Classifications

• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01B—NON-METALLIC ELEMENTS; COMPOUNDS THEREOF; METALLOIDS OR COMPOUNDS THEREOF NOT COVERED BY SUBCLASS C01C
  • C01B21/00—Nitrogen; Compounds thereof
  • C01B21/06—Binary compounds of nitrogen with metals, with silicon, or with boron, or with carbon, i.e. nitrides; Compounds of nitrogen with more than one metal, silicon or boron
  • C01B21/068—Binary compounds of nitrogen with metals, with silicon, or with boron, or with carbon, i.e. nitrides; Compounds of nitrogen with more than one metal, silicon or boron with silicon
• • C—CHEMISTRY; METALLURGY
  • C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
  • C08K—Use of inorganic or non-macromolecular organic substances as compounding ingredients
  • C08K3/00—Use of inorganic substances as compounding ingredients
  • C08K3/34—Silicon-containing compounds
• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01P—INDEXING SCHEME RELATING TO STRUCTURAL AND PHYSICAL ASPECTS OF SOLID INORGANIC COMPOUNDS
  • C01P2004/00—Particle morphology
  • C01P2004/51—Particles with a specific particle size distribution
• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01P—INDEXING SCHEME RELATING TO STRUCTURAL AND PHYSICAL ASPECTS OF SOLID INORGANIC COMPOUNDS
  • C01P2004/00—Particle morphology
  • C01P2004/54—Particles characterised by their aspect ratio, i.e. the ratio of sizes in the longest to the shortest dimension

Definitions

• This disclosure relates to silicon nitride powder and a resin composition using the same.
• Heat generated by passing current through an electronic component is dissipated via a heat sink.
• a technique is known in which a heat dissipation material is filled between the electronic component and the heat sink.
• One type of heat dissipation material is a resin composition containing a resin and inorganic particles, and it is known that silicon nitride powder can be used as the inorganic particles (for example, Patent Document 1).
• Patent document 1 discloses a low-aluminum spherical ⁇ silicon nitride powder used as a filler in electronic packaging materials.
• the silicon nitride powder is characterized by a sphericity of 0.5 to 0.99, an Al impurity content of less than 500 ppm, and a particle size range of 0.5 ⁇ m to 50 ⁇ m.
• Patent Document 2 discloses a method for producing silicon nitride powder suitable for producing silicon nitride sintered bodies and silicon nitride powder obtained by said method.
• the silicon nitride powder has an average particle size of 1-50 ⁇ m, a metal oxide content of 0-10 wt%, and an impurity content of less than 1 wt%, preferably a metal oxide content of less than 1 wt%, and the sintered body has a thermal conductivity of 90 W/mK or more and a bending strength of 700 MPa or more, and preferably the sintering conditions for the sintered body are to mix the silicon nitride powder with MgO and Y 2 O 3 , polish, dry press mold the base, and gas pressure sinter the base at 1900° C. and 1 MPa nitrogen gas pressure for 8 hours.
• Patent Document 3 discloses silicon nitride powder suitable for producing highly thermally conductive silicon nitride sintered bodies.
• the silicon nitride powder is characterized by having a ⁇ fraction of 30-100%, an oxygen content of less than 0.5 wt%, an average particle size of 0.2-10 ⁇ m, an aspect ratio of 10 or less, and containing columnar particles with grooves formed in the long axis direction of the particle.
• silicon nitride powder is increasingly being used as described above, when trying to further improve its productivity, it was discovered that there was a problem with silicon nitride powder, which is that it tends to adhere to other materials.
• one embodiment of the present invention aims to provide a silicon nitride powder used as a filler for resin compositions, which can suppress adhesion to other components. Furthermore, another embodiment of the present invention aims to provide a resin composition using the silicon nitride powder.
• the silicon nitride powder comprises a plurality of silicon nitride particles and has an angle of repose of greater than 40°.
• Aspect 2 of the present invention is 2.
• Aspect 3 of the present invention is The silicon nitride powder according to aspect 1 or 2, wherein the difference between the particle diameter D90 of the cumulative 90% from the fine side of the volume-based cumulative particle size distribution and the particle diameter D10 of the cumulative 10% from the fine side of the volume-based cumulative particle size distribution is 150.0 ⁇ m or less.
• Aspect 4 of the present invention is A silicon nitride powder according to any one of Aspects 1 to 3, wherein the silicon nitride particles have an average aspect ratio of the minor axis to the major axis of greater than 0.50.
• Aspect 5 of the present invention is The silicon nitride powder according to any one of Aspects 1 to 4, wherein the ratio (L2/L1) of the total length L2 of the internal boundary line to the length L1 of the outer edge is 1% or less, and the maximum particle size of the silicon nitride particles is 6.8 ⁇ m or more.
• Aspect 6 of the present invention is A resin composition comprising a resin and the silicon nitride powder according to any one of Aspects 1 to 5.
• silicon nitride powder that can suppress adhesion to other components.
• Silicon nitride powder The present inventors have investigated from various viewpoints in order to realize a silicon nitride powder capable of suppressing adhesion to other members, and have focused on the angle of repose. A common measure to suppress adhesion to other members is to lower the angle of repose so as to improve fluidity. In contrast, the present inventors have found that by increasing the angle of repose to a predetermined value or more, the silicon nitride powder becomes more likely to aggregate, and as a result, it becomes less likely to adhere to other members (such as polystyrene members). Details of each requirement stipulated in the embodiment of the present invention are shown below.
• the silicon nitride powder according to the embodiment of the present invention comprises a plurality of silicon nitride particles and has an angle of repose of more than 40°. This makes it difficult for the silicon nitride powder to adhere to other members (such as polystyrene members).
• the silicon nitride powder in the resin composition containing the silicon nitride powder can be gathered to some extent to form a thermal diffusion path, and the thermal diffusivity of the resin composition can be improved.
• the angle of repose is preferably 41° or more. On the other hand, the angle of repose is preferably 60° or less.
• the angle of repose is more preferably 58° or less, even more preferably less than 56°, even more preferably 50° or less, even more preferably 47° or less, and particularly preferably 45° or less.
• the angle of repose of silicon nitride powder is measured in accordance with JIS R 9301-2-2:1999.
• the ambient temperature during angle of repose measurement is 23°C and humidity is 40%.
• the silicon nitride powder according to the embodiment of the present invention preferably has a compression degree of less than 34.4%. This improves the flowability of the silicon nitride powder, making it possible to disperse the silicon nitride powder more in the resin composition, and further improve the thermal diffusivity of the resin composition.
• the compression degree is more preferably 34.0% or less, even more preferably less than 33.6%, even more preferably less than 24.1%, and particularly preferably 17.0% or less.
• it is preferable that the compression degree is 3.0% or more, so that the silicon nitride powder is less likely to scatter.
• the compression degree is more preferably 5.0 or more, even more preferably 7.0% or more, and even more preferably 8.0% or more.
• the degree of compression of the silicon nitride powder is determined by measuring the tap density in accordance with JIS Z2512:2012 "Metal powder - Tap density measurement method" and calculating the degree of compression from ( D1 - D0)/D1, where D0 (g/ cm3 ) is the bulk density before tapping and D1 (g/ cm3 ) is the bulk density after tapping (i.e., the tap density ) .
• the bulk density after tapping i.e., tap density
• D 1 g/cm 3
• D 1 g/cm 3
• D 1 is preferably more than 0.54 g/cm 3 , more preferably 1.00 g/cm 3 or more, and even more preferably 1.17 g/cm 3 or more.
• D 1 is preferably 2.00 g/cm 3 or less, more preferably 1.90 g/cm 3 or less, and even more preferably less than 1.80 g/cm 3 .
• the bulk density D 0 (g/cm 3 ) before tapping is not particularly limited, but may be, for example, 0.35 to 1.60 g/cm 3 .
• Silicon nitride powder with a sharp particle size distribution is preferred because it is easy to use as a filler for resin compositions and increases the selectivity and freedom when mixing with other powders (particles).
• the difference between the particle size D90 (hereinafter sometimes simply referred to as "D90") at 90% cumulative from the fine particle side of the cumulative particle size distribution based on volume and the particle size D10 (hereinafter sometimes simply referred to as "D10") at 10% cumulative from the fine particle side of the cumulative particle size distribution based on volume is preferably 150.0 ⁇ m or less.More preferably, it is 130.0 ⁇ m or less.
• the difference between D90 and the cumulative 50% particle size D50 from the fine particle side of the volume-based cumulative particle size distribution is preferably 100.0 ⁇ m or less, and more preferably 80.0 ⁇ m or less.
• the difference between D90 and D10 is preferably 3.0 ⁇ m or more, more preferably more than 3.3 ⁇ m, even more preferably more than 6.6 ⁇ m, even more preferably 20.0 ⁇ m or more, and particularly preferably 40.0 ⁇ m or more.
• the difference between D90 and D50 is preferably 1.5 ⁇ m or more, more preferably greater than 2.0 ⁇ m, even more preferably greater than 5.0 ⁇ m, still more preferably greater than 5.5 ⁇ m, even more preferably greater than 20.0 ⁇ m, and particularly preferably greater than 25.0 ⁇ m.
• the D90, D50 and D10 of silicon nitride powder are measured by the laser diffraction method. Specifically, the powder dispersed in water is irradiated with a laser beam, and the diffraction is measured to determine each particle size.
• a measuring device such as the CILAS 1090L can be used.
• the average aspect ratio of the minor axis to the major axis of the silicon nitride particles contained in the silicon nitride powder is preferably more than 0.50, more preferably more than 0.60, and even more preferably 0.65 or more.
• the average aspect ratio of the silicon nitride particles is preferably less than 0.87, more preferably 0.86 or less, and even more preferably 0.85 or less.
• the average aspect ratio of the silicon nitride particles is measured as follows. SEM images of silicon nitride particles contained in the silicon nitride powder are analyzed using image processing software (e.g., Image J (manufactured by the National Institute of Health)). The maximum particle size of the silicon nitride particles (referred to as the "major axis") is identified, and the particle size in the direction perpendicular to the major axis is regarded as the "minor axis”. The major and minor axes are measured for 20 random silicon nitride particles, and the ratio of the minor axis to the major axis (minor axis/major axis) is determined for each particle. The arithmetic mean value of these ratios is regarded as the average aspect ratio of the silicon nitride particles.
• the maximum particle size of silicon nitride particles having a ratio (L2/L1) of the total length L2 of the internal boundary lines to the length L1 of the outer edge of 1% or less is 6.8 ⁇ m or more
• L1 and L2 are obtained by observing the cross section of the silicon nitride particle.
• “grain boundary” and "boundary line” refer to a boundary (also called a high-angle grain boundary) whose crystal orientation difference (oblique angle) exceeds 15° as a result of EBSD analysis.
• silicon nitride particles with a small value of L2/L1 are silicon nitride particles with a low content of boundary lines.
• silicon nitride particles with an L2/L1 of 1% or less are considered to be silicon nitride particles made of a single crystal (these are referred to as "single crystal particles").
• Single crystal particles have a high thermal diffusivity, and therefore tend to improve the thermal diffusivity when used as a filler for resin compositions.
• the maximum particle size of silicon nitride particles with L2/L1 of 1% or less is preferably 6.8 ⁇ m or more, more preferably 10.0 ⁇ m or more, even more preferably 15.0 ⁇ m or more, even more preferably 30.0 ⁇ m or more, even more preferably 45.0 ⁇ m or more, and particularly preferably 55.0 ⁇ m or more.
• Such silicon nitride particles form a long thermal conduction path when filled into a resin, and can therefore improve the thermal diffusivity of the resin composition.
• the ⁇ -phase ratio of the silicon nitride powder is preferably 65% or more.
• the ⁇ -formation rate is more preferably 70% or more, further preferably 80% or more, even more preferably 85% or more, and particularly preferably 90% or more.
• ⁇ -type rate refers to the content (volume %) of ⁇ -type silicon nitride relative to the total silicon nitride contained in the silicon nitride powder.
• a diffraction pattern of the silicon nitride powder is obtained by powder X-ray diffraction (X-ray source: CuK ⁇ radiation), and the diffraction pattern is analyzed by the Gazzara & Messier method (G.P. Gazzara and D.P. Messier, “Determination of Phase Content of Si3N4 by X-ray Diffraction Analysis”, Am. Ceram. Soc. Bull., 56[9]777-80 (1977)) to calculate the ⁇ -phase ratio.
• the silicon nitride powder according to the embodiment of the present invention is (1) synthesizing a silicon nitride composite crystal by a combustion synthesis method under a nitrogen atmosphere using a raw material containing Si; (2) crushing the silicon nitride synthetic crystals to obtain coarsely pulverized silicon nitride powder; and (3) finely pulverizing the coarsely pulverized silicon nitride powder to obtain finely pulverized silicon nitride powder.
• a step of heat treating the finely pulverized silicon nitride powder may be included. Each step will be described in detail below.
• Step (1) Step of synthesizing silicon nitride synthetic crystal
• Si powder is used as the raw material containing Si.
• the average particle diameter D50 of the raw material is, for example, within the range of 2 to 10 ⁇ m. This makes it possible to suppress the amount of oxygen impurities and increase the combustion speed to raise the synthesis temperature, thereby obtaining good crystal growth.
• the average particle diameter D50 of Si is 5 ⁇ m.
• the diluent is used to adjust the amount of Si in the raw materials. Separately prepared silicon nitride powder is used as the diluent.
• the diluent may be either ⁇ -type silicon nitride powder or ⁇ -type silicon nitride powder, or a mixture of these may be used.
• the average particle diameter D50 of the diluent is preferably in the range of 0.5 to 2.0 ⁇ m. As an example, the average particle diameter D50 of the diluent is 1.0 ⁇ m.
• the amount of diluent added is less than 10 mass% of the entire raw materials (including the diluent). As an example, the diluent is added in an amount of 5 to 8 mass% of the entire raw materials. By adding the amount of diluent within the above range, it becomes easier to obtain silicon nitride powder having the specified angle of repose, compressibility, etc.
• a diluent is mixed into the raw materials and filled into an insulating heat-resistant container.
• the insulating heat-resistant container has a thermal conductivity of 1 W/mK or less, and can be made of alumina or zirconia, but carbon is preferred in consideration of the risk of impurities being mixed in.
• the container is covered with a lid made of the same material as the insulating heat-resistant container.
• the thickness of the mixed raw materials is made to be greater than 100 mm, preferably greater than 100 mm and less than 150 mm.
• Combustion synthesis is performed under a nitrogen atmosphere in the range of 0.5 to 1 MPa (for example, 0.9 MPa). By adjusting the pressure range within the above range, efficient synthesis can be achieved while suppressing increases in equipment costs.
• a layer of powder (silicon nitride) with a thickness of 1 mm to 80 mm is laid on the bottom and sides of the crucible, the mixed raw materials are then filled, and the top surface is covered with a layer of powder with a thickness of 1 mm to 80 mm.
• the thickness of the powder is 100 mm or less, and preferably 1 mm to 80 mm. Covering the powder keeps the mixed raw materials warm, and makes it easier to obtain silicon nitride powder with the specified angle of repose, degree of compression, etc.
• a catalyst may be used, for example, about 0.01 to 0.1 mass % of Y 2 O 3 , Fe 2 O 3 , CaO, Ni, Co, C, etc. is added.
• external auxiliary heating in the range of 500° C. to 1700° C. (for example, 1500° C.) is performed to increase the combustion temperature in the combustion synthesis method by self-ignition.
• Step (2) Obtaining a coarsely pulverized silicon nitride powder
• the silicon nitride composite crystal is in the form of an aggregate of multiple silicon nitride particles.
• the silicon nitride composite crystal is crushed to obtain a coarsely pulverized silicon nitride powder.
• the composite is crushed using a general crushing device such as a hammer mill or a disk mill until it passes through a sieve with a predetermined mesh size (for example, a sieve with a mesh size in the range of 400 ⁇ m to 500 ⁇ m).
• Step (3) Step of obtaining finely pulverized silicon nitride powder
• the coarsely pulverized silicon nitride powder is further pulverized to obtain finely pulverized silicon nitride powder.
• the pulverization is carried out using a pulverizing device such as a jet mill or a ball mill. If necessary, the obtained finely pulverized powder may be classified. The classification may be carried out by sieving, wet classification, or the like.
• the finely pulverized silicon nitride powder may be heat treated.
• heat treating an oxide film is formed on the surface of the silicon nitride particles, which has the effect of chemically stabilizing the silicon nitride particles.
• the heat treatment is carried out, for example, in the atmosphere at 500°C or more and 1200°C or less.
• the heat treatment time can be appropriately adjusted according to the heat treatment temperature.
• the heat treatment time is, for example, 5 hours.
• the heat generated by the combustion synthesis method is used to synthesize silicon nitride composite crystals, which are then crushed, classified, and finely pulverized to produce the silicon nitride powder according to this embodiment.
• the resin composition according to the embodiment of the present invention contains a resin and the silicon nitride powder according to the embodiment of the present invention.
• the blending ratio of the resin/silicon nitride powder in the resin composition according to the embodiment of the present invention can be appropriately determined depending on the purpose and/or application.
• the ratio of the resin to the resin composition (composite) may be 5 to 75 volume % and 95 to 25 volume % of the silicon nitride powder.
• the filling rate of the silicon nitride powder in the resin composition refers to the content (volume %) of the silicon nitride powder when the volume of the resin composition (including the silicon nitride powder) is taken as 100 volume %.
• a resin composition can be obtained by mixing silicon nitride powder and a resin using a commonly used known method.
• the resin when the resin is liquid (such as liquid epoxy resin), the resin composition can be obtained by mixing the liquid resin, silicon nitride powder, and a curing agent, and then curing with heat or ultraviolet light.
• Known curing agents, mixing methods, and curing methods can be used.
• the resin when the resin is solid, the silicon nitride powder and the resin are mixed, and then kneaded by a known method such as melt kneading to obtain the desired resin composition.
• the resin used in the resin composition may be a known resin such as an epoxy resin.
• the type of resin may be selected from thermoplastic resins, thermoplastic elastomers, and thermosetting resins.
• the resin may be used alone or in combination of two or more types.
• these resin compositions may contain, as necessary, one or more of known additives such as plasticizers, curing accelerators, coupling agents, fillers, pigments, flame retardants, antioxidants, surfactants, compatibilizers, weather resistance agents, antiblocking agents, antistatic agents, leveling agents, and release agents, within the scope of the invention that does not impair the effects of the invention.
• additives such as plasticizers, curing accelerators, coupling agents, fillers, pigments, flame retardants, antioxidants, surfactants, compatibilizers, weather resistance agents, antiblocking agents, antistatic agents, leveling agents, and release agents, within the scope of the invention that does not impair the effects of the invention.
• the silicon nitride powder according to the embodiment and the resin composition containing the silicon nitride powder are particularly suitable for use as heat dissipating materials.
• a heat dissipating silicon nitride powder and a heat dissipating resin composition can be provided.
• the amount of diluent added was 5 to 8 mass% with respect to the entire raw material (including diluent).
• the mixed powder was filled in a carbonaceous heat-insulating heat-resistant container with a layer of powder having a thickness of 1 mm to 80 mm on the bottom and sides so that the raw material layer thickness was more than 100 mm and 150 mm or less, and further, the raw material layer was covered with a layer of powder having a thickness of 1 mm to 80 mm or less.
• Example No. 1 to 3 The obtained coarsely pulverized powder was further finely pulverized using a nanojetmizer (manufactured by Aisin Nano Technologies Co., Ltd.). For the fine pulverization, a nanojetmizer with a model number shown in Table 1 was used. The obtained finely pulverized powder was classified by the method shown in Table 1. Note that a part of the finely pulverized powder (referred to as sample No. 2) was not classified. Thereafter, the obtained classified powders (samples No. 1 and No. 3) and the finely pulverized powder (sample No.
• D50 is 192.0 ⁇ m
• the powder remaining below the sieve was further sieved using a sieve with an opening of 106 ⁇ m, and the powder remaining on the sieve (sample No. 6, D50 is 118.0 ⁇ m)
• the powder remaining below the sieve was further sieved using a sieve with an opening of 75 ⁇ m, and the powder remaining above the sieve (sample No.
• D50 is 83.0 ⁇ m
• the powder remaining below the sieve was further sieved using a sieve with an opening of 63 ⁇ m, and the powder remaining on the sieve (sample No. 8, D50 is 58.0 ⁇ m)
• Powder that remained under the sieve when sieved using a sieve with an opening of 63 ⁇ m (sample No. 9, D50 is 22.0 ⁇ m)
• the powder of sample No. 9 was further sieved using a sieve with an opening of 10 ⁇ m, the powder remaining under the sieve (sample No. 10, D50 is 3.5 ⁇ m)
• Example No. 4 a commercially available silicon nitride powder (Aldrich, silicon nitride (predominantly ⁇ -phase, ⁇ 10 micron primary particle size, product code 248622); hereafter referred to as "Sample No. 4"
• the SEM images were processed using the image processing software Image J (manufactured by the National Institute of Health) to determine the aspect ratio of 20 randomly selected silicon nitride particles in the SEM images.
• the maximum diameter of the silicon nitride particle was taken as the major axis, and the particle size in the direction perpendicular to the major axis was taken as the minor axis.
• the major and minor axes were measured for 20 randomly selected silicon nitride particles, and the ratio of the minor axis to the major axis (minor axis/major axis) was determined for each particle.
• the arithmetic mean value of these ratios was taken as the average aspect ratio of the silicon nitride particles (referred to as "aspect ratio" in Table 2).
• the maximum particle size of silicon nitride particles having an L2/L1 ratio of 1% or less was prepared using the sample (silicon nitride particles).
• the silicon nitride particles were embedded in resin, and then the resin and silicon nitride particles were cut with a diamond cutter. Thereafter, Pt was vapor-deposited on the cross-section as a protective film, the cross-section was prepared by Ar ion milling, and the sample was fixed to the SEM sample stage with Cu double-sided tape, and SEM-EBSD measurement was performed without vapor deposition.
• the observation position was determined so that two or more silicon nitride particles were completely within the observation area (i.e., two or more silicon nitride particles were not in contact with the frame of the observation area).
• the measurement was performed with ⁇ -type silicon nitride particles.
• Ion milling device E-3500 (manufactured by Hitachi High-Tech Corporation)
• Ion sputtering device E-1030 (manufactured by Hitachi, Ltd.)
• Schottky scanning electron microscope SU5000 (Hitachi High-Tech Corporation)
• Backscattered electron diffraction device Velocity (manufactured by METEK Corporation)
• the total length L2 of the boundary lines was also calculated.
• the “total length L2 of the boundary lines” is the sum of the boundary lines contained inside the silicon nitride particle, and does not include the outer edge of the silicon nitride particle.
• the total length L2 of the boundary lines was calculated by adding the total length of the grain boundaries inside the silicon nitride particle and the total length of the inner wall of the cavity (if there is a cavity inside the silicon nitride particle).
• “grain boundary” and “boundary line” here refer to a boundary (also called a high-angle grain boundary) where the crystal orientation difference (oblique angle) exceeds 15° as a result of EBSD analysis.
• Such measurements were carried out once for any 20 silicon nitride particles, and silicon nitride particles with an L2/L1 ratio of 1% or less were regarded as single crystal particles, and the length of the major axis was measured and recorded as the "maximum particle size of the single crystal particle.”
• the measured 20 silicon nitride particles contained multiple single crystal particles, the arithmetic average value of their maximum particle sizes was calculated.
• a 1 mm thick aluminum plate with a rectangular hole of 1 cm x 10 cm was prepared as a mold form.
• a PET film coated with a release agent (rear side film) was attached to the rear side of the mold form so as to cover the rectangular hole, with the release agent-coated surface facing the mold form.
• a PET film coated with a release agent front side film
• Another aluminum plate was placed on top of the front side film and heated at 100°C for 1 hour to harden the composite. After curing was complete, the aluminum plate was left to cool, and when its temperature had dropped to room temperature, it was removed.
• the PET films on the front and back sides of the cured composite were then peeled off to obtain a sheet-like sample for measuring thermal diffusivity.
• the thermal diffusivity of the obtained sheet sample was measured.
• the thermal diffusivity was measured at room temperature by temperature wave thermal analysis (TWA) using a sheet sample of the resin composition, which was cut into a test piece measuring 10 mm in length, 10 mm in width, and 1 mm in thickness, using an AiPhase Mobile made by AiPhase Corporation as the measuring device.
• TWA temperature wave thermal analysis
• the thermal diffusivity was measured at three arbitrary points on one measurement sample piece, and the average value was calculated from the measurement results at the three points.

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