JPH07104296B2 - X-ray spectroscopic analysis method - Google Patents

Description

Detailed Description of the Invention a. TECHNICAL FIELD The present invention relates to an analytical method for obtaining the concentration of a constituent element in a sample from the intensity of characteristic X-rays.

Let Xa, Xb ... Xn be the characteristic X-ray intensities of the respective constituent elements of the sample containing the elements A, B ... N, and Xa, Xb be the characteristic X-ray intensities under the same measurement conditions of the standard sample with 100% concentration of each element. Xbo, ... Xn
Assuming o, the characteristic X-ray intensity Xa of the sample of an arbitrary component element is measured to be slightly different from the value calculated proportionally from the concentration of the component in the sample and the X-ray intensity Xao of the standard sample. That is, the apparent density Ka = Xa / Xao is different from the true density. This is mainly due to the ZAF effect. From the measured characteristic X-ray intensities Xa, Xb ..., the concentration of each component element Ca, Cb ...
To obtain the primary measurement value of each element, that is, the apparent concentration
Multiplying Ka, ... Kb ... by the correction factors Ga, Gb ... respectively, Ca = Ga × Ka (1). ZAF is a method to find the correction factors Ga, Gb, etc. here.
The law is known. The ZAF method refers to the electron beam excitation effect (Z) determined by the atomic number of each component element that constitutes the sample, the absorption effect due to the coexisting element of the characteristic X-ray observed in the sample (A), and the continuous X-ray of the sample. And a factor such as fluorescence excitation effect (F) excited by characteristic X-rays of other elements, and the effect of these factors is calculated to determine the above correction coefficient (reference document 1982, Nikkan Kogyo Shimbun). Published by the company "Physical Analysis Course I, Physical Analysis Method Guidebook" EPMA Electron Beam Microanalysis ", page 103). However, in order to carry out the ZAF method, values such as the average atomic number and the average atomic weight are necessary, and the concentrations Ca, Cb ... Of the respective component elements are necessary to obtain or. However, since Ca, Cb, etc. are unknown at the beginning, the calculation is started by finding the approximate value of p using the primary measured values Ka, Kb, etc. of each component element. That is, since it is the above-mentioned primary measurement values Ka, Kb, etc. that can be obtained by direct measurement, the correction coefficients Ga ', Gb' are obtained by assuming Ka, Kb, etc. as the correct concentration.
Multiply this by Ka, Kb, etc. to calculate the approximate values of concentration Ca ', Cb', etc., and use these Ca ', Cb', etc. again to perform the correction coefficient by ZAF calculation.
Obtain Ga, Gb, etc., and multiply them by Ka, Kb, etc. (not Ga × Ca ', etc. This is because it is a procedure for finding a correction coefficient for Ka, etc.) and then say Ca, Cb, etc. Use the successive approximation method. Of course, there are cases where a sufficiently accurate answer can be obtained with a single calculation.

As is clear from the above, when attempting quantitative analysis using the ZAF method in X-ray spectroscopic analysis, the characteristic X-ray intensity of each constituent element of the sample is measured and The sample needs to be ready. However, there is no characteristic X-ray for hydrogen and He, and it is not possible to measure characteristic X-ray for Li at present. In samples containing such elements, characteristic X-ray data for those elements are missing. It becomes a thing. Further, when it is difficult to obtain an appropriate standard sample such as oxygen or nitrogen, it may be desired to proceed with the quantitative analysis without measuring the characteristic X-ray. The present invention relates to a method for carrying out a quantitative analysis by applying the ZAF method in such a case.

B. 2. Description of the Related Art It is known or predicted that a sample consisting of the elements A, B, ... N now contains the element N, but the characteristic X-ray data of the element N is missing. Suppose Characteristic X-ray intensity Xa, Xb of each element A, B, ..., 1 of each element
If the characteristic X-ray intensity of a standard sample with a concentration of 00% is Xao, Xbo, etc., the apparent concentration (primary measurement value) is Ki = Xi / Xio (i = a, b ...) (2) Conventionally, the element N The primary measurement value Kn of Kn = 1- (Ka + Kb + ...) (3) is used, and each element A by the ZAF method is calculated using these Ka, Kb ... Kn.
A method of calculating a correction coefficient of ~ N has been used. However, in practice, the coexisting elements generally have the largest absorption effect, and the correction coefficient is a number larger than 1 in many cases. So Ki is smaller than the correct concentration. Therefore, the primary measurement value of the element N obtained by the above equation (3) is larger than the true concentration, and is obviously set too large as a starting point for the calculation of the ZAF method. For this reason, the conventional method often converges to an incorrect value, and the convergence of the iterative approximation slows down the calculation.

C. DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention The present invention is a quantitative analysis of elements by X-ray spectroscopy, and a conventional method in the case of calculating the correction coefficient of each element by the ZAF method when there is an element for which there is no characteristic X-ray measurement data It aims to solve the drawbacks, eliminate the convergence of wrong values, and speed up the convergence of successive approximation.

D. Means for Solving Problems In order to measure the primary measurement value of an element for which there is no characteristic X-ray measurement data, the sum of the primary measurement values of those elements obtained from the characteristic X-ray measurement value of each element is 1 The conventional method using the remaining value subtracted from is amended, and the primary measurement value obtained by this conventional method is subjected to constant conversion as the primary measurement value of the element for which there is no characteristic X-ray measurement data. Calculate the correction coefficient for each element by the ZAF method.

E. As mentioned at the beginning of the operation, the primary measured value obtained from the measured value of the characteristic X-ray is smaller than the true concentration in many cases, and is smaller than the true concentration. Therefore, the difference obtained by subtracting the sum of 1 and If the characteristic X-ray measurement value is the primary measurement value of an element that does not exist, it is set excessively. To calculate the ZAF method, the true average atomic number and average atomic weight are required,
The true concentration C is needed to calculate the true and. However, since the true concentration is unknown, the primary measurement value is used at the start of the calculation. This is because, for example, the average atomic number can be approximated as follows.

Here, Za, Zb, etc. are atomic numbers of component elements, and Ca, Cb, etc. are of course Ca + Cb + ... + Cn = 1 in concentration. On the contrary In the above equation (5), each of Za, Zb, ... is weighted by Ka, Kb ..., but if Kn is the same as the conventional method, Kn = 1- (Ka + Kb + ... + Km) ...... ( 6) Then, Zn is weighted differently from other elements. Moreover, the difference (Ca + Cb + ... + Cn)-(Ka + Kb + ... + Kn) (7) is added to Kn, and the correction coefficient
The error of Kn is large, and due to this effect, the error of Ca, Cb, ... Cn also becomes large. For this reason, it is possible to prevent the convergence to an incorrect result and to speed up the convergence of the iterative approximation method by making a more correct value into the primary measurement value of the element having no characteristic X-ray measurement data by appropriate conversion. You can

F. Embodiment FIG. 2 shows an outline of an apparatus for carrying out the method of the present invention. 1 is an X-ray analysis apparatus, 2 is a computer that controls the entire apparatus,
3 is a memory for storing the data of the measured value of the characteristic X-ray of each element of the sample, and 4 is a data memory for storing the data necessary for the calculation. Data etc. are stored. Reference numeral 5 is a program memory for storing a program for control of the apparatus and calculation of data processing, 6 is a keyboard for inputting data to the data memory 4, and operating the keyboard, the characteristic X-ray of the standard sample described above. Enter the measured value data, etc. The apparatus may be provided with a standard sample measurement mode so that the characteristic X-ray of the standard sample is measured and directly stored in the data memory 4.

Example 1 It is assumed that the constituent elements of the sample are A, B ... M, N by qualitative analysis in advance or prediction as a material, and among them, the elements A, B ... M of the characteristic X-ray It is assumed that the measurement data is actually obtained and that there is no characteristic X-ray measurement data for the element N. The primary measurement values of the elements A, B ... M are Ka, Kb, ... Km. First, Kn '= 1- (Ka + Kb + ... + Km) (8) Let Kn' be the primary measured value of N of the element, Ka, Kb, ...
The correction coefficient Gn 'of the element N is calculated by performing the same ZAF method calculation as the correction coefficient Ga of the equation (1) using Km and Kn'. Then, a value K ^* n closer to the primary measurement value of the element N is obtained by K ^* n = Kn '/ Gn' (9). Based on the consideration that Kn ′ is closer to Cn than Kn, replace Cn of Kn = Cn / Gn for element N in Eq. (1) with Kn ′ and replace Gn with Gn ′. It has been replaced. This point will be described in detail later. The K ^* n obtained here is regarded as the primary measurement value Kn of the element N, K ^* n is substituted into Kn, and the initial measurement value Ka, Kb, ... Correction factor of
Ga, Gb ... Gm, Gn, etc. are calculated by the ZAF method. Concentration C of each component element
a, Cb ... Cn are given by Cj = GjKj (j = a, b ..., m, n) (10). If it is recognized that the concentrations of the respective components have been obtained with sufficient accuracy in the first calculation, the calculation is completed only in the first calculation. If the accuracy is not yet sufficient, the above Ca ~
The correction coefficient for each element is calculated again by CAF using the ZAF method, the concentration of each component is obtained by the same calculation as in equation (10), and the same calculation is repeated thereafter until the target accuracy is reached.

The idea of this method is as follows. In Fig. 3, the line segment a shows the entire sample, and the length is "1" and the range of ΣCi is the components A to M,
The range of Cn indicates the amount of element N. In line b, ΣKi is the component A to M
The sum of the primary measurement values of Kn ′ is a temporary primary measurement value of the element N in the remaining portion. Assuming that the same primary measurement value as that for other elements is obtained for the element N, this is the length of the line segment c.
Kn. When Ki (i = a, b ... m) and Kn are used to obtain the correction coefficient of each element by the ZAF method and multiplication with Ki etc., the correct concentration Ci etc. of each component is obtained. Cn in the line segment of a here
The correction coefficient Gn of the element N is obtained by dividing the length of the element by the length Kn of the line segment c. Here, the correction coefficient for the element N is mostly determined by the ratio of the elements A to M, and even if the concentration of N changes slightly, Gn
The value of is almost unchanged. Therefore, Gn is substantially equal to Gn 'obtained by using Kn' = 1-ΣKi as the primary measurement value.

By the way, comparing FIG. 3b with FIGS. 3a and 3c, it can be said that Kn 'is an approximate value of the concentration rather than an approximate value of the primary measurement value. This may be because the sum of the densities is 1, but the sum of the primary measurement values is not 1 (generally smaller than 1). Therefore, if Kn cannot be obtained and an attempt is made to set a virtual value K ^* n as close as possible to Kn, K ^* n = (true density Cn) / (true correction coefficient Gn) ≈ (temporary density Kn ') Since it is considered to be / (approximate value Gn 'of the correction coefficient), it can be approximated as K ^* n = Kn' / Gn '(11).

FIG. 1 is a flow chart of the correction coefficient calculation operation of the above-described embodiment in the apparatus of FIG. Each component of the sample in step ST1
The characteristic X-ray intensities Xa, Xb, ... Xm of A, B, ... M are measured, the data are stored in the memory 3, and the primary measurement value Ki (i = a, b ... m) is calculated, Kn ′ = 1−ΣKi is calculated in step ST3, step S3
The correction coefficient Gn 'of the element N is calculated by the ZAF method using Ka, Kb ... Km and Kn' at T4, and K ^* n = Kn '/ G at step ST5.
n ′ is calculated, and in step ST6, ZA is calculated using Ka, Kb, ... Km and Kn.
Calculate the correction factors Ga to Gn for each element A to M, N by F method, step
In ST7, the concentration Cj of each element A to N is calculated by Gj × Kj.

Example 2 In the same manner as in Example 1, the primary measurement value Kn of the element N is Kn = K
n '/ Gn' is calculated and each element A is calculated using Ka ~ Km and Kn.
~ M correction coefficient Gi (i = a, b, ... m) is calculated, the concentration Ci of each element A ~ M is obtained by Ki × Gi, the concentration Cn of the element N is 1-Σ
Calculate with Ci. Next, using these Ci and Cn, the correction coefficient Gi of each element A to M is calculated by the ZAF method, and the concentration Ci of each element A to M and the concentration Cn of the element N are obtained by the same formula as above. The same calculation method is repeated until an appropriate place. The feature of this method is that first, a more probable primary measurement value Kn is obtained from the tentative primary measurement value Kn ′, and the correction coefficient of the element N is not calculated in the subsequent calculation, and 1 to each is calculated in each step. Elements A to M
ZA of the next stage by subtracting the concentration of
It is used for F calculation. This method can also be executed by the apparatus shown in FIG. 2 simply by changing the program.

In the above explanation, the primary measurement value is the characteristic X in the sample of a certain element.
The ratio of the characteristic X-ray intensity Xio in the standard sample of the line intensity Xi and 100% concentration of the element is given as Ki = Xi / Xio,
When the standard sample is a compound or mixture and the concentration of the element is α, As the above, each of the above embodiments may be executed.

G. Effect According to the present invention, even if an element whose primary measurement value cannot be determined due to the fact that the characteristic X-ray cannot be measured in the sample or there is no suitable standard sample, the primary measurement value of the element is Since the corresponding ones are appropriately set, a good result can be obtained even by one correction calculation, and even if successive approximation is performed, the convergence is fast, the calculation amount is small, and the quantitative analysis result is accurate.

[Brief description of drawings]

FIG. 1 is a flow chart of the operation for executing the method of the first embodiment of the apparatus of the present invention, FIG. 2 is a block diagram showing the configuration of the apparatus of the above embodiment, and FIG. 3 is the method of the first embodiment. It is a graph explaining the meaning of.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP 59-3246 (JP, A) JP 60-244844 (JP, A) "Radiation measurement handbook" (published by Nikkan Kogyo Shimbun in 1982) P ． 607-609 Ikuyama Iku, Watanabe Toru, Kimoto Shizuo "X-ray Microanalyzer" 5th edition (Sho 49-10-20) Nikkan Kogyo Shimbun P. 127-189 Mineralogy Magazine, 12 [Special] (March 1976) Yui, P .; 66-73

Claims (2)

[Claims] 1. A primary measurement value of each element is obtained from the intensity of the characteristic X-ray of the element constituting the sample, and a correction coefficient of each element is calculated by the ZAF method using these values, and the above primary measurement values are obtained. When applying the method of calculating the concentration of each element by multiplying each of the above correction factors, it has been determined in the case where the sample contains one element N whose primary measurement value cannot be determined based on the characteristic X-ray measurement. The sum of the primary measurement values of each element is subtracted from 1, and the remainder is used as the temporary primary measurement value of the above element N, together with the primary measurement values of other elements, and the correction coefficient for the element N is calculated by the ZAF method. A value obtained by dividing the temporary primary measurement value by the correction coefficient as the primary measurement value of the element N together with the primary measurement values of other elements, and obtaining the correction coefficient of each component element by the ZAF method. Spectroscopic method. 2. A primary measurement value of each element is obtained from the intensity of the characteristic X-ray of the element constituting the sample, and the correction coefficient of each element is calculated by the ZAF method using these values, and the above primary measurement values are obtained. When applying the method of calculating the concentration of each element by multiplying each of the above correction factors, it has been determined in the case where the sample contains one element N whose primary measurement value cannot be determined based on the characteristic X-ray measurement. Calculate the correction coefficient for element N by the ZAF method, using the remainder obtained by subtracting the sum of the primary measurement values of each element from 1 as the temporary primary measurement value of the above element N together with the primary measurement values of other elements. A value obtained by dividing the above-mentioned temporary primary measurement value of N by the above-mentioned correction coefficient of the element N is taken as the primary measurement value of the element N, and using this together with the above-mentioned primary measurement values of other elements, the correction coefficient of other elements except N is calculated. Calculate and multiply the primary measurements of the corresponding elements by Calculate the concentration of the element, subtract the sum from 1 to obtain the concentration of the element N, and then use the concentration of each element obtained in the previous time to calculate the correction coefficient for other elements except N by the ZAF method. An X-ray spectroscopic analysis method, characterized in that the primary measurement values of the elements are multiplied, the concentrations of these elements are calculated, and the sum is subtracted from 1 to obtain the concentration of N of the element, which is repeated a necessary number of times.