Patent Application
20090065731
1. Field of the Invention
The present invention relates to a method for producing a piezoelectric ceramic, more specifically, relates to a production method which includes a heat treatment for improving toughness of a piezoelectric ceramic.
2. Description of the Related Art
Piezoelectric ceramics are widely used as a material for piezoelectric elements such as resonators, filters, actuators, ignition devices, ultrasonic motors or the like. Most piezoelectric ceramics which are currently used in practice are formed from a ferroelectric substance having a perovskite structure, such as a PZT (PbZrO3—PbTiO3 solid solution) system or PT (PbTiO3) system which is tetragonal or rhombohedral at around room temperature.
Recently, along with the miniaturization of electronic devices which include a communication device, surface mounting has been rapidly progressing. During surface mounting, a piezoelectric element which is temporarily mounted on a printed board is soldered thereto. After the soldering process, which involves applying heat, it is desirable that the properties of the piezoelectric element (e.g., resonant frequency, oscillation frequency etc.) do not substantially differ from the initial properties. Accordingly, various investigations have been carried out for improving the heat resistance of a piezoelectric ceramic (e.g., Japanese Patent Laid-Open Nos. 2005-119944 and 2007-1841).
Japanese Patent Laid-Open No. 2005-119944 proposes a production method which includes a polarization treatment step of carrying out a polarization treatment on a piezoelectric ceramic containing a perovskite compound having Pb, Zr, Ti, Mn, and Nb as main components, and a heat treatment step of retaining the polarized piezoelectric ceramic within the temperature range of 0.68Tc or more to less than Tc (wherein Tc is the Curie temperature of the piezoelectric ceramic) for 1 to 100 minutes.
Japanese Patent Laid-Open No. 2007-1841 proposes a piezoelectric ceramic formed from a sintered compact which contains a main component represented by Pba[(Mn1/3Nb2/3)xTiyZrz]O3 (wherein 0.97≦a≦1.01, 0.04≦x≦0.16, 0.48≦y≦0.58, and 0.32≦z≦0.41), and Al as an additive, wherein the mean crystal grain size of the sintered compact is 1.0-4.0 μm.
With the miniaturization of electronic devices, in addition to heat resistance, piezoelectric ceramics also now need to have improved toughness. In particular, this is to suppress processing defects such as chips and cracks during the dicing step and lapping step of a thin piezoelectric ceramic having a thickness of 1 mm or less, and especially, of 0.5 mm or less. Further, this is also to prevent a piezoelectric ceramic from being damaged if it subjected to a shock by being dropped during the production steps. However, Japanese Patent Laid-Open Nos. 2005-119944 and 2007-1841 give no suggestions concerning how to improve toughness thereof.
The present invention was created based on such technical problems, and it is an object of the present invention to provide a method for producing a piezoelectric ceramic which can improve heat resistance and toughness.
The present invention is a method for producing a piezoelectric ceramic comprising the steps of polarizing a piezoelectric ceramic comprising a main component represented by a composition formula Pba[(MnbNbc)dTieZrf]O3, wherein a, b, c, d, e and f satisfy 0.98≦a≦1.01, 0.340≦b≦0.384, 0.616≦c≦0.660, 0.08≦d≦0.12, 0.500≦e≦0.540, 0.37≦f≦0.41, and bd+cd+e+f=1, and 1 to 10% by weight of Al in terms of Al2O3 as an additive; and heat-treating the polarized piezoelectric ceramic for 10 to 60 minutes at 200 to 300° C.
The present invention improves toughness by heat-treating a piezoelectric ceramic with a specific composition, which has been subjected to a polarization treatment. The effects of this improvement in toughness are marked if b in the above composition formula is such that 0.340≦b≦0.384 and c in the above composition formula is such that 0.616≦c≦0.660.
In the present invention, the heat treatment is preferably conducted in a temperature range of 260 to 300° C., and preferably for 20 to 40 minutes.
According to the present invention, toughness can be improved by subjecting a polarized piezoelectric ceramic to a heat treatment for 10 to 60 minutes at 200 to 300° C. Therefore, processing defects during the dicing step and lapping step can be suppressed. Thus, the present invention can achieve an improvement in processing speed. Further, a piezoelectric ceramic can be obtained which is strong against shocks from drops or the like which occur during the production steps.
The production method of a piezoelectric ceramic according to the present invention will now be described in more detail.
First, the composition of the piezoelectric ceramic to which the present invention is directed will be described.
The main component of the piezoelectric ceramic produced according to the present invention is represented by the following composition formula. This main component is composed of a perovskite compound. Composition formula: Pba[(MnbNbc)dTieZrf]O3
In the formula, a, b, c, d, e and f satisfy the following. Here, a, b, c, d, e and f all represent molar ratios.
0.98≦a≦1.01, 0.340≦b0.384, 0.616≦c≦0.660, 0.08≦d≦0.12, 0.500≦e≦0.540, 0.37≦f≦0.41, and bd+cd+e+f=1
The reasons why a, b, c, d, e and f are defined in the above ranges are as follows.
The value of a, which represents the amount of Pb, is in the range of 0.98≦a≦1.01. If a is less than 0.98, it is difficult to obtain a dense sintered body. On the other hand, if a is more than 1.01, good heat resistance cannot be obtained. a is preferably such that 0.985≦a≦1.005, and is more preferably such that 0.985≦a≦1.000.
The stoichiometric composition of Mn and Nb in the perovskite compound having Pb, Zr, Ti, Mn, and Nb as main components is Mn1/3Nb2/3. Japanese Patent Laid-Open No. 2005-119944 employs a stoichiometric composition for Mn and Nb. In contrast, the present invention employs a composition in which the Mn is richer than the stoichiometric amount, and the Nb is poorer than the stoichiometric amount. A composition in which the Mn is richer than the stoichiometric amount and the Nb is poorer than the stoichiometric amount can be defined such that b is 0.340≦b≦0.384 and c is 0.616≦c≦0.660. A piezoelectric ceramic having this composition range has a higher effect on toughness improvement resulting from the heat treatment of the present invention than a piezoelectric ceramic in which the Mn and Nb are present in stoichiometric amounts. Further, by employing this composition range, the heat resistance of the piezoelectric ceramic is improved.
If b is less than 0.34° (c is more than 0.660), the effect on toughness improvement according to the present invention is small, and excellent heat resistance can no longer be obtained. Further, if b is more than 0.384 (c is less than 0.616), ohmic resistance is reduced, whereby polarization becomes impossible. Preferably, b is such that 0.345≦b≦0.375 and c is such that 0.625≦c≦0.655. More preferably, b is such that 0.345≦b≦0.370 and c is such that 0.630≦c≦0.655.
The value of d, which represents the total amount of Mn and Nb in the above composition formula, is in the range of 0.08≦d≦0.12. If d is less than 0.08, the electrical property Qmax becomes smaller. On the other hand, if d is more than 0.12, good heat resistance cannot be obtained. Accordingly, d is such that 0.085≦d≦0.12, preferably such that 0.085≦d≦0.115, and is more preferably such that 0.09≦d≦0.11.
The value of e, which represents the amount of Ti, is in the range of 0.500≦e≦0.540. If e is less than 0.500, good heat resistance cannot be obtained. On the other hand, if e is more than 0.540, the electrical property Qmax becomes smaller. e is preferably such that 0.505≦e≦0.535, and is more preferably 0.505≦e≦0.520.
The value of f, which represents the amount of Zr, is in the range of 0.37≦f≦0.41. If f is less than 0.37, the electrical property Qmax becomes smaller. If f is more than 0.41, good heat resistance cannot be obtained. Therefore, while f is in the range of 0.37≦f≦0.41, preferred is 0.380≦f≦0.405, and more preferred is 0.385≦f≦0.400.
The present invention comprises the above as a main component, and further comprises 1 to 10% by weight of Al in terms of Al2O3 as an additive.
The electromechanical coupling factor of a piezoelectric ceramic can be reduced by adding Al2O3. This is suitable when the piezoelectric ceramic produced according to the present invention is used for a resonator. Like other electronic components, resonators continue to decrease in size. Miniaturized resonators sometimes cannot adequately confine the main vibration. Therefore, in such resonators, unnecessary vibrations (spurious vibrations) are likely to occur. Here, the expression “confine the main vibration” refers to the state wherein a single vibration is generated on the vibrating electrode sections formed on both surfaces of the piezoelectric body, whereby vibrations are attenuated in the sections (non-electrode sections) free from a vibrating electrode so that unnecessary vibrations are scarcely present. If the piezoelectric element is large, vibrations can be sufficiently attenuated since the non-electrode sections can be large. However, for a small resonator, there are less non-electrode sections. In such case, the vibrations might not be sufficiently attenuated, whereby unnecessary vibrations are more likely to occur. If unnecessary vibrations increase, when the electromechanical coupling factor of the piezoelectric material is large, the frequency of the main vibration and that of the unnecessary vibrations overlap or approximate each other, which makes it more difficult to confine only the main vibration. While it is possible to separate the frequency of the main vibration and that of the unnecessary vibrations by reducing the electromechanical coupling factor, the Al2O3 in the present invention can also deal with this issue. Further, as is illustrated in the following Examples, the piezoelectric ceramic produced according to the present invention comprising a predetermined amount of Al2O3 is effective for resonator miniaturization because unnecessary vibrations can be suppressed.
A preferred Al2O3 amount is 2 to 6% by weight, and a more preferred Al2O3 amount is 2 to 4% by weight. If the Al2O3 is in this range, the below-described heat resistance |ΔF0| can be made especially small. Further, if the Al2O3 amount is 6% by weight or less, the electrical property Qmax can be 80 or higher, and if the Al2O3 amount is 4% by weight or less, the electrical property Qmax can be 90 or higher.
The present invention subjects a piezoelectric ceramic having the above composition to a certain heat treatment, which will now be described below. This heat treatment is carried out on a piezoelectric ceramic which has been subjected to a polarization treatment. Carrying out the heat treatment after a polarization treatment allows a polarized state having a higher heat resistance to be realized, and is also effective in reducing the below-described |ΔF0|. Further, although the below-described electromechanical coupling factor k15 is a property which is exhibited after polarization, this electromechanical coupling factor k15 can be reduced as a result of the heat treatment of the present invention, which allows a preferred state for a resonator to be achieved. The steps until the polarization treatment and the steps after the heat treatment will be described below.
The heat treatment temperature of the heat treatment in the present invention is selected in the range of 200 to 300° C. If the heat treatment temperature is less than 200° C., the effects of an improvement in toughness are insufficient. Although toughness increases as the heat treatment temperature increases, conversely, the electrical property Qmax decreases. Therefore, the heat treatment temperature is set at 300° C. or less. If the principal objective is to obtain an effect on toughness improvement, the heat treatment temperature is preferably 250 to 300° C., more preferably 260 to 300° C., and still more preferably 270 to 290° C. In addition, as long as it is within the above range, the heat treatment temperature does not have to be fixed, and may be varied.
The heat treatment time is between 10 and 60 minutes. If the heat treatment time is less than 10 minutes, the effects of an improvement in toughness cannot be sufficiently enjoyed. On the other hand, because the effects of an improvement in toughness level off at about 60 minutes, heat treatment any longer than that is a hindrance on productivity and needlessly consumes thermal energy. Further, carrying out a prolonged heat treatment at a high temperature in the above temperature range is a factor in causing the electrical property Qmax to decrease. Accordingly, the present invention sets the heat treatment time to between 10 and 60 minutes. The specific heat treatment time may be appropriately set in balance with the heat treatment temperature. The atmosphere for carrying out the heat treatment is not especially limited, and may be N2 or air.
Next, a preferred embodiment of the method for producing a piezoelectric ceramic will be described in order of its steps.
Used as the raw materials for the main component are powders of oxides or of compounds which are converted to oxides when heated. More specifically, PbO powder, TiO2 powder, ZrO2 powder, MnCO3 powder, Nb2O5 powder and the like can be used. The raw material powders are each weighed to form the composition according to the above-described composition formula. Then, based on the total weight of the main component raw material powders which were weighed, 1 to 10% by weight of Al2O3 powder as an additive raw material powder is added. The mean particle size of the raw material powders may be appropriately selected in the range of 0.1 to 3.0 μm.
Moreover, without being limited to the above described raw material powders, a powder of a composite oxide containing two or more metals may also be used as a raw material powder.
The raw material powders are subjected to wet mixing, and the resultant mixture is then calcined while being retained at a temperature in the range of 700 to 950° C. for a predetermined period of time. The atmosphere during calcination may be N2 or air. The retention time for the calcination may be appropriately selected in the range of 0.5 to 5 hours. The calcined body is milled after the calcination.
It was described above that the raw material powders of the main component are mixed together with the raw material powder of the additive and then the resultant mixture is subjected to calcination. However, the timing for adding the raw material powder of the additive is not limited to the above-described timing. For example, first, the powders of the main component may be weighed, mixed, calcined and milled, and then, to the main component powder obtained by grinding, the raw material powder of the additive may be added in a predetermined amount and mixed therein.
The milled powder is formed into granules for the purpose of smoothly carrying out the subsequent compacting step. At this time, a small amount of an appropriate binder, for example polyvinyl alcohol (PVA) is added to the milled powder, and the resultant mixture is sufficiently mixed and granulated through a mesh, for example. The resultant granulated powder is then compacted by pressing at a pressure of 200 to 300 MPa to obtain a compact having a desired shape.
After the binder added during compacting has been removed, the compact is heated and retained at a temperature in the range of 1,170 to 1,250° C. for a predetermined period of time to obtain a sintered body. The atmosphere during sintering may be N2 or air. The retaining time period of the heating may be appropriately set in the range of 0.5 to 4 hours.
After the temporary electrodes used for polarization have been formed on the sintered body, polarization is carried out. The polarization is conducted at a temperature of 50 to 300° C. by applying an electric field of 1.0 to 2.0 Ec (Ec being the coercive field) to the sintered body for 0.5 to 30 minutes.
The polarization is conducted in a bath of an insulating oil such as silicon oil heated to the above described temperature.
The sintered body (piezoelectric ceramic) is lapped to a desired thickness, and then the piezoelectric ceramic is subjected to the above-described heat treatment. During this heat treatment, the temporary-electrodes used for polarization may be left or may be removed. After being subjected to the heat treatment, vibrating electrodes are formed on the piezoelectric ceramic. Then, after cutting into a desired shape with a dicing saw or the like, the piezoelectric ceramic can function as a piezoelectric element. The piezoelectric ceramic produced according to the present invention can be suitably used especially for a resonator.
By subjecting the piezoelectric ceramic obtained by the present invention to a heat treatment, toughness thereof is improved.
Further, the piezoelectric ceramic obtained by the present invention can have improved heat resistance as a result of employing a composition in which the Mn of 0.340≦b≦0.384 is richer than the stoichiometric amount, and the Nb of 0.616≦c≦0.660 is poorer than the stoichiometric amount. Further, if Mn and Nb have such a composition, the effects of an improvement in heat resistance are marked.
In the present invention, toughness is evaluated in terms of fracture toughness value k1C. The fracture toughness value k1C can be measured according to the fracture toughness test method of a fine ceramic specified in JIS R1607.
The piezoelectric ceramic of the present invention exhibits excellent heat resistance as a result of employing a composition in which the Mn is richer than the stoichiometric amount, and the Nb is poorer than the stoichiometric amount. In the present invention, heat resistance was evaluated based on oscillation frequency F0. Specifically, heat resistance was evaluated in terms of the absolute value |ΔF0| of the rate of change (ΔF0) in oscillation frequency F0 according to the following formula 1.
F0 (before test): Oscillation frequency measured before application of a thermal shock.
F0 (after test): Oscillation frequency measured after application of a thermal shock, which was obtained as follows: wrapping a sample whose F0 (before test) had been measured in aluminum foil, immersing the sample in a solder bath at 265° C. for 10 seconds (thermal shock application), then taking the sample out from the aluminum foil and leaving the sample to stand in air at room temperature for 24 hours, and then measuring oscillation frequency F0.
The piezoelectric ceramic produced according to the present invention may have a heat resistance |ΔF0| relating to the oscillation frequency F0 of 0.05% or less, and further of 0.03% or less. Here, the oscillation frequency F0 is defined by the following formulas 2 to 5 employing equivalent circuit constants. In formulas 2 to 5, F0 represents the oscillation frequency, Fr represents the resonant frequency, Fa represents the anti-resonant frequency, C1 represents the motional capacitance, C0 represents the shunt capacitance, CL is defined in formula 5, Cd represents a free capacitance, and CL1 and CL2 each represent a load capacitance. As shown in formula 2, four parameters, resonant frequency Fr, motional capacitance C1, shunt capacitance C0 and CL affect the value of the oscillation frequency F0. Further, as shown in formulas 3 to 5, motional capacitance C1, shunt capacitance C0 and CL are each associated with plural parameters.
(Electromechanical Coupling Factor k15)
In the present invention, the electromechanical coupling factor was determined as one of the piezoelectric properties. The electromechanical coupling factor is a constant representing the energy converting efficiency of the piezoelectric with which the electrical energy applied between the electrodes of a piezoelectric body is converted into mechanical energy. For example, for actuator applications and ultrasonic applications, a large electromechanical coupling factor is desirable. On the other hand, it is desirable for the resonating element of a piezoelectric resonator to have a small electromechanical coupling factor. The electromechanical coupling factor in the piezoelectric ceramic produced according to the present invention can be adjusted by including Al2O3 as an additive. Specifically, the electromechanical coupling factor can be decreased by increasing the amount of Al2O3.
In the present invention, the resonant frequency Fr and anti-resonant frequency Fa were measured in the vicinity of about 4 MHz using the impedance analyzer (4294A manufactured by Agilent Technologies). The electromechanical coupling factor k15 was determined according to the following formula 6.
The electrical property Qmax represents the maximum value of Q (=tan θ; θ being the phase angle (deg)) between the resonant frequency Fr and anti-resonant frequency Fa. The electrical property Qmax is an important property of a resonator. The higher this value is, the lower the voltage capable of driving the device is.
As the raw materials, prepared were lead oxide (PbO) powder, titanium oxide (TiO2) powder, zirconium oxide (ZrO2) powder, manganese carbonate (MnCO3) powder, niobium oxide (Nb2O5) powder and aluminum oxide (Al2O3) powder. These raw material powders were weighed so as to form the compositions shown in Tables 1 to 4, and the resultant mixtures were the wet-mixed in pure water for 0.5 hours by a ball mill (using Zr balls).
The obtained slurry was sufficiently dried, compacted by pressing and then calcined in air at 800 to 950° C. Then, the calcined body was finely milled by a ball mill to have a mean particle size of 0.7 μm, and the finely milled powder was then dried. The dried, finely milled powder was charged with an appropriate amount of PVA (polyvinyl alcohol) as a binder, and the resultant mixture was granulated.
About 3 g of the granulated powder was charged into a die cavity having a 20 mm length and a 20 mm width, and then compacted under a pressure of 245 MPa using a uniaxial press machine. The obtained compacted body was subjected to a treatment for removing the binder, and was then sintered at 1,170 to 1,250° C. for 2 hours in air to obtain a sintered body.
Both surfaces of the sintered body were flattened by a lapping machine to a thickness of 0.350 mm. The sintered body was then cut to a size of 15 mm in length and 15 mm in width using a dicing saw, and temporary electrodes (14 mm long×14 mm wide) for polarization were formed on both the upper and lower surfaces. Then, the sintered body was polarized in a thickness-shear direction by applying an electric field of 3 kV/mm for 15 minutes in a silicon oil bath having a temperature of 150° C. The temporary electrodes were then removed. Here, the size of the sample after removing the temporary electrodes was 15 mm in length×15 mm in width×0.35 mm in thickness. The sample was lapped again by a lapping machine to a thickness of about 0.320 mm, and then cut using a dicing saw to have a length of 3.17 mm and a width of 0.55 mm.
The cut samples were heat-treated under the conditions shown in Tables 1 to 4. The heat treatment was conducted in the air atmosphere. The heat treatment was carried out after removal of the temporary electrodes, so as to be able to avoid the removal thereof with a greater difficulty due to a change of the temporary electrode property caused by the heat treatment.
After the heat treatment, as illustrated in
The fracture toughness value k1C of the specimen 1 was measured.
Further, the heat resistance |ΔF0| for the above specimen 1 was determined. |ΔF0| was determined by measuring the oscillation frequency F0 with a frequency counter (53181A manufactured by Agilent Technologies) and calculating according to the above-described formula 1.
The electromechanical coupling factor k15 and the electrical property Qmax for the above specimen 1 were also determined.
The above results are shown in Tables 1 to 4.
Further, using the above-obtained samples, the resonator illustrated in
As shown in Table 1, the heat resistance |ΔF0| value becomes smaller the higher the heat treatment temperature becomes, so that it can be seen that the heat treatment of the present invention is effective for heat resistance. Further, the value of the electromechanical coupling factor k15 also becomes smaller the higher the heat treatment temperature becomes, so that it can be seen that the heat treatment of the present invention is suitable for a resonator. However, the electrical property Qmax decreases the higher the heat treatment temperature becomes.
In Sample No. 14, since the heat treatment temperature was high, a waveform defect occurred due to deterioration in the impedance property.
From Table 2, it can be seen that the effects of an improvement in fracture toughness value k1C are exhibited at a heat treatment time of 10 to 60 minutes, although the effects of an improvement in fracture toughness value k1C are especially marked at 20 minutes and more. However, the effects of an improvement in fracture toughness value k1C decrease after peaking at a heat treatment time of 40 minutes. On the other hand, the electrical property Qmax decreases as the heat treatment times becomes longer. To combine both fracture toughness value k1C and electrical property Qmax, the heat treatment time is preferably set at 40 minutes or less.
From Table 3, it can be seen that the occurrence of spurious vibrations can be prevented by including Al2O3. Further, Table 3 also shows that the fracture toughness value k1C increases by including Al2O3. However, there is no correlation between the amount of Al2O3 and fracture toughness value k1C in the range of more than 2 wt %.
Heat resistance also improves by including Al2O3. In the range of more than 2 wt % and 10 wt % or less, the heat resistance |ΔF0| is 0.03% or less.
Further, the electromechanical coupling factor k15 decreases in proportion to the increase in the amount of Al2O3. On the other hand, the electrical property Qmax also decreases in proportion to the increase in the amount of Al2O3. If the amount of Al2O3 is 11 wt %, the electrical property Qmax is 40%, which is a low value. Therefore, the amount of Al2O3 in the present invention is 10 wt % or less.
In Table 4, although No. 34 and No. 35 are piezoelectric ceramics with an identical composition, the latter were subjected to a heat treatment (280° C.×30 minutes) and the former were not subjected to a heat treatment. Same explanations apply to No. 36 and No. 37, No. 38 and No. 39, No. 40 and No. 41, and No. 42 and No. 43. No. 34 and No. 35 are examples in which the Mn and Nb are present in stoichiometric amounts (Mn1/3Nb2/3). No. 36 and No. 37, No. 38 and No. 39, No. 40 and No. 41, and No. 42 and No. 43 are examples in which the Mn is richer than in the stoichiometric amount and the Nb is poorer than in the stoichiometric amount. For convenience, in the latter examples, the Mn and Nb will be represented to be non-stoichiometric”.
Whether the Mn and Nb were stoichiometric (No. 34 and No. 35) or non-stoichiometric (No. 36 and No. 37, and No. 38 and No. 39, No. 40 and No. 41, and No. 42 and No. 43), the fracture toughness value k1C were increased by the heat treatment of the present invention. However, comparison of the stoichiometric Mn and Nb cases with the non-stoichiometric cases shows that the non-stoichiometric cases had a higher increase in fracture toughness value k1C.
Next, looking at the relationship between b (Mn amount) and heat resistance |ΔF0|, if b increases, heat resistance |ΔF0| improves. Specifically, it can be seen that excellent heat resistance of |ΔF0| of 0.05% or less is exhibited if the Mn is in the range of 0.340≦b≦0.384 (Nos. 37, 39, 41, 43 and 44), whereas |ΔF0| is 0.09% if b is 0.333 (c is 0.667, No. 35) wherein Mn is a stoichiometric composition. However, if b is further increased, polarization becomes impossible. In the present invention, therefore, b is defined as 0.340≦b≦0.384.
Further, from Table 4 it can be seen that the electromechanical coupling factor k15 tends to decrease if b increases. When the inventive piezoelectric ceramic is to be used as a resonator, a smaller electromechanical coupling factor k15 is more preferable.
Looking at a (Pb amount), the electromechanical coupling factor k15 tends to increase as a increases, although the electromechanical coupling factor k15 can be 37.0% or less in the range (0.98≦a≦1.01) according to the present invention. Further, in this range, an electrical property Qmax of 80 or more can be obtained.
Similarly for d, e (Ti amount) and f (Zr amount), in the ranges (0.08≦d≦0.12, 0.500≦e≦0.540, 0.37≦f≦0.41) according to the present invention, an electromechanical coupling factor k15 of 37.0% or less and an electrical property Qmax of 80 or more were confirmed, thus exhibiting values which would have no problems in practical use as a resonator or other such applications.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2007-230937 | Sep 2007 | JP | national |
