JP2003139680A - Method for measuring particle size distribution - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for measuring particle size in a region of 1000 nm or below. SOLUTION: Content of particles having a specified particle size contained in a matter being measured is determined by obtaining a scattering X-ray spectrum based on small-angle X-ray scattering method from the matter being measured, determining the Y-intercept a line group having an inclination corresponding to a specified particle size such that the error is minimized when the scattering X-ray spectrum is approximated by linear combination of the line group, and determining the existing quantity of particles corresponding to the specified particle size from the inclination of the Y-intercept.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of analyzing a particle size distribution of a particle group of 1000 nm or less from a scattered X-ray spectrum obtained from an object to be measured based on a small angle X-ray scattering method.

[0002]

2. Description of the Related Art From a scattered X-ray spectrum obtained from a measured object based on a small-angle X-ray scattering method, typical particle diameters and particle contents constituting a particle group contained in the measured object based on the Fanchen method. A method for obtaining the rate is known.

Below, from the scattered X-ray spectrum, the above F
The principle of calculating a typical particle diameter and a particle content rate of a particle group contained in the measured object based on the Ankchen method will be described.

The scattered X-ray spectrum obtained by irradiating an object to be measured with X-rays based on the small-angle X-ray scattering method depends on the size of individual particles constituting a particle group contained in the object to be measured. . Since particles having different sizes are mixed in the particle group, the scattered X-ray spectrum obtained from the object to be measured is a superposition of scattered X-ray spectra obtained from particles having different particle diameters. In the Fanchen method, the scattered X-ray spectrum obtained based on the small-angle X-ray scattering method is analyzed as follows.

Scattering X obtained based on the small-angle X-ray scattering method
In the line spectrum, the measurement angle θ is set to the scattering vector k
Squared of k ² = (4πsin θ / λ) ² and the scattered X-ray intensity Y is converted to Log ₁₀ (Y) to obtain a standard spectrum. Here, λ is the wavelength of the X-rays with which the DUT is irradiated.

In the standard spectrum converted as described above, a straight line L _i , Log ₁₀ (Y _i ) = − α _Di k ² _i + Log ₁₀ having a slope equal to the attenuation rate of the standard spectrum in the region where the k ² value is large. (Β _i ) is defined.

The difference spectrum is obtained by subtracting the straight line L _i from the standard spectrum. In the difference spectrum, a straight line L _{i + 1} is defined in the k ² region smaller than the k ² region in which the slope of the straight line L _i is determined, and the difference spectrum is further subtracted to define a further difference spectrum. Ask for.

The above procedure is followed by the slope (-α _{Di + 1} ) of the straight line L _{i + 1}
Is repeated until the value of becomes larger than the value of the slope (−α _Di ) of the straight line L _i .

From the gradient (-α _Di ) of the straight line group L _i thus obtained, the particle diameter D _i (unit: angstrom) when the shape of the particles contained in the object to be measured is assumed to be a sphere ) Is obtained as D _i = (√ ((5α _Di ) / (Log ₁₀ e))) × 2, and the particle content F _i (unit wt%) with respect to the particle diameter D _i is F _i = ( β _i /(0.6 ^1.5 × (0.5D _i ) ³ ) / Σ ((β _i /
It can be obtained as (0.6 ^1.5 × (0.5D _i ) ³ )) × 100.

By the above procedure, from the scattered X-ray spectrum obtained from the substance to be measured, typical particle diameters constituting the group of particles contained in the substance to be measured based on the Fanken method and their particle content rates. Can be calculated.

However, in the above Fanchen method, an arbitrary k ² of the scattered X-ray spectrum obtained from the object to be measured is used.
Since a straight line group having a slope (−α _Di ) that matches the attenuation rate in the region is defined, it is impossible to analyze the particle content rate for a predetermined particle size, which is essential for particle size distribution analysis. That is, there is a problem that the particle size distribution analysis is impossible with the Fanken method.

Further, in the Fanchen method, a group of straight lines L _i
Since the k ² region that draws is not clearly defined, this k ² region can be arbitrarily determined, so there is a problem that the analysis value of the slope (−α _Di ) is different even in the analysis of the same spectrum.

[0013]

In the present invention, the Fank
A method for obtaining a particle content rate F _i with respect to a predetermined particle diameter D _i , which is impossible by the chen method, particularly a particle size distribution measuring method in a region of 1000 nm or less is provided.

[0014]

The present invention is obtained by a linear combination (ΣL _i ) of linear groups L _i having a slope (-α _Di ) corresponding to a predetermined particle size D _i (i = 1 to n). The obtained synthetic spectrum is obtained by optimizing the y-intercept (Log ₁₀ β _i ) of the line group L _i by using the least square method, and converting the scattered X-ray spectrum obtained based on the above-mentioned small-angle X-ray scattering method. This is a method of approximating a standard spectrum. This makes it possible to obtain the particle content rate F _i with respect to the predetermined particle diameter D _i, so that the particle content rate of the particle group contained in the measured object, that is, the particle size distribution can be analyzed.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION The object to be measured in the present invention is a group of particles dispersed in a continuous body, and does not depend on the dispersed state of the group of particles. The particle group mentioned here is an inorganic powder or an organic powder such as metal or ceramics, and the continuum may be a gas, a liquid or a solid as long as it does not react with the contained particles.

The particle group present in the continuum may be a mixture of powders of different materials, but is preferably one kind of powder. This is because the most accurate particle size distribution can be obtained when there is only one type of powder.

The particle size distribution analysis method in the present invention is as follows. The scattered X-ray spectrum obtained from the DUT based on the small-angle X-ray scattering method is plotted along the horizontal axis as the scattering vector k.
The standard spectrum f (k ² ) is calculated by converting the squared value of k ² = (4πsin θ / λ) ² and converting the vertical axis to the common logarithm Log ₁₀ (Y) of the scattering intensity Y. Here, θ is the angle at which the scattered X-ray intensity is measured, and λ is the wavelength of the X-rays irradiated to the object to be measured.

In the present invention, X irradiating the object to be measured
The line may use any wavelength as long as it is monochromatic,
The wavelength of the CuKα characteristic X-ray is preferably 1.54056 × 10
It is desirable to use wavelengths longer than ^-10 m (1.54056Å). When using characteristic X-rays with a shorter wavelength than this,
This is because the upper limit of the particle size that can be analyzed becomes small and the particle size distribution to be measured is limited.

Further, assuming that the shape is a sphere, a group of straight lines L _i Log ₁₀ (Y _i ) = − α _Di k ² + Log ₁₀ (β corresponding to a predetermined particle diameter D _i (unit: angstrom). _i ), (i = 1
From n) Here, a synthetic spectrum g (k ² ), g (k ² ) = Σ (L _i ) represented by a linear combination of α _Di = (Log ₁₀ e × D _i ² ) / 20 is calculated. At this time, in the present invention, a combination of Log ₁₀ (β _i ) which is a y-intercept of the straight line group L _i is calculated so that the standard spectrum f (k ² ) and the synthetic spectrum g (k ² ) match. It is essential to do.

Next, from β _{i of the} straight line group L _i having a predetermined particle diameter D _i when f (k ² ) and g (k ² ) match,
The particle content rate F _i (unit: mass%) for each particle size D _i is F _i = (β _i /(0.6 ^1.5 × (0.5 D _i ) ³ ) / Σ ((β _i /
It is calculated as (0.6 ^1.5 × (0.5D _i ) ³ )) × 100.

By standardizing the obtained particle content F _{i so} that ΣF _i = 100, a predetermined particle diameter D _{i is obtained.}
The particle content F _i can be obtained for

In the particle size distribution measuring method of the present invention,
Predetermined particle size D as a function of the slope of the straight line (-α _Di ).
It is preferable that _i is divided into n at equal intervals from D ₁ to D _{i + 1} (i = ₁ to n) and standardized. Like this
By standardizing _i in advance, the particle size distribution measurement results have generality, and the particle size distribution comparison between measured objects can be performed.
It becomes possible to facilitate comparison between measuring persons. The method for normalizing the particle diameter values D _i by dividing them into n at equal intervals may be a linear method such as a geometric progression or a non-linear method such as a geometric progression.

Further, in the present invention, the method for determining the y-intercept Log ₁₀ (β _i ) of the straight line group L _{i in} order to match the standard spectrum f (k ² ) and the synthetic spectrum g (k ² ) is as follows. Statistical residual RR of f (k ² ) and g (k ² ) RR = Σ | f (k ² ) −g (k ² ) | / Σ | f (k ² ) | It is desirable to find a combination of Log ₁₀ (β _i ) such that Gaus, which is generally used as the least-squares method
Not only the s-Neuton method, the modified Marquard method, and the conjugate direction method, but also an algorithm having equivalent performance to those may be used. As the residual R, R ² value widely used in general statistical analysis may be used.

The maximum particle size that can be measured by the present invention is 1000 nm or less where the X-ray small angle scattering phenomenon is remarkable, but based on the results of the experimental study by the present inventor, the measurement accuracy and the particle size distribution measurement region can be widened. From the balance of the above, it is preferably 200 nm or less, and particularly preferably 100 nm or less.

Since the particle size distribution obtained from the objects to be measured as described above gives the particle content F _i with respect to the standardized particle size value D _i , the particle size distribution between the objects to be measured is relatively large. Can be compared to.

The particle size distribution measuring method of the present invention comprises X-ray irradiating means for generating X-rays and irradiating the measured object, and X-ray detecting means for measuring the scattered X-ray spectrum generated by the measured object. It is applicable to all of the scattered X-ray spectra obtained from the small angle X-ray scattering device.

FIG. 1 is a diagram showing the construction of an apparatus for carrying out the measuring method of the present invention. It is a schematic diagram which shows the apparatus structure for acquiring a scattering X-ray spectrum from a to-be-measured object, and analyzing a particle size distribution using the said small angle X-ray scattering apparatus.

X-rays are emitted from the X-ray irradiation source 1, and the X-rays focused by the slits 2 are scattered by the sample to be measured mounted on the sample holder 3. In order to remove the direct light from the X-ray irradiation source 1, the slit 2 may be of a three-slit type, a crack type or a dispersive crystal type.

Further, the sample holder 3 is not limited to the one in which the sample to be measured is mounted as it is, but may be one having a function of dispersing the sample to be measured in a fluid and circulating it. The scattered X-ray scattered by the sample to be measured is vacuum path 4
And is detected by the detector 5. The detector 5 may be a scintillation counter, PSPC (position sensitive proportional counter), IP (imaging plate) or CCD.

The scattered X-ray intensity data obtained by the detector 5 is stored in the data storage unit 6. The measurement of the scattered X-ray intensity is performed by the device control unit 9 with reference to the measurement condition designated by the input terminal 7 or the measurement condition stored in the condition storage unit 8.

The scattered X-ray intensity data stored in the data storage unit 6 and the straight line group L for the predetermined particle size stored in the condition storage unit 8 for the particle size distribution analysis according to the present invention.
From i, the particle size distribution calculation unit 10 analyzes the particle size distribution and displays the result on the display unit 11.

[0032]

EXAMPLES The present invention will be described in more detail with reference to Examples and Comparative Examples.

The following two powders were prepared as samples. Sample 1: “AEROSIL13” manufactured by Nippon Aerosil Co., Ltd.
0 (SiO ₂ ) ”; average primary particle size 16 nm Sample 2:“ AEROSIL38 ”manufactured by Nippon Aerosil Co., Ltd.
0 (SiO ₂ ) ”; average primary particle size 7 nm, where average primary particle size is TEM (transmission electron microscope)
It is a numerical value obtained by image analysis using.

The scattering X-ray spectra of the above two kinds of sample powders were measured by the small angle X-ray scattering method. For the measurement of scattered X-rays based on the small-angle X-ray scattering method, a small-angle X-ray scattering device unit CN2230F type (manufactured by Rigaku Denki Co., Ltd.) was used.
The measurement conditions are CuKα characteristic X-rays, and the tube voltage is 40k.
It was carried out under the conditions of V and a tube current of 30 mA.

20 ml of an aqueous solution prepared by mixing water and ethanol at a ratio of 1: 1 (mass ratio) to 0.3 g of the sample powder,
After dispersing for 1 minute, the mixture was allowed to stand for 5 minutes and filled in a capillary glass to be used as a sample to be measured.

The results (examples) obtained by the present invention are shown in FIG. In the example, from 7.5 nm to 47.
The particle diameter D _i is divided into 9 parts at intervals of 5 nm up to 5 nm.
The line group L _i corresponding to is analyzed. The results obtained by the Fanken method, which is a conventional technique, show that in Sample 1, the particles having a particle diameter of 11.3 nm are 15% by mass and 2% by mass.
85% by mass of 0.4 nm particles are contained, and
In Sample 2, 52% by mass of particles having a particle size of 9.6 nm were used,
It contained 48 mass% of 9.4 nm particles.

In the examples, the particle content with respect to the standardized particle diameter, that is, the particle size distribution is obtained. On the other hand, according to the Fanchen method which is a conventional technique, as shown in the comparative example, only a particle content ratio with respect to a typical particle diameter can be obtained. Further, from the measurement results of the two samples of the examples, according to the present invention, it is possible to easily and clearly compare the particle size distributions obtained from a plurality of objects to be measured, which is excellent as a particle size distribution measuring method. To be
it is obvious.

[0038]

According to the present invention, from the scattered X-ray spectrum obtained based on the small-angle X-ray scattering method, the particles of 1000 nm or less contained in the object to be measured have a standardized particle diameter. The content rate, that is, the particle size distribution can be easily obtained.

[Brief description of drawings]

FIG. 1 is a configuration diagram of a particle size distribution measuring device according to the present invention.

FIG. 2 is a diagram showing measurement results according to an example of the present invention.

[Explanation of symbols]

1 X-ray irradiation source 2 slits 3 sample holder 4 vacuum path 5 detectors 6 Data storage 7 Input terminal 8 Condition storage 9 Device control section 10 Particle size distribution calculator 11 Display

Claims (6)

[Claims] 1. A scattered X-ray spectrum is obtained from an object to be measured based on a small-angle X-ray scattering method, and a particle content rate for a predetermined particle diameter contained in the object to be measured is determined from the spectrum. Measuring method of particle size distribution. 2. A scattering X obtained based on the small-angle X-ray scattering method.
From the line spectrum, the horizontal axis is the square of the scattering vector k (k
² = (4πsinθ / λ) ² ), the vertical axis is the common logarithm of intensity Y (L
A standard spectrum f (k ² ) that is set to og ₁₀ Y) is obtained, and a straight line group L _i (Log having a slope (−α _Di ) corresponding to the particle diameter D _i (where i = 1 to n is a natural number) is further obtained. ₁₀ Y _i = -α _Di
It is represented by k ² _i + Log ₁₀ β _i . ), The y-intercept (Log ₁₀ β _i ) and the slope (Log ₁₀ β _i ) of the straight line group L _i when the standard spectrum f (k ² ) is approximated by the synthetic spectrum g (k ² ) represented by the linear combination (ΣL _i ). -Α _Di ), the predetermined particle diameter D _i
The particle content rate for
The particle size distribution measuring method described. 3. The particle size distribution measuring method according to claim 2, wherein the predetermined particle diameter D _i is divided into n at equal intervals. 4. A synthetic spectrum g represented by a linear combination of straight line groups L _i having an inclination corresponding to a predetermined particle diameter D _i.
(K ²⁾ and the standard residual of the spectrum f (k ²⁾ so as to minimize claim 2 or claim 3, wherein the determining the beta _i of straight lines L _i by the least squares method Particle size distribution measurement method. 5. The particle size distribution measuring method according to claim 1, wherein the measured particle size range is 1000 nm or less. 6. X-ray irradiating means for generating X-rays and irradiating the object to be measured, and X for measuring X-rays scattered from the object to be measured.
Line detecting means, means for storing the detected X-ray intensity as spectral data in association with the scattering angle, means for storing a mathematical expression of a plurality of straight line groups corresponding to a predetermined grain size, and the spectrum data. A means for calculating a standard spectrum and adjusting and calculating the y-intercept (Log ₁₀ β _i ) of the straight line group by the least squares method so that the linear combination of the straight line group approximates the standard spectrum; As a result, y intercept (Log ₁₀ β _i ) and slope (−α _Di ) of the straight line group
A particle size distribution measuring device comprising means for calculating a particle content rate of a predetermined particle size in an object to be measured and displaying the particle content rate for the predetermined particle size together with the predetermined particle size.