.6</figref> is plotted by detecting the relative dielectric constant of the mixed substance 18 with respect to the volume ratio of the powders by estimating the relative dielectric constant of the mixed substance 18 out of the measuring range based on the detected relative dielectric constant of the mixed substance 18, i.e., by detecting the relative dielectric constant of the mixed substance 18 by extrapolating a plurality of measuring points of the mixed substance 18.

0054In <figref idref="f0005">FIG.6</figref>, the fact that the volume ratio of the powders is 0. 0 signifies that no powder is present in the mixed substance 18 and merely the liquid medium is present. Therefore, a value of the relative dielectric constant obtained when the volume ratio of powders is 0.0 gives the relative dielectric constant of the liquid medium. For this reason, in case the relative dielectric constant of the liquid medium is extremely lower or higher than the relative dielectric constant of the powders, a change of a gradient of the curve become steep. Thus, it is possible that a measuring precision of the relative dielectric constant of the powders derived by the extrapolation is worsened.

0055Therefore, if the liquid medium having a value of the relative dielectric constant close to a value of the detected relative dielectric constant of powders is selected, it is possible to prevent the deterioration of the measuring precision when the relative dielectric constant of powders is derived by the extrapolation. As the criterion applied to select the liquid medium having a value of the relative dielectric constant close to the value of the detected relative dielectric constant of powders, a value of the relative dielectric constant of the ceramic composition made of the measured powders is employed. If the liquid medium having the relative dielectric constant that is 0.5 times to 2.0 times the relative dielectric constant of the ceramic composition made of the powders is selected, a measuring precision of the relative dielectric constant of the powders can be improved.

0056In this case, the foregoing logarithmic mixture rule or Lichtenecker-Rother's Formula is given in the following. As well known, the logarithmic mixture rule is given by the following formula.<maths id="math0001"><math display="block"><mi>log</mi><mo>⁢</mo><msub><mi>ε</mi><mi mathvariant="normal">r</mi></msub><mo mathvariant="normal">=</mo><mi>vo</mi><mo>⁢</mo><mn mathvariant="normal">1</mn><mo>⁢</mo><mi>log</mi><mo>⁢</mo><msub><mi>ε</mi><mrow><mi mathvariant="normal">r</mi><mo>⁢</mo><mn mathvariant="normal">1</mn></mrow></msub><mo mathvariant="normal">+</mo><mi mathvariant="normal">v</mi><mo>⁢</mo><mn mathvariant="normal">2</mn><mo>⁢</mo><mi>log</mi><mo>⁢</mo><msub><mi>ε</mi><mrow><mi mathvariant="normal">r</mi><mo>⁢</mo><mn mathvariant="normal">2</mn></mrow></msub></math><img file="EP1528618B1_D0001.tif" /></maths>

0057Also, the Lichtenecker-Rother's Formula is given by the following formula.<maths id="math0002"><math display="block"><msup><msub><mi>ε</mi><mi mathvariant="normal">r</mi></msub><mi mathvariant="normal">k</mi></msup><mo>=</mo><mi mathvariant="normal">v</mi><mo>⁢</mo><mn>1</mn><mo>⁢</mo><msup><msub><mi>ε</mi><mrow><mi mathvariant="normal">r</mi><mo>⁢</mo><mn>1</mn></mrow></msub><mi mathvariant="normal">k</mi></msup><mo>+</mo><mi mathvariant="normal">v</mi><mo>⁢</mo><mn>2</mn><mo>⁢</mo><msup><msub><mi>ε</mi><mrow><mi mathvariant="normal">r</mi><mo>⁢</mo><mn>2</mn></mrow></msub><mi mathvariant="normal">k</mi></msup></math><img file="EP1528618B1_D0002.tif" /></maths>

0058Where ε _r: relative dielectric constant of powders ε _r1: relative dielectric constant of the liquid medium ε _r2: relative dielectric constant of the mixed substance 18 v1: volume ratio of the liquid medium v2: volume ratio of powders k: fitting parameter (-1≦k≦1).

0059As explained above, according to the second measuring method, the relative dielectric constant of powders can be detected by using the liquid medium a value of the relative dielectric constant of which is close to a value of the detected relative dielectric constant of powders. As a result, the relative dielectric constant of powders can be derived with high precision.

0060In the first and second measuring methods, the mixed substance 18 injected into the tube 12 is fluidized by using the syringe 14a and the syringe 14b. In this case, the mixed substance 18 may be fluidized by using a fluidizing apparatus 38A shown in <figref idref="f0005">FIG.7</figref>. <figref idref="f0005">FIG.7</figref> is a schematic view showing a fluidizing apparatus 38A using a pump.

0061The fluidizing apparatus 38A shown in <figref idref="f0005">FIG. 7</figref> fluidizes the mixed substance 18 by circulating this mixed substance 18 by using a pump 40.

0062The powders in the mixed substance 18 can be diffused uniformly by using the fluidizing apparatus 38A shown in <figref idref="f0005">FIG. 7</figref>. As a result, improvement of the measuring precision of the relative dielectric constant of the powders can be attained.

0063Next, another example of the present invention will be explained hereunder.

0064<figref idref="f0006">FIG.8</figref> is a sectional view of a measuring system for implementing the method of measuring the relative dielectric constant of powders according another example of the present invention.

0065As shown in <figref idref="f0006">FIG.8</figref>, a measuring system 30 includes the network analyzer 6, the processing unit 8, a probe 32, a cable 34, and a vessel 36.

0066The network analyzer 6 and the processing unit 8 are same as those constituting the measuring system 2.

0067The probe 32 is a coaxial cable that inputs the electromagnetic wave fed from the network analyzer 6 into the mixed substance 18 contained in the vessel 36. This probe 32 is connected to the network analyzer 6 via the cable 34.

0068In the measuring system 30 constructed as above, the relative dielectric constant of the powders is measured as described in the following.

0069First, like the case that the relative dielectric constant of powders is measured by the measuring system 2, the liquid such as water, alcohol, or the like or the mixed substance in which water, alcohol, and the like are mixed is prepared as the liquid medium. The relative dielectric constant of the liquid medium is measured by using the publicly-known liquid-medium relative-dielectric-constant measuring method such as the cavity resonator method, the S-parameter method, the capacitance method, or the like.

0070Then, the mixed substance 18 in which the powders as the measured object are mixed in the liquid medium is contained into the vessel 36. Then, the electromagnetic wave fed from the network analyzer 6 is input into the mixed substance 18 from the probe 32 via the cable 34. In response to the input of the electromagnetic wave, such electromagnetic wave is output to the network analyzer 6 from the probe 32 via the cable 34. In the network analyzer 6, a reflection coefficient between an end surface of the probe 32 and the mixed substance 18 is measured based on the electromagnetic wave that is output from the probe 32 to the network analyzer 6. The reflection coefficient is output to the processing unit 8 from the network analyzer 6 as the measured result. The relative dielectric constant of the mixed substance 18 is calculated in the processing unit 8. By now, it is preferable that an ultrasonic wave should be input into the vessel 36 from an ultrasonic generator (not shown) to fluidize the mixed substance 18.

0071When the relative dielectric constant of the mixed substance 18 is calculated in the processing unit 8, a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 is made in the same manner as in the above measuring system 2, and also the relative dielectric constant of the powders is calculated.

0072As explained above, according to another example of the present invention, the relative dielectric constant of powders can be derived by using the probe 32. Therefore, the relative dielectric constant of powders can be detected with high precision.

0073Also, in the above example, the mixed substance 18 contained in the vessel 36 is circulated by using the ultrasonic wave, but such mixed substance 18 may be circulated by using a circulating apparatus 38B shown in <figref idref="f0006">FIG.9. FIG.9</figref> is a schematic view showing the circulating apparatus 38B using stirring blades.

0074As shown in <figref idref="f0006">FIG. 9</figref>, the fluidizing apparatus 38B fluidizes the mixed substance 18 by causing stirring blades 44 connected to a motor 42 to rotate.

0075The powders in the mixed substance 18 can be diffused uniformly by using the fluidizing apparatus 38B shown in <figref idref="f0006">FIG. 9</figref>. As a result, improvement of a measuring precision of the relative dielectric constant of powders can be attained.

0076In order to clarify much more advantages of the present invention, various Examples will be given hereinafter. At first, Example according to the first measuring method will be explained hereunder.

[Example 1]

0077Al₂O₃ powders were prepared as the sample of the powder dielectric substance, and a mixed substance in which the ion-exchange water and the alcohol are mixed was prepared as the liquid medium. Also, the measuring system 2 shown in <figref idref="f0001">FIG.1</figref> was employed as the measuring system.

0078Then, the mixed substance 18 in which the sample as the measured object is mixed in the liquid substance was prepared, and then filled in the syringe 14a and the syringe 14b. The volume ratio of the powders in the sample was set to 0.1 in the mixed substance 18. The relative dielectric constant of the liquid medium was measured by using the cavity resonator method.

0079Then, the syringe 14a was inserted into the tube 12 and then the mixed substance 18 was injected into the tube 12. Then, the syringe 14b was inserted into the tube 12 when the mixed substance 18 was filled in the tube 12. The mixed substance 18 injected into the tube 12 was fluidized in the tube 12 by moving the pistons of the syringe 14a and the syringe 14b. Here, a cavity resonator having a diameter of 80 mm and a height of 10 mm was used as the cavity resonator 10, and a tube made of tetrafluoroethylene to have an inner diameter of 1 mm and an outer diameter of 3 mm was used as the tube 12.

0080Then, the electromagnetic wave of 2.5 to 3.0 GHz fed from the network analyzer 6 was input into the cavity resonator 10 from the loop antenna 22a. In response to the input of the electromagnetic wave, such electromagnetic wave fed from the cavity resonator 10 was output to the network analyzer 6 via the loop antenna 22b. The resonant frequency of the cavity resonator 10 in a TM₀₁₀ mode was measured by the network analyzer 6 based on the electromagnetic wave that was output from the cavity resonator 10 to the network analyzer 6. The resonant frequency was 2.86 GHz. The resonant frequency was output from the network analyzer 6 to the processing unit 8 as the measured result, and then the relative dielectric constant of the mixed substance 18 was calculated by the processing unit 8.

0081In this way, the relative dielectric constant of the mixed substance 18 in which the volume ratio of the sample is 0.1 was calculated by the processing unit 8.

0082Then, while changing gradually the relative dielectric constant of the liquid medium in a range from 8 to 14.7 at the same volume ratio, the relative dielectric constant of the mixed substance 18 with respect to the relative dielectric constant of each liquid medium was calculated by the processing unit 8.

0083A graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 was made in the processing unit 8.

0084<figref idref="f0007">FIG.10</figref> is a graph showing the relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18. Also, in <figref idref="f0007">FIG. 10</figref>, an abscissa denotes the relative dielectric constant of the liquid medium and an ordinate denotes the relative dielectric constant of the mixed substance 18. Also, an auxiliary line representing respective points at which a value of the relative dielectric constant ( ε s) of the mixed substance 18 becomes equal to a value of the relative dielectric constant (ε 1) of the liquid medium, i.e., ε s = ε 1, is depicted.

0085Both the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 were given as 12.07 at the intersection point between the curve showing the relative dielectric constant of the mixed substance 18 with respect to the relative dielectric constant of each liquid medium and the auxiliary line. As a result, the relative dielectric constant of the detected Al₂O₃ powders was calculated as 12.07.

[Example 2]

0086Four types of powders consisting of sample A, sample B, sample C, and sample D respectively were prepared as the samples. All these powders were made of Ba (NdBi) ₂TiO₄. The sample A was formed by breaking tentatively sintered powders, the sample B was formed of spherical powders, the sample C was formed of spherical powders, and the sample D was formed by breaking the sample C. As the liquid medium of the sample, the mixed substance in which the ion-exchange water, the alcohol, and the 0.3 wt% dispersing agent are mixed was prepared. In this case, a volume ratio of the sample A in the mixed substance 18 was set to 0.2, a volume ratio of the sample B was set to 0.2, a volume ratio of the sample C was set to 0.4, and a volume ratio of the sample D was set to 0.4.

0087The mixed substances 18 in which the sample A, the sample B, the sample C, and the sample D as the measured object are mixed in the liquid medium respectively were prepared. Then, the relative dielectric constants of respective mixed substances 18 were calculated by using the measuring system 2 shown in <figref idref="f0001">FIG.1</figref> as the measuring system. In Example 2, the relative dielectric constants of the mixed substances 18 containing the sample A, the sample B, the sample C, and the sample D respectively were calculated while changing the relative dielectric constant of the liquid medium in a range from 66 to 77.

0088<figref idref="f0007">FIG.11</figref> is a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18. Also, in <figref idref="f0007">FIG. 11</figref>, an abscissa denotes the relative dielectric constant of the liquid medium and an ordinate denotes the relative dielectric constant of the mixed substance 18. Also, an auxiliary line representing respective points at which a value of the relative dielectric constant ( ε s) of the mixed substance 18 becomes equal to a value of the relative dielectric constant (ε 1) of the liquid medium, i.e., ε s = ε 1, is depicted.

0089The relative dielectric constants of the sample A, the sample B, the sample C, and the sample D were calculated by reading the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 at the intersection point between the curve and the auxiliary line, in the same way as in Example 1.

0090The relative dielectric constant of the sample A was calculated as 82.22, the relative dielectric constant of the sample B was calculated as 77.71, the relative dielectric constant of the sample C was calculated as 77.34, and the relative dielectric constant of the sample D was calculated as 79.78.

[Example 3]

0091In Example 3, the same samples as in Example 2, i.e., four types of powder dielectric substances consisting of the sample A, the sample B, the sample C, and the sample D respectively were prepared as the samples. As the liquid medium in the sample, the mixed substance in which BaTiO₃ powders and the dispersing agent are mixed in the ion-exchange water was prepared. In this case, a volume ratio of the sample A in the mixed substance 18 was set to 0.2, a volume ratio of the sample B was set to 0.2, a volume ratio of the sample C was set to 0.4, and a volume ratio of the sample D was set to 0.4.

0092The mixed substances 18 in which the sample A, the sample B, the sample C, and the sample D as the measured object are mixed in the liquid medium respectively were prepared, like Example 2. Then, the relative dielectric constants of respective mixed substances 18 were calculated by using the measuring system 2 shown in <figref idref="f0001">FIG.1</figref> as the measuring system. In Example 3, the relative dielectric constants of the mixed substances 18 containing the sample A, the sample B, the sample C, and the sample D respectively were calculated while changing the relative dielectric constant of the liquid medium in a range from 74 to 96.

0093<figref idref="f0008">FIG.12</figref> is a graph showing a relationship between the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18. Also, in <figref idref="f0008">FIG. 12</figref>, an abscissa denotes the relative dielectric constant of the liquid medium and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0094The relative dielectric constants of the sample A, the sample B, the sample C, and the sample D were calculated by reading the relative dielectric constant of the liquid medium and the relative dielectric constant of the mixed substance 18 at the intersection point between the curve and the auxiliary line, in the same way as in Example 1.

0095The relative dielectric constant of the sample A was calculated as 88.71, the relative dielectric constant of the sample B was calculated as 77.80, the relative dielectric constant of the sample C was calculated as 78.04, and the relative dielectric constant of the sample D was calculated as 80.32.

0096In Example 2 and Example 3, calculated results of the relative dielectric constants of the sample A, the sample B, the sample C, and the sample D are given in Table 1. <tables id="tabl0001" num="0001"><table frame="all"><title>TABLE 1</title><tgroup cols="5"><colspec colnum="1" colname="col1" colwidth="20mm" /><colspec colnum="2" colname="col2" colwidth="19mm" /><colspec colnum="3" colname="col3" colwidth="19mm" /><colspec colnum="4" colname="col4" colwidth="19mm" /><colspec colnum="5" colname="col5" colwidth="19mm" /><thead valign="top"><row><entry /><entry align="center">sample A</entry><entry align="center">sample B</entry><entry align="center">sample C</entry><entry align="center">sample D</entry></row></thead><tbody><row><entry align="center">Example 2</entry><entry align="char" char="." charoff="19">82.22</entry><entry align="char" char="." charoff="19">77.71</entry><entry align="char" char="." charoff="19">77.34</entry><entry align="char" char="." charoff="19">79.78</entry></row><row><entry align="center">Example 3</entry><entry align="char" char="." charoff="19">88.71</entry><entry align="char" char="." charoff="19">77.80</entry><entry align="char" char="." charoff="19">78.04</entry><entry align="char" char="." charoff="19">80.32</entry></row></tbody></tgroup></table></tables>

0097As given in Table 1, the relative dielectric constants of respective samples became substantially equal when such relative dielectric constants were measured after the relative dielectric constant of the liquid medium was changed respectively.

0098Next, Examples according to the second measuring method will be explained hereunder.

[Example 4]

0099Three types of powders consisting of sample A, sample B, and sample C respectively were prepared as the samples. All these powders were made of Ba (NdBi) ₂TiO₄ . The sample A was formed by breaking the tentatively sintered powders, the sample B was formed of the spherical powders, and the sample C was formed by breaking the sample B.

0100As the liquid medium of the sample, the mixed substance consisting of the 99.7 wt% ion-exchange water and the 0.3 wt% dispersing agent was prepared. The measuring system 2 shown in <figref idref="f0001">FIG.1</figref> was employed as the measuring system. Here, the relative dielectric constant of the ceramic composition in the sample was 93 and the relative dielectric constant of the liquid medium was 74. Thus, the relative dielectric constant of the liquid medium was 0.80 times the relative dielectric constant of the ceramic composition powders.

0101Then, the mixed substance 18 in which the sample A as the measured object is mixed in the liquid medium was prepared and then filled in the syringe 14a and the syringe 14b. The mixed substance 18 was prepared in such a manner that the volume ratio of the powders in the sample A became 0.4.

0102Then, the syringe 14a was inserted into the tube 12 and then the mixed substance 18 was injected into the tube 12. Then, the syringe 14b was inserted into the tube 12 when the mixed substance 18 was filled in the tube 12. The mixed substance 18 injected into the tube 12 was fluidized in the tube 12 by moving the pistons of the syringe 14a and the syringe 14b. Here, the cavity resonator having a diameter of 80 mm and a height of 10 mm was used as the cavity resonator 10, and the tube formed of tetrafluoroethylene to have an inner diameter of 1 mm and an outer diameter of 3 mm was used as the tube 12.

0103Then, the electromagnetic wave of 2.5 to 3.0 GHz fed from the network analyzer 6 was input into the cavity resonator 10 from the loop antenna 22a. In response to the input of the electromagnetic wave, such electromagnetic wave fed from the cavity resonator 10 was output to the network analyzer 6 via the loop antenna 22b. The resonant frequency of the cavity resonator 10 in a TM₀₁₀ mode was measured by the network analyzer 6 based on the electromagnetic wave that was output from the cavity resonator 10 to the network analyzer 6. The resonant frequency was 2.86 GHz. The resonant frequency was output from the network analyzer 6 to the processing unit 8 as the measured result, and then the relative dielectric constant of the mixed substance 18 was calculated by the processing unit 8.

0104In this fashion, the relative dielectric constant of the mixed substance 18 in which the volume ratio of the sample A was 0.4 was calculated by the processing unit 8.

0105Then, while changing gradually the volume ratio of the sample A occupied in the mixed substance 18 in a range from 0 to 0.4, the relative dielectric constant of the mixed substance 18 was calculated in the same way as the case that the volume ratio of the sample A was 0.4.

0106A graph showing a relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 was made in the processing unit 8.

0107<figref idref="f0008">FIG.13</figref> is a graph obtained by fitting the logarithmic mixture rule to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. Also, in <figref idref="f0008">FIG.13</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0108<figref idref="f0008">FIG.14</figref> is a graph obtained by fitting the Lichtenecker-Rother' s Formula to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. Also, in <figref idref="f0008">FIG.14</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0109In <figref idref="f0008">FIG.13</figref>, the relative dielectric constant of the sample A was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0. Also, in <figref idref="f0008">FIG.14</figref>, the relative dielectric constant of the sample A was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0.

0110Then, the relative dielectric constants of the sample B and the sample C were detected in the same way as in the case that the relative dielectric constant of the sample A was measured.

0111Measured results of the relative dielectric constants of the samples A, B, C are given in Table 2. <tables id="tabl0002" num="0002"><table frame="all"><title>TABLE 2</title><tgroup cols="3"><colspec colnum="1" colname="col1" colwidth="19mm" /><colspec colnum="2" colname="col2" colwidth="37mm" /><colspec colnum="3" colname="col3" colwidth="49mm" /><thead valign="top"><row><entry /><entry align="center">logarithmic mixture rule</entry><entry align="center">Lichtenecker-Rother's Formula</entry></row></thead><tbody><row><entry align="center">sample A</entry><entry align="char" char="." charoff="10">87.5</entry><entry align="char" char="." charoff="8">86.3</entry></row><row><entry align="center">sample B</entry><entry align="char" char="." charoff="10">77.7</entry><entry align="char" char="." charoff="8">76.8</entry></row><row><entry align="center">sample C</entry><entry align="char" char="." charoff="10">80.2</entry><entry align="char" char="." charoff="8">79.6</entry></row></tbody></tgroup></table></tables>

0112As given in Table 2, the relative dielectric constants of the samples A, B, C derived by using the logarithmic mixture rule and the Lichtenecker-Rother' s Formula became almost equal mutually.

[Example 5]

0113As the sample, the spherical powders made of Ba (NdBi) ₂TiO₄ were prepared. As the liquid medium, the mixed substance in which the 15.65 wt% BaTiO₃ powders and the 0.3 wt% dispersing agent are mixed in the 84.10 wt% ion-exchange water was prepared.

0114Like Example 4, the mixed substance 18 in which the sample as the measured object is mixed in the liquid medium, in which the ion-exchange water, the BaTiO₃ powders and the dispersing agent are mixed, was prepared. The relative dielectric constant of the mixed substance 18 was calculated by using the measuring system 2 shown in <figref idref="f0001">FIG.1</figref> as the measuring system. Here, the relative dielectric constant of the ceramic composition in the sample was 93 and the relative dielectric constant of the liquid medium was 80.1. Thus, the relative dielectric constant of the liquid medium was 0.86 times the relative dielectric constant of the ceramic composition powders.

0115In Example 5, the relative dielectric constant of the mixed substance 18 was detected while changing gradually the volume ratio of the sample occupied in the mixed substance 18 in a range from 0 to 0.4.

0116A graph showing a relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 was made in the processing unit 8.

0117<figref idref="f0009">FIG.15</figref> is a graph obtained by fitting the logarithmic mixture rule to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. In <figref idref="f0009">FIG.15</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0118<figref idref="f0009">FIG.16</figref> is a graph obtained by fitting the Lichtenecker-Rother' s Formula to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. In <figref idref="f0009">FIG.16</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0119Like Example 5, in <figref idref="f0009">FIG.15</figref>, the relative dielectric constant of the sample was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0. Also, in <figref idref="f0009">FIG.16</figref>, the relative dielectric constant of the sample was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0.

0120The relative dielectric constant of the sample detected by using the logarithmic mixture rule was 77.7, while the relative dielectric constant of the sample detected by using the Lichtenecker-Rother's Formula was 77.3. Thus, both relative dielectric constants became almost equal values mutually.

[Example 6]

0121As the sample, the Al₂O₃ powders were prepared. As the liquid medium, the mixed substance in which the ion-exchange water and methanol are mixed was prepared. Five types of liquid media consisting of the liquid medium A (relative dielectric constant 10.23), the liquid medium B (same 14.08), the liquid medium C (same 18.26), the liquid medium D (same 22.88), and the liquid medium E (same 41.69) were prepared while changing an amount of methanol that is mixed into the ion-exchange water.

0122The relative dielectric constant of the mixed substance 18 was calculated by employing the measuring system 2 shown in <figref idref="f0001">FIG.1</figref> as the measuring system. Now, the relative dielectric constant of the ceramic composition of the sample was 11. Thus, the relative dielectric constants of five type liquid media were 0.93 times (liquid mediumA) , 1.28 times (liquid medium B) , 1.66 times (liquid medium C), 2.08 times (liquid medium D), and 3.79 times (liquid medium E) the ceramic composition of the sample respectively.

0123In Example 6, the relative dielectric constant of the mixed substance 18 was detected while changing gradually the volume ratio of the sample occupied in the mixed substance 18 to the liquid medium A in a range from 0 to 0.2.

0124A graph showing a relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 was made in the processing unit 8.

0125<figref idref="f0010">FIG.17</figref> is a graph obtained by fitting the logarithmic mixture rule to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. In <figref idref="f0010">FIG.17</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0126<figref idref="f0010">FIG.18</figref> is a graph obtained by fitting the Lichtenecker-Rother' s Formula to the relationship between the volume ratio of the powders and the relative dielectric constant of the mixed substance 18 based on the method of least squares. In <figref idref="f0010">FIG.18</figref>, an abscissa denotes the volume ratio of the powders and an ordinate denotes the relative dielectric constant of the mixed substance 18.

0127As in Example 4, in <figref idref="f0010">FIG.17</figref>, the relative dielectric constant of the sample was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0. Also, in <figref idref="f0010">FIG.18</figref>, the relative dielectric constant of the sample was detected by reading a value of the relative dielectric constant when the volume ratio of the powders is 1.0.

0128The relative dielectric constant of the sample detected with respect to the liquid medium A by using the logarithmic mixture rule was 12.72, while the relative dielectric constant of the sample detected by using the Lichtenecker-Rother's Formula was 12.41. Thus, both relative dielectric constants had almost equal values mutually. Similarly, the relative dielectric constants of the samples were detected with respect to the liquid media B, C, D, E.

0129The relative dielectric constants of the samples detected with respect to the liquid media A, B, C, D, E are given in Table 3. <tables id="tabl0003" num="0003"><table frame="all"><title>TABLE 3</title><tgroup cols="3"><colspec colnum="1" colname="col1" colwidth="19mm" /><colspec colnum="2" colname="col2" colwidth="38mm" /><colspec colnum="3" colname="col3" colwidth="49mm" /><thead valign="top"><row><entry /><entry align="center">Logarithmic mixture rule</entry><entry align="center">Lichtenecker-Rother's Formula</entry></row></thead><tbody><row><entry align="center">sample A</entry><entry align="char" char="." charoff="10">12.723</entry><entry align="char" char="." charoff="8">12.405</entry></row><row><entry align="center">sample B</entry><entry align="char" char="." charoff="10">12.886</entry><entry align="char" char="." charoff="8">12.456</entry></row><row><entry align="center">sample C</entry><entry align="char" char="." charoff="10">12.837</entry><entry align="char" char="." charoff="8">11.776</entry></row><row><entry align="center">sample D</entry><entry align="char" char="." charoff="10">12.144</entry><entry align="char" char="." charoff="8">8.6696</entry></row><row><entry align="center">sample E</entry><entry align="char" char="." charoff="10">15.314</entry><entry align="char" char="." charoff="8">2.2302</entry></row></tbody></tgroup></table></tables>

0130As given in Table 3, the relative dielectric constants of the samples detected with respect to the liquid media A, B, C by using the logarithmic mixture rule and the Lichtenecker-Rother's Formula became almost equal mutually. The relative dielectric constants of the liquid media were 0.93 times (liquid medium A), 1.28 times (liquid medium B), and 1.66 times (liquid medium C) the relative dielectric constant of the ceramic composition of the sample respectively. Thus, the relative dielectric constant of powders can be obtained with high precision when the relative dielectric constant of the mixed substance with respect to the ceramic composition of the sample ranges over 0.93 times to 1.66 times.

0131In the above embodiment and Examples, the TM₀₁₀ mode is used as the resonant mode when the resonant frequency is measured. For example, the TM_0m0 mode (m=2, 3, 4, ...) other than the TM₀₁₀ mode may be used as the resonant mode.

0132Also, in the above embodiment and Examples, the cavity resonator is formed cylindrically. But the cavity resonator may be formed as square, rectangle, triangle, or the like.

0133In addition, in the above embodiment, the ion-exchange water is used as the liquid medium. But either the liquid except the ion-exchange water or the mixed substance containing the liquid and the powder dielectric substance may be used as the liquid medium.

0134Also, in the above Examples, the mixed substance 18 injected into the tube 12 is fluidized by using the syringe 14a and the syringe 14b. But the mixed substance 18 maybe fluidized by using the fluidizing apparatus 38A shown in <figref idref="f0005">FIG.7</figref>.

0135In addition, in the above Examples, the mixed substance 18 injected into the tube 12 is fluidized by using the syringe 14a and the syringe 14b. But the mixed substance 18 may be fluidized by using the fluidizing apparatus 38A shown in <figref idref="f0005">FIG. 7</figref>.

0136Next, the cavity resonator used in the present invention will described with reference to <figref idref="f0011 f0012 f0013">FIGS.19 to 21</figref> hereunder. The distribution of the electric field generated when the cavity resonator is shaped cylindrically will be explained with reference to <figref idref="f0012">FIG.20</figref> hereunder. <figref idref="f0012">FIG.20(a)</figref> shows the distribution of the electric field in the TM₀₁₀ mode in the ideal cylindrical cavity resonator, and the electric fields each indicated with an arrow are concentrated at a center portion of the cylinder. Then, the dielectric substance as the measured object is placed at the maximum electric field point of the resonator.

0137It is desired that, as shown in <figref idref="f0011">FIG.19(a)</figref>, ideally the TM₀₁₀ mode cylindrical cavity resonator used in measurement of the relative dielectric constant of powders in the present invention should be formed as a closed cylinder. However, actually it is impossible to take out the dielectric substance as the measured object from the closed cylinder. Therefore, as shown in <figref idref="f0011">FIG. 19(b)</figref> , it is made possible by a structure in which an opening portion is provided to one of center portions of the resonator, to take out the dielectric substance as the measured object.

0138Meanwhile, as shown in <figref idref="f0012">FIG.20(b)</figref>, the electromagnetic wave leaks out from the inside of the resonator to the outside via the opening portion in the structure in which the opening portion is formed in the resonator, as shown in <figref idref="f0011">FIG.19(b)</figref>. There existed the problem that measurement of the resonant frequency or the unloaded Q value becomes unstable due to the leakage of the electromagnetic wave, which has an influence upon measurement of the dielectric constant and the dielectric loss tangent.

0139In order to handle this problem, as shown in <figref idref="f0011">FIG.19 (c) (d)</figref>, it is effective to provide a supporter on the outside of the opening portion. <figref idref="f0011">FIG.19(c)</figref> shows an example in which the supporter is provided on the outside of the opening portion when the opening portion is provided to one of the center portions of the resonator. <figref idref="f0011">FIG.19(d)</figref> shows an example in which the supporter is provided on the outside of both opening portions when the opening portion is provided to both of the center portions of the resonator.

0140As shown in <figref idref="f0011">FIG. 19 (c) (d)</figref> , when the opening portion of the supporter portion is constructed sufficiently smaller than a diameter of the resonator, such supporter portion can act as a cut-off region. A cut-off frequency of the supporter portion (TM₀₁₀ mode) is shown in <figref idref="f0013">FIG.21</figref>. It is appreciated from <figref idref="f0013">FIG.21</figref> that the cut-off frequency becomes higher when a length of the opening portion becomes shorter. If a difference between the resonant frequency of the resonator and the cut-off frequency of the supporter portion is increased larger, the cut-off characteristic is excellent and therefore the leakage of the electromagnetic wave from the resonator can be suppressed.

0141A distribution of the electric field when the supporters are provided as shown in <figref idref="f0011">FIG.19(d)</figref> is shown in <figref idref="f0012">FIG.20(c)</figref>. A diameter is set to a length of the opening portion, as shown in <figref idref="f0012">FIG. 20 (d)</figref> , when the opening portion is circular. The longest portion of the opening portion is set to the length of the opening portion when the opening portion has a shape other than the circle. Such mechanism makes it possible to prevent the leakage of the electromagnetic wave and get a cut-off structure, so that the resonant frequency and the unloaded Q value of the resonator can be measured stably. Also, it is supposed easily that the better cut-off can be obtained as the length of the supporter becomes longer. Actually, it is difficult to get the optimum length of the supporter applied to get the cut-off. In some cases the unnecessarily long supporter is used.

0142Next, a simulation to detect the optimum value of the supporter in the cylindrical resonator will be explained hereunder. <figref idref="f0014">FIG.22</figref> is a view showing conditions required for a resonator shape to execute the simulation to detect the optimum value of the supporter of the cylindrical cavity resonator. Now, the resonant frequency is simulated by setting shapes of respective portions of the resonator and the dielectric constant of the dielectric substance, as shown in <figref idref="f0014">FIG.22</figref>.

0143The results of the simulation are shown in <figref idref="f0015">FIG.23</figref>. It is appreciated from <figref idref="f0015">FIG.23</figref> that such a cut-off structure is obtained that the resonant frequency becomes constant within a range of h in excess of about 1.5 mm when the length of the supporter is changed.

0144Next, differences due to the relative dielectric constant ε of the measured dielectric substance will be explained hereunder. FIG. 24 (a) is a graph showing raw data of the relationship between the length of the supporter and the resonant frequency when the relative dielectric constant of the dielectric substance is set to ε <i>=</i> 1, ε = 100, and ε = 500 respectively, and FIG.24(b) is a graph showing normalized data of the same. It is seen from FIG.24 (b) that the cut-off structure can be obtained if h/d is in excess of 0.5.

0145Also, differences due to a height H of the resonator will be explained hereunder. FIG.25(a) is a graph showing raw data of a relationship between the length of the supporter and the resonant frequency when the height of the resonator is set to H=12.5 mm, H=25 mm, H=50 mm, H=100 mm, and H=140 mm respectively, and FIG. 25 (b) is a graph showing normalized data of the same. It is seen from FIG. 25 (b) that the cut-off structure can be obtained if h/d is in excess of 0.5.

0146In addition, differences due to a diameter d of the insertion hole in the dielectric substance will be explained hereunder. FIG.26(a) is a graph showing raw data of a relationship between the length of the supporter and the resonant frequency when the diameter d of the insertion hole is set to d=1 mm, d=3 mm, and d=5 mm respectively, and FIG.26(b) is a graph showing normalized data of the same. It is seen from FIG.26 (b) that the cut-off structure can be obtained if h/d is in excess of 0.5. In this case, the above simulation is applied to the resonator in <figref idref="f0014">FIG.22</figref>. But results of the above simulation can be substantially applied to the case that the shape of the resonator and the shape of the opening portion are varied. Also, the cavity resonator of the present invention is not limited to the application of the powders, and may be applied to any measured sample if such measured sample is formed of the dielectric substance.

0147In the above embodiment and Examples, in the measurement of the relative dielectric constant of the mixed substance 18, the relative dielectric constant of the mixed substance 18 is detected by inputting the electromagnetic wave into the cavity resonator and then measuring the resonant frequency based on the replied electromagnetic wave. For example, as disclosed in Patent Literature 1, the relative dielectric constant of the mixed substance may be detected by applying a voltage into a vessel in which a pair of electrodes are arranged and the mixed substance is filled. Also, the relative dielectric constant of the mixed substance may be detected by inputting the electromagnetic wave into a rectangular waveguide and then measuring a transmission coefficient and a reflection coefficient of the replied electromagnetic wave.

0148Also, in above Examples, the TM₀₁₀ mode is used as the resonance mode applied when the resonant frequency is measured. The TM_0m0 mode (m=2, 3, 4, ...) other than the TM₀₁₀ mode may be used as the resonant mode.

0149Also, in the above embodiment and Examples, the relative dielectric constant of the liquid substance may be measured by using the measuring system 2.

0150Also, in the above embodiment and Examples, the cavity resonator is formed cylindrically. But the cavity resonator may be shaped into the square, the rectangle, the triangle, or the like.

0151In addition, in the above embodiment and Examples, the relative dielectric constant of the mixed substance is measured by changing the relative dielectric constant of the liquid substance in the situation that the volume ratio of the powders is kept constant. In case the relative dielectric constant of the mixed substance is measured by changing the relative dielectric constant of the liquid substance in the situation that the volume ratio of the powders is selected differently, the relative dielectric constant of the mixed substance 18 can be measured by using either the logarithmic mixture rule or Lichtenecker-Rother's Formula.

0152Also, in the above embodiment, the liquid such as water, alcohol, or the like or the mixed substance in which water, alcohol, and the like are mixed is employed as the liquidmedium. But the liquid except the water or the alcohol, their mixed substance, or the mixed substance consisting of the liquid and the powder dielectric substance may be employed as the liquid medium.

0153In addition, in above Examples, the mixed substance 18 injected into the tube 12 is fluidized by using the syringe 14a and the syringe 14b. But the mixed substance 18 maybe fluidized by using the fluidizing apparatus 38A shown in <figref idref="f0005">FIG.7</figref>.

0154The TM₀₁₀ mode in the cavity resonator can be applied to a following system by utilizing the characteristics that the mode is the lowest mode (which has the lowest resonant frequency out of an infinite number of resonance peaks) and the electric filed are concentrated at a center axis of the cavity resonator.

0155The dielectric substance measuring system for inserting the rod-like-shaped dielectric substance into the electric-field concentrated portion on the center axis of the cavity resonator to which the supporter is provided, then measuring the resonant frequency and the unloaded Q value of the cavity resonator, and then measuring the relative dielectric constant and the dielectric loss tangent of the inserted rod-like dielectric substance based on the measured results can be implemented.

0156Since the TM₀₁₀ mode in the cavity resonator to which the supporter is provided is the lowest mode, the resonator or the filter that is excellent in the spurious characteristics can be implemented. In this case, when the rod-like-shaped dielectric substance is inserted into the electric-field concentrated portion on the center axis of the cavity resonator to which the supporter is provided, the intended resonance characteristic can be attained.