JP2001305081A - Epma quantitative analysis method using analytical curve - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an EPMA quantitative analysis method using an analytical curve, allowing the easy determination of minor elements solid-solved in a matrix of a bulk sample, by an EPMA analysis with practical accuracy. SOLUTION: In this EPMA quantitative analysis method for making a quantitative analysis of minor elements solid-solved in the matrix of the bulk sample, using the analytical curve, a plurality of samples with a measuring object element solid-solved at the specified content in the matrix sufficiently larger than an X-ray generating region are assumed, and the relative X-ray intensity of the measuring object element is computed on each assumed sample by Monte Carlo simulation. The analytical curve is obtained from the obtained computed relative X-ray intensity of each assumed sample and the assumed content of each assumed sample, and the relative X-ray intensity of the measuring object element is measured by EPMA on an unknown sample with the unknown content of the measured object element. The measuring object element of the unknown sample is determined from the analytical curve and the measured value of the relative X-ray intensity of the unknown sample.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for irradiating a bulk sample with an electron beam, measuring characteristic X-rays emitted from the sample, and performing a quantitative analysis of trace elements dissolved in a matrix of the bulk sample. According to the method for performing, in particular, using a technique of Monte Carlo simulation to create a calibration curve,
Electron probe microan
alyser; hereinafter referred to as “EPMA”).

[0002]

2. Description of the Related Art In order to clarify the relationship between a specific element and a material property in a bulk sample, it is necessary to measure the average composition of the entire bulk sample by chemical analysis or the like to determine the average content of the element. Besides, for the element, the content of solid solution in the matrix, the content in precipitates and inclusions, the content at the crystal grain boundary and its vicinity, etc. are individually measured, and the concentration and concentration of the element It must be obtained as information such as distribution.

For example, the effects of trace elements P on the ductility and fracture of Al-Cu alloys are investigated, and the changes in the solid solution of Mg, Si, and Cu with trace impurities V on the composition and properties of Al alloys are investigated. In addition, research has been conducted on investigating the influence of a trace amount of Ti element on the corrosion resistance of Al-Mn-Mg-Si-Cu alloys.

An electron beam microanalyzer (EPMA) is used as a means for measuring the content of a specific element in such a bulk sample. This EP
MA irradiates an extremely narrowly focused electron beam (Electron probe) onto the sample surface, measures the wavelength and intensity of characteristic X-rays radiated from that portion using an X-ray spectrometer or a detector, and thereby obtains a sample. Because it quantifies the elements contained in the minute part, it is possible to know which part of the sample is being measured, and it is non-destructive without dissolving the sample like chemical analysis Because it can be analyzed in various fields, it is applied to the analysis of various samples in various fields.

[0005] However, in the EPMA analysis, the element to be measured is not directly measured as the content such as the concentration, but is measured as the X-ray intensity (count) of the element. It is necessary to convert the strength into element content. As a method of converting the X-ray intensity into a content such as a concentration, a ZA for obtaining a concentration by comparison with one standard sample (a normal substance or a pure simple substance) is used.
The F method and a calibration curve method in which the relationship between the X-ray intensity and the concentration is obtained in advance as a calibration curve using a plurality of standard samples having compositions close to the composition of the unknown sample are known.

However, the calculation of the ZAF method is extremely complicated, and even if it has become possible in recent years to calculate by computer, it takes a long time to perform measurement at many places. However, when there are a large number of samples and a measurement result in a short time is required, it may not be adopted.

In the calibration curve method, a plurality of standard samples having components close to the composition of the unknown sample must be prepared and a calibration curve must be prepared in advance. It is necessary to prepare a standard sample, and the preparation of this standard sample requires a great deal of labor, and sometimes it is difficult to prepare.

[0008]

Therefore, the present inventor has proposed:
For bulk samples, the content of certain elements dissolved in the matrix can be individually measured by EPMA analysis, and the measured X-ray intensity can be converted to the element content in a short time. As a result of intensive studies on an EPMA quantitative analysis method that does not require the preparation of a plurality of standard samples having compositions close to the composition, it has been found that a plurality of elements having a predetermined content of the element to be measured are dissolved in a matrix sufficiently larger than the X-ray generation region. For each of these assumed samples, the relative X-ray intensity of the element to be measured is calculated by Monte Carlo simulation for each of these assumed samples, a calibration curve between the calculated relative X-ray intensity and the assumed content is obtained, and the obtained calibration curve is used. As a result, they have found that trace elements dissolved in a matrix of a bulk sample can be quantified with practically accurate accuracy, and have completed the present invention.

Accordingly, an object of the present invention is to provide an EPMA using a calibration curve capable of easily quantifying a trace element dissolved in a matrix of a bulk sample with EPMA analysis with a practically accurate accuracy. It is to provide a quantitative analysis method.

[0010]

That is, the present invention relates to a method for quantitatively analyzing trace elements dissolved in a matrix of a bulk sample, wherein the method comprises the steps of: Assuming a plurality of samples in which the element to be measured is dissolved in a predetermined content, the relative X-ray intensity of the element to be measured is calculated for each of these assumed samples by Monte Carlo simulation, and the calculated relative X-rays of each of the obtained assumed samples are calculated. A calibration curve is determined from the intensity and the assumed content of each assumed sample, and the relative X-ray intensity of the element to be measured is actually measured by EPMA for an unknown sample in which the content of the element to be measured is unknown. This is an EPMA quantitative analysis method using a calibration curve, characterized by quantifying an element to be measured in an unknown sample from an actually measured relative X-ray intensity of the sample.

In the method of the present invention, the applicable bulk sample is not particularly limited as long as its matrix is sufficiently larger than the X-ray generation region. Metal, ceramics, rubber, paper, cardboard, plastic, etc. Various samples can be mentioned. In particular,
A bulk sample preferable for applying the method of the present invention is a metal or an alloy thereof in which a trace element to be measured is in solid solution, and specifically, for example, Al, Fe, Cu, Au, Si, Ni, Cr,
Samples composed of a single metal element such as Ti, Al-Cu, Al-Cr,
Binary Al alloys such as Al-Zn, Al-Mg, Al-Fe, Al-Si, Al-Fe-Mn, Al-Fe-Si, Al-Fe-Mg-Si, Al-Fe-Mn -Si
Ternary or higher ternary Al alloys, and trace elements in compounds.

The method of the present invention performs quantitative analysis of trace elements dissolved in the matrix of such a bulk sample, and there is no particular limitation on the trace elements to be measured. Mg, C in aluminum
Examples include elements such as u, Si, Zr, Zn, and P, and elements such as Al and S in iron.

In the method of the present invention, not only can the quantitative analysis of the trace elements uniformly dispersed and dissolved in the matrix of the bulk sample be performed, but also the type of the sample depends on the purpose of the analysis. For example, it is also possible to measure how the trace elements in the matrix of the bulk sample in the ingot are unevenly distributed and forming a solid solution, and it is also possible to measure segregation in grains during soaking. .

In the method of the present invention, first, X
Assuming a plurality of samples in which the element to be measured is solid-dissolved at a predetermined content in a matrix sufficiently larger than the line generating region, and for each of these assumed samples, calculate the relative X-ray intensity of the element to be measured by Monte Carlo simulation and obtain A calibration curve is determined from the calculated relative X-ray intensity of each assumed sample and the assumed content of each assumed sample.

Here, the assumption of a plurality of samples will be specifically described with reference to an example. For example, a bulk sample in which Cu element is solid-dissolved in a range of about 100 to 1000 ppm of Cu element is described.
Al-Cu alloy whose concentration is unknown, and Cu in this Al-Cu alloy
If you want to measure the concentration, use Al-Cu (100ppm), Al-Cu (600p
pm), Al-Cu (1200ppm), etc. Assume multiple Al-Cu alloy samples with at least two or more assumed Cu contents (Cu concentration), and use these assumed samples as standard samples to measure by Monte Carlo simulation The relative X-ray intensity of the element (Cu) is calculated.

The calculation of the relative X-ray intensity of the element to be measured by Monte Carlo simulation for each of these assumed samples is carried out by an EPM actually performed on an unknown sample.
Electron beam irradiation conditions (sample density, sample size,
The X-ray extraction angle, acceleration voltage, type of X-ray, etc.) are assumed and the same conditions are used. The calculated X-ray intensity of each relative sample obtained by this calculation and the assumed content (concentration) of the element to be measured ) To prepare a calibration curve.

In the calculation by the Monte Carlo simulation, the trajectory of the electron is assumed to be a broken line, and one of the broken lines is defined as the mean free path, and the angle (scattering angle) between one line and the next line is assumed. ) Is a probability corresponding to a certain random number, further assumes a model assuming that electron energy is lost for each line segment, and calculates a mean free path equation (1), a scattering angle (ω), and a rotation angle (φ). Equation (2), Equation (3) for calculating electron energy loss (ΔE), Equation (4) for calculating the probability (P) that an electron collides with an element, Equation (5) for calculating the position after electron scattering, Then, the relative X-ray intensity is calculated based on each calculation formula (6) of the generated X-ray quantum number.

Formula for calculating mean free path (λ) (1) λ [cm] = [(0.0554E × 10 ³ ) / ρ] × ｛ΣA
C / [Z ^1/3 (Z + 1)]｝ × 10 ⁻⁸ Calculation formula of scattering angle (ω) and rotation angle (φ) (2) cos (ω, radian) = 1-2βR / (1 + β−R) φ (Radian) = 2πR Formula for calculating electron energy loss (ΔE) (3) When E> 6.338 J ΔE [Kev / cm] = 7.85 × 10 ⁴ ρΣ [ZC / A · ln (1.16
6E / J)] / EE ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10 ⁴ ρΣ (ZC / A / J ^1/2 ) /
1.26E ^1/2

[However, in the above formulas (1) to (3), E is the possessed energy of the electron (Kev), and ρ is the density (g / cm).
³ ), Z is the atomic number, A is the atomic weight, C is the composition,
β is a screening parameter, R is a uniform random number (0 to 1)
, Π indicates the pi (3.14), and J indicates the ionization potential (Kev). ]

Here, the above ionization potential (J)
Has been described in the literature, the following three values J = 11.5Z × 10 ⁻³ [Kev] J = 0.9776Z + 0.0588 / Z ^0.19 [Kev] J = ｛14.0 [1-exp ( −0.1Z)] + 75.5
/ Z ^{Z / 7.5} −Z / (100 + Z)｝ Z × 10 ⁻³ [Kev] has been proposed. Regarding the screening parameter (β), the following three values β = ^{{5.44Z 2/3 / E} × 10} -3 β = {3.4Z 2/3 /E(1.13+3.76α 2)
^1/2 ｝ × 10 ^-3 β = {3.4Z ^2/3 / E} × 10 ^-3 [where α = {3.69 (Z / E)} × 10 ^-3 ] has been proposed. In the method of the present invention, among these constants,
In particular, J = 11.5Z × 10 ⁻³ [Kev] and β = ｛5.44
A value of Z ^2/3 / E｝ × 10 ⁻³ is used. By adopting a combination of the constant of the ionization potential (J) and the constant of the screening parameter (β), the calculation result by the Monte Carlo simulation matches well with the actually measured value measured using the standard sample, and is input to the calculation. As a result, the number of incident electrons can be reduced as much as possible, and calculation can be performed without a large computer.

The uniform random number (R) used in the equation (2) for calculating the scattering angle (ω) has also been described in the literature, for example, in the central square method (x _{k + 1} = x _k ² Several digits), multiplication type combination method [x _{k + 1} = λ · x _k (mod, M)], mixed type congruential method [x _{k + 1} = λ · x _k + μ (mod, M)], etc. Although many methods have been proposed, in the method of the present invention, those incorporated in an ordinary personal computer can be used as they are, for example, a random number incorporated in a commercially available personal computer manufactured by NEC Corporation. Can be suitably used.

Here, which atom the electron incident on the multi-system compound collides with is determined by the probability (P) based on the collision cross section of the element, and is expressed by the following equation (4). Formula (4) for calculating the probability (P) that an electron collides with an element: P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe ⁴ Z (Z + 1)] / [4E
_n ² _{β (β} + 1)] e: electron charge ^{(-4.8029 × 10 -10 esu) E} n: electron kinetic energy (eE / 300 × 10 ³⁾ For example, in the following the case of ternary compound Do as follows. 0 <F ≦ P _a ... if collides with a elemental _{P a <F ≦ P a +} P b ... if collides with b element _{P a + P b <F ≦} P a + P b + P c ... if collides with c elements ( Here, F is a uniform random value.)

Further, the position after electron scattering is calculated by the following equation (5) for calculating the position after electron scattering. That is, the XY axis is set on the sample surface, and the Z direction is set in the depth direction.
Taking the axis, the electron of the n-th electron of the end position which is incident at the origin (x _n, y _n, z _n) When, (n + 1) -th position of the electron _{(x n + 1, y n} + 1 , Z _{n + 1} ) are first scattered from the n-th position by the collision in the direction (ω, φ) (ω: scattering angle from the incident direction due to the collision, φ: rotation angle). The position of the (n + 1) th electron in the direction (θ _{n + 1} , ψ _{n + 1} ) with respect to the (x, y, z) coordinate axis
When expressed as follows,

Formula for calculating the position after electron scattering (5) cos (θ _{n + 1} ) = cos (θ _n ) cos (ω) -sin (θ _n ) sin (ω) co
_{s (φ) sin (ψ n} + 1) = Asin (ψ n) + Bcos (ψ n) cos (ψ n + 1) = Acos (ψ n) -Bsin (ψ n) A = [cos (ω) -cos (θ _n ) cos (θ _{n + 1} )] / [sin (θ _n )
sin (θn _{+ 1} )] B = sin (φ) sin (ω) / sin (θn _{+ 1} ) _{xn + 1} = _xn + λsin (θn _{+ 1} ) cos (ψn _{+ 1} ) × 10 ⁴ (Μ
m) y _{n + 1} = y _n + λsin (θ _{n + 1} ) sin (+ 1n _{+ 1} ) × 10 ⁴ (μ
_{m) z n + 1 = z} n + λcos (θ n + 1) × 10 4 (μm)

Then, the calculation of the generated X-ray quantum number I at which the electron having the energy E is generated at the distance λ in the sample is calculated by the following equation (6) for calculating the generated X-ray quantum number. The process is repeated until the energy of the electrons becomes lower than the excitation voltage of the element, and the X-ray quantum number is calculated as an integrated value after scattering.

Formula for calculating the generated X-ray quantum number (6) I = N _A ρ Q (E) W _K Cλ / A N _A : Avogadro number (6.02 × 10 ²³ ) A: Atomic weight ρ: Density (g / cm) ³ ) Q (E): ionization cross section Q (E) · E _k ² = 7.92 × 10 ⁻²⁰ / U · ln
(U) U = E / E _k E _k : excitation voltage of element [Kev] W _k : fluorescence yield [W _k = α ⁴ / (1 + α ⁴ )] α = −0.0217 + 0.0332Z−1.14Z ³ ×
10 ^-6 Calculation of X-ray quantum number after X-ray absorption I ₁ = I exp (−μρd) μ: X-ray mass absorption coefficient d: X-ray passage distance (cm)

In the present invention, the above formulas (1) to (1)
The Monte Carlo simulation performed using (6) is usually sufficient for less than 1000 electrons, and is preferably performed for about 100 or more and 500 or less electrons. Even if the number of electrons to be calculated (the number of incident electrons) is 1000 or more, a large amount of time is required for the calculation, and the calculation accuracy cannot be expected to be much improved. May not provide sufficient calculation accuracy.

In the method of the present invention, the above formulas (1) to (5)
According to (6), the calculated relative X-ray intensity of the element to be measured in each assumed sample is defined as the ratio of the X-ray quantum number obtained from the sample with the same number of incident electrons to the X-ray quantum number obtained from the 100% sample. Is calculated. Then, the calibration curve is obtained as a relationship between the calculated relative X-ray intensity of each assumed sample thus obtained and the assumed content (concentration) of the element to be measured in each assumed sample.

Next, in the method of the present invention, the relative X-ray intensity of the element to be measured is determined by EPMA for an unknown sample whose content of the element to be measured is unknown under the same conditions as those used in the calculation by the Monte Carlo simulation. Is measured, and the element to be measured in the unknown sample is quantified from the calibration curve and the measured value of the relative X-ray intensity of the unknown sample.

The actual measurement of the relative X-ray intensity by the EPMA can be appropriately performed according to the type of the unknown sample to be measured, the purpose of the measurement, and the like. For example, when a specific minute portion of the unknown sample is to be measured, May be performed for only one measurement point of the unknown sample, or when comparing two or more types of unknown samples, measurement is performed at two or more measurement points and the average value is calculated as relative X It may be an actual measured value of the line intensity, and furthermore, when it is possible to measure a minute precipitate, set a plurality of measurement regions for the unknown sample and find the relative X-ray intensity of the minimum value. A technique such as estimating the solid solution concentration may be used.

Further, in the method of the present invention, the measurement points at the time of the actual measurement of the relative X-ray intensity by EPMA are intended to perform quantitative analysis of the trace elements dissolved in the matrix of the bulk sample. When contaminants such as precipitates, inclusions, and grain boundaries are present in the matrix of the bulk sample, a CRT (Cathod Ray Tube) is used to observe a backscattered electron image at a magnification of 1,000 times or more. It is preferable to select a measurement point while avoiding these contaminants, so that trace elements dissolved in the matrix can be quantitatively analyzed more accurately.

The method of the present invention is not particularly limited since the trace elements dissolved in the matrix of the bulk sample can be easily or accurately determined by EPMA analysis.
Relationship between micro-segregation of Mg and mechanical strength, relationship between micro-segregation of Cu solid solution in aluminum and corrosion, relationship between micro-segregation with increase in solid solution by rapid solidification of element and mechanical strength It is useful for quantitative analysis for the purpose of, for example, the relationship between micro-segregation of the amount of solid solution of Zr in aluminum electric wires and heat resistance.

[0033]

BEST MODE FOR CARRYING OUT THE INVENTION Preferred embodiments of the present invention will be described below based on examples performed using a wavelength dispersion type EPMA (EPMA-8705 manufactured by Shimadzu Corporation; X-ray extraction angle δ: 52.5 °). The form will be specifically described.

Example 1 (Al-Cu alloy sample) As standard samples, the assumed Cu concentrations were 100 ppm and 6 ppm, respectively.
And the expected sample size is 100 μm in the vertical direction × 100 μm in the horizontal direction × 100 in the depth direction.
Assuming three kinds of Al-Cu alloy samples having a size of μm and a density of 2.7 g / cm ³ , using a personal computer (PC N88 BASIC) manufactured by NEC Corporation, Table 1
Using the physical property values shown in Table 1, a Monte Carlo simulation (electron beam trajectory simulation) was performed under two measurement conditions of 150 incident electrons and acceleration voltages of 15 kV and 20 kV to calculate the calculated relative X-ray intensity of Cu (Kα ray). I asked.

[0035]

[Table 1]

The results are as shown in Table 2, and the calculated relative X
The calculation results are plotted with the line intensity on the horizontal axis and the assumed Cu concentration on the vertical axis. As shown in FIGS. 1 and 2, when the acceleration voltage is 15 kV, Y = 11.4X and the acceleration voltage are 20 kV. In this case, a calibration curve of Y = 11.5X was prepared.

[0037]

[Table 2]

Next, Cu-100% whose chemical analysis value is clear
A sample and three types of Al-Cu samples were prepared, and these three types
The Al-Cu sample was subjected to elemental mapping and line analysis by EPMA analysis to confirm that there was no segregation of Cu concentration depending on the location, and a verification sample for verifying the calibration curve obtained by the electron beam locus simulation [ a: Cu-100%,
b: Al-Cu (99 ppm), c: Al-Cu (310 ppm), and d: Al-C
u (1000 ppm)]. For these test samples, the X-ray intensity of Cu was measured at 5 measurement points (1 for the background (BG)) under the conditions shown in Table 3 below. The relative X-ray intensity of the sample was determined.

[0039]

[Table 3]

In the measurement of the X-ray intensity of the test sample by EPMA, the X-ray profile of Cu is measured, the peak wavelength, the upper and lower background wavelengths are determined, and the peak wavelength and the upper and lower background wavelengths are determined. Were set in a spectroscope and X-ray intensities at these wavelengths were measured. The measurement results of the X-ray profile are shown in FIGS. 3 to 9, the measurement results of the X-ray intensity are shown in Tables 4 and 5, and the relative X-ray intensity-Cu concentration of the three types of Al-Cu samples for verification are further shown. The relationships are plotted in FIGS. 1 and 2, respectively.

[0041]

[Table 4]

[0042]

[Table 5]

As is clear from the results of FIGS. 1 and 2,
The plot showing the relationship between the relative X-ray intensity and the Cu concentration in the actually measured three types of Al-Cu samples for verification was confirmed to be accurately positioned on the calibration curve, and this calibration curve could be used for EPMA quantitative analysis. It was verified that. From the relative X-ray intensities measured for the three types of Al-Cu samples for verification, using the calibration curves obtained above, these three types of Al-Cu for verification were used.
When the Cu concentration of the sample was calculated, the calculated calculated concentration was as shown in Table 6.
This shows that the calibration curve can also be used for EPMA quantitative analysis.

[0044]

[Table 6]

Example 2 (Al-Cr alloy sample) As a standard sample, the assumed Cr concentrations were 50 ppm and 10 ppm, respectively.
0 ppm, and 1000 ppm, and the assumed sample size is 100 μm in the vertical direction × 100 μm in the horizontal direction × 100 μm in the depth direction.
Assuming three kinds of Al-Cr alloy samples, each of which is a cube having a size of m and a density of 2.7 g / cm ³ , using a personal computer (PC N88 BASIC) manufactured by NEC Corporation, Table 7 Using the physical properties shown, electron beam trajectory simulation was performed under the measurement conditions of 150 incident electrons and an acceleration voltage of 15 kV, and the calculated relative X-ray intensity of Cr (Kα ray) was obtained.

[0046]

[Table 7]

The results are as shown in Table 8, and the calculated relative X
The calculation results are plotted with the line intensity on the horizontal axis and the assumed Cr concentration on the vertical axis, and as shown in FIG.
Was prepared.

[0048]

[Table 8]

Next, Cr-100% whose chemical analysis value is clear
A sample and two Al-Cr samples were prepared, and these two
The Al-Cr sample was subjected to elemental mapping and line analysis by EPMA analysis to confirm that there was no segregation of Cr concentration depending on the location, and a verification sample for verifying the calibration curve obtained by the electron beam locus simulation [ a: Cr-100%,
b: Al-Cr (106 ppm) and c: Al-Cr (540 ppm)]. For these verification samples, the X-ray intensity of Cr was measured at 5 measurement points (1 for the background (BG)) under the conditions shown in Table 9 below, and two types of Al-Cr for verification were used. The relative X-ray intensity of the sample was determined.

[0050]

[Table 9]

The X-ray intensity of the test sample by EPMA was measured by measuring the X-ray profile of Cr, determining the peak wavelength, the upper and lower background wavelengths, and determining the peak wavelength and the upper and lower background wavelengths. Were set in a spectroscope and X-ray intensities at these wavelengths were measured. The peak wavelength of Cr is 2.291 °, and the upper and lower background wavelengths are 2.301 °, respectively.
And 2.279 °. Table 10 shows the measurement results of the X-ray intensity, and FIG. 10 shows the relationship between the relative X-ray intensity and the Cr concentration in the two kinds of Al-Cr samples for verification.

[0052]

[Table 10]

As is apparent from the results shown in FIG. 10, the relative X-ray intensities—Cr
It was confirmed that the plot showing the relationship between the concentrations was accurately located on the calibration curve, and it was verified that this calibration curve could be used for EPMA quantitative analysis. In addition, two types of Al-C for verification
r From the relative X-ray intensity measured in the sample, using the calibration curve obtained above, the two types of verification Al-Cr samples
When the Cr concentration was calculated, the calculated concentrations were as shown in Table 11, and it was verified from this point that the calibration curve could be used for EPMA quantitative analysis.

[0054]

[Table 11]

Example 3 (Al-Zn alloy sample) As a standard sample, the assumed Zn concentrations were 100 ppm and 1 ppm, respectively.
5,000 ppm, and 5000 ppm, and the assumed sample size is 100 μm in the vertical direction × 100 μm in the horizontal direction × 10 in the depth direction.
Using a personal computer (PC N88 BASIC) manufactured by NEC Corporation, assuming three kinds of Al-Zn alloy samples each having a cube having a size of 0 μm and a density of 2.7 g / cm ^3. Using the physical property values shown, electron beam trajectory simulation was performed under the measurement conditions of 150 incident electrons and an acceleration voltage of 15 kV, and the calculated relative X-ray intensity of Zn (Kα ray) was obtained.

[0056]

[Table 12]

The results are as shown in Table 13, and the calculated results are plotted with the calculated relative X-ray intensity on the horizontal axis and the assumed Zn concentration on the vertical axis. As shown in FIG. 9
A calibration curve for X was prepared.

[0058]

[Table 13]

Next, Zn-100%, whose chemical analysis value is clear,
A sample and an Al-Zn sample were prepared, and elemental mapping and line analysis were performed on the Al-Zn sample by EPMA analysis to confirm that there was no segregation of Zn concentration by location. Verification sample for performing line verification [a: Zn-100%, b: Al-Zn (101 ppm),
And c: Al-Zn (960 ppm)]. For these test samples, the X-ray intensity of Zn was measured at 5 measurement points (1 for the background (BG)) under the conditions shown in Table 14 below, and for the test Al-Zn sample, The relative X-ray intensity was determined.

[0060]

[Table 14]

For measuring the X-ray intensity of the test sample by EPMA, the X-ray profile of Zn is measured, the peak wavelength, the upper and lower background wavelengths are determined, and the peak wavelength and the upper and lower background wavelengths are determined. Were set in a spectroscope and X-ray intensities at these wavelengths were measured. The peak wavelength of Zn is 1.438 °, and the upper and lower background wavelengths are respectively 1.420 °.
And 1.456 °. The measurement results of X-ray intensity are plotted in Table 15, and the relationship between relative X-ray intensity and Zn concentration in the Al-Zn sample for verification is plotted in FIG.

[0062]

[Table 15]

As is clear from the results shown in FIG. 11, the plot showing the relationship between the relative X-ray intensity and the Zn concentration of the actually measured Al-Zn sample for verification was accurately located on the calibration curve. It was verified that the line could be used for EPMA quantitative analysis. Further, when the Zn concentration of the Al-Zn sample for verification was calculated from the relative X-ray intensity measured for the Al-Zn sample for verification using the calibration curve obtained above, the calculated concentration is shown in Table 16. As shown, it was verified from this point that the calibration curve can be used for EPMA quantitative analysis.

[0064]

[Table 16]

Example 4 (Regarding Al-Mg alloy sample) As standard samples, assumed Mg concentrations were 100 ppm and 5 ppm, respectively.
00ppm, 1000ppm, 5000ppm, 3.0%,
6.0%, 8.0%, 9.0%, and 10.0%, and the assumed sample size is 100 μm in the vertical direction × 100 in the horizontal direction.
Assuming three kinds of Al-Mg alloy samples having a size of μm × 100 μm in the depth direction and a density of 2.7 g / cm ³ , a personal computer (PCN) manufactured by NEC Corporation
88 BASIC), using the physical property values shown in Table 17, simulating an electron beam trajectory under the measurement conditions of 150 incident electrons and an acceleration voltage of 15 kV or 20 kV, and using Mg (Kα
The relative X-ray intensity was calculated.

[0066]

[Table 17]

The results are as shown in Table 18. The calculated results are plotted with the calculated relative X-ray intensity on the horizontal axis and the assumed Mg concentration on the vertical axis. As shown in FIGS. Y (ppm) = 9.9X and Y (%) = 9 when the voltage is 15 kV
A calibration curve of Y (%) = 103 × was prepared at 9 × and an acceleration voltage of 20 kV.

[0068]

[Table 18]

Next, Mg-100% whose chemical analysis value is clear
A sample and 10 kinds of Al-Mg samples were prepared.
For elemental Al-Mg samples, elemental mapping by EPMA analysis and line analysis were performed to confirm that there was no segregation of Mg concentration by location, and for verification to verify the calibration curve obtained by the electron beam trajectory simulation. Sample [a: Mg-100%
, B: Al-Mg (82 ppm), c: Al-Mg (0.522%), d: Al-Mg
(1.01%), e: Al-Mg (1.99%), f: Al-Mg (3.01%), g: A
l-Mg (4.12%), h: Al-Mg (4.81%), i: Al-Mg (5.70%),
j: Al-Mg (7.55%) and k: Al-Mg (8.38%)]. For these verification samples, the X-ray intensity of Mg was measured at ten measurement points (one for the background (BG)) under the conditions shown in Table 19 below, and the average value was determined. The relative X-ray intensity of the Al-Mg sample for verification was determined.

[0070]

[Table 19]

The X-ray intensity of the test sample by EPMA was measured by measuring the X-ray profile of Mg, determining the peak wavelength, the upper and lower background wavelengths, and determining the peak wavelength and the upper and lower background wavelengths. Were set in a spectroscope and X-ray intensities at these wavelengths were measured. The peak wavelength of Mg is 9.889 °, and the upper and lower background wavelengths are 9.949 °, respectively.
And 9.789 °. Table 20 shows the measurement results of the X-ray intensity, and FIGS. 12 to 14 show the relationship between the relative X-ray intensity and the Mg concentration in the Al-Mg sample for verification.

[0072]

[Table 20]

[0073]

[Table 21]

As is clear from the results shown in FIGS. 12 to 14, plots showing the relationship between the relative X-ray intensity and the Mg concentration in the ten kinds of Al-Mg samples for verification actually measured are accurately positioned on the calibration curve. It was confirmed that this calibration curve
A It was verified that it can be used for quantitative analysis. Also, 10
From the relative X-ray intensities measured in the test Al-Mg samples, the Mg concentrations of these 10 test Al-Mg samples were calculated using the calibration curve obtained above, and the calculated calculated concentration was obtained. Is as shown in Table 22, and from this point, it was verified that the calibration curve could be used for EPMA quantitative analysis.

[0075]

[Table 22]

[0076]

According to the EPMA quantitative analysis method of the present invention,
Trace elements dissolved in the matrix of the bulk sample can be easily quantified by EPMA analysis and with practically accurate accuracy.

[Brief description of the drawings]

FIG. 1 is a calibration curve at an acceleration voltage of 15 kV obtained in Example 1 of the present invention.

FIG. 2 is a calibration curve at an acceleration voltage of 20 kV obtained in Example 1 of the present invention.

FIG. 3 is a diagram showing an EPMA according to the first embodiment of the present invention;
FIG. 3 is a graph showing an X-ray profile of a Cu-100% verification sample measured at an acceleration voltage of 15 kV using the method shown in FIG.

FIG. 4 is a diagram showing EPMA according to the first embodiment of the present invention;
FIG. 5 is a graph showing an X-ray profile of a sample for verification of Al-Cu (99 ppm) measured at an acceleration voltage of 15 kV by using FIG.

FIG. 5 is a diagram showing an EPMA according to the first embodiment of the present invention.
FIG. 5 is a graph showing an X-ray profile of a verification sample of Al-Cu (310 ppm) measured at an acceleration voltage of 15 kV using the method shown in FIG.

FIG. 6 is a diagram showing EPMA according to the first embodiment of the present invention.
FIG. 6 is a graph showing an X-ray profile of a sample for verification of Al-Cu (1000 ppm) measured at an acceleration voltage of 15 kV by using FIG.

FIG. 3 is a diagram showing an EPMA according to the first embodiment of the present invention;
FIG. 4 is a graph showing an X-ray profile of a Cu-100% verification sample measured at an acceleration voltage of 20 kV using the above method.

FIG. 8 is a diagram showing EPMA according to the first embodiment of the present invention;
FIG. 6 is a graph showing an X-ray profile of a sample for verification of Al-Cu (310 ppm) measured at an acceleration voltage of 20 kV using the method shown in FIG.

FIG. 9 is a diagram showing an EPMA according to the first embodiment of the present invention.
FIG. 6 is a graph showing an X-ray profile of a sample for verification of Al-Cu (1000 ppm) measured at an acceleration voltage of 20 kV by using FIG.

FIG. 10 is a calibration curve at an acceleration voltage of 15 kV obtained in Example 2 of the present invention.

FIG. 11 is a calibration curve at an acceleration voltage of 15 kV obtained in Example 3 of the present invention.

FIG. 12 shows Mg obtained in Example 4 of the present invention.
7 is a calibration curve at an acceleration voltage of 15 kV in a concentration ppm range.

FIG. 13 shows Mg obtained in Example 4 of the present invention.
It is a calibration curve at an acceleration voltage of 15 kV in a concentration% region.

FIG. 14 shows Mg obtained in Example 4 of the present invention.
5 is a calibration curve at an acceleration voltage of 20 kV in a concentration% region.

Claims (6)

[Claims] 1. A method for quantitatively analyzing trace elements dissolved in a matrix of a bulk sample, wherein a predetermined amount of an element to be measured is contained in a matrix sufficiently larger than an X-ray generation region. Assuming a plurality of dissolved samples, for each of these assumed samples, the relative X-ray intensity of the element to be measured is calculated by Monte Carlo simulation, and the calculated relative X-ray intensity of each of the obtained assumed samples and the assumed content of each assumed sample are calculated. From the calibration curve, the relative X-ray intensity of the element to be measured is actually measured by EPMA for an unknown sample in which the content of the element to be measured is unknown. EPMA quantitative analysis method using a calibration curve, characterized by quantifying an element to be measured in an unknown sample from a sample. 2. The method for quantitatively analyzing EPMA using a calibration curve according to claim 1, wherein the EPMA is a wavelength dispersive EPMA. 3. The EPMA quantitative analysis method using a calibration curve according to claim 1, wherein the matrix of the sample is a metal or an alloy thereof. 4. The metal or its alloy is aluminum, copper,
The EPMA using the calibration curve according to claim 3, wherein the EPMA is a metal selected from magnesium, titanium, and iron or an alloy thereof.
Quantitative analysis method. 5. The calibration according to claim 1, wherein the value of the measured relative X-ray intensity of the unknown sample is an average value of the measured relative X-ray intensity measured at a plurality of measurement points of the unknown sample. EPMA quantitative analysis using X-ray. 6. A total number calculated by a Monte Carlo simulation.
Is calculated by the following formulas (2) to
(4) Calculation formula of scattering angle (ω) and rotation angle (φ) (2) cos (ω, radian) = 1-2βR / (1 + β-R) φ (radian) = 2πR Energy loss of electron (ΔE) Formula (3) When E> 6.338 J ΔE [Kev / cm] = 7.85 × 10^FourρΣ [ZC / A · ln (1.16
6E / J)] / E When E ≦ 6.338J ΔE [Kev / cm] = 7.85 × 10^FourρΣ (ZC / A / J^1/2) /
1.26E^1/2 Equation (4) for calculating the probability (P) that an electron collides with an element: P = (σC / A) / Σ (σC / A) σ (total scattering cross section) = [πe^FourZ (Z + 1)] / [4E
_n ^Twoβ (β + 1)] [However, in the above formulas (2) to (4), E is an electron
Is the owned energy (Kev), A is the atomic weight, ρ is the density (g /
cm^Three), Z is the atomic number, J is the ionization potential
(Kev), β is the screening parameter, R is uniform
Random number (0 to 1), π is pi (3.14), C is composition
And e is the electron charge (−4.8029 × 10 ^-Tenesu)
To E_nIs the kinetic energy of the electron (eE / 300 × 10
^Three) Respectively], J = 11.5Z × 10^-3 [Kev] and β = ｛5.44Z^2/3/ E｝ × 10^-3 And using less than 1,000 incident electrons.
EPMA quantitative analysis using the calibration curve described in any of
Law.