Diffraction pattern analysis method and device for mixture and information storage medium

Abstract

The present invention provides a diffraction pattern analysis method for a mixture, comprising the following steps: obtaining an observed pattern of X-ray diffraction; using a first intensity ratio, a second intensity ratio, and a fitting pattern of an unknown pattern as fitting parameters, the fitting pattern including a term obtained by multiplying a known target pattern representing a target component by the first intensity ratio, and a term obtained by multiplying the unknown pattern representing a residual group composed of one or more residual components by the second intensity ratio; a first fitting step (S106), in which the fitting pattern is fitted with the observed pattern by changing the first intensity ratio and the second intensity ratio while setting the unknown pattern as an initial pattern; and a second fitting step (S107, S108), after the first fitting step, limiting the change of the first intensity ratio and the second intensity ratio and changing the unknown pattern to fit the fitting pattern with the observed pattern.

Description

Technical Field

[0001] The present invention relates to a method and apparatus for analyzing a diffraction pattern of a mixture, and an information storage medium, and to a technique for calculating the intensity ratio of one or more known diffraction patterns contained in an observed X-ray diffraction pattern. Background Art

[0002] X-ray diffraction can be used to quantitatively analyze a mixture. The diffraction pattern of the mixture actually observed includes overlapping known diffraction patterns originating from each component. When performing quantitative analysis, the intensity of the known diffraction pattern originating from each component in the actually observed diffraction pattern is calculated. If such intensity ratios are known, the weight fraction of each component can be calculated using, for example, the Direct Derivation method, a quantitative analysis method developed by the present inventors. For example, the following Patent Documents 1 to 3 disclose methods for calculating the weight fraction of each component using the Direct Derivation method.

[0003] Prior art literature

[0004] Patent Literature

[0005] Patent Document 1: Japanese Patent Application No. 2017 / 149913

[0006] Patent Document 2: Japanese Patent Application No. 2019 / 031019

[0007] Patent Document 3: Japanese Patent Application Publication No. 2019-184254 Summary of the Invention

[0008] Problems to be solved by the invention

[0009] According to the above-mentioned conventional methods, decomposing an observed diffraction pattern into multiple known diffraction patterns requires preparing known diffraction patterns for all possible components. However, in practice, it is often difficult to prepare known diffraction patterns for all components. On the other hand, in the quantitative analysis of mixtures using X-ray diffraction, only the weight fraction of a specific known substance, such as the amount of a known substance mixed with an unknown substance, is often required.

[0010] The present invention has been completed in view of the above-mentioned problems, and its purpose is to provide a diffraction pattern analysis method, device, and computer-readable information storage medium for a mixture that can calculate the intensity ratio of the diffraction patterns of these components even if the diffraction patterns of only some components are known.

[0011] Means for solving problems

[0012] In order to solve the above-mentioned problems, the diffraction pattern analysis method of the mixture involved in the present invention includes: an observation pattern acquisition step, acquiring an observation pattern of X-ray diffraction; a fitting pattern acquisition step, acquiring a fitting pattern with a first intensity ratio, a second intensity ratio and an unknown pattern as fitting parameters, the fitting pattern including a term obtained by multiplying a known target pattern representing a target component by the first intensity ratio, and a term obtained by multiplying the unknown pattern representing a residual group composed of more than one residual component by the second intensity ratio; a first fitting step, setting the unknown pattern to an initial pattern, fitting the fitting pattern to the observation pattern by changing the first intensity ratio and the second intensity ratio; and a second fitting step, after the first fitting step, limiting the change of the first intensity ratio and the second intensity ratio and changing the unknown pattern to fit the fitting pattern to the observation pattern.

[0013] Alternatively, the first fitting step and the second fitting step may be repeated multiple times.

[0014] Alternatively, the fitting pattern may include a term of a provisional pattern as a fitting parameter. Alternatively, in the first fitting step, the provisional pattern may be modified in addition to the first intensity ratio and the second intensity ratio to fit the fitting pattern to the observed pattern. Alternatively, in the second fitting step, the unknown pattern may be modified so that the term associated with the remaining group absorbs at least a portion of the term of the provisional pattern.

[0015] Furthermore, the quantitative analysis of the target component may be performed based on the first intensity ratio and the second intensity ratio.

[0016] In addition, the diffraction pattern analysis device of the present invention includes: an observation pattern storage unit, which stores data of an observation pattern of X-ray diffraction; a fitting pattern storage unit, which stores data representing a fitting pattern with a first intensity ratio, a second intensity ratio, and an unknown pattern as fitting parameters, the data including a term representing a known target pattern of a target component multiplied by the first intensity ratio, and a term representing the unknown pattern of a residual group composed of one or more residual components multiplied by the second intensity ratio; a first fitting unit, which changes the first intensity ratio and the second intensity ratio when the unknown pattern is set as an initial pattern to fit the fitting pattern with the observation pattern; and a second fitting unit, which limits the change of the first intensity ratio and the second intensity ratio and changes the unknown pattern after the first fitting unit performs fitting to fit the fitting pattern with the observation pattern.

[0017] In addition, the information storage medium involved in the present invention stores a program for causing a computer to run, which causes the computer to perform the following processing: observation pattern storage processing, storing data of the observation pattern of X-ray diffraction; fitting pattern storage processing, storing data representing the fitting pattern with the first intensity ratio, the second intensity ratio and the unknown pattern as fitting parameters, the data including a term representing a known target pattern of the target component multiplied by the first intensity ratio, and a term representing the unknown pattern of the residual group composed of one or more residual components multiplied by the second intensity ratio; a first fitting processing, in which the first intensity ratio and the second intensity ratio are changed while the unknown pattern is set as the initial pattern, so that the fitting pattern fits the observation pattern; and a second fitting processing, after performing fitting in the first fitting processing, limiting the change of the first intensity ratio and the second intensity ratio and changing the unknown pattern so that the fitting pattern fits the observation pattern. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a diagram showing the configuration of an analysis system according to an embodiment of the present invention.

[0019] Figure 2 This is a flowchart showing the operation of the analysis device.

[0020] Figure 3 This is a flowchart showing the operation of the analysis device.

[0021] Figure 4 To indicate a change R_av Flowchart of the calculation sequence.

[0022] Figure 5 It is a diagram showing an analysis example by the analysis system according to the embodiment of the present invention.

[0023] Figure 6 It is a diagram showing an analysis example by the analysis system according to the embodiment of the present invention. DETAILED DESCRIPTION

[0024] An embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0025] (System Configuration)

[0026] Figure 1 1 is a diagram showing the configuration of an analysis system according to one embodiment of the present invention. As shown in the diagram, the analysis system 10 includes an X-ray diffractometer 12 , an analyzer 14 , a storage unit 16 , and a display unit 18 .

[0027] The X-ray diffractometer 12 performs powder X-ray diffraction measurements. Specifically, the X-ray diffractometer 12 directs X-rays of a known wavelength into the sample and measures the intensity of the diffracted X-rays. Data on the X-ray intensity for each diffraction angle 2θ is output from the X-ray diffractometer 12 to the analyzer 14 as an observation pattern. Furthermore, the observation pattern output to the analyzer 14 may be corrected using the Lorentz polarization factor (Lp correction).

[0028] The sample substance analyzed by this system here is a mixture, which includes one or more target components (target substances) and a residual group. The target component refers to the component that is the object of quantitative measurement. The residual group is composed of one or more residual components (substances other than the target component). As an example of the residual group, an example can be cited in which the diffraction pattern of the components of which chemical composition is unknown although it is known which chemical composition exists in which mixing ratio. In addition, as another example, an example can be cited in which the chemical composition of the mixture as a whole can be known by fluorescence analysis or the like, but the chemical composition and mixing ratio of the residual group are unknown.

[0029] The analysis device 14 is composed of, for example, a well-known computer system including a computing device and memory. The analysis device 14 is connected to a storage unit 16 composed of a computer-readable information storage medium such as an SSD (Solid State Disk) or HDD (Hard Drive Disk). The storage unit 16 stores an analysis program according to an embodiment of the present invention. This analysis program is executed by the analysis device 14, thereby embodying the analysis method according to an embodiment of the present invention.

[0030] The storage unit 16 also stores X-ray diffraction patterns of each target component as target patterns. These target patterns may be X-ray diffraction patterns measured by the X-ray diffraction device 12 using the target component as a sample.

[0031] The storage unit 16 also stores the X-ray diffraction pattern of the remaining group, that is, the initial pattern of the unknown pattern. This embodiment is to change the initial pattern while making the unknown pattern closer to the true pattern. The initial pattern can be the X-ray diffraction pattern of the main component among the components contained in the remaining group. Alternatively, the initial pattern can be a linear combination of the X-ray diffraction patterns of multiple components contained in the remaining group. However, the initial pattern is not limited to this. As described later, the initial pattern is changed to a suitable pattern during the calculation process, so the X-ray diffraction pattern of a substance that is not actually contained in the remaining group can also be used as the initial pattern.

[0032] The storage unit 16 also stores chemical composition information (types and atomic weights of atoms contained) of each target component. Alternatively, the storage unit 16 may store chemical composition information of the entire mixture serving as a sample.

[0033] The display unit 18 is a display device that displays the analysis results of the analyzer 14. For example, the display unit 18 displays the intensity ratio of the target pattern and the unknown pattern, the weight fraction of each target component, and the weight fraction of the entire remaining group.

[0034] (Theoretical Background)

[0035] Here, the theoretical background of the X-ray diffraction pattern analysis performed by the analyzer 14 will be described. The analysis performed by the analyzer 14 applies the Direct Derivation method to analyze observed patterns including unknown patterns.

[0036] According to the Direct Derivation method, when the sample mixture has K components, the weight fraction w of the kth component is k It is represented by the following formula (1).

[0037]

Formula 1

[0038]

[0039] S k is the sum of the intensities of the kth component after Lp correction, which is equivalent to the observed intensity. k It is a parameter calculated based on the chemical composition information of the kth component stored in the storage unit 16, and is equivalent to the inverse of the scattering intensity per unit weight. k It is represented by the following formula (2).

[0040]

Formula 2

[0041]

[0042] In this M k is the chemical formula weight of the kth component. ki′ is the number of electrons contained in the i-th atom that constitutes the k-th component. Σ is the sum of all atoms that constitute the k-th component.

[0043] Next, when the number of target components is KT (k=1 to KT) and the remaining components are K-KT (k=KT+1 to K), the weight fraction w of the kth target component is k (k=1 to KT) is represented by the following formula (3).

[0044]

Formula 3

[0045]

[0046] In this S R is the sum of the observed intensities of the remaining groups after Lp correction. R It refers to the following formula (4).

[0047]

Formula 4

[0048] S R =S KT+1 +S KT+2 +…+S K …(4)

[0049] However, in this embodiment, S related to the entire remaining group is calculated. R Instead of calculating the sum of the observed intensities S of the remaining components separately, we take the point as one of the features. KT+1 、S KT+2 ,…,S K .

[0050] In addition, a R_av It is calculated based on the chemical composition information of the remaining group as a whole. R_av The calculation method of will be described later.

[0051] The weight fraction w of the remaining group as a whole R It is represented by the following formula (5).

[0052]

Formula 5

[0053]

[0054] Regarding the target component, a k (k=1~KT) is known, S can also be calculated based on the intensity ratio of the target pattern contained in the observation pattern. k (k=1~KT). As described later, a R_av There are also various calculation methods. Moreover, as described below, the unknown pattern related to the remaining group can also be calculated, and S can also be calculated based on the intensity ratio. R Therefore, the weight fraction w of each target component can be calculated by formula (3) and (5): k , and the weight fraction w involving the remaining groups R .

[0055] (Fitting pattern)

[0056] The fitting pattern is expressed by the following equation (6).

[0057]

Formula 6

[0058]

[0059] Here, i represents each diffraction angle (i=1 to N). i calc Sc represents the intensity of the i-th diffraction angle in the fitting pattern. k T Y represents the intensity ratio of the kth target component. ki T Sc represents the intensity of the i-th diffraction angle in the diffraction pattern of the k-th target component. R Sc represents the intensity ratio of the remaining groups. i ×Y i R The diffraction patterns of the remaining groups are unknown patterns. i R Represents the initial pattern of the unknown pattern. Specifically, it represents the intensity of the i-th diffraction angle in the initial pattern. S ci Sc is the correction factor for the intensity at the i-th diffraction angle, which is multiplied by the initial pattern. i At the beginning of the fitting, all are set to 1. To fix the integrated intensity of the unknown pattern, Sc i The constraint condition is as follows (7).

[0060]

Formula 7

[0061]

[0062] That is, the fitting pattern shown in equation (6) includes a term representing the known target pattern of the target component multiplied by its intensity ratio, and a term representing the unknown pattern of the remaining group multiplied by its intensity ratio. Moreover, the two intensity ratios and the unknown pattern are fitting parameters.

[0063] In addition, in formula (6), Y i TMP Y represents the intensity of the i-th diffraction angle in the temporary pattern. i TMP For example, a polynomial with each coefficient as the fitting parameter can be used. i TMP This is a provisional term that plays a role in improving the convergence of the unknown pattern, and is returned to zero or becomes a value extremely close to zero when the calculation is completed.

[0064] (First fitting step)

[0065] When fitting, first, the unknown pattern is set as the initial pattern, that is, Y i R In the state, change the first intensity ratio SckT, the second intensity ratio Sc R , and Y i TMP , to make the fitting pattern Y icalc With the observation pattern Y i obs Specifically, since the unknown pattern is set as the initial pattern, that is, Y i R , so Sc i All are set to 1. For example, using the least square method, the Y i calc The observed pattern Y obtained by the X-ray diffraction device 12 i obs The difference between the two is minimized to determine Sc k T Sc R and Y i TMP .

[0066] (Second fitting step)

[0067] Next, Sc k T Sc R and Y i TMP While the value determined in the first fitting step is fixed, the unknown pattern Sc is changed. i ×Y i R , to make the fitting pattern Y i calc With the observation pattern Y i obs Fitting. Here, by changing Sc i To change the unknown pattern Sc i ×Y i R .

[0068] Specifically, Sci is calculated by the following formula (8).

[0069]

Formula 8

[0070]

[0071] Sc shown in formula (8) i The requirements of formula (7) are not satisfied. Here, Sc is made i Normalization.

[0072]

Formula 9

[0073]

[0074] Here Sc i new represents the normalized Sc i , Sci old The left side of formula (8) is represented by A and S Bk It is represented by the following formulas (10) and (11).

[0075]

Formula 10

[0076]

[0077]

Formula 11

[0078]

[0079] After that, the normalized Sci is used to perform the first fitting step again. That is, the first fitting step and the second fitting step are repeated multiple times until Y i obs With Y i calc In addition, equation (8) assumes that the sum of the first and second terms on the right side of equation (6) is equal to the observed pattern Y i obs Time Sc i Therefore, the temporary pattern Y i TMP The value of is absorbed by the second term related to the remaining group. Therefore, at the end of the calculation, the temporary pattern Y i TMP The value of is converged to zero, or a value very close to zero.

[0080] When Sc is determined in the above manner k T and Sc R When these values ​​are used to calculate S k and S R For example, if Y ki T and Y i R Standardization, then S k Equal to Sc k T , S R Equal to Sc R Then, these values ​​are substituted into formula (3) to calculate the weight fraction w k In addition, the weight fraction w k Substitute the value of into formula (5) to calculate the weight fraction w associated with the remaining group R .

[0081] (a R_av Calculation method (1)

[0082] In this R_avThe calculation method of is explained.

[0083] For the remaining groups, if we know which chemical compositions exist in which mixing ratios, we can directly calculate a based on this information. R_av .

[0084] That is, the remaining group consists of substance A (W Ag ) and substance B(W Bg ), the remaining group imparts the scattering intensity shown in the following formula (12).

[0085]

Formula 12

[0086]

[0087] If the scattering intensity is divided by the total weight of the remaining group, the scattering intensity per unit weight, i.e., a, is obtained. R_av That is, a R_av It is given by the following formula (13).

[0088]

Formula 13

[0089]

[0090] Formula (13) is summarized as the residual group consisting of KT components, with weight fraction w k To express a R_av When , it is as shown in the following formula (14).

[0091]

Formula 14

[0092]

[0093] Here, about a k′ , can be calculated using formula (2) based on the chemical composition information. Therefore, when we know which chemical composition components exist in which mixing ratio in the remaining group, we can calculate a by formula (14). R_av .

[0094] (a R_av Calculation method (2)

[0095] Next, we will explain the case where, while the chemical composition information for the entire mixture (batch composition) is known, the chemical composition information for the remaining groups is unknown. Chemical composition information for the batch composition can be obtained, for example, by applying fluorescence analysis to the batch composition. Alternatively, if the absence of volatile components can be assumed, the chemical composition information for the raw materials used to synthesize the mixture can be used as is.

[0096] In this case, the chemical composition information of the batch composition is substituted into formula (2) to calculate a relative to the entire mixture sample.k . Express this value as a B .

[0097] As in formula (14), the batch composition a B It is represented by the following formula (15).

[0098]

Formula 15

[0099]

[0100] Transform Equation (15) and the a related to the remaining group R_av It is represented by the following formula (16).

[0101]

Formula 16

[0102]

[0103] In the formula (16), a B and a k′ It is known that the weight fraction w R and w k′ Unknown. Here, for example, a R_av The initial value is assumed to be a B , and calculate the weight fraction w by formula (3) (5) R and w k′ , and substitute it into formula (16) again, and then calculate a R_av Calculate. Repeat this operation to calculate a close to the true value. R_av .

[0104] Figure 2 and Figure 3 Flowchart showing the operation of the analysis device 14.

[0105] The analysis device 14 first obtains the observation pattern Y from the X-ray diffraction device 12 i obs (S101) Then, the target pattern Y is read from the storage unit 16. ki T (S102). Then, S is calculated by equations (10) and (11). A and S Bk (S103) Then, the initial pattern Y is read from the storage unit 16. i R (S104).

[0106] After that, the correction pattern S ci The values ​​of are all initialized to 1 (S105), and the first fitting step (S106) is performed. That is, the Y shown in formula (6) is i calc With the observation pattern Yi obs Minimize the error of Sc to determine the fitting parameter k T Sc R and Y i TMP In S106, obtain Y shown in formula (6) i calc , and substitute the values ​​obtained in S102, S104 and S105.

[0107] Next, the correction pattern Sc is calculated using equation (8): i (Before normalization) (S107), and normalized by equation (9) (S108).

[0108] Repeat the above steps S105 to S108 until Y i calc With the observation pattern Y i obs Until the error satisfies the convergence condition (S109).

[0109] Afterwards, the analyzer 14 reads the chemical composition information of the target component from the storage unit 16 and calculates a by using formula (2). k (S110). Then, the analyzing means 14 calculates a related to the remaining groups. R_av (S111) For example, when it is known which chemical composition components exist in which mixing ratio in the remaining group, a is calculated by formula (14). R_av .

[0110] Then, the weight fraction w of the target component is calculated by formula (3): k (S112) Then, the weight fraction w of the remaining group is calculated by formula (5) R (S113). Then, the weight fraction w k and w R The result is displayed on the display unit 18 (S114).

[0111] Figure 4 To indicate a change R_av The process shown in this figure is Figure 3 The analysis device 14 reads the chemical composition information of the batch composition from the storage unit 16 and calculates a related to the batch composition using the formula (15). B -1 (S201). Next, set a B -1 As a R_av -1The initial value (S202) is used, and the weight fraction w is calculated by equations (3) and (5) k and w R (S203) Substituting these values ​​into equation (16) to calculate a R_av -1 (S204). Until a R_av -1 Repeat the process of S203 and S204 until the convergence condition is met. As long as the convergence condition is met, the output is a R_av -1 (S206) This value can be used in the process of S112.

[0112] Figure 5 and Figure 6 This figure shows an example of an X-ray diffraction pattern of a mixture sample analyzed using analysis system 10 according to an embodiment of the present invention. The sample is a mixture of α-quartz, albite, and kaolinite in a 1:1:1 ratio. The target component is α-quartz. The remaining component is a mixture of albite and kaolinite. The diffraction pattern of the remaining component itself is unknown.

[0113] Figure 5 In the formula (6), the known diffraction pattern of albite monomer is used as Y i R , calculate the weight fraction of the target pattern. Figure 5 The symbol 5A in the middle represents the observation pattern Y i obs and the fitting pattern Y i calc Symbol 5B represents the observation pattern Y i obs and the fitting pattern Y i calc The error is linear due to the perfect fit. Symbol 5C represents the corrected pattern Sci as an error. The pattern shown by symbol 5C is highly consistent with the known diffraction pattern of kaolinite alone (not shown). Calculating the weight fraction of α-quartz under the above conditions yields an error of approximately 0.17% relative to the true value.

[0114] On the other hand, Figure 6 In the formula (6), the known diffraction pattern of glass-SiO2 monomer is used as Y i R To calculate the weight fraction of the target pattern. Figure 6 The symbol 6A in the middle represents the observation pattern Y i obs and the fitting pattern Y i calcSymbol 6B represents the observation pattern Y i obs and the fitting pattern Y i calc Due to a perfect fit, the error here is linear. Symbol 6C represents the corrected pattern Sci. The pattern shown in symbol 6C is similar to the known diffraction patterns of synthetic albite and kaolinite (not shown). The calculated weight fraction of α-quartz also shows an error of approximately 0.70% relative to the true value.

[0115] According to the present embodiment described above, even when the diffraction patterns of only some components are known, the intensity ratio can be calculated for not only the components with known diffraction patterns but also the remaining groups with unknown diffraction patterns, and the weight fractions of these components can be calculated with high accuracy.

[0116] In addition, although the above description uses the method to calculate the intensity ratio to perform quantitative analysis, each intensity ratio can also be used for other purposes than quantitative analysis. For example, in the case where the remaining group contains only one component, the unknown pattern Sc after the calculation converges can be used. i ×Y i R to identify the components that make up the remaining groups.

Claims

1. A method for analyzing a diffraction pattern of a mixture, characterized in that: include: an observation pattern acquisition step of acquiring an X-ray diffraction observation pattern; a fitting pattern acquiring step of acquiring a fitting pattern using the first intensity ratio, the second intensity ratio, and the unknown pattern as fitting parameters, the fitting pattern including a term obtained by multiplying a known target pattern representing a target component by the first intensity ratio, and a term obtained by multiplying the unknown pattern representing a residual group consisting of one or more residual components by the second intensity ratio; a first fitting step of fitting the fitting pattern to the observed pattern by changing the first intensity ratio and the second intensity ratio while setting the unknown pattern as an initial pattern; as well as The second fitting step, after the first fitting step, limits changes in the first intensity ratio and the second intensity ratio and changes the unknown pattern to fit the fitting pattern to the observed pattern.

2. The diffraction pattern analysis method of a mixture according to claim 1, characterized in that: The first fitting step and the second fitting step are repeated multiple times.

3. The diffraction pattern analysis method of a mixture according to claim 1 or 2, characterized in that: The fitting pattern also includes items of the temporary pattern as fitting parameters, In the first fitting step, in addition to the first intensity ratio and the second intensity ratio, the temporary pattern is changed so that the fitting pattern fits the observation pattern. In the second fitting step, the unknown pattern is modified so that the terms of the remaining set of correlations absorb at least a portion of the terms of the provisional pattern.

4. The diffraction pattern analysis method of a mixture according to claim 1 or 2, characterized in that: The target component is quantitatively analyzed based on the first intensity ratio and the second intensity ratio.

5. The diffraction pattern analysis method of a mixture according to claim 3, characterized in that: The target component is quantitatively analyzed based on the first intensity ratio and the second intensity ratio.

6. A diffraction pattern analysis device for a mixture, characterized in that: include: an observation pattern storage unit for storing data of an observation pattern of X-ray diffraction; a fitting pattern storage unit storing data representing a fitting pattern using a first intensity ratio, a second intensity ratio, and an unknown pattern as fitting parameters, the data including a term representing a known target pattern of a target component multiplied by the first intensity ratio, and a term representing a residual group consisting of one or more residual components multiplied by the second intensity ratio; a first fitting unit configured to change the first intensity ratio and the second intensity ratio in a state where the unknown pattern is set as an initial pattern, so as to fit the fitting pattern to the observed pattern; as well as The second fitting unit restricts changes in the first intensity ratio and the second intensity ratio and changes the unknown pattern after the first fitting unit performs fitting, so that the fitting pattern fits the observed pattern.

7. A computer-readable information storage medium storing a program, characterized in that: Make the computer execute the following processing: Observation pattern storage processing, storing data of X-ray diffraction observation patterns; a fitting pattern storage process for storing data representing the fitting pattern using the first intensity ratio, the second intensity ratio, and the unknown pattern as fitting parameters, the data including a term representing a known target pattern of a target component multiplied by the first intensity ratio, and a term representing a residual group consisting of one or more residual components multiplied by the second intensity ratio; a first fitting process of changing the first intensity ratio and the second intensity ratio while setting the unknown pattern as an initial pattern so as to fit the fitting pattern to the observed pattern; as well as The second fitting process, after performing fitting in the first fitting process, restricts changes in the first intensity ratio and the second intensity ratio and changes the unknown pattern to fit the fitting pattern to the observed pattern.

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